Datasets:
Parallel-Reasoning
/
sosp_sft_data

Dataset card Data Studio Files
xet
Community
nums
listlengths
4
4
target
int64
10
100
solution
listlengths
3
3
optimal_path
stringlengths
282
529
start_size
int64
4
4
search_path
stringlengths
505
16.8k
rating
float64
0
0.99
search_type
stringclasses
5 values
heuristic
stringclasses
2 values
[ 5, 63, 3, 17 ]
99
[ "17-5=12", "3*12=36", "63+36=99" ]
Current State: 99:[5, 63, 3, 17], Operations: [] Exploring Operation: 17-5=12, Resulting Numbers: [63, 3, 12] Generated Node #2: [63, 3, 12] from Operation: 17-5=12 Current State: 99:[63, 3, 12], Operations: ['17-5=12'] Exploring Operation: 3*12=36, Resulting Numbers: [63, 36] Generated Node #3: [63, 36] from Operation: 3*12=36 Current State: 99:[63, 36], Operations: ['17-5=12', '3*12=36'] Exploring Operation: 63+36=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[5, 63, 3, 17], Operations: [] Exploring Operation: 63/3=21, Resulting Numbers: [5, 17, 21] Generated Node #0,0: 99:[5, 17, 21] Operation: 63/3=21 Exploring Operation: 63+17=80, Resulting Numbers: [5, 3, 80] Generated Node #0,1: 99:[5, 3, 80] Operation: 63+17=80 Exploring Operation: 63-17=46, Resulting Numbers: [5, 3, 46] Generated Node #0,2: 99:[5, 3, 46] Operation: 63-17=46 Exploring Operation: 63-5=58, Resulting Numbers: [3, 17, 58] Generated Node #0,3: 99:[3, 17, 58] Operation: 63-5=58 Moving to Node #0,2 Current State: 99:[5, 3, 46], Operations: ['63-17=46'] Exploring Operation: 5-3=2, Resulting Numbers: [46, 2] Generated Node #0,2,0: 99:[46, 2] Operation: 5-3=2 Exploring Operation: 5+3=8, Resulting Numbers: [46, 8] Generated Node #0,2,1: 99:[46, 8] Operation: 5+3=8 Exploring Operation: 46-5=41, Resulting Numbers: [3, 41] Generated Node #0,2,2: 99:[3, 41] Operation: 46-5=41 Exploring Operation: 46-3=43, Resulting Numbers: [5, 43] Generated Node #0,2,3: 99:[5, 43] Operation: 46-3=43 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 99:[3, 41], Operations: ['63-17=46', '46-5=41'] Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,99 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,99 unequal: No Solution Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 99:[5, 43], Operations: ['63-17=46', '46-3=43'] Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,99 unequal: No Solution Exploring Operation: 5*43=215, Resulting Numbers: [215] 215,99 unequal: No Solution Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 99:[46, 2], Operations: ['63-17=46', '5-3=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,99 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,99 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 99:[46, 8], Operations: ['63-17=46', '5+3=8'] Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,99 unequal: No Solution Exploring Operation: 46*8=368, Resulting Numbers: [368] 368,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 99:[5, 17, 21], Operations: ['63/3=21'] Exploring Operation: 17-5=12, Resulting Numbers: [21, 12] Generated Node #0,0,0: 99:[21, 12] Operation: 17-5=12 Exploring Operation: 21-17=4, Resulting Numbers: [5, 4] Generated Node #0,0,1: 99:[5, 4] Operation: 21-17=4 Exploring Operation: 21-5=16, Resulting Numbers: [17, 16] Generated Node #0,0,2: 99:[17, 16] Operation: 21-5=16 Exploring Operation: 17+21=38, Resulting Numbers: [5, 38] Generated Node #0,0,3: 99:[5, 38] Operation: 17+21=38 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[5, 4], Operations: ['63/3=21', '21-17=4'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,99 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 99:[5, 38], Operations: ['63/3=21', '17+21=38'] Exploring Operation: 5+38=43, Resulting Numbers: [43] 43,99 unequal: No Solution Exploring Operation: 5*38=190, Resulting Numbers: [190] 190,99 unequal: No Solution Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[21, 12], Operations: ['63/3=21', '17-5=12'] Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,99 unequal: No Solution Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 21*12=252, Resulting Numbers: [252] 252,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 99:[17, 16], Operations: ['63/3=21', '21-5=16'] Exploring Operation: 17*16=272, Resulting Numbers: [272] 272,99 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 17+16=33, Resulting Numbers: [33] 33,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 99:[5, 3, 80], Operations: ['63+17=80'] Exploring Operation: 5+80=85, Resulting Numbers: [3, 85] Generated Node #0,1,0: 99:[3, 85] Operation: 5+80=85 Exploring Operation: 80/5=16, Resulting Numbers: [3, 16] Generated Node #0,1,1: 99:[3, 16] Operation: 80/5=16 Exploring Operation: 5+3=8, Resulting Numbers: [80, 8] Generated Node #0,1,2: 99:[80, 8] Operation: 5+3=8 Exploring Operation: 3+80=83, Resulting Numbers: [5, 83] Generated Node #0,1,3: 99:[5, 83] Operation: 3+80=83 Moving to Node #0,3 Current State: 99:[3, 17, 58], Operations: ['63-5=58'] Exploring Operation: 17-3=14, Resulting Numbers: [58, 14] Generated Node #0,3,0: 99:[58, 14] Operation: 17-3=14 Exploring Operation: 58-17=41, Resulting Numbers: [3, 41] Generated Node #0,3,1: 99:[3, 41] Operation: 58-17=41 Exploring Operation: 17+58=75, Resulting Numbers: [3, 75] Generated Node #0,3,2: 99:[3, 75] Operation: 17+58=75 Exploring Operation: 58-3=55, Resulting Numbers: [17, 55] Generated Node #0,3,3: 99:[17, 55] Operation: 58-3=55 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 99:[3, 41], Operations: ['63-5=58', '58-17=41'] Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,99 unequal: No Solution Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 99:[3, 75], Operations: ['63-5=58', '17+58=75'] Exploring Operation: 3+75=78, Resulting Numbers: [78] 78,99 unequal: No Solution Exploring Operation: 75/3=25, Resulting Numbers: [25] 25,99 unequal: No Solution Exploring Operation: 3*75=225, Resulting Numbers: [225] 225,99 unequal: No Solution Exploring Operation: 75-3=72, Resulting Numbers: [72] 72,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 99:[58, 14], Operations: ['63-5=58', '17-3=14'] Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 58*14=812, Resulting Numbers: [812] 812,99 unequal: No Solution Exploring Operation: 58+14=72, Resulting Numbers: [72] 72,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 99:[17, 55], Operations: ['63-5=58', '58-3=55'] Exploring Operation: 55-17=38, Resulting Numbers: [38] 38,99 unequal: No Solution Exploring Operation: 17*55=935, Resulting Numbers: [935] 935,99 unequal: No Solution Exploring Operation: 17+55=72, Resulting Numbers: [72] 72,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 99:[3, 16], Operations: ['63+17=80', '80/5=16'] Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,99 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[3, 85], Operations: ['63+17=80', '5+80=85'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,99 unequal: No Solution Exploring Operation: 3*85=255, Resulting Numbers: [255] 255,99 unequal: No Solution Exploring Operation: 3+85=88, Resulting Numbers: [88] 88,99 unequal: No Solution Moving to Node #0,1,3 Current State: 99:[5, 83], Operations: ['63+17=80', '3+80=83'] Exploring Operation: 5+83=88, Resulting Numbers: [88] 88,99 unequal: No Solution Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,99 unequal: No Solution Exploring Operation: 5*83=415, Resulting Numbers: [415] 415,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[80, 8], Operations: ['63+17=80', '5+3=8'] Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,99 unequal: No Solution Exploring Operation: 80*8=640, Resulting Numbers: [640] 640,99 unequal: No Solution Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,99 unequal: No Solution Exploring Operation: 80+8=88, Resulting Numbers: [88] 88,99 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 11, 46, 8, 13 ]
99
[ "11-8=3", "46-13=33", "3*33=99" ]
Current State: 99:[11, 46, 8, 13], Operations: [] Exploring Operation: 11-8=3, Resulting Numbers: [46, 13, 3] Generated Node #2: [46, 13, 3] from Operation: 11-8=3 Current State: 99:[46, 13, 3], Operations: ['11-8=3'] Exploring Operation: 46-13=33, Resulting Numbers: [3, 33] Generated Node #3: [3, 33] from Operation: 46-13=33 Current State: 99:[3, 33], Operations: ['11-8=3', '46-13=33'] Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[11, 46, 8, 13], Operations: [] Exploring Operation: 46-8=38, Resulting Numbers: [11, 13, 38] Generated Node #0,0: 99:[11, 13, 38] Operation: 46-8=38 Exploring Operation: 46-11=35, Resulting Numbers: [8, 13, 35] Generated Node #0,1: 99:[8, 13, 35] Operation: 46-11=35 Exploring Operation: 46-13=33, Resulting Numbers: [11, 8, 33] Generated Node #0,2: 99:[11, 8, 33] Operation: 46-13=33 Moving to Node #0,2 Current State: 99:[11, 8, 33], Operations: ['46-13=33'] Exploring Operation: 11-8=3, Resulting Numbers: [33, 3] Generated Node #0,2,0: 99:[33, 3] Operation: 11-8=3 Exploring Operation: 33/11=3, Resulting Numbers: [8, 3] Generated Node #0,2,1: 99:[8, 3] Operation: 33/11=3 Exploring Operation: 11+8=19, Resulting Numbers: [33, 19] Generated Node #0,2,2: 99:[33, 19] Operation: 11+8=19 Moving to Node #0,1 Current State: 99:[8, 13, 35], Operations: ['46-11=35'] Exploring Operation: 8*13=104, Resulting Numbers: [35, 104] Generated Node #0,1,0: 99:[35, 104] Operation: 8*13=104 Exploring Operation: 13-8=5, Resulting Numbers: [35, 5] Generated Node #0,1,1: 99:[35, 5] Operation: 13-8=5 Exploring Operation: 35-8=27, Resulting Numbers: [13, 27] Generated Node #0,1,2: 99:[13, 27] Operation: 35-8=27 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[35, 5], Operations: ['46-11=35', '13-8=5'] Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,99 unequal: No Solution Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[35, 104], Operations: ['46-11=35', '8*13=104'] Exploring Operation: 35*104=3640, Resulting Numbers: [3640] 3640,99 unequal: No Solution Exploring Operation: 35+104=139, Resulting Numbers: [139] 139,99 unequal: No Solution Exploring Operation: 104-35=69, Resulting Numbers: [69] 69,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 99:[13, 27], Operations: ['46-11=35', '35-8=27'] Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,99 unequal: No Solution Exploring Operation: 13+27=40, Resulting Numbers: [40] 40,99 unequal: No Solution Exploring Operation: 13*27=351, Resulting Numbers: [351] 351,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 99:[11, 13, 38], Operations: ['46-8=38'] Exploring Operation: 13-11=2, Resulting Numbers: [38, 2] Generated Node #0,0,0: 99:[38, 2] Operation: 13-11=2 Exploring Operation: 38-13=25, Resulting Numbers: [11, 25] Generated Node #0,0,1: 99:[11, 25] Operation: 38-13=25 Exploring Operation: 38-11=27, Resulting Numbers: [13, 27] Generated Node #0,0,2: 99:[13, 27] Operation: 38-11=27 Moving to Node #0,2,0 Current State: 99:[33, 3], Operations: ['46-13=33', '11-8=3'] Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[11, 46, 8, 13], Operations: [] Exploring Operation: 46-13=33, Resulting Numbers: [11, 8, 33] Generated Node #0,2: 99:[11, 8, 33] Operation: 46-13=33 Moving to Node #0,2 Current State: 99:[11, 8, 33], Operations: ['46-13=33'] Exploring Operation: 11-8=3, Resulting Numbers: [33, 3] Generated Node #0,2,0: 99:[33, 3] Operation: 11-8=3 Moving to Node #0,2,0 Current State: 99:[33, 3], Operations: ['46-13=33', '11-8=3'] Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
0.977431
hs_3
sum_heuristic
[ 63, 81, 83, 88 ]
19
[ "83-81=2", "88/2=44", "63-44=19" ]
Current State: 19:[63, 81, 83, 88], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [63, 88, 2] Generated Node #2: [63, 88, 2] from Operation: 83-81=2 Current State: 19:[63, 88, 2], Operations: ['83-81=2'] Exploring Operation: 88/2=44, Resulting Numbers: [63, 44] Generated Node #3: [63, 44] from Operation: 88/2=44 Current State: 19:[63, 44], Operations: ['83-81=2', '88/2=44'] Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[63, 81, 83, 88], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [63, 88, 2] Generated Node #0,0: 19:[63, 88, 2] Operation: 83-81=2 Exploring Operation: 83-63=20, Resulting Numbers: [81, 88, 20] Generated Node #0,1: 19:[81, 88, 20] Operation: 83-63=20 Exploring Operation: 88-83=5, Resulting Numbers: [63, 81, 5] Generated Node #0,2: 19:[63, 81, 5] Operation: 88-83=5 Exploring Operation: 88-81=7, Resulting Numbers: [63, 83, 7] Generated Node #0,3: 19:[63, 83, 7] Operation: 88-81=7 Exploring Operation: 88-63=25, Resulting Numbers: [81, 83, 25] Generated Node #0,4: 19:[81, 83, 25] Operation: 88-63=25 Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[63, 81, 5], Operations: ['88-83=5'] Exploring Operation: 63-5=58, Resulting Numbers: [81, 58] Generated Node #0,2,0: 19:[81, 58] Operation: 63-5=58 Exploring Operation: 81+5=86, Resulting Numbers: [63, 86] Generated Node #0,2,1: 19:[63, 86] Operation: 81+5=86 Exploring Operation: 81-63=18, Resulting Numbers: [5, 18] Generated Node #0,2,2: 19:[5, 18] Operation: 81-63=18 Exploring Operation: 81-5=76, Resulting Numbers: [63, 76] Generated Node #0,2,3: 19:[63, 76] Operation: 81-5=76 Exploring Operation: 63+5=68, Resulting Numbers: [81, 68] Generated Node #0,2,4: 19:[81, 68] Operation: 63+5=68 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 19:[5, 18], Operations: ['88-83=5', '81-63=18'] Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,19 unequal: No Solution Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 19:[81, 58], Operations: ['88-83=5', '63-5=58'] Exploring Operation: 81-58=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 81*58=4698, Resulting Numbers: [4698] 4698,19 unequal: No Solution Exploring Operation: 81+58=139, Resulting Numbers: [139] 139,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 19:[63, 76], Operations: ['88-83=5', '81-5=76'] Exploring Operation: 63*76=4788, Resulting Numbers: [4788] 4788,19 unequal: No Solution Exploring Operation: 63+76=139, Resulting Numbers: [139] 139,19 unequal: No Solution Exploring Operation: 76-63=13, Resulting Numbers: [13] 13,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 19:[63, 86], Operations: ['88-83=5', '81+5=86'] Exploring Operation: 63*86=5418, Resulting Numbers: [5418] 5418,19 unequal: No Solution Exploring Operation: 63+86=149, Resulting Numbers: [149] 149,19 unequal: No Solution Exploring Operation: 86-63=23, Resulting Numbers: [23] 23,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 19:[81, 68], Operations: ['88-83=5', '63+5=68'] Exploring Operation: 81-68=13, Resulting Numbers: [13] 13,19 unequal: No Solution Exploring Operation: 81*68=5508, Resulting Numbers: [5508] 5508,19 unequal: No Solution Exploring Operation: 81+68=149, Resulting Numbers: [149] 149,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 19:[63, 83, 7], Operations: ['88-81=7'] Exploring Operation: 63-7=56, Resulting Numbers: [83, 56] Generated Node #0,3,0: 19:[83, 56] Operation: 63-7=56 Exploring Operation: 83-7=76, Resulting Numbers: [63, 76] Generated Node #0,3,1: 19:[63, 76] Operation: 83-7=76 Exploring Operation: 63/7=9, Resulting Numbers: [83, 9] Generated Node #0,3,2: 19:[83, 9] Operation: 63/7=9 Exploring Operation: 83-63=20, Resulting Numbers: [7, 20] Generated Node #0,3,3: 19:[7, 20] Operation: 83-63=20 Exploring Operation: 63+7=70, Resulting Numbers: [83, 70] Generated Node #0,3,4: 19:[83, 70] Operation: 63+7=70 Moving to Node #0,3,3 Current State: 19:[7, 20], Operations: ['88-81=7', '83-63=20'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,19 unequal: No Solution Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,19 unequal: No Solution Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,19 unequal: No Solution Moving to Node #0,3,2 Current State: 19:[83, 9], Operations: ['88-81=7', '63/7=9'] Exploring Operation: 83*9=747, Resulting Numbers: [747] 747,19 unequal: No Solution Exploring Operation: 83+9=92, Resulting Numbers: [92] 92,19 unequal: No Solution Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,19 unequal: No Solution Moving to Node #0,3,0 Current State: 19:[83, 56], Operations: ['88-81=7', '63-7=56'] Exploring Operation: 83+56=139, Resulting Numbers: [139] 139,19 unequal: No Solution Exploring Operation: 83-56=27, Resulting Numbers: [27] 27,19 unequal: No Solution Exploring Operation: 83*56=4648, Resulting Numbers: [4648] 4648,19 unequal: No Solution Moving to Node #0,3,1 Current State: 19:[63, 76], Operations: ['88-81=7', '83-7=76'] Exploring Operation: 76-63=13, Resulting Numbers: [13] 13,19 unequal: No Solution Exploring Operation: 63*76=4788, Resulting Numbers: [4788] 4788,19 unequal: No Solution Exploring Operation: 63+76=139, Resulting Numbers: [139] 139,19 unequal: No Solution Moving to Node #0,3,4 Current State: 19:[83, 70], Operations: ['88-81=7', '63+7=70'] Exploring Operation: 83-70=13, Resulting Numbers: [13] 13,19 unequal: No Solution Exploring Operation: 83+70=153, Resulting Numbers: [153] 153,19 unequal: No Solution Exploring Operation: 83*70=5810, Resulting Numbers: [5810] 5810,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[63, 88, 2], Operations: ['83-81=2'] Exploring Operation: 88/2=44, Resulting Numbers: [63, 44] Generated Node #0,0,0: 19:[63, 44] Operation: 88/2=44 Exploring Operation: 63+2=65, Resulting Numbers: [88, 65] Generated Node #0,0,1: 19:[88, 65] Operation: 63+2=65 Exploring Operation: 88-2=86, Resulting Numbers: [63, 86] Generated Node #0,0,2: 19:[63, 86] Operation: 88-2=86 Exploring Operation: 88-63=25, Resulting Numbers: [2, 25] Generated Node #0,0,3: 19:[2, 25] Operation: 88-63=25 Exploring Operation: 63-2=61, Resulting Numbers: [88, 61] Generated Node #0,0,4: 19:[88, 61] Operation: 63-2=61 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 19:[2, 25], Operations: ['83-81=2', '88-63=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,19 unequal: No Solution Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[63, 44], Operations: ['83-81=2', '88/2=44'] Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[63, 81, 83, 88], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [63, 88, 2] Generated Node #0,0: 19:[63, 88, 2] Operation: 83-81=2 Moving to Node #0,0 Current State: 19:[63, 88, 2], Operations: ['83-81=2'] Exploring Operation: 88/2=44, Resulting Numbers: [63, 44] Generated Node #0,0,0: 19:[63, 44] Operation: 88/2=44 Moving to Node #0,0,0 Current State: 19:[63, 44], Operations: ['83-81=2', '88/2=44'] Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.949653
hs_5
sum_heuristic
[ 86, 7, 43, 22 ]
100
[ "86-7=79", "43-22=21", "79+21=100" ]
Current State: 100:[86, 7, 43, 22], Operations: [] Exploring Operation: 86-7=79, Resulting Numbers: [43, 22, 79] Generated Node #2: [43, 22, 79] from Operation: 86-7=79 Current State: 100:[43, 22, 79], Operations: ['86-7=79'] Exploring Operation: 43-22=21, Resulting Numbers: [79, 21] Generated Node #3: [79, 21] from Operation: 43-22=21 Current State: 100:[79, 21], Operations: ['86-7=79', '43-22=21'] Exploring Operation: 79+21=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[86, 7, 43, 22], Operations: [] Exploring Operation: 86-43=43, Resulting Numbers: [7, 22, 43] Generated Node #0,0: 100:[7, 22, 43] Operation: 86-43=43 Exploring Operation: 86/43=2, Resulting Numbers: [7, 22, 2] Generated Node #0,1: 100:[7, 22, 2] Operation: 86/43=2 Exploring Operation: 86+7=93, Resulting Numbers: [43, 22, 93] Generated Node #0,2: 100:[43, 22, 93] Operation: 86+7=93 Exploring Operation: 7+43=50, Resulting Numbers: [86, 22, 50] Generated Node #0,3: 100:[86, 22, 50] Operation: 7+43=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[7, 22, 2], Operations: ['86/43=2'] Exploring Operation: 7+2=9, Resulting Numbers: [22, 9] Generated Node #0,1,0: 100:[22, 9] Operation: 7+2=9 Exploring Operation: 7-2=5, Resulting Numbers: [22, 5] Generated Node #0,1,1: 100:[22, 5] Operation: 7-2=5 Exploring Operation: 22+2=24, Resulting Numbers: [7, 24] Generated Node #0,1,2: 100:[7, 24] Operation: 22+2=24 Exploring Operation: 22-2=20, Resulting Numbers: [7, 20] Generated Node #0,1,3: 100:[7, 20] Operation: 22-2=20 Moving to Node #0,1,1 Current State: 100:[22, 5], Operations: ['86/43=2', '7-2=5'] Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,100 unequal: No Solution Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,100 unequal: No Solution Moving to Node #0,1,3 Current State: 100:[7, 20], Operations: ['86/43=2', '22-2=20'] Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,100 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,100 unequal: No Solution Moving to Node #0,1,2 Current State: 100:[7, 24], Operations: ['86/43=2', '22+2=24'] Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,100 unequal: No Solution Exploring Operation: 7*24=168, Resulting Numbers: [168] 168,100 unequal: No Solution Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,100 unequal: No Solution Moving to Node #0,1,0 Current State: 100:[22, 9], Operations: ['86/43=2', '7+2=9'] Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,100 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,100 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[7, 22, 43], Operations: ['86-43=43'] Exploring Operation: 43-22=21, Resulting Numbers: [7, 21] Generated Node #0,0,0: 100:[7, 21] Operation: 43-22=21 Exploring Operation: 7+22=29, Resulting Numbers: [43, 29] Generated Node #0,0,1: 100:[43, 29] Operation: 7+22=29 Exploring Operation: 22-7=15, Resulting Numbers: [43, 15] Generated Node #0,0,2: 100:[43, 15] Operation: 22-7=15 Exploring Operation: 7+43=50, Resulting Numbers: [22, 50] Generated Node #0,0,3: 100:[22, 50] Operation: 7+43=50 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 100:[22, 50], Operations: ['86-43=43', '7+43=50'] Exploring Operation: 22*50=1100, Resulting Numbers: [1100] 1100,100 unequal: No Solution Exploring Operation: 22+50=72, Resulting Numbers: [72] 72,100 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 100:[7, 21], Operations: ['86-43=43', '43-22=21'] Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,100 unequal: No Solution Exploring Operation: 7*21=147, Resulting Numbers: [147] 147,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 100:[43, 29], Operations: ['86-43=43', '7+22=29'] Exploring Operation: 43*29=1247, Resulting Numbers: [1247] 1247,100 unequal: No Solution Exploring Operation: 43+29=72, Resulting Numbers: [72] 72,100 unequal: No Solution Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 100:[43, 15], Operations: ['86-43=43', '22-7=15'] Exploring Operation: 43-15=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 43*15=645, Resulting Numbers: [645] 645,100 unequal: No Solution Exploring Operation: 43+15=58, Resulting Numbers: [58] 58,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[43, 22, 93], Operations: ['86+7=93'] Exploring Operation: 43-22=21, Resulting Numbers: [93, 21] Generated Node #0,2,0: 100:[93, 21] Operation: 43-22=21 Exploring Operation: 43+22=65, Resulting Numbers: [93, 65] Generated Node #0,2,1: 100:[93, 65] Operation: 43+22=65 Exploring Operation: 22+93=115, Resulting Numbers: [43, 115] Generated Node #0,2,2: 100:[43, 115] Operation: 22+93=115 Exploring Operation: 93-43=50, Resulting Numbers: [22, 50] Generated Node #0,2,3: 100:[22, 50] Operation: 93-43=50 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 100:[22, 50], Operations: ['86+7=93', '93-43=50'] Exploring Operation: 22*50=1100, Resulting Numbers: [1100] 1100,100 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 22+50=72, Resulting Numbers: [72] 72,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 100:[93, 21], Operations: ['86+7=93', '43-22=21'] Exploring Operation: 93-21=72, Resulting Numbers: [72] 72,100 unequal: No Solution Exploring Operation: 93*21=1953, Resulting Numbers: [1953] 1953,100 unequal: No Solution Exploring Operation: 93+21=114, Resulting Numbers: [114] 114,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 100:[93, 65], Operations: ['86+7=93', '43+22=65'] Exploring Operation: 93-65=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 93*65=6045, Resulting Numbers: [6045] 6045,100 unequal: No Solution Exploring Operation: 93+65=158, Resulting Numbers: [158] 158,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 100:[43, 115], Operations: ['86+7=93', '22+93=115'] Exploring Operation: 43*115=4945, Resulting Numbers: [4945] 4945,100 unequal: No Solution Exploring Operation: 43+115=158, Resulting Numbers: [158] 158,100 unequal: No Solution Exploring Operation: 115-43=72, Resulting Numbers: [72] 72,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[86, 22, 50], Operations: ['7+43=50'] Exploring Operation: 86-50=36, Resulting Numbers: [22, 36] Generated Node #0,3,0: 100:[22, 36] Operation: 86-50=36 Exploring Operation: 86+22=108, Resulting Numbers: [50, 108] Generated Node #0,3,1: 100:[50, 108] Operation: 86+22=108 Exploring Operation: 86-22=64, Resulting Numbers: [50, 64] Generated Node #0,3,2: 100:[50, 64] Operation: 86-22=64 Exploring Operation: 50-22=28, Resulting Numbers: [86, 28] Generated Node #0,3,3: 100:[86, 28] Operation: 50-22=28 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 100:[50, 108], Operations: ['7+43=50', '86+22=108'] Exploring Operation: 108-50=58, Resulting Numbers: [58] 58,100 unequal: No Solution Exploring Operation: 50*108=5400, Resulting Numbers: [5400] 5400,100 unequal: No Solution Exploring Operation: 50+108=158, Resulting Numbers: [158] 158,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 100:[22, 36], Operations: ['7+43=50', '86-50=36'] Exploring Operation: 22+36=58, Resulting Numbers: [58] 58,100 unequal: No Solution Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,100 unequal: No Solution Exploring Operation: 22*36=792, Resulting Numbers: [792] 792,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 100:[50, 64], Operations: ['7+43=50', '86-22=64'] Exploring Operation: 64-50=14, Resulting Numbers: [14] 14,100 unequal: No Solution Exploring Operation: 50*64=3200, Resulting Numbers: [3200] 3200,100 unequal: No Solution Exploring Operation: 50+64=114, Resulting Numbers: [114] 114,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 100:[86, 28], Operations: ['7+43=50', '50-22=28'] Exploring Operation: 86+28=114, Resulting Numbers: [114] 114,100 unequal: No Solution Exploring Operation: 86*28=2408, Resulting Numbers: [2408] 2408,100 unequal: No Solution Exploring Operation: 86-28=58, Resulting Numbers: [58] 58,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 62, 39, 23, 87 ]
78
[ "62+23=85", "87-85=2", "39*2=78" ]
Current State: 78:[62, 39, 23, 87], Operations: [] Exploring Operation: 62+23=85, Resulting Numbers: [39, 87, 85] Generated Node #2: [39, 87, 85] from Operation: 62+23=85 Current State: 78:[39, 87, 85], Operations: ['62+23=85'] Exploring Operation: 87-85=2, Resulting Numbers: [39, 2] Generated Node #3: [39, 2] from Operation: 87-85=2 Current State: 78:[39, 2], Operations: ['62+23=85', '87-85=2'] Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[62, 39, 23, 87], Operations: [] Exploring Operation: 62+23=85, Resulting Numbers: [39, 87, 85] Generated Node #0,0: 78:[39, 87, 85] Operation: 62+23=85 Exploring Operation: 62-23=39, Resulting Numbers: [39, 87, 39] Generated Node #0,1: 78:[39, 87, 39] Operation: 62-23=39 Exploring Operation: 87-62=25, Resulting Numbers: [39, 23, 25] Generated Node #0,2: 78:[39, 23, 25] Operation: 87-62=25 Exploring Operation: 62-39=23, Resulting Numbers: [23, 87, 23] Generated Node #0,3: 78:[23, 87, 23] Operation: 62-39=23 Moving to Node #0,2 Current State: 78:[39, 23, 25], Operations: ['87-62=25'] Exploring Operation: 23+25=48, Resulting Numbers: [39, 48] Generated Node #0,2,0: 78:[39, 48] Operation: 23+25=48 Exploring Operation: 39-25=14, Resulting Numbers: [23, 14] Generated Node #0,2,1: 78:[23, 14] Operation: 39-25=14 Exploring Operation: 25-23=2, Resulting Numbers: [39, 2] Generated Node #0,2,2: 78:[39, 2] Operation: 25-23=2 Exploring Operation: 39-23=16, Resulting Numbers: [25, 16] Generated Node #0,2,3: 78:[25, 16] Operation: 39-23=16 Moving to Node #0,1 Current State: 78:[39, 87, 39], Operations: ['62-23=39'] Exploring Operation: 39/39=1, Resulting Numbers: [87, 1] Generated Node #0,1,0: 78:[87, 1] Operation: 39/39=1 Exploring Operation: 39+39=78, Resulting Numbers: [87, 78] Generated Node #0,1,1: 78:[87, 78] Operation: 39+39=78 Exploring Operation: 87-39=48, Resulting Numbers: [39, 48] Generated Node #0,1,2: 78:[39, 48] Operation: 87-39=48 Exploring Operation: 87-39=48, Resulting Numbers: [39, 48] Generated Node #0,1,3: 78:[39, 48] Operation: 87-39=48 Moving to Node #0,3 Current State: 78:[23, 87, 23], Operations: ['62-39=23'] Exploring Operation: 23+23=46, Resulting Numbers: [87, 46] Generated Node #0,3,0: 78:[87, 46] Operation: 23+23=46 Exploring Operation: 23-23=0, Resulting Numbers: [87, 0] Generated Node #0,3,1: 78:[87, 0] Operation: 23-23=0 Exploring Operation: 87-23=64, Resulting Numbers: [23, 64] Generated Node #0,3,2: 78:[23, 64] Operation: 87-23=64 Exploring Operation: 23/23=1, Resulting Numbers: [87, 1] Generated Node #0,3,3: 78:[87, 1] Operation: 23/23=1 Moving to Node #0,0 Current State: 78:[39, 87, 85], Operations: ['62+23=85'] Exploring Operation: 85-39=46, Resulting Numbers: [87, 46] Generated Node #0,0,0: 78:[87, 46] Operation: 85-39=46 Exploring Operation: 87-85=2, Resulting Numbers: [39, 2] Generated Node #0,0,1: 78:[39, 2] Operation: 87-85=2 Exploring Operation: 87-39=48, Resulting Numbers: [85, 48] Generated Node #0,0,2: 78:[85, 48] Operation: 87-39=48 Exploring Operation: 39+87=126, Resulting Numbers: [85, 126] Generated Node #0,0,3: 78:[85, 126] Operation: 39+87=126 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[39, 2], Operations: ['62+23=85', '87-85=2'] Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[62, 39, 23, 87], Operations: [] Exploring Operation: 62+23=85, Resulting Numbers: [39, 87, 85] Generated Node #0,0: 78:[39, 87, 85] Operation: 62+23=85 Moving to Node #0,0 Current State: 78:[39, 87, 85], Operations: ['62+23=85'] Exploring Operation: 87-85=2, Resulting Numbers: [39, 2] Generated Node #0,0,1: 78:[39, 2] Operation: 87-85=2 Moving to Node #0,0,1 Current State: 78:[39, 2], Operations: ['62+23=85', '87-85=2'] Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_4
sum_heuristic
[ 9, 82, 8, 20 ]
69
[ "9+82=91", "8*20=160", "160-91=69" ]
Current State: 69:[9, 82, 8, 20], Operations: [] Exploring Operation: 9+82=91, Resulting Numbers: [8, 20, 91] Generated Node #2: [8, 20, 91] from Operation: 9+82=91 Current State: 69:[8, 20, 91], Operations: ['9+82=91'] Exploring Operation: 8*20=160, Resulting Numbers: [91, 160] Generated Node #3: [91, 160] from Operation: 8*20=160 Current State: 69:[91, 160], Operations: ['9+82=91', '8*20=160'] Exploring Operation: 160-91=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[9, 82, 8, 20], Operations: [] Exploring Operation: 9-8=1, Resulting Numbers: [82, 20, 1] Generated Node #0,0: 69:[82, 20, 1] Operation: 9-8=1 Exploring Operation: 82-20=62, Resulting Numbers: [9, 8, 62] Generated Node #0,1: 69:[9, 8, 62] Operation: 82-20=62 Exploring Operation: 82-8=74, Resulting Numbers: [9, 20, 74] Generated Node #0,2: 69:[9, 20, 74] Operation: 82-8=74 Exploring Operation: 9*8=72, Resulting Numbers: [82, 20, 72] Generated Node #0,3: 69:[82, 20, 72] Operation: 9*8=72 Exploring Operation: 82-9=73, Resulting Numbers: [8, 20, 73] Generated Node #0,4: 69:[8, 20, 73] Operation: 82-9=73 Start Sub Search at level 1: Moving to Node #0,4 Current State: 69:[8, 20, 73], Operations: ['82-9=73'] Exploring Operation: 8+20=28, Resulting Numbers: [73, 28] Generated Node #0,4,0: 69:[73, 28] Operation: 8+20=28 Exploring Operation: 20-8=12, Resulting Numbers: [73, 12] Generated Node #0,4,1: 69:[73, 12] Operation: 20-8=12 Exploring Operation: 73-20=53, Resulting Numbers: [8, 53] Generated Node #0,4,2: 69:[8, 53] Operation: 73-20=53 Exploring Operation: 8+73=81, Resulting Numbers: [20, 81] Generated Node #0,4,3: 69:[20, 81] Operation: 8+73=81 Exploring Operation: 73-8=65, Resulting Numbers: [20, 65] Generated Node #0,4,4: 69:[20, 65] Operation: 73-8=65 Moving to Node #0,4,4 Current State: 69:[20, 65], Operations: ['82-9=73', '73-8=65'] Exploring Operation: 65-20=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 20*65=1300, Resulting Numbers: [1300] 1300,69 unequal: No Solution Exploring Operation: 20+65=85, Resulting Numbers: [85] 85,69 unequal: No Solution Moving to Node #0,4,0 Current State: 69:[73, 28], Operations: ['82-9=73', '8+20=28'] Exploring Operation: 73*28=2044, Resulting Numbers: [2044] 2044,69 unequal: No Solution Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 73+28=101, Resulting Numbers: [101] 101,69 unequal: No Solution Moving to Node #0,4,1 Current State: 69:[73, 12], Operations: ['82-9=73', '20-8=12'] Exploring Operation: 73-12=61, Resulting Numbers: [61] 61,69 unequal: No Solution Exploring Operation: 73+12=85, Resulting Numbers: [85] 85,69 unequal: No Solution Exploring Operation: 73*12=876, Resulting Numbers: [876] 876,69 unequal: No Solution Moving to Node #0,4,3 Current State: 69:[20, 81], Operations: ['82-9=73', '8+73=81'] Exploring Operation: 81-20=61, Resulting Numbers: [61] 61,69 unequal: No Solution Exploring Operation: 20+81=101, Resulting Numbers: [101] 101,69 unequal: No Solution Exploring Operation: 20*81=1620, Resulting Numbers: [1620] 1620,69 unequal: No Solution Moving to Node #0,4,2 Current State: 69:[8, 53], Operations: ['82-9=73', '73-20=53'] Exploring Operation: 8*53=424, Resulting Numbers: [424] 424,69 unequal: No Solution Exploring Operation: 8+53=61, Resulting Numbers: [61] 61,69 unequal: No Solution Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[9, 20, 74], Operations: ['82-8=74'] Exploring Operation: 74-9=65, Resulting Numbers: [20, 65] Generated Node #0,2,0: 69:[20, 65] Operation: 74-9=65 Exploring Operation: 20-9=11, Resulting Numbers: [74, 11] Generated Node #0,2,1: 69:[74, 11] Operation: 20-9=11 Exploring Operation: 74-20=54, Resulting Numbers: [9, 54] Generated Node #0,2,2: 69:[9, 54] Operation: 74-20=54 Exploring Operation: 9+74=83, Resulting Numbers: [20, 83] Generated Node #0,2,3: 69:[20, 83] Operation: 9+74=83 Exploring Operation: 9+20=29, Resulting Numbers: [74, 29] Generated Node #0,2,4: 69:[74, 29] Operation: 9+20=29 Moving to Node #0,2,0 Current State: 69:[20, 65], Operations: ['82-8=74', '74-9=65'] Exploring Operation: 65-20=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 20*65=1300, Resulting Numbers: [1300] 1300,69 unequal: No Solution Exploring Operation: 20+65=85, Resulting Numbers: [85] 85,69 unequal: No Solution Moving to Node #0,2,4 Current State: 69:[74, 29], Operations: ['82-8=74', '9+20=29'] Exploring Operation: 74*29=2146, Resulting Numbers: [2146] 2146,69 unequal: No Solution Exploring Operation: 74+29=103, Resulting Numbers: [103] 103,69 unequal: No Solution Exploring Operation: 74-29=45, Resulting Numbers: [45] 45,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[74, 11], Operations: ['82-8=74', '20-9=11'] Exploring Operation: 74+11=85, Resulting Numbers: [85] 85,69 unequal: No Solution Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,69 unequal: No Solution Exploring Operation: 74*11=814, Resulting Numbers: [814] 814,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[20, 83], Operations: ['82-8=74', '9+74=83'] Exploring Operation: 20+83=103, Resulting Numbers: [103] 103,69 unequal: No Solution Exploring Operation: 83-20=63, Resulting Numbers: [63] 63,69 unequal: No Solution Exploring Operation: 20*83=1660, Resulting Numbers: [1660] 1660,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[9, 54], Operations: ['82-8=74', '74-20=54'] Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,69 unequal: No Solution Exploring Operation: 9*54=486, Resulting Numbers: [486] 486,69 unequal: No Solution Exploring Operation: 9+54=63, Resulting Numbers: [63] 63,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[82, 20, 1], Operations: ['9-8=1'] Exploring Operation: 20+1=21, Resulting Numbers: [82, 21] Generated Node #0,0,0: 69:[82, 21] Operation: 20+1=21 Exploring Operation: 82-20=62, Resulting Numbers: [1, 62] Generated Node #0,0,1: 69:[1, 62] Operation: 82-20=62 Exploring Operation: 82-1=81, Resulting Numbers: [20, 81] Generated Node #0,0,2: 69:[20, 81] Operation: 82-1=81 Exploring Operation: 82*1=82, Resulting Numbers: [20, 82] Generated Node #0,0,3: 69:[20, 82] Operation: 82*1=82 Exploring Operation: 82/1=82, Resulting Numbers: [20, 82] Generated Node #0,0,4: 69:[20, 82] Operation: 82/1=82 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 69:[1, 62], Operations: ['9-8=1', '82-20=62'] Exploring Operation: 1*62=62, Resulting Numbers: [62] 62,69 unequal: No Solution Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,69 unequal: No Solution Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,69 unequal: No Solution Exploring Operation: 1+62=63, Resulting Numbers: [63] 63,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[82, 21], Operations: ['9-8=1', '20+1=21'] Exploring Operation: 82*21=1722, Resulting Numbers: [1722] 1722,69 unequal: No Solution Exploring Operation: 82+21=103, Resulting Numbers: [103] 103,69 unequal: No Solution Exploring Operation: 82-21=61, Resulting Numbers: [61] 61,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 69:[20, 81], Operations: ['9-8=1', '82-1=81'] Exploring Operation: 20+81=101, Resulting Numbers: [101] 101,69 unequal: No Solution Exploring Operation: 20*81=1620, Resulting Numbers: [1620] 1620,69 unequal: No Solution Exploring Operation: 81-20=61, Resulting Numbers: [61] 61,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 69:[20, 82], Operations: ['9-8=1', '82*1=82'] Exploring Operation: 20*82=1640, Resulting Numbers: [1640] 1640,69 unequal: No Solution Exploring Operation: 20+82=102, Resulting Numbers: [102] 102,69 unequal: No Solution Exploring Operation: 82-20=62, Resulting Numbers: [62] 62,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 69:[20, 82], Operations: ['9-8=1', '82/1=82'] Exploring Operation: 20*82=1640, Resulting Numbers: [1640] 1640,69 unequal: No Solution Exploring Operation: 82-20=62, Resulting Numbers: [62] 62,69 unequal: No Solution Exploring Operation: 20+82=102, Resulting Numbers: [102] 102,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[9, 8, 62], Operations: ['82-20=62'] Exploring Operation: 9-8=1, Resulting Numbers: [62, 1] Generated Node #0,1,0: 69:[62, 1] Operation: 9-8=1 Exploring Operation: 9+62=71, Resulting Numbers: [8, 71] Generated Node #0,1,1: 69:[8, 71] Operation: 9+62=71 Exploring Operation: 9*8=72, Resulting Numbers: [62, 72] Generated Node #0,1,2: 69:[62, 72] Operation: 9*8=72 Exploring Operation: 9+8=17, Resulting Numbers: [62, 17] Generated Node #0,1,3: 69:[62, 17] Operation: 9+8=17 Exploring Operation: 8+62=70, Resulting Numbers: [9, 70] Generated Node #0,1,4: 69:[9, 70] Operation: 8+62=70 Moving to Node #0,1,1 Current State: 69:[8, 71], Operations: ['82-20=62', '9+62=71'] Exploring Operation: 8+71=79, Resulting Numbers: [79] 79,69 unequal: No Solution Exploring Operation: 71-8=63, Resulting Numbers: [63] 63,69 unequal: No Solution Exploring Operation: 8*71=568, Resulting Numbers: [568] 568,69 unequal: No Solution Moving to Node #0,1,4 Current State: 69:[9, 70], Operations: ['82-20=62', '8+62=70'] Exploring Operation: 9+70=79, Resulting Numbers: [79] 79,69 unequal: No Solution Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,69 unequal: No Solution Exploring Operation: 9*70=630, Resulting Numbers: [630] 630,69 unequal: No Solution Moving to Node #0,1,0 Current State: 69:[62, 1], Operations: ['82-20=62', '9-8=1'] Exploring Operation: 62*1=62, Resulting Numbers: [62] 62,69 unequal: No Solution Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,69 unequal: No Solution Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,69 unequal: No Solution Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[62, 72], Operations: ['82-20=62', '9*8=72'] Exploring Operation: 62+72=134, Resulting Numbers: [134] 134,69 unequal: No Solution Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,69 unequal: No Solution Exploring Operation: 62*72=4464, Resulting Numbers: [4464] 4464,69 unequal: No Solution Moving to Node #0,1,3 Current State: 69:[62, 17], Operations: ['82-20=62', '9+8=17'] Exploring Operation: 62-17=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 62*17=1054, Resulting Numbers: [1054] 1054,69 unequal: No Solution Exploring Operation: 62+17=79, Resulting Numbers: [79] 79,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 69:[82, 20, 72], Operations: ['9*8=72'] Exploring Operation: 72-20=52, Resulting Numbers: [82, 52] Generated Node #0,3,0: 69:[82, 52] Operation: 72-20=52 Exploring Operation: 82-72=10, Resulting Numbers: [20, 10] Generated Node #0,3,1: 69:[20, 10] Operation: 82-72=10 Exploring Operation: 20+72=92, Resulting Numbers: [82, 92] Generated Node #0,3,2: 69:[82, 92] Operation: 20+72=92 Exploring Operation: 82-20=62, Resulting Numbers: [72, 62] Generated Node #0,3,3: 69:[72, 62] Operation: 82-20=62 Exploring Operation: 82+20=102, Resulting Numbers: [72, 102] Generated Node #0,3,4: 69:[72, 102] Operation: 82+20=102 Moving to Node #0,3,1 Current State: 69:[20, 10], Operations: ['9*8=72', '82-72=10'] Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,69 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[72, 62], Operations: ['9*8=72', '82-20=62'] Exploring Operation: 72+62=134, Resulting Numbers: [134] 134,69 unequal: No Solution Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,69 unequal: No Solution Exploring Operation: 72*62=4464, Resulting Numbers: [4464] 4464,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[82, 52], Operations: ['9*8=72', '72-20=52'] Exploring Operation: 82-52=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 82+52=134, Resulting Numbers: [134] 134,69 unequal: No Solution Exploring Operation: 82*52=4264, Resulting Numbers: [4264] 4264,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[82, 92], Operations: ['9*8=72', '20+72=92'] Exploring Operation: 82*92=7544, Resulting Numbers: [7544] 7544,69 unequal: No Solution Exploring Operation: 82+92=174, Resulting Numbers: [174] 174,69 unequal: No Solution Exploring Operation: 92-82=10, Resulting Numbers: [10] 10,69 unequal: No Solution Moving to Node #0,3,4 Current State: 69:[72, 102], Operations: ['9*8=72', '82+20=102'] Exploring Operation: 102-72=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 72*102=7344, Resulting Numbers: [7344] 7344,69 unequal: No Solution Exploring Operation: 72+102=174, Resulting Numbers: [174] 174,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 97, 56, 83, 90 ]
48
[ "97-56=41", "90-83=7", "41+7=48" ]
Current State: 48:[97, 56, 83, 90], Operations: [] Exploring Operation: 97-56=41, Resulting Numbers: [83, 90, 41] Generated Node #2: [83, 90, 41] from Operation: 97-56=41 Current State: 48:[83, 90, 41], Operations: ['97-56=41'] Exploring Operation: 90-83=7, Resulting Numbers: [41, 7] Generated Node #3: [41, 7] from Operation: 90-83=7 Current State: 48:[41, 7], Operations: ['97-56=41', '90-83=7'] Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[97, 56, 83, 90], Operations: [] Exploring Operation: 97-90=7, Resulting Numbers: [56, 83, 7] Generated Node #0,0: 48:[56, 83, 7] Operation: 97-90=7 Exploring Operation: 90-83=7, Resulting Numbers: [97, 56, 7] Generated Node #0,1: 48:[97, 56, 7] Operation: 90-83=7 Exploring Operation: 97-83=14, Resulting Numbers: [56, 90, 14] Generated Node #0,2: 48:[56, 90, 14] Operation: 97-83=14 Moving to Node #0,0 Current State: 48:[56, 83, 7], Operations: ['97-90=7'] Exploring Operation: 83-56=27, Resulting Numbers: [7, 27] Generated Node #0,0,0: 48:[7, 27] Operation: 83-56=27 Exploring Operation: 56-7=49, Resulting Numbers: [83, 49] Generated Node #0,0,1: 48:[83, 49] Operation: 56-7=49 Exploring Operation: 56/7=8, Resulting Numbers: [83, 8] Generated Node #0,0,2: 48:[83, 8] Operation: 56/7=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[7, 27], Operations: ['97-90=7', '83-56=27'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,48 unequal: No Solution Exploring Operation: 7*27=189, Resulting Numbers: [189] 189,48 unequal: No Solution Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 48:[83, 8], Operations: ['97-90=7', '56/7=8'] Exploring Operation: 83+8=91, Resulting Numbers: [91] 91,48 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 83*8=664, Resulting Numbers: [664] 664,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 48:[83, 49], Operations: ['97-90=7', '56-7=49'] Exploring Operation: 83*49=4067, Resulting Numbers: [4067] 4067,48 unequal: No Solution Exploring Operation: 83-49=34, Resulting Numbers: [34] 34,48 unequal: No Solution Exploring Operation: 83+49=132, Resulting Numbers: [132] 132,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 48:[56, 90, 14], Operations: ['97-83=14'] Exploring Operation: 90-14=76, Resulting Numbers: [56, 76] Generated Node #0,2,0: 48:[56, 76] Operation: 90-14=76 Exploring Operation: 90-56=34, Resulting Numbers: [14, 34] Generated Node #0,2,1: 48:[14, 34] Operation: 90-56=34 Exploring Operation: 56/14=4, Resulting Numbers: [90, 4] Generated Node #0,2,2: 48:[90, 4] Operation: 56/14=4 Moving to Node #0,1 Current State: 48:[97, 56, 7], Operations: ['90-83=7'] Exploring Operation: 97-56=41, Resulting Numbers: [7, 41] Generated Node #0,1,0: 48:[7, 41] Operation: 97-56=41 Exploring Operation: 56/7=8, Resulting Numbers: [97, 8] Generated Node #0,1,1: 48:[97, 8] Operation: 56/7=8 Exploring Operation: 97-7=90, Resulting Numbers: [56, 90] Generated Node #0,1,2: 48:[56, 90] Operation: 97-7=90 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[7, 41], Operations: ['90-83=7', '97-56=41'] Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,48 unequal: No Solution Exploring Operation: 7+41=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[97, 56, 83, 90], Operations: [] Exploring Operation: 90-83=7, Resulting Numbers: [97, 56, 7] Generated Node #0,1: 48:[97, 56, 7] Operation: 90-83=7 Moving to Node #0,1 Current State: 48:[97, 56, 7], Operations: ['90-83=7'] Exploring Operation: 97-56=41, Resulting Numbers: [7, 41] Generated Node #0,1,0: 48:[7, 41] Operation: 97-56=41 Moving to Node #0,1,0 Current State: 48:[7, 41], Operations: ['90-83=7', '97-56=41'] Exploring Operation: 7+41=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_3
sum_heuristic
[ 55, 76, 20, 11 ]
12
[ "76-55=21", "20-11=9", "21-9=12" ]
Current State: 12:[55, 76, 20, 11], Operations: [] Exploring Operation: 76-55=21, Resulting Numbers: [20, 11, 21] Generated Node #2: [20, 11, 21] from Operation: 76-55=21 Current State: 12:[20, 11, 21], Operations: ['76-55=21'] Exploring Operation: 20-11=9, Resulting Numbers: [21, 9] Generated Node #3: [21, 9] from Operation: 20-11=9 Current State: 12:[21, 9], Operations: ['76-55=21', '20-11=9'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[55, 76, 20, 11], Operations: [] Exploring Operation: 55-20=35, Resulting Numbers: [76, 11, 35] Generated Node #0,0: 12:[76, 11, 35] Operation: 55-20=35 Exploring Operation: 76-20=56, Resulting Numbers: [55, 11, 56] Generated Node #0,1: 12:[55, 11, 56] Operation: 76-20=56 Exploring Operation: 55/11=5, Resulting Numbers: [76, 20, 5] Generated Node #0,2: 12:[76, 20, 5] Operation: 55/11=5 Exploring Operation: 76-55=21, Resulting Numbers: [20, 11, 21] Generated Node #0,3: 12:[20, 11, 21] Operation: 76-55=21 Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[20, 11, 21], Operations: ['76-55=21'] Exploring Operation: 21-20=1, Resulting Numbers: [11, 1] Generated Node #0,3,0: 12:[11, 1] Operation: 21-20=1 Exploring Operation: 20-11=9, Resulting Numbers: [21, 9] Generated Node #0,3,1: 12:[21, 9] Operation: 20-11=9 Exploring Operation: 20+11=31, Resulting Numbers: [21, 31] Generated Node #0,3,2: 12:[21, 31] Operation: 20+11=31 Exploring Operation: 21-11=10, Resulting Numbers: [20, 10] Generated Node #0,3,3: 12:[20, 10] Operation: 21-11=10 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 12:[11, 1], Operations: ['76-55=21', '21-20=1'] Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,12 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,12 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[55, 76, 20, 11], Operations: [] Exploring Operation: 76-55=21, Resulting Numbers: [20, 11, 21] Generated Node #0,3: 12:[20, 11, 21] Operation: 76-55=21 Moving to Node #0,3 Current State: 12:[20, 11, 21], Operations: ['76-55=21'] Exploring Operation: 21-20=1, Resulting Numbers: [11, 1] Generated Node #0,3,0: 12:[11, 1] Operation: 21-20=1 Moving to Node #0,3,0 Current State: 12:[11, 1], Operations: ['76-55=21', '21-20=1'] Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 42, 49, 8, 8 ]
64
[ "49-42=7", "8*7=56", "8+56=64" ]
Current State: 64:[42, 49, 8, 8], Operations: [] Exploring Operation: 49-42=7, Resulting Numbers: [8, 8, 7] Generated Node #2: [8, 8, 7] from Operation: 49-42=7 Current State: 64:[8, 8, 7], Operations: ['49-42=7'] Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,64 equal: Goal Reached Exploring Operation: 8+56=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[42, 49, 8, 8], Operations: [] Exploring Operation: 49-42=7, Resulting Numbers: [8, 8, 7] Generated Node #0,0: 64:[8, 8, 7] Operation: 49-42=7 Exploring Operation: 42-8=34, Resulting Numbers: [49, 8, 34] Generated Node #0,1: 64:[49, 8, 34] Operation: 42-8=34 Exploring Operation: 42-8=34, Resulting Numbers: [49, 8, 34] Generated Node #0,2: 64:[49, 8, 34] Operation: 42-8=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[8, 8, 7], Operations: ['49-42=7'] Exploring Operation: 8+8=16, Resulting Numbers: [7, 16] Generated Node #0,0,0: 64:[7, 16] Operation: 8+8=16 Exploring Operation: 8*8=64, Resulting Numbers: [7, 64] Generated Node #0,0,1: 64:[7, 64] Operation: 8*8=64 Exploring Operation: 8+7=15, Resulting Numbers: [8, 15] Generated Node #0,0,2: 64:[8, 15] Operation: 8+7=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 64:[7, 16], Operations: ['49-42=7', '8+8=16'] Exploring Operation: 7*16=112, Resulting Numbers: [112] 112,64 unequal: No Solution Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,64 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 64:[7, 64], Operations: ['49-42=7', '8*8=64'] Exploring Operation: 7*64=448, Resulting Numbers: [448] 448,64 unequal: No Solution Exploring Operation: 7+64=71, Resulting Numbers: [71] 71,64 unequal: No Solution Exploring Operation: 64-7=57, Resulting Numbers: [57] 57,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 64:[8, 15], Operations: ['49-42=7', '8+7=15'] Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,64 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 8*15=120, Resulting Numbers: [120] 120,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[49, 8, 34], Operations: ['42-8=34'] Exploring Operation: 49+8=57, Resulting Numbers: [34, 57] Generated Node #0,1,0: 64:[34, 57] Operation: 49+8=57 Exploring Operation: 49-34=15, Resulting Numbers: [8, 15] Generated Node #0,1,1: 64:[8, 15] Operation: 49-34=15 Exploring Operation: 49-8=41, Resulting Numbers: [34, 41] Generated Node #0,1,2: 64:[34, 41] Operation: 49-8=41 Moving to Node #0,1,1 Current State: 64:[8, 15], Operations: ['42-8=34', '49-34=15'] Exploring Operation: 8*15=120, Resulting Numbers: [120] 120,64 unequal: No Solution Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,64 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,64 unequal: No Solution Moving to Node #0,1,0 Current State: 64:[34, 57], Operations: ['42-8=34', '49+8=57'] Exploring Operation: 34*57=1938, Resulting Numbers: [1938] 1938,64 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,64 unequal: No Solution Exploring Operation: 34+57=91, Resulting Numbers: [91] 91,64 unequal: No Solution Moving to Node #0,1,2 Current State: 64:[34, 41], Operations: ['42-8=34', '49-8=41'] Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 34*41=1394, Resulting Numbers: [1394] 1394,64 unequal: No Solution Exploring Operation: 34+41=75, Resulting Numbers: [75] 75,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[49, 8, 34], Operations: ['42-8=34'] Exploring Operation: 49+8=57, Resulting Numbers: [34, 57] Generated Node #0,2,0: 64:[34, 57] Operation: 49+8=57 Exploring Operation: 49-34=15, Resulting Numbers: [8, 15] Generated Node #0,2,1: 64:[8, 15] Operation: 49-34=15 Exploring Operation: 49-8=41, Resulting Numbers: [34, 41] Generated Node #0,2,2: 64:[34, 41] Operation: 49-8=41 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 64:[8, 15], Operations: ['42-8=34', '49-34=15'] Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,64 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 8*15=120, Resulting Numbers: [120] 120,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 64:[34, 57], Operations: ['42-8=34', '49+8=57'] Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,64 unequal: No Solution Exploring Operation: 34*57=1938, Resulting Numbers: [1938] 1938,64 unequal: No Solution Exploring Operation: 34+57=91, Resulting Numbers: [91] 91,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 64:[34, 41], Operations: ['42-8=34', '49-8=41'] Exploring Operation: 34*41=1394, Resulting Numbers: [1394] 1394,64 unequal: No Solution Exploring Operation: 34+41=75, Resulting Numbers: [75] 75,64 unequal: No Solution Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 65, 54, 18, 44 ]
18
[ "65-18=47", "47-44=3", "54/3=18" ]
Current State: 18:[65, 54, 18, 44], Operations: [] Exploring Operation: 65-18=47, Resulting Numbers: [54, 44, 47] Generated Node #2: [54, 44, 47] from Operation: 65-18=47 Current State: 18:[54, 44, 47], Operations: ['65-18=47'] Exploring Operation: 47-44=3, Resulting Numbers: [54, 3] Generated Node #3: [54, 3] from Operation: 47-44=3 Current State: 18:[54, 3], Operations: ['65-18=47', '47-44=3'] Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[65, 54, 18, 44], Operations: [] Exploring Operation: 54-44=10, Resulting Numbers: [65, 18, 10] Generated Node #0,0: 18:[65, 18, 10] Operation: 54-44=10 Exploring Operation: 65-54=11, Resulting Numbers: [18, 44, 11] Generated Node #0,1: 18:[18, 44, 11] Operation: 65-54=11 Exploring Operation: 65-44=21, Resulting Numbers: [54, 18, 21] Generated Node #0,2: 18:[54, 18, 21] Operation: 65-44=21 Exploring Operation: 65-18=47, Resulting Numbers: [54, 44, 47] Generated Node #0,3: 18:[54, 44, 47] Operation: 65-18=47 Exploring Operation: 54/18=3, Resulting Numbers: [65, 44, 3] Generated Node #0,4: 18:[65, 44, 3] Operation: 54/18=3 Moving to Node #0,1 Current State: 18:[18, 44, 11], Operations: ['65-54=11'] Exploring Operation: 18+11=29, Resulting Numbers: [44, 29] Generated Node #0,1,0: 18:[44, 29] Operation: 18+11=29 Exploring Operation: 44-18=26, Resulting Numbers: [11, 26] Generated Node #0,1,1: 18:[11, 26] Operation: 44-18=26 Exploring Operation: 44/11=4, Resulting Numbers: [18, 4] Generated Node #0,1,2: 18:[18, 4] Operation: 44/11=4 Exploring Operation: 44-11=33, Resulting Numbers: [18, 33] Generated Node #0,1,3: 18:[18, 33] Operation: 44-11=33 Exploring Operation: 18-11=7, Resulting Numbers: [44, 7] Generated Node #0,1,4: 18:[44, 7] Operation: 18-11=7 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[18, 4], Operations: ['65-54=11', '44/11=4'] Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[11, 26], Operations: ['65-54=11', '44-18=26'] Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,18 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,18 unequal: No Solution Exploring Operation: 11*26=286, Resulting Numbers: [286] 286,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[18, 33], Operations: ['65-54=11', '44-11=33'] Exploring Operation: 18*33=594, Resulting Numbers: [594] 594,18 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,18 unequal: No Solution Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 18:[44, 7], Operations: ['65-54=11', '18-11=7'] Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,18 unequal: No Solution Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[44, 29], Operations: ['65-54=11', '18+11=29'] Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,18 unequal: No Solution Exploring Operation: 44+29=73, Resulting Numbers: [73] 73,18 unequal: No Solution Exploring Operation: 44*29=1276, Resulting Numbers: [1276] 1276,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 18:[54, 18, 21], Operations: ['65-44=21'] Exploring Operation: 54+18=72, Resulting Numbers: [21, 72] Generated Node #0,2,0: 18:[21, 72] Operation: 54+18=72 Exploring Operation: 54-18=36, Resulting Numbers: [21, 36] Generated Node #0,2,1: 18:[21, 36] Operation: 54-18=36 Exploring Operation: 54-21=33, Resulting Numbers: [18, 33] Generated Node #0,2,2: 18:[18, 33] Operation: 54-21=33 Exploring Operation: 21-18=3, Resulting Numbers: [54, 3] Generated Node #0,2,3: 18:[54, 3] Operation: 21-18=3 Exploring Operation: 54/18=3, Resulting Numbers: [21, 3] Generated Node #0,2,4: 18:[21, 3] Operation: 54/18=3 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 18:[21, 3], Operations: ['65-44=21', '54/18=3'] Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 21*3=63, Resulting Numbers: [63] 63,18 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[65, 54, 18, 44], Operations: [] Exploring Operation: 65-44=21, Resulting Numbers: [54, 18, 21] Generated Node #0,2: 18:[54, 18, 21] Operation: 65-44=21 Moving to Node #0,2 Current State: 18:[54, 18, 21], Operations: ['65-44=21'] Exploring Operation: 54/18=3, Resulting Numbers: [21, 3] Generated Node #0,2,4: 18:[21, 3] Operation: 54/18=3 Moving to Node #0,2,4 Current State: 18:[21, 3], Operations: ['65-44=21', '54/18=3'] Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
mult_heuristic
[ 44, 82, 2, 73 ]
92
[ "82-44=38", "38/2=19", "73+19=92" ]
Current State: 92:[44, 82, 2, 73], Operations: [] Exploring Operation: 82-44=38, Resulting Numbers: [2, 73, 38] Generated Node #2: [2, 73, 38] from Operation: 82-44=38 Current State: 92:[2, 73, 38], Operations: ['82-44=38'] Exploring Operation: 38/2=19, Resulting Numbers: [73, 19] Generated Node #3: [73, 19] from Operation: 38/2=19 Current State: 92:[73, 19], Operations: ['82-44=38', '38/2=19'] Exploring Operation: 73+19=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[44, 82, 2, 73], Operations: [] Exploring Operation: 82-73=9, Resulting Numbers: [44, 2, 9] Generated Node #0,0: 92:[44, 2, 9] Operation: 82-73=9 Exploring Operation: 82-44=38, Resulting Numbers: [2, 73, 38] Generated Node #0,1: 92:[2, 73, 38] Operation: 82-44=38 Exploring Operation: 82/2=41, Resulting Numbers: [44, 73, 41] Generated Node #0,2: 92:[44, 73, 41] Operation: 82/2=41 Exploring Operation: 73-44=29, Resulting Numbers: [82, 2, 29] Generated Node #0,3: 92:[82, 2, 29] Operation: 73-44=29 Moving to Node #0,0 Current State: 92:[44, 2, 9], Operations: ['82-73=9'] Exploring Operation: 9-2=7, Resulting Numbers: [44, 7] Generated Node #0,0,0: 92:[44, 7] Operation: 9-2=7 Exploring Operation: 44+9=53, Resulting Numbers: [2, 53] Generated Node #0,0,1: 92:[2, 53] Operation: 44+9=53 Exploring Operation: 44/2=22, Resulting Numbers: [9, 22] Generated Node #0,0,2: 92:[9, 22] Operation: 44/2=22 Exploring Operation: 44+2=46, Resulting Numbers: [9, 46] Generated Node #0,0,3: 92:[9, 46] Operation: 44+2=46 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[44, 7], Operations: ['82-73=9', '9-2=7'] Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,92 unequal: No Solution Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,92 unequal: No Solution Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 92:[9, 46], Operations: ['82-73=9', '44+2=46'] Exploring Operation: 9*46=414, Resulting Numbers: [414] 414,92 unequal: No Solution Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,92 unequal: No Solution Exploring Operation: 9+46=55, Resulting Numbers: [55] 55,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 92:[9, 22], Operations: ['82-73=9', '44/2=22'] Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,92 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,92 unequal: No Solution Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[2, 53], Operations: ['82-73=9', '44+9=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,92 unequal: No Solution Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,92 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 92:[82, 2, 29], Operations: ['73-44=29'] Exploring Operation: 82+2=84, Resulting Numbers: [29, 84] Generated Node #0,3,0: 92:[29, 84] Operation: 82+2=84 Exploring Operation: 82-29=53, Resulting Numbers: [2, 53] Generated Node #0,3,1: 92:[2, 53] Operation: 82-29=53 Exploring Operation: 29-2=27, Resulting Numbers: [82, 27] Generated Node #0,3,2: 92:[82, 27] Operation: 29-2=27 Exploring Operation: 82/2=41, Resulting Numbers: [29, 41] Generated Node #0,3,3: 92:[29, 41] Operation: 82/2=41 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 92:[2, 53], Operations: ['73-44=29', '82-29=53'] Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,92 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,92 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 92:[29, 41], Operations: ['73-44=29', '82/2=41'] Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,92 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,92 unequal: No Solution Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 92:[29, 84], Operations: ['73-44=29', '82+2=84'] Exploring Operation: 29+84=113, Resulting Numbers: [113] 113,92 unequal: No Solution Exploring Operation: 29*84=2436, Resulting Numbers: [2436] 2436,92 unequal: No Solution Exploring Operation: 84-29=55, Resulting Numbers: [55] 55,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 92:[82, 27], Operations: ['73-44=29', '29-2=27'] Exploring Operation: 82-27=55, Resulting Numbers: [55] 55,92 unequal: No Solution Exploring Operation: 82+27=109, Resulting Numbers: [109] 109,92 unequal: No Solution Exploring Operation: 82*27=2214, Resulting Numbers: [2214] 2214,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 92:[44, 73, 41], Operations: ['82/2=41'] Exploring Operation: 73-41=32, Resulting Numbers: [44, 32] Generated Node #0,2,0: 92:[44, 32] Operation: 73-41=32 Exploring Operation: 73+41=114, Resulting Numbers: [44, 114] Generated Node #0,2,1: 92:[44, 114] Operation: 73+41=114 Exploring Operation: 44-41=3, Resulting Numbers: [73, 3] Generated Node #0,2,2: 92:[73, 3] Operation: 44-41=3 Exploring Operation: 73-44=29, Resulting Numbers: [41, 29] Generated Node #0,2,3: 92:[41, 29] Operation: 73-44=29 Moving to Node #0,1 Current State: 92:[2, 73, 38], Operations: ['82-44=38'] Exploring Operation: 73-38=35, Resulting Numbers: [2, 35] Generated Node #0,1,0: 92:[2, 35] Operation: 73-38=35 Exploring Operation: 2+73=75, Resulting Numbers: [38, 75] Generated Node #0,1,1: 92:[38, 75] Operation: 2+73=75 Exploring Operation: 73+38=111, Resulting Numbers: [2, 111] Generated Node #0,1,2: 92:[2, 111] Operation: 73+38=111 Exploring Operation: 38/2=19, Resulting Numbers: [73, 19] Generated Node #0,1,3: 92:[73, 19] Operation: 38/2=19 Moving to Node #0,2,0 Current State: 92:[44, 32], Operations: ['82/2=41', '73-41=32'] Exploring Operation: 44*32=1408, Resulting Numbers: [1408] 1408,92 unequal: No Solution Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,92 unequal: No Solution Exploring Operation: 44+32=76, Resulting Numbers: [76] 76,92 unequal: No Solution Moving to Node #0,2,3 Current State: 92:[41, 29], Operations: ['82/2=41', '73-44=29'] Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,92 unequal: No Solution Exploring Operation: 41*29=1189, Resulting Numbers: [1189] 1189,92 unequal: No Solution Exploring Operation: 41+29=70, Resulting Numbers: [70] 70,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[2, 35], Operations: ['82-44=38', '73-38=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,92 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,92 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,92 unequal: No Solution Moving to Node #0,1,2 Current State: 92:[2, 111], Operations: ['82-44=38', '73+38=111'] Exploring Operation: 2+111=113, Resulting Numbers: [113] 113,92 unequal: No Solution Exploring Operation: 2*111=222, Resulting Numbers: [222] 222,92 unequal: No Solution Exploring Operation: 111-2=109, Resulting Numbers: [109] 109,92 unequal: No Solution Moving to Node #0,2,2 Current State: 92:[73, 3], Operations: ['82/2=41', '44-41=3'] Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,92 unequal: No Solution Exploring Operation: 73*3=219, Resulting Numbers: [219] 219,92 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,92 unequal: No Solution Moving to Node #0,1,3 Current State: 92:[73, 19], Operations: ['82-44=38', '38/2=19'] Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,92 unequal: No Solution Exploring Operation: 73+19=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[44, 82, 2, 73], Operations: [] Exploring Operation: 82-44=38, Resulting Numbers: [2, 73, 38] Generated Node #0,1: 92:[2, 73, 38] Operation: 82-44=38 Moving to Node #0,1 Current State: 92:[2, 73, 38], Operations: ['82-44=38'] Exploring Operation: 38/2=19, Resulting Numbers: [73, 19] Generated Node #0,1,3: 92:[73, 19] Operation: 38/2=19 Moving to Node #0,1,3 Current State: 92:[73, 19], Operations: ['82-44=38', '38/2=19'] Exploring Operation: 73+19=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
0.943576
hs_4
sum_heuristic
[ 99, 77, 97, 86 ]
16
[ "99+77=176", "97-86=11", "176/11=16" ]
Current State: 16:[99, 77, 97, 86], Operations: [] Exploring Operation: 99+77=176, Resulting Numbers: [97, 86, 176] Generated Node #2: [97, 86, 176] from Operation: 99+77=176 Current State: 16:[97, 86, 176], Operations: ['99+77=176'] Exploring Operation: 97-86=11, Resulting Numbers: [176, 11] Generated Node #3: [176, 11] from Operation: 97-86=11 Current State: 16:[176, 11], Operations: ['99+77=176', '97-86=11'] Exploring Operation: 176/11=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[99, 77, 97, 86], Operations: [] Exploring Operation: 97-86=11, Resulting Numbers: [99, 77, 11] Generated Node #0,0: 16:[99, 77, 11] Operation: 97-86=11 Exploring Operation: 99-77=22, Resulting Numbers: [97, 86, 22] Generated Node #0,1: 16:[97, 86, 22] Operation: 99-77=22 Exploring Operation: 99-86=13, Resulting Numbers: [77, 97, 13] Generated Node #0,2: 16:[77, 97, 13] Operation: 99-86=13 Exploring Operation: 99-97=2, Resulting Numbers: [77, 86, 2] Generated Node #0,3: 16:[77, 86, 2] Operation: 99-97=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 16:[77, 86, 2], Operations: ['99-97=2'] Exploring Operation: 86-2=84, Resulting Numbers: [77, 84] Generated Node #0,3,0: 16:[77, 84] Operation: 86-2=84 Exploring Operation: 86/2=43, Resulting Numbers: [77, 43] Generated Node #0,3,1: 16:[77, 43] Operation: 86/2=43 Exploring Operation: 86-77=9, Resulting Numbers: [2, 9] Generated Node #0,3,2: 16:[2, 9] Operation: 86-77=9 Exploring Operation: 77-2=75, Resulting Numbers: [86, 75] Generated Node #0,3,3: 16:[86, 75] Operation: 77-2=75 Moving to Node #0,3,2 Current State: 16:[2, 9], Operations: ['99-97=2', '86-77=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,16 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,16 unequal: No Solution Moving to Node #0,3,1 Current State: 16:[77, 43], Operations: ['99-97=2', '86/2=43'] Exploring Operation: 77+43=120, Resulting Numbers: [120] 120,16 unequal: No Solution Exploring Operation: 77-43=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 77*43=3311, Resulting Numbers: [3311] 3311,16 unequal: No Solution Moving to Node #0,3,3 Current State: 16:[86, 75], Operations: ['99-97=2', '77-2=75'] Exploring Operation: 86*75=6450, Resulting Numbers: [6450] 6450,16 unequal: No Solution Exploring Operation: 86+75=161, Resulting Numbers: [161] 161,16 unequal: No Solution Exploring Operation: 86-75=11, Resulting Numbers: [11] 11,16 unequal: No Solution Moving to Node #0,3,0 Current State: 16:[77, 84], Operations: ['99-97=2', '86-2=84'] Exploring Operation: 77+84=161, Resulting Numbers: [161] 161,16 unequal: No Solution Exploring Operation: 84-77=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 77*84=6468, Resulting Numbers: [6468] 6468,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[77, 97, 13], Operations: ['99-86=13'] Exploring Operation: 77+13=90, Resulting Numbers: [97, 90] Generated Node #0,2,0: 16:[97, 90] Operation: 77+13=90 Exploring Operation: 77-13=64, Resulting Numbers: [97, 64] Generated Node #0,2,1: 16:[97, 64] Operation: 77-13=64 Exploring Operation: 97-77=20, Resulting Numbers: [13, 20] Generated Node #0,2,2: 16:[13, 20] Operation: 97-77=20 Exploring Operation: 97-13=84, Resulting Numbers: [77, 84] Generated Node #0,2,3: 16:[77, 84] Operation: 97-13=84 Moving to Node #0,2,2 Current State: 16:[13, 20], Operations: ['99-86=13', '97-77=20'] Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 13+20=33, Resulting Numbers: [33] 33,16 unequal: No Solution Exploring Operation: 13*20=260, Resulting Numbers: [260] 260,16 unequal: No Solution Moving to Node #0,2,3 Current State: 16:[77, 84], Operations: ['99-86=13', '97-13=84'] Exploring Operation: 84-77=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 77+84=161, Resulting Numbers: [161] 161,16 unequal: No Solution Exploring Operation: 77*84=6468, Resulting Numbers: [6468] 6468,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[97, 64], Operations: ['99-86=13', '77-13=64'] Exploring Operation: 97+64=161, Resulting Numbers: [161] 161,16 unequal: No Solution Exploring Operation: 97*64=6208, Resulting Numbers: [6208] 6208,16 unequal: No Solution Exploring Operation: 97-64=33, Resulting Numbers: [33] 33,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[97, 90], Operations: ['99-86=13', '77+13=90'] Exploring Operation: 97+90=187, Resulting Numbers: [187] 187,16 unequal: No Solution Exploring Operation: 97*90=8730, Resulting Numbers: [8730] 8730,16 unequal: No Solution Exploring Operation: 97-90=7, Resulting Numbers: [7] 7,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[99, 77, 11], Operations: ['97-86=11'] Exploring Operation: 77/11=7, Resulting Numbers: [99, 7] Generated Node #0,0,0: 16:[99, 7] Operation: 77/11=7 Exploring Operation: 99-77=22, Resulting Numbers: [11, 22] Generated Node #0,0,1: 16:[11, 22] Operation: 99-77=22 Exploring Operation: 99/11=9, Resulting Numbers: [77, 9] Generated Node #0,0,2: 16:[77, 9] Operation: 99/11=9 Exploring Operation: 99-11=88, Resulting Numbers: [77, 88] Generated Node #0,0,3: 16:[77, 88] Operation: 99-11=88 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 16:[11, 22], Operations: ['97-86=11', '99-77=22'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 11*22=242, Resulting Numbers: [242] 242,16 unequal: No Solution Exploring Operation: 11+22=33, Resulting Numbers: [33] 33,16 unequal: No Solution Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 16:[77, 9], Operations: ['97-86=11', '99/11=9'] Exploring Operation: 77*9=693, Resulting Numbers: [693] 693,16 unequal: No Solution Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,16 unequal: No Solution Exploring Operation: 77+9=86, Resulting Numbers: [86] 86,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 16:[99, 7], Operations: ['97-86=11', '77/11=7'] Exploring Operation: 99*7=693, Resulting Numbers: [693] 693,16 unequal: No Solution Exploring Operation: 99+7=106, Resulting Numbers: [106] 106,16 unequal: No Solution Exploring Operation: 99-7=92, Resulting Numbers: [92] 92,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 16:[77, 88], Operations: ['97-86=11', '99-11=88'] Exploring Operation: 77*88=6776, Resulting Numbers: [6776] 6776,16 unequal: No Solution Exploring Operation: 77+88=165, Resulting Numbers: [165] 165,16 unequal: No Solution Exploring Operation: 88-77=11, Resulting Numbers: [11] 11,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[97, 86, 22], Operations: ['99-77=22'] Exploring Operation: 86-22=64, Resulting Numbers: [97, 64] Generated Node #0,1,0: 16:[97, 64] Operation: 86-22=64 Exploring Operation: 97-22=75, Resulting Numbers: [86, 75] Generated Node #0,1,1: 16:[86, 75] Operation: 97-22=75 Exploring Operation: 97-86=11, Resulting Numbers: [22, 11] Generated Node #0,1,2: 16:[22, 11] Operation: 97-86=11 Exploring Operation: 97+86=183, Resulting Numbers: [22, 183] Generated Node #0,1,3: 16:[22, 183] Operation: 97+86=183 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 16:[22, 11], Operations: ['99-77=22', '97-86=11'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 22*11=242, Resulting Numbers: [242] 242,16 unequal: No Solution Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[97, 64], Operations: ['99-77=22', '86-22=64'] Exploring Operation: 97*64=6208, Resulting Numbers: [6208] 6208,16 unequal: No Solution Exploring Operation: 97-64=33, Resulting Numbers: [33] 33,16 unequal: No Solution Exploring Operation: 97+64=161, Resulting Numbers: [161] 161,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[86, 75], Operations: ['99-77=22', '97-22=75'] Exploring Operation: 86*75=6450, Resulting Numbers: [6450] 6450,16 unequal: No Solution Exploring Operation: 86-75=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 86+75=161, Resulting Numbers: [161] 161,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 16:[22, 183], Operations: ['99-77=22', '97+86=183'] Exploring Operation: 22+183=205, Resulting Numbers: [205] 205,16 unequal: No Solution Exploring Operation: 183-22=161, Resulting Numbers: [161] 161,16 unequal: No Solution Exploring Operation: 22*183=4026, Resulting Numbers: [4026] 4026,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 82, 61, 41, 61 ]
81
[ "82-61=21", "41+61=102", "102-21=81" ]
Current State: 81:[82, 61, 41, 61], Operations: [] Exploring Operation: 82-61=21, Resulting Numbers: [41, 21] Generated Node #2: [41, 21] from Operation: 82-61=21 Current State: 81:[41, 21], Operations: ['82-61=21'] Exploring Operation: 41+61=102, Resulting Numbers: [21, 102] Generated Node #3: [21, 102] from Operation: 41+61=102 Current State: 81:[21, 102], Operations: ['82-61=21', '41+61=102'] Exploring Operation: 102-21=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[82, 61, 41, 61], Operations: [] Exploring Operation: 61/61=1, Resulting Numbers: [82, 41, 1] Generated Node #0,0: 81:[82, 41, 1] Operation: 61/61=1 Exploring Operation: 61-61=0, Resulting Numbers: [82, 41, 0] Generated Node #0,1: 81:[82, 41, 0] Operation: 61-61=0 Moving to Node #0,0 Current State: 81:[82, 41, 1], Operations: ['61/61=1'] Exploring Operation: 82-1=81, Resulting Numbers: [41, 81] Generated Node #0,0,0: 81:[41, 81] Operation: 82-1=81 Exploring Operation: 82/41=2, Resulting Numbers: [1, 2] Generated Node #0,0,1: 81:[1, 2] Operation: 82/41=2 Moving to Node #0,1 Current State: 81:[82, 41, 0], Operations: ['61-61=0'] Exploring Operation: 41*0=0, Resulting Numbers: [82, 0] Generated Node #0,1,0: 81:[82, 0] Operation: 41*0=0 Exploring Operation: 82/41=2, Resulting Numbers: [0, 2] Generated Node #0,1,1: 81:[0, 2] Operation: 82/41=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 81:[82, 0], Operations: ['61-61=0', '41*0=0'] Exploring Operation: 82-0=82, Resulting Numbers: [82] 82,81 unequal: No Solution Exploring Operation: 82+0=82, Resulting Numbers: [82] 82,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 81:[0, 2], Operations: ['61-61=0', '82/41=2'] Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,81 unequal: No Solution Exploring Operation: 0+2=2, Resulting Numbers: [2] 2,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 81:[1, 2], Operations: ['61/61=1', '82/41=2'] Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,81 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[41, 81], Operations: ['61/61=1', '82-1=81'] Exploring Operation: 41+81=122, Resulting Numbers: [122] 122,81 unequal: No Solution Exploring Operation: 81-41=40, Resulting Numbers: [40] 40,81 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 77, 52, 11, 58 ]
22
[ "77-52=25", "58-11=47", "47-25=22" ]
Current State: 22:[77, 52, 11, 58], Operations: [] Exploring Operation: 77-52=25, Resulting Numbers: [11, 58, 25] Generated Node #2: [11, 58, 25] from Operation: 77-52=25 Current State: 22:[11, 58, 25], Operations: ['77-52=25'] Exploring Operation: 58-11=47, Resulting Numbers: [25, 47] Generated Node #3: [25, 47] from Operation: 58-11=47 Current State: 22:[25, 47], Operations: ['77-52=25', '58-11=47'] Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[77, 52, 11, 58], Operations: [] Exploring Operation: 77-58=19, Resulting Numbers: [52, 11, 19] Generated Node #0,0: 22:[52, 11, 19] Operation: 77-58=19 Exploring Operation: 77-52=25, Resulting Numbers: [11, 58, 25] Generated Node #0,1: 22:[11, 58, 25] Operation: 77-52=25 Moving to Node #0,0 Current State: 22:[52, 11, 19], Operations: ['77-58=19'] Exploring Operation: 52-19=33, Resulting Numbers: [11, 33] Generated Node #0,0,0: 22:[11, 33] Operation: 52-19=33 Exploring Operation: 52-11=41, Resulting Numbers: [19, 41] Generated Node #0,0,1: 22:[19, 41] Operation: 52-11=41 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[11, 33], Operations: ['77-58=19', '52-19=33'] Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[77, 52, 11, 58], Operations: [] Exploring Operation: 77-58=19, Resulting Numbers: [52, 11, 19] Generated Node #0,0: 22:[52, 11, 19] Operation: 77-58=19 Moving to Node #0,0 Current State: 22:[52, 11, 19], Operations: ['77-58=19'] Exploring Operation: 52-19=33, Resulting Numbers: [11, 33] Generated Node #0,0,0: 22:[11, 33] Operation: 52-19=33 Moving to Node #0,0,0 Current State: 22:[11, 33], Operations: ['77-58=19', '52-19=33'] Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 16, 76, 18, 46 ]
32
[ "76-16=60", "46-18=28", "60-28=32" ]
Current State: 32:[16, 76, 18, 46], Operations: [] Exploring Operation: 76-16=60, Resulting Numbers: [18, 46, 60] Generated Node #2: [18, 46, 60] from Operation: 76-16=60 Current State: 32:[18, 46, 60], Operations: ['76-16=60'] Exploring Operation: 46-18=28, Resulting Numbers: [60, 28] Generated Node #3: [60, 28] from Operation: 46-18=28 Current State: 32:[60, 28], Operations: ['76-16=60', '46-18=28'] Exploring Operation: 60-28=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[16, 76, 18, 46], Operations: [] Exploring Operation: 76-18=58, Resulting Numbers: [16, 46, 58] Generated Node #0,0: 32:[16, 46, 58] Operation: 76-18=58 Exploring Operation: 76-16=60, Resulting Numbers: [18, 46, 60] Generated Node #0,1: 32:[18, 46, 60] Operation: 76-16=60 Exploring Operation: 76-46=30, Resulting Numbers: [16, 18, 30] Generated Node #0,2: 32:[16, 18, 30] Operation: 76-46=30 Exploring Operation: 46-16=30, Resulting Numbers: [76, 18, 30] Generated Node #0,3: 32:[76, 18, 30] Operation: 46-16=30 Moving to Node #0,2 Current State: 32:[16, 18, 30], Operations: ['76-46=30'] Exploring Operation: 18-16=2, Resulting Numbers: [30, 2] Generated Node #0,2,0: 32:[30, 2] Operation: 18-16=2 Exploring Operation: 16+18=34, Resulting Numbers: [30, 34] Generated Node #0,2,1: 32:[30, 34] Operation: 16+18=34 Exploring Operation: 30-18=12, Resulting Numbers: [16, 12] Generated Node #0,2,2: 32:[16, 12] Operation: 30-18=12 Exploring Operation: 30-16=14, Resulting Numbers: [18, 14] Generated Node #0,2,3: 32:[18, 14] Operation: 30-16=14 Moving to Node #0,0 Current State: 32:[16, 46, 58], Operations: ['76-18=58'] Exploring Operation: 58-16=42, Resulting Numbers: [46, 42] Generated Node #0,0,0: 32:[46, 42] Operation: 58-16=42 Exploring Operation: 16+46=62, Resulting Numbers: [58, 62] Generated Node #0,0,1: 32:[58, 62] Operation: 16+46=62 Exploring Operation: 46-16=30, Resulting Numbers: [58, 30] Generated Node #0,0,2: 32:[58, 30] Operation: 46-16=30 Exploring Operation: 58-46=12, Resulting Numbers: [16, 12] Generated Node #0,0,3: 32:[16, 12] Operation: 58-46=12 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 32:[16, 12], Operations: ['76-18=58', '58-46=12'] Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,32 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[46, 42], Operations: ['76-18=58', '58-16=42'] Exploring Operation: 46*42=1932, Resulting Numbers: [1932] 1932,32 unequal: No Solution Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 46+42=88, Resulting Numbers: [88] 88,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 32:[58, 30], Operations: ['76-18=58', '46-16=30'] Exploring Operation: 58*30=1740, Resulting Numbers: [1740] 1740,32 unequal: No Solution Exploring Operation: 58+30=88, Resulting Numbers: [88] 88,32 unequal: No Solution Exploring Operation: 58-30=28, Resulting Numbers: [28] 28,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[58, 62], Operations: ['76-18=58', '16+46=62'] Exploring Operation: 62-58=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 58*62=3596, Resulting Numbers: [3596] 3596,32 unequal: No Solution Exploring Operation: 58+62=120, Resulting Numbers: [120] 120,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 32:[18, 46, 60], Operations: ['76-16=60'] Exploring Operation: 46-18=28, Resulting Numbers: [60, 28] Generated Node #0,1,0: 32:[60, 28] Operation: 46-18=28 Exploring Operation: 60-46=14, Resulting Numbers: [18, 14] Generated Node #0,1,1: 32:[18, 14] Operation: 60-46=14 Exploring Operation: 60-18=42, Resulting Numbers: [46, 42] Generated Node #0,1,2: 32:[46, 42] Operation: 60-18=42 Exploring Operation: 18+46=64, Resulting Numbers: [60, 64] Generated Node #0,1,3: 32:[60, 64] Operation: 18+46=64 Moving to Node #0,3 Current State: 32:[76, 18, 30], Operations: ['46-16=30'] Exploring Operation: 30-18=12, Resulting Numbers: [76, 12] Generated Node #0,3,0: 32:[76, 12] Operation: 30-18=12 Exploring Operation: 76-18=58, Resulting Numbers: [30, 58] Generated Node #0,3,1: 32:[30, 58] Operation: 76-18=58 Exploring Operation: 76-30=46, Resulting Numbers: [18, 46] Generated Node #0,3,2: 32:[18, 46] Operation: 76-30=46 Exploring Operation: 18+30=48, Resulting Numbers: [76, 48] Generated Node #0,3,3: 32:[76, 48] Operation: 18+30=48 Moving to Node #0,2,0 Current State: 32:[30, 2], Operations: ['76-46=30', '18-16=2'] Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 30+2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[16, 76, 18, 46], Operations: [] Exploring Operation: 76-46=30, Resulting Numbers: [16, 18, 30] Generated Node #0,2: 32:[16, 18, 30] Operation: 76-46=30 Moving to Node #0,2 Current State: 32:[16, 18, 30], Operations: ['76-46=30'] Exploring Operation: 18-16=2, Resulting Numbers: [30, 2] Generated Node #0,2,0: 32:[30, 2] Operation: 18-16=2 Moving to Node #0,2,0 Current State: 32:[30, 2], Operations: ['76-46=30', '18-16=2'] Exploring Operation: 30+2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.966146
hs_4
mult_heuristic
[ 7, 37, 55, 83 ]
72
[ "7+37=44", "83-55=28", "44+28=72" ]
Current State: 72:[7, 37, 55, 83], Operations: [] Exploring Operation: 7+37=44, Resulting Numbers: [55, 83, 44] Generated Node #2: [55, 83, 44] from Operation: 7+37=44 Current State: 72:[55, 83, 44], Operations: ['7+37=44'] Exploring Operation: 83-55=28, Resulting Numbers: [44, 28] Generated Node #3: [44, 28] from Operation: 83-55=28 Current State: 72:[44, 28], Operations: ['7+37=44', '83-55=28'] Exploring Operation: 44+28=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[7, 37, 55, 83], Operations: [] Exploring Operation: 83-55=28, Resulting Numbers: [7, 37, 28] Generated Node #0,0: 72:[7, 37, 28] Operation: 83-55=28 Exploring Operation: 55-37=18, Resulting Numbers: [7, 83, 18] Generated Node #0,1: 72:[7, 83, 18] Operation: 55-37=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[7, 37, 28], Operations: ['83-55=28'] Exploring Operation: 37-28=9, Resulting Numbers: [7, 9] Generated Node #0,0,0: 72:[7, 9] Operation: 37-28=9 Exploring Operation: 28/7=4, Resulting Numbers: [37, 4] Generated Node #0,0,1: 72:[37, 4] Operation: 28/7=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[7, 9], Operations: ['83-55=28', '37-28=9'] Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 72:[37, 4], Operations: ['83-55=28', '28/7=4'] Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,72 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[7, 83, 18], Operations: ['55-37=18'] Exploring Operation: 83-7=76, Resulting Numbers: [18, 76] Generated Node #0,1,0: 72:[18, 76] Operation: 83-7=76 Exploring Operation: 83-18=65, Resulting Numbers: [7, 65] Generated Node #0,1,1: 72:[7, 65] Operation: 83-18=65 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 72:[18, 76], Operations: ['55-37=18', '83-7=76'] Exploring Operation: 18+76=94, Resulting Numbers: [94] 94,72 unequal: No Solution Exploring Operation: 76-18=58, Resulting Numbers: [58] 58,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 72:[7, 65], Operations: ['55-37=18', '83-18=65'] Exploring Operation: 7+65=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[7, 37, 55, 83], Operations: [] Exploring Operation: 55-37=18, Resulting Numbers: [7, 83, 18] Generated Node #0,1: 72:[7, 83, 18] Operation: 55-37=18 Moving to Node #0,1 Current State: 72:[7, 83, 18], Operations: ['55-37=18'] Exploring Operation: 83-18=65, Resulting Numbers: [7, 65] Generated Node #0,1,1: 72:[7, 65] Operation: 83-18=65 Moving to Node #0,1,1 Current State: 72:[7, 65], Operations: ['55-37=18', '83-18=65'] Exploring Operation: 7+65=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_2
mult_heuristic
[ 4, 42, 6, 96 ]
17
[ "96/4=24", "42/6=7", "24-7=17" ]
Current State: 17:[4, 42, 6, 96], Operations: [] Exploring Operation: 96/4=24, Resulting Numbers: [42, 6, 24] Generated Node #2: [42, 6, 24] from Operation: 96/4=24 Current State: 17:[42, 6, 24], Operations: ['96/4=24'] Exploring Operation: 42/6=7, Resulting Numbers: [24, 7] Generated Node #3: [24, 7] from Operation: 42/6=7 Current State: 17:[24, 7], Operations: ['96/4=24', '42/6=7'] Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[4, 42, 6, 96], Operations: [] Exploring Operation: 96-42=54, Resulting Numbers: [4, 6, 54] Generated Node #0,0: 17:[4, 6, 54] Operation: 96-42=54 Exploring Operation: 96/4=24, Resulting Numbers: [42, 6, 24] Generated Node #0,1: 17:[42, 6, 24] Operation: 96/4=24 Exploring Operation: 96/6=16, Resulting Numbers: [4, 42, 16] Generated Node #0,2: 17:[4, 42, 16] Operation: 96/6=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[4, 42, 16], Operations: ['96/6=16'] Exploring Operation: 4+16=20, Resulting Numbers: [42, 20] Generated Node #0,2,0: 17:[42, 20] Operation: 4+16=20 Exploring Operation: 42-4=38, Resulting Numbers: [16, 38] Generated Node #0,2,1: 17:[16, 38] Operation: 42-4=38 Exploring Operation: 42-16=26, Resulting Numbers: [4, 26] Generated Node #0,2,2: 17:[4, 26] Operation: 42-16=26 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 17:[16, 38], Operations: ['96/6=16', '42-4=38'] Exploring Operation: 16*38=608, Resulting Numbers: [608] 608,17 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 16+38=54, Resulting Numbers: [54] 54,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 17:[4, 26], Operations: ['96/6=16', '42-16=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,17 unequal: No Solution Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 17:[42, 20], Operations: ['96/6=16', '4+16=20'] Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 42*20=840, Resulting Numbers: [840] 840,17 unequal: No Solution Exploring Operation: 42+20=62, Resulting Numbers: [62] 62,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[42, 6, 24], Operations: ['96/4=24'] Exploring Operation: 42/6=7, Resulting Numbers: [24, 7] Generated Node #0,1,0: 17:[24, 7] Operation: 42/6=7 Exploring Operation: 42-24=18, Resulting Numbers: [6, 18] Generated Node #0,1,1: 17:[6, 18] Operation: 42-24=18 Exploring Operation: 42-6=36, Resulting Numbers: [24, 36] Generated Node #0,1,2: 17:[24, 36] Operation: 42-6=36 Moving to Node #0,1,1 Current State: 17:[6, 18], Operations: ['96/4=24', '42-24=18'] Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,17 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[24, 7], Operations: ['96/4=24', '42/6=7'] Exploring Operation: 24*7=168, Resulting Numbers: [168] 168,17 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[4, 42, 6, 96], Operations: [] Exploring Operation: 96/4=24, Resulting Numbers: [42, 6, 24] Generated Node #0,1: 17:[42, 6, 24] Operation: 96/4=24 Moving to Node #0,1 Current State: 17:[42, 6, 24], Operations: ['96/4=24'] Exploring Operation: 42/6=7, Resulting Numbers: [24, 7] Generated Node #0,1,0: 17:[24, 7] Operation: 42/6=7 Moving to Node #0,1,0 Current State: 17:[24, 7], Operations: ['96/4=24', '42/6=7'] Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_3
mult_heuristic
[ 37, 6, 56, 39 ]
64
[ "37-6=31", "56+39=95", "95-31=64" ]
Current State: 64:[37, 6, 56, 39], Operations: [] Exploring Operation: 37-6=31, Resulting Numbers: [56, 39, 31] Generated Node #2: [56, 39, 31] from Operation: 37-6=31 Current State: 64:[56, 39, 31], Operations: ['37-6=31'] Exploring Operation: 56+39=95, Resulting Numbers: [31, 95] Generated Node #3: [31, 95] from Operation: 56+39=95 Current State: 64:[31, 95], Operations: ['37-6=31', '56+39=95'] Exploring Operation: 95-31=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[37, 6, 56, 39], Operations: [] Exploring Operation: 56-39=17, Resulting Numbers: [37, 6, 17] Generated Node #0,0: 64:[37, 6, 17] Operation: 56-39=17 Exploring Operation: 56-37=19, Resulting Numbers: [6, 39, 19] Generated Node #0,1: 64:[6, 39, 19] Operation: 56-37=19 Exploring Operation: 39-37=2, Resulting Numbers: [6, 56, 2] Generated Node #0,2: 64:[6, 56, 2] Operation: 39-37=2 Exploring Operation: 6+56=62, Resulting Numbers: [37, 39, 62] Generated Node #0,3: 64:[37, 39, 62] Operation: 6+56=62 Exploring Operation: 39-6=33, Resulting Numbers: [37, 56, 33] Generated Node #0,4: 64:[37, 56, 33] Operation: 39-6=33 Moving to Node #0,0 Current State: 64:[37, 6, 17], Operations: ['56-39=17'] Exploring Operation: 17-6=11, Resulting Numbers: [37, 11] Generated Node #0,0,0: 64:[37, 11] Operation: 17-6=11 Exploring Operation: 37-17=20, Resulting Numbers: [6, 20] Generated Node #0,0,1: 64:[6, 20] Operation: 37-17=20 Exploring Operation: 37+6=43, Resulting Numbers: [17, 43] Generated Node #0,0,2: 64:[17, 43] Operation: 37+6=43 Exploring Operation: 37+17=54, Resulting Numbers: [6, 54] Generated Node #0,0,3: 64:[6, 54] Operation: 37+17=54 Exploring Operation: 37-6=31, Resulting Numbers: [17, 31] Generated Node #0,0,4: 64:[17, 31] Operation: 37-6=31 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 64:[17, 31], Operations: ['56-39=17', '37-6=31'] Exploring Operation: 17*31=527, Resulting Numbers: [527] 527,64 unequal: No Solution Exploring Operation: 17+31=48, Resulting Numbers: [48] 48,64 unequal: No Solution Exploring Operation: 31-17=14, Resulting Numbers: [14] 14,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 64:[6, 20], Operations: ['56-39=17', '37-17=20'] Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,64 unequal: No Solution Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[37, 11], Operations: ['56-39=17', '17-6=11'] Exploring Operation: 37+11=48, Resulting Numbers: [48] 48,64 unequal: No Solution Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 37*11=407, Resulting Numbers: [407] 407,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 64:[17, 43], Operations: ['56-39=17', '37+6=43'] Exploring Operation: 17*43=731, Resulting Numbers: [731] 731,64 unequal: No Solution Exploring Operation: 43-17=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 17+43=60, Resulting Numbers: [60] 60,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 64:[6, 54], Operations: ['56-39=17', '37+17=54'] Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,64 unequal: No Solution Exploring Operation: 6*54=324, Resulting Numbers: [324] 324,64 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,64 unequal: No Solution Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 64:[6, 56, 2], Operations: ['39-37=2'] Exploring Operation: 6-2=4, Resulting Numbers: [56, 4] Generated Node #0,2,0: 64:[56, 4] Operation: 6-2=4 Exploring Operation: 6+56=62, Resulting Numbers: [2, 62] Generated Node #0,2,1: 64:[2, 62] Operation: 6+56=62 Exploring Operation: 56/2=28, Resulting Numbers: [6, 28] Generated Node #0,2,2: 64:[6, 28] Operation: 56/2=28 Exploring Operation: 6+2=8, Resulting Numbers: [56, 8] Generated Node #0,2,3: 64:[56, 8] Operation: 6+2=8 Exploring Operation: 56+2=58, Resulting Numbers: [6, 58] Generated Node #0,2,4: 64:[6, 58] Operation: 56+2=58 Moving to Node #0,1 Current State: 64:[6, 39, 19], Operations: ['56-37=19'] Exploring Operation: 6+19=25, Resulting Numbers: [39, 25] Generated Node #0,1,0: 64:[39, 25] Operation: 6+19=25 Exploring Operation: 39+19=58, Resulting Numbers: [6, 58] Generated Node #0,1,1: 64:[6, 58] Operation: 39+19=58 Exploring Operation: 39-6=33, Resulting Numbers: [19, 33] Generated Node #0,1,2: 64:[19, 33] Operation: 39-6=33 Exploring Operation: 39-19=20, Resulting Numbers: [6, 20] Generated Node #0,1,3: 64:[6, 20] Operation: 39-19=20 Exploring Operation: 19-6=13, Resulting Numbers: [39, 13] Generated Node #0,1,4: 64:[39, 13] Operation: 19-6=13 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 64:[19, 33], Operations: ['56-37=19', '39-6=33'] Exploring Operation: 19*33=627, Resulting Numbers: [627] 627,64 unequal: No Solution Exploring Operation: 33-19=14, Resulting Numbers: [14] 14,64 unequal: No Solution Exploring Operation: 19+33=52, Resulting Numbers: [52] 52,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 64:[6, 20], Operations: ['56-37=19', '39-19=20'] Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,64 unequal: No Solution Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 64:[6, 58], Operations: ['56-37=19', '39+19=58'] Exploring Operation: 6+58=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[37, 6, 56, 39], Operations: [] Exploring Operation: 56-37=19, Resulting Numbers: [6, 39, 19] Generated Node #0,1: 64:[6, 39, 19] Operation: 56-37=19 Moving to Node #0,1 Current State: 64:[6, 39, 19], Operations: ['56-37=19'] Exploring Operation: 39+19=58, Resulting Numbers: [6, 58] Generated Node #0,1,1: 64:[6, 58] Operation: 39+19=58 Moving to Node #0,1,1 Current State: 64:[6, 58], Operations: ['56-37=19', '39+19=58'] Exploring Operation: 6+58=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
sum_heuristic
[ 26, 22, 24, 45 ]
27
[ "26+22=48", "45-24=21", "48-21=27" ]
Current State: 27:[26, 22, 24, 45], Operations: [] Exploring Operation: 26+22=48, Resulting Numbers: [24, 45, 48] Generated Node #2: [24, 45, 48] from Operation: 26+22=48 Current State: 27:[24, 45, 48], Operations: ['26+22=48'] Exploring Operation: 45-24=21, Resulting Numbers: [48, 21] Generated Node #3: [48, 21] from Operation: 45-24=21 Current State: 27:[48, 21], Operations: ['26+22=48', '45-24=21'] Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[26, 22, 24, 45], Operations: [] Exploring Operation: 45-26=19, Resulting Numbers: [22, 24, 19] Generated Node #0,0: 27:[22, 24, 19] Operation: 45-26=19 Exploring Operation: 45-22=23, Resulting Numbers: [26, 24, 23] Generated Node #0,1: 27:[26, 24, 23] Operation: 45-22=23 Exploring Operation: 45-24=21, Resulting Numbers: [26, 22, 21] Generated Node #0,2: 27:[26, 22, 21] Operation: 45-24=21 Exploring Operation: 24-22=2, Resulting Numbers: [26, 45, 2] Generated Node #0,3: 27:[26, 45, 2] Operation: 24-22=2 Moving to Node #0,1 Current State: 27:[26, 24, 23], Operations: ['45-22=23'] Exploring Operation: 24-23=1, Resulting Numbers: [26, 1] Generated Node #0,1,0: 27:[26, 1] Operation: 24-23=1 Exploring Operation: 26-24=2, Resulting Numbers: [23, 2] Generated Node #0,1,1: 27:[23, 2] Operation: 26-24=2 Exploring Operation: 24+23=47, Resulting Numbers: [26, 47] Generated Node #0,1,2: 27:[26, 47] Operation: 24+23=47 Exploring Operation: 26-23=3, Resulting Numbers: [24, 3] Generated Node #0,1,3: 27:[24, 3] Operation: 26-23=3 Moving to Node #0,2 Current State: 27:[26, 22, 21], Operations: ['45-24=21'] Exploring Operation: 26-21=5, Resulting Numbers: [22, 5] Generated Node #0,2,0: 27:[22, 5] Operation: 26-21=5 Exploring Operation: 26-22=4, Resulting Numbers: [21, 4] Generated Node #0,2,1: 27:[21, 4] Operation: 26-22=4 Exploring Operation: 22+21=43, Resulting Numbers: [26, 43] Generated Node #0,2,2: 27:[26, 43] Operation: 22+21=43 Exploring Operation: 22-21=1, Resulting Numbers: [26, 1] Generated Node #0,2,3: 27:[26, 1] Operation: 22-21=1 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 27:[26, 1], Operations: ['45-24=21', '22-21=1'] Exploring Operation: 26*1=26, Resulting Numbers: [26] 26,27 unequal: No Solution Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,27 unequal: No Solution Exploring Operation: 26+1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[26, 22, 24, 45], Operations: [] Exploring Operation: 45-24=21, Resulting Numbers: [26, 22, 21] Generated Node #0,2: 27:[26, 22, 21] Operation: 45-24=21 Moving to Node #0,2 Current State: 27:[26, 22, 21], Operations: ['45-24=21'] Exploring Operation: 22-21=1, Resulting Numbers: [26, 1] Generated Node #0,2,3: 27:[26, 1] Operation: 22-21=1 Moving to Node #0,2,3 Current State: 27:[26, 1], Operations: ['45-24=21', '22-21=1'] Exploring Operation: 26+1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 87, 73, 5, 84 ]
88
[ "87-84=3", "5*3=15", "73+15=88" ]
Current State: 88:[87, 73, 5, 84], Operations: [] Exploring Operation: 87-84=3, Resulting Numbers: [73, 5, 3] Generated Node #2: [73, 5, 3] from Operation: 87-84=3 Current State: 88:[73, 5, 3], Operations: ['87-84=3'] Exploring Operation: 5*3=15, Resulting Numbers: [73, 15] Generated Node #3: [73, 15] from Operation: 5*3=15 Current State: 88:[73, 15], Operations: ['87-84=3', '5*3=15'] Exploring Operation: 73+15=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[87, 73, 5, 84], Operations: [] Exploring Operation: 84-73=11, Resulting Numbers: [87, 5, 11] Generated Node #0,0: 88:[87, 5, 11] Operation: 84-73=11 Exploring Operation: 73+5=78, Resulting Numbers: [87, 84, 78] Generated Node #0,1: 88:[87, 84, 78] Operation: 73+5=78 Exploring Operation: 87-73=14, Resulting Numbers: [5, 84, 14] Generated Node #0,2: 88:[5, 84, 14] Operation: 87-73=14 Exploring Operation: 5+84=89, Resulting Numbers: [87, 73, 89] Generated Node #0,3: 88:[87, 73, 89] Operation: 5+84=89 Exploring Operation: 87-84=3, Resulting Numbers: [73, 5, 3] Generated Node #0,4: 88:[73, 5, 3] Operation: 87-84=3 Moving to Node #0,0 Current State: 88:[87, 5, 11], Operations: ['84-73=11'] Exploring Operation: 87-5=82, Resulting Numbers: [11, 82] Generated Node #0,0,0: 88:[11, 82] Operation: 87-5=82 Exploring Operation: 87+11=98, Resulting Numbers: [5, 98] Generated Node #0,0,1: 88:[5, 98] Operation: 87+11=98 Exploring Operation: 11-5=6, Resulting Numbers: [87, 6] Generated Node #0,0,2: 88:[87, 6] Operation: 11-5=6 Exploring Operation: 5+11=16, Resulting Numbers: [87, 16] Generated Node #0,0,3: 88:[87, 16] Operation: 5+11=16 Exploring Operation: 87+5=92, Resulting Numbers: [11, 92] Generated Node #0,0,4: 88:[11, 92] Operation: 87+5=92 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 88:[87, 6], Operations: ['84-73=11', '11-5=6'] Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,88 unequal: No Solution Exploring Operation: 87*6=522, Resulting Numbers: [522] 522,88 unequal: No Solution Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 88:[11, 92], Operations: ['84-73=11', '87+5=92'] Exploring Operation: 11+92=103, Resulting Numbers: [103] 103,88 unequal: No Solution Exploring Operation: 11*92=1012, Resulting Numbers: [1012] 1012,88 unequal: No Solution Exploring Operation: 92-11=81, Resulting Numbers: [81] 81,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[11, 82], Operations: ['84-73=11', '87-5=82'] Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 11*82=902, Resulting Numbers: [902] 902,88 unequal: No Solution Exploring Operation: 11+82=93, Resulting Numbers: [93] 93,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 88:[87, 16], Operations: ['84-73=11', '5+11=16'] Exploring Operation: 87-16=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 87+16=103, Resulting Numbers: [103] 103,88 unequal: No Solution Exploring Operation: 87*16=1392, Resulting Numbers: [1392] 1392,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 88:[5, 98], Operations: ['84-73=11', '87+11=98'] Exploring Operation: 5*98=490, Resulting Numbers: [490] 490,88 unequal: No Solution Exploring Operation: 5+98=103, Resulting Numbers: [103] 103,88 unequal: No Solution Exploring Operation: 98-5=93, Resulting Numbers: [93] 93,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 88:[5, 84, 14], Operations: ['87-73=14'] Exploring Operation: 5+84=89, Resulting Numbers: [14, 89] Generated Node #0,2,0: 88:[14, 89] Operation: 5+84=89 Exploring Operation: 5+14=19, Resulting Numbers: [84, 19] Generated Node #0,2,1: 88:[84, 19] Operation: 5+14=19 Exploring Operation: 84+14=98, Resulting Numbers: [5, 98] Generated Node #0,2,2: 88:[5, 98] Operation: 84+14=98 Exploring Operation: 84/14=6, Resulting Numbers: [5, 6] Generated Node #0,2,3: 88:[5, 6] Operation: 84/14=6 Exploring Operation: 14-5=9, Resulting Numbers: [84, 9] Generated Node #0,2,4: 88:[84, 9] Operation: 14-5=9 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 88:[5, 6], Operations: ['87-73=14', '84/14=6'] Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,88 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,88 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 88:[14, 89], Operations: ['87-73=14', '5+84=89'] Exploring Operation: 14+89=103, Resulting Numbers: [103] 103,88 unequal: No Solution Exploring Operation: 14*89=1246, Resulting Numbers: [1246] 1246,88 unequal: No Solution Exploring Operation: 89-14=75, Resulting Numbers: [75] 75,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 88:[84, 9], Operations: ['87-73=14', '14-5=9'] Exploring Operation: 84-9=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 84+9=93, Resulting Numbers: [93] 93,88 unequal: No Solution Exploring Operation: 84*9=756, Resulting Numbers: [756] 756,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 88:[84, 19], Operations: ['87-73=14', '5+14=19'] Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 84+19=103, Resulting Numbers: [103] 103,88 unequal: No Solution Exploring Operation: 84*19=1596, Resulting Numbers: [1596] 1596,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 88:[5, 98], Operations: ['87-73=14', '84+14=98'] Exploring Operation: 98-5=93, Resulting Numbers: [93] 93,88 unequal: No Solution Exploring Operation: 5*98=490, Resulting Numbers: [490] 490,88 unequal: No Solution Exploring Operation: 5+98=103, Resulting Numbers: [103] 103,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 88:[87, 84, 78], Operations: ['73+5=78'] Exploring Operation: 84-78=6, Resulting Numbers: [87, 6] Generated Node #0,1,0: 88:[87, 6] Operation: 84-78=6 Exploring Operation: 87+78=165, Resulting Numbers: [84, 165] Generated Node #0,1,1: 88:[84, 165] Operation: 87+78=165 Exploring Operation: 87-78=9, Resulting Numbers: [84, 9] Generated Node #0,1,2: 88:[84, 9] Operation: 87-78=9 Exploring Operation: 87-84=3, Resulting Numbers: [78, 3] Generated Node #0,1,3: 88:[78, 3] Operation: 87-84=3 Exploring Operation: 84+78=162, Resulting Numbers: [87, 162] Generated Node #0,1,4: 88:[87, 162] Operation: 84+78=162 Moving to Node #0,3 Current State: 88:[87, 73, 89], Operations: ['5+84=89'] Exploring Operation: 73+89=162, Resulting Numbers: [87, 162] Generated Node #0,3,0: 88:[87, 162] Operation: 73+89=162 Exploring Operation: 87+73=160, Resulting Numbers: [89, 160] Generated Node #0,3,1: 88:[89, 160] Operation: 87+73=160 Exploring Operation: 89-87=2, Resulting Numbers: [73, 2] Generated Node #0,3,2: 88:[73, 2] Operation: 89-87=2 Exploring Operation: 87-73=14, Resulting Numbers: [89, 14] Generated Node #0,3,3: 88:[89, 14] Operation: 87-73=14 Exploring Operation: 89-73=16, Resulting Numbers: [87, 16] Generated Node #0,3,4: 88:[87, 16] Operation: 89-73=16 Moving to Node #0,4 Current State: 88:[73, 5, 3], Operations: ['87-84=3'] Exploring Operation: 5-3=2, Resulting Numbers: [73, 2] Generated Node #0,4,0: 88:[73, 2] Operation: 5-3=2 Exploring Operation: 73-3=70, Resulting Numbers: [5, 70] Generated Node #0,4,1: 88:[5, 70] Operation: 73-3=70 Exploring Operation: 73+5=78, Resulting Numbers: [3, 78] Generated Node #0,4,2: 88:[3, 78] Operation: 73+5=78 Exploring Operation: 5+3=8, Resulting Numbers: [73, 8] Generated Node #0,4,3: 88:[73, 8] Operation: 5+3=8 Exploring Operation: 73+3=76, Resulting Numbers: [5, 76] Generated Node #0,4,4: 88:[5, 76] Operation: 73+3=76 Moving to Node #0,1,0 Current State: 88:[87, 6], Operations: ['73+5=78', '84-78=6'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,88 unequal: No Solution Exploring Operation: 87*6=522, Resulting Numbers: [522] 522,88 unequal: No Solution Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,88 unequal: No Solution Moving to Node #0,3,3 Current State: 88:[89, 14], Operations: ['5+84=89', '87-73=14'] Exploring Operation: 89*14=1246, Resulting Numbers: [1246] 1246,88 unequal: No Solution Exploring Operation: 89-14=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 89+14=103, Resulting Numbers: [103] 103,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[84, 9], Operations: ['73+5=78', '87-78=9'] Exploring Operation: 84+9=93, Resulting Numbers: [93] 93,88 unequal: No Solution Exploring Operation: 84-9=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 84*9=756, Resulting Numbers: [756] 756,88 unequal: No Solution Moving to Node #0,3,4 Current State: 88:[87, 16], Operations: ['5+84=89', '89-73=16'] Exploring Operation: 87*16=1392, Resulting Numbers: [1392] 1392,88 unequal: No Solution Exploring Operation: 87-16=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 87+16=103, Resulting Numbers: [103] 103,88 unequal: No Solution Moving to Node #0,1,3 Current State: 88:[78, 3], Operations: ['73+5=78', '87-84=3'] Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,88 unequal: No Solution Exploring Operation: 78*3=234, Resulting Numbers: [234] 234,88 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,88 unequal: No Solution Moving to Node #0,4,2 Current State: 88:[3, 78], Operations: ['87-84=3', '73+5=78'] Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 3*78=234, Resulting Numbers: [234] 234,88 unequal: No Solution Exploring Operation: 3+78=81, Resulting Numbers: [81] 81,88 unequal: No Solution Moving to Node #0,4,4 Current State: 88:[5, 76], Operations: ['87-84=3', '73+3=76'] Exploring Operation: 5*76=380, Resulting Numbers: [380] 380,88 unequal: No Solution Exploring Operation: 76-5=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 5+76=81, Resulting Numbers: [81] 81,88 unequal: No Solution Moving to Node #0,4,3 Current State: 88:[73, 8], Operations: ['87-84=3', '5+3=8'] Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 73*8=584, Resulting Numbers: [584] 584,88 unequal: No Solution Exploring Operation: 73+8=81, Resulting Numbers: [81] 81,88 unequal: No Solution Moving to Node #0,4,0 Current State: 88:[73, 2], Operations: ['87-84=3', '5-3=2'] Exploring Operation: 73*2=146, Resulting Numbers: [146] 146,88 unequal: No Solution Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,88 unequal: No Solution Moving to Node #0,3,2 Current State: 88:[73, 2], Operations: ['5+84=89', '89-87=2'] Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 73*2=146, Resulting Numbers: [146] 146,88 unequal: No Solution Moving to Node #0,4,1 Current State: 88:[5, 70], Operations: ['87-84=3', '73-3=70'] Exploring Operation: 5*70=350, Resulting Numbers: [350] 350,88 unequal: No Solution Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 5+70=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,88 unequal: No Solution Moving to Node #0,3,1 Current State: 88:[89, 160], Operations: ['5+84=89', '87+73=160'] Exploring Operation: 89*160=14240, Resulting Numbers: [14240] 14240,88 unequal: No Solution Exploring Operation: 89+160=249, Resulting Numbers: [249] 249,88 unequal: No Solution Exploring Operation: 160-89=71, Resulting Numbers: [71] 71,88 unequal: No Solution Moving to Node #0,3,0 Current State: 88:[87, 162], Operations: ['5+84=89', '73+89=162'] Exploring Operation: 87*162=14094, Resulting Numbers: [14094] 14094,88 unequal: No Solution Exploring Operation: 162-87=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 87+162=249, Resulting Numbers: [249] 249,88 unequal: No Solution Moving to Node #0,1,4 Current State: 88:[87, 162], Operations: ['73+5=78', '84+78=162'] Exploring Operation: 87+162=249, Resulting Numbers: [249] 249,88 unequal: No Solution Exploring Operation: 162-87=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 87*162=14094, Resulting Numbers: [14094] 14094,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[84, 165], Operations: ['73+5=78', '87+78=165'] Exploring Operation: 84*165=13860, Resulting Numbers: [13860] 13860,88 unequal: No Solution Exploring Operation: 84+165=249, Resulting Numbers: [249] 249,88 unequal: No Solution Exploring Operation: 165-84=81, Resulting Numbers: [81] 81,88 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 87, 56, 63, 71 ]
39
[ "87-56=31", "71-63=8", "31+8=39" ]
Current State: 39:[87, 56, 63, 71], Operations: [] Exploring Operation: 87-56=31, Resulting Numbers: [63, 71, 31] Generated Node #2: [63, 71, 31] from Operation: 87-56=31 Current State: 39:[63, 71, 31], Operations: ['87-56=31'] Exploring Operation: 71-63=8, Resulting Numbers: [31, 8] Generated Node #3: [31, 8] from Operation: 71-63=8 Current State: 39:[31, 8], Operations: ['87-56=31', '71-63=8'] Exploring Operation: 31+8=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[87, 56, 63, 71], Operations: [] Exploring Operation: 87-71=16, Resulting Numbers: [56, 63, 16] Generated Node #0,0: 39:[56, 63, 16] Operation: 87-71=16 Exploring Operation: 87-63=24, Resulting Numbers: [56, 71, 24] Generated Node #0,1: 39:[56, 71, 24] Operation: 87-63=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[56, 63, 16], Operations: ['87-71=16'] Exploring Operation: 63-56=7, Resulting Numbers: [16, 7] Generated Node #0,0,0: 39:[16, 7] Operation: 63-56=7 Exploring Operation: 56-16=40, Resulting Numbers: [63, 40] Generated Node #0,0,1: 39:[63, 40] Operation: 56-16=40 Moving to Node #0,0,0 Current State: 39:[16, 7], Operations: ['87-71=16', '63-56=7'] Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,39 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[63, 40], Operations: ['87-71=16', '56-16=40'] Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,39 unequal: No Solution Exploring Operation: 63+40=103, Resulting Numbers: [103] 103,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[56, 71, 24], Operations: ['87-63=24'] Exploring Operation: 71-24=47, Resulting Numbers: [56, 47] Generated Node #0,1,0: 39:[56, 47] Operation: 71-24=47 Exploring Operation: 71-56=15, Resulting Numbers: [24, 15] Generated Node #0,1,1: 39:[24, 15] Operation: 71-56=15 Moving to Node #0,1,1 Current State: 39:[24, 15], Operations: ['87-63=24', '71-56=15'] Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[87, 56, 63, 71], Operations: [] Exploring Operation: 87-63=24, Resulting Numbers: [56, 71, 24] Generated Node #0,1: 39:[56, 71, 24] Operation: 87-63=24 Moving to Node #0,1 Current State: 39:[56, 71, 24], Operations: ['87-63=24'] Exploring Operation: 71-56=15, Resulting Numbers: [24, 15] Generated Node #0,1,1: 39:[24, 15] Operation: 71-56=15 Moving to Node #0,1,1 Current State: 39:[24, 15], Operations: ['87-63=24', '71-56=15'] Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 70, 92, 82, 57 ]
50
[ "92-82=10", "70/10=7", "57-7=50" ]
Current State: 50:[70, 92, 82, 57], Operations: [] Exploring Operation: 92-82=10, Resulting Numbers: [70, 57, 10] Generated Node #2: [70, 57, 10] from Operation: 92-82=10 Current State: 50:[70, 57, 10], Operations: ['92-82=10'] Exploring Operation: 70/10=7, Resulting Numbers: [57, 7] Generated Node #3: [57, 7] from Operation: 70/10=7 Current State: 50:[57, 7], Operations: ['92-82=10', '70/10=7'] Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[70, 92, 82, 57], Operations: [] Exploring Operation: 82-70=12, Resulting Numbers: [92, 57, 12] Generated Node #0,0: 50:[92, 57, 12] Operation: 82-70=12 Exploring Operation: 92-70=22, Resulting Numbers: [82, 57, 22] Generated Node #0,1: 50:[82, 57, 22] Operation: 92-70=22 Exploring Operation: 92-82=10, Resulting Numbers: [70, 57, 10] Generated Node #0,2: 50:[70, 57, 10] Operation: 92-82=10 Exploring Operation: 82-57=25, Resulting Numbers: [70, 92, 25] Generated Node #0,3: 50:[70, 92, 25] Operation: 82-57=25 Exploring Operation: 92-57=35, Resulting Numbers: [70, 82, 35] Generated Node #0,4: 50:[70, 82, 35] Operation: 92-57=35 Start Sub Search at level 1: Moving to Node #0,2 Current State: 50:[70, 57, 10], Operations: ['92-82=10'] Exploring Operation: 70/10=7, Resulting Numbers: [57, 7] Generated Node #0,2,0: 50:[57, 7] Operation: 70/10=7 Exploring Operation: 70-10=60, Resulting Numbers: [57, 60] Generated Node #0,2,1: 50:[57, 60] Operation: 70-10=60 Exploring Operation: 70-57=13, Resulting Numbers: [10, 13] Generated Node #0,2,2: 50:[10, 13] Operation: 70-57=13 Exploring Operation: 57-10=47, Resulting Numbers: [70, 47] Generated Node #0,2,3: 50:[70, 47] Operation: 57-10=47 Exploring Operation: 70+10=80, Resulting Numbers: [57, 80] Generated Node #0,2,4: 50:[57, 80] Operation: 70+10=80 Moving to Node #0,2,2 Current State: 50:[10, 13], Operations: ['92-82=10', '70-57=13'] Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 10*13=130, Resulting Numbers: [130] 130,50 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,50 unequal: No Solution Moving to Node #0,2,0 Current State: 50:[57, 7], Operations: ['92-82=10', '70/10=7'] Exploring Operation: 57*7=399, Resulting Numbers: [399] 399,50 unequal: No Solution Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[70, 92, 82, 57], Operations: [] Exploring Operation: 92-82=10, Resulting Numbers: [70, 57, 10] Generated Node #0,2: 50:[70, 57, 10] Operation: 92-82=10 Moving to Node #0,2 Current State: 50:[70, 57, 10], Operations: ['92-82=10'] Exploring Operation: 70/10=7, Resulting Numbers: [57, 7] Generated Node #0,2,0: 50:[57, 7] Operation: 70/10=7 Moving to Node #0,2,0 Current State: 50:[57, 7], Operations: ['92-82=10', '70/10=7'] Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 4, 18, 54, 32 ]
44
[ "4+18=22", "54-32=22", "22+22=44" ]
Current State: 44:[4, 18, 54, 32], Operations: [] Exploring Operation: 4+18=22, Resulting Numbers: [54, 32, 22] Generated Node #2: [54, 32, 22] from Operation: 4+18=22 Current State: 44:[54, 32, 22], Operations: ['4+18=22'] Exploring Operation: 54-32=22, Resulting Numbers: [22, 22] Generated Node #3: [22, 22] from Operation: 54-32=22 Current State: 44:[22, 22], Operations: ['4+18=22', '54-32=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[4, 18, 54, 32], Operations: [] Exploring Operation: 54-32=22, Resulting Numbers: [4, 18, 22] Generated Node #0,0: 44:[4, 18, 22] Operation: 54-32=22 Exploring Operation: 54/18=3, Resulting Numbers: [4, 32, 3] Generated Node #0,1: 44:[4, 32, 3] Operation: 54/18=3 Moving to Node #0,0 Current State: 44:[4, 18, 22], Operations: ['54-32=22'] Exploring Operation: 4+18=22, Resulting Numbers: [22, 22] Generated Node #0,0,0: 44:[22, 22] Operation: 4+18=22 Exploring Operation: 22-18=4, Resulting Numbers: [4, 4] Generated Node #0,0,1: 44:[4, 4] Operation: 22-18=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[22, 22], Operations: ['54-32=22', '4+18=22'] Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,44 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[4, 18, 54, 32], Operations: [] Exploring Operation: 54-32=22, Resulting Numbers: [4, 18, 22] Generated Node #0,0: 44:[4, 18, 22] Operation: 54-32=22 Moving to Node #0,0 Current State: 44:[4, 18, 22], Operations: ['54-32=22'] Exploring Operation: 4+18=22, Resulting Numbers: [22, 22] Generated Node #0,0,0: 44:[22, 22] Operation: 4+18=22 Moving to Node #0,0,0 Current State: 44:[22, 22], Operations: ['54-32=22', '4+18=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 18, 17, 36, 84 ]
59
[ "36/18=2", "84/2=42", "17+42=59" ]
Current State: 59:[18, 17, 36, 84], Operations: [] Exploring Operation: 36/18=2, Resulting Numbers: [17, 84, 2] Generated Node #2: [17, 84, 2] from Operation: 36/18=2 Current State: 59:[17, 84, 2], Operations: ['36/18=2'] Exploring Operation: 84/2=42, Resulting Numbers: [17, 42] Generated Node #3: [17, 42] from Operation: 84/2=42 Current State: 59:[17, 42], Operations: ['36/18=2', '84/2=42'] Exploring Operation: 17+42=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[18, 17, 36, 84], Operations: [] Exploring Operation: 18+36=54, Resulting Numbers: [17, 84, 54] Generated Node #0,0: 59:[17, 84, 54] Operation: 18+36=54 Exploring Operation: 17+36=53, Resulting Numbers: [18, 84, 53] Generated Node #0,1: 59:[18, 84, 53] Operation: 17+36=53 Exploring Operation: 18+17=35, Resulting Numbers: [36, 84, 35] Generated Node #0,2: 59:[36, 84, 35] Operation: 18+17=35 Exploring Operation: 84-18=66, Resulting Numbers: [17, 36, 66] Generated Node #0,3: 59:[17, 36, 66] Operation: 84-18=66 Moving to Node #0,0 Current State: 59:[17, 84, 54], Operations: ['18+36=54'] Exploring Operation: 54-17=37, Resulting Numbers: [84, 37] Generated Node #0,0,0: 59:[84, 37] Operation: 54-17=37 Exploring Operation: 17+54=71, Resulting Numbers: [84, 71] Generated Node #0,0,1: 59:[84, 71] Operation: 17+54=71 Exploring Operation: 17+84=101, Resulting Numbers: [54, 101] Generated Node #0,0,2: 59:[54, 101] Operation: 17+84=101 Exploring Operation: 84-17=67, Resulting Numbers: [54, 67] Generated Node #0,0,3: 59:[54, 67] Operation: 84-17=67 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 59:[54, 67], Operations: ['18+36=54', '84-17=67'] Exploring Operation: 54*67=3618, Resulting Numbers: [3618] 3618,59 unequal: No Solution Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 54+67=121, Resulting Numbers: [121] 121,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[84, 71], Operations: ['18+36=54', '17+54=71'] Exploring Operation: 84*71=5964, Resulting Numbers: [5964] 5964,59 unequal: No Solution Exploring Operation: 84-71=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 84+71=155, Resulting Numbers: [155] 155,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[84, 37], Operations: ['18+36=54', '54-17=37'] Exploring Operation: 84-37=47, Resulting Numbers: [47] 47,59 unequal: No Solution Exploring Operation: 84+37=121, Resulting Numbers: [121] 121,59 unequal: No Solution Exploring Operation: 84*37=3108, Resulting Numbers: [3108] 3108,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 59:[54, 101], Operations: ['18+36=54', '17+84=101'] Exploring Operation: 54*101=5454, Resulting Numbers: [5454] 5454,59 unequal: No Solution Exploring Operation: 101-54=47, Resulting Numbers: [47] 47,59 unequal: No Solution Exploring Operation: 54+101=155, Resulting Numbers: [155] 155,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 59:[36, 84, 35], Operations: ['18+17=35'] Exploring Operation: 84-36=48, Resulting Numbers: [35, 48] Generated Node #0,2,0: 59:[35, 48] Operation: 84-36=48 Exploring Operation: 84-35=49, Resulting Numbers: [36, 49] Generated Node #0,2,1: 59:[36, 49] Operation: 84-35=49 Exploring Operation: 36+35=71, Resulting Numbers: [84, 71] Generated Node #0,2,2: 59:[84, 71] Operation: 36+35=71 Exploring Operation: 36-35=1, Resulting Numbers: [84, 1] Generated Node #0,2,3: 59:[84, 1] Operation: 36-35=1 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[36, 49], Operations: ['18+17=35', '84-35=49'] Exploring Operation: 36*49=1764, Resulting Numbers: [1764] 1764,59 unequal: No Solution Exploring Operation: 36+49=85, Resulting Numbers: [85] 85,59 unequal: No Solution Exploring Operation: 49-36=13, Resulting Numbers: [13] 13,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[35, 48], Operations: ['18+17=35', '84-36=48'] Exploring Operation: 35*48=1680, Resulting Numbers: [1680] 1680,59 unequal: No Solution Exploring Operation: 48-35=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 35+48=83, Resulting Numbers: [83] 83,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[84, 71], Operations: ['18+17=35', '36+35=71'] Exploring Operation: 84-71=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 84+71=155, Resulting Numbers: [155] 155,59 unequal: No Solution Exploring Operation: 84*71=5964, Resulting Numbers: [5964] 5964,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 59:[84, 1], Operations: ['18+17=35', '36-35=1'] Exploring Operation: 84-1=83, Resulting Numbers: [83] 83,59 unequal: No Solution Exploring Operation: 84+1=85, Resulting Numbers: [85] 85,59 unequal: No Solution Exploring Operation: 84*1=84, Resulting Numbers: [84] 84,59 unequal: No Solution Exploring Operation: 84/1=84, Resulting Numbers: [84] 84,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 59:[18, 84, 53], Operations: ['17+36=53'] Exploring Operation: 18+53=71, Resulting Numbers: [84, 71] Generated Node #0,1,0: 59:[84, 71] Operation: 18+53=71 Exploring Operation: 84-18=66, Resulting Numbers: [53, 66] Generated Node #0,1,1: 59:[53, 66] Operation: 84-18=66 Exploring Operation: 18+84=102, Resulting Numbers: [53, 102] Generated Node #0,1,2: 59:[53, 102] Operation: 18+84=102 Exploring Operation: 53-18=35, Resulting Numbers: [84, 35] Generated Node #0,1,3: 59:[84, 35] Operation: 53-18=35 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[53, 66], Operations: ['17+36=53', '84-18=66'] Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 53*66=3498, Resulting Numbers: [3498] 3498,59 unequal: No Solution Exploring Operation: 53+66=119, Resulting Numbers: [119] 119,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[84, 71], Operations: ['17+36=53', '18+53=71'] Exploring Operation: 84-71=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 84+71=155, Resulting Numbers: [155] 155,59 unequal: No Solution Exploring Operation: 84*71=5964, Resulting Numbers: [5964] 5964,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[53, 102], Operations: ['17+36=53', '18+84=102'] Exploring Operation: 102-53=49, Resulting Numbers: [49] 49,59 unequal: No Solution Exploring Operation: 53+102=155, Resulting Numbers: [155] 155,59 unequal: No Solution Exploring Operation: 53*102=5406, Resulting Numbers: [5406] 5406,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 59:[84, 35], Operations: ['17+36=53', '53-18=35'] Exploring Operation: 84+35=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 84*35=2940, Resulting Numbers: [2940] 2940,59 unequal: No Solution Exploring Operation: 84-35=49, Resulting Numbers: [49] 49,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 59:[17, 36, 66], Operations: ['84-18=66'] Exploring Operation: 17+36=53, Resulting Numbers: [66, 53] Generated Node #0,3,0: 59:[66, 53] Operation: 17+36=53 Exploring Operation: 17+66=83, Resulting Numbers: [36, 83] Generated Node #0,3,1: 59:[36, 83] Operation: 17+66=83 Exploring Operation: 36-17=19, Resulting Numbers: [66, 19] Generated Node #0,3,2: 59:[66, 19] Operation: 36-17=19 Exploring Operation: 66-17=49, Resulting Numbers: [36, 49] Generated Node #0,3,3: 59:[36, 49] Operation: 66-17=49 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 59:[66, 53], Operations: ['84-18=66', '17+36=53'] Exploring Operation: 66*53=3498, Resulting Numbers: [3498] 3498,59 unequal: No Solution Exploring Operation: 66+53=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 59:[36, 49], Operations: ['84-18=66', '66-17=49'] Exploring Operation: 49-36=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 36+49=85, Resulting Numbers: [85] 85,59 unequal: No Solution Exploring Operation: 36*49=1764, Resulting Numbers: [1764] 1764,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 59:[36, 83], Operations: ['84-18=66', '17+66=83'] Exploring Operation: 36*83=2988, Resulting Numbers: [2988] 2988,59 unequal: No Solution Exploring Operation: 36+83=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 83-36=47, Resulting Numbers: [47] 47,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 59:[66, 19], Operations: ['84-18=66', '36-17=19'] Exploring Operation: 66+19=85, Resulting Numbers: [85] 85,59 unequal: No Solution Exploring Operation: 66-19=47, Resulting Numbers: [47] 47,59 unequal: No Solution Exploring Operation: 66*19=1254, Resulting Numbers: [1254] 1254,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 39, 26, 63, 16 ]
66
[ "39-26=13", "63+16=79", "79-13=66" ]
Current State: 66:[39, 26, 63, 16], Operations: [] Exploring Operation: 39-26=13, Resulting Numbers: [63, 16, 13] Generated Node #2: [63, 16, 13] from Operation: 39-26=13 Current State: 66:[63, 16, 13], Operations: ['39-26=13'] Exploring Operation: 63+16=79, Resulting Numbers: [13, 79] Generated Node #3: [13, 79] from Operation: 63+16=79 Current State: 66:[13, 79], Operations: ['39-26=13', '63+16=79'] Exploring Operation: 79-13=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[39, 26, 63, 16], Operations: [] Exploring Operation: 39-26=13, Resulting Numbers: [63, 16, 13] Generated Node #0,0: 66:[63, 16, 13] Operation: 39-26=13 Exploring Operation: 39+26=65, Resulting Numbers: [63, 16, 65] Generated Node #0,1: 66:[63, 16, 65] Operation: 39+26=65 Exploring Operation: 39-16=23, Resulting Numbers: [26, 63, 23] Generated Node #0,2: 66:[26, 63, 23] Operation: 39-16=23 Start Sub Search at level 1: Moving to Node #0,2 Current State: 66:[26, 63, 23], Operations: ['39-16=23'] Exploring Operation: 63-26=37, Resulting Numbers: [23, 37] Generated Node #0,2,0: 66:[23, 37] Operation: 63-26=37 Exploring Operation: 26-23=3, Resulting Numbers: [63, 3] Generated Node #0,2,1: 66:[63, 3] Operation: 26-23=3 Exploring Operation: 63-23=40, Resulting Numbers: [26, 40] Generated Node #0,2,2: 66:[26, 40] Operation: 63-23=40 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 66:[63, 3], Operations: ['39-16=23', '26-23=3'] Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[39, 26, 63, 16], Operations: [] Exploring Operation: 39-16=23, Resulting Numbers: [26, 63, 23] Generated Node #0,2: 66:[26, 63, 23] Operation: 39-16=23 Moving to Node #0,2 Current State: 66:[26, 63, 23], Operations: ['39-16=23'] Exploring Operation: 26-23=3, Resulting Numbers: [63, 3] Generated Node #0,2,1: 66:[63, 3] Operation: 26-23=3 Moving to Node #0,2,1 Current State: 66:[63, 3], Operations: ['39-16=23', '26-23=3'] Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 99, 6, 53, 8 ]
23
[ "99-53=46", "8-6=2", "46/2=23" ]
Current State: 23:[99, 6, 53, 8], Operations: [] Exploring Operation: 99-53=46, Resulting Numbers: [6, 8, 46] Generated Node #2: [6, 8, 46] from Operation: 99-53=46 Current State: 23:[6, 8, 46], Operations: ['99-53=46'] Exploring Operation: 8-6=2, Resulting Numbers: [46, 2] Generated Node #3: [46, 2] from Operation: 8-6=2 Current State: 23:[46, 2], Operations: ['99-53=46', '8-6=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[99, 6, 53, 8], Operations: [] Exploring Operation: 99-53=46, Resulting Numbers: [6, 8, 46] Generated Node #0,0: 23:[6, 8, 46] Operation: 99-53=46 Exploring Operation: 99-6=93, Resulting Numbers: [53, 8, 93] Generated Node #0,1: 23:[53, 8, 93] Operation: 99-6=93 Exploring Operation: 6+8=14, Resulting Numbers: [99, 53, 14] Generated Node #0,2: 23:[99, 53, 14] Operation: 6+8=14 Exploring Operation: 53-6=47, Resulting Numbers: [99, 8, 47] Generated Node #0,3: 23:[99, 8, 47] Operation: 53-6=47 Exploring Operation: 99-8=91, Resulting Numbers: [6, 53, 91] Generated Node #0,4: 23:[6, 53, 91] Operation: 99-8=91 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[6, 8, 46], Operations: ['99-53=46'] Exploring Operation: 46-8=38, Resulting Numbers: [6, 38] Generated Node #0,0,0: 23:[6, 38] Operation: 46-8=38 Exploring Operation: 46-6=40, Resulting Numbers: [8, 40] Generated Node #0,0,1: 23:[8, 40] Operation: 46-6=40 Exploring Operation: 6+46=52, Resulting Numbers: [8, 52] Generated Node #0,0,2: 23:[8, 52] Operation: 6+46=52 Exploring Operation: 8-6=2, Resulting Numbers: [46, 2] Generated Node #0,0,3: 23:[46, 2] Operation: 8-6=2 Exploring Operation: 6+8=14, Resulting Numbers: [46, 14] Generated Node #0,0,4: 23:[46, 14] Operation: 6+8=14 Moving to Node #0,0,0 Current State: 23:[6, 38], Operations: ['99-53=46', '46-8=38'] Exploring Operation: 6*38=228, Resulting Numbers: [228] 228,23 unequal: No Solution Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,23 unequal: No Solution Moving to Node #0,0,4 Current State: 23:[46, 14], Operations: ['99-53=46', '6+8=14'] Exploring Operation: 46+14=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,23 unequal: No Solution Exploring Operation: 46*14=644, Resulting Numbers: [644] 644,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[8, 40], Operations: ['99-53=46', '46-6=40'] Exploring Operation: 8*40=320, Resulting Numbers: [320] 320,23 unequal: No Solution Exploring Operation: 8+40=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,23 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[8, 52], Operations: ['99-53=46', '6+46=52'] Exploring Operation: 8+52=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 8*52=416, Resulting Numbers: [416] 416,23 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[46, 2], Operations: ['99-53=46', '8-6=2'] Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,23 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[99, 6, 53, 8], Operations: [] Exploring Operation: 99-53=46, Resulting Numbers: [6, 8, 46] Generated Node #0,0: 23:[6, 8, 46] Operation: 99-53=46 Moving to Node #0,0 Current State: 23:[6, 8, 46], Operations: ['99-53=46'] Exploring Operation: 8-6=2, Resulting Numbers: [46, 2] Generated Node #0,0,3: 23:[46, 2] Operation: 8-6=2 Moving to Node #0,0,3 Current State: 23:[46, 2], Operations: ['99-53=46', '8-6=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_5
mult_heuristic
[ 2, 20, 27, 35 ]
11
[ "27+35=62", "62/2=31", "31-20=11" ]
Current State: 11:[2, 20, 27, 35], Operations: [] Exploring Operation: 27+35=62, Resulting Numbers: [2, 20, 62] Generated Node #2: [2, 20, 62] from Operation: 27+35=62 Current State: 11:[2, 20, 62], Operations: ['27+35=62'] Exploring Operation: 62/2=31, Resulting Numbers: [20, 31] Generated Node #3: [20, 31] from Operation: 62/2=31 Current State: 11:[20, 31], Operations: ['27+35=62', '62/2=31'] Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[2, 20, 27, 35], Operations: [] Exploring Operation: 35-27=8, Resulting Numbers: [2, 20, 8] Generated Node #0,0: 11:[2, 20, 8] Operation: 35-27=8 Exploring Operation: 27-20=7, Resulting Numbers: [2, 35, 7] Generated Node #0,1: 11:[2, 35, 7] Operation: 27-20=7 Exploring Operation: 35-20=15, Resulting Numbers: [2, 27, 15] Generated Node #0,2: 11:[2, 27, 15] Operation: 35-20=15 Moving to Node #0,0 Current State: 11:[2, 20, 8], Operations: ['35-27=8'] Exploring Operation: 20/2=10, Resulting Numbers: [8, 10] Generated Node #0,0,0: 11:[8, 10] Operation: 20/2=10 Exploring Operation: 2+8=10, Resulting Numbers: [20, 10] Generated Node #0,0,1: 11:[20, 10] Operation: 2+8=10 Exploring Operation: 20-2=18, Resulting Numbers: [8, 18] Generated Node #0,0,2: 11:[8, 18] Operation: 20-2=18 Moving to Node #0,2 Current State: 11:[2, 27, 15], Operations: ['35-20=15'] Exploring Operation: 27-15=12, Resulting Numbers: [2, 12] Generated Node #0,2,0: 11:[2, 12] Operation: 27-15=12 Exploring Operation: 15-2=13, Resulting Numbers: [27, 13] Generated Node #0,2,1: 11:[27, 13] Operation: 15-2=13 Exploring Operation: 27-2=25, Resulting Numbers: [15, 25] Generated Node #0,2,2: 11:[15, 25] Operation: 27-2=25 Moving to Node #0,1 Current State: 11:[2, 35, 7], Operations: ['27-20=7'] Exploring Operation: 35/7=5, Resulting Numbers: [2, 5] Generated Node #0,1,0: 11:[2, 5] Operation: 35/7=5 Exploring Operation: 35-2=33, Resulting Numbers: [7, 33] Generated Node #0,1,1: 11:[7, 33] Operation: 35-2=33 Exploring Operation: 2+7=9, Resulting Numbers: [35, 9] Generated Node #0,1,2: 11:[35, 9] Operation: 2+7=9 Moving to Node #0,0,0 Current State: 11:[8, 10], Operations: ['35-27=8', '20/2=10'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,11 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[8, 18], Operations: ['35-27=8', '20-2=18'] Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,11 unequal: No Solution Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[20, 10], Operations: ['35-27=8', '2+8=10'] Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,11 unequal: No Solution Moving to Node #0,2,0 Current State: 11:[2, 12], Operations: ['35-20=15', '27-15=12'] Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,11 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[2, 5], Operations: ['27-20=7', '35/7=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,11 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,11 unequal: No Solution Moving to Node #0,2,2 Current State: 11:[15, 25], Operations: ['35-20=15', '27-2=25'] Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,11 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,11 unequal: No Solution Exploring Operation: 15*25=375, Resulting Numbers: [375] 375,11 unequal: No Solution Moving to Node #0,2,1 Current State: 11:[27, 13], Operations: ['35-20=15', '15-2=13'] Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 27+13=40, Resulting Numbers: [40] 40,11 unequal: No Solution Exploring Operation: 27*13=351, Resulting Numbers: [351] 351,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[7, 33], Operations: ['27-20=7', '35-2=33'] Exploring Operation: 7+33=40, Resulting Numbers: [40] 40,11 unequal: No Solution Exploring Operation: 7*33=231, Resulting Numbers: [231] 231,11 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[35, 9], Operations: ['27-20=7', '2+7=9'] Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,11 unequal: No Solution Exploring Operation: 35*9=315, Resulting Numbers: [315] 315,11 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 24, 4, 95, 6 ]
53
[ "24*6=144", "95-4=91", "144-91=53" ]
Current State: 53:[24, 4, 95, 6], Operations: [] Exploring Operation: 24*6=144, Resulting Numbers: [4, 95, 144] Generated Node #2: [4, 95, 144] from Operation: 24*6=144 Current State: 53:[4, 95, 144], Operations: ['24*6=144'] Exploring Operation: 95-4=91, Resulting Numbers: [144, 91] Generated Node #3: [144, 91] from Operation: 95-4=91 Current State: 53:[144, 91], Operations: ['24*6=144', '95-4=91'] Exploring Operation: 144-91=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[24, 4, 95, 6], Operations: [] Exploring Operation: 24+4=28, Resulting Numbers: [95, 6, 28] Generated Node #0,0: 53:[95, 6, 28] Operation: 24+4=28 Exploring Operation: 95-24=71, Resulting Numbers: [4, 6, 71] Generated Node #0,1: 53:[4, 6, 71] Operation: 95-24=71 Exploring Operation: 95-4=91, Resulting Numbers: [24, 6, 91] Generated Node #0,2: 53:[24, 6, 91] Operation: 95-4=91 Exploring Operation: 24+6=30, Resulting Numbers: [4, 95, 30] Generated Node #0,3: 53:[4, 95, 30] Operation: 24+6=30 Exploring Operation: 4*6=24, Resulting Numbers: [24, 95, 24] Generated Node #0,4: 53:[24, 95, 24] Operation: 4*6=24 Start Sub Search at level 1: Moving to Node #0,4 Current State: 53:[24, 95, 24], Operations: ['4*6=24'] Exploring Operation: 95-24=71, Resulting Numbers: [24, 71] Generated Node #0,4,0: 53:[24, 71] Operation: 95-24=71 Exploring Operation: 24/24=1, Resulting Numbers: [95, 1] Generated Node #0,4,1: 53:[95, 1] Operation: 24/24=1 Exploring Operation: 95-24=71, Resulting Numbers: [24, 71] Generated Node #0,4,2: 53:[24, 71] Operation: 95-24=71 Exploring Operation: 24+24=48, Resulting Numbers: [95, 48] Generated Node #0,4,3: 53:[95, 48] Operation: 24+24=48 Exploring Operation: 24+95=119, Resulting Numbers: [24, 119] Generated Node #0,4,4: 53:[24, 119] Operation: 24+95=119 Moving to Node #0,4,0 Current State: 53:[24, 71], Operations: ['4*6=24', '95-24=71'] Exploring Operation: 24+71=95, Resulting Numbers: [95] 95,53 unequal: No Solution Exploring Operation: 71-24=47, Resulting Numbers: [47] 47,53 unequal: No Solution Exploring Operation: 24*71=1704, Resulting Numbers: [1704] 1704,53 unequal: No Solution Moving to Node #0,4,3 Current State: 53:[95, 48], Operations: ['4*6=24', '24+24=48'] Exploring Operation: 95-48=47, Resulting Numbers: [47] 47,53 unequal: No Solution Exploring Operation: 95*48=4560, Resulting Numbers: [4560] 4560,53 unequal: No Solution Exploring Operation: 95+48=143, Resulting Numbers: [143] 143,53 unequal: No Solution Moving to Node #0,4,2 Current State: 53:[24, 71], Operations: ['4*6=24', '95-24=71'] Exploring Operation: 24*71=1704, Resulting Numbers: [1704] 1704,53 unequal: No Solution Exploring Operation: 24+71=95, Resulting Numbers: [95] 95,53 unequal: No Solution Exploring Operation: 71-24=47, Resulting Numbers: [47] 47,53 unequal: No Solution Moving to Node #0,4,1 Current State: 53:[95, 1], Operations: ['4*6=24', '24/24=1'] Exploring Operation: 95-1=94, Resulting Numbers: [94] 94,53 unequal: No Solution Exploring Operation: 95*1=95, Resulting Numbers: [95] 95,53 unequal: No Solution Exploring Operation: 95/1=95, Resulting Numbers: [95] 95,53 unequal: No Solution Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,53 unequal: No Solution Moving to Node #0,4,4 Current State: 53:[24, 119], Operations: ['4*6=24', '24+95=119'] Exploring Operation: 24*119=2856, Resulting Numbers: [2856] 2856,53 unequal: No Solution Exploring Operation: 119-24=95, Resulting Numbers: [95] 95,53 unequal: No Solution Exploring Operation: 24+119=143, Resulting Numbers: [143] 143,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[95, 6, 28], Operations: ['24+4=28'] Exploring Operation: 95+6=101, Resulting Numbers: [28, 101] Generated Node #0,0,0: 53:[28, 101] Operation: 95+6=101 Exploring Operation: 28-6=22, Resulting Numbers: [95, 22] Generated Node #0,0,1: 53:[95, 22] Operation: 28-6=22 Exploring Operation: 6+28=34, Resulting Numbers: [95, 34] Generated Node #0,0,2: 53:[95, 34] Operation: 6+28=34 Exploring Operation: 95-6=89, Resulting Numbers: [28, 89] Generated Node #0,0,3: 53:[28, 89] Operation: 95-6=89 Exploring Operation: 95-28=67, Resulting Numbers: [6, 67] Generated Node #0,0,4: 53:[6, 67] Operation: 95-28=67 Moving to Node #0,0,2 Current State: 53:[95, 34], Operations: ['24+4=28', '6+28=34'] Exploring Operation: 95-34=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 95+34=129, Resulting Numbers: [129] 129,53 unequal: No Solution Exploring Operation: 95*34=3230, Resulting Numbers: [3230] 3230,53 unequal: No Solution Moving to Node #0,0,4 Current State: 53:[6, 67], Operations: ['24+4=28', '95-28=67'] Exploring Operation: 6+67=73, Resulting Numbers: [73] 73,53 unequal: No Solution Exploring Operation: 6*67=402, Resulting Numbers: [402] 402,53 unequal: No Solution Exploring Operation: 67-6=61, Resulting Numbers: [61] 61,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[28, 89], Operations: ['24+4=28', '95-6=89'] Exploring Operation: 28*89=2492, Resulting Numbers: [2492] 2492,53 unequal: No Solution Exploring Operation: 89-28=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 28+89=117, Resulting Numbers: [117] 117,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[28, 101], Operations: ['24+4=28', '95+6=101'] Exploring Operation: 28*101=2828, Resulting Numbers: [2828] 2828,53 unequal: No Solution Exploring Operation: 101-28=73, Resulting Numbers: [73] 73,53 unequal: No Solution Exploring Operation: 28+101=129, Resulting Numbers: [129] 129,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[95, 22], Operations: ['24+4=28', '28-6=22'] Exploring Operation: 95*22=2090, Resulting Numbers: [2090] 2090,53 unequal: No Solution Exploring Operation: 95-22=73, Resulting Numbers: [73] 73,53 unequal: No Solution Exploring Operation: 95+22=117, Resulting Numbers: [117] 117,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[4, 6, 71], Operations: ['95-24=71'] Exploring Operation: 4+6=10, Resulting Numbers: [71, 10] Generated Node #0,1,0: 53:[71, 10] Operation: 4+6=10 Exploring Operation: 6-4=2, Resulting Numbers: [71, 2] Generated Node #0,1,1: 53:[71, 2] Operation: 6-4=2 Exploring Operation: 71-6=65, Resulting Numbers: [4, 65] Generated Node #0,1,2: 53:[4, 65] Operation: 71-6=65 Exploring Operation: 71-4=67, Resulting Numbers: [6, 67] Generated Node #0,1,3: 53:[6, 67] Operation: 71-4=67 Exploring Operation: 4*6=24, Resulting Numbers: [71, 24] Generated Node #0,1,4: 53:[71, 24] Operation: 4*6=24 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 53:[71, 24], Operations: ['95-24=71', '4*6=24'] Exploring Operation: 71-24=47, Resulting Numbers: [47] 47,53 unequal: No Solution Exploring Operation: 71+24=95, Resulting Numbers: [95] 95,53 unequal: No Solution Exploring Operation: 71*24=1704, Resulting Numbers: [1704] 1704,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[71, 10], Operations: ['95-24=71', '4+6=10'] Exploring Operation: 71+10=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 71-10=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 71*10=710, Resulting Numbers: [710] 710,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 53:[4, 65], Operations: ['95-24=71', '71-6=65'] Exploring Operation: 65-4=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 4*65=260, Resulting Numbers: [260] 260,53 unequal: No Solution Exploring Operation: 4+65=69, Resulting Numbers: [69] 69,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 53:[6, 67], Operations: ['95-24=71', '71-4=67'] Exploring Operation: 67-6=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 6*67=402, Resulting Numbers: [402] 402,53 unequal: No Solution Exploring Operation: 6+67=73, Resulting Numbers: [73] 73,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[71, 2], Operations: ['95-24=71', '6-4=2'] Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,53 unequal: No Solution Exploring Operation: 71*2=142, Resulting Numbers: [142] 142,53 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 53:[24, 6, 91], Operations: ['95-4=91'] Exploring Operation: 91-24=67, Resulting Numbers: [6, 67] Generated Node #0,2,0: 53:[6, 67] Operation: 91-24=67 Exploring Operation: 24-6=18, Resulting Numbers: [91, 18] Generated Node #0,2,1: 53:[91, 18] Operation: 24-6=18 Exploring Operation: 91-6=85, Resulting Numbers: [24, 85] Generated Node #0,2,2: 53:[24, 85] Operation: 91-6=85 Exploring Operation: 6+91=97, Resulting Numbers: [24, 97] Generated Node #0,2,3: 53:[24, 97] Operation: 6+91=97 Exploring Operation: 24+6=30, Resulting Numbers: [91, 30] Generated Node #0,2,4: 53:[91, 30] Operation: 24+6=30 Moving to Node #0,2,0 Current State: 53:[6, 67], Operations: ['95-4=91', '91-24=67'] Exploring Operation: 6*67=402, Resulting Numbers: [402] 402,53 unequal: No Solution Exploring Operation: 67-6=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 6+67=73, Resulting Numbers: [73] 73,53 unequal: No Solution Moving to Node #0,2,4 Current State: 53:[91, 30], Operations: ['95-4=91', '24+6=30'] Exploring Operation: 91+30=121, Resulting Numbers: [121] 121,53 unequal: No Solution Exploring Operation: 91*30=2730, Resulting Numbers: [2730] 2730,53 unequal: No Solution Exploring Operation: 91-30=61, Resulting Numbers: [61] 61,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[24, 85], Operations: ['95-4=91', '91-6=85'] Exploring Operation: 24*85=2040, Resulting Numbers: [2040] 2040,53 unequal: No Solution Exploring Operation: 85-24=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 24+85=109, Resulting Numbers: [109] 109,53 unequal: No Solution Moving to Node #0,2,1 Current State: 53:[91, 18], Operations: ['95-4=91', '24-6=18'] Exploring Operation: 91+18=109, Resulting Numbers: [109] 109,53 unequal: No Solution Exploring Operation: 91*18=1638, Resulting Numbers: [1638] 1638,53 unequal: No Solution Exploring Operation: 91-18=73, Resulting Numbers: [73] 73,53 unequal: No Solution Moving to Node #0,2,3 Current State: 53:[24, 97], Operations: ['95-4=91', '6+91=97'] Exploring Operation: 24+97=121, Resulting Numbers: [121] 121,53 unequal: No Solution Exploring Operation: 97-24=73, Resulting Numbers: [73] 73,53 unequal: No Solution Exploring Operation: 24*97=2328, Resulting Numbers: [2328] 2328,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 53:[4, 95, 30], Operations: ['24+6=30'] Exploring Operation: 4+95=99, Resulting Numbers: [30, 99] Generated Node #0,3,0: 53:[30, 99] Operation: 4+95=99 Exploring Operation: 4+30=34, Resulting Numbers: [95, 34] Generated Node #0,3,1: 53:[95, 34] Operation: 4+30=34 Exploring Operation: 95-30=65, Resulting Numbers: [4, 65] Generated Node #0,3,2: 53:[4, 65] Operation: 95-30=65 Exploring Operation: 30-4=26, Resulting Numbers: [95, 26] Generated Node #0,3,3: 53:[95, 26] Operation: 30-4=26 Exploring Operation: 95-4=91, Resulting Numbers: [30, 91] Generated Node #0,3,4: 53:[30, 91] Operation: 95-4=91 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 53:[95, 34], Operations: ['24+6=30', '4+30=34'] Exploring Operation: 95-34=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 95+34=129, Resulting Numbers: [129] 129,53 unequal: No Solution Exploring Operation: 95*34=3230, Resulting Numbers: [3230] 3230,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 53:[4, 65], Operations: ['24+6=30', '95-30=65'] Exploring Operation: 4*65=260, Resulting Numbers: [260] 260,53 unequal: No Solution Exploring Operation: 65-4=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 4+65=69, Resulting Numbers: [69] 69,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 53:[30, 91], Operations: ['24+6=30', '95-4=91'] Exploring Operation: 30+91=121, Resulting Numbers: [121] 121,53 unequal: No Solution Exploring Operation: 91-30=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 30*91=2730, Resulting Numbers: [2730] 2730,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 53:[30, 99], Operations: ['24+6=30', '4+95=99'] Exploring Operation: 99-30=69, Resulting Numbers: [69] 69,53 unequal: No Solution Exploring Operation: 30+99=129, Resulting Numbers: [129] 129,53 unequal: No Solution Exploring Operation: 30*99=2970, Resulting Numbers: [2970] 2970,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 53:[95, 26], Operations: ['24+6=30', '30-4=26'] Exploring Operation: 95-26=69, Resulting Numbers: [69] 69,53 unequal: No Solution Exploring Operation: 95*26=2470, Resulting Numbers: [2470] 2470,53 unequal: No Solution Exploring Operation: 95+26=121, Resulting Numbers: [121] 121,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 28, 95, 19, 18 ]
30
[ "95-28=67", "19+18=37", "67-37=30" ]
Current State: 30:[28, 95, 19, 18], Operations: [] Exploring Operation: 95-28=67, Resulting Numbers: [19, 18, 67] Generated Node #2: [19, 18, 67] from Operation: 95-28=67 Current State: 30:[19, 18, 67], Operations: ['95-28=67'] Exploring Operation: 19+18=37, Resulting Numbers: [67, 37] Generated Node #3: [67, 37] from Operation: 19+18=37 Current State: 30:[67, 37], Operations: ['95-28=67', '19+18=37'] Exploring Operation: 67-37=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[28, 95, 19, 18], Operations: [] Exploring Operation: 95-19=76, Resulting Numbers: [28, 18, 76] Generated Node #0,0: 30:[28, 18, 76] Operation: 95-19=76 Exploring Operation: 95/19=5, Resulting Numbers: [28, 18, 5] Generated Node #0,1: 30:[28, 18, 5] Operation: 95/19=5 Exploring Operation: 95-28=67, Resulting Numbers: [19, 18, 67] Generated Node #0,2: 30:[19, 18, 67] Operation: 95-28=67 Exploring Operation: 95-18=77, Resulting Numbers: [28, 19, 77] Generated Node #0,3: 30:[28, 19, 77] Operation: 95-18=77 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[28, 18, 5], Operations: ['95/19=5'] Exploring Operation: 18+5=23, Resulting Numbers: [28, 23] Generated Node #0,1,0: 30:[28, 23] Operation: 18+5=23 Exploring Operation: 28+5=33, Resulting Numbers: [18, 33] Generated Node #0,1,1: 30:[18, 33] Operation: 28+5=33 Exploring Operation: 28-18=10, Resulting Numbers: [5, 10] Generated Node #0,1,2: 30:[5, 10] Operation: 28-18=10 Exploring Operation: 18-5=13, Resulting Numbers: [28, 13] Generated Node #0,1,3: 30:[28, 13] Operation: 18-5=13 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 30:[5, 10], Operations: ['95/19=5', '28-18=10'] Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,30 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 30:[28, 13], Operations: ['95/19=5', '18-5=13'] Exploring Operation: 28+13=41, Resulting Numbers: [41] 41,30 unequal: No Solution Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 28*13=364, Resulting Numbers: [364] 364,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[18, 33], Operations: ['95/19=5', '28+5=33'] Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 18*33=594, Resulting Numbers: [594] 594,30 unequal: No Solution Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[28, 23], Operations: ['95/19=5', '18+5=23'] Exploring Operation: 28*23=644, Resulting Numbers: [644] 644,30 unequal: No Solution Exploring Operation: 28+23=51, Resulting Numbers: [51] 51,30 unequal: No Solution Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[19, 18, 67], Operations: ['95-28=67'] Exploring Operation: 19-18=1, Resulting Numbers: [67, 1] Generated Node #0,2,0: 30:[67, 1] Operation: 19-18=1 Exploring Operation: 19+18=37, Resulting Numbers: [67, 37] Generated Node #0,2,1: 30:[67, 37] Operation: 19+18=37 Exploring Operation: 67-19=48, Resulting Numbers: [18, 48] Generated Node #0,2,2: 30:[18, 48] Operation: 67-19=48 Exploring Operation: 67-18=49, Resulting Numbers: [19, 49] Generated Node #0,2,3: 30:[19, 49] Operation: 67-18=49 Moving to Node #0,2,2 Current State: 30:[18, 48], Operations: ['95-28=67', '67-19=48'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[28, 95, 19, 18], Operations: [] Exploring Operation: 95-28=67, Resulting Numbers: [19, 18, 67] Generated Node #0,2: 30:[19, 18, 67] Operation: 95-28=67 Moving to Node #0,2 Current State: 30:[19, 18, 67], Operations: ['95-28=67'] Exploring Operation: 67-19=48, Resulting Numbers: [18, 48] Generated Node #0,2,2: 30:[18, 48] Operation: 67-19=48 Moving to Node #0,2,2 Current State: 30:[18, 48], Operations: ['95-28=67', '67-19=48'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 12, 94, 62, 77 ]
67
[ "94-12=82", "77-62=15", "82-15=67" ]
Current State: 67:[12, 94, 62, 77], Operations: [] Exploring Operation: 94-12=82, Resulting Numbers: [62, 77, 82] Generated Node #2: [62, 77, 82] from Operation: 94-12=82 Current State: 67:[62, 77, 82], Operations: ['94-12=82'] Exploring Operation: 77-62=15, Resulting Numbers: [82, 15] Generated Node #3: [82, 15] from Operation: 77-62=15 Current State: 67:[82, 15], Operations: ['94-12=82', '77-62=15'] Exploring Operation: 82-15=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[12, 94, 62, 77], Operations: [] Exploring Operation: 12+62=74, Resulting Numbers: [94, 77, 74] Generated Node #0,0: 67:[94, 77, 74] Operation: 12+62=74 Exploring Operation: 12+94=106, Resulting Numbers: [62, 77, 106] Generated Node #0,1: 67:[62, 77, 106] Operation: 12+94=106 Exploring Operation: 77-12=65, Resulting Numbers: [94, 62, 65] Generated Node #0,2: 67:[94, 62, 65] Operation: 77-12=65 Exploring Operation: 62-12=50, Resulting Numbers: [94, 77, 50] Generated Node #0,3: 67:[94, 77, 50] Operation: 62-12=50 Exploring Operation: 94-12=82, Resulting Numbers: [62, 77, 82] Generated Node #0,4: 67:[62, 77, 82] Operation: 94-12=82 Moving to Node #0,4 Current State: 67:[62, 77, 82], Operations: ['94-12=82'] Exploring Operation: 82-62=20, Resulting Numbers: [77, 20] Generated Node #0,4,0: 67:[77, 20] Operation: 82-62=20 Exploring Operation: 82-77=5, Resulting Numbers: [62, 5] Generated Node #0,4,1: 67:[62, 5] Operation: 82-77=5 Exploring Operation: 62+82=144, Resulting Numbers: [77, 144] Generated Node #0,4,2: 67:[77, 144] Operation: 62+82=144 Exploring Operation: 77-62=15, Resulting Numbers: [82, 15] Generated Node #0,4,3: 67:[82, 15] Operation: 77-62=15 Exploring Operation: 62+77=139, Resulting Numbers: [82, 139] Generated Node #0,4,4: 67:[82, 139] Operation: 62+77=139 Moving to Node #0,2 Current State: 67:[94, 62, 65], Operations: ['77-12=65'] Exploring Operation: 65-62=3, Resulting Numbers: [94, 3] Generated Node #0,2,0: 67:[94, 3] Operation: 65-62=3 Exploring Operation: 62+65=127, Resulting Numbers: [94, 127] Generated Node #0,2,1: 67:[94, 127] Operation: 62+65=127 Exploring Operation: 94+62=156, Resulting Numbers: [65, 156] Generated Node #0,2,2: 67:[65, 156] Operation: 94+62=156 Exploring Operation: 94-62=32, Resulting Numbers: [65, 32] Generated Node #0,2,3: 67:[65, 32] Operation: 94-62=32 Exploring Operation: 94-65=29, Resulting Numbers: [62, 29] Generated Node #0,2,4: 67:[62, 29] Operation: 94-65=29 Moving to Node #0,0 Current State: 67:[94, 77, 74], Operations: ['12+62=74'] Exploring Operation: 94-74=20, Resulting Numbers: [77, 20] Generated Node #0,0,0: 67:[77, 20] Operation: 94-74=20 Exploring Operation: 94+77=171, Resulting Numbers: [74, 171] Generated Node #0,0,1: 67:[74, 171] Operation: 94+77=171 Exploring Operation: 77-74=3, Resulting Numbers: [94, 3] Generated Node #0,0,2: 67:[94, 3] Operation: 77-74=3 Exploring Operation: 94-77=17, Resulting Numbers: [74, 17] Generated Node #0,0,3: 67:[74, 17] Operation: 94-77=17 Exploring Operation: 94+74=168, Resulting Numbers: [77, 168] Generated Node #0,0,4: 67:[77, 168] Operation: 94+74=168 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[77, 20], Operations: ['12+62=74', '94-74=20'] Exploring Operation: 77*20=1540, Resulting Numbers: [1540] 1540,67 unequal: No Solution Exploring Operation: 77+20=97, Resulting Numbers: [97] 97,67 unequal: No Solution Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 67:[74, 17], Operations: ['12+62=74', '94-77=17'] Exploring Operation: 74*17=1258, Resulting Numbers: [1258] 1258,67 unequal: No Solution Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,67 unequal: No Solution Exploring Operation: 74+17=91, Resulting Numbers: [91] 91,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 67:[94, 3], Operations: ['12+62=74', '77-74=3'] Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 94*3=282, Resulting Numbers: [282] 282,67 unequal: No Solution Exploring Operation: 94+3=97, Resulting Numbers: [97] 97,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[74, 171], Operations: ['12+62=74', '94+77=171'] Exploring Operation: 74+171=245, Resulting Numbers: [245] 245,67 unequal: No Solution Exploring Operation: 74*171=12654, Resulting Numbers: [12654] 12654,67 unequal: No Solution Exploring Operation: 171-74=97, Resulting Numbers: [97] 97,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 67:[77, 168], Operations: ['12+62=74', '94+74=168'] Exploring Operation: 77*168=12936, Resulting Numbers: [12936] 12936,67 unequal: No Solution Exploring Operation: 77+168=245, Resulting Numbers: [245] 245,67 unequal: No Solution Exploring Operation: 168-77=91, Resulting Numbers: [91] 91,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 67:[62, 77, 106], Operations: ['12+94=106'] Exploring Operation: 106-77=29, Resulting Numbers: [62, 29] Generated Node #0,1,0: 67:[62, 29] Operation: 106-77=29 Exploring Operation: 62+77=139, Resulting Numbers: [106, 139] Generated Node #0,1,1: 67:[106, 139] Operation: 62+77=139 Exploring Operation: 62+106=168, Resulting Numbers: [77, 168] Generated Node #0,1,2: 67:[77, 168] Operation: 62+106=168 Exploring Operation: 106-62=44, Resulting Numbers: [77, 44] Generated Node #0,1,3: 67:[77, 44] Operation: 106-62=44 Exploring Operation: 77-62=15, Resulting Numbers: [106, 15] Generated Node #0,1,4: 67:[106, 15] Operation: 77-62=15 Moving to Node #0,3 Current State: 67:[94, 77, 50], Operations: ['62-12=50'] Exploring Operation: 77+50=127, Resulting Numbers: [94, 127] Generated Node #0,3,0: 67:[94, 127] Operation: 77+50=127 Exploring Operation: 94-77=17, Resulting Numbers: [50, 17] Generated Node #0,3,1: 67:[50, 17] Operation: 94-77=17 Exploring Operation: 94+50=144, Resulting Numbers: [77, 144] Generated Node #0,3,2: 67:[77, 144] Operation: 94+50=144 Exploring Operation: 77-50=27, Resulting Numbers: [94, 27] Generated Node #0,3,3: 67:[94, 27] Operation: 77-50=27 Exploring Operation: 94-50=44, Resulting Numbers: [77, 44] Generated Node #0,3,4: 67:[77, 44] Operation: 94-50=44 Moving to Node #0,1,3 Current State: 67:[77, 44], Operations: ['12+94=106', '106-62=44'] Exploring Operation: 77*44=3388, Resulting Numbers: [3388] 3388,67 unequal: No Solution Exploring Operation: 77-44=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 77+44=121, Resulting Numbers: [121] 121,67 unequal: No Solution Moving to Node #0,3,4 Current State: 67:[77, 44], Operations: ['62-12=50', '94-50=44'] Exploring Operation: 77+44=121, Resulting Numbers: [121] 121,67 unequal: No Solution Exploring Operation: 77-44=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 77*44=3388, Resulting Numbers: [3388] 3388,67 unequal: No Solution Moving to Node #0,2,3 Current State: 67:[65, 32], Operations: ['77-12=65', '94-62=32'] Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 65*32=2080, Resulting Numbers: [2080] 2080,67 unequal: No Solution Exploring Operation: 65+32=97, Resulting Numbers: [97] 97,67 unequal: No Solution Moving to Node #0,2,4 Current State: 67:[62, 29], Operations: ['77-12=65', '94-65=29'] Exploring Operation: 62+29=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 62*29=1798, Resulting Numbers: [1798] 1798,67 unequal: No Solution Exploring Operation: 62-29=33, Resulting Numbers: [33] 33,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[62, 29], Operations: ['12+94=106', '106-77=29'] Exploring Operation: 62*29=1798, Resulting Numbers: [1798] 1798,67 unequal: No Solution Exploring Operation: 62+29=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 62-29=33, Resulting Numbers: [33] 33,67 unequal: No Solution Moving to Node #0,4,0 Current State: 67:[77, 20], Operations: ['94-12=82', '82-62=20'] Exploring Operation: 77*20=1540, Resulting Numbers: [1540] 1540,67 unequal: No Solution Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,67 unequal: No Solution Exploring Operation: 77+20=97, Resulting Numbers: [97] 97,67 unequal: No Solution Moving to Node #0,4,3 Current State: 67:[82, 15], Operations: ['94-12=82', '77-62=15'] Exploring Operation: 82*15=1230, Resulting Numbers: [1230] 1230,67 unequal: No Solution Exploring Operation: 82+15=97, Resulting Numbers: [97] 97,67 unequal: No Solution Exploring Operation: 82-15=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[12, 94, 62, 77], Operations: [] Exploring Operation: 94-12=82, Resulting Numbers: [62, 77, 82] Generated Node #0,4: 67:[62, 77, 82] Operation: 94-12=82 Moving to Node #0,4 Current State: 67:[62, 77, 82], Operations: ['94-12=82'] Exploring Operation: 77-62=15, Resulting Numbers: [82, 15] Generated Node #0,4,3: 67:[82, 15] Operation: 77-62=15 Moving to Node #0,4,3 Current State: 67:[82, 15], Operations: ['94-12=82', '77-62=15'] Exploring Operation: 82-15=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
0.939236
hs_5
sum_heuristic
[ 49, 50, 57, 9 ]
49
[ "50-49=1", "57-9=48", "1+48=49" ]
Current State: 49:[49, 50, 57, 9], Operations: [] Exploring Operation: 50-49=1, Resulting Numbers: [57, 9, 1] Generated Node #2: [57, 9, 1] from Operation: 50-49=1 Current State: 49:[57, 9, 1], Operations: ['50-49=1'] Exploring Operation: 57-9=48, Resulting Numbers: [1, 48] Generated Node #3: [1, 48] from Operation: 57-9=48 Current State: 49:[1, 48], Operations: ['50-49=1', '57-9=48'] Exploring Operation: 1+48=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[49, 50, 57, 9], Operations: [] Exploring Operation: 57-50=7, Resulting Numbers: [49, 9, 7] Generated Node #0,0: 49:[49, 9, 7] Operation: 57-50=7 Moving to Node #0,0 Current State: 49:[49, 9, 7], Operations: ['57-50=7'] Exploring Operation: 49/7=7, Resulting Numbers: [9, 7] Generated Node #0,0,0: 49:[9, 7] Operation: 49/7=7 Moving to Node #0,0,0 Current State: 49:[9, 7], Operations: ['57-50=7', '49/7=7'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,49 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 84, 22, 73, 11 ]
99
[ "84-73=11", "11*11=121", "121-22=99" ]
Current State: 99:[84, 22, 73, 11], Operations: [] Exploring Operation: 84-73=11, Resulting Numbers: [22, 11, 11] Generated Node #2: [22, 11, 11] from Operation: 84-73=11 Current State: 99:[22, 11, 11], Operations: ['84-73=11'] Exploring Operation: 11*11=121, Resulting Numbers: [22, 121] Generated Node #3: [22, 121] from Operation: 11*11=121 Current State: 99:[22, 121], Operations: ['84-73=11', '11*11=121'] Exploring Operation: 121-22=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[84, 22, 73, 11], Operations: [] Exploring Operation: 84-73=11, Resulting Numbers: [22, 11, 11] Generated Node #0,0: 99:[22, 11, 11] Operation: 84-73=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[22, 11, 11], Operations: ['84-73=11'] Exploring Operation: 22+11=33, Resulting Numbers: [11, 33] Generated Node #0,0,0: 99:[11, 33] Operation: 22+11=33 Moving to Node #0,0,0 Current State: 99:[11, 33], Operations: ['84-73=11', '22+11=33'] Exploring Operation: 33/11=3, Resulting Numbers: [3] 3,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 84, 4, 8, 42 ]
63
[ "84+42=126", "8/4=2", "126/2=63" ]
Current State: 63:[84, 4, 8, 42], Operations: [] Exploring Operation: 84+42=126, Resulting Numbers: [4, 8, 126] Generated Node #2: [4, 8, 126] from Operation: 84+42=126 Current State: 63:[4, 8, 126], Operations: ['84+42=126'] Exploring Operation: 8/4=2, Resulting Numbers: [126, 2] Generated Node #3: [126, 2] from Operation: 8/4=2 Current State: 63:[126, 2], Operations: ['84+42=126', '8/4=2'] Exploring Operation: 126/2=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[84, 4, 8, 42], Operations: [] Exploring Operation: 84-8=76, Resulting Numbers: [4, 42, 76] Generated Node #0,0: 63:[4, 42, 76] Operation: 84-8=76 Exploring Operation: 84/42=2, Resulting Numbers: [4, 8, 2] Generated Node #0,1: 63:[4, 8, 2] Operation: 84/42=2 Exploring Operation: 84-42=42, Resulting Numbers: [4, 8, 42] Generated Node #0,2: 63:[4, 8, 42] Operation: 84-42=42 Exploring Operation: 84/4=21, Resulting Numbers: [8, 42, 21] Generated Node #0,3: 63:[8, 42, 21] Operation: 84/4=21 Exploring Operation: 8+42=50, Resulting Numbers: [84, 4, 50] Generated Node #0,4: 63:[84, 4, 50] Operation: 8+42=50 Moving to Node #0,1 Current State: 63:[4, 8, 2], Operations: ['84/42=2'] Exploring Operation: 4-2=2, Resulting Numbers: [8, 2] Generated Node #0,1,0: 63:[8, 2] Operation: 4-2=2 Exploring Operation: 8-4=4, Resulting Numbers: [2, 4] Generated Node #0,1,1: 63:[2, 4] Operation: 8-4=4 Exploring Operation: 4+2=6, Resulting Numbers: [8, 6] Generated Node #0,1,2: 63:[8, 6] Operation: 4+2=6 Exploring Operation: 8/4=2, Resulting Numbers: [2, 2] Generated Node #0,1,3: 63:[2, 2] Operation: 8/4=2 Exploring Operation: 4*2=8, Resulting Numbers: [8, 8] Generated Node #0,1,4: 63:[8, 8] Operation: 4*2=8 Moving to Node #0,3 Current State: 63:[8, 42, 21], Operations: ['84/4=21'] Exploring Operation: 8+42=50, Resulting Numbers: [21, 50] Generated Node #0,3,0: 63:[21, 50] Operation: 8+42=50 Exploring Operation: 42-8=34, Resulting Numbers: [21, 34] Generated Node #0,3,1: 63:[21, 34] Operation: 42-8=34 Exploring Operation: 42-21=21, Resulting Numbers: [8, 21] Generated Node #0,3,2: 63:[8, 21] Operation: 42-21=21 Exploring Operation: 42+21=63, Resulting Numbers: [8, 63] Generated Node #0,3,3: 63:[8, 63] Operation: 42+21=63 Exploring Operation: 42/21=2, Resulting Numbers: [8, 2] Generated Node #0,3,4: 63:[8, 2] Operation: 42/21=2 Moving to Node #0,2 Current State: 63:[4, 8, 42], Operations: ['84-42=42'] Exploring Operation: 42-4=38, Resulting Numbers: [8, 38] Generated Node #0,2,0: 63:[8, 38] Operation: 42-4=38 Exploring Operation: 42-8=34, Resulting Numbers: [4, 34] Generated Node #0,2,1: 63:[4, 34] Operation: 42-8=34 Exploring Operation: 8+42=50, Resulting Numbers: [4, 50] Generated Node #0,2,2: 63:[4, 50] Operation: 8+42=50 Exploring Operation: 4+42=46, Resulting Numbers: [8, 46] Generated Node #0,2,3: 63:[8, 46] Operation: 4+42=46 Exploring Operation: 8-4=4, Resulting Numbers: [42, 4] Generated Node #0,2,4: 63:[42, 4] Operation: 8-4=4 Moving to Node #0,0 Current State: 63:[4, 42, 76], Operations: ['84-8=76'] Exploring Operation: 42-4=38, Resulting Numbers: [76, 38] Generated Node #0,0,0: 63:[76, 38] Operation: 42-4=38 Exploring Operation: 4+42=46, Resulting Numbers: [76, 46] Generated Node #0,0,1: 63:[76, 46] Operation: 4+42=46 Exploring Operation: 76-4=72, Resulting Numbers: [42, 72] Generated Node #0,0,2: 63:[42, 72] Operation: 76-4=72 Exploring Operation: 76-42=34, Resulting Numbers: [4, 34] Generated Node #0,0,3: 63:[4, 34] Operation: 76-42=34 Exploring Operation: 76/4=19, Resulting Numbers: [42, 19] Generated Node #0,0,4: 63:[42, 19] Operation: 76/4=19 Moving to Node #0,4 Current State: 63:[84, 4, 50], Operations: ['8+42=50'] Exploring Operation: 84/4=21, Resulting Numbers: [50, 21] Generated Node #0,4,0: 63:[50, 21] Operation: 84/4=21 Exploring Operation: 84-4=80, Resulting Numbers: [50, 80] Generated Node #0,4,1: 63:[50, 80] Operation: 84-4=80 Exploring Operation: 4+50=54, Resulting Numbers: [84, 54] Generated Node #0,4,2: 63:[84, 54] Operation: 4+50=54 Exploring Operation: 84+4=88, Resulting Numbers: [50, 88] Generated Node #0,4,3: 63:[50, 88] Operation: 84+4=88 Exploring Operation: 84-50=34, Resulting Numbers: [4, 34] Generated Node #0,4,4: 63:[4, 34] Operation: 84-50=34 Moving to Node #0,3,2 Current State: 63:[8, 21], Operations: ['84/4=21', '42-21=21'] Exploring Operation: 8*21=168, Resulting Numbers: [168] 168,63 unequal: No Solution Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,63 unequal: No Solution Exploring Operation: 8+21=29, Resulting Numbers: [29] 29,63 unequal: No Solution Moving to Node #0,3,3 Current State: 63:[8, 63], Operations: ['84/4=21', '42+21=63'] Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,63 unequal: No Solution Exploring Operation: 8*63=504, Resulting Numbers: [504] 504,63 unequal: No Solution Exploring Operation: 8+63=71, Resulting Numbers: [71] 71,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[8, 2], Operations: ['84/42=2', '4-2=2'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,63 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,63 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[8, 6], Operations: ['84/42=2', '4+2=6'] Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,63 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,63 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[2, 4], Operations: ['84/42=2', '8-4=4'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,63 unequal: No Solution Moving to Node #0,1,4 Current State: 63:[8, 8], Operations: ['84/42=2', '4*2=8'] Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,63 unequal: No Solution Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,63 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,63 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,63 unequal: No Solution Moving to Node #0,1,3 Current State: 63:[2, 2], Operations: ['84/42=2', '8/4=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,63 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,63 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,63 unequal: No Solution Moving to Node #0,3,4 Current State: 63:[8, 2], Operations: ['84/4=21', '42/21=2'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,63 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,63 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,63 unequal: No Solution Moving to Node #0,3,1 Current State: 63:[21, 34], Operations: ['84/4=21', '42-8=34'] Exploring Operation: 34-21=13, Resulting Numbers: [13] 13,63 unequal: No Solution Exploring Operation: 21+34=55, Resulting Numbers: [55] 55,63 unequal: No Solution Exploring Operation: 21*34=714, Resulting Numbers: [714] 714,63 unequal: No Solution Moving to Node #0,4,0 Current State: 63:[50, 21], Operations: ['8+42=50', '84/4=21'] Exploring Operation: 50+21=71, Resulting Numbers: [71] 71,63 unequal: No Solution Exploring Operation: 50*21=1050, Resulting Numbers: [1050] 1050,63 unequal: No Solution Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,63 unequal: No Solution Moving to Node #0,3,0 Current State: 63:[21, 50], Operations: ['84/4=21', '8+42=50'] Exploring Operation: 21*50=1050, Resulting Numbers: [1050] 1050,63 unequal: No Solution Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,63 unequal: No Solution Exploring Operation: 21+50=71, Resulting Numbers: [71] 71,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[4, 50], Operations: ['84-42=42', '8+42=50'] Exploring Operation: 4*50=200, Resulting Numbers: [200] 200,63 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,63 unequal: No Solution Exploring Operation: 4+50=54, Resulting Numbers: [54] 54,63 unequal: No Solution Moving to Node #0,2,1 Current State: 63:[4, 34], Operations: ['84-42=42', '42-8=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,63 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,63 unequal: No Solution Moving to Node #0,0,3 Current State: 63:[4, 34], Operations: ['84-8=76', '76-42=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,63 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,63 unequal: No Solution Moving to Node #0,4,4 Current State: 63:[4, 34], Operations: ['8+42=50', '84-50=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,63 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,63 unequal: No Solution Moving to Node #0,2,3 Current State: 63:[8, 46], Operations: ['84-42=42', '4+42=46'] Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,63 unequal: No Solution Exploring Operation: 8*46=368, Resulting Numbers: [368] 368,63 unequal: No Solution Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,63 unequal: No Solution Moving to Node #0,2,0 Current State: 63:[8, 38], Operations: ['84-42=42', '42-4=38'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 8*38=304, Resulting Numbers: [304] 304,63 unequal: No Solution Exploring Operation: 8+38=46, Resulting Numbers: [46] 46,63 unequal: No Solution Moving to Node #0,2,4 Current State: 63:[42, 4], Operations: ['84-42=42', '8-4=4'] Exploring Operation: 42*4=168, Resulting Numbers: [168] 168,63 unequal: No Solution Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,63 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,63 unequal: No Solution Moving to Node #0,0,4 Current State: 63:[42, 19], Operations: ['84-8=76', '76/4=19'] Exploring Operation: 42*19=798, Resulting Numbers: [798] 798,63 unequal: No Solution Exploring Operation: 42+19=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 42-19=23, Resulting Numbers: [23] 23,63 unequal: No Solution Moving to Node #0,0,2 Current State: 63:[42, 72], Operations: ['84-8=76', '76-4=72'] Exploring Operation: 72-42=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 42+72=114, Resulting Numbers: [114] 114,63 unequal: No Solution Exploring Operation: 42*72=3024, Resulting Numbers: [3024] 3024,63 unequal: No Solution Moving to Node #0,4,2 Current State: 63:[84, 54], Operations: ['8+42=50', '4+50=54'] Exploring Operation: 84-54=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 84*54=4536, Resulting Numbers: [4536] 4536,63 unequal: No Solution Exploring Operation: 84+54=138, Resulting Numbers: [138] 138,63 unequal: No Solution Moving to Node #0,4,1 Current State: 63:[50, 80], Operations: ['8+42=50', '84-4=80'] Exploring Operation: 50+80=130, Resulting Numbers: [130] 130,63 unequal: No Solution Exploring Operation: 50*80=4000, Resulting Numbers: [4000] 4000,63 unequal: No Solution Exploring Operation: 80-50=30, Resulting Numbers: [30] 30,63 unequal: No Solution Moving to Node #0,0,0 Current State: 63:[76, 38], Operations: ['84-8=76', '42-4=38'] Exploring Operation: 76+38=114, Resulting Numbers: [114] 114,63 unequal: No Solution Exploring Operation: 76-38=38, Resulting Numbers: [38] 38,63 unequal: No Solution Exploring Operation: 76*38=2888, Resulting Numbers: [2888] 2888,63 unequal: No Solution Exploring Operation: 76/38=2, Resulting Numbers: [2] 2,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[76, 46], Operations: ['84-8=76', '4+42=46'] Exploring Operation: 76+46=122, Resulting Numbers: [122] 122,63 unequal: No Solution Exploring Operation: 76*46=3496, Resulting Numbers: [3496] 3496,63 unequal: No Solution Exploring Operation: 76-46=30, Resulting Numbers: [30] 30,63 unequal: No Solution Moving to Node #0,4,3 Current State: 63:[50, 88], Operations: ['8+42=50', '84+4=88'] Exploring Operation: 88-50=38, Resulting Numbers: [38] 38,63 unequal: No Solution Exploring Operation: 50*88=4400, Resulting Numbers: [4400] 4400,63 unequal: No Solution Exploring Operation: 50+88=138, Resulting Numbers: [138] 138,63 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 49, 81, 15, 89 ]
71
[ "89-81=8", "15*8=120", "120-49=71" ]
Current State: 71:[49, 81, 15, 89], Operations: [] Exploring Operation: 89-81=8, Resulting Numbers: [49, 15, 8] Generated Node #2: [49, 15, 8] from Operation: 89-81=8 Current State: 71:[49, 15, 8], Operations: ['89-81=8'] Exploring Operation: 15*8=120, Resulting Numbers: [49, 120] Generated Node #3: [49, 120] from Operation: 15*8=120 Current State: 71:[49, 120], Operations: ['89-81=8', '15*8=120'] Exploring Operation: 120-49=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[49, 81, 15, 89], Operations: [] Exploring Operation: 89-15=74, Resulting Numbers: [49, 81, 74] Generated Node #0,0: 71:[49, 81, 74] Operation: 89-15=74 Exploring Operation: 49+15=64, Resulting Numbers: [81, 89, 64] Generated Node #0,1: 71:[81, 89, 64] Operation: 49+15=64 Exploring Operation: 81-15=66, Resulting Numbers: [49, 89, 66] Generated Node #0,2: 71:[49, 89, 66] Operation: 81-15=66 Moving to Node #0,0 Current State: 71:[49, 81, 74], Operations: ['89-15=74'] Exploring Operation: 81-49=32, Resulting Numbers: [74, 32] Generated Node #0,0,0: 71:[74, 32] Operation: 81-49=32 Exploring Operation: 74-49=25, Resulting Numbers: [81, 25] Generated Node #0,0,1: 71:[81, 25] Operation: 74-49=25 Exploring Operation: 49+81=130, Resulting Numbers: [74, 130] Generated Node #0,0,2: 71:[74, 130] Operation: 49+81=130 Moving to Node #0,1 Current State: 71:[81, 89, 64], Operations: ['49+15=64'] Exploring Operation: 81-64=17, Resulting Numbers: [89, 17] Generated Node #0,1,0: 71:[89, 17] Operation: 81-64=17 Exploring Operation: 89-64=25, Resulting Numbers: [81, 25] Generated Node #0,1,1: 71:[81, 25] Operation: 89-64=25 Exploring Operation: 89-81=8, Resulting Numbers: [64, 8] Generated Node #0,1,2: 71:[64, 8] Operation: 89-81=8 Moving to Node #0,2 Current State: 71:[49, 89, 66], Operations: ['81-15=66'] Exploring Operation: 49+66=115, Resulting Numbers: [89, 115] Generated Node #0,2,0: 71:[89, 115] Operation: 49+66=115 Exploring Operation: 89-49=40, Resulting Numbers: [66, 40] Generated Node #0,2,1: 71:[66, 40] Operation: 89-49=40 Exploring Operation: 89-66=23, Resulting Numbers: [49, 23] Generated Node #0,2,2: 71:[49, 23] Operation: 89-66=23 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 71:[66, 40], Operations: ['81-15=66', '89-49=40'] Exploring Operation: 66*40=2640, Resulting Numbers: [2640] 2640,71 unequal: No Solution Exploring Operation: 66-40=26, Resulting Numbers: [26] 26,71 unequal: No Solution Exploring Operation: 66+40=106, Resulting Numbers: [106] 106,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 71:[89, 115], Operations: ['81-15=66', '49+66=115'] Exploring Operation: 89+115=204, Resulting Numbers: [204] 204,71 unequal: No Solution Exploring Operation: 115-89=26, Resulting Numbers: [26] 26,71 unequal: No Solution Exploring Operation: 89*115=10235, Resulting Numbers: [10235] 10235,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 71:[49, 23], Operations: ['81-15=66', '89-66=23'] Exploring Operation: 49*23=1127, Resulting Numbers: [1127] 1127,71 unequal: No Solution Exploring Operation: 49-23=26, Resulting Numbers: [26] 26,71 unequal: No Solution Exploring Operation: 49+23=72, Resulting Numbers: [72] 72,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 71:[74, 32], Operations: ['89-15=74', '81-49=32'] Exploring Operation: 74*32=2368, Resulting Numbers: [2368] 2368,71 unequal: No Solution Exploring Operation: 74-32=42, Resulting Numbers: [42] 42,71 unequal: No Solution Exploring Operation: 74+32=106, Resulting Numbers: [106] 106,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[81, 25], Operations: ['89-15=74', '74-49=25'] Exploring Operation: 81*25=2025, Resulting Numbers: [2025] 2025,71 unequal: No Solution Exploring Operation: 81-25=56, Resulting Numbers: [56] 56,71 unequal: No Solution Exploring Operation: 81+25=106, Resulting Numbers: [106] 106,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[81, 25], Operations: ['49+15=64', '89-64=25'] Exploring Operation: 81*25=2025, Resulting Numbers: [2025] 2025,71 unequal: No Solution Exploring Operation: 81+25=106, Resulting Numbers: [106] 106,71 unequal: No Solution Exploring Operation: 81-25=56, Resulting Numbers: [56] 56,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[74, 130], Operations: ['89-15=74', '49+81=130'] Exploring Operation: 130-74=56, Resulting Numbers: [56] 56,71 unequal: No Solution Exploring Operation: 74*130=9620, Resulting Numbers: [9620] 9620,71 unequal: No Solution Exploring Operation: 74+130=204, Resulting Numbers: [204] 204,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[64, 8], Operations: ['49+15=64', '89-81=8'] Exploring Operation: 64+8=72, Resulting Numbers: [72] 72,71 unequal: No Solution Exploring Operation: 64-8=56, Resulting Numbers: [56] 56,71 unequal: No Solution Exploring Operation: 64/8=8, Resulting Numbers: [8] 8,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[89, 17], Operations: ['49+15=64', '81-64=17'] Exploring Operation: 89*17=1513, Resulting Numbers: [1513] 1513,71 unequal: No Solution Exploring Operation: 89-17=72, Resulting Numbers: [72] 72,71 unequal: No Solution Exploring Operation: 89+17=106, Resulting Numbers: [106] 106,71 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 4, 14, 78, 61 ]
45
[ "78-14=64", "64/4=16", "61-16=45" ]
Current State: 45:[4, 14, 78, 61], Operations: [] Exploring Operation: 78-14=64, Resulting Numbers: [4, 61, 64] Generated Node #2: [4, 61, 64] from Operation: 78-14=64 Current State: 45:[4, 61, 64], Operations: ['78-14=64'] Exploring Operation: 64/4=16, Resulting Numbers: [61, 16] Generated Node #3: [61, 16] from Operation: 64/4=16 Current State: 45:[61, 16], Operations: ['78-14=64', '64/4=16'] Exploring Operation: 61-16=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[4, 14, 78, 61], Operations: [] Exploring Operation: 61-14=47, Resulting Numbers: [4, 78, 47] Generated Node #0,0: 45:[4, 78, 47] Operation: 61-14=47 Exploring Operation: 78-61=17, Resulting Numbers: [4, 14, 17] Generated Node #0,1: 45:[4, 14, 17] Operation: 78-61=17 Exploring Operation: 78-4=74, Resulting Numbers: [14, 61, 74] Generated Node #0,2: 45:[14, 61, 74] Operation: 78-4=74 Exploring Operation: 78-14=64, Resulting Numbers: [4, 61, 64] Generated Node #0,3: 45:[4, 61, 64] Operation: 78-14=64 Moving to Node #0,1 Current State: 45:[4, 14, 17], Operations: ['78-61=17'] Exploring Operation: 4+14=18, Resulting Numbers: [17, 18] Generated Node #0,1,0: 45:[17, 18] Operation: 4+14=18 Exploring Operation: 17-4=13, Resulting Numbers: [14, 13] Generated Node #0,1,1: 45:[14, 13] Operation: 17-4=13 Exploring Operation: 14-4=10, Resulting Numbers: [17, 10] Generated Node #0,1,2: 45:[17, 10] Operation: 14-4=10 Exploring Operation: 17-14=3, Resulting Numbers: [4, 3] Generated Node #0,1,3: 45:[4, 3] Operation: 17-14=3 Moving to Node #0,3 Current State: 45:[4, 61, 64], Operations: ['78-14=64'] Exploring Operation: 64-4=60, Resulting Numbers: [61, 60] Generated Node #0,3,0: 45:[61, 60] Operation: 64-4=60 Exploring Operation: 64-61=3, Resulting Numbers: [4, 3] Generated Node #0,3,1: 45:[4, 3] Operation: 64-61=3 Exploring Operation: 61-4=57, Resulting Numbers: [64, 57] Generated Node #0,3,2: 45:[64, 57] Operation: 61-4=57 Exploring Operation: 64/4=16, Resulting Numbers: [61, 16] Generated Node #0,3,3: 45:[61, 16] Operation: 64/4=16 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 45:[4, 3], Operations: ['78-14=64', '64-61=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,45 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 45:[61, 16], Operations: ['78-14=64', '64/4=16'] Exploring Operation: 61-16=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[4, 14, 78, 61], Operations: [] Exploring Operation: 78-14=64, Resulting Numbers: [4, 61, 64] Generated Node #0,3: 45:[4, 61, 64] Operation: 78-14=64 Moving to Node #0,3 Current State: 45:[4, 61, 64], Operations: ['78-14=64'] Exploring Operation: 64/4=16, Resulting Numbers: [61, 16] Generated Node #0,3,3: 45:[61, 16] Operation: 64/4=16 Moving to Node #0,3,3 Current State: 45:[61, 16], Operations: ['78-14=64', '64/4=16'] Exploring Operation: 61-16=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 76, 54, 8, 81 ]
51
[ "76-54=22", "81-8=73", "73-22=51" ]
Current State: 51:[76, 54, 8, 81], Operations: [] Exploring Operation: 76-54=22, Resulting Numbers: [8, 81, 22] Generated Node #2: [8, 81, 22] from Operation: 76-54=22 Current State: 51:[8, 81, 22], Operations: ['76-54=22'] Exploring Operation: 81-8=73, Resulting Numbers: [22, 73] Generated Node #3: [22, 73] from Operation: 81-8=73 Current State: 51:[22, 73], Operations: ['76-54=22', '81-8=73'] Exploring Operation: 73-22=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[76, 54, 8, 81], Operations: [] Exploring Operation: 76-54=22, Resulting Numbers: [8, 81, 22] Generated Node #0,0: 51:[8, 81, 22] Operation: 76-54=22 Exploring Operation: 76-8=68, Resulting Numbers: [54, 81, 68] Generated Node #0,1: 51:[54, 81, 68] Operation: 76-8=68 Exploring Operation: 81-8=73, Resulting Numbers: [76, 54, 73] Generated Node #0,2: 51:[76, 54, 73] Operation: 81-8=73 Exploring Operation: 81-76=5, Resulting Numbers: [54, 8, 5] Generated Node #0,3: 51:[54, 8, 5] Operation: 81-76=5 Exploring Operation: 81-54=27, Resulting Numbers: [76, 8, 27] Generated Node #0,4: 51:[76, 8, 27] Operation: 81-54=27 Moving to Node #0,3 Current State: 51:[54, 8, 5], Operations: ['81-76=5'] Exploring Operation: 54-5=49, Resulting Numbers: [8, 49] Generated Node #0,3,0: 51:[8, 49] Operation: 54-5=49 Exploring Operation: 54+8=62, Resulting Numbers: [5, 62] Generated Node #0,3,1: 51:[5, 62] Operation: 54+8=62 Exploring Operation: 8+5=13, Resulting Numbers: [54, 13] Generated Node #0,3,2: 51:[54, 13] Operation: 8+5=13 Exploring Operation: 54-8=46, Resulting Numbers: [5, 46] Generated Node #0,3,3: 51:[5, 46] Operation: 54-8=46 Exploring Operation: 8-5=3, Resulting Numbers: [54, 3] Generated Node #0,3,4: 51:[54, 3] Operation: 8-5=3 Moving to Node #0,4 Current State: 51:[76, 8, 27], Operations: ['81-54=27'] Exploring Operation: 76-27=49, Resulting Numbers: [8, 49] Generated Node #0,4,0: 51:[8, 49] Operation: 76-27=49 Exploring Operation: 27-8=19, Resulting Numbers: [76, 19] Generated Node #0,4,1: 51:[76, 19] Operation: 27-8=19 Exploring Operation: 76-8=68, Resulting Numbers: [27, 68] Generated Node #0,4,2: 51:[27, 68] Operation: 76-8=68 Exploring Operation: 76+8=84, Resulting Numbers: [27, 84] Generated Node #0,4,3: 51:[27, 84] Operation: 76+8=84 Exploring Operation: 8+27=35, Resulting Numbers: [76, 35] Generated Node #0,4,4: 51:[76, 35] Operation: 8+27=35 Moving to Node #0,0 Current State: 51:[8, 81, 22], Operations: ['76-54=22'] Exploring Operation: 81-22=59, Resulting Numbers: [8, 59] Generated Node #0,0,0: 51:[8, 59] Operation: 81-22=59 Exploring Operation: 8+81=89, Resulting Numbers: [22, 89] Generated Node #0,0,1: 51:[22, 89] Operation: 8+81=89 Exploring Operation: 81-8=73, Resulting Numbers: [22, 73] Generated Node #0,0,2: 51:[22, 73] Operation: 81-8=73 Exploring Operation: 22-8=14, Resulting Numbers: [81, 14] Generated Node #0,0,3: 51:[81, 14] Operation: 22-8=14 Exploring Operation: 8+22=30, Resulting Numbers: [81, 30] Generated Node #0,0,4: 51:[81, 30] Operation: 8+22=30 Moving to Node #0,1 Current State: 51:[54, 81, 68], Operations: ['76-8=68'] Exploring Operation: 81-54=27, Resulting Numbers: [68, 27] Generated Node #0,1,0: 51:[68, 27] Operation: 81-54=27 Exploring Operation: 54+81=135, Resulting Numbers: [68, 135] Generated Node #0,1,1: 51:[68, 135] Operation: 54+81=135 Exploring Operation: 68-54=14, Resulting Numbers: [81, 14] Generated Node #0,1,2: 51:[81, 14] Operation: 68-54=14 Exploring Operation: 54+68=122, Resulting Numbers: [81, 122] Generated Node #0,1,3: 51:[81, 122] Operation: 54+68=122 Exploring Operation: 81-68=13, Resulting Numbers: [54, 13] Generated Node #0,1,4: 51:[54, 13] Operation: 81-68=13 Moving to Node #0,2 Current State: 51:[76, 54, 73], Operations: ['81-8=73'] Exploring Operation: 76+73=149, Resulting Numbers: [54, 149] Generated Node #0,2,0: 51:[54, 149] Operation: 76+73=149 Exploring Operation: 73-54=19, Resulting Numbers: [76, 19] Generated Node #0,2,1: 51:[76, 19] Operation: 73-54=19 Exploring Operation: 76+54=130, Resulting Numbers: [73, 130] Generated Node #0,2,2: 51:[73, 130] Operation: 76+54=130 Exploring Operation: 76-54=22, Resulting Numbers: [73, 22] Generated Node #0,2,3: 51:[73, 22] Operation: 76-54=22 Exploring Operation: 76-73=3, Resulting Numbers: [54, 3] Generated Node #0,2,4: 51:[54, 3] Operation: 76-73=3 Moving to Node #0,3,4 Current State: 51:[54, 3], Operations: ['81-76=5', '8-5=3'] Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[76, 54, 8, 81], Operations: [] Exploring Operation: 81-76=5, Resulting Numbers: [54, 8, 5] Generated Node #0,3: 51:[54, 8, 5] Operation: 81-76=5 Moving to Node #0,3 Current State: 51:[54, 8, 5], Operations: ['81-76=5'] Exploring Operation: 8-5=3, Resulting Numbers: [54, 3] Generated Node #0,3,4: 51:[54, 3] Operation: 8-5=3 Moving to Node #0,3,4 Current State: 51:[54, 3], Operations: ['81-76=5', '8-5=3'] Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
0.969618
hs_5
sum_heuristic
[ 3, 43, 84, 80 ]
31
[ "84-80=4", "3*4=12", "43-12=31" ]
Current State: 31:[3, 43, 84, 80], Operations: [] Exploring Operation: 84-80=4, Resulting Numbers: [3, 43, 4] Generated Node #2: [3, 43, 4] from Operation: 84-80=4 Current State: 31:[3, 43, 4], Operations: ['84-80=4'] Exploring Operation: 3*4=12, Resulting Numbers: [43, 12] Generated Node #3: [43, 12] from Operation: 3*4=12 Current State: 31:[43, 12], Operations: ['84-80=4', '3*4=12'] Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[3, 43, 84, 80], Operations: [] Exploring Operation: 84-43=41, Resulting Numbers: [3, 80, 41] Generated Node #0,0: 31:[3, 80, 41] Operation: 84-43=41 Exploring Operation: 84/3=28, Resulting Numbers: [43, 80, 28] Generated Node #0,1: 31:[43, 80, 28] Operation: 84/3=28 Exploring Operation: 84-80=4, Resulting Numbers: [3, 43, 4] Generated Node #0,2: 31:[3, 43, 4] Operation: 84-80=4 Moving to Node #0,1 Current State: 31:[43, 80, 28], Operations: ['84/3=28'] Exploring Operation: 43-28=15, Resulting Numbers: [80, 15] Generated Node #0,1,0: 31:[80, 15] Operation: 43-28=15 Exploring Operation: 80-28=52, Resulting Numbers: [43, 52] Generated Node #0,1,1: 31:[43, 52] Operation: 80-28=52 Exploring Operation: 80-43=37, Resulting Numbers: [28, 37] Generated Node #0,1,2: 31:[28, 37] Operation: 80-43=37 Moving to Node #0,2 Current State: 31:[3, 43, 4], Operations: ['84-80=4'] Exploring Operation: 43-3=40, Resulting Numbers: [4, 40] Generated Node #0,2,0: 31:[4, 40] Operation: 43-3=40 Exploring Operation: 3+4=7, Resulting Numbers: [43, 7] Generated Node #0,2,1: 31:[43, 7] Operation: 3+4=7 Exploring Operation: 3*4=12, Resulting Numbers: [43, 12] Generated Node #0,2,2: 31:[43, 12] Operation: 3*4=12 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 31:[43, 12], Operations: ['84-80=4', '3*4=12'] Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,31 unequal: No Solution Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[3, 43, 84, 80], Operations: [] Exploring Operation: 84-80=4, Resulting Numbers: [3, 43, 4] Generated Node #0,2: 31:[3, 43, 4] Operation: 84-80=4 Moving to Node #0,2 Current State: 31:[3, 43, 4], Operations: ['84-80=4'] Exploring Operation: 3*4=12, Resulting Numbers: [43, 12] Generated Node #0,2,2: 31:[43, 12] Operation: 3*4=12 Moving to Node #0,2,2 Current State: 31:[43, 12], Operations: ['84-80=4', '3*4=12'] Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 90, 39, 79, 74 ]
57
[ "79-74=5", "90/5=18", "39+18=57" ]
Current State: 57:[90, 39, 79, 74], Operations: [] Exploring Operation: 79-74=5, Resulting Numbers: [90, 39, 5] Generated Node #2: [90, 39, 5] from Operation: 79-74=5 Current State: 57:[90, 39, 5], Operations: ['79-74=5'] Exploring Operation: 90/5=18, Resulting Numbers: [39, 18] Generated Node #3: [39, 18] from Operation: 90/5=18 Current State: 57:[39, 18], Operations: ['79-74=5', '90/5=18'] Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[90, 39, 79, 74], Operations: [] Exploring Operation: 90-74=16, Resulting Numbers: [39, 79, 16] Generated Node #0,0: 57:[39, 79, 16] Operation: 90-74=16 Exploring Operation: 90-79=11, Resulting Numbers: [39, 74, 11] Generated Node #0,1: 57:[39, 74, 11] Operation: 90-79=11 Exploring Operation: 79-39=40, Resulting Numbers: [90, 74, 40] Generated Node #0,2: 57:[90, 74, 40] Operation: 79-39=40 Exploring Operation: 79-74=5, Resulting Numbers: [90, 39, 5] Generated Node #0,3: 57:[90, 39, 5] Operation: 79-74=5 Exploring Operation: 90-39=51, Resulting Numbers: [79, 74, 51] Generated Node #0,4: 57:[79, 74, 51] Operation: 90-39=51 Moving to Node #0,0 Current State: 57:[39, 79, 16], Operations: ['90-74=16'] Exploring Operation: 79-16=63, Resulting Numbers: [39, 63] Generated Node #0,0,0: 57:[39, 63] Operation: 79-16=63 Exploring Operation: 39-16=23, Resulting Numbers: [79, 23] Generated Node #0,0,1: 57:[79, 23] Operation: 39-16=23 Exploring Operation: 39+16=55, Resulting Numbers: [79, 55] Generated Node #0,0,2: 57:[79, 55] Operation: 39+16=55 Exploring Operation: 79+16=95, Resulting Numbers: [39, 95] Generated Node #0,0,3: 57:[39, 95] Operation: 79+16=95 Exploring Operation: 79-39=40, Resulting Numbers: [16, 40] Generated Node #0,0,4: 57:[16, 40] Operation: 79-39=40 Moving to Node #0,1 Current State: 57:[39, 74, 11], Operations: ['90-79=11'] Exploring Operation: 74-11=63, Resulting Numbers: [39, 63] Generated Node #0,1,0: 57:[39, 63] Operation: 74-11=63 Exploring Operation: 39+11=50, Resulting Numbers: [74, 50] Generated Node #0,1,1: 57:[74, 50] Operation: 39+11=50 Exploring Operation: 74+11=85, Resulting Numbers: [39, 85] Generated Node #0,1,2: 57:[39, 85] Operation: 74+11=85 Exploring Operation: 74-39=35, Resulting Numbers: [11, 35] Generated Node #0,1,3: 57:[11, 35] Operation: 74-39=35 Exploring Operation: 39-11=28, Resulting Numbers: [74, 28] Generated Node #0,1,4: 57:[74, 28] Operation: 39-11=28 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[39, 63], Operations: ['90-79=11', '74-11=63'] Exploring Operation: 39+63=102, Resulting Numbers: [102] 102,57 unequal: No Solution Exploring Operation: 39*63=2457, Resulting Numbers: [2457] 2457,57 unequal: No Solution Exploring Operation: 63-39=24, Resulting Numbers: [24] 24,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 57:[74, 50], Operations: ['90-79=11', '39+11=50'] Exploring Operation: 74-50=24, Resulting Numbers: [24] 24,57 unequal: No Solution Exploring Operation: 74+50=124, Resulting Numbers: [124] 124,57 unequal: No Solution Exploring Operation: 74*50=3700, Resulting Numbers: [3700] 3700,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 57:[11, 35], Operations: ['90-79=11', '74-39=35'] Exploring Operation: 35-11=24, Resulting Numbers: [24] 24,57 unequal: No Solution Exploring Operation: 11*35=385, Resulting Numbers: [385] 385,57 unequal: No Solution Exploring Operation: 11+35=46, Resulting Numbers: [46] 46,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 57:[74, 28], Operations: ['90-79=11', '39-11=28'] Exploring Operation: 74+28=102, Resulting Numbers: [102] 102,57 unequal: No Solution Exploring Operation: 74*28=2072, Resulting Numbers: [2072] 2072,57 unequal: No Solution Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 57:[39, 85], Operations: ['90-79=11', '74+11=85'] Exploring Operation: 39*85=3315, Resulting Numbers: [3315] 3315,57 unequal: No Solution Exploring Operation: 39+85=124, Resulting Numbers: [124] 124,57 unequal: No Solution Exploring Operation: 85-39=46, Resulting Numbers: [46] 46,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 57:[79, 74, 51], Operations: ['90-39=51'] Exploring Operation: 74-51=23, Resulting Numbers: [79, 23] Generated Node #0,4,0: 57:[79, 23] Operation: 74-51=23 Exploring Operation: 74+51=125, Resulting Numbers: [79, 125] Generated Node #0,4,1: 57:[79, 125] Operation: 74+51=125 Exploring Operation: 79+51=130, Resulting Numbers: [74, 130] Generated Node #0,4,2: 57:[74, 130] Operation: 79+51=130 Exploring Operation: 79-74=5, Resulting Numbers: [51, 5] Generated Node #0,4,3: 57:[51, 5] Operation: 79-74=5 Exploring Operation: 79-51=28, Resulting Numbers: [74, 28] Generated Node #0,4,4: 57:[74, 28] Operation: 79-51=28 Moving to Node #0,3 Current State: 57:[90, 39, 5], Operations: ['79-74=5'] Exploring Operation: 90-39=51, Resulting Numbers: [5, 51] Generated Node #0,3,0: 57:[5, 51] Operation: 90-39=51 Exploring Operation: 39+5=44, Resulting Numbers: [90, 44] Generated Node #0,3,1: 57:[90, 44] Operation: 39+5=44 Exploring Operation: 39-5=34, Resulting Numbers: [90, 34] Generated Node #0,3,2: 57:[90, 34] Operation: 39-5=34 Exploring Operation: 90-5=85, Resulting Numbers: [39, 85] Generated Node #0,3,3: 57:[39, 85] Operation: 90-5=85 Exploring Operation: 90/5=18, Resulting Numbers: [39, 18] Generated Node #0,3,4: 57:[39, 18] Operation: 90/5=18 Moving to Node #0,2 Current State: 57:[90, 74, 40], Operations: ['79-39=40'] Exploring Operation: 74+40=114, Resulting Numbers: [90, 114] Generated Node #0,2,0: 57:[90, 114] Operation: 74+40=114 Exploring Operation: 90+40=130, Resulting Numbers: [74, 130] Generated Node #0,2,1: 57:[74, 130] Operation: 90+40=130 Exploring Operation: 74-40=34, Resulting Numbers: [90, 34] Generated Node #0,2,2: 57:[90, 34] Operation: 74-40=34 Exploring Operation: 90-40=50, Resulting Numbers: [74, 50] Generated Node #0,2,3: 57:[74, 50] Operation: 90-40=50 Exploring Operation: 90-74=16, Resulting Numbers: [40, 16] Generated Node #0,2,4: 57:[40, 16] Operation: 90-74=16 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 57:[40, 16], Operations: ['79-39=40', '90-74=16'] Exploring Operation: 40-16=24, Resulting Numbers: [24] 24,57 unequal: No Solution Exploring Operation: 40*16=640, Resulting Numbers: [640] 640,57 unequal: No Solution Exploring Operation: 40+16=56, Resulting Numbers: [56] 56,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 57:[74, 50], Operations: ['79-39=40', '90-40=50'] Exploring Operation: 74-50=24, Resulting Numbers: [24] 24,57 unequal: No Solution Exploring Operation: 74*50=3700, Resulting Numbers: [3700] 3700,57 unequal: No Solution Exploring Operation: 74+50=124, Resulting Numbers: [124] 124,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 57:[90, 34], Operations: ['79-39=40', '74-40=34'] Exploring Operation: 90*34=3060, Resulting Numbers: [3060] 3060,57 unequal: No Solution Exploring Operation: 90+34=124, Resulting Numbers: [124] 124,57 unequal: No Solution Exploring Operation: 90-34=56, Resulting Numbers: [56] 56,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 57:[90, 114], Operations: ['79-39=40', '74+40=114'] Exploring Operation: 114-90=24, Resulting Numbers: [24] 24,57 unequal: No Solution Exploring Operation: 90*114=10260, Resulting Numbers: [10260] 10260,57 unequal: No Solution Exploring Operation: 90+114=204, Resulting Numbers: [204] 204,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 57:[74, 130], Operations: ['79-39=40', '90+40=130'] Exploring Operation: 130-74=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 74*130=9620, Resulting Numbers: [9620] 9620,57 unequal: No Solution Exploring Operation: 74+130=204, Resulting Numbers: [204] 204,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,3 Current State: 57:[51, 5], Operations: ['90-39=51', '79-74=5'] Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,57 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,57 unequal: No Solution Moving to Node #0,3,0 Current State: 57:[5, 51], Operations: ['79-74=5', '90-39=51'] Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,57 unequal: No Solution Exploring Operation: 5*51=255, Resulting Numbers: [255] 255,57 unequal: No Solution Moving to Node #0,3,4 Current State: 57:[39, 18], Operations: ['79-74=5', '90/5=18'] Exploring Operation: 39*18=702, Resulting Numbers: [702] 702,57 unequal: No Solution Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[90, 39, 79, 74], Operations: [] Exploring Operation: 79-74=5, Resulting Numbers: [90, 39, 5] Generated Node #0,3: 57:[90, 39, 5] Operation: 79-74=5 Moving to Node #0,3 Current State: 57:[90, 39, 5], Operations: ['79-74=5'] Exploring Operation: 90/5=18, Resulting Numbers: [39, 18] Generated Node #0,3,4: 57:[39, 18] Operation: 90/5=18 Moving to Node #0,3,4 Current State: 57:[39, 18], Operations: ['79-74=5', '90/5=18'] Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
0.9375
hs_5
sum_heuristic
[ 93, 62, 51, 85 ]
65
[ "93-62=31", "85-51=34", "31+34=65" ]
Current State: 65:[93, 62, 51, 85], Operations: [] Exploring Operation: 93-62=31, Resulting Numbers: [51, 85, 31] Generated Node #2: [51, 85, 31] from Operation: 93-62=31 Current State: 65:[51, 85, 31], Operations: ['93-62=31'] Exploring Operation: 85-51=34, Resulting Numbers: [31, 34] Generated Node #3: [31, 34] from Operation: 85-51=34 Current State: 65:[31, 34], Operations: ['93-62=31', '85-51=34'] Exploring Operation: 31+34=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[93, 62, 51, 85], Operations: [] Exploring Operation: 93-85=8, Resulting Numbers: [62, 51, 8] Generated Node #0,0: 65:[62, 51, 8] Operation: 93-85=8 Exploring Operation: 93-62=31, Resulting Numbers: [51, 85, 31] Generated Node #0,1: 65:[51, 85, 31] Operation: 93-62=31 Exploring Operation: 62-51=11, Resulting Numbers: [93, 85, 11] Generated Node #0,2: 65:[93, 85, 11] Operation: 62-51=11 Exploring Operation: 93-51=42, Resulting Numbers: [62, 85, 42] Generated Node #0,3: 65:[62, 85, 42] Operation: 93-51=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[62, 51, 8], Operations: ['93-85=8'] Exploring Operation: 62+8=70, Resulting Numbers: [51, 70] Generated Node #0,0,0: 65:[51, 70] Operation: 62+8=70 Exploring Operation: 62-8=54, Resulting Numbers: [51, 54] Generated Node #0,0,1: 65:[51, 54] Operation: 62-8=54 Exploring Operation: 62-51=11, Resulting Numbers: [8, 11] Generated Node #0,0,2: 65:[8, 11] Operation: 62-51=11 Exploring Operation: 51+8=59, Resulting Numbers: [62, 59] Generated Node #0,0,3: 65:[62, 59] Operation: 51+8=59 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 65:[8, 11], Operations: ['93-85=8', '62-51=11'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,65 unequal: No Solution Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 65:[62, 59], Operations: ['93-85=8', '51+8=59'] Exploring Operation: 62*59=3658, Resulting Numbers: [3658] 3658,65 unequal: No Solution Exploring Operation: 62+59=121, Resulting Numbers: [121] 121,65 unequal: No Solution Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 65:[51, 70], Operations: ['93-85=8', '62+8=70'] Exploring Operation: 51+70=121, Resulting Numbers: [121] 121,65 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,65 unequal: No Solution Exploring Operation: 51*70=3570, Resulting Numbers: [3570] 3570,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 65:[51, 54], Operations: ['93-85=8', '62-8=54'] Exploring Operation: 54-51=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 51*54=2754, Resulting Numbers: [2754] 2754,65 unequal: No Solution Exploring Operation: 51+54=105, Resulting Numbers: [105] 105,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 65:[62, 85, 42], Operations: ['93-51=42'] Exploring Operation: 85-62=23, Resulting Numbers: [42, 23] Generated Node #0,3,0: 65:[42, 23] Operation: 85-62=23 Exploring Operation: 62-42=20, Resulting Numbers: [85, 20] Generated Node #0,3,1: 65:[85, 20] Operation: 62-42=20 Exploring Operation: 85-42=43, Resulting Numbers: [62, 43] Generated Node #0,3,2: 65:[62, 43] Operation: 85-42=43 Exploring Operation: 62+42=104, Resulting Numbers: [85, 104] Generated Node #0,3,3: 65:[85, 104] Operation: 62+42=104 Moving to Node #0,3,2 Current State: 65:[62, 43], Operations: ['93-51=42', '85-42=43'] Exploring Operation: 62-43=19, Resulting Numbers: [19] 19,65 unequal: No Solution Exploring Operation: 62+43=105, Resulting Numbers: [105] 105,65 unequal: No Solution Exploring Operation: 62*43=2666, Resulting Numbers: [2666] 2666,65 unequal: No Solution Moving to Node #0,3,1 Current State: 65:[85, 20], Operations: ['93-51=42', '62-42=20'] Exploring Operation: 85+20=105, Resulting Numbers: [105] 105,65 unequal: No Solution Exploring Operation: 85-20=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[93, 62, 51, 85], Operations: [] Exploring Operation: 93-51=42, Resulting Numbers: [62, 85, 42] Generated Node #0,3: 65:[62, 85, 42] Operation: 93-51=42 Moving to Node #0,3 Current State: 65:[62, 85, 42], Operations: ['93-51=42'] Exploring Operation: 62-42=20, Resulting Numbers: [85, 20] Generated Node #0,3,1: 65:[85, 20] Operation: 62-42=20 Moving to Node #0,3,1 Current State: 65:[85, 20], Operations: ['93-51=42', '62-42=20'] Exploring Operation: 85-20=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
sum_heuristic
[ 73, 19, 10, 28 ]
54
[ "73+19=92", "10+28=38", "92-38=54" ]
Current State: 54:[73, 19, 10, 28], Operations: [] Exploring Operation: 73+19=92, Resulting Numbers: [10, 28, 92] Generated Node #2: [10, 28, 92] from Operation: 73+19=92 Current State: 54:[10, 28, 92], Operations: ['73+19=92'] Exploring Operation: 10+28=38, Resulting Numbers: [92, 38] Generated Node #3: [92, 38] from Operation: 10+28=38 Current State: 54:[92, 38], Operations: ['73+19=92', '10+28=38'] Exploring Operation: 92-38=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[73, 19, 10, 28], Operations: [] Exploring Operation: 73-10=63, Resulting Numbers: [19, 28, 63] Generated Node #0,0: 54:[19, 28, 63] Operation: 73-10=63 Exploring Operation: 73-28=45, Resulting Numbers: [19, 10, 45] Generated Node #0,1: 54:[19, 10, 45] Operation: 73-28=45 Exploring Operation: 73-19=54, Resulting Numbers: [10, 28, 54] Generated Node #0,2: 54:[10, 28, 54] Operation: 73-19=54 Moving to Node #0,2 Current State: 54:[10, 28, 54], Operations: ['73-19=54'] Exploring Operation: 54-28=26, Resulting Numbers: [10, 26] Generated Node #0,2,0: 54:[10, 26] Operation: 54-28=26 Exploring Operation: 28-10=18, Resulting Numbers: [54, 18] Generated Node #0,2,1: 54:[54, 18] Operation: 28-10=18 Exploring Operation: 10+28=38, Resulting Numbers: [54, 38] Generated Node #0,2,2: 54:[54, 38] Operation: 10+28=38 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 54:[54, 18], Operations: ['73-19=54', '28-10=18'] Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,54 unequal: No Solution Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 54+18=72, Resulting Numbers: [72] 72,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 54:[10, 26], Operations: ['73-19=54', '54-28=26'] Exploring Operation: 10*26=260, Resulting Numbers: [260] 260,54 unequal: No Solution Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 10+26=36, Resulting Numbers: [36] 36,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 54:[54, 38], Operations: ['73-19=54', '10+28=38'] Exploring Operation: 54-38=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 54+38=92, Resulting Numbers: [92] 92,54 unequal: No Solution Exploring Operation: 54*38=2052, Resulting Numbers: [2052] 2052,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 54:[19, 28, 63], Operations: ['73-10=63'] Exploring Operation: 63-28=35, Resulting Numbers: [19, 35] Generated Node #0,0,0: 54:[19, 35] Operation: 63-28=35 Exploring Operation: 28-19=9, Resulting Numbers: [63, 9] Generated Node #0,0,1: 54:[63, 9] Operation: 28-19=9 Exploring Operation: 63-19=44, Resulting Numbers: [28, 44] Generated Node #0,0,2: 54:[28, 44] Operation: 63-19=44 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[19, 35], Operations: ['73-10=63', '63-28=35'] Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 19+35=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[73, 19, 10, 28], Operations: [] Exploring Operation: 73-10=63, Resulting Numbers: [19, 28, 63] Generated Node #0,0: 54:[19, 28, 63] Operation: 73-10=63 Moving to Node #0,0 Current State: 54:[19, 28, 63], Operations: ['73-10=63'] Exploring Operation: 63-28=35, Resulting Numbers: [19, 35] Generated Node #0,0,0: 54:[19, 35] Operation: 63-28=35 Moving to Node #0,0,0 Current State: 54:[19, 35], Operations: ['73-10=63', '63-28=35'] Exploring Operation: 19+35=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 15, 24, 35, 46 ]
20
[ "24-15=9", "46-35=11", "9+11=20" ]
Current State: 20:[15, 24, 35, 46], Operations: [] Exploring Operation: 24-15=9, Resulting Numbers: [35, 46, 9] Generated Node #2: [35, 46, 9] from Operation: 24-15=9 Current State: 20:[35, 46, 9], Operations: ['24-15=9'] Exploring Operation: 46-35=11, Resulting Numbers: [9, 11] Generated Node #3: [9, 11] from Operation: 46-35=11 Current State: 20:[9, 11], Operations: ['24-15=9', '46-35=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[15, 24, 35, 46], Operations: [] Exploring Operation: 46-24=22, Resulting Numbers: [15, 35, 22] Generated Node #0,0: 20:[15, 35, 22] Operation: 46-24=22 Exploring Operation: 35-15=20, Resulting Numbers: [24, 46, 20] Generated Node #0,1: 20:[24, 46, 20] Operation: 35-15=20 Exploring Operation: 46-35=11, Resulting Numbers: [15, 24, 11] Generated Node #0,2: 20:[15, 24, 11] Operation: 46-35=11 Start Sub Search at level 1: Moving to Node #0,2 Current State: 20:[15, 24, 11], Operations: ['46-35=11'] Exploring Operation: 24-11=13, Resulting Numbers: [15, 13] Generated Node #0,2,0: 20:[15, 13] Operation: 24-11=13 Exploring Operation: 15-11=4, Resulting Numbers: [24, 4] Generated Node #0,2,1: 20:[24, 4] Operation: 15-11=4 Exploring Operation: 24-15=9, Resulting Numbers: [11, 9] Generated Node #0,2,2: 20:[11, 9] Operation: 24-15=9 Moving to Node #0,2,2 Current State: 20:[11, 9], Operations: ['46-35=11', '24-15=9'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,20 unequal: No Solution Exploring Operation: 11+9=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[15, 24, 35, 46], Operations: [] Exploring Operation: 46-35=11, Resulting Numbers: [15, 24, 11] Generated Node #0,2: 20:[15, 24, 11] Operation: 46-35=11 Moving to Node #0,2 Current State: 20:[15, 24, 11], Operations: ['46-35=11'] Exploring Operation: 24-15=9, Resulting Numbers: [11, 9] Generated Node #0,2,2: 20:[11, 9] Operation: 24-15=9 Moving to Node #0,2,2 Current State: 20:[11, 9], Operations: ['46-35=11', '24-15=9'] Exploring Operation: 11+9=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 55, 46, 55, 96 ]
51
[ "55/55=1", "96-46=50", "1+50=51" ]
Current State: 51:[55, 46, 55, 96], Operations: [] Exploring Operation: 55/55=1, Resulting Numbers: [46, 96, 1] Generated Node #2: [46, 96, 1] from Operation: 55/55=1 Current State: 51:[46, 96, 1], Operations: ['55/55=1'] Exploring Operation: 96-46=50, Resulting Numbers: [1, 50] Generated Node #3: [1, 50] from Operation: 96-46=50 Current State: 51:[1, 50], Operations: ['55/55=1', '96-46=50'] Exploring Operation: 1+50=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[55, 46, 55, 96], Operations: [] Exploring Operation: 96-46=50, Resulting Numbers: [55, 55, 50] Generated Node #0,0: 51:[55, 55, 50] Operation: 96-46=50 Moving to Node #0,0 Current State: 51:[55, 55, 50], Operations: ['96-46=50'] Exploring Operation: 55/55=1, Resulting Numbers: [50, 1] Generated Node #0,0,0: 51:[50, 1] Operation: 55/55=1 Moving to Node #0,0,0 Current State: 51:[50, 1], Operations: ['96-46=50', '55/55=1'] Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[55, 46, 55, 96], Operations: [] Exploring Operation: 96-46=50, Resulting Numbers: [55, 55, 50] Generated Node #0,0: 51:[55, 55, 50] Operation: 96-46=50 Moving to Node #0,0 Current State: 51:[55, 55, 50], Operations: ['96-46=50'] Exploring Operation: 55/55=1, Resulting Numbers: [50, 1] Generated Node #0,0,0: 51:[50, 1] Operation: 55/55=1 Moving to Node #0,0,0 Current State: 51:[50, 1], Operations: ['96-46=50', '55/55=1'] Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 4, 50, 73, 65 ]
46
[ "4+50=54", "73-65=8", "54-8=46" ]
Current State: 46:[4, 50, 73, 65], Operations: [] Exploring Operation: 4+50=54, Resulting Numbers: [73, 65, 54] Generated Node #2: [73, 65, 54] from Operation: 4+50=54 Current State: 46:[73, 65, 54], Operations: ['4+50=54'] Exploring Operation: 73-65=8, Resulting Numbers: [54, 8] Generated Node #3: [54, 8] from Operation: 73-65=8 Current State: 46:[54, 8], Operations: ['4+50=54', '73-65=8'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[4, 50, 73, 65], Operations: [] Exploring Operation: 73-50=23, Resulting Numbers: [4, 65, 23] Generated Node #0,0: 46:[4, 65, 23] Operation: 73-50=23 Exploring Operation: 73-65=8, Resulting Numbers: [4, 50, 8] Generated Node #0,1: 46:[4, 50, 8] Operation: 73-65=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[4, 50, 8], Operations: ['73-65=8'] Exploring Operation: 8/4=2, Resulting Numbers: [50, 2] Generated Node #0,1,0: 46:[50, 2] Operation: 8/4=2 Exploring Operation: 50-4=46, Resulting Numbers: [8, 46] Generated Node #0,1,1: 46:[8, 46] Operation: 50-4=46 Moving to Node #0,1,0 Current State: 46:[50, 2], Operations: ['73-65=8', '8/4=2'] Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,46 unequal: No Solution Moving to Node #0,1,1 Current State: 46:[8, 46], Operations: ['73-65=8', '50-4=46'] Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,46 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[4, 65, 23], Operations: ['73-50=23'] Exploring Operation: 65-23=42, Resulting Numbers: [4, 42] Generated Node #0,0,0: 46:[4, 42] Operation: 65-23=42 Exploring Operation: 65-4=61, Resulting Numbers: [23, 61] Generated Node #0,0,1: 46:[23, 61] Operation: 65-4=61 Moving to Node #0,0,0 Current State: 46:[4, 42], Operations: ['73-50=23', '65-23=42'] Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[4, 50, 73, 65], Operations: [] Exploring Operation: 73-50=23, Resulting Numbers: [4, 65, 23] Generated Node #0,0: 46:[4, 65, 23] Operation: 73-50=23 Moving to Node #0,0 Current State: 46:[4, 65, 23], Operations: ['73-50=23'] Exploring Operation: 65-23=42, Resulting Numbers: [4, 42] Generated Node #0,0,0: 46:[4, 42] Operation: 65-23=42 Moving to Node #0,0,0 Current State: 46:[4, 42], Operations: ['73-50=23', '65-23=42'] Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 81, 96, 45, 27 ]
54
[ "81/27=3", "96-45=51", "3+51=54" ]
Current State: 54:[81, 96, 45, 27], Operations: [] Exploring Operation: 81/27=3, Resulting Numbers: [96, 45, 3] Generated Node #2: [96, 45, 3] from Operation: 81/27=3 Current State: 54:[96, 45, 3], Operations: ['81/27=3'] Exploring Operation: 96-45=51, Resulting Numbers: [3, 51] Generated Node #3: [3, 51] from Operation: 96-45=51 Current State: 54:[3, 51], Operations: ['81/27=3', '96-45=51'] Exploring Operation: 3+51=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[81, 96, 45, 27], Operations: [] Exploring Operation: 81-45=36, Resulting Numbers: [96, 27, 36] Generated Node #0,0: 54:[96, 27, 36] Operation: 81-45=36 Exploring Operation: 96-81=15, Resulting Numbers: [45, 27, 15] Generated Node #0,1: 54:[45, 27, 15] Operation: 96-81=15 Exploring Operation: 96-45=51, Resulting Numbers: [81, 27, 51] Generated Node #0,2: 54:[81, 27, 51] Operation: 96-45=51 Moving to Node #0,1 Current State: 54:[45, 27, 15], Operations: ['96-81=15'] Exploring Operation: 45-15=30, Resulting Numbers: [27, 30] Generated Node #0,1,0: 54:[27, 30] Operation: 45-15=30 Exploring Operation: 45-27=18, Resulting Numbers: [15, 18] Generated Node #0,1,1: 54:[15, 18] Operation: 45-27=18 Exploring Operation: 45/15=3, Resulting Numbers: [27, 3] Generated Node #0,1,2: 54:[27, 3] Operation: 45/15=3 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 54:[27, 3], Operations: ['96-81=15', '45/15=3'] Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,54 unequal: No Solution Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 54:[27, 30], Operations: ['96-81=15', '45-15=30'] Exploring Operation: 27+30=57, Resulting Numbers: [57] 57,54 unequal: No Solution Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 27*30=810, Resulting Numbers: [810] 810,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 54:[15, 18], Operations: ['96-81=15', '45-27=18'] Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,54 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 54:[81, 27, 51], Operations: ['96-45=51'] Exploring Operation: 81-27=54, Resulting Numbers: [51, 54] Generated Node #0,2,0: 54:[51, 54] Operation: 81-27=54 Exploring Operation: 81/27=3, Resulting Numbers: [51, 3] Generated Node #0,2,1: 54:[51, 3] Operation: 81/27=3 Exploring Operation: 81-51=30, Resulting Numbers: [27, 30] Generated Node #0,2,2: 54:[27, 30] Operation: 81-51=30 Moving to Node #0,0 Current State: 54:[96, 27, 36], Operations: ['81-45=36'] Exploring Operation: 36-27=9, Resulting Numbers: [96, 9] Generated Node #0,0,0: 54:[96, 9] Operation: 36-27=9 Exploring Operation: 96-27=69, Resulting Numbers: [36, 69] Generated Node #0,0,1: 54:[36, 69] Operation: 96-27=69 Exploring Operation: 96-36=60, Resulting Numbers: [27, 60] Generated Node #0,0,2: 54:[27, 60] Operation: 96-36=60 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 54:[27, 60], Operations: ['81-45=36', '96-36=60'] Exploring Operation: 27*60=1620, Resulting Numbers: [1620] 1620,54 unequal: No Solution Exploring Operation: 27+60=87, Resulting Numbers: [87] 87,54 unequal: No Solution Exploring Operation: 60-27=33, Resulting Numbers: [33] 33,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[36, 69], Operations: ['81-45=36', '96-27=69'] Exploring Operation: 36+69=105, Resulting Numbers: [105] 105,54 unequal: No Solution Exploring Operation: 36*69=2484, Resulting Numbers: [2484] 2484,54 unequal: No Solution Exploring Operation: 69-36=33, Resulting Numbers: [33] 33,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[96, 9], Operations: ['81-45=36', '36-27=9'] Exploring Operation: 96*9=864, Resulting Numbers: [864] 864,54 unequal: No Solution Exploring Operation: 96-9=87, Resulting Numbers: [87] 87,54 unequal: No Solution Exploring Operation: 96+9=105, Resulting Numbers: [105] 105,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 54:[51, 54], Operations: ['96-45=51', '81-27=54'] Exploring Operation: 51*54=2754, Resulting Numbers: [2754] 2754,54 unequal: No Solution Exploring Operation: 54-51=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 51+54=105, Resulting Numbers: [105] 105,54 unequal: No Solution Moving to Node #0,2,1 Current State: 54:[51, 3], Operations: ['96-45=51', '81/27=3'] Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[81, 96, 45, 27], Operations: [] Exploring Operation: 96-45=51, Resulting Numbers: [81, 27, 51] Generated Node #0,2: 54:[81, 27, 51] Operation: 96-45=51 Moving to Node #0,2 Current State: 54:[81, 27, 51], Operations: ['96-45=51'] Exploring Operation: 81/27=3, Resulting Numbers: [51, 3] Generated Node #0,2,1: 54:[51, 3] Operation: 81/27=3 Moving to Node #0,2,1 Current State: 54:[51, 3], Operations: ['96-45=51', '81/27=3'] Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
0.966146
hs_3
sum_heuristic
[ 56, 77, 32, 2 ]
33
[ "56+32=88", "88/2=44", "77-44=33" ]
Current State: 33:[56, 77, 32, 2], Operations: [] Exploring Operation: 56+32=88, Resulting Numbers: [77, 2, 88] Generated Node #2: [77, 2, 88] from Operation: 56+32=88 Current State: 33:[77, 2, 88], Operations: ['56+32=88'] Exploring Operation: 88/2=44, Resulting Numbers: [77, 44] Generated Node #3: [77, 44] from Operation: 88/2=44 Current State: 33:[77, 44], Operations: ['56+32=88', '88/2=44'] Exploring Operation: 77-44=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[56, 77, 32, 2], Operations: [] Exploring Operation: 77-56=21, Resulting Numbers: [32, 2, 21] Generated Node #0,0: 33:[32, 2, 21] Operation: 77-56=21 Moving to Node #0,0 Current State: 33:[32, 2, 21], Operations: ['77-56=21'] Exploring Operation: 32-21=11, Resulting Numbers: [2, 11] Generated Node #0,0,0: 33:[2, 11] Operation: 32-21=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[2, 11], Operations: ['77-56=21', '32-21=11'] Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 5, 95, 27, 84 ]
11
[ "5+95=100", "27+84=111", "111-100=11" ]
Current State: 11:[5, 95, 27, 84], Operations: [] Exploring Operation: 5+95=100, Resulting Numbers: [27, 84, 100] Generated Node #2: [27, 84, 100] from Operation: 5+95=100 Current State: 11:[27, 84, 100], Operations: ['5+95=100'] Exploring Operation: 27+84=111, Resulting Numbers: [100, 111] Generated Node #3: [100, 111] from Operation: 27+84=111 Current State: 11:[100, 111], Operations: ['5+95=100', '27+84=111'] Exploring Operation: 111-100=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[5, 95, 27, 84], Operations: [] Exploring Operation: 95-84=11, Resulting Numbers: [5, 27, 11] Generated Node #0,0: 11:[5, 27, 11] Operation: 95-84=11 Exploring Operation: 84-27=57, Resulting Numbers: [5, 95, 57] Generated Node #0,1: 11:[5, 95, 57] Operation: 84-27=57 Exploring Operation: 95-27=68, Resulting Numbers: [5, 84, 68] Generated Node #0,2: 11:[5, 84, 68] Operation: 95-27=68 Exploring Operation: 95/5=19, Resulting Numbers: [27, 84, 19] Generated Node #0,3: 11:[27, 84, 19] Operation: 95/5=19 Moving to Node #0,0 Current State: 11:[5, 27, 11], Operations: ['95-84=11'] Exploring Operation: 5+27=32, Resulting Numbers: [11, 32] Generated Node #0,0,0: 11:[11, 32] Operation: 5+27=32 Exploring Operation: 27-11=16, Resulting Numbers: [5, 16] Generated Node #0,0,1: 11:[5, 16] Operation: 27-11=16 Exploring Operation: 5+11=16, Resulting Numbers: [27, 16] Generated Node #0,0,2: 11:[27, 16] Operation: 5+11=16 Exploring Operation: 27-5=22, Resulting Numbers: [11, 22] Generated Node #0,0,3: 11:[11, 22] Operation: 27-5=22 Moving to Node #0,3 Current State: 11:[27, 84, 19], Operations: ['95/5=19'] Exploring Operation: 27+84=111, Resulting Numbers: [19, 111] Generated Node #0,3,0: 11:[19, 111] Operation: 27+84=111 Exploring Operation: 84-19=65, Resulting Numbers: [27, 65] Generated Node #0,3,1: 11:[27, 65] Operation: 84-19=65 Exploring Operation: 27-19=8, Resulting Numbers: [84, 8] Generated Node #0,3,2: 11:[84, 8] Operation: 27-19=8 Exploring Operation: 84-27=57, Resulting Numbers: [19, 57] Generated Node #0,3,3: 11:[19, 57] Operation: 84-27=57 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 11:[19, 57], Operations: ['95/5=19', '84-27=57'] Exploring Operation: 19+57=76, Resulting Numbers: [76] 76,11 unequal: No Solution Exploring Operation: 19*57=1083, Resulting Numbers: [1083] 1083,11 unequal: No Solution Exploring Operation: 57-19=38, Resulting Numbers: [38] 38,11 unequal: No Solution Exploring Operation: 57/19=3, Resulting Numbers: [3] 3,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 11:[27, 65], Operations: ['95/5=19', '84-19=65'] Exploring Operation: 27+65=92, Resulting Numbers: [92] 92,11 unequal: No Solution Exploring Operation: 27*65=1755, Resulting Numbers: [1755] 1755,11 unequal: No Solution Exploring Operation: 65-27=38, Resulting Numbers: [38] 38,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 11:[84, 8], Operations: ['95/5=19', '27-19=8'] Exploring Operation: 84+8=92, Resulting Numbers: [92] 92,11 unequal: No Solution Exploring Operation: 84*8=672, Resulting Numbers: [672] 672,11 unequal: No Solution Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 11:[19, 111], Operations: ['95/5=19', '27+84=111'] Exploring Operation: 111-19=92, Resulting Numbers: [92] 92,11 unequal: No Solution Exploring Operation: 19*111=2109, Resulting Numbers: [2109] 2109,11 unequal: No Solution Exploring Operation: 19+111=130, Resulting Numbers: [130] 130,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 11:[5, 84, 68], Operations: ['95-27=68'] Exploring Operation: 68-5=63, Resulting Numbers: [84, 63] Generated Node #0,2,0: 11:[84, 63] Operation: 68-5=63 Exploring Operation: 5+84=89, Resulting Numbers: [68, 89] Generated Node #0,2,1: 11:[68, 89] Operation: 5+84=89 Exploring Operation: 84-68=16, Resulting Numbers: [5, 16] Generated Node #0,2,2: 11:[5, 16] Operation: 84-68=16 Exploring Operation: 84-5=79, Resulting Numbers: [68, 79] Generated Node #0,2,3: 11:[68, 79] Operation: 84-5=79 Moving to Node #0,1 Current State: 11:[5, 95, 57], Operations: ['84-27=57'] Exploring Operation: 95-57=38, Resulting Numbers: [5, 38] Generated Node #0,1,0: 11:[5, 38] Operation: 95-57=38 Exploring Operation: 57-5=52, Resulting Numbers: [95, 52] Generated Node #0,1,1: 11:[95, 52] Operation: 57-5=52 Exploring Operation: 95/5=19, Resulting Numbers: [57, 19] Generated Node #0,1,2: 11:[57, 19] Operation: 95/5=19 Exploring Operation: 95-5=90, Resulting Numbers: [57, 90] Generated Node #0,1,3: 11:[57, 90] Operation: 95-5=90 Moving to Node #0,0,1 Current State: 11:[5, 16], Operations: ['95-84=11', '27-11=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[5, 95, 27, 84], Operations: [] Exploring Operation: 95-84=11, Resulting Numbers: [5, 27, 11] Generated Node #0,0: 11:[5, 27, 11] Operation: 95-84=11 Moving to Node #0,0 Current State: 11:[5, 27, 11], Operations: ['95-84=11'] Exploring Operation: 27-11=16, Resulting Numbers: [5, 16] Generated Node #0,0,1: 11:[5, 16] Operation: 27-11=16 Moving to Node #0,0,1 Current State: 11:[5, 16], Operations: ['95-84=11', '27-11=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
0.966146
hs_4
mult_heuristic
[ 48, 11, 92, 99 ]
52
[ "48+11=59", "99-92=7", "59-7=52" ]
Current State: 52:[48, 11, 92, 99], Operations: [] Exploring Operation: 48+11=59, Resulting Numbers: [92, 99, 59] Generated Node #2: [92, 99, 59] from Operation: 48+11=59 Current State: 52:[92, 99, 59], Operations: ['48+11=59'] Exploring Operation: 99-92=7, Resulting Numbers: [59, 7] Generated Node #3: [59, 7] from Operation: 99-92=7 Current State: 52:[59, 7], Operations: ['48+11=59', '99-92=7'] Exploring Operation: 59-7=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[48, 11, 92, 99], Operations: [] Exploring Operation: 99-92=7, Resulting Numbers: [48, 11, 7] Generated Node #0,0: 52:[48, 11, 7] Operation: 99-92=7 Exploring Operation: 99-48=51, Resulting Numbers: [11, 92, 51] Generated Node #0,1: 52:[11, 92, 51] Operation: 99-48=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[48, 11, 7], Operations: ['99-92=7'] Exploring Operation: 48+7=55, Resulting Numbers: [11, 55] Generated Node #0,0,0: 52:[11, 55] Operation: 48+7=55 Exploring Operation: 11-7=4, Resulting Numbers: [48, 4] Generated Node #0,0,1: 52:[48, 4] Operation: 11-7=4 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[48, 4], Operations: ['99-92=7', '11-7=4'] Exploring Operation: 48+4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[48, 11, 92, 99], Operations: [] Exploring Operation: 99-92=7, Resulting Numbers: [48, 11, 7] Generated Node #0,0: 52:[48, 11, 7] Operation: 99-92=7 Moving to Node #0,0 Current State: 52:[48, 11, 7], Operations: ['99-92=7'] Exploring Operation: 11-7=4, Resulting Numbers: [48, 4] Generated Node #0,0,1: 52:[48, 4] Operation: 11-7=4 Moving to Node #0,0,1 Current State: 52:[48, 4], Operations: ['99-92=7', '11-7=4'] Exploring Operation: 48+4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 14, 5, 69, 49 ]
39
[ "14+5=19", "69-49=20", "19+20=39" ]
Current State: 39:[14, 5, 69, 49], Operations: [] Exploring Operation: 14+5=19, Resulting Numbers: [69, 49, 19] Generated Node #2: [69, 49, 19] from Operation: 14+5=19 Current State: 39:[69, 49, 19], Operations: ['14+5=19'] Exploring Operation: 69-49=20, Resulting Numbers: [19, 20] Generated Node #3: [19, 20] from Operation: 69-49=20 Current State: 39:[19, 20], Operations: ['14+5=19', '69-49=20'] Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[14, 5, 69, 49], Operations: [] Exploring Operation: 69-49=20, Resulting Numbers: [14, 5, 20] Generated Node #0,0: 39:[14, 5, 20] Operation: 69-49=20 Exploring Operation: 69-14=55, Resulting Numbers: [5, 49, 55] Generated Node #0,1: 39:[5, 49, 55] Operation: 69-14=55 Exploring Operation: 49-14=35, Resulting Numbers: [5, 69, 35] Generated Node #0,2: 39:[5, 69, 35] Operation: 49-14=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[14, 5, 20], Operations: ['69-49=20'] Exploring Operation: 20-14=6, Resulting Numbers: [5, 6] Generated Node #0,0,0: 39:[5, 6] Operation: 20-14=6 Exploring Operation: 20-5=15, Resulting Numbers: [14, 15] Generated Node #0,0,1: 39:[14, 15] Operation: 20-5=15 Exploring Operation: 20/5=4, Resulting Numbers: [14, 4] Generated Node #0,0,2: 39:[14, 4] Operation: 20/5=4 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 39:[14, 4], Operations: ['69-49=20', '20/5=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,39 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 39:[14, 15], Operations: ['69-49=20', '20-5=15'] Exploring Operation: 14*15=210, Resulting Numbers: [210] 210,39 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[5, 6], Operations: ['69-49=20', '20-14=6'] Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[5, 49, 55], Operations: ['69-14=55'] Exploring Operation: 49-5=44, Resulting Numbers: [55, 44] Generated Node #0,1,0: 39:[55, 44] Operation: 49-5=44 Exploring Operation: 55/5=11, Resulting Numbers: [49, 11] Generated Node #0,1,1: 39:[49, 11] Operation: 55/5=11 Exploring Operation: 55-49=6, Resulting Numbers: [5, 6] Generated Node #0,1,2: 39:[5, 6] Operation: 55-49=6 Moving to Node #0,1,2 Current State: 39:[5, 6], Operations: ['69-14=55', '55-49=6'] Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,39 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[49, 11], Operations: ['69-14=55', '55/5=11'] Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,39 unequal: No Solution Exploring Operation: 49*11=539, Resulting Numbers: [539] 539,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[55, 44], Operations: ['69-14=55', '49-5=44'] Exploring Operation: 55-44=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 55+44=99, Resulting Numbers: [99] 99,39 unequal: No Solution Exploring Operation: 55*44=2420, Resulting Numbers: [2420] 2420,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[5, 69, 35], Operations: ['49-14=35'] Exploring Operation: 69-5=64, Resulting Numbers: [35, 64] Generated Node #0,2,0: 39:[35, 64] Operation: 69-5=64 Exploring Operation: 69-35=34, Resulting Numbers: [5, 34] Generated Node #0,2,1: 39:[5, 34] Operation: 69-35=34 Exploring Operation: 5+35=40, Resulting Numbers: [69, 40] Generated Node #0,2,2: 39:[69, 40] Operation: 5+35=40 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 39:[5, 34], Operations: ['49-14=35', '69-35=34'] Exploring Operation: 5*34=170, Resulting Numbers: [170] 170,39 unequal: No Solution Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,39 unequal: No Solution Exploring Operation: 5+34=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[14, 5, 69, 49], Operations: [] Exploring Operation: 49-14=35, Resulting Numbers: [5, 69, 35] Generated Node #0,2: 39:[5, 69, 35] Operation: 49-14=35 Moving to Node #0,2 Current State: 39:[5, 69, 35], Operations: ['49-14=35'] Exploring Operation: 69-35=34, Resulting Numbers: [5, 34] Generated Node #0,2,1: 39:[5, 34] Operation: 69-35=34 Moving to Node #0,2,1 Current State: 39:[5, 34], Operations: ['49-14=35', '69-35=34'] Exploring Operation: 5+34=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_3
mult_heuristic
[ 43, 6, 30, 21 ]
88
[ "43-6=37", "30+21=51", "37+51=88" ]
Current State: 88:[43, 6, 30, 21], Operations: [] Exploring Operation: 43-6=37, Resulting Numbers: [30, 21, 37] Generated Node #2: [30, 21, 37] from Operation: 43-6=37 Current State: 88:[30, 21, 37], Operations: ['43-6=37'] Exploring Operation: 30+21=51, Resulting Numbers: [37, 51] Generated Node #3: [37, 51] from Operation: 30+21=51 Current State: 88:[37, 51], Operations: ['43-6=37', '30+21=51'] Exploring Operation: 37+51=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[43, 6, 30, 21], Operations: [] Exploring Operation: 30/6=5, Resulting Numbers: [43, 21, 5] Generated Node #0,0: 88:[43, 21, 5] Operation: 30/6=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[43, 21, 5], Operations: ['30/6=5'] Exploring Operation: 43-21=22, Resulting Numbers: [5, 22] Generated Node #0,0,0: 88:[5, 22] Operation: 43-21=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[5, 22], Operations: ['30/6=5', '43-21=22'] Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 4, 8, 67, 44 ]
76
[ "44-8=36", "36/4=9", "67+9=76" ]
Current State: 76:[4, 8, 67, 44], Operations: [] Exploring Operation: 44-8=36, Resulting Numbers: [4, 67, 36] Generated Node #2: [4, 67, 36] from Operation: 44-8=36 Current State: 76:[4, 67, 36], Operations: ['44-8=36'] Exploring Operation: 36/4=9, Resulting Numbers: [67, 9] Generated Node #3: [67, 9] from Operation: 36/4=9 Current State: 76:[67, 9], Operations: ['44-8=36', '36/4=9'] Exploring Operation: 67+9=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[4, 8, 67, 44], Operations: [] Exploring Operation: 44-8=36, Resulting Numbers: [4, 67, 36] Generated Node #0,0: 76:[4, 67, 36] Operation: 44-8=36 Exploring Operation: 8+67=75, Resulting Numbers: [4, 44, 75] Generated Node #0,1: 76:[4, 44, 75] Operation: 8+67=75 Exploring Operation: 67-44=23, Resulting Numbers: [4, 8, 23] Generated Node #0,2: 76:[4, 8, 23] Operation: 67-44=23 Exploring Operation: 8-4=4, Resulting Numbers: [67, 44, 4] Generated Node #0,3: 76:[67, 44, 4] Operation: 8-4=4 Moving to Node #0,1 Current State: 76:[4, 44, 75], Operations: ['8+67=75'] Exploring Operation: 4+75=79, Resulting Numbers: [44, 79] Generated Node #0,1,0: 76:[44, 79] Operation: 4+75=79 Exploring Operation: 44/4=11, Resulting Numbers: [75, 11] Generated Node #0,1,1: 76:[75, 11] Operation: 44/4=11 Exploring Operation: 75-44=31, Resulting Numbers: [4, 31] Generated Node #0,1,2: 76:[4, 31] Operation: 75-44=31 Exploring Operation: 44-4=40, Resulting Numbers: [75, 40] Generated Node #0,1,3: 76:[75, 40] Operation: 44-4=40 Moving to Node #0,2 Current State: 76:[4, 8, 23], Operations: ['67-44=23'] Exploring Operation: 8/4=2, Resulting Numbers: [23, 2] Generated Node #0,2,0: 76:[23, 2] Operation: 8/4=2 Exploring Operation: 23-4=19, Resulting Numbers: [8, 19] Generated Node #0,2,1: 76:[8, 19] Operation: 23-4=19 Exploring Operation: 8-4=4, Resulting Numbers: [23, 4] Generated Node #0,2,2: 76:[23, 4] Operation: 8-4=4 Exploring Operation: 23-8=15, Resulting Numbers: [4, 15] Generated Node #0,2,3: 76:[4, 15] Operation: 23-8=15 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 76:[23, 2], Operations: ['67-44=23', '8/4=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,76 unequal: No Solution Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,76 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 76:[8, 19], Operations: ['67-44=23', '23-4=19'] Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,76 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 76:[23, 4], Operations: ['67-44=23', '8-4=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 76:[4, 15], Operations: ['67-44=23', '23-8=15'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,76 unequal: No Solution Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,76 unequal: No Solution Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 76:[4, 67, 36], Operations: ['44-8=36'] Exploring Operation: 4+67=71, Resulting Numbers: [36, 71] Generated Node #0,0,0: 76:[36, 71] Operation: 4+67=71 Exploring Operation: 4+36=40, Resulting Numbers: [67, 40] Generated Node #0,0,1: 76:[67, 40] Operation: 4+36=40 Exploring Operation: 67-36=31, Resulting Numbers: [4, 31] Generated Node #0,0,2: 76:[4, 31] Operation: 67-36=31 Exploring Operation: 36/4=9, Resulting Numbers: [67, 9] Generated Node #0,0,3: 76:[67, 9] Operation: 36/4=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[36, 71], Operations: ['44-8=36', '4+67=71'] Exploring Operation: 71-36=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 36*71=2556, Resulting Numbers: [2556] 2556,76 unequal: No Solution Exploring Operation: 36+71=107, Resulting Numbers: [107] 107,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 76:[4, 31], Operations: ['44-8=36', '67-36=31'] Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,76 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 76:[67, 40], Operations: ['44-8=36', '4+36=40'] Exploring Operation: 67*40=2680, Resulting Numbers: [2680] 2680,76 unequal: No Solution Exploring Operation: 67-40=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 67+40=107, Resulting Numbers: [107] 107,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 76:[67, 9], Operations: ['44-8=36', '36/4=9'] Exploring Operation: 67*9=603, Resulting Numbers: [603] 603,76 unequal: No Solution Exploring Operation: 67+9=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[4, 8, 67, 44], Operations: [] Exploring Operation: 44-8=36, Resulting Numbers: [4, 67, 36] Generated Node #0,0: 76:[4, 67, 36] Operation: 44-8=36 Moving to Node #0,0 Current State: 76:[4, 67, 36], Operations: ['44-8=36'] Exploring Operation: 36/4=9, Resulting Numbers: [67, 9] Generated Node #0,0,3: 76:[67, 9] Operation: 36/4=9 Moving to Node #0,0,3 Current State: 76:[67, 9], Operations: ['44-8=36', '36/4=9'] Exploring Operation: 67+9=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_4
sum_heuristic
[ 45, 54, 65, 1 ]
79
[ "54*65=3510", "3510/45=78", "1+78=79" ]
Current State: 79:[45, 54, 65, 1], Operations: [] Exploring Operation: 54*65=3510, Resulting Numbers: [45, 1, 3510] Generated Node #2: [45, 1, 3510] from Operation: 54*65=3510 Current State: 79:[45, 1, 3510], Operations: ['54*65=3510'] Exploring Operation: 3510/45=78, Resulting Numbers: [1, 78] Generated Node #3: [1, 78] from Operation: 3510/45=78 Current State: 79:[1, 78], Operations: ['54*65=3510', '3510/45=78'] Exploring Operation: 1+78=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[45, 54, 65, 1], Operations: [] Exploring Operation: 54+1=55, Resulting Numbers: [45, 65, 55] Generated Node #0,0: 79:[45, 65, 55] Operation: 54+1=55 Exploring Operation: 45+1=46, Resulting Numbers: [54, 65, 46] Generated Node #0,1: 79:[54, 65, 46] Operation: 45+1=46 Exploring Operation: 45/1=45, Resulting Numbers: [54, 65, 45] Generated Node #0,2: 79:[54, 65, 45] Operation: 45/1=45 Exploring Operation: 45*1=45, Resulting Numbers: [54, 65, 45] Generated Node #0,3: 79:[54, 65, 45] Operation: 45*1=45 Exploring Operation: 65+1=66, Resulting Numbers: [45, 54, 66] Generated Node #0,4: 79:[45, 54, 66] Operation: 65+1=66 Moving to Node #0,0 Current State: 79:[45, 65, 55], Operations: ['54+1=55'] Exploring Operation: 65-45=20, Resulting Numbers: [55, 20] Generated Node #0,0,0: 79:[55, 20] Operation: 65-45=20 Exploring Operation: 45+65=110, Resulting Numbers: [55, 110] Generated Node #0,0,1: 79:[55, 110] Operation: 45+65=110 Exploring Operation: 65+55=120, Resulting Numbers: [45, 120] Generated Node #0,0,2: 79:[45, 120] Operation: 65+55=120 Exploring Operation: 45+55=100, Resulting Numbers: [65, 100] Generated Node #0,0,3: 79:[65, 100] Operation: 45+55=100 Exploring Operation: 55-45=10, Resulting Numbers: [65, 10] Generated Node #0,0,4: 79:[65, 10] Operation: 55-45=10 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 79:[65, 100], Operations: ['54+1=55', '45+55=100'] Exploring Operation: 65+100=165, Resulting Numbers: [165] 165,79 unequal: No Solution Exploring Operation: 100-65=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 65*100=6500, Resulting Numbers: [6500] 6500,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[55, 110], Operations: ['54+1=55', '45+65=110'] Exploring Operation: 110/55=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 110-55=55, Resulting Numbers: [55] 55,79 unequal: No Solution Exploring Operation: 55*110=6050, Resulting Numbers: [6050] 6050,79 unequal: No Solution Exploring Operation: 55+110=165, Resulting Numbers: [165] 165,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 79:[45, 120], Operations: ['54+1=55', '65+55=120'] Exploring Operation: 45+120=165, Resulting Numbers: [165] 165,79 unequal: No Solution Exploring Operation: 120-45=75, Resulting Numbers: [75] 75,79 unequal: No Solution Exploring Operation: 45*120=5400, Resulting Numbers: [5400] 5400,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[55, 20], Operations: ['54+1=55', '65-45=20'] Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 55+20=75, Resulting Numbers: [75] 75,79 unequal: No Solution Exploring Operation: 55*20=1100, Resulting Numbers: [1100] 1100,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 79:[65, 10], Operations: ['54+1=55', '55-45=10'] Exploring Operation: 65*10=650, Resulting Numbers: [650] 650,79 unequal: No Solution Exploring Operation: 65-10=55, Resulting Numbers: [55] 55,79 unequal: No Solution Exploring Operation: 65+10=75, Resulting Numbers: [75] 75,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 79:[45, 54, 66], Operations: ['65+1=66'] Exploring Operation: 54-45=9, Resulting Numbers: [66, 9] Generated Node #0,4,0: 79:[66, 9] Operation: 54-45=9 Exploring Operation: 45+66=111, Resulting Numbers: [54, 111] Generated Node #0,4,1: 79:[54, 111] Operation: 45+66=111 Exploring Operation: 45+54=99, Resulting Numbers: [66, 99] Generated Node #0,4,2: 79:[66, 99] Operation: 45+54=99 Exploring Operation: 54+66=120, Resulting Numbers: [45, 120] Generated Node #0,4,3: 79:[45, 120] Operation: 54+66=120 Exploring Operation: 66-45=21, Resulting Numbers: [54, 21] Generated Node #0,4,4: 79:[54, 21] Operation: 66-45=21 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 79:[66, 99], Operations: ['65+1=66', '45+54=99'] Exploring Operation: 66+99=165, Resulting Numbers: [165] 165,79 unequal: No Solution Exploring Operation: 99-66=33, Resulting Numbers: [33] 33,79 unequal: No Solution Exploring Operation: 66*99=6534, Resulting Numbers: [6534] 6534,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 79:[54, 111], Operations: ['65+1=66', '45+66=111'] Exploring Operation: 111-54=57, Resulting Numbers: [57] 57,79 unequal: No Solution Exploring Operation: 54*111=5994, Resulting Numbers: [5994] 5994,79 unequal: No Solution Exploring Operation: 54+111=165, Resulting Numbers: [165] 165,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 79:[45, 120], Operations: ['65+1=66', '54+66=120'] Exploring Operation: 120-45=75, Resulting Numbers: [75] 75,79 unequal: No Solution Exploring Operation: 45+120=165, Resulting Numbers: [165] 165,79 unequal: No Solution Exploring Operation: 45*120=5400, Resulting Numbers: [5400] 5400,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 79:[66, 9], Operations: ['65+1=66', '54-45=9'] Exploring Operation: 66-9=57, Resulting Numbers: [57] 57,79 unequal: No Solution Exploring Operation: 66*9=594, Resulting Numbers: [594] 594,79 unequal: No Solution Exploring Operation: 66+9=75, Resulting Numbers: [75] 75,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 79:[54, 21], Operations: ['65+1=66', '66-45=21'] Exploring Operation: 54-21=33, Resulting Numbers: [33] 33,79 unequal: No Solution Exploring Operation: 54*21=1134, Resulting Numbers: [1134] 1134,79 unequal: No Solution Exploring Operation: 54+21=75, Resulting Numbers: [75] 75,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 79:[54, 65, 46], Operations: ['45+1=46'] Exploring Operation: 54-46=8, Resulting Numbers: [65, 8] Generated Node #0,1,0: 79:[65, 8] Operation: 54-46=8 Exploring Operation: 65-46=19, Resulting Numbers: [54, 19] Generated Node #0,1,1: 79:[54, 19] Operation: 65-46=19 Exploring Operation: 65+46=111, Resulting Numbers: [54, 111] Generated Node #0,1,2: 79:[54, 111] Operation: 65+46=111 Exploring Operation: 54+46=100, Resulting Numbers: [65, 100] Generated Node #0,1,3: 79:[65, 100] Operation: 54+46=100 Exploring Operation: 54+65=119, Resulting Numbers: [46, 119] Generated Node #0,1,4: 79:[46, 119] Operation: 54+65=119 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 79:[65, 100], Operations: ['45+1=46', '54+46=100'] Exploring Operation: 65+100=165, Resulting Numbers: [165] 165,79 unequal: No Solution Exploring Operation: 65*100=6500, Resulting Numbers: [6500] 6500,79 unequal: No Solution Exploring Operation: 100-65=35, Resulting Numbers: [35] 35,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[54, 111], Operations: ['45+1=46', '65+46=111'] Exploring Operation: 54+111=165, Resulting Numbers: [165] 165,79 unequal: No Solution Exploring Operation: 54*111=5994, Resulting Numbers: [5994] 5994,79 unequal: No Solution Exploring Operation: 111-54=57, Resulting Numbers: [57] 57,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 79:[46, 119], Operations: ['45+1=46', '54+65=119'] Exploring Operation: 119-46=73, Resulting Numbers: [73] 73,79 unequal: No Solution Exploring Operation: 46+119=165, Resulting Numbers: [165] 165,79 unequal: No Solution Exploring Operation: 46*119=5474, Resulting Numbers: [5474] 5474,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[65, 8], Operations: ['45+1=46', '54-46=8'] Exploring Operation: 65+8=73, Resulting Numbers: [73] 73,79 unequal: No Solution Exploring Operation: 65*8=520, Resulting Numbers: [520] 520,79 unequal: No Solution Exploring Operation: 65-8=57, Resulting Numbers: [57] 57,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[54, 19], Operations: ['45+1=46', '65-46=19'] Exploring Operation: 54*19=1026, Resulting Numbers: [1026] 1026,79 unequal: No Solution Exploring Operation: 54-19=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 54+19=73, Resulting Numbers: [73] 73,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 79:[54, 65, 45], Operations: ['45/1=45'] Exploring Operation: 54+45=99, Resulting Numbers: [65, 99] Generated Node #0,2,0: 79:[65, 99] Operation: 54+45=99 Exploring Operation: 65-45=20, Resulting Numbers: [54, 20] Generated Node #0,2,1: 79:[54, 20] Operation: 65-45=20 Exploring Operation: 54-45=9, Resulting Numbers: [65, 9] Generated Node #0,2,2: 79:[65, 9] Operation: 54-45=9 Exploring Operation: 65+45=110, Resulting Numbers: [54, 110] Generated Node #0,2,3: 79:[54, 110] Operation: 65+45=110 Exploring Operation: 54+65=119, Resulting Numbers: [45, 119] Generated Node #0,2,4: 79:[45, 119] Operation: 54+65=119 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[65, 99], Operations: ['45/1=45', '54+45=99'] Exploring Operation: 99-65=34, Resulting Numbers: [34] 34,79 unequal: No Solution Exploring Operation: 65*99=6435, Resulting Numbers: [6435] 6435,79 unequal: No Solution Exploring Operation: 65+99=164, Resulting Numbers: [164] 164,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 79:[54, 110], Operations: ['45/1=45', '65+45=110'] Exploring Operation: 54*110=5940, Resulting Numbers: [5940] 5940,79 unequal: No Solution Exploring Operation: 54+110=164, Resulting Numbers: [164] 164,79 unequal: No Solution Exploring Operation: 110-54=56, Resulting Numbers: [56] 56,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 79:[45, 119], Operations: ['45/1=45', '54+65=119'] Exploring Operation: 45*119=5355, Resulting Numbers: [5355] 5355,79 unequal: No Solution Exploring Operation: 119-45=74, Resulting Numbers: [74] 74,79 unequal: No Solution Exploring Operation: 45+119=164, Resulting Numbers: [164] 164,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[54, 20], Operations: ['45/1=45', '65-45=20'] Exploring Operation: 54+20=74, Resulting Numbers: [74] 74,79 unequal: No Solution Exploring Operation: 54-20=34, Resulting Numbers: [34] 34,79 unequal: No Solution Exploring Operation: 54*20=1080, Resulting Numbers: [1080] 1080,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[65, 9], Operations: ['45/1=45', '54-45=9'] Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,79 unequal: No Solution Exploring Operation: 65*9=585, Resulting Numbers: [585] 585,79 unequal: No Solution Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 79:[54, 65, 45], Operations: ['45*1=45'] Exploring Operation: 54+45=99, Resulting Numbers: [65, 99] Generated Node #0,3,0: 79:[65, 99] Operation: 54+45=99 Exploring Operation: 65-45=20, Resulting Numbers: [54, 20] Generated Node #0,3,1: 79:[54, 20] Operation: 65-45=20 Exploring Operation: 54+65=119, Resulting Numbers: [45, 119] Generated Node #0,3,2: 79:[45, 119] Operation: 54+65=119 Exploring Operation: 54-45=9, Resulting Numbers: [65, 9] Generated Node #0,3,3: 79:[65, 9] Operation: 54-45=9 Exploring Operation: 65+45=110, Resulting Numbers: [54, 110] Generated Node #0,3,4: 79:[54, 110] Operation: 65+45=110 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 79:[65, 99], Operations: ['45*1=45', '54+45=99'] Exploring Operation: 65+99=164, Resulting Numbers: [164] 164,79 unequal: No Solution Exploring Operation: 65*99=6435, Resulting Numbers: [6435] 6435,79 unequal: No Solution Exploring Operation: 99-65=34, Resulting Numbers: [34] 34,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 79:[54, 110], Operations: ['45*1=45', '65+45=110'] Exploring Operation: 54+110=164, Resulting Numbers: [164] 164,79 unequal: No Solution Exploring Operation: 54*110=5940, Resulting Numbers: [5940] 5940,79 unequal: No Solution Exploring Operation: 110-54=56, Resulting Numbers: [56] 56,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 79:[45, 119], Operations: ['45*1=45', '54+65=119'] Exploring Operation: 45+119=164, Resulting Numbers: [164] 164,79 unequal: No Solution Exploring Operation: 45*119=5355, Resulting Numbers: [5355] 5355,79 unequal: No Solution Exploring Operation: 119-45=74, Resulting Numbers: [74] 74,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 79:[54, 20], Operations: ['45*1=45', '65-45=20'] Exploring Operation: 54*20=1080, Resulting Numbers: [1080] 1080,79 unequal: No Solution Exploring Operation: 54-20=34, Resulting Numbers: [34] 34,79 unequal: No Solution Exploring Operation: 54+20=74, Resulting Numbers: [74] 74,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 79:[65, 9], Operations: ['45*1=45', '54-45=9'] Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,79 unequal: No Solution Exploring Operation: 65*9=585, Resulting Numbers: [585] 585,79 unequal: No Solution Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 30, 12, 59, 55 ]
96
[ "30-12=18", "59+55=114", "114-18=96" ]
Current State: 96:[30, 12, 59, 55], Operations: [] Exploring Operation: 30-12=18, Resulting Numbers: [59, 55, 18] Generated Node #2: [59, 55, 18] from Operation: 30-12=18 Current State: 96:[59, 55, 18], Operations: ['30-12=18'] Exploring Operation: 59+55=114, Resulting Numbers: [18, 114] Generated Node #3: [18, 114] from Operation: 59+55=114 Current State: 96:[18, 114], Operations: ['30-12=18', '59+55=114'] Exploring Operation: 114-18=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[30, 12, 59, 55], Operations: [] Exploring Operation: 59-55=4, Resulting Numbers: [30, 12, 4] Generated Node #0,0: 96:[30, 12, 4] Operation: 59-55=4 Exploring Operation: 59-30=29, Resulting Numbers: [12, 55, 29] Generated Node #0,1: 96:[12, 55, 29] Operation: 59-30=29 Moving to Node #0,0 Current State: 96:[30, 12, 4], Operations: ['59-55=4'] Exploring Operation: 30+4=34, Resulting Numbers: [12, 34] Generated Node #0,0,0: 96:[12, 34] Operation: 30+4=34 Exploring Operation: 30-12=18, Resulting Numbers: [4, 18] Generated Node #0,0,1: 96:[4, 18] Operation: 30-12=18 Moving to Node #0,1 Current State: 96:[12, 55, 29], Operations: ['59-30=29'] Exploring Operation: 55-12=43, Resulting Numbers: [29, 43] Generated Node #0,1,0: 96:[29, 43] Operation: 55-12=43 Exploring Operation: 55-29=26, Resulting Numbers: [12, 26] Generated Node #0,1,1: 96:[12, 26] Operation: 55-29=26 Moving to Node #0,0,0 Current State: 96:[12, 34], Operations: ['59-55=4', '30+4=34'] Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 12+34=46, Resulting Numbers: [46] 46,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[12, 26], Operations: ['59-30=29', '55-29=26'] Exploring Operation: 12+26=38, Resulting Numbers: [38] 38,96 unequal: No Solution Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[4, 18], Operations: ['59-55=4', '30-12=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,96 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[29, 43], Operations: ['59-30=29', '55-12=43'] Exploring Operation: 29+43=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,96 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 20, 70, 10, 69 ]
34
[ "20/10=2", "70/2=35", "69-35=34" ]
Current State: 34:[20, 70, 10, 69], Operations: [] Exploring Operation: 20/10=2, Resulting Numbers: [70, 69, 2] Generated Node #2: [70, 69, 2] from Operation: 20/10=2 Current State: 34:[70, 69, 2], Operations: ['20/10=2'] Exploring Operation: 70/2=35, Resulting Numbers: [69, 35] Generated Node #3: [69, 35] from Operation: 70/2=35 Current State: 34:[69, 35], Operations: ['20/10=2', '70/2=35'] Exploring Operation: 69-35=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[20, 70, 10, 69], Operations: [] Exploring Operation: 70-69=1, Resulting Numbers: [20, 10, 1] Generated Node #0,0: 34:[20, 10, 1] Operation: 70-69=1 Exploring Operation: 70-10=60, Resulting Numbers: [20, 69, 60] Generated Node #0,1: 34:[20, 69, 60] Operation: 70-10=60 Exploring Operation: 70/10=7, Resulting Numbers: [20, 69, 7] Generated Node #0,2: 34:[20, 69, 7] Operation: 70/10=7 Exploring Operation: 69-20=49, Resulting Numbers: [70, 10, 49] Generated Node #0,3: 34:[70, 10, 49] Operation: 69-20=49 Exploring Operation: 70-20=50, Resulting Numbers: [10, 69, 50] Generated Node #0,4: 34:[10, 69, 50] Operation: 70-20=50 Moving to Node #0,0 Current State: 34:[20, 10, 1], Operations: ['70-69=1'] Exploring Operation: 20/10=2, Resulting Numbers: [1, 2] Generated Node #0,0,0: 34:[1, 2] Operation: 20/10=2 Exploring Operation: 20-1=19, Resulting Numbers: [10, 19] Generated Node #0,0,1: 34:[10, 19] Operation: 20-1=19 Exploring Operation: 20+10=30, Resulting Numbers: [1, 30] Generated Node #0,0,2: 34:[1, 30] Operation: 20+10=30 Exploring Operation: 10+1=11, Resulting Numbers: [20, 11] Generated Node #0,0,3: 34:[20, 11] Operation: 10+1=11 Exploring Operation: 20-10=10, Resulting Numbers: [1, 10] Generated Node #0,0,4: 34:[1, 10] Operation: 20-10=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 34:[1, 2], Operations: ['70-69=1', '20/10=2'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 34:[1, 30], Operations: ['70-69=1', '20+10=30'] Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,34 unequal: No Solution Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,34 unequal: No Solution Exploring Operation: 1+30=31, Resulting Numbers: [31] 31,34 unequal: No Solution Exploring Operation: 30/1=30, Resulting Numbers: [30] 30,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 34:[1, 10], Operations: ['70-69=1', '20-10=10'] Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,34 unequal: No Solution Exploring Operation: 1+10=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 1*10=10, Resulting Numbers: [10] 10,34 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 34:[10, 19], Operations: ['70-69=1', '20-1=19'] Exploring Operation: 10+19=29, Resulting Numbers: [29] 29,34 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,34 unequal: No Solution Exploring Operation: 10*19=190, Resulting Numbers: [190] 190,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 34:[20, 11], Operations: ['70-69=1', '10+1=11'] Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,34 unequal: No Solution Exploring Operation: 20*11=220, Resulting Numbers: [220] 220,34 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 34:[20, 69, 7], Operations: ['70/10=7'] Exploring Operation: 69-20=49, Resulting Numbers: [7, 49] Generated Node #0,2,0: 34:[7, 49] Operation: 69-20=49 Exploring Operation: 69+7=76, Resulting Numbers: [20, 76] Generated Node #0,2,1: 34:[20, 76] Operation: 69+7=76 Exploring Operation: 69-7=62, Resulting Numbers: [20, 62] Generated Node #0,2,2: 34:[20, 62] Operation: 69-7=62 Exploring Operation: 20+7=27, Resulting Numbers: [69, 27] Generated Node #0,2,3: 34:[69, 27] Operation: 20+7=27 Exploring Operation: 20-7=13, Resulting Numbers: [69, 13] Generated Node #0,2,4: 34:[69, 13] Operation: 20-7=13 Moving to Node #0,3 Current State: 34:[70, 10, 49], Operations: ['69-20=49'] Exploring Operation: 70-10=60, Resulting Numbers: [49, 60] Generated Node #0,3,0: 34:[49, 60] Operation: 70-10=60 Exploring Operation: 70-49=21, Resulting Numbers: [10, 21] Generated Node #0,3,1: 34:[10, 21] Operation: 70-49=21 Exploring Operation: 49-10=39, Resulting Numbers: [70, 39] Generated Node #0,3,2: 34:[70, 39] Operation: 49-10=39 Exploring Operation: 70+10=80, Resulting Numbers: [49, 80] Generated Node #0,3,3: 34:[49, 80] Operation: 70+10=80 Exploring Operation: 70/10=7, Resulting Numbers: [49, 7] Generated Node #0,3,4: 34:[49, 7] Operation: 70/10=7 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 34:[10, 21], Operations: ['69-20=49', '70-49=21'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 10*21=210, Resulting Numbers: [210] 210,34 unequal: No Solution Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 34:[49, 7], Operations: ['69-20=49', '70/10=7'] Exploring Operation: 49*7=343, Resulting Numbers: [343] 343,34 unequal: No Solution Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,34 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 34:[49, 60], Operations: ['69-20=49', '70-10=60'] Exploring Operation: 49+60=109, Resulting Numbers: [109] 109,34 unequal: No Solution Exploring Operation: 49*60=2940, Resulting Numbers: [2940] 2940,34 unequal: No Solution Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 34:[70, 39], Operations: ['69-20=49', '49-10=39'] Exploring Operation: 70-39=31, Resulting Numbers: [31] 31,34 unequal: No Solution Exploring Operation: 70+39=109, Resulting Numbers: [109] 109,34 unequal: No Solution Exploring Operation: 70*39=2730, Resulting Numbers: [2730] 2730,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 34:[49, 80], Operations: ['69-20=49', '70+10=80'] Exploring Operation: 49*80=3920, Resulting Numbers: [3920] 3920,34 unequal: No Solution Exploring Operation: 80-49=31, Resulting Numbers: [31] 31,34 unequal: No Solution Exploring Operation: 49+80=129, Resulting Numbers: [129] 129,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 34:[10, 69, 50], Operations: ['70-20=50'] Exploring Operation: 50-10=40, Resulting Numbers: [69, 40] Generated Node #0,4,0: 34:[69, 40] Operation: 50-10=40 Exploring Operation: 10+69=79, Resulting Numbers: [50, 79] Generated Node #0,4,1: 34:[50, 79] Operation: 10+69=79 Exploring Operation: 69-10=59, Resulting Numbers: [50, 59] Generated Node #0,4,2: 34:[50, 59] Operation: 69-10=59 Exploring Operation: 50/10=5, Resulting Numbers: [69, 5] Generated Node #0,4,3: 34:[69, 5] Operation: 50/10=5 Exploring Operation: 69-50=19, Resulting Numbers: [10, 19] Generated Node #0,4,4: 34:[10, 19] Operation: 69-50=19 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 34:[10, 19], Operations: ['70-20=50', '69-50=19'] Exploring Operation: 10+19=29, Resulting Numbers: [29] 29,34 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,34 unequal: No Solution Exploring Operation: 10*19=190, Resulting Numbers: [190] 190,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 34:[69, 5], Operations: ['70-20=50', '50/10=5'] Exploring Operation: 69*5=345, Resulting Numbers: [345] 345,34 unequal: No Solution Exploring Operation: 69+5=74, Resulting Numbers: [74] 74,34 unequal: No Solution Exploring Operation: 69-5=64, Resulting Numbers: [64] 64,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 34:[69, 40], Operations: ['70-20=50', '50-10=40'] Exploring Operation: 69+40=109, Resulting Numbers: [109] 109,34 unequal: No Solution Exploring Operation: 69*40=2760, Resulting Numbers: [2760] 2760,34 unequal: No Solution Exploring Operation: 69-40=29, Resulting Numbers: [29] 29,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 34:[50, 59], Operations: ['70-20=50', '69-10=59'] Exploring Operation: 59-50=9, Resulting Numbers: [9] 9,34 unequal: No Solution Exploring Operation: 50+59=109, Resulting Numbers: [109] 109,34 unequal: No Solution Exploring Operation: 50*59=2950, Resulting Numbers: [2950] 2950,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 34:[50, 79], Operations: ['70-20=50', '10+69=79'] Exploring Operation: 79-50=29, Resulting Numbers: [29] 29,34 unequal: No Solution Exploring Operation: 50*79=3950, Resulting Numbers: [3950] 3950,34 unequal: No Solution Exploring Operation: 50+79=129, Resulting Numbers: [129] 129,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 34:[20, 69, 60], Operations: ['70-10=60'] Exploring Operation: 60/20=3, Resulting Numbers: [69, 3] Generated Node #0,1,0: 34:[69, 3] Operation: 60/20=3 Exploring Operation: 69-20=49, Resulting Numbers: [60, 49] Generated Node #0,1,1: 34:[60, 49] Operation: 69-20=49 Exploring Operation: 60-20=40, Resulting Numbers: [69, 40] Generated Node #0,1,2: 34:[69, 40] Operation: 60-20=40 Exploring Operation: 20+69=89, Resulting Numbers: [60, 89] Generated Node #0,1,3: 34:[60, 89] Operation: 20+69=89 Exploring Operation: 69-60=9, Resulting Numbers: [20, 9] Generated Node #0,1,4: 34:[20, 9] Operation: 69-60=9 Moving to Node #0,1,4 Current State: 34:[20, 9], Operations: ['70-10=60', '69-60=9'] Exploring Operation: 20*9=180, Resulting Numbers: [180] 180,34 unequal: No Solution Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 20+9=29, Resulting Numbers: [29] 29,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[7, 49], Operations: ['70/10=7', '69-20=49'] Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,34 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,34 unequal: No Solution Exploring Operation: 7*49=343, Resulting Numbers: [343] 343,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[20, 62], Operations: ['70/10=7', '69-7=62'] Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,34 unequal: No Solution Exploring Operation: 20*62=1240, Resulting Numbers: [1240] 1240,34 unequal: No Solution Exploring Operation: 20+62=82, Resulting Numbers: [82] 82,34 unequal: No Solution Moving to Node #0,1,0 Current State: 34:[69, 3], Operations: ['70-10=60', '60/20=3'] Exploring Operation: 69+3=72, Resulting Numbers: [72] 72,34 unequal: No Solution Exploring Operation: 69*3=207, Resulting Numbers: [207] 207,34 unequal: No Solution Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,34 unequal: No Solution Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,34 unequal: No Solution Moving to Node #0,2,4 Current State: 34:[69, 13], Operations: ['70/10=7', '20-7=13'] Exploring Operation: 69*13=897, Resulting Numbers: [897] 897,34 unequal: No Solution Exploring Operation: 69+13=82, Resulting Numbers: [82] 82,34 unequal: No Solution Exploring Operation: 69-13=56, Resulting Numbers: [56] 56,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[60, 49], Operations: ['70-10=60', '69-20=49'] Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 60+49=109, Resulting Numbers: [109] 109,34 unequal: No Solution Exploring Operation: 60*49=2940, Resulting Numbers: [2940] 2940,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[69, 40], Operations: ['70-10=60', '60-20=40'] Exploring Operation: 69*40=2760, Resulting Numbers: [2760] 2760,34 unequal: No Solution Exploring Operation: 69-40=29, Resulting Numbers: [29] 29,34 unequal: No Solution Exploring Operation: 69+40=109, Resulting Numbers: [109] 109,34 unequal: No Solution Moving to Node #0,2,3 Current State: 34:[69, 27], Operations: ['70/10=7', '20+7=27'] Exploring Operation: 69-27=42, Resulting Numbers: [42] 42,34 unequal: No Solution Exploring Operation: 69+27=96, Resulting Numbers: [96] 96,34 unequal: No Solution Exploring Operation: 69*27=1863, Resulting Numbers: [1863] 1863,34 unequal: No Solution Moving to Node #0,2,1 Current State: 34:[20, 76], Operations: ['70/10=7', '69+7=76'] Exploring Operation: 20*76=1520, Resulting Numbers: [1520] 1520,34 unequal: No Solution Exploring Operation: 20+76=96, Resulting Numbers: [96] 96,34 unequal: No Solution Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,34 unequal: No Solution Moving to Node #0,1,3 Current State: 34:[60, 89], Operations: ['70-10=60', '20+69=89'] Exploring Operation: 89-60=29, Resulting Numbers: [29] 29,34 unequal: No Solution Exploring Operation: 60+89=149, Resulting Numbers: [149] 149,34 unequal: No Solution Exploring Operation: 60*89=5340, Resulting Numbers: [5340] 5340,34 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 9, 14, 21, 59 ]
88
[ "9*14=126", "59-21=38", "126-38=88" ]
Current State: 88:[9, 14, 21, 59], Operations: [] Exploring Operation: 9*14=126, Resulting Numbers: [21, 59, 126] Generated Node #2: [21, 59, 126] from Operation: 9*14=126 Current State: 88:[21, 59, 126], Operations: ['9*14=126'] Exploring Operation: 59-21=38, Resulting Numbers: [126, 38] Generated Node #3: [126, 38] from Operation: 59-21=38 Current State: 88:[126, 38], Operations: ['9*14=126', '59-21=38'] Exploring Operation: 126-38=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[9, 14, 21, 59], Operations: [] Exploring Operation: 59-14=45, Resulting Numbers: [9, 21, 45] Generated Node #0,0: 88:[9, 21, 45] Operation: 59-14=45 Exploring Operation: 59-9=50, Resulting Numbers: [14, 21, 50] Generated Node #0,1: 88:[14, 21, 50] Operation: 59-9=50 Moving to Node #0,0 Current State: 88:[9, 21, 45], Operations: ['59-14=45'] Exploring Operation: 45/9=5, Resulting Numbers: [21, 5] Generated Node #0,0,0: 88:[21, 5] Operation: 45/9=5 Exploring Operation: 21-9=12, Resulting Numbers: [45, 12] Generated Node #0,0,1: 88:[45, 12] Operation: 21-9=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[21, 5], Operations: ['59-14=45', '45/9=5'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,88 unequal: No Solution Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 88:[45, 12], Operations: ['59-14=45', '21-9=12'] Exploring Operation: 45+12=57, Resulting Numbers: [57] 57,88 unequal: No Solution Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 88:[14, 21, 50], Operations: ['59-9=50'] Exploring Operation: 21-14=7, Resulting Numbers: [50, 7] Generated Node #0,1,0: 88:[50, 7] Operation: 21-14=7 Exploring Operation: 50-14=36, Resulting Numbers: [21, 36] Generated Node #0,1,1: 88:[21, 36] Operation: 50-14=36 Moving to Node #0,1,0 Current State: 88:[50, 7], Operations: ['59-9=50', '21-14=7'] Exploring Operation: 50+7=57, Resulting Numbers: [57] 57,88 unequal: No Solution Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[21, 36], Operations: ['59-9=50', '50-14=36'] Exploring Operation: 21+36=57, Resulting Numbers: [57] 57,88 unequal: No Solution Exploring Operation: 36-21=15, Resulting Numbers: [15] 15,88 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 33, 27, 18, 39 ]
54
[ "39-33=6", "27-18=9", "6*9=54" ]
Current State: 54:[33, 27, 18, 39], Operations: [] Exploring Operation: 39-33=6, Resulting Numbers: [27, 18, 6] Generated Node #2: [27, 18, 6] from Operation: 39-33=6 Current State: 54:[27, 18, 6], Operations: ['39-33=6'] Exploring Operation: 27-18=9, Resulting Numbers: [6, 9] Generated Node #3: [6, 9] from Operation: 27-18=9 Current State: 54:[6, 9], Operations: ['39-33=6', '27-18=9'] Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[33, 27, 18, 39], Operations: [] Exploring Operation: 39-33=6, Resulting Numbers: [27, 18, 6] Generated Node #0,0: 54:[27, 18, 6] Operation: 39-33=6 Exploring Operation: 39-27=12, Resulting Numbers: [33, 18, 12] Generated Node #0,1: 54:[33, 18, 12] Operation: 39-27=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[27, 18, 6], Operations: ['39-33=6'] Exploring Operation: 27-18=9, Resulting Numbers: [6, 9] Generated Node #0,0,0: 54:[6, 9] Operation: 27-18=9 Exploring Operation: 18/6=3, Resulting Numbers: [27, 3] Generated Node #0,0,1: 54:[27, 3] Operation: 18/6=3 Moving to Node #0,0,0 Current State: 54:[6, 9], Operations: ['39-33=6', '27-18=9'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[33, 27, 18, 39], Operations: [] Exploring Operation: 39-33=6, Resulting Numbers: [27, 18, 6] Generated Node #0,0: 54:[27, 18, 6] Operation: 39-33=6 Moving to Node #0,0 Current State: 54:[27, 18, 6], Operations: ['39-33=6'] Exploring Operation: 27-18=9, Resulting Numbers: [6, 9] Generated Node #0,0,0: 54:[6, 9] Operation: 27-18=9 Moving to Node #0,0,0 Current State: 54:[6, 9], Operations: ['39-33=6', '27-18=9'] Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 66, 62, 71, 78 ]
16
[ "66+78=144", "71-62=9", "144/9=16" ]
Current State: 16:[66, 62, 71, 78], Operations: [] Exploring Operation: 66+78=144, Resulting Numbers: [62, 71, 144] Generated Node #2: [62, 71, 144] from Operation: 66+78=144 Current State: 16:[62, 71, 144], Operations: ['66+78=144'] Exploring Operation: 71-62=9, Resulting Numbers: [144, 9] Generated Node #3: [144, 9] from Operation: 71-62=9 Current State: 16:[144, 9], Operations: ['66+78=144', '71-62=9'] Exploring Operation: 144/9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[66, 62, 71, 78], Operations: [] Exploring Operation: 78-71=7, Resulting Numbers: [66, 62, 7] Generated Node #0,0: 16:[66, 62, 7] Operation: 78-71=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[66, 62, 7], Operations: ['78-71=7'] Exploring Operation: 66-62=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 16:[7, 4] Operation: 66-62=4 Moving to Node #0,0,0 Current State: 16:[7, 4], Operations: ['78-71=7', '66-62=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 13, 49, 64, 52 ]
65
[ "13*64=832", "832/52=16", "49+16=65" ]
Current State: 65:[13, 49, 64, 52], Operations: [] Exploring Operation: 13*64=832, Resulting Numbers: [49, 52, 832] Generated Node #2: [49, 52, 832] from Operation: 13*64=832 Current State: 65:[49, 52, 832], Operations: ['13*64=832'] Exploring Operation: 832/52=16, Resulting Numbers: [49, 16] Generated Node #3: [49, 16] from Operation: 832/52=16 Current State: 65:[49, 16], Operations: ['13*64=832', '832/52=16'] Exploring Operation: 49+16=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[13, 49, 64, 52], Operations: [] Exploring Operation: 52-49=3, Resulting Numbers: [13, 64, 3] Generated Node #0,0: 65:[13, 64, 3] Operation: 52-49=3 Exploring Operation: 64-49=15, Resulting Numbers: [13, 52, 15] Generated Node #0,1: 65:[13, 52, 15] Operation: 64-49=15 Exploring Operation: 13+49=62, Resulting Numbers: [64, 52, 62] Generated Node #0,2: 65:[64, 52, 62] Operation: 13+49=62 Moving to Node #0,0 Current State: 65:[13, 64, 3], Operations: ['52-49=3'] Exploring Operation: 13+3=16, Resulting Numbers: [64, 16] Generated Node #0,0,0: 65:[64, 16] Operation: 13+3=16 Exploring Operation: 13-3=10, Resulting Numbers: [64, 10] Generated Node #0,0,1: 65:[64, 10] Operation: 13-3=10 Exploring Operation: 64+3=67, Resulting Numbers: [13, 67] Generated Node #0,0,2: 65:[13, 67] Operation: 64+3=67 Moving to Node #0,1 Current State: 65:[13, 52, 15], Operations: ['64-49=15'] Exploring Operation: 52/13=4, Resulting Numbers: [15, 4] Generated Node #0,1,0: 65:[15, 4] Operation: 52/13=4 Exploring Operation: 52+15=67, Resulting Numbers: [13, 67] Generated Node #0,1,1: 65:[13, 67] Operation: 52+15=67 Exploring Operation: 13+52=65, Resulting Numbers: [15, 65] Generated Node #0,1,2: 65:[15, 65] Operation: 13+52=65 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[13, 67], Operations: ['64-49=15', '52+15=67'] Exploring Operation: 13*67=871, Resulting Numbers: [871] 871,65 unequal: No Solution Exploring Operation: 67-13=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 13+67=80, Resulting Numbers: [80] 80,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[15, 65], Operations: ['64-49=15', '13+52=65'] Exploring Operation: 15*65=975, Resulting Numbers: [975] 975,65 unequal: No Solution Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,65 unequal: No Solution Exploring Operation: 15+65=80, Resulting Numbers: [80] 80,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[15, 4], Operations: ['64-49=15', '52/13=4'] Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,65 unequal: No Solution Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,65 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 65:[64, 52, 62], Operations: ['13+49=62'] Exploring Operation: 64-62=2, Resulting Numbers: [52, 2] Generated Node #0,2,0: 65:[52, 2] Operation: 64-62=2 Exploring Operation: 64-52=12, Resulting Numbers: [62, 12] Generated Node #0,2,1: 65:[62, 12] Operation: 64-52=12 Exploring Operation: 62-52=10, Resulting Numbers: [64, 10] Generated Node #0,2,2: 65:[64, 10] Operation: 62-52=10 Moving to Node #0,0,2 Current State: 65:[13, 67], Operations: ['52-49=3', '64+3=67'] Exploring Operation: 13*67=871, Resulting Numbers: [871] 871,65 unequal: No Solution Exploring Operation: 67-13=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 13+67=80, Resulting Numbers: [80] 80,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[64, 10], Operations: ['52-49=3', '13-3=10'] Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,65 unequal: No Solution Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 64*10=640, Resulting Numbers: [640] 640,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[64, 16], Operations: ['52-49=3', '13+3=16'] Exploring Operation: 64-16=48, Resulting Numbers: [48] 48,65 unequal: No Solution Exploring Operation: 64/16=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 64+16=80, Resulting Numbers: [80] 80,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[62, 12], Operations: ['13+49=62', '64-52=12'] Exploring Operation: 62-12=50, Resulting Numbers: [50] 50,65 unequal: No Solution Exploring Operation: 62+12=74, Resulting Numbers: [74] 74,65 unequal: No Solution Exploring Operation: 62*12=744, Resulting Numbers: [744] 744,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[64, 10], Operations: ['13+49=62', '62-52=10'] Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,65 unequal: No Solution Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 64*10=640, Resulting Numbers: [640] 640,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[52, 2], Operations: ['13+49=62', '64-62=2'] Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,65 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 3, 50, 68, 57 ]
89
[ "57-50=7", "3*7=21", "68+21=89" ]
Current State: 89:[3, 50, 68, 57], Operations: [] Exploring Operation: 57-50=7, Resulting Numbers: [3, 68, 7] Generated Node #2: [3, 68, 7] from Operation: 57-50=7 Current State: 89:[3, 68, 7], Operations: ['57-50=7'] Exploring Operation: 3*7=21, Resulting Numbers: [68, 21] Generated Node #3: [68, 21] from Operation: 3*7=21 Current State: 89:[68, 21], Operations: ['57-50=7', '3*7=21'] Exploring Operation: 68+21=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[3, 50, 68, 57], Operations: [] Exploring Operation: 3+50=53, Resulting Numbers: [68, 57, 53] Generated Node #0,0: 89:[68, 57, 53] Operation: 3+50=53 Exploring Operation: 3+68=71, Resulting Numbers: [50, 57, 71] Generated Node #0,1: 89:[50, 57, 71] Operation: 3+68=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[68, 57, 53], Operations: ['3+50=53'] Exploring Operation: 68+53=121, Resulting Numbers: [57, 121] Generated Node #0,0,0: 89:[57, 121] Operation: 68+53=121 Exploring Operation: 57+53=110, Resulting Numbers: [68, 110] Generated Node #0,0,1: 89:[68, 110] Operation: 57+53=110 Moving to Node #0,0,1 Current State: 89:[68, 110], Operations: ['3+50=53', '57+53=110'] Exploring Operation: 110-68=42, Resulting Numbers: [42] 42,89 unequal: No Solution Exploring Operation: 68+110=178, Resulting Numbers: [178] 178,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[57, 121], Operations: ['3+50=53', '68+53=121'] Exploring Operation: 57+121=178, Resulting Numbers: [178] 178,89 unequal: No Solution Exploring Operation: 121-57=64, Resulting Numbers: [64] 64,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[50, 57, 71], Operations: ['3+68=71'] Exploring Operation: 50+71=121, Resulting Numbers: [57, 121] Generated Node #0,1,0: 89:[57, 121] Operation: 50+71=121 Exploring Operation: 50+57=107, Resulting Numbers: [71, 107] Generated Node #0,1,1: 89:[71, 107] Operation: 50+57=107 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 89:[71, 107], Operations: ['3+68=71', '50+57=107'] Exploring Operation: 71+107=178, Resulting Numbers: [178] 178,89 unequal: No Solution Exploring Operation: 107-71=36, Resulting Numbers: [36] 36,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[57, 121], Operations: ['3+68=71', '50+71=121'] Exploring Operation: 121-57=64, Resulting Numbers: [64] 64,89 unequal: No Solution Exploring Operation: 57+121=178, Resulting Numbers: [178] 178,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 45, 4, 8, 61 ]
94
[ "45-4=41", "61-8=53", "41+53=94" ]
Current State: 94:[45, 4, 8, 61], Operations: [] Exploring Operation: 45-4=41, Resulting Numbers: [8, 61, 41] Generated Node #2: [8, 61, 41] from Operation: 45-4=41 Current State: 94:[8, 61, 41], Operations: ['45-4=41'] Exploring Operation: 61-8=53, Resulting Numbers: [41, 53] Generated Node #3: [41, 53] from Operation: 61-8=53 Current State: 94:[41, 53], Operations: ['45-4=41', '61-8=53'] Exploring Operation: 41+53=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[45, 4, 8, 61], Operations: [] Exploring Operation: 61-8=53, Resulting Numbers: [45, 4, 53] Generated Node #0,0: 94:[45, 4, 53] Operation: 61-8=53 Exploring Operation: 61-4=57, Resulting Numbers: [45, 8, 57] Generated Node #0,1: 94:[45, 8, 57] Operation: 61-4=57 Exploring Operation: 8-4=4, Resulting Numbers: [45, 61, 4] Generated Node #0,2: 94:[45, 61, 4] Operation: 8-4=4 Exploring Operation: 8/4=2, Resulting Numbers: [45, 61, 2] Generated Node #0,3: 94:[45, 61, 2] Operation: 8/4=2 Moving to Node #0,0 Current State: 94:[45, 4, 53], Operations: ['61-8=53'] Exploring Operation: 45+53=98, Resulting Numbers: [4, 98] Generated Node #0,0,0: 94:[4, 98] Operation: 45+53=98 Exploring Operation: 53-45=8, Resulting Numbers: [4, 8] Generated Node #0,0,1: 94:[4, 8] Operation: 53-45=8 Exploring Operation: 45+4=49, Resulting Numbers: [53, 49] Generated Node #0,0,2: 94:[53, 49] Operation: 45+4=49 Exploring Operation: 53-4=49, Resulting Numbers: [45, 49] Generated Node #0,0,3: 94:[45, 49] Operation: 53-4=49 Moving to Node #0,3 Current State: 94:[45, 61, 2], Operations: ['8/4=2'] Exploring Operation: 61-2=59, Resulting Numbers: [45, 59] Generated Node #0,3,0: 94:[45, 59] Operation: 61-2=59 Exploring Operation: 45+61=106, Resulting Numbers: [2, 106] Generated Node #0,3,1: 94:[2, 106] Operation: 45+61=106 Exploring Operation: 61-45=16, Resulting Numbers: [2, 16] Generated Node #0,3,2: 94:[2, 16] Operation: 61-45=16 Exploring Operation: 45+2=47, Resulting Numbers: [61, 47] Generated Node #0,3,3: 94:[61, 47] Operation: 45+2=47 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 94:[2, 106], Operations: ['8/4=2', '45+61=106'] Exploring Operation: 106-2=104, Resulting Numbers: [104] 104,94 unequal: No Solution Exploring Operation: 2+106=108, Resulting Numbers: [108] 108,94 unequal: No Solution Exploring Operation: 2*106=212, Resulting Numbers: [212] 212,94 unequal: No Solution Exploring Operation: 106/2=53, Resulting Numbers: [53] 53,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 94:[45, 59], Operations: ['8/4=2', '61-2=59'] Exploring Operation: 59-45=14, Resulting Numbers: [14] 14,94 unequal: No Solution Exploring Operation: 45+59=104, Resulting Numbers: [104] 104,94 unequal: No Solution Exploring Operation: 45*59=2655, Resulting Numbers: [2655] 2655,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 94:[2, 16], Operations: ['8/4=2', '61-45=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,94 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,94 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 94:[61, 47], Operations: ['8/4=2', '45+2=47'] Exploring Operation: 61-47=14, Resulting Numbers: [14] 14,94 unequal: No Solution Exploring Operation: 61*47=2867, Resulting Numbers: [2867] 2867,94 unequal: No Solution Exploring Operation: 61+47=108, Resulting Numbers: [108] 108,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 94:[45, 61, 4], Operations: ['8-4=4'] Exploring Operation: 45+61=106, Resulting Numbers: [4, 106] Generated Node #0,2,0: 94:[4, 106] Operation: 45+61=106 Exploring Operation: 45+4=49, Resulting Numbers: [61, 49] Generated Node #0,2,1: 94:[61, 49] Operation: 45+4=49 Exploring Operation: 61-4=57, Resulting Numbers: [45, 57] Generated Node #0,2,2: 94:[45, 57] Operation: 61-4=57 Exploring Operation: 61-45=16, Resulting Numbers: [4, 16] Generated Node #0,2,3: 94:[4, 16] Operation: 61-45=16 Moving to Node #0,1 Current State: 94:[45, 8, 57], Operations: ['61-4=57'] Exploring Operation: 45+8=53, Resulting Numbers: [57, 53] Generated Node #0,1,0: 94:[57, 53] Operation: 45+8=53 Exploring Operation: 57-8=49, Resulting Numbers: [45, 49] Generated Node #0,1,1: 94:[45, 49] Operation: 57-8=49 Exploring Operation: 45+57=102, Resulting Numbers: [8, 102] Generated Node #0,1,2: 94:[8, 102] Operation: 45+57=102 Exploring Operation: 57-45=12, Resulting Numbers: [8, 12] Generated Node #0,1,3: 94:[8, 12] Operation: 57-45=12 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 94:[45, 49], Operations: ['61-4=57', '57-8=49'] Exploring Operation: 45*49=2205, Resulting Numbers: [2205] 2205,94 unequal: No Solution Exploring Operation: 45+49=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[45, 4, 8, 61], Operations: [] Exploring Operation: 61-4=57, Resulting Numbers: [45, 8, 57] Generated Node #0,1: 94:[45, 8, 57] Operation: 61-4=57 Moving to Node #0,1 Current State: 94:[45, 8, 57], Operations: ['61-4=57'] Exploring Operation: 57-8=49, Resulting Numbers: [45, 49] Generated Node #0,1,1: 94:[45, 49] Operation: 57-8=49 Moving to Node #0,1,1 Current State: 94:[45, 49], Operations: ['61-4=57', '57-8=49'] Exploring Operation: 45+49=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_4
mult_heuristic
[ 5, 18, 9, 2 ]
44
[ "18-5=13", "9+13=22", "2*22=44" ]
Current State: 44:[5, 18, 9, 2], Operations: [] Exploring Operation: 18-5=13, Resulting Numbers: [9, 2, 13] Generated Node #2: [9, 2, 13] from Operation: 18-5=13 Current State: 44:[9, 2, 13], Operations: ['18-5=13'] Exploring Operation: 9+13=22, Resulting Numbers: [2, 22] Generated Node #3: [2, 22] from Operation: 9+13=22 Current State: 44:[2, 22], Operations: ['18-5=13', '9+13=22'] Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[5, 18, 9, 2], Operations: [] Exploring Operation: 5+18=23, Resulting Numbers: [9, 2, 23] Generated Node #0,0: 44:[9, 2, 23] Operation: 5+18=23 Exploring Operation: 18/9=2, Resulting Numbers: [5, 2, 2] Generated Node #0,1: 44:[5, 2, 2] Operation: 18/9=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[5, 2, 2], Operations: ['18/9=2'] Exploring Operation: 5-2=3, Resulting Numbers: [2, 3] Generated Node #0,1,0: 44:[2, 3] Operation: 5-2=3 Exploring Operation: 5*2=10, Resulting Numbers: [2, 10] Generated Node #0,1,1: 44:[2, 10] Operation: 5*2=10 Moving to Node #0,1,0 Current State: 44:[2, 3], Operations: ['18/9=2', '5-2=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,44 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[2, 10], Operations: ['18/9=2', '5*2=10'] Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[9, 2, 23], Operations: ['5+18=23'] Exploring Operation: 23-9=14, Resulting Numbers: [2, 14] Generated Node #0,0,0: 44:[2, 14] Operation: 23-9=14 Exploring Operation: 9+2=11, Resulting Numbers: [23, 11] Generated Node #0,0,1: 44:[23, 11] Operation: 9+2=11 Moving to Node #0,0,1 Current State: 44:[23, 11], Operations: ['5+18=23', '9+2=11'] Exploring Operation: 23+11=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,44 unequal: No Solution Moving to Node #0,0,0 Current State: 44:[2, 14], Operations: ['5+18=23', '23-9=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,44 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 41, 35, 73, 33 ]
100
[ "41-35=6", "73+33=106", "106-6=100" ]
Current State: 100:[41, 35, 73, 33], Operations: [] Exploring Operation: 41-35=6, Resulting Numbers: [73, 33, 6] Generated Node #2: [73, 33, 6] from Operation: 41-35=6 Current State: 100:[73, 33, 6], Operations: ['41-35=6'] Exploring Operation: 73+33=106, Resulting Numbers: [6, 106] Generated Node #3: [6, 106] from Operation: 73+33=106 Current State: 100:[6, 106], Operations: ['41-35=6', '73+33=106'] Exploring Operation: 106-6=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[41, 35, 73, 33], Operations: [] Exploring Operation: 35+73=108, Resulting Numbers: [41, 33, 108] Generated Node #0,0: 100:[41, 33, 108] Operation: 35+73=108 Exploring Operation: 73-35=38, Resulting Numbers: [41, 33, 38] Generated Node #0,1: 100:[41, 33, 38] Operation: 73-35=38 Exploring Operation: 73+33=106, Resulting Numbers: [41, 35, 106] Generated Node #0,2: 100:[41, 35, 106] Operation: 73+33=106 Exploring Operation: 73-41=32, Resulting Numbers: [35, 33, 32] Generated Node #0,3: 100:[35, 33, 32] Operation: 73-41=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[41, 33, 108], Operations: ['35+73=108'] Exploring Operation: 41-33=8, Resulting Numbers: [108, 8] Generated Node #0,0,0: 100:[108, 8] Operation: 41-33=8 Exploring Operation: 41+33=74, Resulting Numbers: [108, 74] Generated Node #0,0,1: 100:[108, 74] Operation: 41+33=74 Exploring Operation: 108-33=75, Resulting Numbers: [41, 75] Generated Node #0,0,2: 100:[41, 75] Operation: 108-33=75 Exploring Operation: 108-41=67, Resulting Numbers: [33, 67] Generated Node #0,0,3: 100:[33, 67] Operation: 108-41=67 Moving to Node #0,0,0 Current State: 100:[108, 8], Operations: ['35+73=108', '41-33=8'] Exploring Operation: 108+8=116, Resulting Numbers: [116] 116,100 unequal: No Solution Exploring Operation: 108-8=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[41, 35, 73, 33], Operations: [] Exploring Operation: 35+73=108, Resulting Numbers: [41, 33, 108] Generated Node #0,0: 100:[41, 33, 108] Operation: 35+73=108 Moving to Node #0,0 Current State: 100:[41, 33, 108], Operations: ['35+73=108'] Exploring Operation: 41-33=8, Resulting Numbers: [108, 8] Generated Node #0,0,0: 100:[108, 8] Operation: 41-33=8 Moving to Node #0,0,0 Current State: 100:[108, 8], Operations: ['35+73=108', '41-33=8'] Exploring Operation: 108-8=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 14, 28, 13, 67 ]
39
[ "14-13=1", "67-28=39", "1*39=39" ]
Current State: 39:[14, 28, 13, 67], Operations: [] Exploring Operation: 14-13=1, Resulting Numbers: [28, 67, 1] Generated Node #2: [28, 67, 1] from Operation: 14-13=1 Current State: 39:[28, 67, 1], Operations: ['14-13=1'] Exploring Operation: 67-28=39, Resulting Numbers: [1, 39] Generated Node #3: [1, 39] from Operation: 67-28=39 Current State: 39:[1, 39], Operations: ['14-13=1', '67-28=39'] Exploring Operation: 1*39=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[14, 28, 13, 67], Operations: [] Exploring Operation: 67-13=54, Resulting Numbers: [14, 28, 54] Generated Node #0,0: 39:[14, 28, 54] Operation: 67-13=54 Exploring Operation: 67-28=39, Resulting Numbers: [14, 13, 39] Generated Node #0,1: 39:[14, 13, 39] Operation: 67-28=39 Exploring Operation: 67-14=53, Resulting Numbers: [28, 13, 53] Generated Node #0,2: 39:[28, 13, 53] Operation: 67-14=53 Exploring Operation: 28-14=14, Resulting Numbers: [13, 67, 14] Generated Node #0,3: 39:[13, 67, 14] Operation: 28-14=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[14, 13, 39], Operations: ['67-28=39'] Exploring Operation: 14+13=27, Resulting Numbers: [39, 27] Generated Node #0,1,0: 39:[39, 27] Operation: 14+13=27 Exploring Operation: 14-13=1, Resulting Numbers: [39, 1] Generated Node #0,1,1: 39:[39, 1] Operation: 14-13=1 Exploring Operation: 39-14=25, Resulting Numbers: [13, 25] Generated Node #0,1,2: 39:[13, 25] Operation: 39-14=25 Exploring Operation: 39/13=3, Resulting Numbers: [14, 3] Generated Node #0,1,3: 39:[14, 3] Operation: 39/13=3 Moving to Node #0,1,3 Current State: 39:[14, 3], Operations: ['67-28=39', '39/13=3'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,39 unequal: No Solution Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[39, 1], Operations: ['67-28=39', '14-13=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[14, 28, 13, 67], Operations: [] Exploring Operation: 67-28=39, Resulting Numbers: [14, 13, 39] Generated Node #0,1: 39:[14, 13, 39] Operation: 67-28=39 Moving to Node #0,1 Current State: 39:[14, 13, 39], Operations: ['67-28=39'] Exploring Operation: 14-13=1, Resulting Numbers: [39, 1] Generated Node #0,1,1: 39:[39, 1] Operation: 14-13=1 Moving to Node #0,1,1 Current State: 39:[39, 1], Operations: ['67-28=39', '14-13=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 28, 60, 46, 32 ]
46
[ "60-28=32", "46+32=78", "78-32=46" ]
Current State: 46:[28, 60, 46, 32], Operations: [] Exploring Operation: 60-28=32, Resulting Numbers: [46, 32, 32] Generated Node #2: [46, 32, 32] from Operation: 60-28=32 Current State: 46:[46, 32, 32], Operations: ['60-28=32'] Exploring Operation: 46+32=78, Resulting Numbers: [78] 78,46 equal: Goal Reached Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[28, 60, 46, 32], Operations: [] Exploring Operation: 60-32=28, Resulting Numbers: [28, 46, 28] Generated Node #0,0: 46:[28, 46, 28] Operation: 60-32=28 Exploring Operation: 32-28=4, Resulting Numbers: [60, 46, 4] Generated Node #0,1: 46:[60, 46, 4] Operation: 32-28=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[28, 46, 28], Operations: ['60-32=28'] Exploring Operation: 28-28=0, Resulting Numbers: [46, 0] Generated Node #0,0,0: 46:[46, 0] Operation: 28-28=0 Exploring Operation: 28/28=1, Resulting Numbers: [46, 1] Generated Node #0,0,1: 46:[46, 1] Operation: 28/28=1 Moving to Node #0,0,1 Current State: 46:[46, 1], Operations: ['60-32=28', '28/28=1'] Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[28, 60, 46, 32], Operations: [] Exploring Operation: 60-32=28, Resulting Numbers: [28, 46, 28] Generated Node #0,0: 46:[28, 46, 28] Operation: 60-32=28 Moving to Node #0,0 Current State: 46:[28, 46, 28], Operations: ['60-32=28'] Exploring Operation: 28/28=1, Resulting Numbers: [46, 1] Generated Node #0,0,1: 46:[46, 1] Operation: 28/28=1 Moving to Node #0,0,1 Current State: 46:[46, 1], Operations: ['60-32=28', '28/28=1'] Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 2, 21, 72, 29 ]
68
[ "29-21=8", "8/2=4", "72-4=68" ]
Current State: 68:[2, 21, 72, 29], Operations: [] Exploring Operation: 29-21=8, Resulting Numbers: [2, 72, 8] Generated Node #2: [2, 72, 8] from Operation: 29-21=8 Current State: 68:[2, 72, 8], Operations: ['29-21=8'] Exploring Operation: 8/2=4, Resulting Numbers: [72, 4] Generated Node #3: [72, 4] from Operation: 8/2=4 Current State: 68:[72, 4], Operations: ['29-21=8', '8/2=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[2, 21, 72, 29], Operations: [] Exploring Operation: 21-2=19, Resulting Numbers: [72, 29, 19] Generated Node #0,0: 68:[72, 29, 19] Operation: 21-2=19 Exploring Operation: 29-21=8, Resulting Numbers: [2, 72, 8] Generated Node #0,1: 68:[2, 72, 8] Operation: 29-21=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[2, 72, 8], Operations: ['29-21=8'] Exploring Operation: 8/2=4, Resulting Numbers: [72, 4] Generated Node #0,1,0: 68:[72, 4] Operation: 8/2=4 Exploring Operation: 72-8=64, Resulting Numbers: [2, 64] Generated Node #0,1,1: 68:[2, 64] Operation: 72-8=64 Moving to Node #0,1,0 Current State: 68:[72, 4], Operations: ['29-21=8', '8/2=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[2, 21, 72, 29], Operations: [] Exploring Operation: 29-21=8, Resulting Numbers: [2, 72, 8] Generated Node #0,1: 68:[2, 72, 8] Operation: 29-21=8 Moving to Node #0,1 Current State: 68:[2, 72, 8], Operations: ['29-21=8'] Exploring Operation: 8/2=4, Resulting Numbers: [72, 4] Generated Node #0,1,0: 68:[72, 4] Operation: 8/2=4 Moving to Node #0,1,0 Current State: 68:[72, 4], Operations: ['29-21=8', '8/2=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 1, 82, 8, 16 ]
89
[ "82-1=81", "16-8=8", "81+8=89" ]
Current State: 89:[1, 82, 8, 16], Operations: [] Exploring Operation: 82-1=81, Resulting Numbers: [8, 16, 81] Generated Node #2: [8, 16, 81] from Operation: 82-1=81 Current State: 89:[8, 16, 81], Operations: ['82-1=81'] Exploring Operation: 16-8=8, Resulting Numbers: [81, 8] Generated Node #3: [81, 8] from Operation: 16-8=8 Current State: 89:[81, 8], Operations: ['82-1=81', '16-8=8'] Exploring Operation: 81+8=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[1, 82, 8, 16], Operations: [] Exploring Operation: 8*16=128, Resulting Numbers: [1, 82, 128] Generated Node #0,0: 89:[1, 82, 128] Operation: 8*16=128 Exploring Operation: 1+82=83, Resulting Numbers: [8, 16, 83] Generated Node #0,1: 89:[8, 16, 83] Operation: 1+82=83 Exploring Operation: 1+8=9, Resulting Numbers: [82, 16, 9] Generated Node #0,2: 89:[82, 16, 9] Operation: 1+8=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[1, 82, 128], Operations: ['8*16=128'] Exploring Operation: 1+82=83, Resulting Numbers: [128, 83] Generated Node #0,0,0: 89:[128, 83] Operation: 1+82=83 Exploring Operation: 1*82=82, Resulting Numbers: [128, 82] Generated Node #0,0,1: 89:[128, 82] Operation: 1*82=82 Exploring Operation: 128-1=127, Resulting Numbers: [82, 127] Generated Node #0,0,2: 89:[82, 127] Operation: 128-1=127 Moving to Node #0,0,0 Current State: 89:[128, 83], Operations: ['8*16=128', '1+82=83'] Exploring Operation: 128*83=10624, Resulting Numbers: [10624] 10624,89 unequal: No Solution Exploring Operation: 128+83=211, Resulting Numbers: [211] 211,89 unequal: No Solution Exploring Operation: 128-83=45, Resulting Numbers: [45] 45,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[82, 127], Operations: ['8*16=128', '128-1=127'] Exploring Operation: 127-82=45, Resulting Numbers: [45] 45,89 unequal: No Solution Exploring Operation: 82+127=209, Resulting Numbers: [209] 209,89 unequal: No Solution Exploring Operation: 82*127=10414, Resulting Numbers: [10414] 10414,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[128, 82], Operations: ['8*16=128', '1*82=82'] Exploring Operation: 128-82=46, Resulting Numbers: [46] 46,89 unequal: No Solution Exploring Operation: 128+82=210, Resulting Numbers: [210] 210,89 unequal: No Solution Exploring Operation: 128*82=10496, Resulting Numbers: [10496] 10496,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[8, 16, 83], Operations: ['1+82=83'] Exploring Operation: 8+83=91, Resulting Numbers: [16, 91] Generated Node #0,1,0: 89:[16, 91] Operation: 8+83=91 Exploring Operation: 8*16=128, Resulting Numbers: [83, 128] Generated Node #0,1,1: 89:[83, 128] Operation: 8*16=128 Exploring Operation: 8+16=24, Resulting Numbers: [83, 24] Generated Node #0,1,2: 89:[83, 24] Operation: 8+16=24 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 89:[83, 128], Operations: ['1+82=83', '8*16=128'] Exploring Operation: 128-83=45, Resulting Numbers: [45] 45,89 unequal: No Solution Exploring Operation: 83+128=211, Resulting Numbers: [211] 211,89 unequal: No Solution Exploring Operation: 83*128=10624, Resulting Numbers: [10624] 10624,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 89:[83, 24], Operations: ['1+82=83', '8+16=24'] Exploring Operation: 83-24=59, Resulting Numbers: [59] 59,89 unequal: No Solution Exploring Operation: 83+24=107, Resulting Numbers: [107] 107,89 unequal: No Solution Exploring Operation: 83*24=1992, Resulting Numbers: [1992] 1992,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[16, 91], Operations: ['1+82=83', '8+83=91'] Exploring Operation: 16*91=1456, Resulting Numbers: [1456] 1456,89 unequal: No Solution Exploring Operation: 91-16=75, Resulting Numbers: [75] 75,89 unequal: No Solution Exploring Operation: 16+91=107, Resulting Numbers: [107] 107,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[82, 16, 9], Operations: ['1+8=9'] Exploring Operation: 82+9=91, Resulting Numbers: [16, 91] Generated Node #0,2,0: 89:[16, 91] Operation: 82+9=91 Exploring Operation: 16*9=144, Resulting Numbers: [82, 144] Generated Node #0,2,1: 89:[82, 144] Operation: 16*9=144 Exploring Operation: 16+9=25, Resulting Numbers: [82, 25] Generated Node #0,2,2: 89:[82, 25] Operation: 16+9=25 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 89:[82, 144], Operations: ['1+8=9', '16*9=144'] Exploring Operation: 82+144=226, Resulting Numbers: [226] 226,89 unequal: No Solution Exploring Operation: 82*144=11808, Resulting Numbers: [11808] 11808,89 unequal: No Solution Exploring Operation: 144-82=62, Resulting Numbers: [62] 62,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 89:[82, 25], Operations: ['1+8=9', '16+9=25'] Exploring Operation: 82+25=107, Resulting Numbers: [107] 107,89 unequal: No Solution Exploring Operation: 82-25=57, Resulting Numbers: [57] 57,89 unequal: No Solution Exploring Operation: 82*25=2050, Resulting Numbers: [2050] 2050,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 89:[16, 91], Operations: ['1+8=9', '82+9=91'] Exploring Operation: 16*91=1456, Resulting Numbers: [1456] 1456,89 unequal: No Solution Exploring Operation: 16+91=107, Resulting Numbers: [107] 107,89 unequal: No Solution Exploring Operation: 91-16=75, Resulting Numbers: [75] 75,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 94, 92, 26, 96 ]
24
[ "92+96=188", "188/94=2", "26-2=24" ]
Current State: 24:[94, 92, 26, 96], Operations: [] Exploring Operation: 92+96=188, Resulting Numbers: [94, 26, 188] Generated Node #2: [94, 26, 188] from Operation: 92+96=188 Current State: 24:[94, 26, 188], Operations: ['92+96=188'] Exploring Operation: 188/94=2, Resulting Numbers: [26, 2] Generated Node #3: [26, 2] from Operation: 188/94=2 Current State: 24:[26, 2], Operations: ['92+96=188', '188/94=2'] Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[94, 92, 26, 96], Operations: [] Exploring Operation: 94-26=68, Resulting Numbers: [92, 96, 68] Generated Node #0,0: 24:[92, 96, 68] Operation: 94-26=68 Exploring Operation: 94-92=2, Resulting Numbers: [26, 96, 2] Generated Node #0,1: 24:[26, 96, 2] Operation: 94-92=2 Exploring Operation: 96-94=2, Resulting Numbers: [92, 26, 2] Generated Node #0,2: 24:[92, 26, 2] Operation: 96-94=2 Exploring Operation: 96-92=4, Resulting Numbers: [94, 26, 4] Generated Node #0,3: 24:[94, 26, 4] Operation: 96-92=4 Exploring Operation: 92-26=66, Resulting Numbers: [94, 96, 66] Generated Node #0,4: 24:[94, 96, 66] Operation: 92-26=66 Moving to Node #0,2 Current State: 24:[92, 26, 2], Operations: ['96-94=2'] Exploring Operation: 92-26=66, Resulting Numbers: [2, 66] Generated Node #0,2,0: 24:[2, 66] Operation: 92-26=66 Exploring Operation: 26/2=13, Resulting Numbers: [92, 13] Generated Node #0,2,1: 24:[92, 13] Operation: 26/2=13 Exploring Operation: 26-2=24, Resulting Numbers: [92, 24] Generated Node #0,2,2: 24:[92, 24] Operation: 26-2=24 Exploring Operation: 92/2=46, Resulting Numbers: [26, 46] Generated Node #0,2,3: 24:[26, 46] Operation: 92/2=46 Exploring Operation: 92-2=90, Resulting Numbers: [26, 90] Generated Node #0,2,4: 24:[26, 90] Operation: 92-2=90 Moving to Node #0,3 Current State: 24:[94, 26, 4], Operations: ['96-92=4'] Exploring Operation: 94-26=68, Resulting Numbers: [4, 68] Generated Node #0,3,0: 24:[4, 68] Operation: 94-26=68 Exploring Operation: 26-4=22, Resulting Numbers: [94, 22] Generated Node #0,3,1: 24:[94, 22] Operation: 26-4=22 Exploring Operation: 94+4=98, Resulting Numbers: [26, 98] Generated Node #0,3,2: 24:[26, 98] Operation: 94+4=98 Exploring Operation: 26+4=30, Resulting Numbers: [94, 30] Generated Node #0,3,3: 24:[94, 30] Operation: 26+4=30 Exploring Operation: 94-4=90, Resulting Numbers: [26, 90] Generated Node #0,3,4: 24:[26, 90] Operation: 94-4=90 Moving to Node #0,1 Current State: 24:[26, 96, 2], Operations: ['94-92=2'] Exploring Operation: 96/2=48, Resulting Numbers: [26, 48] Generated Node #0,1,0: 24:[26, 48] Operation: 96/2=48 Exploring Operation: 96-26=70, Resulting Numbers: [2, 70] Generated Node #0,1,1: 24:[2, 70] Operation: 96-26=70 Exploring Operation: 26-2=24, Resulting Numbers: [96, 24] Generated Node #0,1,2: 24:[96, 24] Operation: 26-2=24 Exploring Operation: 26/2=13, Resulting Numbers: [96, 13] Generated Node #0,1,3: 24:[96, 13] Operation: 26/2=13 Exploring Operation: 96-2=94, Resulting Numbers: [26, 94] Generated Node #0,1,4: 24:[26, 94] Operation: 96-2=94 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[26, 48], Operations: ['94-92=2', '96/2=48'] Exploring Operation: 48-26=22, Resulting Numbers: [22] 22,24 unequal: No Solution Exploring Operation: 26*48=1248, Resulting Numbers: [1248] 1248,24 unequal: No Solution Exploring Operation: 26+48=74, Resulting Numbers: [74] 74,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 24:[2, 70], Operations: ['94-92=2', '96-26=70'] Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,24 unequal: No Solution Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 2*70=140, Resulting Numbers: [140] 140,24 unequal: No Solution Exploring Operation: 2+70=72, Resulting Numbers: [72] 72,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[96, 24], Operations: ['94-92=2', '26-2=24'] Exploring Operation: 96+24=120, Resulting Numbers: [120] 120,24 unequal: No Solution Exploring Operation: 96-24=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 96*24=2304, Resulting Numbers: [2304] 2304,24 unequal: No Solution Exploring Operation: 96/24=4, Resulting Numbers: [4] 4,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 24:[26, 94], Operations: ['94-92=2', '96-2=94'] Exploring Operation: 26+94=120, Resulting Numbers: [120] 120,24 unequal: No Solution Exploring Operation: 94-26=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 26*94=2444, Resulting Numbers: [2444] 2444,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 24:[96, 13], Operations: ['94-92=2', '26/2=13'] Exploring Operation: 96+13=109, Resulting Numbers: [109] 109,24 unequal: No Solution Exploring Operation: 96*13=1248, Resulting Numbers: [1248] 1248,24 unequal: No Solution Exploring Operation: 96-13=83, Resulting Numbers: [83] 83,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 24:[92, 96, 68], Operations: ['94-26=68'] Exploring Operation: 96-68=28, Resulting Numbers: [92, 28] Generated Node #0,0,0: 24:[92, 28] Operation: 96-68=28 Exploring Operation: 92-68=24, Resulting Numbers: [96, 24] Generated Node #0,0,1: 24:[96, 24] Operation: 92-68=24 Exploring Operation: 96-92=4, Resulting Numbers: [68, 4] Generated Node #0,0,2: 24:[68, 4] Operation: 96-92=4 Exploring Operation: 92+68=160, Resulting Numbers: [96, 160] Generated Node #0,0,3: 24:[96, 160] Operation: 92+68=160 Exploring Operation: 92+96=188, Resulting Numbers: [68, 188] Generated Node #0,0,4: 24:[68, 188] Operation: 92+96=188 Moving to Node #0,4 Current State: 24:[94, 96, 66], Operations: ['92-26=66'] Exploring Operation: 96-66=30, Resulting Numbers: [94, 30] Generated Node #0,4,0: 24:[94, 30] Operation: 96-66=30 Exploring Operation: 94+66=160, Resulting Numbers: [96, 160] Generated Node #0,4,1: 24:[96, 160] Operation: 94+66=160 Exploring Operation: 96-94=2, Resulting Numbers: [66, 2] Generated Node #0,4,2: 24:[66, 2] Operation: 96-94=2 Exploring Operation: 94-66=28, Resulting Numbers: [96, 28] Generated Node #0,4,3: 24:[96, 28] Operation: 94-66=28 Exploring Operation: 94+96=190, Resulting Numbers: [66, 190] Generated Node #0,4,4: 24:[66, 190] Operation: 94+96=190 Moving to Node #0,2,3 Current State: 24:[26, 46], Operations: ['96-94=2', '92/2=46'] Exploring Operation: 26*46=1196, Resulting Numbers: [1196] 1196,24 unequal: No Solution Exploring Operation: 26+46=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[2, 66], Operations: ['96-94=2', '92-26=66'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,24 unequal: No Solution Exploring Operation: 2*66=132, Resulting Numbers: [132] 132,24 unequal: No Solution Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,24 unequal: No Solution Moving to Node #0,4,2 Current State: 24:[66, 2], Operations: ['92-26=66', '96-94=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,24 unequal: No Solution Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,24 unequal: No Solution Exploring Operation: 66*2=132, Resulting Numbers: [132] 132,24 unequal: No Solution Moving to Node #0,3,0 Current State: 24:[4, 68], Operations: ['96-92=4', '94-26=68'] Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,24 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,24 unequal: No Solution Moving to Node #0,0,2 Current State: 24:[68, 4], Operations: ['94-26=68', '96-92=4'] Exploring Operation: 68+4=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 68*4=272, Resulting Numbers: [272] 272,24 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,24 unequal: No Solution Moving to Node #0,3,4 Current State: 24:[26, 90], Operations: ['96-92=4', '94-4=90'] Exploring Operation: 26+90=116, Resulting Numbers: [116] 116,24 unequal: No Solution Exploring Operation: 90-26=64, Resulting Numbers: [64] 64,24 unequal: No Solution Exploring Operation: 26*90=2340, Resulting Numbers: [2340] 2340,24 unequal: No Solution Moving to Node #0,2,2 Current State: 24:[92, 24], Operations: ['96-94=2', '26-2=24'] Exploring Operation: 92-24=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 92*24=2208, Resulting Numbers: [2208] 2208,24 unequal: No Solution Exploring Operation: 92+24=116, Resulting Numbers: [116] 116,24 unequal: No Solution Moving to Node #0,2,4 Current State: 24:[26, 90], Operations: ['96-94=2', '92-2=90'] Exploring Operation: 90-26=64, Resulting Numbers: [64] 64,24 unequal: No Solution Exploring Operation: 26*90=2340, Resulting Numbers: [2340] 2340,24 unequal: No Solution Exploring Operation: 26+90=116, Resulting Numbers: [116] 116,24 unequal: No Solution Moving to Node #0,2,1 Current State: 24:[92, 13], Operations: ['96-94=2', '26/2=13'] Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,24 unequal: No Solution Exploring Operation: 92*13=1196, Resulting Numbers: [1196] 1196,24 unequal: No Solution Exploring Operation: 92+13=105, Resulting Numbers: [105] 105,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[96, 24], Operations: ['94-26=68', '92-68=24'] Exploring Operation: 96/24=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 96-24=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 96*24=2304, Resulting Numbers: [2304] 2304,24 unequal: No Solution Exploring Operation: 96+24=120, Resulting Numbers: [120] 120,24 unequal: No Solution Moving to Node #0,0,0 Current State: 24:[92, 28], Operations: ['94-26=68', '96-68=28'] Exploring Operation: 92+28=120, Resulting Numbers: [120] 120,24 unequal: No Solution Exploring Operation: 92-28=64, Resulting Numbers: [64] 64,24 unequal: No Solution Exploring Operation: 92*28=2576, Resulting Numbers: [2576] 2576,24 unequal: No Solution Moving to Node #0,3,1 Current State: 24:[94, 22], Operations: ['96-92=4', '26-4=22'] Exploring Operation: 94+22=116, Resulting Numbers: [116] 116,24 unequal: No Solution Exploring Operation: 94-22=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 94*22=2068, Resulting Numbers: [2068] 2068,24 unequal: No Solution Moving to Node #0,4,3 Current State: 24:[96, 28], Operations: ['92-26=66', '94-66=28'] Exploring Operation: 96*28=2688, Resulting Numbers: [2688] 2688,24 unequal: No Solution Exploring Operation: 96+28=124, Resulting Numbers: [124] 124,24 unequal: No Solution Exploring Operation: 96-28=68, Resulting Numbers: [68] 68,24 unequal: No Solution Moving to Node #0,3,3 Current State: 24:[94, 30], Operations: ['96-92=4', '26+4=30'] Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,24 unequal: No Solution Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,24 unequal: No Solution Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[26, 98], Operations: ['96-92=4', '94+4=98'] Exploring Operation: 26*98=2548, Resulting Numbers: [2548] 2548,24 unequal: No Solution Exploring Operation: 98-26=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 26+98=124, Resulting Numbers: [124] 124,24 unequal: No Solution Moving to Node #0,4,0 Current State: 24:[94, 30], Operations: ['92-26=66', '96-66=30'] Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,24 unequal: No Solution Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,24 unequal: No Solution Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,24 unequal: No Solution Moving to Node #0,4,1 Current State: 24:[96, 160], Operations: ['92-26=66', '94+66=160'] Exploring Operation: 96+160=256, Resulting Numbers: [256] 256,24 unequal: No Solution Exploring Operation: 160-96=64, Resulting Numbers: [64] 64,24 unequal: No Solution Exploring Operation: 96*160=15360, Resulting Numbers: [15360] 15360,24 unequal: No Solution Moving to Node #0,0,4 Current State: 24:[68, 188], Operations: ['94-26=68', '92+96=188'] Exploring Operation: 68*188=12784, Resulting Numbers: [12784] 12784,24 unequal: No Solution Exploring Operation: 188-68=120, Resulting Numbers: [120] 120,24 unequal: No Solution Exploring Operation: 68+188=256, Resulting Numbers: [256] 256,24 unequal: No Solution Moving to Node #0,0,3 Current State: 24:[96, 160], Operations: ['94-26=68', '92+68=160'] Exploring Operation: 160-96=64, Resulting Numbers: [64] 64,24 unequal: No Solution Exploring Operation: 96*160=15360, Resulting Numbers: [15360] 15360,24 unequal: No Solution Exploring Operation: 96+160=256, Resulting Numbers: [256] 256,24 unequal: No Solution Moving to Node #0,4,4 Current State: 24:[66, 190], Operations: ['92-26=66', '94+96=190'] Exploring Operation: 66+190=256, Resulting Numbers: [256] 256,24 unequal: No Solution Exploring Operation: 190-66=124, Resulting Numbers: [124] 124,24 unequal: No Solution Exploring Operation: 66*190=12540, Resulting Numbers: [12540] 12540,24 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 51, 89, 2, 99 ]
71
[ "99-89=10", "2*10=20", "51+20=71" ]
Current State: 71:[51, 89, 2, 99], Operations: [] Exploring Operation: 99-89=10, Resulting Numbers: [51, 2, 10] Generated Node #2: [51, 2, 10] from Operation: 99-89=10 Current State: 71:[51, 2, 10], Operations: ['99-89=10'] Exploring Operation: 2*10=20, Resulting Numbers: [51, 20] Generated Node #3: [51, 20] from Operation: 2*10=20 Current State: 71:[51, 20], Operations: ['99-89=10', '2*10=20'] Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[51, 89, 2, 99], Operations: [] Exploring Operation: 89+2=91, Resulting Numbers: [51, 99, 91] Generated Node #0,0: 71:[51, 99, 91] Operation: 89+2=91 Exploring Operation: 51-2=49, Resulting Numbers: [89, 99, 49] Generated Node #0,1: 71:[89, 99, 49] Operation: 51-2=49 Exploring Operation: 89-2=87, Resulting Numbers: [51, 99, 87] Generated Node #0,2: 71:[51, 99, 87] Operation: 89-2=87 Exploring Operation: 51+2=53, Resulting Numbers: [89, 99, 53] Generated Node #0,3: 71:[89, 99, 53] Operation: 51+2=53 Exploring Operation: 99-2=97, Resulting Numbers: [51, 89, 97] Generated Node #0,4: 71:[51, 89, 97] Operation: 99-2=97 Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[51, 99, 87], Operations: ['89-2=87'] Exploring Operation: 99-87=12, Resulting Numbers: [51, 12] Generated Node #0,2,0: 71:[51, 12] Operation: 99-87=12 Exploring Operation: 51+87=138, Resulting Numbers: [99, 138] Generated Node #0,2,1: 71:[99, 138] Operation: 51+87=138 Exploring Operation: 99-51=48, Resulting Numbers: [87, 48] Generated Node #0,2,2: 71:[87, 48] Operation: 99-51=48 Exploring Operation: 51+99=150, Resulting Numbers: [87, 150] Generated Node #0,2,3: 71:[87, 150] Operation: 51+99=150 Exploring Operation: 87-51=36, Resulting Numbers: [99, 36] Generated Node #0,2,4: 71:[99, 36] Operation: 87-51=36 Moving to Node #0,2,2 Current State: 71:[87, 48], Operations: ['89-2=87', '99-51=48'] Exploring Operation: 87-48=39, Resulting Numbers: [39] 39,71 unequal: No Solution Exploring Operation: 87*48=4176, Resulting Numbers: [4176] 4176,71 unequal: No Solution Exploring Operation: 87+48=135, Resulting Numbers: [135] 135,71 unequal: No Solution Moving to Node #0,2,4 Current State: 71:[99, 36], Operations: ['89-2=87', '87-51=36'] Exploring Operation: 99+36=135, Resulting Numbers: [135] 135,71 unequal: No Solution Exploring Operation: 99-36=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 99*36=3564, Resulting Numbers: [3564] 3564,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[51, 12], Operations: ['89-2=87', '99-87=12'] Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 51*12=612, Resulting Numbers: [612] 612,71 unequal: No Solution Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[99, 138], Operations: ['89-2=87', '51+87=138'] Exploring Operation: 138-99=39, Resulting Numbers: [39] 39,71 unequal: No Solution Exploring Operation: 99*138=13662, Resulting Numbers: [13662] 13662,71 unequal: No Solution Exploring Operation: 99+138=237, Resulting Numbers: [237] 237,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[87, 150], Operations: ['89-2=87', '51+99=150'] Exploring Operation: 87*150=13050, Resulting Numbers: [13050] 13050,71 unequal: No Solution Exploring Operation: 150-87=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 87+150=237, Resulting Numbers: [237] 237,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 71:[89, 99, 53], Operations: ['51+2=53'] Exploring Operation: 89+53=142, Resulting Numbers: [99, 142] Generated Node #0,3,0: 71:[99, 142] Operation: 89+53=142 Exploring Operation: 99-53=46, Resulting Numbers: [89, 46] Generated Node #0,3,1: 71:[89, 46] Operation: 99-53=46 Exploring Operation: 89-53=36, Resulting Numbers: [99, 36] Generated Node #0,3,2: 71:[99, 36] Operation: 89-53=36 Exploring Operation: 99+53=152, Resulting Numbers: [89, 152] Generated Node #0,3,3: 71:[89, 152] Operation: 99+53=152 Exploring Operation: 99-89=10, Resulting Numbers: [53, 10] Generated Node #0,3,4: 71:[53, 10] Operation: 99-89=10 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 71:[89, 46], Operations: ['51+2=53', '99-53=46'] Exploring Operation: 89-46=43, Resulting Numbers: [43] 43,71 unequal: No Solution Exploring Operation: 89+46=135, Resulting Numbers: [135] 135,71 unequal: No Solution Exploring Operation: 89*46=4094, Resulting Numbers: [4094] 4094,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 71:[99, 36], Operations: ['51+2=53', '89-53=36'] Exploring Operation: 99+36=135, Resulting Numbers: [135] 135,71 unequal: No Solution Exploring Operation: 99-36=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 99*36=3564, Resulting Numbers: [3564] 3564,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 71:[53, 10], Operations: ['51+2=53', '99-89=10'] Exploring Operation: 53-10=43, Resulting Numbers: [43] 43,71 unequal: No Solution Exploring Operation: 53+10=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 53*10=530, Resulting Numbers: [530] 530,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 71:[99, 142], Operations: ['51+2=53', '89+53=142'] Exploring Operation: 99*142=14058, Resulting Numbers: [14058] 14058,71 unequal: No Solution Exploring Operation: 142-99=43, Resulting Numbers: [43] 43,71 unequal: No Solution Exploring Operation: 99+142=241, Resulting Numbers: [241] 241,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 71:[89, 152], Operations: ['51+2=53', '99+53=152'] Exploring Operation: 152-89=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 89*152=13528, Resulting Numbers: [13528] 13528,71 unequal: No Solution Exploring Operation: 89+152=241, Resulting Numbers: [241] 241,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 71:[51, 89, 97], Operations: ['99-2=97'] Exploring Operation: 97-51=46, Resulting Numbers: [89, 46] Generated Node #0,4,0: 71:[89, 46] Operation: 97-51=46 Exploring Operation: 51+97=148, Resulting Numbers: [89, 148] Generated Node #0,4,1: 71:[89, 148] Operation: 51+97=148 Exploring Operation: 97-89=8, Resulting Numbers: [51, 8] Generated Node #0,4,2: 71:[51, 8] Operation: 97-89=8 Exploring Operation: 89-51=38, Resulting Numbers: [97, 38] Generated Node #0,4,3: 71:[97, 38] Operation: 89-51=38 Exploring Operation: 51+89=140, Resulting Numbers: [97, 140] Generated Node #0,4,4: 71:[97, 140] Operation: 51+89=140 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 71:[89, 46], Operations: ['99-2=97', '97-51=46'] Exploring Operation: 89*46=4094, Resulting Numbers: [4094] 4094,71 unequal: No Solution Exploring Operation: 89-46=43, Resulting Numbers: [43] 43,71 unequal: No Solution Exploring Operation: 89+46=135, Resulting Numbers: [135] 135,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 71:[97, 38], Operations: ['99-2=97', '89-51=38'] Exploring Operation: 97*38=3686, Resulting Numbers: [3686] 3686,71 unequal: No Solution Exploring Operation: 97+38=135, Resulting Numbers: [135] 135,71 unequal: No Solution Exploring Operation: 97-38=59, Resulting Numbers: [59] 59,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 71:[51, 8], Operations: ['99-2=97', '97-89=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,71 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,71 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 71:[89, 148], Operations: ['99-2=97', '51+97=148'] Exploring Operation: 148-89=59, Resulting Numbers: [59] 59,71 unequal: No Solution Exploring Operation: 89+148=237, Resulting Numbers: [237] 237,71 unequal: No Solution Exploring Operation: 89*148=13172, Resulting Numbers: [13172] 13172,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 71:[97, 140], Operations: ['99-2=97', '51+89=140'] Exploring Operation: 97+140=237, Resulting Numbers: [237] 237,71 unequal: No Solution Exploring Operation: 140-97=43, Resulting Numbers: [43] 43,71 unequal: No Solution Exploring Operation: 97*140=13580, Resulting Numbers: [13580] 13580,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[51, 99, 91], Operations: ['89+2=91'] Exploring Operation: 51+91=142, Resulting Numbers: [99, 142] Generated Node #0,0,0: 71:[99, 142] Operation: 51+91=142 Exploring Operation: 99-51=48, Resulting Numbers: [91, 48] Generated Node #0,0,1: 71:[91, 48] Operation: 99-51=48 Exploring Operation: 51+99=150, Resulting Numbers: [91, 150] Generated Node #0,0,2: 71:[91, 150] Operation: 51+99=150 Exploring Operation: 91-51=40, Resulting Numbers: [99, 40] Generated Node #0,0,3: 71:[99, 40] Operation: 91-51=40 Exploring Operation: 99-91=8, Resulting Numbers: [51, 8] Generated Node #0,0,4: 71:[51, 8] Operation: 99-91=8 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 71:[91, 48], Operations: ['89+2=91', '99-51=48'] Exploring Operation: 91*48=4368, Resulting Numbers: [4368] 4368,71 unequal: No Solution Exploring Operation: 91-48=43, Resulting Numbers: [43] 43,71 unequal: No Solution Exploring Operation: 91+48=139, Resulting Numbers: [139] 139,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 71:[99, 40], Operations: ['89+2=91', '91-51=40'] Exploring Operation: 99-40=59, Resulting Numbers: [59] 59,71 unequal: No Solution Exploring Operation: 99+40=139, Resulting Numbers: [139] 139,71 unequal: No Solution Exploring Operation: 99*40=3960, Resulting Numbers: [3960] 3960,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 71:[51, 8], Operations: ['89+2=91', '99-91=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,71 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,71 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[99, 142], Operations: ['89+2=91', '51+91=142'] Exploring Operation: 99*142=14058, Resulting Numbers: [14058] 14058,71 unequal: No Solution Exploring Operation: 99+142=241, Resulting Numbers: [241] 241,71 unequal: No Solution Exploring Operation: 142-99=43, Resulting Numbers: [43] 43,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 71:[91, 150], Operations: ['89+2=91', '51+99=150'] Exploring Operation: 91*150=13650, Resulting Numbers: [13650] 13650,71 unequal: No Solution Exploring Operation: 91+150=241, Resulting Numbers: [241] 241,71 unequal: No Solution Exploring Operation: 150-91=59, Resulting Numbers: [59] 59,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[89, 99, 49], Operations: ['51-2=49'] Exploring Operation: 99-49=50, Resulting Numbers: [89, 50] Generated Node #0,1,0: 71:[89, 50] Operation: 99-49=50 Exploring Operation: 89-49=40, Resulting Numbers: [99, 40] Generated Node #0,1,1: 71:[99, 40] Operation: 89-49=40 Exploring Operation: 99+49=148, Resulting Numbers: [89, 148] Generated Node #0,1,2: 71:[89, 148] Operation: 99+49=148 Exploring Operation: 99-89=10, Resulting Numbers: [49, 10] Generated Node #0,1,3: 71:[49, 10] Operation: 99-89=10 Exploring Operation: 89+49=138, Resulting Numbers: [99, 138] Generated Node #0,1,4: 71:[99, 138] Operation: 89+49=138 Moving to Node #0,1,0 Current State: 71:[89, 50], Operations: ['51-2=49', '99-49=50'] Exploring Operation: 89-50=39, Resulting Numbers: [39] 39,71 unequal: No Solution Exploring Operation: 89*50=4450, Resulting Numbers: [4450] 4450,71 unequal: No Solution Exploring Operation: 89+50=139, Resulting Numbers: [139] 139,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[99, 40], Operations: ['51-2=49', '89-49=40'] Exploring Operation: 99*40=3960, Resulting Numbers: [3960] 3960,71 unequal: No Solution Exploring Operation: 99+40=139, Resulting Numbers: [139] 139,71 unequal: No Solution Exploring Operation: 99-40=59, Resulting Numbers: [59] 59,71 unequal: No Solution Moving to Node #0,1,3 Current State: 71:[49, 10], Operations: ['51-2=49', '99-89=10'] Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,71 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,71 unequal: No Solution Exploring Operation: 49*10=490, Resulting Numbers: [490] 490,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[89, 148], Operations: ['51-2=49', '99+49=148'] Exploring Operation: 89*148=13172, Resulting Numbers: [13172] 13172,71 unequal: No Solution Exploring Operation: 148-89=59, Resulting Numbers: [59] 59,71 unequal: No Solution Exploring Operation: 89+148=237, Resulting Numbers: [237] 237,71 unequal: No Solution Moving to Node #0,1,4 Current State: 71:[99, 138], Operations: ['51-2=49', '89+49=138'] Exploring Operation: 99*138=13662, Resulting Numbers: [13662] 13662,71 unequal: No Solution Exploring Operation: 138-99=39, Resulting Numbers: [39] 39,71 unequal: No Solution Exploring Operation: 99+138=237, Resulting Numbers: [237] 237,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 98, 36, 35, 6 ]
76
[ "98+36=134", "35*6=210", "210-134=76" ]
Current State: 76:[98, 36, 35, 6], Operations: [] Exploring Operation: 98+36=134, Resulting Numbers: [35, 6, 134] Generated Node #2: [35, 6, 134] from Operation: 98+36=134 Current State: 76:[35, 6, 134], Operations: ['98+36=134'] Exploring Operation: 35*6=210, Resulting Numbers: [134, 210] Generated Node #3: [134, 210] from Operation: 35*6=210 Current State: 76:[134, 210], Operations: ['98+36=134', '35*6=210'] Exploring Operation: 210-134=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[98, 36, 35, 6], Operations: [] Exploring Operation: 98-36=62, Resulting Numbers: [35, 6, 62] Generated Node #0,0: 76:[35, 6, 62] Operation: 98-36=62 Exploring Operation: 98-35=63, Resulting Numbers: [36, 6, 63] Generated Node #0,1: 76:[36, 6, 63] Operation: 98-35=63 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[36, 6, 63], Operations: ['98-35=63'] Exploring Operation: 63-36=27, Resulting Numbers: [6, 27] Generated Node #0,1,0: 76:[6, 27] Operation: 63-36=27 Exploring Operation: 6+63=69, Resulting Numbers: [36, 69] Generated Node #0,1,1: 76:[36, 69] Operation: 6+63=69 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 76:[36, 69], Operations: ['98-35=63', '6+63=69'] Exploring Operation: 69-36=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 36+69=105, Resulting Numbers: [105] 105,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 76:[6, 27], Operations: ['98-35=63', '63-36=27'] Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,76 unequal: No Solution Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[35, 6, 62], Operations: ['98-36=62'] Exploring Operation: 6+62=68, Resulting Numbers: [35, 68] Generated Node #0,0,0: 76:[35, 68] Operation: 6+62=68 Exploring Operation: 62-35=27, Resulting Numbers: [6, 27] Generated Node #0,0,1: 76:[6, 27] Operation: 62-35=27 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 76:[6, 27], Operations: ['98-36=62', '62-35=27'] Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 76:[35, 68], Operations: ['98-36=62', '6+62=68'] Exploring Operation: 68-35=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 35+68=103, Resulting Numbers: [103] 103,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 35, 81, 6, 10 ]
11
[ "35+81=116", "116-6=110", "110/10=11" ]
Current State: 11:[35, 81, 6, 10], Operations: [] Exploring Operation: 35+81=116, Resulting Numbers: [6, 10, 116] Generated Node #2: [6, 10, 116] from Operation: 35+81=116 Current State: 11:[6, 10, 116], Operations: ['35+81=116'] Exploring Operation: 116-6=110, Resulting Numbers: [10, 110] Generated Node #3: [10, 110] from Operation: 116-6=110 Current State: 11:[10, 110], Operations: ['35+81=116', '116-6=110'] Exploring Operation: 110/10=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[35, 81, 6, 10], Operations: [] Exploring Operation: 35-10=25, Resulting Numbers: [81, 6, 25] Generated Node #0,0: 11:[81, 6, 25] Operation: 35-10=25 Exploring Operation: 35-6=29, Resulting Numbers: [81, 10, 29] Generated Node #0,1: 11:[81, 10, 29] Operation: 35-6=29 Exploring Operation: 81-10=71, Resulting Numbers: [35, 6, 71] Generated Node #0,2: 11:[35, 6, 71] Operation: 81-10=71 Exploring Operation: 81-35=46, Resulting Numbers: [6, 10, 46] Generated Node #0,3: 11:[6, 10, 46] Operation: 81-35=46 Exploring Operation: 81-6=75, Resulting Numbers: [35, 10, 75] Generated Node #0,4: 11:[35, 10, 75] Operation: 81-6=75 Start Sub Search at level 1: Moving to Node #0,3 Current State: 11:[6, 10, 46], Operations: ['81-35=46'] Exploring Operation: 6+46=52, Resulting Numbers: [10, 52] Generated Node #0,3,0: 11:[10, 52] Operation: 6+46=52 Exploring Operation: 10-6=4, Resulting Numbers: [46, 4] Generated Node #0,3,1: 11:[46, 4] Operation: 10-6=4 Exploring Operation: 46-6=40, Resulting Numbers: [10, 40] Generated Node #0,3,2: 11:[10, 40] Operation: 46-6=40 Exploring Operation: 46-10=36, Resulting Numbers: [6, 36] Generated Node #0,3,3: 11:[6, 36] Operation: 46-10=36 Exploring Operation: 6+10=16, Resulting Numbers: [46, 16] Generated Node #0,3,4: 11:[46, 16] Operation: 6+10=16 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 11:[10, 40], Operations: ['81-35=46', '46-6=40'] Exploring Operation: 10+40=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 10*40=400, Resulting Numbers: [400] 400,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 11:[6, 36], Operations: ['81-35=46', '46-10=36'] Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 6*36=216, Resulting Numbers: [216] 216,11 unequal: No Solution Exploring Operation: 6+36=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 11:[46, 16], Operations: ['81-35=46', '6+10=16'] Exploring Operation: 46+16=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 46*16=736, Resulting Numbers: [736] 736,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 11:[10, 52], Operations: ['81-35=46', '6+46=52'] Exploring Operation: 10+52=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 10*52=520, Resulting Numbers: [520] 520,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 11:[46, 4], Operations: ['81-35=46', '10-6=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[81, 6, 25], Operations: ['35-10=25'] Exploring Operation: 25-6=19, Resulting Numbers: [81, 19] Generated Node #0,0,0: 11:[81, 19] Operation: 25-6=19 Exploring Operation: 81-6=75, Resulting Numbers: [25, 75] Generated Node #0,0,1: 11:[25, 75] Operation: 81-6=75 Exploring Operation: 6+25=31, Resulting Numbers: [81, 31] Generated Node #0,0,2: 11:[81, 31] Operation: 6+25=31 Exploring Operation: 81+6=87, Resulting Numbers: [25, 87] Generated Node #0,0,3: 11:[25, 87] Operation: 81+6=87 Exploring Operation: 81-25=56, Resulting Numbers: [6, 56] Generated Node #0,0,4: 11:[6, 56] Operation: 81-25=56 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 11:[6, 56], Operations: ['35-10=25', '81-25=56'] Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 6*56=336, Resulting Numbers: [336] 336,11 unequal: No Solution Exploring Operation: 6+56=62, Resulting Numbers: [62] 62,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[81, 19], Operations: ['35-10=25', '25-6=19'] Exploring Operation: 81*19=1539, Resulting Numbers: [1539] 1539,11 unequal: No Solution Exploring Operation: 81+19=100, Resulting Numbers: [100] 100,11 unequal: No Solution Exploring Operation: 81-19=62, Resulting Numbers: [62] 62,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 11:[25, 75], Operations: ['35-10=25', '81-6=75'] Exploring Operation: 25*75=1875, Resulting Numbers: [1875] 1875,11 unequal: No Solution Exploring Operation: 25+75=100, Resulting Numbers: [100] 100,11 unequal: No Solution Exploring Operation: 75/25=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 75-25=50, Resulting Numbers: [50] 50,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 11:[81, 31], Operations: ['35-10=25', '6+25=31'] Exploring Operation: 81*31=2511, Resulting Numbers: [2511] 2511,11 unequal: No Solution Exploring Operation: 81-31=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 81+31=112, Resulting Numbers: [112] 112,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 11:[25, 87], Operations: ['35-10=25', '81+6=87'] Exploring Operation: 25+87=112, Resulting Numbers: [112] 112,11 unequal: No Solution Exploring Operation: 87-25=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 25*87=2175, Resulting Numbers: [2175] 2175,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[81, 10, 29], Operations: ['35-6=29'] Exploring Operation: 10+29=39, Resulting Numbers: [81, 39] Generated Node #0,1,0: 11:[81, 39] Operation: 10+29=39 Exploring Operation: 81+10=91, Resulting Numbers: [29, 91] Generated Node #0,1,1: 11:[29, 91] Operation: 81+10=91 Exploring Operation: 81-29=52, Resulting Numbers: [10, 52] Generated Node #0,1,2: 11:[10, 52] Operation: 81-29=52 Exploring Operation: 29-10=19, Resulting Numbers: [81, 19] Generated Node #0,1,3: 11:[81, 19] Operation: 29-10=19 Exploring Operation: 81-10=71, Resulting Numbers: [29, 71] Generated Node #0,1,4: 11:[29, 71] Operation: 81-10=71 Moving to Node #0,1,2 Current State: 11:[10, 52], Operations: ['35-6=29', '81-29=52'] Exploring Operation: 10*52=520, Resulting Numbers: [520] 520,11 unequal: No Solution Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 10+52=62, Resulting Numbers: [62] 62,11 unequal: No Solution Moving to Node #0,1,4 Current State: 11:[29, 71], Operations: ['35-6=29', '81-10=71'] Exploring Operation: 29+71=100, Resulting Numbers: [100] 100,11 unequal: No Solution Exploring Operation: 29*71=2059, Resulting Numbers: [2059] 2059,11 unequal: No Solution Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,11 unequal: No Solution Moving to Node #0,1,3 Current State: 11:[81, 19], Operations: ['35-6=29', '29-10=19'] Exploring Operation: 81+19=100, Resulting Numbers: [100] 100,11 unequal: No Solution Exploring Operation: 81*19=1539, Resulting Numbers: [1539] 1539,11 unequal: No Solution Exploring Operation: 81-19=62, Resulting Numbers: [62] 62,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[81, 39], Operations: ['35-6=29', '10+29=39'] Exploring Operation: 81+39=120, Resulting Numbers: [120] 120,11 unequal: No Solution Exploring Operation: 81*39=3159, Resulting Numbers: [3159] 3159,11 unequal: No Solution Exploring Operation: 81-39=42, Resulting Numbers: [42] 42,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[29, 91], Operations: ['35-6=29', '81+10=91'] Exploring Operation: 91-29=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 29*91=2639, Resulting Numbers: [2639] 2639,11 unequal: No Solution Exploring Operation: 29+91=120, Resulting Numbers: [120] 120,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 11:[35, 6, 71], Operations: ['81-10=71'] Exploring Operation: 35+6=41, Resulting Numbers: [71, 41] Generated Node #0,2,0: 11:[71, 41] Operation: 35+6=41 Exploring Operation: 71-6=65, Resulting Numbers: [35, 65] Generated Node #0,2,1: 11:[35, 65] Operation: 71-6=65 Exploring Operation: 71-35=36, Resulting Numbers: [6, 36] Generated Node #0,2,2: 11:[6, 36] Operation: 71-35=36 Exploring Operation: 35-6=29, Resulting Numbers: [71, 29] Generated Node #0,2,3: 11:[71, 29] Operation: 35-6=29 Exploring Operation: 6+71=77, Resulting Numbers: [35, 77] Generated Node #0,2,4: 11:[35, 77] Operation: 6+71=77 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 11:[6, 36], Operations: ['81-10=71', '71-35=36'] Exploring Operation: 6+36=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 6*36=216, Resulting Numbers: [216] 216,11 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 11:[35, 65], Operations: ['81-10=71', '71-6=65'] Exploring Operation: 35*65=2275, Resulting Numbers: [2275] 2275,11 unequal: No Solution Exploring Operation: 35+65=100, Resulting Numbers: [100] 100,11 unequal: No Solution Exploring Operation: 65-35=30, Resulting Numbers: [30] 30,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 11:[71, 29], Operations: ['81-10=71', '35-6=29'] Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 71*29=2059, Resulting Numbers: [2059] 2059,11 unequal: No Solution Exploring Operation: 71+29=100, Resulting Numbers: [100] 100,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 11:[71, 41], Operations: ['81-10=71', '35+6=41'] Exploring Operation: 71-41=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 71*41=2911, Resulting Numbers: [2911] 2911,11 unequal: No Solution Exploring Operation: 71+41=112, Resulting Numbers: [112] 112,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 11:[35, 77], Operations: ['81-10=71', '6+71=77'] Exploring Operation: 35*77=2695, Resulting Numbers: [2695] 2695,11 unequal: No Solution Exploring Operation: 77-35=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 35+77=112, Resulting Numbers: [112] 112,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 11:[35, 10, 75], Operations: ['81-6=75'] Exploring Operation: 10+75=85, Resulting Numbers: [35, 85] Generated Node #0,4,0: 11:[35, 85] Operation: 10+75=85 Exploring Operation: 35-10=25, Resulting Numbers: [75, 25] Generated Node #0,4,1: 11:[75, 25] Operation: 35-10=25 Exploring Operation: 75-10=65, Resulting Numbers: [35, 65] Generated Node #0,4,2: 11:[35, 65] Operation: 75-10=65 Exploring Operation: 35+10=45, Resulting Numbers: [75, 45] Generated Node #0,4,3: 11:[75, 45] Operation: 35+10=45 Exploring Operation: 75-35=40, Resulting Numbers: [10, 40] Generated Node #0,4,4: 11:[10, 40] Operation: 75-35=40 Moving to Node #0,4,4 Current State: 11:[10, 40], Operations: ['81-6=75', '75-35=40'] Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 10+40=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 10*40=400, Resulting Numbers: [400] 400,11 unequal: No Solution Moving to Node #0,4,2 Current State: 11:[35, 65], Operations: ['81-6=75', '75-10=65'] Exploring Operation: 65-35=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 35+65=100, Resulting Numbers: [100] 100,11 unequal: No Solution Exploring Operation: 35*65=2275, Resulting Numbers: [2275] 2275,11 unequal: No Solution Moving to Node #0,4,1 Current State: 11:[75, 25], Operations: ['81-6=75', '35-10=25'] Exploring Operation: 75-25=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 75+25=100, Resulting Numbers: [100] 100,11 unequal: No Solution Exploring Operation: 75/25=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 75*25=1875, Resulting Numbers: [1875] 1875,11 unequal: No Solution Moving to Node #0,4,0 Current State: 11:[35, 85], Operations: ['81-6=75', '10+75=85'] Exploring Operation: 35+85=120, Resulting Numbers: [120] 120,11 unequal: No Solution Exploring Operation: 35*85=2975, Resulting Numbers: [2975] 2975,11 unequal: No Solution Exploring Operation: 85-35=50, Resulting Numbers: [50] 50,11 unequal: No Solution Moving to Node #0,4,3 Current State: 11:[75, 45], Operations: ['81-6=75', '35+10=45'] Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 75+45=120, Resulting Numbers: [120] 120,11 unequal: No Solution Exploring Operation: 75*45=3375, Resulting Numbers: [3375] 3375,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 97, 3, 82, 47 ]
92
[ "97-82=15", "3*15=45", "47+45=92" ]
Current State: 92:[97, 3, 82, 47], Operations: [] Exploring Operation: 97-82=15, Resulting Numbers: [3, 47, 15] Generated Node #2: [3, 47, 15] from Operation: 97-82=15 Current State: 92:[3, 47, 15], Operations: ['97-82=15'] Exploring Operation: 3*15=45, Resulting Numbers: [47, 45] Generated Node #3: [47, 45] from Operation: 3*15=45 Current State: 92:[47, 45], Operations: ['97-82=15', '3*15=45'] Exploring Operation: 47+45=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[97, 3, 82, 47], Operations: [] Exploring Operation: 97-47=50, Resulting Numbers: [3, 82, 50] Generated Node #0,0: 92:[3, 82, 50] Operation: 97-47=50 Exploring Operation: 3+82=85, Resulting Numbers: [97, 47, 85] Generated Node #0,1: 92:[97, 47, 85] Operation: 3+82=85 Exploring Operation: 97-82=15, Resulting Numbers: [3, 47, 15] Generated Node #0,2: 92:[3, 47, 15] Operation: 97-82=15 Exploring Operation: 97-3=94, Resulting Numbers: [82, 47, 94] Generated Node #0,3: 92:[82, 47, 94] Operation: 97-3=94 Exploring Operation: 47-3=44, Resulting Numbers: [97, 82, 44] Generated Node #0,4: 92:[97, 82, 44] Operation: 47-3=44 Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[3, 47, 15], Operations: ['97-82=15'] Exploring Operation: 3+15=18, Resulting Numbers: [47, 18] Generated Node #0,2,0: 92:[47, 18] Operation: 3+15=18 Exploring Operation: 3*15=45, Resulting Numbers: [47, 45] Generated Node #0,2,1: 92:[47, 45] Operation: 3*15=45 Exploring Operation: 15-3=12, Resulting Numbers: [47, 12] Generated Node #0,2,2: 92:[47, 12] Operation: 15-3=12 Exploring Operation: 15/3=5, Resulting Numbers: [47, 5] Generated Node #0,2,3: 92:[47, 5] Operation: 15/3=5 Exploring Operation: 47-3=44, Resulting Numbers: [15, 44] Generated Node #0,2,4: 92:[15, 44] Operation: 47-3=44 Moving to Node #0,2,1 Current State: 92:[47, 45], Operations: ['97-82=15', '3*15=45'] Exploring Operation: 47*45=2115, Resulting Numbers: [2115] 2115,92 unequal: No Solution Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 47+45=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[97, 3, 82, 47], Operations: [] Exploring Operation: 97-82=15, Resulting Numbers: [3, 47, 15] Generated Node #0,2: 92:[3, 47, 15] Operation: 97-82=15 Moving to Node #0,2 Current State: 92:[3, 47, 15], Operations: ['97-82=15'] Exploring Operation: 3*15=45, Resulting Numbers: [47, 45] Generated Node #0,2,1: 92:[47, 45] Operation: 3*15=45 Moving to Node #0,2,1 Current State: 92:[47, 45], Operations: ['97-82=15', '3*15=45'] Exploring Operation: 47+45=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 89, 37, 87, 6 ]
34
[ "89-87=2", "6/2=3", "37-3=34" ]
Current State: 34:[89, 37, 87, 6], Operations: [] Exploring Operation: 89-87=2, Resulting Numbers: [37, 6, 2] Generated Node #2: [37, 6, 2] from Operation: 89-87=2 Current State: 34:[37, 6, 2], Operations: ['89-87=2'] Exploring Operation: 6/2=3, Resulting Numbers: [37, 3] Generated Node #3: [37, 3] from Operation: 6/2=3 Current State: 34:[37, 3], Operations: ['89-87=2', '6/2=3'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[89, 37, 87, 6], Operations: [] Exploring Operation: 89-87=2, Resulting Numbers: [37, 6, 2] Generated Node #0,0: 34:[37, 6, 2] Operation: 89-87=2 Exploring Operation: 89-37=52, Resulting Numbers: [87, 6, 52] Generated Node #0,1: 34:[87, 6, 52] Operation: 89-37=52 Exploring Operation: 87-37=50, Resulting Numbers: [89, 6, 50] Generated Node #0,2: 34:[89, 6, 50] Operation: 87-37=50 Exploring Operation: 89-6=83, Resulting Numbers: [37, 87, 83] Generated Node #0,3: 34:[37, 87, 83] Operation: 89-6=83 Exploring Operation: 87-6=81, Resulting Numbers: [89, 37, 81] Generated Node #0,4: 34:[89, 37, 81] Operation: 87-6=81 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[37, 6, 2], Operations: ['89-87=2'] Exploring Operation: 37-6=31, Resulting Numbers: [2, 31] Generated Node #0,0,0: 34:[2, 31] Operation: 37-6=31 Exploring Operation: 6*2=12, Resulting Numbers: [37, 12] Generated Node #0,0,1: 34:[37, 12] Operation: 6*2=12 Exploring Operation: 6-2=4, Resulting Numbers: [37, 4] Generated Node #0,0,2: 34:[37, 4] Operation: 6-2=4 Exploring Operation: 37-2=35, Resulting Numbers: [6, 35] Generated Node #0,0,3: 34:[6, 35] Operation: 37-2=35 Exploring Operation: 6/2=3, Resulting Numbers: [37, 3] Generated Node #0,0,4: 34:[37, 3] Operation: 6/2=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[2, 31], Operations: ['89-87=2', '37-6=31'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,34 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,34 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 34:[37, 3], Operations: ['89-87=2', '6/2=3'] Exploring Operation: 37+3=40, Resulting Numbers: [40] 40,34 unequal: No Solution Exploring Operation: 37*3=111, Resulting Numbers: [111] 111,34 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[89, 37, 87, 6], Operations: [] Exploring Operation: 89-87=2, Resulting Numbers: [37, 6, 2] Generated Node #0,0: 34:[37, 6, 2] Operation: 89-87=2 Moving to Node #0,0 Current State: 34:[37, 6, 2], Operations: ['89-87=2'] Exploring Operation: 6/2=3, Resulting Numbers: [37, 3] Generated Node #0,0,4: 34:[37, 3] Operation: 6/2=3 Moving to Node #0,0,4 Current State: 34:[37, 3], Operations: ['89-87=2', '6/2=3'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 98, 68, 26, 56 ]
24
[ "68-26=42", "56*42=2352", "2352/98=24" ]
Current State: 24:[98, 68, 26, 56], Operations: [] Exploring Operation: 68-26=42, Resulting Numbers: [98, 56, 42] Generated Node #2: [98, 56, 42] from Operation: 68-26=42 Current State: 24:[98, 56, 42], Operations: ['68-26=42'] Exploring Operation: 56*42=2352, Resulting Numbers: [98, 2352] Generated Node #3: [98, 2352] from Operation: 56*42=2352 Current State: 24:[98, 2352], Operations: ['68-26=42', '56*42=2352'] Exploring Operation: 2352/98=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[98, 68, 26, 56], Operations: [] Exploring Operation: 98-68=30, Resulting Numbers: [26, 56, 30] Generated Node #0,0: 24:[26, 56, 30] Operation: 98-68=30 Moving to Node #0,0 Current State: 24:[26, 56, 30], Operations: ['98-68=30'] Exploring Operation: 56-30=26, Resulting Numbers: [26, 26] Generated Node #0,0,0: 24:[26, 26] Operation: 56-30=26 Moving to Node #0,0,0 Current State: 24:[26, 26], Operations: ['98-68=30', '56-30=26'] Exploring Operation: 26/26=1, Resulting Numbers: [1] 1,24 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 38, 5, 69, 91 ]
80
[ "38+69=107", "107-91=16", "5*16=80" ]
Current State: 80:[38, 5, 69, 91], Operations: [] Exploring Operation: 38+69=107, Resulting Numbers: [5, 91, 107] Generated Node #2: [5, 91, 107] from Operation: 38+69=107 Current State: 80:[5, 91, 107], Operations: ['38+69=107'] Exploring Operation: 107-91=16, Resulting Numbers: [5, 16] Generated Node #3: [5, 16] from Operation: 107-91=16 Current State: 80:[5, 16], Operations: ['38+69=107', '107-91=16'] Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[38, 5, 69, 91], Operations: [] Exploring Operation: 5+69=74, Resulting Numbers: [38, 91, 74] Generated Node #0,0: 80:[38, 91, 74] Operation: 5+69=74 Exploring Operation: 91-5=86, Resulting Numbers: [38, 69, 86] Generated Node #0,1: 80:[38, 69, 86] Operation: 91-5=86 Exploring Operation: 91-69=22, Resulting Numbers: [38, 5, 22] Generated Node #0,2: 80:[38, 5, 22] Operation: 91-69=22 Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[38, 5, 22], Operations: ['91-69=22'] Exploring Operation: 38+5=43, Resulting Numbers: [22, 43] Generated Node #0,2,0: 80:[22, 43] Operation: 38+5=43 Exploring Operation: 22-5=17, Resulting Numbers: [38, 17] Generated Node #0,2,1: 80:[38, 17] Operation: 22-5=17 Exploring Operation: 38-22=16, Resulting Numbers: [5, 16] Generated Node #0,2,2: 80:[5, 16] Operation: 38-22=16 Moving to Node #0,2,2 Current State: 80:[5, 16], Operations: ['91-69=22', '38-22=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[38, 5, 69, 91], Operations: [] Exploring Operation: 91-69=22, Resulting Numbers: [38, 5, 22] Generated Node #0,2: 80:[38, 5, 22] Operation: 91-69=22 Moving to Node #0,2 Current State: 80:[38, 5, 22], Operations: ['91-69=22'] Exploring Operation: 38-22=16, Resulting Numbers: [5, 16] Generated Node #0,2,2: 80:[5, 16] Operation: 38-22=16 Moving to Node #0,2,2 Current State: 80:[5, 16], Operations: ['91-69=22', '38-22=16'] Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 39, 79, 57, 79 ]
17
[ "57-39=18", "79/79=1", "18-1=17" ]
Current State: 17:[39, 79, 57, 79], Operations: [] Exploring Operation: 57-39=18, Resulting Numbers: [79, 79, 18] Generated Node #2: [79, 79, 18] from Operation: 57-39=18 Current State: 17:[79, 79, 18], Operations: ['57-39=18'] Exploring Operation: 79/79=1, Resulting Numbers: [18, 1] Generated Node #3: [18, 1] from Operation: 79/79=1 Current State: 17:[18, 1], Operations: ['57-39=18', '79/79=1'] Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[39, 79, 57, 79], Operations: [] Exploring Operation: 79-57=22, Resulting Numbers: [39, 79, 22] Generated Node #0,0: 17:[39, 79, 22] Operation: 79-57=22 Exploring Operation: 79-79=0, Resulting Numbers: [39, 57, 0] Generated Node #0,1: 17:[39, 57, 0] Operation: 79-79=0 Exploring Operation: 79-39=40, Resulting Numbers: [57, 79, 40] Generated Node #0,2: 17:[57, 79, 40] Operation: 79-39=40 Exploring Operation: 79-57=22, Resulting Numbers: [39, 79, 22] Generated Node #0,3: 17:[39, 79, 22] Operation: 79-57=22 Exploring Operation: 79/79=1, Resulting Numbers: [39, 57, 1] Generated Node #0,4: 17:[39, 57, 1] Operation: 79/79=1 Start Sub Search at level 1: Moving to Node #0,4 Current State: 17:[39, 57, 1], Operations: ['79/79=1'] Exploring Operation: 57-39=18, Resulting Numbers: [1, 18] Generated Node #0,4,0: 17:[1, 18] Operation: 57-39=18 Exploring Operation: 39*1=39, Resulting Numbers: [57, 39] Generated Node #0,4,1: 17:[57, 39] Operation: 39*1=39 Exploring Operation: 39/1=39, Resulting Numbers: [57, 39] Generated Node #0,4,2: 17:[57, 39] Operation: 39/1=39 Exploring Operation: 57-1=56, Resulting Numbers: [39, 56] Generated Node #0,4,3: 17:[39, 56] Operation: 57-1=56 Exploring Operation: 39-1=38, Resulting Numbers: [57, 38] Generated Node #0,4,4: 17:[57, 38] Operation: 39-1=38 Moving to Node #0,4,0 Current State: 17:[1, 18], Operations: ['79/79=1', '57-39=18'] Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,17 unequal: No Solution Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[39, 79, 57, 79], Operations: [] Exploring Operation: 79/79=1, Resulting Numbers: [39, 57, 1] Generated Node #0,4: 17:[39, 57, 1] Operation: 79/79=1 Moving to Node #0,4 Current State: 17:[39, 57, 1], Operations: ['79/79=1'] Exploring Operation: 57-39=18, Resulting Numbers: [1, 18] Generated Node #0,4,0: 17:[1, 18] Operation: 57-39=18 Moving to Node #0,4,0 Current State: 17:[1, 18], Operations: ['79/79=1', '57-39=18'] Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 11, 3, 25, 56 ]
48
[ "11*3=33", "25+56=81", "81-33=48" ]
Current State: 48:[11, 3, 25, 56], Operations: [] Exploring Operation: 11*3=33, Resulting Numbers: [25, 56, 33] Generated Node #2: [25, 56, 33] from Operation: 11*3=33 Current State: 48:[25, 56, 33], Operations: ['11*3=33'] Exploring Operation: 25+56=81, Resulting Numbers: [33, 81] Generated Node #3: [33, 81] from Operation: 25+56=81 Current State: 48:[33, 81], Operations: ['11*3=33', '25+56=81'] Exploring Operation: 81-33=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[11, 3, 25, 56], Operations: [] Exploring Operation: 56-3=53, Resulting Numbers: [11, 25, 53] Generated Node #0,0: 48:[11, 25, 53] Operation: 56-3=53 Exploring Operation: 56-25=31, Resulting Numbers: [11, 3, 31] Generated Node #0,1: 48:[11, 3, 31] Operation: 56-25=31 Exploring Operation: 11-3=8, Resulting Numbers: [25, 56, 8] Generated Node #0,2: 48:[25, 56, 8] Operation: 11-3=8 Exploring Operation: 56-11=45, Resulting Numbers: [3, 25, 45] Generated Node #0,3: 48:[3, 25, 45] Operation: 56-11=45 Exploring Operation: 25-11=14, Resulting Numbers: [3, 56, 14] Generated Node #0,4: 48:[3, 56, 14] Operation: 25-11=14 Start Sub Search at level 1: Moving to Node #0,3 Current State: 48:[3, 25, 45], Operations: ['56-11=45'] Exploring Operation: 45/3=15, Resulting Numbers: [25, 15] Generated Node #0,3,0: 48:[25, 15] Operation: 45/3=15 Exploring Operation: 45-25=20, Resulting Numbers: [3, 20] Generated Node #0,3,1: 48:[3, 20] Operation: 45-25=20 Exploring Operation: 25-3=22, Resulting Numbers: [45, 22] Generated Node #0,3,2: 48:[45, 22] Operation: 25-3=22 Exploring Operation: 3+45=48, Resulting Numbers: [25, 48] Generated Node #0,3,3: 48:[25, 48] Operation: 3+45=48 Exploring Operation: 3+25=28, Resulting Numbers: [45, 28] Generated Node #0,3,4: 48:[45, 28] Operation: 3+25=28 Moving to Node #0,3,3 Current State: 48:[25, 48], Operations: ['56-11=45', '3+45=48'] Exploring Operation: 48-25=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 25+48=73, Resulting Numbers: [73] 73,48 unequal: No Solution Exploring Operation: 25*48=1200, Resulting Numbers: [1200] 1200,48 unequal: No Solution Moving to Node #0,3,0 Current State: 48:[25, 15], Operations: ['56-11=45', '45/3=15'] Exploring Operation: 25+15=40, Resulting Numbers: [40] 40,48 unequal: No Solution Exploring Operation: 25*15=375, Resulting Numbers: [375] 375,48 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,48 unequal: No Solution Moving to Node #0,3,1 Current State: 48:[3, 20], Operations: ['56-11=45', '45-25=20'] Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,48 unequal: No Solution Moving to Node #0,3,2 Current State: 48:[45, 22], Operations: ['56-11=45', '25-3=22'] Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 45*22=990, Resulting Numbers: [990] 990,48 unequal: No Solution Exploring Operation: 45+22=67, Resulting Numbers: [67] 67,48 unequal: No Solution Moving to Node #0,3,4 Current State: 48:[45, 28], Operations: ['56-11=45', '3+25=28'] Exploring Operation: 45-28=17, Resulting Numbers: [17] 17,48 unequal: No Solution Exploring Operation: 45*28=1260, Resulting Numbers: [1260] 1260,48 unequal: No Solution Exploring Operation: 45+28=73, Resulting Numbers: [73] 73,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[11, 25, 53], Operations: ['56-3=53'] Exploring Operation: 11+25=36, Resulting Numbers: [53, 36] Generated Node #0,0,0: 48:[53, 36] Operation: 11+25=36 Exploring Operation: 25-11=14, Resulting Numbers: [53, 14] Generated Node #0,0,1: 48:[53, 14] Operation: 25-11=14 Exploring Operation: 11+53=64, Resulting Numbers: [25, 64] Generated Node #0,0,2: 48:[25, 64] Operation: 11+53=64 Exploring Operation: 53-11=42, Resulting Numbers: [25, 42] Generated Node #0,0,3: 48:[25, 42] Operation: 53-11=42 Exploring Operation: 53-25=28, Resulting Numbers: [11, 28] Generated Node #0,0,4: 48:[11, 28] Operation: 53-25=28 Moving to Node #0,0,4 Current State: 48:[11, 28], Operations: ['56-3=53', '53-25=28'] Exploring Operation: 11+28=39, Resulting Numbers: [39] 39,48 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,48 unequal: No Solution Exploring Operation: 11*28=308, Resulting Numbers: [308] 308,48 unequal: No Solution Moving to Node #0,0,3 Current State: 48:[25, 42], Operations: ['56-3=53', '53-11=42'] Exploring Operation: 25+42=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 25*42=1050, Resulting Numbers: [1050] 1050,48 unequal: No Solution Exploring Operation: 42-25=17, Resulting Numbers: [17] 17,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[53, 14], Operations: ['56-3=53', '25-11=14'] Exploring Operation: 53+14=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,48 unequal: No Solution Exploring Operation: 53*14=742, Resulting Numbers: [742] 742,48 unequal: No Solution Moving to Node #0,0,0 Current State: 48:[53, 36], Operations: ['56-3=53', '11+25=36'] Exploring Operation: 53-36=17, Resulting Numbers: [17] 17,48 unequal: No Solution Exploring Operation: 53*36=1908, Resulting Numbers: [1908] 1908,48 unequal: No Solution Exploring Operation: 53+36=89, Resulting Numbers: [89] 89,48 unequal: No Solution Moving to Node #0,0,2 Current State: 48:[25, 64], Operations: ['56-3=53', '11+53=64'] Exploring Operation: 25+64=89, Resulting Numbers: [89] 89,48 unequal: No Solution Exploring Operation: 25*64=1600, Resulting Numbers: [1600] 1600,48 unequal: No Solution Exploring Operation: 64-25=39, Resulting Numbers: [39] 39,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[11, 3, 31], Operations: ['56-25=31'] Exploring Operation: 11-3=8, Resulting Numbers: [31, 8] Generated Node #0,1,0: 48:[31, 8] Operation: 11-3=8 Exploring Operation: 31-3=28, Resulting Numbers: [11, 28] Generated Node #0,1,1: 48:[11, 28] Operation: 31-3=28 Exploring Operation: 11+3=14, Resulting Numbers: [31, 14] Generated Node #0,1,2: 48:[31, 14] Operation: 11+3=14 Exploring Operation: 11+31=42, Resulting Numbers: [3, 42] Generated Node #0,1,3: 48:[3, 42] Operation: 11+31=42 Exploring Operation: 31-11=20, Resulting Numbers: [3, 20] Generated Node #0,1,4: 48:[3, 20] Operation: 31-11=20 Moving to Node #0,1,4 Current State: 48:[3, 20], Operations: ['56-25=31', '31-11=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,48 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[11, 28], Operations: ['56-25=31', '31-3=28'] Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,48 unequal: No Solution Exploring Operation: 11+28=39, Resulting Numbers: [39] 39,48 unequal: No Solution Exploring Operation: 11*28=308, Resulting Numbers: [308] 308,48 unequal: No Solution Moving to Node #0,1,3 Current State: 48:[3, 42], Operations: ['56-25=31', '11+31=42'] Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,48 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,48 unequal: No Solution Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,48 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,48 unequal: No Solution Moving to Node #0,1,0 Current State: 48:[31, 8], Operations: ['56-25=31', '11-3=8'] Exploring Operation: 31*8=248, Resulting Numbers: [248] 248,48 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 31+8=39, Resulting Numbers: [39] 39,48 unequal: No Solution Moving to Node #0,1,2 Current State: 48:[31, 14], Operations: ['56-25=31', '11+3=14'] Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,48 unequal: No Solution Exploring Operation: 31*14=434, Resulting Numbers: [434] 434,48 unequal: No Solution Exploring Operation: 31+14=45, Resulting Numbers: [45] 45,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[25, 56, 8], Operations: ['11-3=8'] Exploring Operation: 25-8=17, Resulting Numbers: [56, 17] Generated Node #0,2,0: 48:[56, 17] Operation: 25-8=17 Exploring Operation: 56/8=7, Resulting Numbers: [25, 7] Generated Node #0,2,1: 48:[25, 7] Operation: 56/8=7 Exploring Operation: 56-8=48, Resulting Numbers: [25, 48] Generated Node #0,2,2: 48:[25, 48] Operation: 56-8=48 Exploring Operation: 25+8=33, Resulting Numbers: [56, 33] Generated Node #0,2,3: 48:[56, 33] Operation: 25+8=33 Exploring Operation: 56-25=31, Resulting Numbers: [8, 31] Generated Node #0,2,4: 48:[8, 31] Operation: 56-25=31 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 48:[25, 48], Operations: ['11-3=8', '56-8=48'] Exploring Operation: 48-25=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 25*48=1200, Resulting Numbers: [1200] 1200,48 unequal: No Solution Exploring Operation: 25+48=73, Resulting Numbers: [73] 73,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 48:[25, 7], Operations: ['11-3=8', '56/8=7'] Exploring Operation: 25*7=175, Resulting Numbers: [175] 175,48 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,48 unequal: No Solution Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 48:[8, 31], Operations: ['11-3=8', '56-25=31'] Exploring Operation: 8+31=39, Resulting Numbers: [39] 39,48 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 8*31=248, Resulting Numbers: [248] 248,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 48:[56, 17], Operations: ['11-3=8', '25-8=17'] Exploring Operation: 56*17=952, Resulting Numbers: [952] 952,48 unequal: No Solution Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,48 unequal: No Solution Exploring Operation: 56+17=73, Resulting Numbers: [73] 73,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 48:[56, 33], Operations: ['11-3=8', '25+8=33'] Exploring Operation: 56+33=89, Resulting Numbers: [89] 89,48 unequal: No Solution Exploring Operation: 56*33=1848, Resulting Numbers: [1848] 1848,48 unequal: No Solution Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 48:[3, 56, 14], Operations: ['25-11=14'] Exploring Operation: 14-3=11, Resulting Numbers: [56, 11] Generated Node #0,4,0: 48:[56, 11] Operation: 14-3=11 Exploring Operation: 56-14=42, Resulting Numbers: [3, 42] Generated Node #0,4,1: 48:[3, 42] Operation: 56-14=42 Exploring Operation: 3+14=17, Resulting Numbers: [56, 17] Generated Node #0,4,2: 48:[56, 17] Operation: 3+14=17 Exploring Operation: 56/14=4, Resulting Numbers: [3, 4] Generated Node #0,4,3: 48:[3, 4] Operation: 56/14=4 Exploring Operation: 56-3=53, Resulting Numbers: [14, 53] Generated Node #0,4,4: 48:[14, 53] Operation: 56-3=53 Moving to Node #0,4,3 Current State: 48:[3, 4], Operations: ['25-11=14', '56/14=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,48 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,48 unequal: No Solution Moving to Node #0,4,1 Current State: 48:[3, 42], Operations: ['25-11=14', '56-14=42'] Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,48 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,48 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,48 unequal: No Solution Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,48 unequal: No Solution Moving to Node #0,4,4 Current State: 48:[14, 53], Operations: ['25-11=14', '56-3=53'] Exploring Operation: 14*53=742, Resulting Numbers: [742] 742,48 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,48 unequal: No Solution Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,48 unequal: No Solution Moving to Node #0,4,0 Current State: 48:[56, 11], Operations: ['25-11=14', '14-3=11'] Exploring Operation: 56+11=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 56-11=45, Resulting Numbers: [45] 45,48 unequal: No Solution Exploring Operation: 56*11=616, Resulting Numbers: [616] 616,48 unequal: No Solution Moving to Node #0,4,2 Current State: 48:[56, 17], Operations: ['25-11=14', '3+14=17'] Exploring Operation: 56*17=952, Resulting Numbers: [952] 952,48 unequal: No Solution Exploring Operation: 56+17=73, Resulting Numbers: [73] 73,48 unequal: No Solution Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 77, 87, 43, 36 ]
69
[ "87-77=10", "43+36=79", "79-10=69" ]
Current State: 69:[77, 87, 43, 36], Operations: [] Exploring Operation: 87-77=10, Resulting Numbers: [43, 36, 10] Generated Node #2: [43, 36, 10] from Operation: 87-77=10 Current State: 69:[43, 36, 10], Operations: ['87-77=10'] Exploring Operation: 43+36=79, Resulting Numbers: [10, 79] Generated Node #3: [10, 79] from Operation: 43+36=79 Current State: 69:[10, 79], Operations: ['87-77=10', '43+36=79'] Exploring Operation: 79-10=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[77, 87, 43, 36], Operations: [] Exploring Operation: 43-36=7, Resulting Numbers: [77, 87, 7] Generated Node #0,0: 69:[77, 87, 7] Operation: 43-36=7 Moving to Node #0,0 Current State: 69:[77, 87, 7], Operations: ['43-36=7'] Exploring Operation: 87-77=10, Resulting Numbers: [7, 10] Generated Node #0,0,0: 69:[7, 10] Operation: 87-77=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[7, 10], Operations: ['43-36=7', '87-77=10'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 17, 81, 31, 83 ]
46
[ "17+81=98", "83-31=52", "98-52=46" ]
Current State: 46:[17, 81, 31, 83], Operations: [] Exploring Operation: 17+81=98, Resulting Numbers: [31, 83, 98] Generated Node #2: [31, 83, 98] from Operation: 17+81=98 Current State: 46:[31, 83, 98], Operations: ['17+81=98'] Exploring Operation: 83-31=52, Resulting Numbers: [98, 52] Generated Node #3: [98, 52] from Operation: 83-31=52 Current State: 46:[98, 52], Operations: ['17+81=98', '83-31=52'] Exploring Operation: 98-52=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[17, 81, 31, 83], Operations: [] Exploring Operation: 83-31=52, Resulting Numbers: [17, 81, 52] Generated Node #0,0: 46:[17, 81, 52] Operation: 83-31=52 Exploring Operation: 81-31=50, Resulting Numbers: [17, 83, 50] Generated Node #0,1: 46:[17, 83, 50] Operation: 81-31=50 Exploring Operation: 81-17=64, Resulting Numbers: [31, 83, 64] Generated Node #0,2: 46:[31, 83, 64] Operation: 81-17=64 Exploring Operation: 83-81=2, Resulting Numbers: [17, 31, 2] Generated Node #0,3: 46:[17, 31, 2] Operation: 83-81=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 46:[17, 31, 2], Operations: ['83-81=2'] Exploring Operation: 17+31=48, Resulting Numbers: [2, 48] Generated Node #0,3,0: 46:[2, 48] Operation: 17+31=48 Exploring Operation: 31-2=29, Resulting Numbers: [17, 29] Generated Node #0,3,1: 46:[17, 29] Operation: 31-2=29 Exploring Operation: 17+2=19, Resulting Numbers: [31, 19] Generated Node #0,3,2: 46:[31, 19] Operation: 17+2=19 Exploring Operation: 31-17=14, Resulting Numbers: [2, 14] Generated Node #0,3,3: 46:[2, 14] Operation: 31-17=14 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 46:[2, 48], Operations: ['83-81=2', '17+31=48'] Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,46 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[17, 81, 31, 83], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [17, 31, 2] Generated Node #0,3: 46:[17, 31, 2] Operation: 83-81=2 Moving to Node #0,3 Current State: 46:[17, 31, 2], Operations: ['83-81=2'] Exploring Operation: 17+31=48, Resulting Numbers: [2, 48] Generated Node #0,3,0: 46:[2, 48] Operation: 17+31=48 Moving to Node #0,3,0 Current State: 46:[2, 48], Operations: ['83-81=2', '17+31=48'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 68, 34, 67, 23 ]
58
[ "68+34=102", "67-23=44", "102-44=58" ]
Current State: 58:[68, 34, 67, 23], Operations: [] Exploring Operation: 68+34=102, Resulting Numbers: [67, 23, 102] Generated Node #2: [67, 23, 102] from Operation: 68+34=102 Current State: 58:[67, 23, 102], Operations: ['68+34=102'] Exploring Operation: 67-23=44, Resulting Numbers: [102, 44] Generated Node #3: [102, 44] from Operation: 67-23=44 Current State: 58:[102, 44], Operations: ['68+34=102', '67-23=44'] Exploring Operation: 102-44=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[68, 34, 67, 23], Operations: [] Exploring Operation: 34+23=57, Resulting Numbers: [68, 67, 57] Generated Node #0,0: 58:[68, 67, 57] Operation: 34+23=57 Exploring Operation: 68-34=34, Resulting Numbers: [67, 23, 34] Generated Node #0,1: 58:[67, 23, 34] Operation: 68-34=34 Exploring Operation: 67-34=33, Resulting Numbers: [68, 23, 33] Generated Node #0,2: 58:[68, 23, 33] Operation: 67-34=33 Exploring Operation: 68/34=2, Resulting Numbers: [67, 23, 2] Generated Node #0,3: 58:[67, 23, 2] Operation: 68/34=2 Exploring Operation: 68-67=1, Resulting Numbers: [34, 23, 1] Generated Node #0,4: 58:[34, 23, 1] Operation: 68-67=1 Moving to Node #0,4 Current State: 58:[34, 23, 1], Operations: ['68-67=1'] Exploring Operation: 34-1=33, Resulting Numbers: [23, 33] Generated Node #0,4,0: 58:[23, 33] Operation: 34-1=33 Exploring Operation: 23+1=24, Resulting Numbers: [34, 24] Generated Node #0,4,1: 58:[34, 24] Operation: 23+1=24 Exploring Operation: 34-23=11, Resulting Numbers: [1, 11] Generated Node #0,4,2: 58:[1, 11] Operation: 34-23=11 Exploring Operation: 34*1=34, Resulting Numbers: [23, 34] Generated Node #0,4,3: 58:[23, 34] Operation: 34*1=34 Exploring Operation: 34+23=57, Resulting Numbers: [1, 57] Generated Node #0,4,4: 58:[1, 57] Operation: 34+23=57 Moving to Node #0,3 Current State: 58:[67, 23, 2], Operations: ['68/34=2'] Exploring Operation: 67-2=65, Resulting Numbers: [23, 65] Generated Node #0,3,0: 58:[23, 65] Operation: 67-2=65 Exploring Operation: 67-23=44, Resulting Numbers: [2, 44] Generated Node #0,3,1: 58:[2, 44] Operation: 67-23=44 Exploring Operation: 67+2=69, Resulting Numbers: [23, 69] Generated Node #0,3,2: 58:[23, 69] Operation: 67+2=69 Exploring Operation: 23-2=21, Resulting Numbers: [67, 21] Generated Node #0,3,3: 58:[67, 21] Operation: 23-2=21 Exploring Operation: 23+2=25, Resulting Numbers: [67, 25] Generated Node #0,3,4: 58:[67, 25] Operation: 23+2=25 Moving to Node #0,0 Current State: 58:[68, 67, 57], Operations: ['34+23=57'] Exploring Operation: 67+57=124, Resulting Numbers: [68, 124] Generated Node #0,0,0: 58:[68, 124] Operation: 67+57=124 Exploring Operation: 67-57=10, Resulting Numbers: [68, 10] Generated Node #0,0,1: 58:[68, 10] Operation: 67-57=10 Exploring Operation: 68+57=125, Resulting Numbers: [67, 125] Generated Node #0,0,2: 58:[67, 125] Operation: 68+57=125 Exploring Operation: 68-57=11, Resulting Numbers: [67, 11] Generated Node #0,0,3: 58:[67, 11] Operation: 68-57=11 Exploring Operation: 68-67=1, Resulting Numbers: [57, 1] Generated Node #0,0,4: 58:[57, 1] Operation: 68-67=1 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 58:[57, 1], Operations: ['34+23=57', '68-67=1'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[68, 34, 67, 23], Operations: [] Exploring Operation: 34+23=57, Resulting Numbers: [68, 67, 57] Generated Node #0,0: 58:[68, 67, 57] Operation: 34+23=57 Moving to Node #0,0 Current State: 58:[68, 67, 57], Operations: ['34+23=57'] Exploring Operation: 68-67=1, Resulting Numbers: [57, 1] Generated Node #0,0,4: 58:[57, 1] Operation: 68-67=1 Moving to Node #0,0,4 Current State: 58:[57, 1], Operations: ['34+23=57', '68-67=1'] Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_5
mult_heuristic
[ 25, 41, 23, 40 ]
57
[ "25*40=1000", "41*23=943", "1000-943=57" ]
Current State: 57:[25, 41, 23, 40], Operations: [] Exploring Operation: 25*40=1000, Resulting Numbers: [41, 23, 1000] Generated Node #2: [41, 23, 1000] from Operation: 25*40=1000 Current State: 57:[41, 23, 1000], Operations: ['25*40=1000'] Exploring Operation: 41*23=943, Resulting Numbers: [1000, 943] Generated Node #3: [1000, 943] from Operation: 41*23=943 Current State: 57:[1000, 943], Operations: ['25*40=1000', '41*23=943'] Exploring Operation: 1000-943=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[25, 41, 23, 40], Operations: [] Exploring Operation: 41-25=16, Resulting Numbers: [23, 40, 16] Generated Node #0,0: 57:[23, 40, 16] Operation: 41-25=16 Exploring Operation: 41-40=1, Resulting Numbers: [25, 23, 1] Generated Node #0,1: 57:[25, 23, 1] Operation: 41-40=1 Moving to Node #0,1 Current State: 57:[25, 23, 1], Operations: ['41-40=1'] Exploring Operation: 25-23=2, Resulting Numbers: [1, 2] Generated Node #0,1,0: 57:[1, 2] Operation: 25-23=2 Exploring Operation: 25-1=24, Resulting Numbers: [23, 24] Generated Node #0,1,1: 57:[23, 24] Operation: 25-1=24 Moving to Node #0,0 Current State: 57:[23, 40, 16], Operations: ['41-25=16'] Exploring Operation: 40-23=17, Resulting Numbers: [16, 17] Generated Node #0,0,0: 57:[16, 17] Operation: 40-23=17 Exploring Operation: 40+16=56, Resulting Numbers: [23, 56] Generated Node #0,0,1: 57:[23, 56] Operation: 40+16=56 Moving to Node #0,1,0 Current State: 57:[1, 2], Operations: ['41-40=1', '25-23=2'] Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,57 unequal: No Solution Moving to Node #0,0,0 Current State: 57:[16, 17], Operations: ['41-25=16', '40-23=17'] Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[23, 56], Operations: ['41-25=16', '40+16=56'] Exploring Operation: 56-23=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 23+56=79, Resulting Numbers: [79] 79,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[23, 24], Operations: ['41-40=1', '25-1=24'] Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,57 unequal: No Solution Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,57 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 64, 30, 15, 97 ]
31
[ "64*30=1920", "1920/15=128", "128-97=31" ]
Current State: 31:[64, 30, 15, 97], Operations: [] Exploring Operation: 64*30=1920, Resulting Numbers: [15, 97, 1920] Generated Node #2: [15, 97, 1920] from Operation: 64*30=1920 Current State: 31:[15, 97, 1920], Operations: ['64*30=1920'] Exploring Operation: 1920/15=128, Resulting Numbers: [97, 128] Generated Node #3: [97, 128] from Operation: 1920/15=128 Current State: 31:[97, 128], Operations: ['64*30=1920', '1920/15=128'] Exploring Operation: 128-97=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[64, 30, 15, 97], Operations: [] Exploring Operation: 97-30=67, Resulting Numbers: [64, 15, 67] Generated Node #0,0: 31:[64, 15, 67] Operation: 97-30=67 Exploring Operation: 64-15=49, Resulting Numbers: [30, 97, 49] Generated Node #0,1: 31:[30, 97, 49] Operation: 64-15=49 Exploring Operation: 97-64=33, Resulting Numbers: [30, 15, 33] Generated Node #0,2: 31:[30, 15, 33] Operation: 97-64=33 Exploring Operation: 64-30=34, Resulting Numbers: [15, 97, 34] Generated Node #0,3: 31:[15, 97, 34] Operation: 64-30=34 Moving to Node #0,2 Current State: 31:[30, 15, 33], Operations: ['97-64=33'] Exploring Operation: 15+33=48, Resulting Numbers: [30, 48] Generated Node #0,2,0: 31:[30, 48] Operation: 15+33=48 Exploring Operation: 33-15=18, Resulting Numbers: [30, 18] Generated Node #0,2,1: 31:[30, 18] Operation: 33-15=18 Exploring Operation: 30-15=15, Resulting Numbers: [33, 15] Generated Node #0,2,2: 31:[33, 15] Operation: 30-15=15 Exploring Operation: 30+15=45, Resulting Numbers: [33, 45] Generated Node #0,2,3: 31:[33, 45] Operation: 30+15=45 Moving to Node #0,1 Current State: 31:[30, 97, 49], Operations: ['64-15=49'] Exploring Operation: 97-49=48, Resulting Numbers: [30, 48] Generated Node #0,1,0: 31:[30, 48] Operation: 97-49=48 Exploring Operation: 30+97=127, Resulting Numbers: [49, 127] Generated Node #0,1,1: 31:[49, 127] Operation: 30+97=127 Exploring Operation: 49-30=19, Resulting Numbers: [97, 19] Generated Node #0,1,2: 31:[97, 19] Operation: 49-30=19 Exploring Operation: 97-30=67, Resulting Numbers: [49, 67] Generated Node #0,1,3: 31:[49, 67] Operation: 97-30=67 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[30, 48], Operations: ['64-15=49', '97-49=48'] Exploring Operation: 30*48=1440, Resulting Numbers: [1440] 1440,31 unequal: No Solution Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 30+48=78, Resulting Numbers: [78] 78,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 31:[49, 67], Operations: ['64-15=49', '97-30=67'] Exploring Operation: 49+67=116, Resulting Numbers: [116] 116,31 unequal: No Solution Exploring Operation: 49*67=3283, Resulting Numbers: [3283] 3283,31 unequal: No Solution Exploring Operation: 67-49=18, Resulting Numbers: [18] 18,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[97, 19], Operations: ['64-15=49', '49-30=19'] Exploring Operation: 97+19=116, Resulting Numbers: [116] 116,31 unequal: No Solution Exploring Operation: 97*19=1843, Resulting Numbers: [1843] 1843,31 unequal: No Solution Exploring Operation: 97-19=78, Resulting Numbers: [78] 78,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[49, 127], Operations: ['64-15=49', '30+97=127'] Exploring Operation: 49+127=176, Resulting Numbers: [176] 176,31 unequal: No Solution Exploring Operation: 49*127=6223, Resulting Numbers: [6223] 6223,31 unequal: No Solution Exploring Operation: 127-49=78, Resulting Numbers: [78] 78,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 31:[64, 15, 67], Operations: ['97-30=67'] Exploring Operation: 67-15=52, Resulting Numbers: [64, 52] Generated Node #0,0,0: 31:[64, 52] Operation: 67-15=52 Exploring Operation: 67-64=3, Resulting Numbers: [15, 3] Generated Node #0,0,1: 31:[15, 3] Operation: 67-64=3 Exploring Operation: 64-15=49, Resulting Numbers: [67, 49] Generated Node #0,0,2: 31:[67, 49] Operation: 64-15=49 Exploring Operation: 64+15=79, Resulting Numbers: [67, 79] Generated Node #0,0,3: 31:[67, 79] Operation: 64+15=79 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[15, 3], Operations: ['97-30=67', '67-64=3'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,31 unequal: No Solution Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[64, 52], Operations: ['97-30=67', '67-15=52'] Exploring Operation: 64+52=116, Resulting Numbers: [116] 116,31 unequal: No Solution Exploring Operation: 64-52=12, Resulting Numbers: [12] 12,31 unequal: No Solution Exploring Operation: 64*52=3328, Resulting Numbers: [3328] 3328,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 31:[67, 49], Operations: ['97-30=67', '64-15=49'] Exploring Operation: 67*49=3283, Resulting Numbers: [3283] 3283,31 unequal: No Solution Exploring Operation: 67+49=116, Resulting Numbers: [116] 116,31 unequal: No Solution Exploring Operation: 67-49=18, Resulting Numbers: [18] 18,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 31:[67, 79], Operations: ['97-30=67', '64+15=79'] Exploring Operation: 67+79=146, Resulting Numbers: [146] 146,31 unequal: No Solution Exploring Operation: 79-67=12, Resulting Numbers: [12] 12,31 unequal: No Solution Exploring Operation: 67*79=5293, Resulting Numbers: [5293] 5293,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 31:[15, 97, 34], Operations: ['64-30=34'] Exploring Operation: 97-15=82, Resulting Numbers: [34, 82] Generated Node #0,3,0: 31:[34, 82] Operation: 97-15=82 Exploring Operation: 15+97=112, Resulting Numbers: [34, 112] Generated Node #0,3,1: 31:[34, 112] Operation: 15+97=112 Exploring Operation: 97-34=63, Resulting Numbers: [15, 63] Generated Node #0,3,2: 31:[15, 63] Operation: 97-34=63 Exploring Operation: 34-15=19, Resulting Numbers: [97, 19] Generated Node #0,3,3: 31:[97, 19] Operation: 34-15=19 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 31:[15, 63], Operations: ['64-30=34', '97-34=63'] Exploring Operation: 15*63=945, Resulting Numbers: [945] 945,31 unequal: No Solution Exploring Operation: 15+63=78, Resulting Numbers: [78] 78,31 unequal: No Solution Exploring Operation: 63-15=48, Resulting Numbers: [48] 48,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 31:[34, 82], Operations: ['64-30=34', '97-15=82'] Exploring Operation: 82-34=48, Resulting Numbers: [48] 48,31 unequal: No Solution Exploring Operation: 34+82=116, Resulting Numbers: [116] 116,31 unequal: No Solution Exploring Operation: 34*82=2788, Resulting Numbers: [2788] 2788,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 31:[97, 19], Operations: ['64-30=34', '34-15=19'] Exploring Operation: 97-19=78, Resulting Numbers: [78] 78,31 unequal: No Solution Exploring Operation: 97*19=1843, Resulting Numbers: [1843] 1843,31 unequal: No Solution Exploring Operation: 97+19=116, Resulting Numbers: [116] 116,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 31:[34, 112], Operations: ['64-30=34', '15+97=112'] Exploring Operation: 34+112=146, Resulting Numbers: [146] 146,31 unequal: No Solution Exploring Operation: 112-34=78, Resulting Numbers: [78] 78,31 unequal: No Solution Exploring Operation: 34*112=3808, Resulting Numbers: [3808] 3808,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 31:[30, 18], Operations: ['97-64=33', '33-15=18'] Exploring Operation: 30*18=540, Resulting Numbers: [540] 540,31 unequal: No Solution Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,31 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,31 unequal: No Solution Moving to Node #0,2,3 Current State: 31:[33, 45], Operations: ['97-64=33', '30+15=45'] Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,31 unequal: No Solution Exploring Operation: 33+45=78, Resulting Numbers: [78] 78,31 unequal: No Solution Exploring Operation: 33*45=1485, Resulting Numbers: [1485] 1485,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[33, 15], Operations: ['97-64=33', '30-15=15'] Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,31 unequal: No Solution Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,31 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,31 unequal: No Solution Moving to Node #0,2,0 Current State: 31:[30, 48], Operations: ['97-64=33', '15+33=48'] Exploring Operation: 30+48=78, Resulting Numbers: [78] 78,31 unequal: No Solution Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 30*48=1440, Resulting Numbers: [1440] 1440,31 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 23, 38, 14, 66 ]
70
[ "23+38=61", "66-61=5", "14*5=70" ]
Current State: 70:[23, 38, 14, 66], Operations: [] Exploring Operation: 23+38=61, Resulting Numbers: [14, 66, 61] Generated Node #2: [14, 66, 61] from Operation: 23+38=61 Current State: 70:[14, 66, 61], Operations: ['23+38=61'] Exploring Operation: 66-61=5, Resulting Numbers: [14, 5] Generated Node #3: [14, 5] from Operation: 66-61=5 Current State: 70:[14, 5], Operations: ['23+38=61', '66-61=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[23, 38, 14, 66], Operations: [] Exploring Operation: 23-14=9, Resulting Numbers: [38, 66, 9] Generated Node #0,0: 70:[38, 66, 9] Operation: 23-14=9 Exploring Operation: 23+38=61, Resulting Numbers: [14, 66, 61] Generated Node #0,1: 70:[14, 66, 61] Operation: 23+38=61 Exploring Operation: 38-23=15, Resulting Numbers: [14, 66, 15] Generated Node #0,2: 70:[14, 66, 15] Operation: 38-23=15 Exploring Operation: 66-23=43, Resulting Numbers: [38, 14, 43] Generated Node #0,3: 70:[38, 14, 43] Operation: 66-23=43 Exploring Operation: 23+14=37, Resulting Numbers: [38, 66, 37] Generated Node #0,4: 70:[38, 66, 37] Operation: 23+14=37 Moving to Node #0,2 Current State: 70:[14, 66, 15], Operations: ['38-23=15'] Exploring Operation: 66+15=81, Resulting Numbers: [14, 81] Generated Node #0,2,0: 70:[14, 81] Operation: 66+15=81 Exploring Operation: 14+66=80, Resulting Numbers: [15, 80] Generated Node #0,2,1: 70:[15, 80] Operation: 14+66=80 Exploring Operation: 66-15=51, Resulting Numbers: [14, 51] Generated Node #0,2,2: 70:[14, 51] Operation: 66-15=51 Exploring Operation: 14+15=29, Resulting Numbers: [66, 29] Generated Node #0,2,3: 70:[66, 29] Operation: 14+15=29 Exploring Operation: 15-14=1, Resulting Numbers: [66, 1] Generated Node #0,2,4: 70:[66, 1] Operation: 15-14=1 Moving to Node #0,0 Current State: 70:[38, 66, 9], Operations: ['23-14=9'] Exploring Operation: 66-38=28, Resulting Numbers: [9, 28] Generated Node #0,0,0: 70:[9, 28] Operation: 66-38=28 Exploring Operation: 38+9=47, Resulting Numbers: [66, 47] Generated Node #0,0,1: 70:[66, 47] Operation: 38+9=47 Exploring Operation: 66-9=57, Resulting Numbers: [38, 57] Generated Node #0,0,2: 70:[38, 57] Operation: 66-9=57 Exploring Operation: 38-9=29, Resulting Numbers: [66, 29] Generated Node #0,0,3: 70:[66, 29] Operation: 38-9=29 Exploring Operation: 66+9=75, Resulting Numbers: [38, 75] Generated Node #0,0,4: 70:[38, 75] Operation: 66+9=75 Moving to Node #0,4 Current State: 70:[38, 66, 37], Operations: ['23+14=37'] Exploring Operation: 38+66=104, Resulting Numbers: [37, 104] Generated Node #0,4,0: 70:[37, 104] Operation: 38+66=104 Exploring Operation: 38+37=75, Resulting Numbers: [66, 75] Generated Node #0,4,1: 70:[66, 75] Operation: 38+37=75 Exploring Operation: 66-38=28, Resulting Numbers: [37, 28] Generated Node #0,4,2: 70:[37, 28] Operation: 66-38=28 Exploring Operation: 66-37=29, Resulting Numbers: [38, 29] Generated Node #0,4,3: 70:[38, 29] Operation: 66-37=29 Exploring Operation: 38-37=1, Resulting Numbers: [66, 1] Generated Node #0,4,4: 70:[66, 1] Operation: 38-37=1 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 70:[66, 1], Operations: ['23+14=37', '38-37=1'] Exploring Operation: 66*1=66, Resulting Numbers: [66] 66,70 unequal: No Solution Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,70 unequal: No Solution Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,70 unequal: No Solution Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 70:[66, 75], Operations: ['23+14=37', '38+37=75'] Exploring Operation: 66+75=141, Resulting Numbers: [141] 141,70 unequal: No Solution Exploring Operation: 66*75=4950, Resulting Numbers: [4950] 4950,70 unequal: No Solution Exploring Operation: 75-66=9, Resulting Numbers: [9] 9,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 70:[37, 28], Operations: ['23+14=37', '66-38=28'] Exploring Operation: 37+28=65, Resulting Numbers: [65] 65,70 unequal: No Solution Exploring Operation: 37*28=1036, Resulting Numbers: [1036] 1036,70 unequal: No Solution Exploring Operation: 37-28=9, Resulting Numbers: [9] 9,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 70:[38, 29], Operations: ['23+14=37', '66-37=29'] Exploring Operation: 38-29=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 38+29=67, Resulting Numbers: [67] 67,70 unequal: No Solution Exploring Operation: 38*29=1102, Resulting Numbers: [1102] 1102,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 70:[37, 104], Operations: ['23+14=37', '38+66=104'] Exploring Operation: 37+104=141, Resulting Numbers: [141] 141,70 unequal: No Solution Exploring Operation: 104-37=67, Resulting Numbers: [67] 67,70 unequal: No Solution Exploring Operation: 37*104=3848, Resulting Numbers: [3848] 3848,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 70:[38, 14, 43], Operations: ['66-23=43'] Exploring Operation: 38+43=81, Resulting Numbers: [14, 81] Generated Node #0,3,0: 70:[14, 81] Operation: 38+43=81 Exploring Operation: 43-38=5, Resulting Numbers: [14, 5] Generated Node #0,3,1: 70:[14, 5] Operation: 43-38=5 Exploring Operation: 43-14=29, Resulting Numbers: [38, 29] Generated Node #0,3,2: 70:[38, 29] Operation: 43-14=29 Exploring Operation: 38-14=24, Resulting Numbers: [43, 24] Generated Node #0,3,3: 70:[43, 24] Operation: 38-14=24 Exploring Operation: 14+43=57, Resulting Numbers: [38, 57] Generated Node #0,3,4: 70:[38, 57] Operation: 14+43=57 Moving to Node #0,1 Current State: 70:[14, 66, 61], Operations: ['23+38=61'] Exploring Operation: 14+61=75, Resulting Numbers: [66, 75] Generated Node #0,1,0: 70:[66, 75] Operation: 14+61=75 Exploring Operation: 14+66=80, Resulting Numbers: [61, 80] Generated Node #0,1,1: 70:[61, 80] Operation: 14+66=80 Exploring Operation: 61-14=47, Resulting Numbers: [66, 47] Generated Node #0,1,2: 70:[66, 47] Operation: 61-14=47 Exploring Operation: 66-14=52, Resulting Numbers: [61, 52] Generated Node #0,1,3: 70:[61, 52] Operation: 66-14=52 Exploring Operation: 66-61=5, Resulting Numbers: [14, 5] Generated Node #0,1,4: 70:[14, 5] Operation: 66-61=5 Moving to Node #0,3,1 Current State: 70:[14, 5], Operations: ['66-23=43', '43-38=5'] Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[23, 38, 14, 66], Operations: [] Exploring Operation: 66-23=43, Resulting Numbers: [38, 14, 43] Generated Node #0,3: 70:[38, 14, 43] Operation: 66-23=43 Moving to Node #0,3 Current State: 70:[38, 14, 43], Operations: ['66-23=43'] Exploring Operation: 43-38=5, Resulting Numbers: [14, 5] Generated Node #0,3,1: 70:[14, 5] Operation: 43-38=5 Moving to Node #0,3,1 Current State: 70:[14, 5], Operations: ['66-23=43', '43-38=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
0.954861
hs_5
mult_heuristic
[ 37, 76, 74, 60 ]
14
[ "74/37=2", "76-60=16", "16-2=14" ]
Current State: 14:[37, 76, 74, 60], Operations: [] Exploring Operation: 74/37=2, Resulting Numbers: [76, 60, 2] Generated Node #2: [76, 60, 2] from Operation: 74/37=2 Current State: 14:[76, 60, 2], Operations: ['74/37=2'] Exploring Operation: 76-60=16, Resulting Numbers: [2, 16] Generated Node #3: [2, 16] from Operation: 76-60=16 Current State: 14:[2, 16], Operations: ['74/37=2', '76-60=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[37, 76, 74, 60], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [37, 60, 2] Generated Node #0,0: 14:[37, 60, 2] Operation: 76-74=2 Exploring Operation: 74-60=14, Resulting Numbers: [37, 76, 14] Generated Node #0,1: 14:[37, 76, 14] Operation: 74-60=14 Exploring Operation: 76-60=16, Resulting Numbers: [37, 74, 16] Generated Node #0,2: 14:[37, 74, 16] Operation: 76-60=16 Moving to Node #0,0 Current State: 14:[37, 60, 2], Operations: ['76-74=2'] Exploring Operation: 60/2=30, Resulting Numbers: [37, 30] Generated Node #0,0,0: 14:[37, 30] Operation: 60/2=30 Exploring Operation: 37-2=35, Resulting Numbers: [60, 35] Generated Node #0,0,1: 14:[60, 35] Operation: 37-2=35 Exploring Operation: 60-37=23, Resulting Numbers: [2, 23] Generated Node #0,0,2: 14:[2, 23] Operation: 60-37=23 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 14:[2, 23], Operations: ['76-74=2', '60-37=23'] Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,14 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,14 unequal: No Solution Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[37, 30], Operations: ['76-74=2', '60/2=30'] Exploring Operation: 37*30=1110, Resulting Numbers: [1110] 1110,14 unequal: No Solution Exploring Operation: 37+30=67, Resulting Numbers: [67] 67,14 unequal: No Solution Exploring Operation: 37-30=7, Resulting Numbers: [7] 7,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 14:[60, 35], Operations: ['76-74=2', '37-2=35'] Exploring Operation: 60-35=25, Resulting Numbers: [25] 25,14 unequal: No Solution Exploring Operation: 60*35=2100, Resulting Numbers: [2100] 2100,14 unequal: No Solution Exploring Operation: 60+35=95, Resulting Numbers: [95] 95,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 14:[37, 76, 14], Operations: ['74-60=14'] Exploring Operation: 37-14=23, Resulting Numbers: [76, 23] Generated Node #0,1,0: 14:[76, 23] Operation: 37-14=23 Exploring Operation: 76-37=39, Resulting Numbers: [14, 39] Generated Node #0,1,1: 14:[14, 39] Operation: 76-37=39 Exploring Operation: 76-14=62, Resulting Numbers: [37, 62] Generated Node #0,1,2: 14:[37, 62] Operation: 76-14=62 Moving to Node #0,2 Current State: 14:[37, 74, 16], Operations: ['76-60=16'] Exploring Operation: 37-16=21, Resulting Numbers: [74, 21] Generated Node #0,2,0: 14:[74, 21] Operation: 37-16=21 Exploring Operation: 74/37=2, Resulting Numbers: [16, 2] Generated Node #0,2,1: 14:[16, 2] Operation: 74/37=2 Exploring Operation: 74-37=37, Resulting Numbers: [16, 37] Generated Node #0,2,2: 14:[16, 37] Operation: 74-37=37 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 14:[16, 2], Operations: ['76-60=16', '74/37=2'] Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[37, 76, 74, 60], Operations: [] Exploring Operation: 76-60=16, Resulting Numbers: [37, 74, 16] Generated Node #0,2: 14:[37, 74, 16] Operation: 76-60=16 Moving to Node #0,2 Current State: 14:[37, 74, 16], Operations: ['76-60=16'] Exploring Operation: 74/37=2, Resulting Numbers: [16, 2] Generated Node #0,2,1: 14:[16, 2] Operation: 74/37=2 Moving to Node #0,2,1 Current State: 14:[16, 2], Operations: ['76-60=16', '74/37=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_3
mult_heuristic
[ 93, 61, 52, 51 ]
33
[ "93-61=32", "52-51=1", "32+1=33" ]
Current State: 33:[93, 61, 52, 51], Operations: [] Exploring Operation: 93-61=32, Resulting Numbers: [52, 51, 32] Generated Node #2: [52, 51, 32] from Operation: 93-61=32 Current State: 33:[52, 51, 32], Operations: ['93-61=32'] Exploring Operation: 52-51=1, Resulting Numbers: [32, 1] Generated Node #3: [32, 1] from Operation: 52-51=1 Current State: 33:[32, 1], Operations: ['93-61=32', '52-51=1'] Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[93, 61, 52, 51], Operations: [] Exploring Operation: 93-61=32, Resulting Numbers: [52, 51, 32] Generated Node #0,0: 33:[52, 51, 32] Operation: 93-61=32 Moving to Node #0,0 Current State: 33:[52, 51, 32], Operations: ['93-61=32'] Exploring Operation: 52-51=1, Resulting Numbers: [32, 1] Generated Node #0,0,0: 33:[32, 1] Operation: 52-51=1 Moving to Node #0,0,0 Current State: 33:[32, 1], Operations: ['93-61=32', '52-51=1'] Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[93, 61, 52, 51], Operations: [] Exploring Operation: 93-61=32, Resulting Numbers: [52, 51, 32] Generated Node #0,0: 33:[52, 51, 32] Operation: 93-61=32 Moving to Node #0,0 Current State: 33:[52, 51, 32], Operations: ['93-61=32'] Exploring Operation: 52-51=1, Resulting Numbers: [32, 1] Generated Node #0,0,0: 33:[32, 1] Operation: 52-51=1 Moving to Node #0,0,0 Current State: 33:[32, 1], Operations: ['93-61=32', '52-51=1'] Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 8, 54, 49, 51 ]
58
[ "51-49=2", "8/2=4", "54+4=58" ]
Current State: 58:[8, 54, 49, 51], Operations: [] Exploring Operation: 51-49=2, Resulting Numbers: [8, 54, 2] Generated Node #2: [8, 54, 2] from Operation: 51-49=2 Current State: 58:[8, 54, 2], Operations: ['51-49=2'] Exploring Operation: 8/2=4, Resulting Numbers: [54, 4] Generated Node #3: [54, 4] from Operation: 8/2=4 Current State: 58:[54, 4], Operations: ['51-49=2', '8/2=4'] Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[8, 54, 49, 51], Operations: [] Exploring Operation: 51-49=2, Resulting Numbers: [8, 54, 2] Generated Node #0,0: 58:[8, 54, 2] Operation: 51-49=2 Moving to Node #0,0 Current State: 58:[8, 54, 2], Operations: ['51-49=2'] Exploring Operation: 8+54=62, Resulting Numbers: [2, 62] Generated Node #0,0,0: 58:[2, 62] Operation: 8+54=62 Moving to Node #0,0,0 Current State: 58:[2, 62], Operations: ['51-49=2', '8+54=62'] Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,58 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 75, 5, 60, 54 ]
57
[ "75-60=15", "15/5=3", "54+3=57" ]
Current State: 57:[75, 5, 60, 54], Operations: [] Exploring Operation: 75-60=15, Resulting Numbers: [5, 54, 15] Generated Node #2: [5, 54, 15] from Operation: 75-60=15 Current State: 57:[5, 54, 15], Operations: ['75-60=15'] Exploring Operation: 15/5=3, Resulting Numbers: [54, 3] Generated Node #3: [54, 3] from Operation: 15/5=3 Current State: 57:[54, 3], Operations: ['75-60=15', '15/5=3'] Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[75, 5, 60, 54], Operations: [] Exploring Operation: 75-5=70, Resulting Numbers: [60, 54, 70] Generated Node #0,0: 57:[60, 54, 70] Operation: 75-5=70 Exploring Operation: 75-54=21, Resulting Numbers: [5, 60, 21] Generated Node #0,1: 57:[5, 60, 21] Operation: 75-54=21 Exploring Operation: 75-60=15, Resulting Numbers: [5, 54, 15] Generated Node #0,2: 57:[5, 54, 15] Operation: 75-60=15 Exploring Operation: 75/5=15, Resulting Numbers: [60, 54, 15] Generated Node #0,3: 57:[60, 54, 15] Operation: 75/5=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[5, 60, 21], Operations: ['75-54=21'] Exploring Operation: 60-5=55, Resulting Numbers: [21, 55] Generated Node #0,1,0: 57:[21, 55] Operation: 60-5=55 Exploring Operation: 21-5=16, Resulting Numbers: [60, 16] Generated Node #0,1,1: 57:[60, 16] Operation: 21-5=16 Exploring Operation: 5+60=65, Resulting Numbers: [21, 65] Generated Node #0,1,2: 57:[21, 65] Operation: 5+60=65 Exploring Operation: 60/5=12, Resulting Numbers: [21, 12] Generated Node #0,1,3: 57:[21, 12] Operation: 60/5=12 Moving to Node #0,1,0 Current State: 57:[21, 55], Operations: ['75-54=21', '60-5=55'] Exploring Operation: 21+55=76, Resulting Numbers: [76] 76,57 unequal: No Solution Exploring Operation: 21*55=1155, Resulting Numbers: [1155] 1155,57 unequal: No Solution Exploring Operation: 55-21=34, Resulting Numbers: [34] 34,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[60, 16], Operations: ['75-54=21', '21-5=16'] Exploring Operation: 60+16=76, Resulting Numbers: [76] 76,57 unequal: No Solution Exploring Operation: 60*16=960, Resulting Numbers: [960] 960,57 unequal: No Solution Exploring Operation: 60-16=44, Resulting Numbers: [44] 44,57 unequal: No Solution Moving to Node #0,1,3 Current State: 57:[21, 12], Operations: ['75-54=21', '60/5=12'] Exploring Operation: 21*12=252, Resulting Numbers: [252] 252,57 unequal: No Solution Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,57 unequal: No Solution Moving to Node #0,1,2 Current State: 57:[21, 65], Operations: ['75-54=21', '5+60=65'] Exploring Operation: 65-21=44, Resulting Numbers: [44] 44,57 unequal: No Solution Exploring Operation: 21*65=1365, Resulting Numbers: [1365] 1365,57 unequal: No Solution Exploring Operation: 21+65=86, Resulting Numbers: [86] 86,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[5, 54, 15], Operations: ['75-60=15'] Exploring Operation: 5+54=59, Resulting Numbers: [15, 59] Generated Node #0,2,0: 57:[15, 59] Operation: 5+54=59 Exploring Operation: 5+15=20, Resulting Numbers: [54, 20] Generated Node #0,2,1: 57:[54, 20] Operation: 5+15=20 Exploring Operation: 15-5=10, Resulting Numbers: [54, 10] Generated Node #0,2,2: 57:[54, 10] Operation: 15-5=10 Exploring Operation: 15/5=3, Resulting Numbers: [54, 3] Generated Node #0,2,3: 57:[54, 3] Operation: 15/5=3 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 57:[54, 3], Operations: ['75-60=15', '15/5=3'] Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,57 unequal: No Solution Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[75, 5, 60, 54], Operations: [] Exploring Operation: 75-60=15, Resulting Numbers: [5, 54, 15] Generated Node #0,2: 57:[5, 54, 15] Operation: 75-60=15 Moving to Node #0,2 Current State: 57:[5, 54, 15], Operations: ['75-60=15'] Exploring Operation: 15/5=3, Resulting Numbers: [54, 3] Generated Node #0,2,3: 57:[54, 3] Operation: 15/5=3 Moving to Node #0,2,3 Current State: 57:[54, 3], Operations: ['75-60=15', '15/5=3'] Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 65, 15, 89, 25 ]
50
[ "65*15=975", "975/25=39", "89-39=50" ]
Current State: 50:[65, 15, 89, 25], Operations: [] Exploring Operation: 65*15=975, Resulting Numbers: [89, 25, 975] Generated Node #2: [89, 25, 975] from Operation: 65*15=975 Current State: 50:[89, 25, 975], Operations: ['65*15=975'] Exploring Operation: 975/25=39, Resulting Numbers: [89, 39] Generated Node #3: [89, 39] from Operation: 975/25=39 Current State: 50:[89, 39], Operations: ['65*15=975', '975/25=39'] Exploring Operation: 89-39=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[65, 15, 89, 25], Operations: [] Exploring Operation: 89-65=24, Resulting Numbers: [15, 25, 24] Generated Node #0,0: 50:[15, 25, 24] Operation: 89-65=24 Exploring Operation: 89-25=64, Resulting Numbers: [65, 15, 64] Generated Node #0,1: 50:[65, 15, 64] Operation: 89-25=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[15, 25, 24], Operations: ['89-65=24'] Exploring Operation: 25-15=10, Resulting Numbers: [24, 10] Generated Node #0,0,0: 50:[24, 10] Operation: 25-15=10 Exploring Operation: 24-15=9, Resulting Numbers: [25, 9] Generated Node #0,0,1: 50:[25, 9] Operation: 24-15=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 50:[24, 10], Operations: ['89-65=24', '25-15=10'] Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,50 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 50:[25, 9], Operations: ['89-65=24', '24-15=9'] Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,50 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[65, 15, 64], Operations: ['89-25=64'] Exploring Operation: 65-15=50, Resulting Numbers: [64, 50] Generated Node #0,1,0: 50:[64, 50] Operation: 65-15=50 Exploring Operation: 65-64=1, Resulting Numbers: [15, 1] Generated Node #0,1,1: 50:[15, 1] Operation: 65-64=1 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 50:[15, 1], Operations: ['89-25=64', '65-64=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,50 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 50:[64, 50], Operations: ['89-25=64', '65-15=50'] Exploring Operation: 64-50=14, Resulting Numbers: [14] 14,50 unequal: No Solution Exploring Operation: 64+50=114, Resulting Numbers: [114] 114,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 6, 34, 29, 42 ]
58
[ "6+34=40", "42-40=2", "29*2=58" ]
Current State: 58:[6, 34, 29, 42], Operations: [] Exploring Operation: 6+34=40, Resulting Numbers: [29, 42, 40] Generated Node #2: [29, 42, 40] from Operation: 6+34=40 Current State: 58:[29, 42, 40], Operations: ['6+34=40'] Exploring Operation: 42-40=2, Resulting Numbers: [29, 2] Generated Node #3: [29, 2] from Operation: 42-40=2 Current State: 58:[29, 2], Operations: ['6+34=40', '42-40=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[6, 34, 29, 42], Operations: [] Exploring Operation: 42-6=36, Resulting Numbers: [34, 29, 36] Generated Node #0,0: 58:[34, 29, 36] Operation: 42-6=36 Exploring Operation: 42/6=7, Resulting Numbers: [34, 29, 7] Generated Node #0,1: 58:[34, 29, 7] Operation: 42/6=7 Exploring Operation: 42-34=8, Resulting Numbers: [6, 29, 8] Generated Node #0,2: 58:[6, 29, 8] Operation: 42-34=8 Exploring Operation: 34-6=28, Resulting Numbers: [29, 42, 28] Generated Node #0,3: 58:[29, 42, 28] Operation: 34-6=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[34, 29, 7], Operations: ['42/6=7'] Exploring Operation: 34+29=63, Resulting Numbers: [7, 63] Generated Node #0,1,0: 58:[7, 63] Operation: 34+29=63 Exploring Operation: 34+7=41, Resulting Numbers: [29, 41] Generated Node #0,1,1: 58:[29, 41] Operation: 34+7=41 Exploring Operation: 34-7=27, Resulting Numbers: [29, 27] Generated Node #0,1,2: 58:[29, 27] Operation: 34-7=27 Exploring Operation: 34-29=5, Resulting Numbers: [7, 5] Generated Node #0,1,3: 58:[7, 5] Operation: 34-29=5 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 58:[29, 27], Operations: ['42/6=7', '34-7=27'] Exploring Operation: 29+27=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 29*27=783, Resulting Numbers: [783] 783,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 58:[7, 5], Operations: ['42/6=7', '34-29=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,58 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 58:[7, 63], Operations: ['42/6=7', '34+29=63'] Exploring Operation: 7+63=70, Resulting Numbers: [70] 70,58 unequal: No Solution Exploring Operation: 7*63=441, Resulting Numbers: [441] 441,58 unequal: No Solution Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,58 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 58:[29, 41], Operations: ['42/6=7', '34+7=41'] Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,58 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,58 unequal: No Solution Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[6, 29, 8], Operations: ['42-34=8'] Exploring Operation: 8-6=2, Resulting Numbers: [29, 2] Generated Node #0,2,0: 58:[29, 2] Operation: 8-6=2 Exploring Operation: 6*8=48, Resulting Numbers: [29, 48] Generated Node #0,2,1: 58:[29, 48] Operation: 6*8=48 Exploring Operation: 29-6=23, Resulting Numbers: [8, 23] Generated Node #0,2,2: 58:[8, 23] Operation: 29-6=23 Exploring Operation: 6+29=35, Resulting Numbers: [8, 35] Generated Node #0,2,3: 58:[8, 35] Operation: 6+29=35 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 58:[29, 2], Operations: ['42-34=8', '8-6=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[6, 34, 29, 42], Operations: [] Exploring Operation: 42-34=8, Resulting Numbers: [6, 29, 8] Generated Node #0,2: 58:[6, 29, 8] Operation: 42-34=8 Moving to Node #0,2 Current State: 58:[6, 29, 8], Operations: ['42-34=8'] Exploring Operation: 8-6=2, Resulting Numbers: [29, 2] Generated Node #0,2,0: 58:[29, 2] Operation: 8-6=2 Moving to Node #0,2,0 Current State: 58:[29, 2], Operations: ['42-34=8', '8-6=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 14, 21, 93, 69 ]
31
[ "21-14=7", "93-69=24", "7+24=31" ]
Current State: 31:[14, 21, 93, 69], Operations: [] Exploring Operation: 21-14=7, Resulting Numbers: [93, 69, 7] Generated Node #2: [93, 69, 7] from Operation: 21-14=7 Current State: 31:[93, 69, 7], Operations: ['21-14=7'] Exploring Operation: 93-69=24, Resulting Numbers: [7, 24] Generated Node #3: [7, 24] from Operation: 93-69=24 Current State: 31:[7, 24], Operations: ['21-14=7', '93-69=24'] Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[14, 21, 93, 69], Operations: [] Exploring Operation: 93-69=24, Resulting Numbers: [14, 21, 24] Generated Node #0,0: 31:[14, 21, 24] Operation: 93-69=24 Exploring Operation: 93-14=79, Resulting Numbers: [21, 69, 79] Generated Node #0,1: 31:[21, 69, 79] Operation: 93-14=79 Moving to Node #0,0 Current State: 31:[14, 21, 24], Operations: ['93-69=24'] Exploring Operation: 14+21=35, Resulting Numbers: [24, 35] Generated Node #0,0,0: 31:[24, 35] Operation: 14+21=35 Exploring Operation: 14+24=38, Resulting Numbers: [21, 38] Generated Node #0,0,1: 31:[21, 38] Operation: 14+24=38 Moving to Node #0,1 Current State: 31:[21, 69, 79], Operations: ['93-14=79'] Exploring Operation: 69-21=48, Resulting Numbers: [79, 48] Generated Node #0,1,0: 31:[79, 48] Operation: 69-21=48 Exploring Operation: 79-69=10, Resulting Numbers: [21, 10] Generated Node #0,1,1: 31:[21, 10] Operation: 79-69=10 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[21, 10], Operations: ['93-14=79', '79-69=10'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,31 unequal: No Solution Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[14, 21, 93, 69], Operations: [] Exploring Operation: 93-14=79, Resulting Numbers: [21, 69, 79] Generated Node #0,1: 31:[21, 69, 79] Operation: 93-14=79 Moving to Node #0,1 Current State: 31:[21, 69, 79], Operations: ['93-14=79'] Exploring Operation: 79-69=10, Resulting Numbers: [21, 10] Generated Node #0,1,1: 31:[21, 10] Operation: 79-69=10 Moving to Node #0,1,1 Current State: 31:[21, 10], Operations: ['93-14=79', '79-69=10'] Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 44, 96, 80, 44 ]
72
[ "96-44=52", "80+44=124", "124-52=72" ]
Current State: 72:[44, 96, 80, 44], Operations: [] Exploring Operation: 96-44=52, Resulting Numbers: [80, 52] Generated Node #2: [80, 52] from Operation: 96-44=52 Current State: 72:[80, 52], Operations: ['96-44=52'] Exploring Operation: 80+44=124, Resulting Numbers: [52, 124] Generated Node #3: [52, 124] from Operation: 80+44=124 Current State: 72:[52, 124], Operations: ['96-44=52', '80+44=124'] Exploring Operation: 124-52=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[44, 96, 80, 44], Operations: [] Exploring Operation: 96-44=52, Resulting Numbers: [44, 80, 52] Generated Node #0,0: 72:[44, 80, 52] Operation: 96-44=52 Exploring Operation: 96-80=16, Resulting Numbers: [44, 44, 16] Generated Node #0,1: 72:[44, 44, 16] Operation: 96-80=16 Exploring Operation: 96-44=52, Resulting Numbers: [80, 44, 52] Generated Node #0,2: 72:[80, 44, 52] Operation: 96-44=52 Exploring Operation: 80-44=36, Resulting Numbers: [44, 96, 36] Generated Node #0,3: 72:[44, 96, 36] Operation: 80-44=36 Exploring Operation: 80-44=36, Resulting Numbers: [96, 44, 36] Generated Node #0,4: 72:[96, 44, 36] Operation: 80-44=36 Moving to Node #0,1 Current State: 72:[44, 44, 16], Operations: ['96-80=16'] Exploring Operation: 44-44=0, Resulting Numbers: [16, 0] Generated Node #0,1,0: 72:[16, 0] Operation: 44-44=0 Exploring Operation: 44+44=88, Resulting Numbers: [16, 88] Generated Node #0,1,1: 72:[16, 88] Operation: 44+44=88 Exploring Operation: 44-16=28, Resulting Numbers: [44, 28] Generated Node #0,1,2: 72:[44, 28] Operation: 44-16=28 Exploring Operation: 44/44=1, Resulting Numbers: [16, 1] Generated Node #0,1,3: 72:[16, 1] Operation: 44/44=1 Exploring Operation: 44-16=28, Resulting Numbers: [44, 28] Generated Node #0,1,4: 72:[44, 28] Operation: 44-16=28 Moving to Node #0,2 Current State: 72:[80, 44, 52], Operations: ['96-44=52'] Exploring Operation: 80-52=28, Resulting Numbers: [44, 28] Generated Node #0,2,0: 72:[44, 28] Operation: 80-52=28 Exploring Operation: 80+44=124, Resulting Numbers: [52, 124] Generated Node #0,2,1: 72:[52, 124] Operation: 80+44=124 Exploring Operation: 52-44=8, Resulting Numbers: [80, 8] Generated Node #0,2,2: 72:[80, 8] Operation: 52-44=8 Exploring Operation: 44+52=96, Resulting Numbers: [80, 96] Generated Node #0,2,3: 72:[80, 96] Operation: 44+52=96 Exploring Operation: 80-44=36, Resulting Numbers: [52, 36] Generated Node #0,2,4: 72:[52, 36] Operation: 80-44=36 Moving to Node #0,4 Current State: 72:[96, 44, 36], Operations: ['80-44=36'] Exploring Operation: 96+44=140, Resulting Numbers: [36, 140] Generated Node #0,4,0: 72:[36, 140] Operation: 96+44=140 Exploring Operation: 44-36=8, Resulting Numbers: [96, 8] Generated Node #0,4,1: 72:[96, 8] Operation: 44-36=8 Exploring Operation: 44+36=80, Resulting Numbers: [96, 80] Generated Node #0,4,2: 72:[96, 80] Operation: 44+36=80 Exploring Operation: 96-44=52, Resulting Numbers: [36, 52] Generated Node #0,4,3: 72:[36, 52] Operation: 96-44=52 Exploring Operation: 96-36=60, Resulting Numbers: [44, 60] Generated Node #0,4,4: 72:[44, 60] Operation: 96-36=60 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 72:[36, 52], Operations: ['80-44=36', '96-44=52'] Exploring Operation: 36+52=88, Resulting Numbers: [88] 88,72 unequal: No Solution Exploring Operation: 52-36=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 36*52=1872, Resulting Numbers: [1872] 1872,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 72:[44, 60], Operations: ['80-44=36', '96-36=60'] Exploring Operation: 60-44=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 44+60=104, Resulting Numbers: [104] 104,72 unequal: No Solution Exploring Operation: 44*60=2640, Resulting Numbers: [2640] 2640,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 72:[96, 8], Operations: ['80-44=36', '44-36=8'] Exploring Operation: 96/8=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 96*8=768, Resulting Numbers: [768] 768,72 unequal: No Solution Exploring Operation: 96-8=88, Resulting Numbers: [88] 88,72 unequal: No Solution Exploring Operation: 96+8=104, Resulting Numbers: [104] 104,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 72:[96, 80], Operations: ['80-44=36', '44+36=80'] Exploring Operation: 96*80=7680, Resulting Numbers: [7680] 7680,72 unequal: No Solution Exploring Operation: 96-80=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 96+80=176, Resulting Numbers: [176] 176,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 72:[36, 140], Operations: ['80-44=36', '96+44=140'] Exploring Operation: 140-36=104, Resulting Numbers: [104] 104,72 unequal: No Solution Exploring Operation: 36+140=176, Resulting Numbers: [176] 176,72 unequal: No Solution Exploring Operation: 36*140=5040, Resulting Numbers: [5040] 5040,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 72:[44, 80, 52], Operations: ['96-44=52'] Exploring Operation: 52-44=8, Resulting Numbers: [80, 8] Generated Node #0,0,0: 72:[80, 8] Operation: 52-44=8 Exploring Operation: 80-44=36, Resulting Numbers: [52, 36] Generated Node #0,0,1: 72:[52, 36] Operation: 80-44=36 Exploring Operation: 44+80=124, Resulting Numbers: [52, 124] Generated Node #0,0,2: 72:[52, 124] Operation: 44+80=124 Exploring Operation: 44+52=96, Resulting Numbers: [80, 96] Generated Node #0,0,3: 72:[80, 96] Operation: 44+52=96 Exploring Operation: 80-52=28, Resulting Numbers: [44, 28] Generated Node #0,0,4: 72:[44, 28] Operation: 80-52=28 Moving to Node #0,3 Current State: 72:[44, 96, 36], Operations: ['80-44=36'] Exploring Operation: 44+96=140, Resulting Numbers: [36, 140] Generated Node #0,3,0: 72:[36, 140] Operation: 44+96=140 Exploring Operation: 96-44=52, Resulting Numbers: [36, 52] Generated Node #0,3,1: 72:[36, 52] Operation: 96-44=52 Exploring Operation: 44+36=80, Resulting Numbers: [96, 80] Generated Node #0,3,2: 72:[96, 80] Operation: 44+36=80 Exploring Operation: 44-36=8, Resulting Numbers: [96, 8] Generated Node #0,3,3: 72:[96, 8] Operation: 44-36=8 Exploring Operation: 96-36=60, Resulting Numbers: [44, 60] Generated Node #0,3,4: 72:[44, 60] Operation: 96-36=60 Moving to Node #0,1,3 Current State: 72:[16, 1], Operations: ['96-80=16', '44/44=1'] Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 16*1=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 16+1=17, Resulting Numbers: [17] 17,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[16, 0], Operations: ['96-80=16', '44-44=0'] Exploring Operation: 16-0=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 16+0=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 16*0=0, Resulting Numbers: [0] 0,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[80, 8], Operations: ['96-44=52', '52-44=8'] Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[44, 96, 80, 44], Operations: [] Exploring Operation: 96-44=52, Resulting Numbers: [80, 44, 52] Generated Node #0,2: 72:[80, 44, 52] Operation: 96-44=52 Moving to Node #0,2 Current State: 72:[80, 44, 52], Operations: ['96-44=52'] Exploring Operation: 52-44=8, Resulting Numbers: [80, 8] Generated Node #0,2,2: 72:[80, 8] Operation: 52-44=8 Moving to Node #0,2,2 Current State: 72:[80, 8], Operations: ['96-44=52', '52-44=8'] Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.949653
hs_5
sum_heuristic
[ 3, 33, 3, 52 ]
38
[ "33-3=30", "3*30=90", "90-52=38" ]
Current State: 38:[3, 33, 3, 52], Operations: [] Exploring Operation: 33-3=30, Resulting Numbers: [52, 30] Generated Node #2: [52, 30] from Operation: 33-3=30 Current State: 38:[52, 30], Operations: ['33-3=30'] Exploring Operation: 3*30=90, Resulting Numbers: [52, 90] Generated Node #3: [52, 90] from Operation: 3*30=90 Current State: 38:[52, 90], Operations: ['33-3=30', '3*30=90'] Exploring Operation: 90-52=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[3, 33, 3, 52], Operations: [] Exploring Operation: 52-33=19, Resulting Numbers: [3, 3, 19] Generated Node #0,0: 38:[3, 3, 19] Operation: 52-33=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[3, 3, 19], Operations: ['52-33=19'] Exploring Operation: 3/3=1, Resulting Numbers: [19, 1] Generated Node #0,0,0: 38:[19, 1] Operation: 3/3=1 Moving to Node #0,0,0 Current State: 38:[19, 1], Operations: ['52-33=19', '3/3=1'] Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 78, 26, 3, 1 ]
87
[ "26+1=27", "27/3=9", "78+9=87" ]
Current State: 87:[78, 26, 3, 1], Operations: [] Exploring Operation: 26+1=27, Resulting Numbers: [78, 3, 27] Generated Node #2: [78, 3, 27] from Operation: 26+1=27 Current State: 87:[78, 3, 27], Operations: ['26+1=27'] Exploring Operation: 27/3=9, Resulting Numbers: [78, 9] Generated Node #3: [78, 9] from Operation: 27/3=9 Current State: 87:[78, 9], Operations: ['26+1=27', '27/3=9'] Exploring Operation: 78+9=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[78, 26, 3, 1], Operations: [] Exploring Operation: 78/26=3, Resulting Numbers: [3, 1, 3] Generated Node #0,0: 87:[3, 1, 3] Operation: 78/26=3 Exploring Operation: 78/3=26, Resulting Numbers: [26, 1, 26] Generated Node #0,1: 87:[26, 1, 26] Operation: 78/3=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[3, 1, 3], Operations: ['78/26=3'] Exploring Operation: 3/1=3, Resulting Numbers: [3, 3] Generated Node #0,0,0: 87:[3, 3] Operation: 3/1=3 Exploring Operation: 3*1=3, Resulting Numbers: [3, 3] Generated Node #0,0,1: 87:[3, 3] Operation: 3*1=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[3, 3], Operations: ['78/26=3', '3/1=3'] Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[3, 3], Operations: ['78/26=3', '3*1=3'] Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,87 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[26, 1, 26], Operations: ['78/3=26'] Exploring Operation: 26+1=27, Resulting Numbers: [26, 27] Generated Node #0,1,0: 87:[26, 27] Operation: 26+1=27 Exploring Operation: 26/26=1, Resulting Numbers: [1, 1] Generated Node #0,1,1: 87:[1, 1] Operation: 26/26=1 Moving to Node #0,1,1 Current State: 87:[1, 1], Operations: ['78/3=26', '26/26=1'] Exploring Operation: 1+1=2, Resulting Numbers: [2] 2,87 unequal: No Solution Exploring Operation: 1*1=1, Resulting Numbers: [1] 1,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[26, 27], Operations: ['78/3=26', '26+1=27'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,87 unequal: No Solution Exploring Operation: 26+27=53, Resulting Numbers: [53] 53,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 46, 95, 94, 93 ]
71
[ "95-93=2", "46/2=23", "94-23=71" ]
Current State: 71:[46, 95, 94, 93], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [46, 94, 2] Generated Node #2: [46, 94, 2] from Operation: 95-93=2 Current State: 71:[46, 94, 2], Operations: ['95-93=2'] Exploring Operation: 46/2=23, Resulting Numbers: [94, 23] Generated Node #3: [94, 23] from Operation: 46/2=23 Current State: 71:[94, 23], Operations: ['95-93=2', '46/2=23'] Exploring Operation: 94-23=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[46, 95, 94, 93], Operations: [] Exploring Operation: 93-46=47, Resulting Numbers: [95, 94, 47] Generated Node #0,0: 71:[95, 94, 47] Operation: 93-46=47 Exploring Operation: 94-46=48, Resulting Numbers: [95, 93, 48] Generated Node #0,1: 71:[95, 93, 48] Operation: 94-46=48 Exploring Operation: 46+95=141, Resulting Numbers: [94, 93, 141] Generated Node #0,2: 71:[94, 93, 141] Operation: 46+95=141 Exploring Operation: 95-46=49, Resulting Numbers: [94, 93, 49] Generated Node #0,3: 71:[94, 93, 49] Operation: 95-46=49 Moving to Node #0,3 Current State: 71:[94, 93, 49], Operations: ['95-46=49'] Exploring Operation: 94-49=45, Resulting Numbers: [93, 45] Generated Node #0,3,0: 71:[93, 45] Operation: 94-49=45 Exploring Operation: 93-49=44, Resulting Numbers: [94, 44] Generated Node #0,3,1: 71:[94, 44] Operation: 93-49=44 Exploring Operation: 94+49=143, Resulting Numbers: [93, 143] Generated Node #0,3,2: 71:[93, 143] Operation: 94+49=143 Exploring Operation: 94-93=1, Resulting Numbers: [49, 1] Generated Node #0,3,3: 71:[49, 1] Operation: 94-93=1 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 71:[93, 45], Operations: ['95-46=49', '94-49=45'] Exploring Operation: 93*45=4185, Resulting Numbers: [4185] 4185,71 unequal: No Solution Exploring Operation: 93+45=138, Resulting Numbers: [138] 138,71 unequal: No Solution Exploring Operation: 93-45=48, Resulting Numbers: [48] 48,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 71:[94, 44], Operations: ['95-46=49', '93-49=44'] Exploring Operation: 94*44=4136, Resulting Numbers: [4136] 4136,71 unequal: No Solution Exploring Operation: 94+44=138, Resulting Numbers: [138] 138,71 unequal: No Solution Exploring Operation: 94-44=50, Resulting Numbers: [50] 50,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 71:[49, 1], Operations: ['95-46=49', '94-93=1'] Exploring Operation: 49+1=50, Resulting Numbers: [50] 50,71 unequal: No Solution Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,71 unequal: No Solution Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,71 unequal: No Solution Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 71:[93, 143], Operations: ['95-46=49', '94+49=143'] Exploring Operation: 93+143=236, Resulting Numbers: [236] 236,71 unequal: No Solution Exploring Operation: 143-93=50, Resulting Numbers: [50] 50,71 unequal: No Solution Exploring Operation: 93*143=13299, Resulting Numbers: [13299] 13299,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 71:[95, 93, 48], Operations: ['94-46=48'] Exploring Operation: 93-48=45, Resulting Numbers: [95, 45] Generated Node #0,1,0: 71:[95, 45] Operation: 93-48=45 Exploring Operation: 95+48=143, Resulting Numbers: [93, 143] Generated Node #0,1,1: 71:[93, 143] Operation: 95+48=143 Exploring Operation: 95-93=2, Resulting Numbers: [48, 2] Generated Node #0,1,2: 71:[48, 2] Operation: 95-93=2 Exploring Operation: 95-48=47, Resulting Numbers: [93, 47] Generated Node #0,1,3: 71:[93, 47] Operation: 95-48=47 Moving to Node #0,0 Current State: 71:[95, 94, 47], Operations: ['93-46=47'] Exploring Operation: 95-47=48, Resulting Numbers: [94, 48] Generated Node #0,0,0: 71:[94, 48] Operation: 95-47=48 Exploring Operation: 94/47=2, Resulting Numbers: [95, 2] Generated Node #0,0,1: 71:[95, 2] Operation: 94/47=2 Exploring Operation: 94-47=47, Resulting Numbers: [95, 47] Generated Node #0,0,2: 71:[95, 47] Operation: 94-47=47 Exploring Operation: 95-94=1, Resulting Numbers: [47, 1] Generated Node #0,0,3: 71:[47, 1] Operation: 95-94=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[94, 48], Operations: ['93-46=47', '95-47=48'] Exploring Operation: 94-48=46, Resulting Numbers: [46] 46,71 unequal: No Solution Exploring Operation: 94+48=142, Resulting Numbers: [142] 142,71 unequal: No Solution Exploring Operation: 94*48=4512, Resulting Numbers: [4512] 4512,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 71:[95, 47], Operations: ['93-46=47', '94-47=47'] Exploring Operation: 95+47=142, Resulting Numbers: [142] 142,71 unequal: No Solution Exploring Operation: 95*47=4465, Resulting Numbers: [4465] 4465,71 unequal: No Solution Exploring Operation: 95-47=48, Resulting Numbers: [48] 48,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 71:[95, 2], Operations: ['93-46=47', '94/47=2'] Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,71 unequal: No Solution Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,71 unequal: No Solution Exploring Operation: 95*2=190, Resulting Numbers: [190] 190,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 71:[47, 1], Operations: ['93-46=47', '95-94=1'] Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,71 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,71 unequal: No Solution Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,71 unequal: No Solution Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 71:[94, 93, 141], Operations: ['46+95=141'] Exploring Operation: 141-94=47, Resulting Numbers: [93, 47] Generated Node #0,2,0: 71:[93, 47] Operation: 141-94=47 Exploring Operation: 141-93=48, Resulting Numbers: [94, 48] Generated Node #0,2,1: 71:[94, 48] Operation: 141-93=48 Exploring Operation: 94+93=187, Resulting Numbers: [141, 187] Generated Node #0,2,2: 71:[141, 187] Operation: 94+93=187 Exploring Operation: 94-93=1, Resulting Numbers: [141, 1] Generated Node #0,2,3: 71:[141, 1] Operation: 94-93=1 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 71:[93, 47], Operations: ['46+95=141', '141-94=47'] Exploring Operation: 93+47=140, Resulting Numbers: [140] 140,71 unequal: No Solution Exploring Operation: 93*47=4371, Resulting Numbers: [4371] 4371,71 unequal: No Solution Exploring Operation: 93-47=46, Resulting Numbers: [46] 46,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 71:[94, 48], Operations: ['46+95=141', '141-93=48'] Exploring Operation: 94*48=4512, Resulting Numbers: [4512] 4512,71 unequal: No Solution Exploring Operation: 94-48=46, Resulting Numbers: [46] 46,71 unequal: No Solution Exploring Operation: 94+48=142, Resulting Numbers: [142] 142,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 71:[141, 1], Operations: ['46+95=141', '94-93=1'] Exploring Operation: 141-1=140, Resulting Numbers: [140] 140,71 unequal: No Solution Exploring Operation: 141/1=141, Resulting Numbers: [141] 141,71 unequal: No Solution Exploring Operation: 141*1=141, Resulting Numbers: [141] 141,71 unequal: No Solution Exploring Operation: 141+1=142, Resulting Numbers: [142] 142,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 71:[141, 187], Operations: ['46+95=141', '94+93=187'] Exploring Operation: 141*187=26367, Resulting Numbers: [26367] 26367,71 unequal: No Solution Exploring Operation: 141+187=328, Resulting Numbers: [328] 328,71 unequal: No Solution Exploring Operation: 187-141=46, Resulting Numbers: [46] 46,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 71:[93, 47], Operations: ['94-46=48', '95-48=47'] Exploring Operation: 93*47=4371, Resulting Numbers: [4371] 4371,71 unequal: No Solution Exploring Operation: 93-47=46, Resulting Numbers: [46] 46,71 unequal: No Solution Exploring Operation: 93+47=140, Resulting Numbers: [140] 140,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[95, 45], Operations: ['94-46=48', '93-48=45'] Exploring Operation: 95-45=50, Resulting Numbers: [50] 50,71 unequal: No Solution Exploring Operation: 95*45=4275, Resulting Numbers: [4275] 4275,71 unequal: No Solution Exploring Operation: 95+45=140, Resulting Numbers: [140] 140,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[48, 2], Operations: ['94-46=48', '95-93=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,71 unequal: No Solution Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,71 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,71 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[93, 143], Operations: ['94-46=48', '95+48=143'] Exploring Operation: 93*143=13299, Resulting Numbers: [13299] 13299,71 unequal: No Solution Exploring Operation: 93+143=236, Resulting Numbers: [236] 236,71 unequal: No Solution Exploring Operation: 143-93=50, Resulting Numbers: [50] 50,71 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 98, 10, 20, 13 ]
16
[ "98-20=78", "78/13=6", "10+6=16" ]
Current State: 16:[98, 10, 20, 13], Operations: [] Exploring Operation: 98-20=78, Resulting Numbers: [10, 13, 78] Generated Node #2: [10, 13, 78] from Operation: 98-20=78 Current State: 16:[10, 13, 78], Operations: ['98-20=78'] Exploring Operation: 78/13=6, Resulting Numbers: [10, 6] Generated Node #3: [10, 6] from Operation: 78/13=6 Current State: 16:[10, 6], Operations: ['98-20=78', '78/13=6'] Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[98, 10, 20, 13], Operations: [] Exploring Operation: 98-13=85, Resulting Numbers: [10, 20, 85] Generated Node #0,0: 16:[10, 20, 85] Operation: 98-13=85 Exploring Operation: 98-20=78, Resulting Numbers: [10, 13, 78] Generated Node #0,1: 16:[10, 13, 78] Operation: 98-20=78 Moving to Node #0,1 Current State: 16:[10, 13, 78], Operations: ['98-20=78'] Exploring Operation: 78/13=6, Resulting Numbers: [10, 6] Generated Node #0,1,0: 16:[10, 6] Operation: 78/13=6 Exploring Operation: 78-13=65, Resulting Numbers: [10, 65] Generated Node #0,1,1: 16:[10, 65] Operation: 78-13=65 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[10, 6], Operations: ['98-20=78', '78/13=6'] Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[98, 10, 20, 13], Operations: [] Exploring Operation: 98-20=78, Resulting Numbers: [10, 13, 78] Generated Node #0,1: 16:[10, 13, 78] Operation: 98-20=78 Moving to Node #0,1 Current State: 16:[10, 13, 78], Operations: ['98-20=78'] Exploring Operation: 78/13=6, Resulting Numbers: [10, 6] Generated Node #0,1,0: 16:[10, 6] Operation: 78/13=6 Moving to Node #0,1,0 Current State: 16:[10, 6], Operations: ['98-20=78', '78/13=6'] Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 76, 80, 67, 18 ]
81
[ "80-76=4", "67+18=85", "85-4=81" ]
Current State: 81:[76, 80, 67, 18], Operations: [] Exploring Operation: 80-76=4, Resulting Numbers: [67, 18, 4] Generated Node #2: [67, 18, 4] from Operation: 80-76=4 Current State: 81:[67, 18, 4], Operations: ['80-76=4'] Exploring Operation: 67+18=85, Resulting Numbers: [4, 85] Generated Node #3: [4, 85] from Operation: 67+18=85 Current State: 81:[4, 85], Operations: ['80-76=4', '67+18=85'] Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[76, 80, 67, 18], Operations: [] Exploring Operation: 80-67=13, Resulting Numbers: [76, 18, 13] Generated Node #0,0: 81:[76, 18, 13] Operation: 80-67=13 Exploring Operation: 67+18=85, Resulting Numbers: [76, 80, 85] Generated Node #0,1: 81:[76, 80, 85] Operation: 67+18=85 Exploring Operation: 80-76=4, Resulting Numbers: [67, 18, 4] Generated Node #0,2: 81:[67, 18, 4] Operation: 80-76=4 Exploring Operation: 76-67=9, Resulting Numbers: [80, 18, 9] Generated Node #0,3: 81:[80, 18, 9] Operation: 76-67=9 Moving to Node #0,1 Current State: 81:[76, 80, 85], Operations: ['67+18=85'] Exploring Operation: 85-76=9, Resulting Numbers: [80, 9] Generated Node #0,1,0: 81:[80, 9] Operation: 85-76=9 Exploring Operation: 85-80=5, Resulting Numbers: [76, 5] Generated Node #0,1,1: 81:[76, 5] Operation: 85-80=5 Exploring Operation: 76+80=156, Resulting Numbers: [85, 156] Generated Node #0,1,2: 81:[85, 156] Operation: 76+80=156 Exploring Operation: 80-76=4, Resulting Numbers: [85, 4] Generated Node #0,1,3: 81:[85, 4] Operation: 80-76=4 Moving to Node #0,3 Current State: 81:[80, 18, 9], Operations: ['76-67=9'] Exploring Operation: 18+9=27, Resulting Numbers: [80, 27] Generated Node #0,3,0: 81:[80, 27] Operation: 18+9=27 Exploring Operation: 18-9=9, Resulting Numbers: [80, 9] Generated Node #0,3,1: 81:[80, 9] Operation: 18-9=9 Exploring Operation: 80+18=98, Resulting Numbers: [9, 98] Generated Node #0,3,2: 81:[9, 98] Operation: 80+18=98 Exploring Operation: 18/9=2, Resulting Numbers: [80, 2] Generated Node #0,3,3: 81:[80, 2] Operation: 18/9=2 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 81:[80, 27], Operations: ['76-67=9', '18+9=27'] Exploring Operation: 80-27=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 80*27=2160, Resulting Numbers: [2160] 2160,81 unequal: No Solution Exploring Operation: 80+27=107, Resulting Numbers: [107] 107,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 81:[80, 9], Operations: ['76-67=9', '18-9=9'] Exploring Operation: 80+9=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 80*9=720, Resulting Numbers: [720] 720,81 unequal: No Solution Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 81:[80, 2], Operations: ['76-67=9', '18/9=2'] Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,81 unequal: No Solution Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,81 unequal: No Solution Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,81 unequal: No Solution Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 81:[9, 98], Operations: ['76-67=9', '80+18=98'] Exploring Operation: 98-9=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 9*98=882, Resulting Numbers: [882] 882,81 unequal: No Solution Exploring Operation: 9+98=107, Resulting Numbers: [107] 107,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 81:[76, 18, 13], Operations: ['80-67=13'] Exploring Operation: 76+13=89, Resulting Numbers: [18, 89] Generated Node #0,0,0: 81:[18, 89] Operation: 76+13=89 Exploring Operation: 76+18=94, Resulting Numbers: [13, 94] Generated Node #0,0,1: 81:[13, 94] Operation: 76+18=94 Exploring Operation: 18-13=5, Resulting Numbers: [76, 5] Generated Node #0,0,2: 81:[76, 5] Operation: 18-13=5 Exploring Operation: 18+13=31, Resulting Numbers: [76, 31] Generated Node #0,0,3: 81:[76, 31] Operation: 18+13=31 Moving to Node #0,2 Current State: 81:[67, 18, 4], Operations: ['80-76=4'] Exploring Operation: 67+4=71, Resulting Numbers: [18, 71] Generated Node #0,2,0: 81:[18, 71] Operation: 67+4=71 Exploring Operation: 18-4=14, Resulting Numbers: [67, 14] Generated Node #0,2,1: 81:[67, 14] Operation: 18-4=14 Exploring Operation: 18+4=22, Resulting Numbers: [67, 22] Generated Node #0,2,2: 81:[67, 22] Operation: 18+4=22 Exploring Operation: 67+18=85, Resulting Numbers: [4, 85] Generated Node #0,2,3: 81:[4, 85] Operation: 67+18=85 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 81:[4, 85], Operations: ['80-76=4', '67+18=85'] Exploring Operation: 4*85=340, Resulting Numbers: [340] 340,81 unequal: No Solution Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[76, 80, 67, 18], Operations: [] Exploring Operation: 80-76=4, Resulting Numbers: [67, 18, 4] Generated Node #0,2: 81:[67, 18, 4] Operation: 80-76=4 Moving to Node #0,2 Current State: 81:[67, 18, 4], Operations: ['80-76=4'] Exploring Operation: 67+18=85, Resulting Numbers: [4, 85] Generated Node #0,2,3: 81:[4, 85] Operation: 67+18=85 Moving to Node #0,2,3 Current State: 81:[4, 85], Operations: ['80-76=4', '67+18=85'] Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_4
sum_heuristic
[ 51, 12, 89, 79 ]
69
[ "89-79=10", "12*10=120", "120-51=69" ]
Current State: 69:[51, 12, 89, 79], Operations: [] Exploring Operation: 89-79=10, Resulting Numbers: [51, 12, 10] Generated Node #2: [51, 12, 10] from Operation: 89-79=10 Current State: 69:[51, 12, 10], Operations: ['89-79=10'] Exploring Operation: 12*10=120, Resulting Numbers: [51, 120] Generated Node #3: [51, 120] from Operation: 12*10=120 Current State: 69:[51, 120], Operations: ['89-79=10', '12*10=120'] Exploring Operation: 120-51=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[51, 12, 89, 79], Operations: [] Exploring Operation: 79-51=28, Resulting Numbers: [12, 89, 28] Generated Node #0,0: 69:[12, 89, 28] Operation: 79-51=28 Exploring Operation: 89-51=38, Resulting Numbers: [12, 79, 38] Generated Node #0,1: 69:[12, 79, 38] Operation: 89-51=38 Exploring Operation: 89-79=10, Resulting Numbers: [51, 12, 10] Generated Node #0,2: 69:[51, 12, 10] Operation: 89-79=10 Exploring Operation: 51+12=63, Resulting Numbers: [89, 79, 63] Generated Node #0,3: 69:[89, 79, 63] Operation: 51+12=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[12, 89, 28], Operations: ['79-51=28'] Exploring Operation: 28-12=16, Resulting Numbers: [89, 16] Generated Node #0,0,0: 69:[89, 16] Operation: 28-12=16 Exploring Operation: 89-28=61, Resulting Numbers: [12, 61] Generated Node #0,0,1: 69:[12, 61] Operation: 89-28=61 Exploring Operation: 12+89=101, Resulting Numbers: [28, 101] Generated Node #0,0,2: 69:[28, 101] Operation: 12+89=101 Exploring Operation: 89-12=77, Resulting Numbers: [28, 77] Generated Node #0,0,3: 69:[28, 77] Operation: 89-12=77 Moving to Node #0,0,3 Current State: 69:[28, 77], Operations: ['79-51=28', '89-12=77'] Exploring Operation: 28+77=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 28*77=2156, Resulting Numbers: [2156] 2156,69 unequal: No Solution Exploring Operation: 77-28=49, Resulting Numbers: [49] 49,69 unequal: No Solution Moving to Node #0,0,1 Current State: 69:[12, 61], Operations: ['79-51=28', '89-28=61'] Exploring Operation: 12+61=73, Resulting Numbers: [73] 73,69 unequal: No Solution Exploring Operation: 12*61=732, Resulting Numbers: [732] 732,69 unequal: No Solution Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[89, 16], Operations: ['79-51=28', '28-12=16'] Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,69 unequal: No Solution Exploring Operation: 89+16=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 89*16=1424, Resulting Numbers: [1424] 1424,69 unequal: No Solution Moving to Node #0,0,2 Current State: 69:[28, 101], Operations: ['79-51=28', '12+89=101'] Exploring Operation: 28*101=2828, Resulting Numbers: [2828] 2828,69 unequal: No Solution Exploring Operation: 101-28=73, Resulting Numbers: [73] 73,69 unequal: No Solution Exploring Operation: 28+101=129, Resulting Numbers: [129] 129,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[12, 79, 38], Operations: ['89-51=38'] Exploring Operation: 79-12=67, Resulting Numbers: [38, 67] Generated Node #0,1,0: 69:[38, 67] Operation: 79-12=67 Exploring Operation: 79-38=41, Resulting Numbers: [12, 41] Generated Node #0,1,1: 69:[12, 41] Operation: 79-38=41 Exploring Operation: 38-12=26, Resulting Numbers: [79, 26] Generated Node #0,1,2: 69:[79, 26] Operation: 38-12=26 Exploring Operation: 12+38=50, Resulting Numbers: [79, 50] Generated Node #0,1,3: 69:[79, 50] Operation: 12+38=50 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 69:[79, 26], Operations: ['89-51=38', '38-12=26'] Exploring Operation: 79-26=53, Resulting Numbers: [53] 53,69 unequal: No Solution Exploring Operation: 79+26=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 79*26=2054, Resulting Numbers: [2054] 2054,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 69:[38, 67], Operations: ['89-51=38', '79-12=67'] Exploring Operation: 38+67=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,69 unequal: No Solution Exploring Operation: 38*67=2546, Resulting Numbers: [2546] 2546,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 69:[12, 41], Operations: ['89-51=38', '79-38=41'] Exploring Operation: 12*41=492, Resulting Numbers: [492] 492,69 unequal: No Solution Exploring Operation: 41-12=29, Resulting Numbers: [29] 29,69 unequal: No Solution Exploring Operation: 12+41=53, Resulting Numbers: [53] 53,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 69:[79, 50], Operations: ['89-51=38', '12+38=50'] Exploring Operation: 79-50=29, Resulting Numbers: [29] 29,69 unequal: No Solution Exploring Operation: 79+50=129, Resulting Numbers: [129] 129,69 unequal: No Solution Exploring Operation: 79*50=3950, Resulting Numbers: [3950] 3950,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[51, 12, 10], Operations: ['89-79=10'] Exploring Operation: 51+10=61, Resulting Numbers: [12, 61] Generated Node #0,2,0: 69:[12, 61] Operation: 51+10=61 Exploring Operation: 12-10=2, Resulting Numbers: [51, 2] Generated Node #0,2,1: 69:[51, 2] Operation: 12-10=2 Exploring Operation: 12+10=22, Resulting Numbers: [51, 22] Generated Node #0,2,2: 69:[51, 22] Operation: 12+10=22 Exploring Operation: 51+12=63, Resulting Numbers: [10, 63] Generated Node #0,2,3: 69:[10, 63] Operation: 51+12=63 Moving to Node #0,2,3 Current State: 69:[10, 63], Operations: ['89-79=10', '51+12=63'] Exploring Operation: 10*63=630, Resulting Numbers: [630] 630,69 unequal: No Solution Exploring Operation: 63-10=53, Resulting Numbers: [53] 53,69 unequal: No Solution Exploring Operation: 10+63=73, Resulting Numbers: [73] 73,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[12, 61], Operations: ['89-79=10', '51+10=61'] Exploring Operation: 12*61=732, Resulting Numbers: [732] 732,69 unequal: No Solution Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,69 unequal: No Solution Exploring Operation: 12+61=73, Resulting Numbers: [73] 73,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[51, 22], Operations: ['89-79=10', '12+10=22'] Exploring Operation: 51*22=1122, Resulting Numbers: [1122] 1122,69 unequal: No Solution Exploring Operation: 51-22=29, Resulting Numbers: [29] 29,69 unequal: No Solution Exploring Operation: 51+22=73, Resulting Numbers: [73] 73,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[51, 2], Operations: ['89-79=10', '12-10=2'] Exploring Operation: 51*2=102, Resulting Numbers: [102] 102,69 unequal: No Solution Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,69 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 69:[89, 79, 63], Operations: ['51+12=63'] Exploring Operation: 89-79=10, Resulting Numbers: [63, 10] Generated Node #0,3,0: 69:[63, 10] Operation: 89-79=10 Exploring Operation: 79-63=16, Resulting Numbers: [89, 16] Generated Node #0,3,1: 69:[89, 16] Operation: 79-63=16 Exploring Operation: 89+63=152, Resulting Numbers: [79, 152] Generated Node #0,3,2: 69:[79, 152] Operation: 89+63=152 Exploring Operation: 89-63=26, Resulting Numbers: [79, 26] Generated Node #0,3,3: 69:[79, 26] Operation: 89-63=26 Moving to Node #0,3,0 Current State: 69:[63, 10], Operations: ['51+12=63', '89-79=10'] Exploring Operation: 63*10=630, Resulting Numbers: [630] 630,69 unequal: No Solution Exploring Operation: 63-10=53, Resulting Numbers: [53] 53,69 unequal: No Solution Exploring Operation: 63+10=73, Resulting Numbers: [73] 73,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[79, 26], Operations: ['51+12=63', '89-63=26'] Exploring Operation: 79+26=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 79*26=2054, Resulting Numbers: [2054] 2054,69 unequal: No Solution Exploring Operation: 79-26=53, Resulting Numbers: [53] 53,69 unequal: No Solution Moving to Node #0,3,1 Current State: 69:[89, 16], Operations: ['51+12=63', '79-63=16'] Exploring Operation: 89*16=1424, Resulting Numbers: [1424] 1424,69 unequal: No Solution Exploring Operation: 89+16=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[79, 152], Operations: ['51+12=63', '89+63=152'] Exploring Operation: 79*152=12008, Resulting Numbers: [12008] 12008,69 unequal: No Solution Exploring Operation: 79+152=231, Resulting Numbers: [231] 231,69 unequal: No Solution Exploring Operation: 152-79=73, Resulting Numbers: [73] 73,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 36, 15, 35, 96 ]
31
[ "96-36=60", "60/15=4", "35-4=31" ]
Current State: 31:[36, 15, 35, 96], Operations: [] Exploring Operation: 96-36=60, Resulting Numbers: [15, 35, 60] Generated Node #2: [15, 35, 60] from Operation: 96-36=60 Current State: 31:[15, 35, 60], Operations: ['96-36=60'] Exploring Operation: 60/15=4, Resulting Numbers: [35, 4] Generated Node #3: [35, 4] from Operation: 60/15=4 Current State: 31:[35, 4], Operations: ['96-36=60', '60/15=4'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[36, 15, 35, 96], Operations: [] Exploring Operation: 96-35=61, Resulting Numbers: [36, 15, 61] Generated Node #0,0: 31:[36, 15, 61] Operation: 96-35=61 Exploring Operation: 96-15=81, Resulting Numbers: [36, 35, 81] Generated Node #0,1: 31:[36, 35, 81] Operation: 96-15=81 Exploring Operation: 96-36=60, Resulting Numbers: [15, 35, 60] Generated Node #0,2: 31:[15, 35, 60] Operation: 96-36=60 Start Sub Search at level 1: Moving to Node #0,2 Current State: 31:[15, 35, 60], Operations: ['96-36=60'] Exploring Operation: 60/15=4, Resulting Numbers: [35, 4] Generated Node #0,2,0: 31:[35, 4] Operation: 60/15=4 Exploring Operation: 60-15=45, Resulting Numbers: [35, 45] Generated Node #0,2,1: 31:[35, 45] Operation: 60-15=45 Exploring Operation: 60-35=25, Resulting Numbers: [15, 25] Generated Node #0,2,2: 31:[15, 25] Operation: 60-35=25 Moving to Node #0,2,1 Current State: 31:[35, 45], Operations: ['96-36=60', '60-15=45'] Exploring Operation: 35*45=1575, Resulting Numbers: [1575] 1575,31 unequal: No Solution Exploring Operation: 35+45=80, Resulting Numbers: [80] 80,31 unequal: No Solution Exploring Operation: 45-35=10, Resulting Numbers: [10] 10,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[15, 25], Operations: ['96-36=60', '60-35=25'] Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 15*25=375, Resulting Numbers: [375] 375,31 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,31 unequal: No Solution Moving to Node #0,2,0 Current State: 31:[35, 4], Operations: ['96-36=60', '60/15=4'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[36, 15, 35, 96], Operations: [] Exploring Operation: 96-36=60, Resulting Numbers: [15, 35, 60] Generated Node #0,2: 31:[15, 35, 60] Operation: 96-36=60 Moving to Node #0,2 Current State: 31:[15, 35, 60], Operations: ['96-36=60'] Exploring Operation: 60/15=4, Resulting Numbers: [35, 4] Generated Node #0,2,0: 31:[35, 4] Operation: 60/15=4 Moving to Node #0,2,0 Current State: 31:[35, 4], Operations: ['96-36=60', '60/15=4'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 72, 66, 24, 22 ]
18
[ "72-66=6", "24/6=4", "22-4=18" ]
Current State: 18:[72, 66, 24, 22], Operations: [] Exploring Operation: 72-66=6, Resulting Numbers: [24, 22, 6] Generated Node #2: [24, 22, 6] from Operation: 72-66=6 Current State: 18:[24, 22, 6], Operations: ['72-66=6'] Exploring Operation: 24/6=4, Resulting Numbers: [22, 4] Generated Node #3: [22, 4] from Operation: 24/6=4 Current State: 18:[22, 4], Operations: ['72-66=6', '24/6=4'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[72, 66, 24, 22], Operations: [] Exploring Operation: 72-66=6, Resulting Numbers: [24, 22, 6] Generated Node #0,0: 18:[24, 22, 6] Operation: 72-66=6 Moving to Node #0,0 Current State: 18:[24, 22, 6], Operations: ['72-66=6'] Exploring Operation: 24-22=2, Resulting Numbers: [6, 2] Generated Node #0,0,0: 18:[6, 2] Operation: 24-22=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[6, 2], Operations: ['72-66=6', '24-22=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 29, 85, 1, 42 ]
98
[ "85-29=56", "1*42=42", "56+42=98" ]
Current State: 98:[29, 85, 1, 42], Operations: [] Exploring Operation: 85-29=56, Resulting Numbers: [1, 42, 56] Generated Node #2: [1, 42, 56] from Operation: 85-29=56 Current State: 98:[1, 42, 56], Operations: ['85-29=56'] Exploring Operation: 1*42=42, Resulting Numbers: [56, 42] Generated Node #3: [56, 42] from Operation: 1*42=42 Current State: 98:[56, 42], Operations: ['85-29=56', '1*42=42'] Exploring Operation: 56+42=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[29, 85, 1, 42], Operations: [] Exploring Operation: 85-29=56, Resulting Numbers: [1, 42, 56] Generated Node #0,0: 98:[1, 42, 56] Operation: 85-29=56 Exploring Operation: 42-29=13, Resulting Numbers: [85, 1, 13] Generated Node #0,1: 98:[85, 1, 13] Operation: 42-29=13 Exploring Operation: 29-1=28, Resulting Numbers: [85, 42, 28] Generated Node #0,2: 98:[85, 42, 28] Operation: 29-1=28 Exploring Operation: 29+85=114, Resulting Numbers: [1, 42, 114] Generated Node #0,3: 98:[1, 42, 114] Operation: 29+85=114 Exploring Operation: 85-42=43, Resulting Numbers: [29, 1, 43] Generated Node #0,4: 98:[29, 1, 43] Operation: 85-42=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[1, 42, 56], Operations: ['85-29=56'] Exploring Operation: 56-1=55, Resulting Numbers: [42, 55] Generated Node #0,0,0: 98:[42, 55] Operation: 56-1=55 Exploring Operation: 1+42=43, Resulting Numbers: [56, 43] Generated Node #0,0,1: 98:[56, 43] Operation: 1+42=43 Exploring Operation: 1*42=42, Resulting Numbers: [56, 42] Generated Node #0,0,2: 98:[56, 42] Operation: 1*42=42 Exploring Operation: 56-42=14, Resulting Numbers: [1, 14] Generated Node #0,0,3: 98:[1, 14] Operation: 56-42=14 Exploring Operation: 42+56=98, Resulting Numbers: [1, 98] Generated Node #0,0,4: 98:[1, 98] Operation: 42+56=98 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 98:[1, 14], Operations: ['85-29=56', '56-42=14'] Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,98 unequal: No Solution Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,98 unequal: No Solution Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,98 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 98:[1, 98], Operations: ['85-29=56', '42+56=98'] Exploring Operation: 1*98=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[29, 85, 1, 42], Operations: [] Exploring Operation: 85-29=56, Resulting Numbers: [1, 42, 56] Generated Node #0,0: 98:[1, 42, 56] Operation: 85-29=56 Moving to Node #0,0 Current State: 98:[1, 42, 56], Operations: ['85-29=56'] Exploring Operation: 42+56=98, Resulting Numbers: [1, 98] Generated Node #0,0,4: 98:[1, 98] Operation: 42+56=98 Moving to Node #0,0,4 Current State: 98:[1, 98], Operations: ['85-29=56', '42+56=98'] Exploring Operation: 1*98=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 48, 53, 79, 51 ]
44
[ "51-48=3", "53+79=132", "132/3=44" ]
Current State: 44:[48, 53, 79, 51], Operations: [] Exploring Operation: 51-48=3, Resulting Numbers: [53, 79, 3] Generated Node #2: [53, 79, 3] from Operation: 51-48=3 Current State: 44:[53, 79, 3], Operations: ['51-48=3'] Exploring Operation: 53+79=132, Resulting Numbers: [3, 132] Generated Node #3: [3, 132] from Operation: 53+79=132 Current State: 44:[3, 132], Operations: ['51-48=3', '53+79=132'] Exploring Operation: 132/3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[48, 53, 79, 51], Operations: [] Exploring Operation: 79-53=26, Resulting Numbers: [48, 51, 26] Generated Node #0,0: 44:[48, 51, 26] Operation: 79-53=26 Moving to Node #0,0 Current State: 44:[48, 51, 26], Operations: ['79-53=26'] Exploring Operation: 51-48=3, Resulting Numbers: [26, 3] Generated Node #0,0,0: 44:[26, 3] Operation: 51-48=3 Moving to Node #0,0,0 Current State: 44:[26, 3], Operations: ['79-53=26', '51-48=3'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,44 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 1, 17, 14, 39 ]
20
[ "14-1=13", "39/13=3", "17+3=20" ]
Current State: 20:[1, 17, 14, 39], Operations: [] Exploring Operation: 14-1=13, Resulting Numbers: [17, 39, 13] Generated Node #2: [17, 39, 13] from Operation: 14-1=13 Current State: 20:[17, 39, 13], Operations: ['14-1=13'] Exploring Operation: 39/13=3, Resulting Numbers: [17, 3] Generated Node #3: [17, 3] from Operation: 39/13=3 Current State: 20:[17, 3], Operations: ['14-1=13', '39/13=3'] Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[1, 17, 14, 39], Operations: [] Exploring Operation: 39-17=22, Resulting Numbers: [1, 14, 22] Generated Node #0,0: 20:[1, 14, 22] Operation: 39-17=22 Moving to Node #0,0 Current State: 20:[1, 14, 22], Operations: ['39-17=22'] Exploring Operation: 22-14=8, Resulting Numbers: [1, 8] Generated Node #0,0,0: 20:[1, 8] Operation: 22-14=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[1, 8], Operations: ['39-17=22', '22-14=8'] Exploring Operation: 1+8=9, Resulting Numbers: [9] 9,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic