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
[ 19, 59, 6, 75 ]
62
[ "19+59=78", "78/6=13", "75-13=62" ]
Current State: 62:[19, 59, 6, 75], Operations: [] Exploring Operation: 19+59=78, Resulting Numbers: [6, 75, 78] Generated Node #2: [6, 75, 78] from Operation: 19+59=78 Current State: 62:[6, 75, 78], Operations: ['19+59=78'] Exploring Operation: 78/6=13, Resulting Numbers: [75, 13] Generated Node #3: [75, 13] from Operation: 78/6=13 Current State: 62:[75, 13], Operations: ['19+59=78', '78/6=13'] Exploring Operation: 75-13=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[19, 59, 6, 75], Operations: [] Exploring Operation: 75-19=56, Resulting Numbers: [59, 6, 56] Generated Node #0,0: 62:[59, 6, 56] Operation: 75-19=56 Exploring Operation: 59-19=40, Resulting Numbers: [6, 75, 40] Generated Node #0,1: 62:[6, 75, 40] Operation: 59-19=40 Exploring Operation: 19+6=25, Resulting Numbers: [59, 75, 25] Generated Node #0,2: 62:[59, 75, 25] Operation: 19+6=25 Exploring Operation: 75-6=69, Resulting Numbers: [19, 59, 69] Generated Node #0,3: 62:[19, 59, 69] Operation: 75-6=69 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[59, 6, 56], Operations: ['75-19=56'] Exploring Operation: 59+6=65, Resulting Numbers: [56, 65] Generated Node #0,0,0: 62:[56, 65] Operation: 59+6=65 Exploring Operation: 6+56=62, Resulting Numbers: [59, 62] Generated Node #0,0,1: 62:[59, 62] Operation: 6+56=62 Exploring Operation: 59-56=3, Resulting Numbers: [6, 3] Generated Node #0,0,2: 62:[6, 3] Operation: 59-56=3 Exploring Operation: 59-6=53, Resulting Numbers: [56, 53] Generated Node #0,0,3: 62:[56, 53] Operation: 59-6=53 Moving to Node #0,0,1 Current State: 62:[59, 62], Operations: ['75-19=56', '6+56=62'] Exploring Operation: 59*62=3658, Resulting Numbers: [3658] 3658,62 unequal: No Solution Exploring Operation: 59+62=121, Resulting Numbers: [121] 121,62 unequal: No Solution Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[6, 3], Operations: ['75-19=56', '59-56=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,62 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,62 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,62 unequal: No Solution Moving to Node #0,0,0 Current State: 62:[56, 65], Operations: ['75-19=56', '59+6=65'] Exploring Operation: 56*65=3640, Resulting Numbers: [3640] 3640,62 unequal: No Solution Exploring Operation: 56+65=121, Resulting Numbers: [121] 121,62 unequal: No Solution Exploring Operation: 65-56=9, Resulting Numbers: [9] 9,62 unequal: No Solution Moving to Node #0,0,3 Current State: 62:[56, 53], Operations: ['75-19=56', '59-6=53'] Exploring Operation: 56+53=109, Resulting Numbers: [109] 109,62 unequal: No Solution Exploring Operation: 56-53=3, Resulting Numbers: [3] 3,62 unequal: No Solution Exploring Operation: 56*53=2968, Resulting Numbers: [2968] 2968,62 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: 62:[59, 75, 25], Operations: ['19+6=25'] Exploring Operation: 75-25=50, Resulting Numbers: [59, 50] Generated Node #0,2,0: 62:[59, 50] Operation: 75-25=50 Exploring Operation: 75/25=3, Resulting Numbers: [59, 3] Generated Node #0,2,1: 62:[59, 3] Operation: 75/25=3 Exploring Operation: 59-25=34, Resulting Numbers: [75, 34] Generated Node #0,2,2: 62:[75, 34] Operation: 59-25=34 Exploring Operation: 75-59=16, Resulting Numbers: [25, 16] Generated Node #0,2,3: 62:[25, 16] Operation: 75-59=16 Moving to Node #0,2,1 Current State: 62:[59, 3], Operations: ['19+6=25', '75/25=3'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,62 unequal: No Solution Exploring Operation: 59*3=177, Resulting Numbers: [177] 177,62 unequal: No Solution Exploring Operation: 59+3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[19, 59, 6, 75], Operations: [] Exploring Operation: 19+6=25, Resulting Numbers: [59, 75, 25] Generated Node #0,2: 62:[59, 75, 25] Operation: 19+6=25 Moving to Node #0,2 Current State: 62:[59, 75, 25], Operations: ['19+6=25'] Exploring Operation: 75/25=3, Resulting Numbers: [59, 3] Generated Node #0,2,1: 62:[59, 3] Operation: 75/25=3 Moving to Node #0,2,1 Current State: 62:[59, 3], Operations: ['19+6=25', '75/25=3'] Exploring Operation: 59+3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 24, 52, 10, 36 ]
26
[ "24+10=34", "36-34=2", "52/2=26" ]
Current State: 26:[24, 52, 10, 36], Operations: [] Exploring Operation: 24+10=34, Resulting Numbers: [52, 36, 34] Generated Node #2: [52, 36, 34] from Operation: 24+10=34 Current State: 26:[52, 36, 34], Operations: ['24+10=34'] Exploring Operation: 36-34=2, Resulting Numbers: [52, 2] Generated Node #3: [52, 2] from Operation: 36-34=2 Current State: 26:[52, 2], Operations: ['24+10=34', '36-34=2'] Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[24, 52, 10, 36], Operations: [] Exploring Operation: 36-24=12, Resulting Numbers: [52, 10, 12] Generated Node #0,0: 26:[52, 10, 12] Operation: 36-24=12 Exploring Operation: 52-36=16, Resulting Numbers: [24, 10, 16] Generated Node #0,1: 26:[24, 10, 16] Operation: 52-36=16 Exploring Operation: 52-24=28, Resulting Numbers: [10, 36, 28] Generated Node #0,2: 26:[10, 36, 28] Operation: 52-24=28 Exploring Operation: 36-10=26, Resulting Numbers: [24, 52, 26] Generated Node #0,3: 26:[24, 52, 26] Operation: 36-10=26 Exploring Operation: 52-10=42, Resulting Numbers: [24, 36, 42] Generated Node #0,4: 26:[24, 36, 42] Operation: 52-10=42 Moving to Node #0,1 Current State: 26:[24, 10, 16], Operations: ['52-36=16'] Exploring Operation: 24-10=14, Resulting Numbers: [16, 14] Generated Node #0,1,0: 26:[16, 14] Operation: 24-10=14 Exploring Operation: 16-10=6, Resulting Numbers: [24, 6] Generated Node #0,1,1: 26:[24, 6] Operation: 16-10=6 Exploring Operation: 24-16=8, Resulting Numbers: [10, 8] Generated Node #0,1,2: 26:[10, 8] Operation: 24-16=8 Exploring Operation: 10+16=26, Resulting Numbers: [24, 26] Generated Node #0,1,3: 26:[24, 26] Operation: 10+16=26 Exploring Operation: 24+10=34, Resulting Numbers: [16, 34] Generated Node #0,1,4: 26:[16, 34] Operation: 24+10=34 Moving to Node #0,2 Current State: 26:[10, 36, 28], Operations: ['52-24=28'] Exploring Operation: 10+36=46, Resulting Numbers: [28, 46] Generated Node #0,2,0: 26:[28, 46] Operation: 10+36=46 Exploring Operation: 36-28=8, Resulting Numbers: [10, 8] Generated Node #0,2,1: 26:[10, 8] Operation: 36-28=8 Exploring Operation: 28-10=18, Resulting Numbers: [36, 18] Generated Node #0,2,2: 26:[36, 18] Operation: 28-10=18 Exploring Operation: 36-10=26, Resulting Numbers: [28, 26] Generated Node #0,2,3: 26:[28, 26] Operation: 36-10=26 Exploring Operation: 10+28=38, Resulting Numbers: [36, 38] Generated Node #0,2,4: 26:[36, 38] Operation: 10+28=38 Moving to Node #0,3 Current State: 26:[24, 52, 26], Operations: ['36-10=26'] Exploring Operation: 52/26=2, Resulting Numbers: [24, 2] Generated Node #0,3,0: 26:[24, 2] Operation: 52/26=2 Exploring Operation: 52-26=26, Resulting Numbers: [24, 26] Generated Node #0,3,1: 26:[24, 26] Operation: 52-26=26 Exploring Operation: 52-24=28, Resulting Numbers: [26, 28] Generated Node #0,3,2: 26:[26, 28] Operation: 52-24=28 Exploring Operation: 24+52=76, Resulting Numbers: [26, 76] Generated Node #0,3,3: 26:[26, 76] Operation: 24+52=76 Exploring Operation: 26-24=2, Resulting Numbers: [52, 2] Generated Node #0,3,4: 26:[52, 2] Operation: 26-24=2 Moving to Node #0,4 Current State: 26:[24, 36, 42], Operations: ['52-10=42'] Exploring Operation: 24+42=66, Resulting Numbers: [36, 66] Generated Node #0,4,0: 26:[36, 66] Operation: 24+42=66 Exploring Operation: 24+36=60, Resulting Numbers: [42, 60] Generated Node #0,4,1: 26:[42, 60] Operation: 24+36=60 Exploring Operation: 42-24=18, Resulting Numbers: [36, 18] Generated Node #0,4,2: 26:[36, 18] Operation: 42-24=18 Exploring Operation: 42-36=6, Resulting Numbers: [24, 6] Generated Node #0,4,3: 26:[24, 6] Operation: 42-36=6 Exploring Operation: 36-24=12, Resulting Numbers: [42, 12] Generated Node #0,4,4: 26:[42, 12] Operation: 36-24=12 Moving to Node #0,0 Current State: 26:[52, 10, 12], Operations: ['36-24=12'] Exploring Operation: 52+10=62, Resulting Numbers: [12, 62] Generated Node #0,0,0: 26:[12, 62] Operation: 52+10=62 Exploring Operation: 12-10=2, Resulting Numbers: [52, 2] Generated Node #0,0,1: 26:[52, 2] Operation: 12-10=2 Exploring Operation: 52-12=40, Resulting Numbers: [10, 40] Generated Node #0,0,2: 26:[10, 40] Operation: 52-12=40 Exploring Operation: 52-10=42, Resulting Numbers: [12, 42] Generated Node #0,0,3: 26:[12, 42] Operation: 52-10=42 Exploring Operation: 10+12=22, Resulting Numbers: [52, 22] Generated Node #0,0,4: 26:[52, 22] Operation: 10+12=22 Moving to Node #0,1,3 Current State: 26:[24, 26], Operations: ['52-36=16', '10+16=26'] Exploring Operation: 24*26=624, Resulting Numbers: [624] 624,26 unequal: No Solution Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,26 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,26 unequal: No Solution Moving to Node #0,2,3 Current State: 26:[28, 26], Operations: ['52-24=28', '36-10=26'] Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 28*26=728, Resulting Numbers: [728] 728,26 unequal: No Solution Exploring Operation: 28+26=54, Resulting Numbers: [54] 54,26 unequal: No Solution Moving to Node #0,3,1 Current State: 26:[24, 26], Operations: ['36-10=26', '52-26=26'] Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,26 unequal: No Solution Exploring Operation: 24*26=624, Resulting Numbers: [624] 624,26 unequal: No Solution Moving to Node #0,3,2 Current State: 26:[26, 28], Operations: ['36-10=26', '52-24=28'] Exploring Operation: 26*28=728, Resulting Numbers: [728] 728,26 unequal: No Solution Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,26 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,26 unequal: No Solution Moving to Node #0,3,0 Current State: 26:[24, 2], Operations: ['36-10=26', '52/26=2'] Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,26 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,26 unequal: No Solution Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[24, 52, 10, 36], Operations: [] Exploring Operation: 36-10=26, Resulting Numbers: [24, 52, 26] Generated Node #0,3: 26:[24, 52, 26] Operation: 36-10=26 Moving to Node #0,3 Current State: 26:[24, 52, 26], Operations: ['36-10=26'] Exploring Operation: 52/26=2, Resulting Numbers: [24, 2] Generated Node #0,3,0: 26:[24, 2] Operation: 52/26=2 Moving to Node #0,3,0 Current State: 26:[24, 2], Operations: ['36-10=26', '52/26=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
0.956597
hs_5
sum_heuristic
[ 74, 88, 74, 41 ]
47
[ "74+88=162", "74+41=115", "162-115=47" ]
Current State: 47:[74, 88, 74, 41], Operations: [] Exploring Operation: 74+88=162, Resulting Numbers: [41, 162] Generated Node #2: [41, 162] from Operation: 74+88=162 Current State: 47:[41, 162], Operations: ['74+88=162'] Exploring Operation: 74+41=115, Resulting Numbers: [162, 115] Generated Node #3: [162, 115] from Operation: 74+41=115 Current State: 47:[162, 115], Operations: ['74+88=162', '74+41=115'] Exploring Operation: 162-115=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[74, 88, 74, 41], Operations: [] Exploring Operation: 88-74=14, Resulting Numbers: [74, 41, 14] Generated Node #0,0: 47:[74, 41, 14] Operation: 88-74=14 Exploring Operation: 88-74=14, Resulting Numbers: [74, 41, 14] Generated Node #0,1: 47:[74, 41, 14] Operation: 88-74=14 Exploring Operation: 88-41=47, Resulting Numbers: [74, 74, 47] Generated Node #0,2: 47:[74, 74, 47] Operation: 88-41=47 Exploring Operation: 74-41=33, Resulting Numbers: [74, 88, 33] Generated Node #0,3: 47:[74, 88, 33] Operation: 74-41=33 Exploring Operation: 74-41=33, Resulting Numbers: [88, 74, 33] Generated Node #0,4: 47:[88, 74, 33] Operation: 74-41=33 Moving to Node #0,2 Current State: 47:[74, 74, 47], Operations: ['88-41=47'] Exploring Operation: 74-74=0, Resulting Numbers: [47, 0] Generated Node #0,2,0: 47:[47, 0] Operation: 74-74=0 Exploring Operation: 74-47=27, Resulting Numbers: [74, 27] Generated Node #0,2,1: 47:[74, 27] Operation: 74-47=27 Exploring Operation: 74+74=148, Resulting Numbers: [47, 148] Generated Node #0,2,2: 47:[47, 148] Operation: 74+74=148 Exploring Operation: 74/74=1, Resulting Numbers: [47, 1] Generated Node #0,2,3: 47:[47, 1] Operation: 74/74=1 Exploring Operation: 74-47=27, Resulting Numbers: [74, 27] Generated Node #0,2,4: 47:[74, 27] Operation: 74-47=27 Moving to Node #0,1 Current State: 47:[74, 41, 14], Operations: ['88-74=14'] Exploring Operation: 74+14=88, Resulting Numbers: [41, 88] Generated Node #0,1,0: 47:[41, 88] Operation: 74+14=88 Exploring Operation: 74-14=60, Resulting Numbers: [41, 60] Generated Node #0,1,1: 47:[41, 60] Operation: 74-14=60 Exploring Operation: 41-14=27, Resulting Numbers: [74, 27] Generated Node #0,1,2: 47:[74, 27] Operation: 41-14=27 Exploring Operation: 74-41=33, Resulting Numbers: [14, 33] Generated Node #0,1,3: 47:[14, 33] Operation: 74-41=33 Exploring Operation: 41+14=55, Resulting Numbers: [74, 55] Generated Node #0,1,4: 47:[74, 55] Operation: 41+14=55 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 47:[41, 60], Operations: ['88-74=14', '74-14=60'] Exploring Operation: 60-41=19, Resulting Numbers: [19] 19,47 unequal: No Solution Exploring Operation: 41*60=2460, Resulting Numbers: [2460] 2460,47 unequal: No Solution Exploring Operation: 41+60=101, Resulting Numbers: [101] 101,47 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: 47:[74, 55], Operations: ['88-74=14', '41+14=55'] Exploring Operation: 74-55=19, Resulting Numbers: [19] 19,47 unequal: No Solution Exploring Operation: 74+55=129, Resulting Numbers: [129] 129,47 unequal: No Solution Exploring Operation: 74*55=4070, Resulting Numbers: [4070] 4070,47 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: 47:[41, 88], Operations: ['88-74=14', '74+14=88'] Exploring Operation: 41+88=129, Resulting Numbers: [129] 129,47 unequal: No Solution Exploring Operation: 88-41=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[74, 88, 74, 41], Operations: [] Exploring Operation: 88-74=14, Resulting Numbers: [74, 41, 14] Generated Node #0,1: 47:[74, 41, 14] Operation: 88-74=14 Moving to Node #0,1 Current State: 47:[74, 41, 14], Operations: ['88-74=14'] Exploring Operation: 74+14=88, Resulting Numbers: [41, 88] Generated Node #0,1,0: 47:[41, 88] Operation: 74+14=88 Moving to Node #0,1,0 Current State: 47:[41, 88], Operations: ['88-74=14', '74+14=88'] Exploring Operation: 88-41=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_5
sum_heuristic
[ 20, 40, 83, 20 ]
43
[ "20+40=60", "83+20=103", "103-60=43" ]
Current State: 43:[20, 40, 83, 20], Operations: [] Exploring Operation: 20+40=60, Resulting Numbers: [83, 60] Generated Node #2: [83, 60] from Operation: 20+40=60 Current State: 43:[83, 60], Operations: ['20+40=60'] Exploring Operation: 83+20=103, Resulting Numbers: [60, 103] Generated Node #3: [60, 103] from Operation: 83+20=103 Current State: 43:[60, 103], Operations: ['20+40=60', '83+20=103'] Exploring Operation: 103-60=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[20, 40, 83, 20], Operations: [] Exploring Operation: 83-40=43, Resulting Numbers: [20, 20, 43] Generated Node #0,0: 43:[20, 20, 43] Operation: 83-40=43 Exploring Operation: 20+40=60, Resulting Numbers: [83, 20, 60] Generated Node #0,1: 43:[83, 20, 60] Operation: 20+40=60 Exploring Operation: 83-20=63, Resulting Numbers: [20, 40, 63] Generated Node #0,2: 43:[20, 40, 63] Operation: 83-20=63 Exploring Operation: 83-20=63, Resulting Numbers: [40, 20, 63] Generated Node #0,3: 43:[40, 20, 63] Operation: 83-20=63 Exploring Operation: 20+20=40, Resulting Numbers: [40, 83, 40] Generated Node #0,4: 43:[40, 83, 40] Operation: 20+20=40 Moving to Node #0,0 Current State: 43:[20, 20, 43], Operations: ['83-40=43'] Exploring Operation: 20/20=1, Resulting Numbers: [43, 1] Generated Node #0,0,0: 43:[43, 1] Operation: 20/20=1 Exploring Operation: 20+20=40, Resulting Numbers: [43, 40] Generated Node #0,0,1: 43:[43, 40] Operation: 20+20=40 Exploring Operation: 43-20=23, Resulting Numbers: [20, 23] Generated Node #0,0,2: 43:[20, 23] Operation: 43-20=23 Exploring Operation: 20+43=63, Resulting Numbers: [20, 63] Generated Node #0,0,3: 43:[20, 63] Operation: 20+43=63 Exploring Operation: 20-20=0, Resulting Numbers: [43, 0] Generated Node #0,0,4: 43:[43, 0] Operation: 20-20=0 Moving to Node #0,3 Current State: 43:[40, 20, 63], Operations: ['83-20=63'] Exploring Operation: 63-20=43, Resulting Numbers: [40, 43] Generated Node #0,3,0: 43:[40, 43] Operation: 63-20=43 Exploring Operation: 40-20=20, Resulting Numbers: [63, 20] Generated Node #0,3,1: 43:[63, 20] Operation: 40-20=20 Exploring Operation: 40+20=60, Resulting Numbers: [63, 60] Generated Node #0,3,2: 43:[63, 60] Operation: 40+20=60 Exploring Operation: 63-40=23, Resulting Numbers: [20, 23] Generated Node #0,3,3: 43:[20, 23] Operation: 63-40=23 Exploring Operation: 20+63=83, Resulting Numbers: [40, 83] Generated Node #0,3,4: 43:[40, 83] Operation: 20+63=83 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 43:[40, 43], Operations: ['83-20=63', '63-20=43'] Exploring Operation: 40*43=1720, Resulting Numbers: [1720] 1720,43 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 40+43=83, Resulting Numbers: [83] 83,43 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: 43:[63, 60], Operations: ['83-20=63', '40+20=60'] Exploring Operation: 63-60=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 63*60=3780, Resulting Numbers: [3780] 3780,43 unequal: No Solution Exploring Operation: 63+60=123, Resulting Numbers: [123] 123,43 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: 43:[63, 20], Operations: ['83-20=63', '40-20=20'] Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[20, 40, 83, 20], Operations: [] Exploring Operation: 83-20=63, Resulting Numbers: [40, 20, 63] Generated Node #0,3: 43:[40, 20, 63] Operation: 83-20=63 Moving to Node #0,3 Current State: 43:[40, 20, 63], Operations: ['83-20=63'] Exploring Operation: 40-20=20, Resulting Numbers: [63, 20] Generated Node #0,3,1: 43:[63, 20] Operation: 40-20=20 Moving to Node #0,3,1 Current State: 43:[63, 20], Operations: ['83-20=63', '40-20=20'] Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
sum_heuristic
[ 26, 3, 2, 90 ]
28
[ "90/3=30", "26+30=56", "56/2=28" ]
Current State: 28:[26, 3, 2, 90], Operations: [] Exploring Operation: 90/3=30, Resulting Numbers: [26, 2, 30] Generated Node #2: [26, 2, 30] from Operation: 90/3=30 Current State: 28:[26, 2, 30], Operations: ['90/3=30'] Exploring Operation: 26+30=56, Resulting Numbers: [2, 56] Generated Node #3: [2, 56] from Operation: 26+30=56 Current State: 28:[2, 56], Operations: ['90/3=30', '26+30=56'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[26, 3, 2, 90], Operations: [] Exploring Operation: 90/3=30, Resulting Numbers: [26, 2, 30] Generated Node #0,0: 28:[26, 2, 30] Operation: 90/3=30 Exploring Operation: 90-3=87, Resulting Numbers: [26, 2, 87] Generated Node #0,1: 28:[26, 2, 87] Operation: 90-3=87 Exploring Operation: 26+3=29, Resulting Numbers: [2, 90, 29] Generated Node #0,2: 28:[2, 90, 29] Operation: 26+3=29 Exploring Operation: 90-26=64, Resulting Numbers: [3, 2, 64] Generated Node #0,3: 28:[3, 2, 64] Operation: 90-26=64 Exploring Operation: 90/2=45, Resulting Numbers: [26, 3, 45] Generated Node #0,4: 28:[26, 3, 45] Operation: 90/2=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[26, 2, 30], Operations: ['90/3=30'] Exploring Operation: 30-2=28, Resulting Numbers: [26, 28] Generated Node #0,0,0: 28:[26, 28] Operation: 30-2=28 Exploring Operation: 26/2=13, Resulting Numbers: [30, 13] Generated Node #0,0,1: 28:[30, 13] Operation: 26/2=13 Exploring Operation: 30/2=15, Resulting Numbers: [26, 15] Generated Node #0,0,2: 28:[26, 15] Operation: 30/2=15 Exploring Operation: 30-26=4, Resulting Numbers: [2, 4] Generated Node #0,0,3: 28:[2, 4] Operation: 30-26=4 Exploring Operation: 26+2=28, Resulting Numbers: [30, 28] Generated Node #0,0,4: 28:[30, 28] Operation: 26+2=28 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 28:[2, 4], Operations: ['90/3=30', '30-26=4'] Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,28 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,28 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: 28:[26, 28], Operations: ['90/3=30', '30-2=28'] Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 26*28=728, Resulting Numbers: [728] 728,28 unequal: No Solution Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,28 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: 28:[30, 28], Operations: ['90/3=30', '26+2=28'] Exploring Operation: 30*28=840, Resulting Numbers: [840] 840,28 unequal: No Solution Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,28 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: 28:[30, 13], Operations: ['90/3=30', '26/2=13'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 30+13=43, Resulting Numbers: [43] 43,28 unequal: No Solution Exploring Operation: 30*13=390, Resulting Numbers: [390] 390,28 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: 28:[26, 15], Operations: ['90/3=30', '30/2=15'] Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,28 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,28 unequal: No Solution Exploring Operation: 26*15=390, Resulting Numbers: [390] 390,28 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: 28:[26, 3, 45], Operations: ['90/2=45'] Exploring Operation: 26-3=23, Resulting Numbers: [45, 23] Generated Node #0,4,0: 28:[45, 23] Operation: 26-3=23 Exploring Operation: 26+3=29, Resulting Numbers: [45, 29] Generated Node #0,4,1: 28:[45, 29] Operation: 26+3=29 Exploring Operation: 45-3=42, Resulting Numbers: [26, 42] Generated Node #0,4,2: 28:[26, 42] Operation: 45-3=42 Exploring Operation: 45/3=15, Resulting Numbers: [26, 15] Generated Node #0,4,3: 28:[26, 15] Operation: 45/3=15 Exploring Operation: 45-26=19, Resulting Numbers: [3, 19] Generated Node #0,4,4: 28:[3, 19] Operation: 45-26=19 Moving to Node #0,4,3 Current State: 28:[26, 15], Operations: ['90/2=45', '45/3=15'] Exploring Operation: 26*15=390, Resulting Numbers: [390] 390,28 unequal: No Solution Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,28 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,28 unequal: No Solution Moving to Node #0,4,4 Current State: 28:[3, 19], Operations: ['90/2=45', '45-26=19'] Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,28 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,28 unequal: No Solution Moving to Node #0,4,2 Current State: 28:[26, 42], Operations: ['90/2=45', '45-3=42'] Exploring Operation: 26*42=1092, Resulting Numbers: [1092] 1092,28 unequal: No Solution Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 26+42=68, Resulting Numbers: [68] 68,28 unequal: No Solution Moving to Node #0,4,1 Current State: 28:[45, 29], Operations: ['90/2=45', '26+3=29'] Exploring Operation: 45-29=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 45*29=1305, Resulting Numbers: [1305] 1305,28 unequal: No Solution Exploring Operation: 45+29=74, Resulting Numbers: [74] 74,28 unequal: No Solution Moving to Node #0,4,0 Current State: 28:[45, 23], Operations: ['90/2=45', '26-3=23'] Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,28 unequal: No Solution Exploring Operation: 45*23=1035, Resulting Numbers: [1035] 1035,28 unequal: No Solution Exploring Operation: 45+23=68, Resulting Numbers: [68] 68,28 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: 28:[3, 2, 64], Operations: ['90-26=64'] Exploring Operation: 3*2=6, Resulting Numbers: [64, 6] Generated Node #0,3,0: 28:[64, 6] Operation: 3*2=6 Exploring Operation: 64/2=32, Resulting Numbers: [3, 32] Generated Node #0,3,1: 28:[3, 32] Operation: 64/2=32 Exploring Operation: 64-3=61, Resulting Numbers: [2, 61] Generated Node #0,3,2: 28:[2, 61] Operation: 64-3=61 Exploring Operation: 64-2=62, Resulting Numbers: [3, 62] Generated Node #0,3,3: 28:[3, 62] Operation: 64-2=62 Exploring Operation: 3+2=5, Resulting Numbers: [64, 5] Generated Node #0,3,4: 28:[64, 5] Operation: 3+2=5 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 28:[3, 32], Operations: ['90-26=64', '64/2=32'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,28 unequal: No Solution Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,28 unequal: No Solution Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,28 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: 28:[2, 61], Operations: ['90-26=64', '64-3=61'] Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,28 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,28 unequal: No Solution Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,28 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: 28:[3, 62], Operations: ['90-26=64', '64-2=62'] Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,28 unequal: No Solution Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,28 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,28 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: 28:[64, 6], Operations: ['90-26=64', '3*2=6'] Exploring Operation: 64-6=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 64*6=384, Resulting Numbers: [384] 384,28 unequal: No Solution Exploring Operation: 64+6=70, Resulting Numbers: [70] 70,28 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: 28:[64, 5], Operations: ['90-26=64', '3+2=5'] Exploring Operation: 64*5=320, Resulting Numbers: [320] 320,28 unequal: No Solution Exploring Operation: 64+5=69, Resulting Numbers: [69] 69,28 unequal: No Solution Exploring Operation: 64-5=59, Resulting Numbers: [59] 59,28 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: 28:[26, 2, 87], Operations: ['90-3=87'] Exploring Operation: 87-2=85, Resulting Numbers: [26, 85] Generated Node #0,1,0: 28:[26, 85] Operation: 87-2=85 Exploring Operation: 26/2=13, Resulting Numbers: [87, 13] Generated Node #0,1,1: 28:[87, 13] Operation: 26/2=13 Exploring Operation: 26-2=24, Resulting Numbers: [87, 24] Generated Node #0,1,2: 28:[87, 24] Operation: 26-2=24 Exploring Operation: 26+2=28, Resulting Numbers: [87, 28] Generated Node #0,1,3: 28:[87, 28] Operation: 26+2=28 Exploring Operation: 87-26=61, Resulting Numbers: [2, 61] Generated Node #0,1,4: 28:[2, 61] Operation: 87-26=61 Moving to Node #0,1,4 Current State: 28:[2, 61], Operations: ['90-3=87', '87-26=61'] Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,28 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,28 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,28 unequal: No Solution Moving to Node #0,1,3 Current State: 28:[87, 28], Operations: ['90-3=87', '26+2=28'] Exploring Operation: 87*28=2436, Resulting Numbers: [2436] 2436,28 unequal: No Solution Exploring Operation: 87-28=59, Resulting Numbers: [59] 59,28 unequal: No Solution Exploring Operation: 87+28=115, Resulting Numbers: [115] 115,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[26, 85], Operations: ['90-3=87', '87-2=85'] Exploring Operation: 26*85=2210, Resulting Numbers: [2210] 2210,28 unequal: No Solution Exploring Operation: 26+85=111, Resulting Numbers: [111] 111,28 unequal: No Solution Exploring Operation: 85-26=59, Resulting Numbers: [59] 59,28 unequal: No Solution Moving to Node #0,1,1 Current State: 28:[87, 13], Operations: ['90-3=87', '26/2=13'] Exploring Operation: 87*13=1131, Resulting Numbers: [1131] 1131,28 unequal: No Solution Exploring Operation: 87-13=74, Resulting Numbers: [74] 74,28 unequal: No Solution Exploring Operation: 87+13=100, Resulting Numbers: [100] 100,28 unequal: No Solution Moving to Node #0,1,2 Current State: 28:[87, 24], Operations: ['90-3=87', '26-2=24'] Exploring Operation: 87+24=111, Resulting Numbers: [111] 111,28 unequal: No Solution Exploring Operation: 87*24=2088, Resulting Numbers: [2088] 2088,28 unequal: No Solution Exploring Operation: 87-24=63, Resulting Numbers: [63] 63,28 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: 28:[2, 90, 29], Operations: ['26+3=29'] Exploring Operation: 90-29=61, Resulting Numbers: [2, 61] Generated Node #0,2,0: 28:[2, 61] Operation: 90-29=61 Exploring Operation: 90-2=88, Resulting Numbers: [29, 88] Generated Node #0,2,1: 28:[29, 88] Operation: 90-2=88 Exploring Operation: 90/2=45, Resulting Numbers: [29, 45] Generated Node #0,2,2: 28:[29, 45] Operation: 90/2=45 Exploring Operation: 29-2=27, Resulting Numbers: [90, 27] Generated Node #0,2,3: 28:[90, 27] Operation: 29-2=27 Exploring Operation: 2+90=92, Resulting Numbers: [29, 92] Generated Node #0,2,4: 28:[29, 92] Operation: 2+90=92 Moving to Node #0,2,2 Current State: 28:[29, 45], Operations: ['26+3=29', '90/2=45'] Exploring Operation: 29*45=1305, Resulting Numbers: [1305] 1305,28 unequal: No Solution Exploring Operation: 45-29=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 29+45=74, Resulting Numbers: [74] 74,28 unequal: No Solution Moving to Node #0,2,0 Current State: 28:[2, 61], Operations: ['26+3=29', '90-29=61'] Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,28 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,28 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,28 unequal: No Solution Moving to Node #0,2,1 Current State: 28:[29, 88], Operations: ['26+3=29', '90-2=88'] Exploring Operation: 29*88=2552, Resulting Numbers: [2552] 2552,28 unequal: No Solution Exploring Operation: 29+88=117, Resulting Numbers: [117] 117,28 unequal: No Solution Exploring Operation: 88-29=59, Resulting Numbers: [59] 59,28 unequal: No Solution Moving to Node #0,2,3 Current State: 28:[90, 27], Operations: ['26+3=29', '29-2=27'] Exploring Operation: 90*27=2430, Resulting Numbers: [2430] 2430,28 unequal: No Solution Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,28 unequal: No Solution Exploring Operation: 90+27=117, Resulting Numbers: [117] 117,28 unequal: No Solution Moving to Node #0,2,4 Current State: 28:[29, 92], Operations: ['26+3=29', '2+90=92'] Exploring Operation: 29+92=121, Resulting Numbers: [121] 121,28 unequal: No Solution Exploring Operation: 29*92=2668, Resulting Numbers: [2668] 2668,28 unequal: No Solution Exploring Operation: 92-29=63, Resulting Numbers: [63] 63,28 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
[ 43, 45, 70, 7 ]
84
[ "45-43=2", "7*2=14", "70+14=84" ]
Current State: 84:[43, 45, 70, 7], Operations: [] Exploring Operation: 45-43=2, Resulting Numbers: [70, 7, 2] Generated Node #2: [70, 7, 2] from Operation: 45-43=2 Current State: 84:[70, 7, 2], Operations: ['45-43=2'] Exploring Operation: 7*2=14, Resulting Numbers: [70, 14] Generated Node #3: [70, 14] from Operation: 7*2=14 Current State: 84:[70, 14], Operations: ['45-43=2', '7*2=14'] Exploring Operation: 70+14=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[43, 45, 70, 7], Operations: [] Exploring Operation: 70/7=10, Resulting Numbers: [43, 45, 10] Generated Node #0,0: 84:[43, 45, 10] Operation: 70/7=10 Exploring Operation: 70+7=77, Resulting Numbers: [43, 45, 77] Generated Node #0,1: 84:[43, 45, 77] Operation: 70+7=77 Exploring Operation: 70-45=25, Resulting Numbers: [43, 7, 25] Generated Node #0,2: 84:[43, 7, 25] Operation: 70-45=25 Exploring Operation: 45-43=2, Resulting Numbers: [70, 7, 2] Generated Node #0,3: 84:[70, 7, 2] Operation: 45-43=2 Exploring Operation: 70-43=27, Resulting Numbers: [45, 7, 27] Generated Node #0,4: 84:[45, 7, 27] Operation: 70-43=27 Moving to Node #0,2 Current State: 84:[43, 7, 25], Operations: ['70-45=25'] Exploring Operation: 43-25=18, Resulting Numbers: [7, 18] Generated Node #0,2,0: 84:[7, 18] Operation: 43-25=18 Exploring Operation: 43+7=50, Resulting Numbers: [25, 50] Generated Node #0,2,1: 84:[25, 50] Operation: 43+7=50 Exploring Operation: 25-7=18, Resulting Numbers: [43, 18] Generated Node #0,2,2: 84:[43, 18] Operation: 25-7=18 Exploring Operation: 43-7=36, Resulting Numbers: [25, 36] Generated Node #0,2,3: 84:[25, 36] Operation: 43-7=36 Exploring Operation: 7+25=32, Resulting Numbers: [43, 32] Generated Node #0,2,4: 84:[43, 32] Operation: 7+25=32 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[7, 18], Operations: ['70-45=25', '43-25=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,84 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,84 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: 84:[43, 18], Operations: ['70-45=25', '25-7=18'] Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,84 unequal: No Solution Exploring Operation: 43+18=61, Resulting Numbers: [61] 61,84 unequal: No Solution Exploring Operation: 43*18=774, Resulting Numbers: [774] 774,84 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: 84:[43, 32], Operations: ['70-45=25', '7+25=32'] Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,84 unequal: No Solution Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,84 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: 84:[25, 36], Operations: ['70-45=25', '43-7=36'] Exploring Operation: 36-25=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 25*36=900, Resulting Numbers: [900] 900,84 unequal: No Solution Exploring Operation: 25+36=61, Resulting Numbers: [61] 61,84 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: 84:[25, 50], Operations: ['70-45=25', '43+7=50'] Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 25*50=1250, Resulting Numbers: [1250] 1250,84 unequal: No Solution Exploring Operation: 25+50=75, Resulting Numbers: [75] 75,84 unequal: No Solution Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,84 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: 84:[45, 7, 27], Operations: ['70-43=27'] Exploring Operation: 45-7=38, Resulting Numbers: [27, 38] Generated Node #0,4,0: 84:[27, 38] Operation: 45-7=38 Exploring Operation: 45+7=52, Resulting Numbers: [27, 52] Generated Node #0,4,1: 84:[27, 52] Operation: 45+7=52 Exploring Operation: 45-27=18, Resulting Numbers: [7, 18] Generated Node #0,4,2: 84:[7, 18] Operation: 45-27=18 Exploring Operation: 27-7=20, Resulting Numbers: [45, 20] Generated Node #0,4,3: 84:[45, 20] Operation: 27-7=20 Exploring Operation: 7+27=34, Resulting Numbers: [45, 34] Generated Node #0,4,4: 84:[45, 34] Operation: 7+27=34 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 84:[7, 18], Operations: ['70-43=27', '45-27=18'] Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,84 unequal: No Solution Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,84 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,84 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: 84:[45, 20], Operations: ['70-43=27', '27-7=20'] Exploring Operation: 45+20=65, Resulting Numbers: [65] 65,84 unequal: No Solution Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,84 unequal: No Solution Exploring Operation: 45*20=900, Resulting Numbers: [900] 900,84 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: 84:[27, 38], Operations: ['70-43=27', '45-7=38'] Exploring Operation: 27+38=65, Resulting Numbers: [65] 65,84 unequal: No Solution Exploring Operation: 27*38=1026, Resulting Numbers: [1026] 1026,84 unequal: No Solution Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,84 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: 84:[45, 34], Operations: ['70-43=27', '7+27=34'] Exploring Operation: 45*34=1530, Resulting Numbers: [1530] 1530,84 unequal: No Solution Exploring Operation: 45+34=79, Resulting Numbers: [79] 79,84 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,84 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: 84:[27, 52], Operations: ['70-43=27', '45+7=52'] Exploring Operation: 27*52=1404, Resulting Numbers: [1404] 1404,84 unequal: No Solution Exploring Operation: 27+52=79, Resulting Numbers: [79] 79,84 unequal: No Solution Exploring Operation: 52-27=25, Resulting Numbers: [25] 25,84 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: 84:[43, 45, 10], Operations: ['70/7=10'] Exploring Operation: 45-10=35, Resulting Numbers: [43, 35] Generated Node #0,0,0: 84:[43, 35] Operation: 45-10=35 Exploring Operation: 45-43=2, Resulting Numbers: [10, 2] Generated Node #0,0,1: 84:[10, 2] Operation: 45-43=2 Exploring Operation: 43+45=88, Resulting Numbers: [10, 88] Generated Node #0,0,2: 84:[10, 88] Operation: 43+45=88 Exploring Operation: 43+10=53, Resulting Numbers: [45, 53] Generated Node #0,0,3: 84:[45, 53] Operation: 43+10=53 Exploring Operation: 43-10=33, Resulting Numbers: [45, 33] Generated Node #0,0,4: 84:[45, 33] Operation: 43-10=33 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[10, 2], Operations: ['70/7=10', '45-43=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,84 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,84 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: 84:[10, 88], Operations: ['70/7=10', '43+45=88'] Exploring Operation: 88-10=78, Resulting Numbers: [78] 78,84 unequal: No Solution Exploring Operation: 10+88=98, Resulting Numbers: [98] 98,84 unequal: No Solution Exploring Operation: 10*88=880, Resulting Numbers: [880] 880,84 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: 84:[43, 35], Operations: ['70/7=10', '45-10=35'] Exploring Operation: 43+35=78, Resulting Numbers: [78] 78,84 unequal: No Solution Exploring Operation: 43*35=1505, Resulting Numbers: [1505] 1505,84 unequal: No Solution Exploring Operation: 43-35=8, Resulting Numbers: [8] 8,84 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: 84:[45, 33], Operations: ['70/7=10', '43-10=33'] Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 45*33=1485, Resulting Numbers: [1485] 1485,84 unequal: No Solution Exploring Operation: 45+33=78, Resulting Numbers: [78] 78,84 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: 84:[45, 53], Operations: ['70/7=10', '43+10=53'] Exploring Operation: 45+53=98, Resulting Numbers: [98] 98,84 unequal: No Solution Exploring Operation: 45*53=2385, Resulting Numbers: [2385] 2385,84 unequal: No Solution Exploring Operation: 53-45=8, Resulting Numbers: [8] 8,84 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: 84:[43, 45, 77], Operations: ['70+7=77'] Exploring Operation: 77-45=32, Resulting Numbers: [43, 32] Generated Node #0,1,0: 84:[43, 32] Operation: 77-45=32 Exploring Operation: 45-43=2, Resulting Numbers: [77, 2] Generated Node #0,1,1: 84:[77, 2] Operation: 45-43=2 Exploring Operation: 43+77=120, Resulting Numbers: [45, 120] Generated Node #0,1,2: 84:[45, 120] Operation: 43+77=120 Exploring Operation: 77-43=34, Resulting Numbers: [45, 34] Generated Node #0,1,3: 84:[45, 34] Operation: 77-43=34 Exploring Operation: 43+45=88, Resulting Numbers: [77, 88] Generated Node #0,1,4: 84:[77, 88] Operation: 43+45=88 Moving to Node #0,3 Current State: 84:[70, 7, 2], Operations: ['45-43=2'] Exploring Operation: 70/7=10, Resulting Numbers: [2, 10] Generated Node #0,3,0: 84:[2, 10] Operation: 70/7=10 Exploring Operation: 70+7=77, Resulting Numbers: [2, 77] Generated Node #0,3,1: 84:[2, 77] Operation: 70+7=77 Exploring Operation: 7*2=14, Resulting Numbers: [70, 14] Generated Node #0,3,2: 84:[70, 14] Operation: 7*2=14 Exploring Operation: 70+2=72, Resulting Numbers: [7, 72] Generated Node #0,3,3: 84:[7, 72] Operation: 70+2=72 Exploring Operation: 70/2=35, Resulting Numbers: [7, 35] Generated Node #0,3,4: 84:[7, 35] Operation: 70/2=35 Moving to Node #0,3,0 Current State: 84:[2, 10], Operations: ['45-43=2', '70/7=10'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,84 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[43, 32], Operations: ['70+7=77', '77-45=32'] Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,84 unequal: No Solution Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,84 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,84 unequal: No Solution Moving to Node #0,3,1 Current State: 84:[2, 77], Operations: ['45-43=2', '70+7=77'] Exploring Operation: 2*77=154, Resulting Numbers: [154] 154,84 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,84 unequal: No Solution Exploring Operation: 2+77=79, Resulting Numbers: [79] 79,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[77, 2], Operations: ['70+7=77', '45-43=2'] Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,84 unequal: No Solution Exploring Operation: 77*2=154, Resulting Numbers: [154] 154,84 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,84 unequal: No Solution Moving to Node #0,3,4 Current State: 84:[7, 35], Operations: ['45-43=2', '70/2=35'] Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,84 unequal: No Solution Exploring Operation: 7*35=245, Resulting Numbers: [245] 245,84 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[45, 34], Operations: ['70+7=77', '77-43=34'] Exploring Operation: 45*34=1530, Resulting Numbers: [1530] 1530,84 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 45+34=79, Resulting Numbers: [79] 79,84 unequal: No Solution Moving to Node #0,1,4 Current State: 84:[77, 88], Operations: ['70+7=77', '43+45=88'] Exploring Operation: 77+88=165, Resulting Numbers: [165] 165,84 unequal: No Solution Exploring Operation: 88-77=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 77*88=6776, Resulting Numbers: [6776] 6776,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[7, 72], Operations: ['45-43=2', '70+2=72'] Exploring Operation: 7+72=79, Resulting Numbers: [79] 79,84 unequal: No Solution Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,84 unequal: No Solution Exploring Operation: 7*72=504, Resulting Numbers: [504] 504,84 unequal: No Solution Moving to Node #0,3,2 Current State: 84:[70, 14], Operations: ['45-43=2', '7*2=14'] Exploring Operation: 70*14=980, Resulting Numbers: [980] 980,84 unequal: No Solution Exploring Operation: 70+14=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[43, 45, 70, 7], Operations: [] Exploring Operation: 45-43=2, Resulting Numbers: [70, 7, 2] Generated Node #0,3: 84:[70, 7, 2] Operation: 45-43=2 Moving to Node #0,3 Current State: 84:[70, 7, 2], Operations: ['45-43=2'] Exploring Operation: 7*2=14, Resulting Numbers: [70, 14] Generated Node #0,3,2: 84:[70, 14] Operation: 7*2=14 Moving to Node #0,3,2 Current State: 84:[70, 14], Operations: ['45-43=2', '7*2=14'] Exploring Operation: 70+14=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.905382
hs_5
sum_heuristic
[ 73, 8, 72, 50 ]
32
[ "73-50=23", "72/8=9", "23+9=32" ]
Current State: 32:[73, 8, 72, 50], Operations: [] Exploring Operation: 73-50=23, Resulting Numbers: [8, 72, 23] Generated Node #2: [8, 72, 23] from Operation: 73-50=23 Current State: 32:[8, 72, 23], Operations: ['73-50=23'] Exploring Operation: 72/8=9, Resulting Numbers: [23, 9] Generated Node #3: [23, 9] from Operation: 72/8=9 Current State: 32:[23, 9], Operations: ['73-50=23', '72/8=9'] Exploring Operation: 23+9=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[73, 8, 72, 50], Operations: [] Exploring Operation: 73-72=1, Resulting Numbers: [8, 50, 1] Generated Node #0,0: 32:[8, 50, 1] Operation: 73-72=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[8, 50, 1], Operations: ['73-72=1'] Exploring Operation: 50-8=42, Resulting Numbers: [1, 42] Generated Node #0,0,0: 32:[1, 42] Operation: 50-8=42 Moving to Node #0,0,0 Current State: 32:[1, 42], Operations: ['73-72=1', '50-8=42'] Exploring Operation: 42-1=41, Resulting Numbers: [41] 41,32 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
[ 28, 58, 92, 78 ]
100
[ "28+58=86", "92-78=14", "86+14=100" ]
Current State: 100:[28, 58, 92, 78], Operations: [] Exploring Operation: 28+58=86, Resulting Numbers: [92, 78, 86] Generated Node #2: [92, 78, 86] from Operation: 28+58=86 Current State: 100:[92, 78, 86], Operations: ['28+58=86'] Exploring Operation: 92-78=14, Resulting Numbers: [86, 14] Generated Node #3: [86, 14] from Operation: 92-78=14 Current State: 100:[86, 14], Operations: ['28+58=86', '92-78=14'] Exploring Operation: 86+14=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[28, 58, 92, 78], Operations: [] Exploring Operation: 78-58=20, Resulting Numbers: [28, 92, 20] Generated Node #0,0: 100:[28, 92, 20] Operation: 78-58=20 Exploring Operation: 78-28=50, Resulting Numbers: [58, 92, 50] Generated Node #0,1: 100:[58, 92, 50] Operation: 78-28=50 Exploring Operation: 92-78=14, Resulting Numbers: [28, 58, 14] Generated Node #0,2: 100:[28, 58, 14] Operation: 92-78=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[28, 92, 20], Operations: ['78-58=20'] Exploring Operation: 92-28=64, Resulting Numbers: [20, 64] Generated Node #0,0,0: 100:[20, 64] Operation: 92-28=64 Exploring Operation: 28-20=8, Resulting Numbers: [92, 8] Generated Node #0,0,1: 100:[92, 8] Operation: 28-20=8 Exploring Operation: 28+20=48, Resulting Numbers: [92, 48] Generated Node #0,0,2: 100:[92, 48] Operation: 28+20=48 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 100:[92, 8], Operations: ['78-58=20', '28-20=8'] Exploring Operation: 92*8=736, Resulting Numbers: [736] 736,100 unequal: No Solution Exploring Operation: 92-8=84, Resulting Numbers: [84] 84,100 unequal: No Solution Exploring Operation: 92+8=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[28, 58, 92, 78], Operations: [] Exploring Operation: 78-58=20, Resulting Numbers: [28, 92, 20] Generated Node #0,0: 100:[28, 92, 20] Operation: 78-58=20 Moving to Node #0,0 Current State: 100:[28, 92, 20], Operations: ['78-58=20'] Exploring Operation: 28-20=8, Resulting Numbers: [92, 8] Generated Node #0,0,1: 100:[92, 8] Operation: 28-20=8 Moving to Node #0,0,1 Current State: 100:[92, 8], Operations: ['78-58=20', '28-20=8'] Exploring Operation: 92+8=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 50, 36, 34, 70 ]
15
[ "36-34=2", "70/2=35", "50-35=15" ]
Current State: 15:[50, 36, 34, 70], Operations: [] Exploring Operation: 36-34=2, Resulting Numbers: [50, 70, 2] Generated Node #2: [50, 70, 2] from Operation: 36-34=2 Current State: 15:[50, 70, 2], Operations: ['36-34=2'] Exploring Operation: 70/2=35, Resulting Numbers: [50, 35] Generated Node #3: [50, 35] from Operation: 70/2=35 Current State: 15:[50, 35], Operations: ['36-34=2', '70/2=35'] Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[50, 36, 34, 70], Operations: [] Exploring Operation: 70-50=20, Resulting Numbers: [36, 34, 20] Generated Node #0,0: 15:[36, 34, 20] Operation: 70-50=20 Exploring Operation: 50-36=14, Resulting Numbers: [34, 70, 14] Generated Node #0,1: 15:[34, 70, 14] Operation: 50-36=14 Exploring Operation: 70-36=34, Resulting Numbers: [50, 34, 34] Generated Node #0,2: 15:[50, 34, 34] Operation: 70-36=34 Exploring Operation: 50-34=16, Resulting Numbers: [36, 70, 16] Generated Node #0,3: 15:[36, 70, 16] Operation: 50-34=16 Moving to Node #0,0 Current State: 15:[36, 34, 20], Operations: ['70-50=20'] Exploring Operation: 36+34=70, Resulting Numbers: [20, 70] Generated Node #0,0,0: 15:[20, 70] Operation: 36+34=70 Exploring Operation: 36-34=2, Resulting Numbers: [20, 2] Generated Node #0,0,1: 15:[20, 2] Operation: 36-34=2 Exploring Operation: 34-20=14, Resulting Numbers: [36, 14] Generated Node #0,0,2: 15:[36, 14] Operation: 34-20=14 Exploring Operation: 36-20=16, Resulting Numbers: [34, 16] Generated Node #0,0,3: 15:[34, 16] Operation: 36-20=16 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 15:[20, 2], Operations: ['70-50=20', '36-34=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,15 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,15 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: 15:[34, 16], Operations: ['70-50=20', '36-20=16'] Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,15 unequal: No Solution Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,15 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: 15:[36, 14], Operations: ['70-50=20', '34-20=14'] Exploring Operation: 36+14=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 36*14=504, Resulting Numbers: [504] 504,15 unequal: No Solution Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,15 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: 15:[20, 70], Operations: ['70-50=20', '36+34=70'] Exploring Operation: 70-20=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 20+70=90, Resulting Numbers: [90] 90,15 unequal: No Solution Exploring Operation: 20*70=1400, Resulting Numbers: [1400] 1400,15 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: 15:[50, 34, 34], Operations: ['70-36=34'] Exploring Operation: 34-34=0, Resulting Numbers: [50, 0] Generated Node #0,2,0: 15:[50, 0] Operation: 34-34=0 Exploring Operation: 50-34=16, Resulting Numbers: [34, 16] Generated Node #0,2,1: 15:[34, 16] Operation: 50-34=16 Exploring Operation: 50-34=16, Resulting Numbers: [34, 16] Generated Node #0,2,2: 15:[34, 16] Operation: 50-34=16 Exploring Operation: 34/34=1, Resulting Numbers: [50, 1] Generated Node #0,2,3: 15:[50, 1] Operation: 34/34=1 Moving to Node #0,1 Current State: 15:[34, 70, 14], Operations: ['50-36=14'] Exploring Operation: 70/14=5, Resulting Numbers: [34, 5] Generated Node #0,1,0: 15:[34, 5] Operation: 70/14=5 Exploring Operation: 70-14=56, Resulting Numbers: [34, 56] Generated Node #0,1,1: 15:[34, 56] Operation: 70-14=56 Exploring Operation: 34-14=20, Resulting Numbers: [70, 20] Generated Node #0,1,2: 15:[70, 20] Operation: 34-14=20 Exploring Operation: 70-34=36, Resulting Numbers: [14, 36] Generated Node #0,1,3: 15:[14, 36] Operation: 70-34=36 Moving to Node #0,3 Current State: 15:[36, 70, 16], Operations: ['50-34=16'] Exploring Operation: 70-36=34, Resulting Numbers: [16, 34] Generated Node #0,3,0: 15:[16, 34] Operation: 70-36=34 Exploring Operation: 36+70=106, Resulting Numbers: [16, 106] Generated Node #0,3,1: 15:[16, 106] Operation: 36+70=106 Exploring Operation: 70-16=54, Resulting Numbers: [36, 54] Generated Node #0,3,2: 15:[36, 54] Operation: 70-16=54 Exploring Operation: 36-16=20, Resulting Numbers: [70, 20] Generated Node #0,3,3: 15:[70, 20] Operation: 36-16=20 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 15:[16, 34], Operations: ['50-34=16', '70-36=34'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 16*34=544, Resulting Numbers: [544] 544,15 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: 15:[36, 54], Operations: ['50-34=16', '70-16=54'] Exploring Operation: 36+54=90, Resulting Numbers: [90] 90,15 unequal: No Solution Exploring Operation: 54-36=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 36*54=1944, Resulting Numbers: [1944] 1944,15 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: 15:[70, 20], Operations: ['50-34=16', '36-16=20'] Exploring Operation: 70-20=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 70*20=1400, Resulting Numbers: [1400] 1400,15 unequal: No Solution Exploring Operation: 70+20=90, Resulting Numbers: [90] 90,15 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: 15:[16, 106], Operations: ['50-34=16', '36+70=106'] Exploring Operation: 106-16=90, Resulting Numbers: [90] 90,15 unequal: No Solution Exploring Operation: 16+106=122, Resulting Numbers: [122] 122,15 unequal: No Solution Exploring Operation: 16*106=1696, Resulting Numbers: [1696] 1696,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 15:[34, 5], Operations: ['50-36=14', '70/14=5'] Exploring Operation: 34*5=170, Resulting Numbers: [170] 170,15 unequal: No Solution Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,15 unequal: No Solution Exploring Operation: 34+5=39, Resulting Numbers: [39] 39,15 unequal: No Solution Moving to Node #0,2,1 Current State: 15:[34, 16], Operations: ['70-36=34', '50-34=16'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,15 unequal: No Solution Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,15 unequal: No Solution Moving to Node #0,2,2 Current State: 15:[34, 16], Operations: ['70-36=34', '50-34=16'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[14, 36], Operations: ['50-36=14', '70-34=36'] Exploring Operation: 14*36=504, Resulting Numbers: [504] 504,15 unequal: No Solution Exploring Operation: 14+36=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,15 unequal: No Solution Moving to Node #0,2,3 Current State: 15:[50, 1], Operations: ['70-36=34', '34/34=1'] Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,15 unequal: No Solution Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,15 unequal: No Solution Moving to Node #0,2,0 Current State: 15:[50, 0], Operations: ['70-36=34', '34-34=0'] Exploring Operation: 50-0=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 50+0=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 50*0=0, Resulting Numbers: [0] 0,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[34, 56], Operations: ['50-36=14', '70-14=56'] Exploring Operation: 34*56=1904, Resulting Numbers: [1904] 1904,15 unequal: No Solution Exploring Operation: 34+56=90, Resulting Numbers: [90] 90,15 unequal: No Solution Exploring Operation: 56-34=22, Resulting Numbers: [22] 22,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[70, 20], Operations: ['50-36=14', '34-14=20'] Exploring Operation: 70+20=90, Resulting Numbers: [90] 90,15 unequal: No Solution Exploring Operation: 70-20=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 70*20=1400, Resulting Numbers: [1400] 1400,15 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 39, 4, 76, 99 ]
79
[ "99-39=60", "76/4=19", "60+19=79" ]
Current State: 79:[39, 4, 76, 99], Operations: [] Exploring Operation: 99-39=60, Resulting Numbers: [4, 76, 60] Generated Node #2: [4, 76, 60] from Operation: 99-39=60 Current State: 79:[4, 76, 60], Operations: ['99-39=60'] Exploring Operation: 76/4=19, Resulting Numbers: [60, 19] Generated Node #3: [60, 19] from Operation: 76/4=19 Current State: 79:[60, 19], Operations: ['99-39=60', '76/4=19'] Exploring Operation: 60+19=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[39, 4, 76, 99], Operations: [] Exploring Operation: 99-4=95, Resulting Numbers: [39, 76, 95] Generated Node #0,0: 79:[39, 76, 95] Operation: 99-4=95 Exploring Operation: 39+4=43, Resulting Numbers: [76, 99, 43] Generated Node #0,1: 79:[76, 99, 43] Operation: 39+4=43 Moving to Node #0,0 Current State: 79:[39, 76, 95], Operations: ['99-4=95'] Exploring Operation: 39+76=115, Resulting Numbers: [95, 115] Generated Node #0,0,0: 79:[95, 115] Operation: 39+76=115 Exploring Operation: 95-39=56, Resulting Numbers: [76, 56] Generated Node #0,0,1: 79:[76, 56] Operation: 95-39=56 Moving to Node #0,1 Current State: 79:[76, 99, 43], Operations: ['39+4=43'] Exploring Operation: 76+43=119, Resulting Numbers: [99, 119] Generated Node #0,1,0: 79:[99, 119] Operation: 76+43=119 Exploring Operation: 99-43=56, Resulting Numbers: [76, 56] Generated Node #0,1,1: 79:[76, 56] Operation: 99-43=56 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[76, 56], Operations: ['39+4=43', '99-43=56'] Exploring Operation: 76+56=132, Resulting Numbers: [132] 132,79 unequal: No Solution Exploring Operation: 76-56=20, Resulting Numbers: [20] 20,79 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:[99, 119], Operations: ['39+4=43', '76+43=119'] Exploring Operation: 119-99=20, Resulting Numbers: [20] 20,79 unequal: No Solution Exploring Operation: 99+119=218, Resulting Numbers: [218] 218,79 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: 79:[76, 56], Operations: ['99-4=95', '95-39=56'] Exploring Operation: 76+56=132, Resulting Numbers: [132] 132,79 unequal: No Solution Exploring Operation: 76-56=20, Resulting Numbers: [20] 20,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[95, 115], Operations: ['99-4=95', '39+76=115'] Exploring Operation: 95+115=210, Resulting Numbers: [210] 210,79 unequal: No Solution Exploring Operation: 115-95=20, Resulting Numbers: [20] 20,79 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 19, 1, 10, 96 ]
87
[ "19*1=19", "10+96=106", "106-19=87" ]
Current State: 87:[19, 1, 10, 96], Operations: [] Exploring Operation: 19*1=19, Resulting Numbers: [10, 96, 19] Generated Node #2: [10, 96, 19] from Operation: 19*1=19 Current State: 87:[10, 96, 19], Operations: ['19*1=19'] Exploring Operation: 10+96=106, Resulting Numbers: [19, 106] Generated Node #3: [19, 106] from Operation: 10+96=106 Current State: 87:[19, 106], Operations: ['19*1=19', '10+96=106'] Exploring Operation: 106-19=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[19, 1, 10, 96], Operations: [] Exploring Operation: 19-10=9, Resulting Numbers: [1, 96, 9] Generated Node #0,0: 87:[1, 96, 9] Operation: 19-10=9 Exploring Operation: 19+10=29, Resulting Numbers: [1, 96, 29] Generated Node #0,1: 87:[1, 96, 29] Operation: 19+10=29 Exploring Operation: 96-19=77, Resulting Numbers: [1, 10, 77] Generated Node #0,2: 87:[1, 10, 77] Operation: 96-19=77 Exploring Operation: 96-10=86, Resulting Numbers: [19, 1, 86] Generated Node #0,3: 87:[19, 1, 86] Operation: 96-10=86 Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[1, 96, 29], Operations: ['19+10=29'] Exploring Operation: 1*96=96, Resulting Numbers: [29, 96] Generated Node #0,1,0: 87:[29, 96] Operation: 1*96=96 Exploring Operation: 96-1=95, Resulting Numbers: [29, 95] Generated Node #0,1,1: 87:[29, 95] Operation: 96-1=95 Exploring Operation: 96/1=96, Resulting Numbers: [29, 96] Generated Node #0,1,2: 87:[29, 96] Operation: 96/1=96 Exploring Operation: 1*29=29, Resulting Numbers: [96, 29] Generated Node #0,1,3: 87:[96, 29] Operation: 1*29=29 Moving to Node #0,1,1 Current State: 87:[29, 95], Operations: ['19+10=29', '96-1=95'] Exploring Operation: 29+95=124, Resulting Numbers: [124] 124,87 unequal: No Solution Exploring Operation: 95-29=66, Resulting Numbers: [66] 66,87 unequal: No Solution Exploring Operation: 29*95=2755, Resulting Numbers: [2755] 2755,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[29, 96], Operations: ['19+10=29', '96/1=96'] Exploring Operation: 29+96=125, Resulting Numbers: [125] 125,87 unequal: No Solution Exploring Operation: 96-29=67, Resulting Numbers: [67] 67,87 unequal: No Solution Exploring Operation: 29*96=2784, Resulting Numbers: [2784] 2784,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[29, 96], Operations: ['19+10=29', '1*96=96'] Exploring Operation: 29*96=2784, Resulting Numbers: [2784] 2784,87 unequal: No Solution Exploring Operation: 96-29=67, Resulting Numbers: [67] 67,87 unequal: No Solution Exploring Operation: 29+96=125, Resulting Numbers: [125] 125,87 unequal: No Solution Moving to Node #0,1,3 Current State: 87:[96, 29], Operations: ['19+10=29', '1*29=29'] Exploring Operation: 96-29=67, Resulting Numbers: [67] 67,87 unequal: No Solution Exploring Operation: 96*29=2784, Resulting Numbers: [2784] 2784,87 unequal: No Solution Exploring Operation: 96+29=125, Resulting Numbers: [125] 125,87 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: 87:[19, 1, 86], Operations: ['96-10=86'] Exploring Operation: 19+1=20, Resulting Numbers: [86, 20] Generated Node #0,3,0: 87:[86, 20] Operation: 19+1=20 Exploring Operation: 19/1=19, Resulting Numbers: [86, 19] Generated Node #0,3,1: 87:[86, 19] Operation: 19/1=19 Exploring Operation: 19*1=19, Resulting Numbers: [86, 19] Generated Node #0,3,2: 87:[86, 19] Operation: 19*1=19 Exploring Operation: 1+86=87, Resulting Numbers: [19, 87] Generated Node #0,3,3: 87:[19, 87] Operation: 1+86=87 Moving to Node #0,3,0 Current State: 87:[86, 20], Operations: ['96-10=86', '19+1=20'] Exploring Operation: 86+20=106, Resulting Numbers: [106] 106,87 unequal: No Solution Exploring Operation: 86*20=1720, Resulting Numbers: [1720] 1720,87 unequal: No Solution Exploring Operation: 86-20=66, Resulting Numbers: [66] 66,87 unequal: No Solution Moving to Node #0,3,3 Current State: 87:[19, 87], Operations: ['96-10=86', '1+86=87'] Exploring Operation: 87-19=68, Resulting Numbers: [68] 68,87 unequal: No Solution Exploring Operation: 19+87=106, Resulting Numbers: [106] 106,87 unequal: No Solution Exploring Operation: 19*87=1653, Resulting Numbers: [1653] 1653,87 unequal: No Solution Moving to Node #0,3,2 Current State: 87:[86, 19], Operations: ['96-10=86', '19*1=19'] Exploring Operation: 86*19=1634, Resulting Numbers: [1634] 1634,87 unequal: No Solution Exploring Operation: 86+19=105, Resulting Numbers: [105] 105,87 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,87 unequal: No Solution Moving to Node #0,3,1 Current State: 87:[86, 19], Operations: ['96-10=86', '19/1=19'] Exploring Operation: 86*19=1634, Resulting Numbers: [1634] 1634,87 unequal: No Solution Exploring Operation: 86+19=105, Resulting Numbers: [105] 105,87 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,87 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: 87:[1, 96, 9], Operations: ['19-10=9'] Exploring Operation: 96-9=87, Resulting Numbers: [1, 87] Generated Node #0,0,0: 87:[1, 87] Operation: 96-9=87 Exploring Operation: 96-1=95, Resulting Numbers: [9, 95] Generated Node #0,0,1: 87:[9, 95] Operation: 96-1=95 Exploring Operation: 9-1=8, Resulting Numbers: [96, 8] Generated Node #0,0,2: 87:[96, 8] Operation: 9-1=8 Exploring Operation: 1*96=96, Resulting Numbers: [9, 96] Generated Node #0,0,3: 87:[9, 96] Operation: 1*96=96 Moving to Node #0,0,0 Current State: 87:[1, 87], Operations: ['19-10=9', '96-9=87'] Exploring Operation: 87-1=86, Resulting Numbers: [86] 86,87 unequal: No Solution Exploring Operation: 1*87=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[19, 1, 10, 96], Operations: [] Exploring Operation: 19-10=9, Resulting Numbers: [1, 96, 9] Generated Node #0,0: 87:[1, 96, 9] Operation: 19-10=9 Moving to Node #0,0 Current State: 87:[1, 96, 9], Operations: ['19-10=9'] Exploring Operation: 96-9=87, Resulting Numbers: [1, 87] Generated Node #0,0,0: 87:[1, 87] Operation: 96-9=87 Moving to Node #0,0,0 Current State: 87:[1, 87], Operations: ['19-10=9', '96-9=87'] Exploring Operation: 1*87=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.960069
hs_4
sum_heuristic
[ 16, 42, 70, 67 ]
30
[ "70-67=3", "42/3=14", "16+14=30" ]
Current State: 30:[16, 42, 70, 67], Operations: [] Exploring Operation: 70-67=3, Resulting Numbers: [16, 42, 3] Generated Node #2: [16, 42, 3] from Operation: 70-67=3 Current State: 30:[16, 42, 3], Operations: ['70-67=3'] Exploring Operation: 42/3=14, Resulting Numbers: [16, 14] Generated Node #3: [16, 14] from Operation: 42/3=14 Current State: 30:[16, 14], Operations: ['70-67=3', '42/3=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[16, 42, 70, 67], Operations: [] Exploring Operation: 70-67=3, Resulting Numbers: [16, 42, 3] Generated Node #0,0: 30:[16, 42, 3] Operation: 70-67=3 Exploring Operation: 70-42=28, Resulting Numbers: [16, 67, 28] Generated Node #0,1: 30:[16, 67, 28] Operation: 70-42=28 Exploring Operation: 67-42=25, Resulting Numbers: [16, 70, 25] Generated Node #0,2: 30:[16, 70, 25] Operation: 67-42=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[16, 42, 3], Operations: ['70-67=3'] Exploring Operation: 42/3=14, Resulting Numbers: [16, 14] Generated Node #0,0,0: 30:[16, 14] Operation: 42/3=14 Exploring Operation: 42-16=26, Resulting Numbers: [3, 26] Generated Node #0,0,1: 30:[3, 26] Operation: 42-16=26 Exploring Operation: 42-3=39, Resulting Numbers: [16, 39] Generated Node #0,0,2: 30:[16, 39] Operation: 42-3=39 Moving to Node #0,0,0 Current State: 30:[16, 14], Operations: ['70-67=3', '42/3=14'] Exploring Operation: 16*14=224, Resulting Numbers: [224] 224,30 unequal: No Solution Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[16, 42, 70, 67], Operations: [] Exploring Operation: 70-67=3, Resulting Numbers: [16, 42, 3] Generated Node #0,0: 30:[16, 42, 3] Operation: 70-67=3 Moving to Node #0,0 Current State: 30:[16, 42, 3], Operations: ['70-67=3'] Exploring Operation: 42/3=14, Resulting Numbers: [16, 14] Generated Node #0,0,0: 30:[16, 14] Operation: 42/3=14 Moving to Node #0,0,0 Current State: 30:[16, 14], Operations: ['70-67=3', '42/3=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 4, 21, 64, 58 ]
42
[ "64-4=60", "60-58=2", "21*2=42" ]
Current State: 42:[4, 21, 64, 58], Operations: [] Exploring Operation: 64-4=60, Resulting Numbers: [21, 58, 60] Generated Node #2: [21, 58, 60] from Operation: 64-4=60 Current State: 42:[21, 58, 60], Operations: ['64-4=60'] Exploring Operation: 60-58=2, Resulting Numbers: [21, 2] Generated Node #3: [21, 2] from Operation: 60-58=2 Current State: 42:[21, 2], Operations: ['64-4=60', '60-58=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[4, 21, 64, 58], Operations: [] Exploring Operation: 64-58=6, Resulting Numbers: [4, 21, 6] Generated Node #0,0: 42:[4, 21, 6] Operation: 64-58=6 Exploring Operation: 64-21=43, Resulting Numbers: [4, 58, 43] Generated Node #0,1: 42:[4, 58, 43] Operation: 64-21=43 Exploring Operation: 64/4=16, Resulting Numbers: [21, 58, 16] Generated Node #0,2: 42:[21, 58, 16] Operation: 64/4=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[4, 21, 6], Operations: ['64-58=6'] Exploring Operation: 6-4=2, Resulting Numbers: [21, 2] Generated Node #0,0,0: 42:[21, 2] Operation: 6-4=2 Exploring Operation: 21-6=15, Resulting Numbers: [4, 15] Generated Node #0,0,1: 42:[4, 15] Operation: 21-6=15 Exploring Operation: 21-4=17, Resulting Numbers: [6, 17] Generated Node #0,0,2: 42:[6, 17] Operation: 21-4=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[21, 2], Operations: ['64-58=6', '6-4=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[4, 21, 64, 58], Operations: [] Exploring Operation: 64-58=6, Resulting Numbers: [4, 21, 6] Generated Node #0,0: 42:[4, 21, 6] Operation: 64-58=6 Moving to Node #0,0 Current State: 42:[4, 21, 6], Operations: ['64-58=6'] Exploring Operation: 6-4=2, Resulting Numbers: [21, 2] Generated Node #0,0,0: 42:[21, 2] Operation: 6-4=2 Moving to Node #0,0,0 Current State: 42:[21, 2], Operations: ['64-58=6', '6-4=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 13, 23, 41, 11 ]
66
[ "13+23=36", "41-11=30", "36+30=66" ]
Current State: 66:[13, 23, 41, 11], Operations: [] Exploring Operation: 13+23=36, Resulting Numbers: [41, 11, 36] Generated Node #2: [41, 11, 36] from Operation: 13+23=36 Current State: 66:[41, 11, 36], Operations: ['13+23=36'] Exploring Operation: 41-11=30, Resulting Numbers: [36, 30] Generated Node #3: [36, 30] from Operation: 41-11=30 Current State: 66:[36, 30], Operations: ['13+23=36', '41-11=30'] Exploring Operation: 36+30=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[13, 23, 41, 11], Operations: [] Exploring Operation: 23-13=10, Resulting Numbers: [41, 11, 10] Generated Node #0,0: 66:[41, 11, 10] Operation: 23-13=10 Exploring Operation: 41-23=18, Resulting Numbers: [13, 11, 18] Generated Node #0,1: 66:[13, 11, 18] Operation: 41-23=18 Exploring Operation: 23+41=64, Resulting Numbers: [13, 11, 64] Generated Node #0,2: 66:[13, 11, 64] Operation: 23+41=64 Exploring Operation: 41-11=30, Resulting Numbers: [13, 23, 30] Generated Node #0,3: 66:[13, 23, 30] Operation: 41-11=30 Exploring Operation: 41-13=28, Resulting Numbers: [23, 11, 28] Generated Node #0,4: 66:[23, 11, 28] Operation: 41-13=28 Moving to Node #0,2 Current State: 66:[13, 11, 64], Operations: ['23+41=64'] Exploring Operation: 11+64=75, Resulting Numbers: [13, 75] Generated Node #0,2,0: 66:[13, 75] Operation: 11+64=75 Exploring Operation: 13+11=24, Resulting Numbers: [64, 24] Generated Node #0,2,1: 66:[64, 24] Operation: 13+11=24 Exploring Operation: 64-13=51, Resulting Numbers: [11, 51] Generated Node #0,2,2: 66:[11, 51] Operation: 64-13=51 Exploring Operation: 13+64=77, Resulting Numbers: [11, 77] Generated Node #0,2,3: 66:[11, 77] Operation: 13+64=77 Exploring Operation: 13-11=2, Resulting Numbers: [64, 2] Generated Node #0,2,4: 66:[64, 2] Operation: 13-11=2 Moving to Node #0,3 Current State: 66:[13, 23, 30], Operations: ['41-11=30'] Exploring Operation: 30-23=7, Resulting Numbers: [13, 7] Generated Node #0,3,0: 66:[13, 7] Operation: 30-23=7 Exploring Operation: 23-13=10, Resulting Numbers: [30, 10] Generated Node #0,3,1: 66:[30, 10] Operation: 23-13=10 Exploring Operation: 13+30=43, Resulting Numbers: [23, 43] Generated Node #0,3,2: 66:[23, 43] Operation: 13+30=43 Exploring Operation: 13+23=36, Resulting Numbers: [30, 36] Generated Node #0,3,3: 66:[30, 36] Operation: 13+23=36 Exploring Operation: 30-13=17, Resulting Numbers: [23, 17] Generated Node #0,3,4: 66:[23, 17] Operation: 30-13=17 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 66:[13, 7], Operations: ['41-11=30', '30-23=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,66 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,66 unequal: No Solution Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,66 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: 66:[30, 10], Operations: ['41-11=30', '23-13=10'] Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,66 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,66 unequal: No Solution Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,66 unequal: No Solution Exploring Operation: 30*10=300, Resulting Numbers: [300] 300,66 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: 66:[30, 36], Operations: ['41-11=30', '13+23=36'] Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,66 unequal: No Solution Exploring Operation: 30+36=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[13, 23, 41, 11], Operations: [] Exploring Operation: 41-11=30, Resulting Numbers: [13, 23, 30] Generated Node #0,3: 66:[13, 23, 30] Operation: 41-11=30 Moving to Node #0,3 Current State: 66:[13, 23, 30], Operations: ['41-11=30'] Exploring Operation: 13+23=36, Resulting Numbers: [30, 36] Generated Node #0,3,3: 66:[30, 36] Operation: 13+23=36 Moving to Node #0,3,3 Current State: 66:[30, 36], Operations: ['41-11=30', '13+23=36'] Exploring Operation: 30+36=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_5
sum_heuristic
[ 53, 1, 25, 11 ]
67
[ "53*1=53", "25-11=14", "53+14=67" ]
Current State: 67:[53, 1, 25, 11], Operations: [] Exploring Operation: 53*1=53, Resulting Numbers: [25, 11, 53] Generated Node #2: [25, 11, 53] from Operation: 53*1=53 Current State: 67:[25, 11, 53], Operations: ['53*1=53'] Exploring Operation: 25-11=14, Resulting Numbers: [53, 14] Generated Node #3: [53, 14] from Operation: 25-11=14 Current State: 67:[53, 14], Operations: ['53*1=53', '25-11=14'] Exploring Operation: 53+14=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[53, 1, 25, 11], Operations: [] Exploring Operation: 53+1=54, Resulting Numbers: [25, 11, 54] Generated Node #0,0: 67:[25, 11, 54] Operation: 53+1=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[25, 11, 54], Operations: ['53+1=54'] Exploring Operation: 25+11=36, Resulting Numbers: [54, 36] Generated Node #0,0,0: 67:[54, 36] Operation: 25+11=36 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[54, 36], Operations: ['53+1=54', '25+11=36'] Exploring Operation: 54+36=90, Resulting Numbers: [90] 90,67 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
sum_heuristic
[ 2, 59, 8, 77 ]
14
[ "8/2=4", "77-59=18", "18-4=14" ]
Current State: 14:[2, 59, 8, 77], Operations: [] Exploring Operation: 8/2=4, Resulting Numbers: [59, 77, 4] Generated Node #2: [59, 77, 4] from Operation: 8/2=4 Current State: 14:[59, 77, 4], Operations: ['8/2=4'] Exploring Operation: 77-59=18, Resulting Numbers: [4, 18] Generated Node #3: [4, 18] from Operation: 77-59=18 Current State: 14:[4, 18], Operations: ['8/2=4', '77-59=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[2, 59, 8, 77], Operations: [] Exploring Operation: 77-59=18, Resulting Numbers: [2, 8, 18] Generated Node #0,0: 14:[2, 8, 18] Operation: 77-59=18 Exploring Operation: 59-8=51, Resulting Numbers: [2, 77, 51] Generated Node #0,1: 14:[2, 77, 51] Operation: 59-8=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[2, 8, 18], Operations: ['77-59=18'] Exploring Operation: 18/2=9, Resulting Numbers: [8, 9] Generated Node #0,0,0: 14:[8, 9] Operation: 18/2=9 Exploring Operation: 18-2=16, Resulting Numbers: [8, 16] Generated Node #0,0,1: 14:[8, 16] Operation: 18-2=16 Moving to Node #0,0,0 Current State: 14:[8, 9], Operations: ['77-59=18', '18/2=9'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,14 unequal: No Solution Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[8, 16], Operations: ['77-59=18', '18-2=16'] Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,14 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 #0,1 Current State: 14:[2, 77, 51], Operations: ['59-8=51'] Exploring Operation: 77-2=75, Resulting Numbers: [51, 75] Generated Node #0,1,0: 14:[51, 75] Operation: 77-2=75 Exploring Operation: 77-51=26, Resulting Numbers: [2, 26] Generated Node #0,1,1: 14:[2, 26] Operation: 77-51=26 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 14:[2, 26], Operations: ['59-8=51', '77-51=26'] Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,14 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: 14:[51, 75], Operations: ['59-8=51', '77-2=75'] Exploring Operation: 51+75=126, Resulting Numbers: [126] 126,14 unequal: No Solution Exploring Operation: 75-51=24, Resulting Numbers: [24] 24,14 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
[ 15, 97, 81, 53 ]
52
[ "97-15=82", "81+53=134", "134-82=52" ]
Current State: 52:[15, 97, 81, 53], Operations: [] Exploring Operation: 97-15=82, Resulting Numbers: [81, 53, 82] Generated Node #2: [81, 53, 82] from Operation: 97-15=82 Current State: 52:[81, 53, 82], Operations: ['97-15=82'] Exploring Operation: 81+53=134, Resulting Numbers: [82, 134] Generated Node #3: [82, 134] from Operation: 81+53=134 Current State: 52:[82, 134], Operations: ['97-15=82', '81+53=134'] Exploring Operation: 134-82=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[15, 97, 81, 53], Operations: [] Exploring Operation: 81-15=66, Resulting Numbers: [97, 53, 66] Generated Node #0,0: 52:[97, 53, 66] Operation: 81-15=66 Exploring Operation: 97-15=82, Resulting Numbers: [81, 53, 82] Generated Node #0,1: 52:[81, 53, 82] Operation: 97-15=82 Exploring Operation: 81-53=28, Resulting Numbers: [15, 97, 28] Generated Node #0,2: 52:[15, 97, 28] Operation: 81-53=28 Exploring Operation: 97-81=16, Resulting Numbers: [15, 53, 16] Generated Node #0,3: 52:[15, 53, 16] Operation: 97-81=16 Exploring Operation: 97-53=44, Resulting Numbers: [15, 81, 44] Generated Node #0,4: 52:[15, 81, 44] Operation: 97-53=44 Moving to Node #0,3 Current State: 52:[15, 53, 16], Operations: ['97-81=16'] Exploring Operation: 53-15=38, Resulting Numbers: [16, 38] Generated Node #0,3,0: 52:[16, 38] Operation: 53-15=38 Exploring Operation: 53-16=37, Resulting Numbers: [15, 37] Generated Node #0,3,1: 52:[15, 37] Operation: 53-16=37 Exploring Operation: 15+16=31, Resulting Numbers: [53, 31] Generated Node #0,3,2: 52:[53, 31] Operation: 15+16=31 Exploring Operation: 15+53=68, Resulting Numbers: [16, 68] Generated Node #0,3,3: 52:[16, 68] Operation: 15+53=68 Exploring Operation: 16-15=1, Resulting Numbers: [53, 1] Generated Node #0,3,4: 52:[53, 1] Operation: 16-15=1 Moving to Node #0,4 Current State: 52:[15, 81, 44], Operations: ['97-53=44'] Exploring Operation: 15+44=59, Resulting Numbers: [81, 59] Generated Node #0,4,0: 52:[81, 59] Operation: 15+44=59 Exploring Operation: 81-44=37, Resulting Numbers: [15, 37] Generated Node #0,4,1: 52:[15, 37] Operation: 81-44=37 Exploring Operation: 44-15=29, Resulting Numbers: [81, 29] Generated Node #0,4,2: 52:[81, 29] Operation: 44-15=29 Exploring Operation: 15+81=96, Resulting Numbers: [44, 96] Generated Node #0,4,3: 52:[44, 96] Operation: 15+81=96 Exploring Operation: 81-15=66, Resulting Numbers: [44, 66] Generated Node #0,4,4: 52:[44, 66] Operation: 81-15=66 Moving to Node #0,2 Current State: 52:[15, 97, 28], Operations: ['81-53=28'] Exploring Operation: 15+28=43, Resulting Numbers: [97, 43] Generated Node #0,2,0: 52:[97, 43] Operation: 15+28=43 Exploring Operation: 97-15=82, Resulting Numbers: [28, 82] Generated Node #0,2,1: 52:[28, 82] Operation: 97-15=82 Exploring Operation: 15+97=112, Resulting Numbers: [28, 112] Generated Node #0,2,2: 52:[28, 112] Operation: 15+97=112 Exploring Operation: 97-28=69, Resulting Numbers: [15, 69] Generated Node #0,2,3: 52:[15, 69] Operation: 97-28=69 Exploring Operation: 28-15=13, Resulting Numbers: [97, 13] Generated Node #0,2,4: 52:[97, 13] Operation: 28-15=13 Moving to Node #0,0 Current State: 52:[97, 53, 66], Operations: ['81-15=66'] Exploring Operation: 97+53=150, Resulting Numbers: [66, 150] Generated Node #0,0,0: 52:[66, 150] Operation: 97+53=150 Exploring Operation: 66-53=13, Resulting Numbers: [97, 13] Generated Node #0,0,1: 52:[97, 13] Operation: 66-53=13 Exploring Operation: 97+66=163, Resulting Numbers: [53, 163] Generated Node #0,0,2: 52:[53, 163] Operation: 97+66=163 Exploring Operation: 97-66=31, Resulting Numbers: [53, 31] Generated Node #0,0,3: 52:[53, 31] Operation: 97-66=31 Exploring Operation: 97-53=44, Resulting Numbers: [66, 44] Generated Node #0,0,4: 52:[66, 44] Operation: 97-53=44 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 52:[53, 31], Operations: ['81-15=66', '97-66=31'] Exploring Operation: 53+31=84, Resulting Numbers: [84] 84,52 unequal: No Solution Exploring Operation: 53*31=1643, Resulting Numbers: [1643] 1643,52 unequal: No Solution Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,52 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: 52:[66, 44], Operations: ['81-15=66', '97-53=44'] Exploring Operation: 66-44=22, Resulting Numbers: [22] 22,52 unequal: No Solution Exploring Operation: 66+44=110, Resulting Numbers: [110] 110,52 unequal: No Solution Exploring Operation: 66*44=2904, Resulting Numbers: [2904] 2904,52 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: 52:[97, 13], Operations: ['81-15=66', '66-53=13'] Exploring Operation: 97*13=1261, Resulting Numbers: [1261] 1261,52 unequal: No Solution Exploring Operation: 97-13=84, Resulting Numbers: [84] 84,52 unequal: No Solution Exploring Operation: 97+13=110, Resulting Numbers: [110] 110,52 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: 52:[66, 150], Operations: ['81-15=66', '97+53=150'] Exploring Operation: 66+150=216, Resulting Numbers: [216] 216,52 unequal: No Solution Exploring Operation: 66*150=9900, Resulting Numbers: [9900] 9900,52 unequal: No Solution Exploring Operation: 150-66=84, Resulting Numbers: [84] 84,52 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: 52:[53, 163], Operations: ['81-15=66', '97+66=163'] Exploring Operation: 53*163=8639, Resulting Numbers: [8639] 8639,52 unequal: No Solution Exploring Operation: 163-53=110, Resulting Numbers: [110] 110,52 unequal: No Solution Exploring Operation: 53+163=216, Resulting Numbers: [216] 216,52 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: 52:[81, 53, 82], Operations: ['97-15=82'] Exploring Operation: 81-53=28, Resulting Numbers: [82, 28] Generated Node #0,1,0: 52:[82, 28] Operation: 81-53=28 Exploring Operation: 82-81=1, Resulting Numbers: [53, 1] Generated Node #0,1,1: 52:[53, 1] Operation: 82-81=1 Exploring Operation: 81+82=163, Resulting Numbers: [53, 163] Generated Node #0,1,2: 52:[53, 163] Operation: 81+82=163 Exploring Operation: 81+53=134, Resulting Numbers: [82, 134] Generated Node #0,1,3: 52:[82, 134] Operation: 81+53=134 Exploring Operation: 82-53=29, Resulting Numbers: [81, 29] Generated Node #0,1,4: 52:[81, 29] Operation: 82-53=29 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 52:[53, 1], Operations: ['97-15=82', '82-81=1'] Exploring Operation: 53-1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[15, 97, 81, 53], Operations: [] Exploring Operation: 97-15=82, Resulting Numbers: [81, 53, 82] Generated Node #0,1: 52:[81, 53, 82] Operation: 97-15=82 Moving to Node #0,1 Current State: 52:[81, 53, 82], Operations: ['97-15=82'] Exploring Operation: 82-81=1, Resulting Numbers: [53, 1] Generated Node #0,1,1: 52:[53, 1] Operation: 82-81=1 Moving to Node #0,1,1 Current State: 52:[53, 1], Operations: ['97-15=82', '82-81=1'] Exploring Operation: 53-1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.956597
hs_5
sum_heuristic
[ 26, 66, 65, 2 ]
71
[ "26/2=13", "65/13=5", "66+5=71" ]
Current State: 71:[26, 66, 65, 2], Operations: [] Exploring Operation: 26/2=13, Resulting Numbers: [66, 65, 13] Generated Node #2: [66, 65, 13] from Operation: 26/2=13 Current State: 71:[66, 65, 13], Operations: ['26/2=13'] Exploring Operation: 65/13=5, Resulting Numbers: [66, 5] Generated Node #3: [66, 5] from Operation: 65/13=5 Current State: 71:[66, 5], Operations: ['26/2=13', '65/13=5'] Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[26, 66, 65, 2], Operations: [] Exploring Operation: 26*2=52, Resulting Numbers: [66, 65, 52] Generated Node #0,0: 71:[66, 65, 52] Operation: 26*2=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[66, 65, 52], Operations: ['26*2=52'] Exploring Operation: 65+52=117, Resulting Numbers: [66, 117] Generated Node #0,0,0: 71:[66, 117] Operation: 65+52=117 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[66, 117], Operations: ['26*2=52', '65+52=117'] Exploring Operation: 117-66=51, Resulting Numbers: [51] 51,71 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 No solution found.
0
hs_1
sum_heuristic
[ 73, 74, 37, 90 ]
34
[ "90-73=17", "74/37=2", "17*2=34" ]
Current State: 34:[73, 74, 37, 90], Operations: [] Exploring Operation: 90-73=17, Resulting Numbers: [74, 37, 17] Generated Node #2: [74, 37, 17] from Operation: 90-73=17 Current State: 34:[74, 37, 17], Operations: ['90-73=17'] Exploring Operation: 74/37=2, Resulting Numbers: [17, 2] Generated Node #3: [17, 2] from Operation: 74/37=2 Current State: 34:[17, 2], Operations: ['90-73=17', '74/37=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[73, 74, 37, 90], Operations: [] Exploring Operation: 90-73=17, Resulting Numbers: [74, 37, 17] Generated Node #0,0: 34:[74, 37, 17] Operation: 90-73=17 Moving to Node #0,0 Current State: 34:[74, 37, 17], Operations: ['90-73=17'] Exploring Operation: 74/37=2, Resulting Numbers: [17, 2] Generated Node #0,0,0: 34:[17, 2] Operation: 74/37=2 Moving to Node #0,0,0 Current State: 34:[17, 2], Operations: ['90-73=17', '74/37=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[73, 74, 37, 90], Operations: [] Exploring Operation: 90-73=17, Resulting Numbers: [74, 37, 17] Generated Node #0,0: 34:[74, 37, 17] Operation: 90-73=17 Moving to Node #0,0 Current State: 34:[74, 37, 17], Operations: ['90-73=17'] Exploring Operation: 74/37=2, Resulting Numbers: [17, 2] Generated Node #0,0,0: 34:[17, 2] Operation: 74/37=2 Moving to Node #0,0,0 Current State: 34:[17, 2], Operations: ['90-73=17', '74/37=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 33, 9, 38, 48 ]
57
[ "48-38=10", "9*10=90", "90-33=57" ]
Current State: 57:[33, 9, 38, 48], Operations: [] Exploring Operation: 48-38=10, Resulting Numbers: [33, 9, 10] Generated Node #2: [33, 9, 10] from Operation: 48-38=10 Current State: 57:[33, 9, 10], Operations: ['48-38=10'] Exploring Operation: 9*10=90, Resulting Numbers: [33, 90] Generated Node #3: [33, 90] from Operation: 9*10=90 Current State: 57:[33, 90], Operations: ['48-38=10', '9*10=90'] Exploring Operation: 90-33=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[33, 9, 38, 48], Operations: [] Exploring Operation: 48-33=15, Resulting Numbers: [9, 38, 15] Generated Node #0,0: 57:[9, 38, 15] Operation: 48-33=15 Exploring Operation: 48-38=10, Resulting Numbers: [33, 9, 10] Generated Node #0,1: 57:[33, 9, 10] Operation: 48-38=10 Exploring Operation: 38-33=5, Resulting Numbers: [9, 48, 5] Generated Node #0,2: 57:[9, 48, 5] Operation: 38-33=5 Exploring Operation: 33-9=24, Resulting Numbers: [38, 48, 24] Generated Node #0,3: 57:[38, 48, 24] Operation: 33-9=24 Exploring Operation: 33+38=71, Resulting Numbers: [9, 48, 71] Generated Node #0,4: 57:[9, 48, 71] Operation: 33+38=71 Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[9, 48, 5], Operations: ['38-33=5'] Exploring Operation: 48+5=53, Resulting Numbers: [9, 53] Generated Node #0,2,0: 57:[9, 53] Operation: 48+5=53 Exploring Operation: 9-5=4, Resulting Numbers: [48, 4] Generated Node #0,2,1: 57:[48, 4] Operation: 9-5=4 Exploring Operation: 9+48=57, Resulting Numbers: [5, 57] Generated Node #0,2,2: 57:[5, 57] Operation: 9+48=57 Exploring Operation: 9+5=14, Resulting Numbers: [48, 14] Generated Node #0,2,3: 57:[48, 14] Operation: 9+5=14 Exploring Operation: 48-9=39, Resulting Numbers: [5, 39] Generated Node #0,2,4: 57:[5, 39] Operation: 48-9=39 Moving to Node #0,2,2 Current State: 57:[5, 57], Operations: ['38-33=5', '9+48=57'] Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,57 unequal: No Solution Exploring Operation: 5*57=285, Resulting Numbers: [285] 285,57 unequal: No Solution Exploring Operation: 5+57=62, Resulting Numbers: [62] 62,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[48, 4], Operations: ['38-33=5', '9-5=4'] Exploring Operation: 48+4=52, Resulting Numbers: [52] 52,57 unequal: No Solution Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,57 unequal: No Solution Exploring Operation: 48/4=12, Resulting Numbers: [12] 12,57 unequal: No Solution Exploring Operation: 48*4=192, Resulting Numbers: [192] 192,57 unequal: No Solution Moving to Node #0,2,0 Current State: 57:[9, 53], Operations: ['38-33=5', '48+5=53'] Exploring Operation: 53-9=44, Resulting Numbers: [44] 44,57 unequal: No Solution Exploring Operation: 9+53=62, Resulting Numbers: [62] 62,57 unequal: No Solution Exploring Operation: 9*53=477, Resulting Numbers: [477] 477,57 unequal: No Solution Moving to Node #0,2,3 Current State: 57:[48, 14], Operations: ['38-33=5', '9+5=14'] Exploring Operation: 48+14=62, Resulting Numbers: [62] 62,57 unequal: No Solution Exploring Operation: 48*14=672, Resulting Numbers: [672] 672,57 unequal: No Solution Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,57 unequal: No Solution Moving to Node #0,2,4 Current State: 57:[5, 39], Operations: ['38-33=5', '48-9=39'] Exploring Operation: 5*39=195, Resulting Numbers: [195] 195,57 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,57 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 Current State: 57:[33, 9, 10], Operations: ['48-38=10'] Exploring Operation: 9+10=19, Resulting Numbers: [33, 19] Generated Node #0,1,0: 57:[33, 19] Operation: 9+10=19 Exploring Operation: 10-9=1, Resulting Numbers: [33, 1] Generated Node #0,1,1: 57:[33, 1] Operation: 10-9=1 Exploring Operation: 33-10=23, Resulting Numbers: [9, 23] Generated Node #0,1,2: 57:[9, 23] Operation: 33-10=23 Exploring Operation: 33-9=24, Resulting Numbers: [10, 24] Generated Node #0,1,3: 57:[10, 24] Operation: 33-9=24 Exploring Operation: 33+10=43, Resulting Numbers: [9, 43] Generated Node #0,1,4: 57:[9, 43] Operation: 33+10=43 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 57:[9, 23], Operations: ['48-38=10', '33-10=23'] Exploring Operation: 9*23=207, Resulting Numbers: [207] 207,57 unequal: No Solution Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,57 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: 57:[10, 24], Operations: ['48-38=10', '33-9=24'] Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 10*24=240, Resulting Numbers: [240] 240,57 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,57 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: 57:[33, 19], Operations: ['48-38=10', '9+10=19'] Exploring Operation: 33+19=52, Resulting Numbers: [52] 52,57 unequal: No Solution Exploring Operation: 33*19=627, Resulting Numbers: [627] 627,57 unequal: No Solution Exploring Operation: 33-19=14, Resulting Numbers: [14] 14,57 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: 57:[33, 1], Operations: ['48-38=10', '10-9=1'] Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,57 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 #0,1,4 Current State: 57:[9, 43], Operations: ['48-38=10', '33+10=43'] Exploring Operation: 9*43=387, Resulting Numbers: [387] 387,57 unequal: No Solution Exploring Operation: 9+43=52, Resulting Numbers: [52] 52,57 unequal: No Solution Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,57 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: 57:[9, 38, 15], Operations: ['48-33=15'] Exploring Operation: 15-9=6, Resulting Numbers: [38, 6] Generated Node #0,0,0: 57:[38, 6] Operation: 15-9=6 Exploring Operation: 38-9=29, Resulting Numbers: [15, 29] Generated Node #0,0,1: 57:[15, 29] Operation: 38-9=29 Exploring Operation: 38-15=23, Resulting Numbers: [9, 23] Generated Node #0,0,2: 57:[9, 23] Operation: 38-15=23 Exploring Operation: 9+38=47, Resulting Numbers: [15, 47] Generated Node #0,0,3: 57:[15, 47] Operation: 9+38=47 Exploring Operation: 38+15=53, Resulting Numbers: [9, 53] Generated Node #0,0,4: 57:[9, 53] Operation: 38+15=53 Moving to Node #0,0,2 Current State: 57:[9, 23], Operations: ['48-33=15', '38-15=23'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 9*23=207, Resulting Numbers: [207] 207,57 unequal: No Solution Moving to Node #0,0,4 Current State: 57:[9, 53], Operations: ['48-33=15', '38+15=53'] Exploring Operation: 9+53=62, Resulting Numbers: [62] 62,57 unequal: No Solution Exploring Operation: 9*53=477, Resulting Numbers: [477] 477,57 unequal: No Solution Exploring Operation: 53-9=44, Resulting Numbers: [44] 44,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[15, 29], Operations: ['48-33=15', '38-9=29'] Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 15+29=44, Resulting Numbers: [44] 44,57 unequal: No Solution Exploring Operation: 15*29=435, Resulting Numbers: [435] 435,57 unequal: No Solution Moving to Node #0,0,3 Current State: 57:[15, 47], Operations: ['48-33=15', '9+38=47'] Exploring Operation: 15+47=62, Resulting Numbers: [62] 62,57 unequal: No Solution Exploring Operation: 15*47=705, Resulting Numbers: [705] 705,57 unequal: No Solution Exploring Operation: 47-15=32, Resulting Numbers: [32] 32,57 unequal: No Solution Moving to Node #0,0,0 Current State: 57:[38, 6], Operations: ['48-33=15', '15-9=6'] Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,57 unequal: No Solution Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,57 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 #0,4 Current State: 57:[9, 48, 71], Operations: ['33+38=71'] Exploring Operation: 9+48=57, Resulting Numbers: [71, 57] Generated Node #0,4,0: 57:[71, 57] Operation: 9+48=57 Exploring Operation: 71-48=23, Resulting Numbers: [9, 23] Generated Node #0,4,1: 57:[9, 23] Operation: 71-48=23 Exploring Operation: 9+71=80, Resulting Numbers: [48, 80] Generated Node #0,4,2: 57:[48, 80] Operation: 9+71=80 Exploring Operation: 71-9=62, Resulting Numbers: [48, 62] Generated Node #0,4,3: 57:[48, 62] Operation: 71-9=62 Exploring Operation: 48-9=39, Resulting Numbers: [71, 39] Generated Node #0,4,4: 57:[71, 39] Operation: 48-9=39 Moving to Node #0,4,1 Current State: 57:[9, 23], Operations: ['33+38=71', '71-48=23'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 9*23=207, Resulting Numbers: [207] 207,57 unequal: No Solution Moving to Node #0,4,3 Current State: 57:[48, 62], Operations: ['33+38=71', '71-9=62'] Exploring Operation: 48+62=110, Resulting Numbers: [110] 110,57 unequal: No Solution Exploring Operation: 48*62=2976, Resulting Numbers: [2976] 2976,57 unequal: No Solution Exploring Operation: 62-48=14, Resulting Numbers: [14] 14,57 unequal: No Solution Moving to Node #0,4,0 Current State: 57:[71, 57], Operations: ['33+38=71', '9+48=57'] Exploring Operation: 71+57=128, Resulting Numbers: [128] 128,57 unequal: No Solution Exploring Operation: 71*57=4047, Resulting Numbers: [4047] 4047,57 unequal: No Solution Exploring Operation: 71-57=14, Resulting Numbers: [14] 14,57 unequal: No Solution Moving to Node #0,4,2 Current State: 57:[48, 80], Operations: ['33+38=71', '9+71=80'] Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 48*80=3840, Resulting Numbers: [3840] 3840,57 unequal: No Solution Exploring Operation: 48+80=128, Resulting Numbers: [128] 128,57 unequal: No Solution Moving to Node #0,4,4 Current State: 57:[71, 39], Operations: ['33+38=71', '48-9=39'] Exploring Operation: 71*39=2769, Resulting Numbers: [2769] 2769,57 unequal: No Solution Exploring Operation: 71+39=110, Resulting Numbers: [110] 110,57 unequal: No Solution Exploring Operation: 71-39=32, Resulting Numbers: [32] 32,57 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 #0,3 Current State: 57:[38, 48, 24], Operations: ['33-9=24'] Exploring Operation: 38+24=62, Resulting Numbers: [48, 62] Generated Node #0,3,0: 57:[48, 62] Operation: 38+24=62 Exploring Operation: 38-24=14, Resulting Numbers: [48, 14] Generated Node #0,3,1: 57:[48, 14] Operation: 38-24=14 Exploring Operation: 48-24=24, Resulting Numbers: [38, 24] Generated Node #0,3,2: 57:[38, 24] Operation: 48-24=24 Exploring Operation: 48-38=10, Resulting Numbers: [24, 10] Generated Node #0,3,3: 57:[24, 10] Operation: 48-38=10 Exploring Operation: 48/24=2, Resulting Numbers: [38, 2] Generated Node #0,3,4: 57:[38, 2] Operation: 48/24=2 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 57:[24, 10], Operations: ['33-9=24', '48-38=10'] Exploring Operation: 24*10=240, Resulting Numbers: [240] 240,57 unequal: No Solution Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,57 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: 57:[48, 62], Operations: ['33-9=24', '38+24=62'] Exploring Operation: 62-48=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 48*62=2976, Resulting Numbers: [2976] 2976,57 unequal: No Solution Exploring Operation: 48+62=110, Resulting Numbers: [110] 110,57 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: 57:[48, 14], Operations: ['33-9=24', '38-24=14'] Exploring Operation: 48+14=62, Resulting Numbers: [62] 62,57 unequal: No Solution Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 48*14=672, Resulting Numbers: [672] 672,57 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: 57:[38, 2], Operations: ['33-9=24', '48/24=2'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,57 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,57 unequal: No Solution Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,57 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: 57:[38, 24], Operations: ['33-9=24', '48-24=24'] Exploring Operation: 38*24=912, Resulting Numbers: [912] 912,57 unequal: No Solution Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 38+24=62, Resulting Numbers: [62] 62,57 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
sum_heuristic
[ 59, 45, 44, 87 ]
29
[ "59-45=14", "87-44=43", "43-14=29" ]
Current State: 29:[59, 45, 44, 87], Operations: [] Exploring Operation: 59-45=14, Resulting Numbers: [44, 87, 14] Generated Node #2: [44, 87, 14] from Operation: 59-45=14 Current State: 29:[44, 87, 14], Operations: ['59-45=14'] Exploring Operation: 87-44=43, Resulting Numbers: [14, 43] Generated Node #3: [14, 43] from Operation: 87-44=43 Current State: 29:[14, 43], Operations: ['59-45=14', '87-44=43'] Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[59, 45, 44, 87], Operations: [] Exploring Operation: 87-59=28, Resulting Numbers: [45, 44, 28] Generated Node #0,0: 29:[45, 44, 28] Operation: 87-59=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[45, 44, 28], Operations: ['87-59=28'] Exploring Operation: 45-28=17, Resulting Numbers: [44, 17] Generated Node #0,0,0: 29:[44, 17] Operation: 45-28=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[44, 17], Operations: ['87-59=28', '45-28=17'] Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,29 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
sum_heuristic
[ 36, 79, 84, 69 ]
82
[ "84*69=5796", "5796/36=161", "161-79=82" ]
Current State: 82:[36, 79, 84, 69], Operations: [] Exploring Operation: 84*69=5796, Resulting Numbers: [36, 79, 5796] Generated Node #2: [36, 79, 5796] from Operation: 84*69=5796 Current State: 82:[36, 79, 5796], Operations: ['84*69=5796'] Exploring Operation: 5796/36=161, Resulting Numbers: [79, 161] Generated Node #3: [79, 161] from Operation: 5796/36=161 Current State: 82:[79, 161], Operations: ['84*69=5796', '5796/36=161'] Exploring Operation: 161-79=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[36, 79, 84, 69], Operations: [] Exploring Operation: 84-79=5, Resulting Numbers: [36, 69, 5] Generated Node #0,0: 82:[36, 69, 5] Operation: 84-79=5 Exploring Operation: 84-69=15, Resulting Numbers: [36, 79, 15] Generated Node #0,1: 82:[36, 79, 15] Operation: 84-69=15 Exploring Operation: 79-36=43, Resulting Numbers: [84, 69, 43] Generated Node #0,2: 82:[84, 69, 43] Operation: 79-36=43 Exploring Operation: 79-69=10, Resulting Numbers: [36, 84, 10] Generated Node #0,3: 82:[36, 84, 10] Operation: 79-69=10 Exploring Operation: 69-36=33, Resulting Numbers: [79, 84, 33] Generated Node #0,4: 82:[79, 84, 33] Operation: 69-36=33 Moving to Node #0,4 Current State: 82:[79, 84, 33], Operations: ['69-36=33'] Exploring Operation: 84+33=117, Resulting Numbers: [79, 117] Generated Node #0,4,0: 82:[79, 117] Operation: 84+33=117 Exploring Operation: 79+33=112, Resulting Numbers: [84, 112] Generated Node #0,4,1: 82:[84, 112] Operation: 79+33=112 Exploring Operation: 84-79=5, Resulting Numbers: [33, 5] Generated Node #0,4,2: 82:[33, 5] Operation: 84-79=5 Exploring Operation: 79-33=46, Resulting Numbers: [84, 46] Generated Node #0,4,3: 82:[84, 46] Operation: 79-33=46 Exploring Operation: 84-33=51, Resulting Numbers: [79, 51] Generated Node #0,4,4: 82:[79, 51] Operation: 84-33=51 Moving to Node #0,3 Current State: 82:[36, 84, 10], Operations: ['79-69=10'] Exploring Operation: 36+10=46, Resulting Numbers: [84, 46] Generated Node #0,3,0: 82:[84, 46] Operation: 36+10=46 Exploring Operation: 84+10=94, Resulting Numbers: [36, 94] Generated Node #0,3,1: 82:[36, 94] Operation: 84+10=94 Exploring Operation: 36-10=26, Resulting Numbers: [84, 26] Generated Node #0,3,2: 82:[84, 26] Operation: 36-10=26 Exploring Operation: 84-10=74, Resulting Numbers: [36, 74] Generated Node #0,3,3: 82:[36, 74] Operation: 84-10=74 Exploring Operation: 84-36=48, Resulting Numbers: [10, 48] Generated Node #0,3,4: 82:[10, 48] Operation: 84-36=48 Moving to Node #0,2 Current State: 82:[84, 69, 43], Operations: ['79-36=43'] Exploring Operation: 84-43=41, Resulting Numbers: [69, 41] Generated Node #0,2,0: 82:[69, 41] Operation: 84-43=41 Exploring Operation: 69+43=112, Resulting Numbers: [84, 112] Generated Node #0,2,1: 82:[84, 112] Operation: 69+43=112 Exploring Operation: 69-43=26, Resulting Numbers: [84, 26] Generated Node #0,2,2: 82:[84, 26] Operation: 69-43=26 Exploring Operation: 84+43=127, Resulting Numbers: [69, 127] Generated Node #0,2,3: 82:[69, 127] Operation: 84+43=127 Exploring Operation: 84-69=15, Resulting Numbers: [43, 15] Generated Node #0,2,4: 82:[43, 15] Operation: 84-69=15 Moving to Node #0,0 Current State: 82:[36, 69, 5], Operations: ['84-79=5'] Exploring Operation: 69+5=74, Resulting Numbers: [36, 74] Generated Node #0,0,0: 82:[36, 74] Operation: 69+5=74 Exploring Operation: 36-5=31, Resulting Numbers: [69, 31] Generated Node #0,0,1: 82:[69, 31] Operation: 36-5=31 Exploring Operation: 69-5=64, Resulting Numbers: [36, 64] Generated Node #0,0,2: 82:[36, 64] Operation: 69-5=64 Exploring Operation: 36+5=41, Resulting Numbers: [69, 41] Generated Node #0,0,3: 82:[69, 41] Operation: 36+5=41 Exploring Operation: 69-36=33, Resulting Numbers: [5, 33] Generated Node #0,0,4: 82:[5, 33] Operation: 69-36=33 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 82:[5, 33], Operations: ['84-79=5', '69-36=33'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 5+33=38, Resulting Numbers: [38] 38,82 unequal: No Solution Exploring Operation: 5*33=165, Resulting Numbers: [165] 165,82 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: 82:[36, 74], Operations: ['84-79=5', '69+5=74'] Exploring Operation: 36+74=110, Resulting Numbers: [110] 110,82 unequal: No Solution Exploring Operation: 74-36=38, Resulting Numbers: [38] 38,82 unequal: No Solution Exploring Operation: 36*74=2664, Resulting Numbers: [2664] 2664,82 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: 82:[69, 41], Operations: ['84-79=5', '36+5=41'] Exploring Operation: 69*41=2829, Resulting Numbers: [2829] 2829,82 unequal: No Solution Exploring Operation: 69-41=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 69+41=110, Resulting Numbers: [110] 110,82 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: 82:[69, 31], Operations: ['84-79=5', '36-5=31'] Exploring Operation: 69*31=2139, Resulting Numbers: [2139] 2139,82 unequal: No Solution Exploring Operation: 69-31=38, Resulting Numbers: [38] 38,82 unequal: No Solution Exploring Operation: 69+31=100, Resulting Numbers: [100] 100,82 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: 82:[36, 64], Operations: ['84-79=5', '69-5=64'] Exploring Operation: 36*64=2304, Resulting Numbers: [2304] 2304,82 unequal: No Solution Exploring Operation: 36+64=100, Resulting Numbers: [100] 100,82 unequal: No Solution Exploring Operation: 64-36=28, Resulting Numbers: [28] 28,82 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: 82:[36, 79, 15], Operations: ['84-69=15'] Exploring Operation: 79-15=64, Resulting Numbers: [36, 64] Generated Node #0,1,0: 82:[36, 64] Operation: 79-15=64 Exploring Operation: 79-36=43, Resulting Numbers: [15, 43] Generated Node #0,1,1: 82:[15, 43] Operation: 79-36=43 Exploring Operation: 36+15=51, Resulting Numbers: [79, 51] Generated Node #0,1,2: 82:[79, 51] Operation: 36+15=51 Exploring Operation: 36-15=21, Resulting Numbers: [79, 21] Generated Node #0,1,3: 82:[79, 21] Operation: 36-15=21 Exploring Operation: 79+15=94, Resulting Numbers: [36, 94] Generated Node #0,1,4: 82:[36, 94] Operation: 79+15=94 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 82:[79, 51], Operations: ['84-69=15', '36+15=51'] Exploring Operation: 79*51=4029, Resulting Numbers: [4029] 4029,82 unequal: No Solution Exploring Operation: 79+51=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 79-51=28, Resulting Numbers: [28] 28,82 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: 82:[15, 43], Operations: ['84-69=15', '79-36=43'] Exploring Operation: 43-15=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 15+43=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 15*43=645, Resulting Numbers: [645] 645,82 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: 82:[36, 94], Operations: ['84-69=15', '79+15=94'] Exploring Operation: 36+94=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 36*94=3384, Resulting Numbers: [3384] 3384,82 unequal: No Solution Exploring Operation: 94-36=58, Resulting Numbers: [58] 58,82 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: 82:[79, 21], Operations: ['84-69=15', '36-15=21'] Exploring Operation: 79*21=1659, Resulting Numbers: [1659] 1659,82 unequal: No Solution Exploring Operation: 79+21=100, Resulting Numbers: [100] 100,82 unequal: No Solution Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,82 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: 82:[36, 64], Operations: ['84-69=15', '79-15=64'] Exploring Operation: 36+64=100, Resulting Numbers: [100] 100,82 unequal: No Solution Exploring Operation: 64-36=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 36*64=2304, Resulting Numbers: [2304] 2304,82 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: 82:[84, 46], Operations: ['69-36=33', '79-33=46'] Exploring Operation: 84+46=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 84-46=38, Resulting Numbers: [38] 38,82 unequal: No Solution Exploring Operation: 84*46=3864, Resulting Numbers: [3864] 3864,82 unequal: No Solution Moving to Node #0,3,0 Current State: 82:[84, 46], Operations: ['79-69=10', '36+10=46'] Exploring Operation: 84*46=3864, Resulting Numbers: [3864] 3864,82 unequal: No Solution Exploring Operation: 84-46=38, Resulting Numbers: [38] 38,82 unequal: No Solution Exploring Operation: 84+46=130, Resulting Numbers: [130] 130,82 unequal: No Solution Moving to Node #0,4,2 Current State: 82:[33, 5], Operations: ['69-36=33', '84-79=5'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,82 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,82 unequal: No Solution Moving to Node #0,3,3 Current State: 82:[36, 74], Operations: ['79-69=10', '84-10=74'] Exploring Operation: 36+74=110, Resulting Numbers: [110] 110,82 unequal: No Solution Exploring Operation: 36*74=2664, Resulting Numbers: [2664] 2664,82 unequal: No Solution Exploring Operation: 74-36=38, Resulting Numbers: [38] 38,82 unequal: No Solution Moving to Node #0,4,4 Current State: 82:[79, 51], Operations: ['69-36=33', '84-33=51'] Exploring Operation: 79+51=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 79-51=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 79*51=4029, Resulting Numbers: [4029] 4029,82 unequal: No Solution Moving to Node #0,2,0 Current State: 82:[69, 41], Operations: ['79-36=43', '84-43=41'] Exploring Operation: 69-41=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 69*41=2829, Resulting Numbers: [2829] 2829,82 unequal: No Solution Exploring Operation: 69+41=110, Resulting Numbers: [110] 110,82 unequal: No Solution Moving to Node #0,2,4 Current State: 82:[43, 15], Operations: ['79-36=43', '84-69=15'] Exploring Operation: 43+15=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 43-15=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 43*15=645, Resulting Numbers: [645] 645,82 unequal: No Solution Moving to Node #0,3,4 Current State: 82:[10, 48], Operations: ['79-69=10', '84-36=48'] Exploring Operation: 10*48=480, Resulting Numbers: [480] 480,82 unequal: No Solution Exploring Operation: 10+48=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,82 unequal: No Solution Moving to Node #0,2,2 Current State: 82:[84, 26], Operations: ['79-36=43', '69-43=26'] Exploring Operation: 84-26=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 84+26=110, Resulting Numbers: [110] 110,82 unequal: No Solution Exploring Operation: 84*26=2184, Resulting Numbers: [2184] 2184,82 unequal: No Solution Moving to Node #0,3,2 Current State: 82:[84, 26], Operations: ['79-69=10', '36-10=26'] Exploring Operation: 84+26=110, Resulting Numbers: [110] 110,82 unequal: No Solution Exploring Operation: 84-26=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 84*26=2184, Resulting Numbers: [2184] 2184,82 unequal: No Solution Moving to Node #0,3,1 Current State: 82:[36, 94], Operations: ['79-69=10', '84+10=94'] Exploring Operation: 36+94=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 36*94=3384, Resulting Numbers: [3384] 3384,82 unequal: No Solution Exploring Operation: 94-36=58, Resulting Numbers: [58] 58,82 unequal: No Solution Moving to Node #0,2,1 Current State: 82:[84, 112], Operations: ['79-36=43', '69+43=112'] Exploring Operation: 84+112=196, Resulting Numbers: [196] 196,82 unequal: No Solution Exploring Operation: 112-84=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 84*112=9408, Resulting Numbers: [9408] 9408,82 unequal: No Solution Moving to Node #0,4,1 Current State: 82:[84, 112], Operations: ['69-36=33', '79+33=112'] Exploring Operation: 84*112=9408, Resulting Numbers: [9408] 9408,82 unequal: No Solution Exploring Operation: 84+112=196, Resulting Numbers: [196] 196,82 unequal: No Solution Exploring Operation: 112-84=28, Resulting Numbers: [28] 28,82 unequal: No Solution Moving to Node #0,4,0 Current State: 82:[79, 117], Operations: ['69-36=33', '84+33=117'] Exploring Operation: 117-79=38, Resulting Numbers: [38] 38,82 unequal: No Solution Exploring Operation: 79+117=196, Resulting Numbers: [196] 196,82 unequal: No Solution Exploring Operation: 79*117=9243, Resulting Numbers: [9243] 9243,82 unequal: No Solution Moving to Node #0,2,3 Current State: 82:[69, 127], Operations: ['79-36=43', '84+43=127'] Exploring Operation: 69+127=196, Resulting Numbers: [196] 196,82 unequal: No Solution Exploring Operation: 127-69=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 69*127=8763, Resulting Numbers: [8763] 8763,82 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 9, 32, 65, 36 ]
14
[ "65-9=56", "36-32=4", "56/4=14" ]
Current State: 14:[9, 32, 65, 36], Operations: [] Exploring Operation: 65-9=56, Resulting Numbers: [32, 36, 56] Generated Node #2: [32, 36, 56] from Operation: 65-9=56 Current State: 14:[32, 36, 56], Operations: ['65-9=56'] Exploring Operation: 36-32=4, Resulting Numbers: [56, 4] Generated Node #3: [56, 4] from Operation: 36-32=4 Current State: 14:[56, 4], Operations: ['65-9=56', '36-32=4'] Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[9, 32, 65, 36], Operations: [] Exploring Operation: 65-36=29, Resulting Numbers: [9, 32, 29] Generated Node #0,0: 14:[9, 32, 29] Operation: 65-36=29 Exploring Operation: 36-32=4, Resulting Numbers: [9, 65, 4] Generated Node #0,1: 14:[9, 65, 4] Operation: 36-32=4 Exploring Operation: 65-32=33, Resulting Numbers: [9, 36, 33] Generated Node #0,2: 14:[9, 36, 33] Operation: 65-32=33 Exploring Operation: 36/9=4, Resulting Numbers: [32, 65, 4] Generated Node #0,3: 14:[32, 65, 4] Operation: 36/9=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[9, 32, 29], Operations: ['65-36=29'] Exploring Operation: 29-9=20, Resulting Numbers: [32, 20] Generated Node #0,0,0: 14:[32, 20] Operation: 29-9=20 Exploring Operation: 9+32=41, Resulting Numbers: [29, 41] Generated Node #0,0,1: 14:[29, 41] Operation: 9+32=41 Exploring Operation: 32-9=23, Resulting Numbers: [29, 23] Generated Node #0,0,2: 14:[29, 23] Operation: 32-9=23 Exploring Operation: 32-29=3, Resulting Numbers: [9, 3] Generated Node #0,0,3: 14:[9, 3] Operation: 32-29=3 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 14:[9, 3], Operations: ['65-36=29', '32-29=3'] Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,14 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: 14:[32, 20], Operations: ['65-36=29', '29-9=20'] Exploring Operation: 32*20=640, Resulting Numbers: [640] 640,14 unequal: No Solution Exploring Operation: 32+20=52, Resulting Numbers: [52] 52,14 unequal: No Solution Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,14 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: 14:[29, 23], Operations: ['65-36=29', '32-9=23'] Exploring Operation: 29*23=667, Resulting Numbers: [667] 667,14 unequal: No Solution Exploring Operation: 29+23=52, Resulting Numbers: [52] 52,14 unequal: No Solution Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,14 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: 14:[29, 41], Operations: ['65-36=29', '9+32=41'] Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,14 unequal: No Solution Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,14 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: 14:[9, 36, 33], Operations: ['65-32=33'] Exploring Operation: 33-9=24, Resulting Numbers: [36, 24] Generated Node #0,2,0: 14:[36, 24] Operation: 33-9=24 Exploring Operation: 36/9=4, Resulting Numbers: [33, 4] Generated Node #0,2,1: 14:[33, 4] Operation: 36/9=4 Exploring Operation: 36-33=3, Resulting Numbers: [9, 3] Generated Node #0,2,2: 14:[9, 3] Operation: 36-33=3 Exploring Operation: 36-9=27, Resulting Numbers: [33, 27] Generated Node #0,2,3: 14:[33, 27] Operation: 36-9=27 Moving to Node #0,2,2 Current State: 14:[9, 3], Operations: ['65-32=33', '36-33=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[33, 4], Operations: ['65-32=33', '36/9=4'] Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,14 unequal: No Solution Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,14 unequal: No Solution Moving to Node #0,2,3 Current State: 14:[33, 27], Operations: ['65-32=33', '36-9=27'] Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,14 unequal: No Solution Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,14 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,14 unequal: No Solution Moving to Node #0,2,0 Current State: 14:[36, 24], Operations: ['65-32=33', '33-9=24'] Exploring Operation: 36-24=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 36+24=60, Resulting Numbers: [60] 60,14 unequal: No Solution Exploring Operation: 36*24=864, Resulting Numbers: [864] 864,14 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 #0,1 Current State: 14:[9, 65, 4], Operations: ['36-32=4'] Exploring Operation: 65-9=56, Resulting Numbers: [4, 56] Generated Node #0,1,0: 14:[4, 56] Operation: 65-9=56 Exploring Operation: 65-4=61, Resulting Numbers: [9, 61] Generated Node #0,1,1: 14:[9, 61] Operation: 65-4=61 Exploring Operation: 9+4=13, Resulting Numbers: [65, 13] Generated Node #0,1,2: 14:[65, 13] Operation: 9+4=13 Exploring Operation: 9-4=5, Resulting Numbers: [65, 5] Generated Node #0,1,3: 14:[65, 5] Operation: 9-4=5 Moving to Node #0,1,0 Current State: 14:[4, 56], Operations: ['36-32=4', '65-9=56'] Exploring Operation: 4*56=224, Resulting Numbers: [224] 224,14 unequal: No Solution Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[9, 32, 65, 36], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [9, 65, 4] Generated Node #0,1: 14:[9, 65, 4] Operation: 36-32=4 Moving to Node #0,1 Current State: 14:[9, 65, 4], Operations: ['36-32=4'] Exploring Operation: 65-9=56, Resulting Numbers: [4, 56] Generated Node #0,1,0: 14:[4, 56] Operation: 65-9=56 Moving to Node #0,1,0 Current State: 14:[4, 56], Operations: ['36-32=4', '65-9=56'] Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.958333
hs_4
sum_heuristic
[ 54, 67, 62, 45 ]
45
[ "54-45=9", "67-62=5", "9*5=45" ]
Current State: 45:[54, 67, 62, 45], Operations: [] Exploring Operation: 54-45=9, Resulting Numbers: [67, 62, 9] Generated Node #2: [67, 62, 9] from Operation: 54-45=9 Current State: 45:[67, 62, 9], Operations: ['54-45=9'] Exploring Operation: 67-62=5, Resulting Numbers: [9, 5] Generated Node #3: [9, 5] from Operation: 67-62=5 Current State: 45:[9, 5], Operations: ['54-45=9', '67-62=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[54, 67, 62, 45], Operations: [] Exploring Operation: 67-62=5, Resulting Numbers: [54, 45, 5] Generated Node #0,0: 45:[54, 45, 5] Operation: 67-62=5 Exploring Operation: 67-54=13, Resulting Numbers: [62, 45, 13] Generated Node #0,1: 45:[62, 45, 13] Operation: 67-54=13 Moving to Node #0,0 Current State: 45:[54, 45, 5], Operations: ['67-62=5'] Exploring Operation: 54-5=49, Resulting Numbers: [45, 49] Generated Node #0,0,0: 45:[45, 49] Operation: 54-5=49 Exploring Operation: 54-45=9, Resulting Numbers: [5, 9] Generated Node #0,0,1: 45:[5, 9] Operation: 54-45=9 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[5, 9], Operations: ['67-62=5', '54-45=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,45 unequal: No Solution Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[54, 67, 62, 45], Operations: [] Exploring Operation: 67-62=5, Resulting Numbers: [54, 45, 5] Generated Node #0,0: 45:[54, 45, 5] Operation: 67-62=5 Moving to Node #0,0 Current State: 45:[54, 45, 5], Operations: ['67-62=5'] Exploring Operation: 54-45=9, Resulting Numbers: [5, 9] Generated Node #0,0,1: 45:[5, 9] Operation: 54-45=9 Moving to Node #0,0,1 Current State: 45:[5, 9], Operations: ['67-62=5', '54-45=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 70, 14, 60, 63 ]
42
[ "63-14=49", "60*49=2940", "2940/70=42" ]
Current State: 42:[70, 14, 60, 63], Operations: [] Exploring Operation: 63-14=49, Resulting Numbers: [70, 60, 49] Generated Node #2: [70, 60, 49] from Operation: 63-14=49 Current State: 42:[70, 60, 49], Operations: ['63-14=49'] Exploring Operation: 60*49=2940, Resulting Numbers: [70, 2940] Generated Node #3: [70, 2940] from Operation: 60*49=2940 Current State: 42:[70, 2940], Operations: ['63-14=49', '60*49=2940'] Exploring Operation: 2940/70=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[70, 14, 60, 63], Operations: [] Exploring Operation: 70-60=10, Resulting Numbers: [14, 63, 10] Generated Node #0,0: 42:[14, 63, 10] Operation: 70-60=10 Exploring Operation: 63-60=3, Resulting Numbers: [70, 14, 3] Generated Node #0,1: 42:[70, 14, 3] Operation: 63-60=3 Exploring Operation: 70-63=7, Resulting Numbers: [14, 60, 7] Generated Node #0,2: 42:[14, 60, 7] Operation: 70-63=7 Moving to Node #0,2 Current State: 42:[14, 60, 7], Operations: ['70-63=7'] Exploring Operation: 60-7=53, Resulting Numbers: [14, 53] Generated Node #0,2,0: 42:[14, 53] Operation: 60-7=53 Exploring Operation: 60-14=46, Resulting Numbers: [7, 46] Generated Node #0,2,1: 42:[7, 46] Operation: 60-14=46 Exploring Operation: 14+7=21, Resulting Numbers: [60, 21] Generated Node #0,2,2: 42:[60, 21] Operation: 14+7=21 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 42:[7, 46], Operations: ['70-63=7', '60-14=46'] Exploring Operation: 7*46=322, Resulting Numbers: [322] 322,42 unequal: No Solution Exploring Operation: 7+46=53, Resulting Numbers: [53] 53,42 unequal: No Solution Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,42 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: 42:[14, 53], Operations: ['70-63=7', '60-7=53'] Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,42 unequal: No Solution Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,42 unequal: No Solution Exploring Operation: 14*53=742, Resulting Numbers: [742] 742,42 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: 42:[60, 21], Operations: ['70-63=7', '14+7=21'] Exploring Operation: 60*21=1260, Resulting Numbers: [1260] 1260,42 unequal: No Solution Exploring Operation: 60+21=81, Resulting Numbers: [81] 81,42 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,42 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: 42:[14, 63, 10], Operations: ['70-60=10'] Exploring Operation: 14-10=4, Resulting Numbers: [63, 4] Generated Node #0,0,0: 42:[63, 4] Operation: 14-10=4 Exploring Operation: 63-10=53, Resulting Numbers: [14, 53] Generated Node #0,0,1: 42:[14, 53] Operation: 63-10=53 Exploring Operation: 63-14=49, Resulting Numbers: [10, 49] Generated Node #0,0,2: 42:[10, 49] Operation: 63-14=49 Moving to Node #0,1 Current State: 42:[70, 14, 3], Operations: ['63-60=3'] Exploring Operation: 70/14=5, Resulting Numbers: [3, 5] Generated Node #0,1,0: 42:[3, 5] Operation: 70/14=5 Exploring Operation: 70-14=56, Resulting Numbers: [3, 56] Generated Node #0,1,1: 42:[3, 56] Operation: 70-14=56 Exploring Operation: 70-3=67, Resulting Numbers: [14, 67] Generated Node #0,1,2: 42:[14, 67] Operation: 70-3=67 Moving to Node #0,1,0 Current State: 42:[3, 5], Operations: ['63-60=3', '70/14=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,42 unequal: No Solution Moving to Node #0,0,2 Current State: 42:[10, 49], Operations: ['70-60=10', '63-14=49'] Exploring Operation: 10*49=490, Resulting Numbers: [490] 490,42 unequal: No Solution Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,42 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[14, 53], Operations: ['70-60=10', '63-10=53'] Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,42 unequal: No Solution Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,42 unequal: No Solution Exploring Operation: 14*53=742, Resulting Numbers: [742] 742,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[3, 56], Operations: ['63-60=3', '70-14=56'] Exploring Operation: 3*56=168, Resulting Numbers: [168] 168,42 unequal: No Solution Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,42 unequal: No Solution Exploring Operation: 3+56=59, Resulting Numbers: [59] 59,42 unequal: No Solution Moving to Node #0,0,0 Current State: 42:[63, 4], Operations: ['70-60=10', '14-10=4'] Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,42 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,42 unequal: No Solution Exploring Operation: 63*4=252, Resulting Numbers: [252] 252,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[14, 67], Operations: ['63-60=3', '70-3=67'] Exploring Operation: 67-14=53, Resulting Numbers: [53] 53,42 unequal: No Solution Exploring Operation: 14+67=81, Resulting Numbers: [81] 81,42 unequal: No Solution Exploring Operation: 14*67=938, Resulting Numbers: [938] 938,42 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 74, 19, 22, 78 ]
98
[ "78-74=4", "19*4=76", "22+76=98" ]
Current State: 98:[74, 19, 22, 78], Operations: [] Exploring Operation: 78-74=4, Resulting Numbers: [19, 22, 4] Generated Node #2: [19, 22, 4] from Operation: 78-74=4 Current State: 98:[19, 22, 4], Operations: ['78-74=4'] Exploring Operation: 19*4=76, Resulting Numbers: [22, 76] Generated Node #3: [22, 76] from Operation: 19*4=76 Current State: 98:[22, 76], Operations: ['78-74=4', '19*4=76'] Exploring Operation: 22+76=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[74, 19, 22, 78], Operations: [] Exploring Operation: 78-74=4, Resulting Numbers: [19, 22, 4] Generated Node #0,0: 98:[19, 22, 4] Operation: 78-74=4 Moving to Node #0,0 Current State: 98:[19, 22, 4], Operations: ['78-74=4'] Exploring Operation: 22-19=3, Resulting Numbers: [4, 3] Generated Node #0,0,0: 98:[4, 3] Operation: 22-19=3 Moving to Node #0,0,0 Current State: 98:[4, 3], Operations: ['78-74=4', '22-19=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,98 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 21, 3, 87, 2 ]
67
[ "21-3=18", "87-2=85", "85-18=67" ]
Current State: 67:[21, 3, 87, 2], Operations: [] Exploring Operation: 21-3=18, Resulting Numbers: [87, 2, 18] Generated Node #2: [87, 2, 18] from Operation: 21-3=18 Current State: 67:[87, 2, 18], Operations: ['21-3=18'] Exploring Operation: 87-2=85, Resulting Numbers: [18, 85] Generated Node #3: [18, 85] from Operation: 87-2=85 Current State: 67:[18, 85], Operations: ['21-3=18', '87-2=85'] Exploring Operation: 85-18=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[21, 3, 87, 2], Operations: [] Exploring Operation: 21*3=63, Resulting Numbers: [87, 2, 63] Generated Node #0,0: 67:[87, 2, 63] Operation: 21*3=63 Exploring Operation: 21*2=42, Resulting Numbers: [3, 87, 42] Generated Node #0,1: 67:[3, 87, 42] Operation: 21*2=42 Exploring Operation: 3*2=6, Resulting Numbers: [21, 87, 6] Generated Node #0,2: 67:[21, 87, 6] Operation: 3*2=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[87, 2, 63], Operations: ['21*3=63'] Exploring Operation: 87-2=85, Resulting Numbers: [63, 85] Generated Node #0,0,0: 67:[63, 85] Operation: 87-2=85 Exploring Operation: 87+2=89, Resulting Numbers: [63, 89] Generated Node #0,0,1: 67:[63, 89] Operation: 87+2=89 Exploring Operation: 2+63=65, Resulting Numbers: [87, 65] Generated Node #0,0,2: 67:[87, 65] Operation: 2+63=65 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[63, 85], Operations: ['21*3=63', '87-2=85'] Exploring Operation: 63+85=148, Resulting Numbers: [148] 148,67 unequal: No Solution Exploring Operation: 63*85=5355, Resulting Numbers: [5355] 5355,67 unequal: No Solution Exploring Operation: 85-63=22, Resulting Numbers: [22] 22,67 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: 67:[87, 65], Operations: ['21*3=63', '2+63=65'] Exploring Operation: 87-65=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 87+65=152, Resulting Numbers: [152] 152,67 unequal: No Solution Exploring Operation: 87*65=5655, Resulting Numbers: [5655] 5655,67 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: 67:[63, 89], Operations: ['21*3=63', '87+2=89'] Exploring Operation: 89-63=26, Resulting Numbers: [26] 26,67 unequal: No Solution Exploring Operation: 63*89=5607, Resulting Numbers: [5607] 5607,67 unequal: No Solution Exploring Operation: 63+89=152, Resulting Numbers: [152] 152,67 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: 67:[3, 87, 42], Operations: ['21*2=42'] Exploring Operation: 87-3=84, Resulting Numbers: [42, 84] Generated Node #0,1,0: 67:[42, 84] Operation: 87-3=84 Exploring Operation: 3+87=90, Resulting Numbers: [42, 90] Generated Node #0,1,1: 67:[42, 90] Operation: 3+87=90 Exploring Operation: 3+42=45, Resulting Numbers: [87, 45] Generated Node #0,1,2: 67:[87, 45] Operation: 3+42=45 Moving to Node #0,1,0 Current State: 67:[42, 84], Operations: ['21*2=42', '87-3=84'] Exploring Operation: 84-42=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 42+84=126, Resulting Numbers: [126] 126,67 unequal: No Solution Exploring Operation: 84/42=2, Resulting Numbers: [2] 2,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[87, 45], Operations: ['21*2=42', '3+42=45'] Exploring Operation: 87-45=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 87+45=132, Resulting Numbers: [132] 132,67 unequal: No Solution Exploring Operation: 87*45=3915, Resulting Numbers: [3915] 3915,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[42, 90], Operations: ['21*2=42', '3+87=90'] Exploring Operation: 42*90=3780, Resulting Numbers: [3780] 3780,67 unequal: No Solution Exploring Operation: 42+90=132, Resulting Numbers: [132] 132,67 unequal: No Solution Exploring Operation: 90-42=48, Resulting Numbers: [48] 48,67 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 #0,2 Current State: 67:[21, 87, 6], Operations: ['3*2=6'] Exploring Operation: 87-6=81, Resulting Numbers: [21, 81] Generated Node #0,2,0: 67:[21, 81] Operation: 87-6=81 Exploring Operation: 87-21=66, Resulting Numbers: [6, 66] Generated Node #0,2,1: 67:[6, 66] Operation: 87-21=66 Exploring Operation: 21+6=27, Resulting Numbers: [87, 27] Generated Node #0,2,2: 67:[87, 27] Operation: 21+6=27 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 67:[21, 81], Operations: ['3*2=6', '87-6=81'] Exploring Operation: 81-21=60, Resulting Numbers: [60] 60,67 unequal: No Solution Exploring Operation: 21*81=1701, Resulting Numbers: [1701] 1701,67 unequal: No Solution Exploring Operation: 21+81=102, Resulting Numbers: [102] 102,67 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: 67:[87, 27], Operations: ['3*2=6', '21+6=27'] Exploring Operation: 87*27=2349, Resulting Numbers: [2349] 2349,67 unequal: No Solution Exploring Operation: 87-27=60, Resulting Numbers: [60] 60,67 unequal: No Solution Exploring Operation: 87+27=114, Resulting Numbers: [114] 114,67 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: 67:[6, 66], Operations: ['3*2=6', '87-21=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,67 unequal: No Solution Exploring Operation: 66-6=60, Resulting Numbers: [60] 60,67 unequal: No Solution Exploring Operation: 6+66=72, Resulting Numbers: [72] 72,67 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
[ 16, 9, 3, 57 ]
38
[ "57-16=41", "9/3=3", "41-3=38" ]
Current State: 38:[16, 9, 3, 57], Operations: [] Exploring Operation: 57-16=41, Resulting Numbers: [9, 3, 41] Generated Node #2: [9, 3, 41] from Operation: 57-16=41 Current State: 38:[9, 3, 41], Operations: ['57-16=41'] Exploring Operation: 9/3=3, Resulting Numbers: [41, 3] Generated Node #3: [41, 3] from Operation: 9/3=3 Current State: 38:[41, 3], Operations: ['57-16=41', '9/3=3'] Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[16, 9, 3, 57], Operations: [] Exploring Operation: 57/3=19, Resulting Numbers: [16, 9, 19] Generated Node #0,0: 38:[16, 9, 19] Operation: 57/3=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[16, 9, 19], Operations: ['57/3=19'] Exploring Operation: 16-9=7, Resulting Numbers: [19, 7] Generated Node #0,0,0: 38:[19, 7] Operation: 16-9=7 Moving to Node #0,0,0 Current State: 38:[19, 7], Operations: ['57/3=19', '16-9=7'] Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,38 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
[ 36, 30, 3, 55 ]
83
[ "36*3=108", "55-30=25", "108-25=83" ]
Current State: 83:[36, 30, 3, 55], Operations: [] Exploring Operation: 36*3=108, Resulting Numbers: [30, 55, 108] Generated Node #2: [30, 55, 108] from Operation: 36*3=108 Current State: 83:[30, 55, 108], Operations: ['36*3=108'] Exploring Operation: 55-30=25, Resulting Numbers: [108, 25] Generated Node #3: [108, 25] from Operation: 55-30=25 Current State: 83:[108, 25], Operations: ['36*3=108', '55-30=25'] Exploring Operation: 108-25=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[36, 30, 3, 55], Operations: [] Exploring Operation: 36+30=66, Resulting Numbers: [3, 55, 66] Generated Node #0,0: 83:[3, 55, 66] Operation: 36+30=66 Exploring Operation: 30*3=90, Resulting Numbers: [36, 55, 90] Generated Node #0,1: 83:[36, 55, 90] Operation: 30*3=90 Exploring Operation: 36*3=108, Resulting Numbers: [30, 55, 108] Generated Node #0,2: 83:[30, 55, 108] Operation: 36*3=108 Exploring Operation: 36+3=39, Resulting Numbers: [30, 55, 39] Generated Node #0,3: 83:[30, 55, 39] Operation: 36+3=39 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[36, 55, 90], Operations: ['30*3=90'] Exploring Operation: 36+55=91, Resulting Numbers: [90, 91] Generated Node #0,1,0: 83:[90, 91] Operation: 36+55=91 Exploring Operation: 55-36=19, Resulting Numbers: [90, 19] Generated Node #0,1,1: 83:[90, 19] Operation: 55-36=19 Exploring Operation: 36+90=126, Resulting Numbers: [55, 126] Generated Node #0,1,2: 83:[55, 126] Operation: 36+90=126 Exploring Operation: 90-36=54, Resulting Numbers: [55, 54] Generated Node #0,1,3: 83:[55, 54] Operation: 90-36=54 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[90, 91], Operations: ['30*3=90', '36+55=91'] Exploring Operation: 90+91=181, Resulting Numbers: [181] 181,83 unequal: No Solution Exploring Operation: 91-90=1, Resulting Numbers: [1] 1,83 unequal: No Solution Exploring Operation: 90*91=8190, Resulting Numbers: [8190] 8190,83 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: 83:[55, 54], Operations: ['30*3=90', '90-36=54'] Exploring Operation: 55*54=2970, Resulting Numbers: [2970] 2970,83 unequal: No Solution Exploring Operation: 55+54=109, Resulting Numbers: [109] 109,83 unequal: No Solution Exploring Operation: 55-54=1, Resulting Numbers: [1] 1,83 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: 83:[90, 19], Operations: ['30*3=90', '55-36=19'] Exploring Operation: 90-19=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 90+19=109, Resulting Numbers: [109] 109,83 unequal: No Solution Exploring Operation: 90*19=1710, Resulting Numbers: [1710] 1710,83 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: 83:[55, 126], Operations: ['30*3=90', '36+90=126'] Exploring Operation: 126-55=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 55*126=6930, Resulting Numbers: [6930] 6930,83 unequal: No Solution Exploring Operation: 55+126=181, Resulting Numbers: [181] 181,83 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: 83:[30, 55, 108], Operations: ['36*3=108'] Exploring Operation: 108-30=78, Resulting Numbers: [55, 78] Generated Node #0,2,0: 83:[55, 78] Operation: 108-30=78 Exploring Operation: 30+108=138, Resulting Numbers: [55, 138] Generated Node #0,2,1: 83:[55, 138] Operation: 30+108=138 Exploring Operation: 55-30=25, Resulting Numbers: [108, 25] Generated Node #0,2,2: 83:[108, 25] Operation: 55-30=25 Exploring Operation: 30+55=85, Resulting Numbers: [108, 85] Generated Node #0,2,3: 83:[108, 85] Operation: 30+55=85 Moving to Node #0,2,3 Current State: 83:[108, 85], Operations: ['36*3=108', '30+55=85'] Exploring Operation: 108-85=23, Resulting Numbers: [23] 23,83 unequal: No Solution Exploring Operation: 108+85=193, Resulting Numbers: [193] 193,83 unequal: No Solution Exploring Operation: 108*85=9180, Resulting Numbers: [9180] 9180,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[55, 78], Operations: ['36*3=108', '108-30=78'] Exploring Operation: 78-55=23, Resulting Numbers: [23] 23,83 unequal: No Solution Exploring Operation: 55*78=4290, Resulting Numbers: [4290] 4290,83 unequal: No Solution Exploring Operation: 55+78=133, Resulting Numbers: [133] 133,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[108, 25], Operations: ['36*3=108', '55-30=25'] Exploring Operation: 108+25=133, Resulting Numbers: [133] 133,83 unequal: No Solution Exploring Operation: 108-25=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[36, 30, 3, 55], Operations: [] Exploring Operation: 36*3=108, Resulting Numbers: [30, 55, 108] Generated Node #0,2: 83:[30, 55, 108] Operation: 36*3=108 Moving to Node #0,2 Current State: 83:[30, 55, 108], Operations: ['36*3=108'] Exploring Operation: 55-30=25, Resulting Numbers: [108, 25] Generated Node #0,2,2: 83:[108, 25] Operation: 55-30=25 Moving to Node #0,2,2 Current State: 83:[108, 25], Operations: ['36*3=108', '55-30=25'] Exploring Operation: 108-25=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_4
sum_heuristic
[ 92, 69, 23, 44 ]
88
[ "92*44=4048", "69-23=46", "4048/46=88" ]
Current State: 88:[92, 69, 23, 44], Operations: [] Exploring Operation: 92*44=4048, Resulting Numbers: [69, 23, 4048] Generated Node #2: [69, 23, 4048] from Operation: 92*44=4048 Current State: 88:[69, 23, 4048], Operations: ['92*44=4048'] Exploring Operation: 69-23=46, Resulting Numbers: [4048, 46] Generated Node #3: [4048, 46] from Operation: 69-23=46 Current State: 88:[4048, 46], Operations: ['92*44=4048', '69-23=46'] Exploring Operation: 4048/46=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[92, 69, 23, 44], Operations: [] Exploring Operation: 92-69=23, Resulting Numbers: [23, 44, 23] Generated Node #0,0: 88:[23, 44, 23] Operation: 92-69=23 Exploring Operation: 69/23=3, Resulting Numbers: [92, 44, 3] Generated Node #0,1: 88:[92, 44, 3] Operation: 69/23=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[23, 44, 23], Operations: ['92-69=23'] Exploring Operation: 23/23=1, Resulting Numbers: [44, 1] Generated Node #0,0,0: 88:[44, 1] Operation: 23/23=1 Exploring Operation: 44-23=21, Resulting Numbers: [23, 21] Generated Node #0,0,1: 88:[23, 21] Operation: 44-23=21 Moving to Node #0,0,0 Current State: 88:[44, 1], Operations: ['92-69=23', '23/23=1'] Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,88 unequal: No Solution Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[23, 21], Operations: ['92-69=23', '44-23=21'] Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,88 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 #0,1 Current State: 88:[92, 44, 3], Operations: ['69/23=3'] Exploring Operation: 92-3=89, Resulting Numbers: [44, 89] Generated Node #0,1,0: 88:[44, 89] Operation: 92-3=89 Exploring Operation: 92-44=48, Resulting Numbers: [3, 48] Generated Node #0,1,1: 88:[3, 48] Operation: 92-44=48 Moving to Node #0,1,0 Current State: 88:[44, 89], Operations: ['69/23=3', '92-3=89'] Exploring Operation: 89-44=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 44+89=133, Resulting Numbers: [133] 133,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[3, 48], Operations: ['69/23=3', '92-44=48'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,88 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,88 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
[ 5, 46, 74, 78 ]
62
[ "74-46=28", "5*28=140", "140-78=62" ]
Current State: 62:[5, 46, 74, 78], Operations: [] Exploring Operation: 74-46=28, Resulting Numbers: [5, 78, 28] Generated Node #2: [5, 78, 28] from Operation: 74-46=28 Current State: 62:[5, 78, 28], Operations: ['74-46=28'] Exploring Operation: 5*28=140, Resulting Numbers: [78, 140] Generated Node #3: [78, 140] from Operation: 5*28=140 Current State: 62:[78, 140], Operations: ['74-46=28', '5*28=140'] Exploring Operation: 140-78=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[5, 46, 74, 78], Operations: [] Exploring Operation: 78-74=4, Resulting Numbers: [5, 46, 4] Generated Node #0,0: 62:[5, 46, 4] Operation: 78-74=4 Exploring Operation: 78-46=32, Resulting Numbers: [5, 74, 32] Generated Node #0,1: 62:[5, 74, 32] Operation: 78-46=32 Moving to Node #0,1 Current State: 62:[5, 74, 32], Operations: ['78-46=32'] Exploring Operation: 74-5=69, Resulting Numbers: [32, 69] Generated Node #0,1,0: 62:[32, 69] Operation: 74-5=69 Exploring Operation: 74-32=42, Resulting Numbers: [5, 42] Generated Node #0,1,1: 62:[5, 42] Operation: 74-32=42 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[32, 69], Operations: ['78-46=32', '74-5=69'] Exploring Operation: 32+69=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,62 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: 62:[5, 42], Operations: ['78-46=32', '74-32=42'] Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 5+42=47, Resulting Numbers: [47] 47,62 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: 62:[5, 46, 4], Operations: ['78-74=4'] Exploring Operation: 46-5=41, Resulting Numbers: [4, 41] Generated Node #0,0,0: 62:[4, 41] Operation: 46-5=41 Exploring Operation: 5+46=51, Resulting Numbers: [4, 51] Generated Node #0,0,1: 62:[4, 51] Operation: 5+46=51 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[4, 41], Operations: ['78-74=4', '46-5=41'] Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,62 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: 62:[4, 51], Operations: ['78-74=4', '5+46=51'] Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,62 unequal: No Solution Exploring Operation: 4+51=55, Resulting Numbers: [55] 55,62 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
[ 25, 49, 3, 59 ]
65
[ "25*3=75", "59-49=10", "75-10=65" ]
Current State: 65:[25, 49, 3, 59], Operations: [] Exploring Operation: 25*3=75, Resulting Numbers: [49, 59, 75] Generated Node #2: [49, 59, 75] from Operation: 25*3=75 Current State: 65:[49, 59, 75], Operations: ['25*3=75'] Exploring Operation: 59-49=10, Resulting Numbers: [75, 10] Generated Node #3: [75, 10] from Operation: 59-49=10 Current State: 65:[75, 10], Operations: ['25*3=75', '59-49=10'] Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[25, 49, 3, 59], Operations: [] Exploring Operation: 25+49=74, Resulting Numbers: [3, 59, 74] Generated Node #0,0: 65:[3, 59, 74] Operation: 25+49=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[3, 59, 74], Operations: ['25+49=74'] Exploring Operation: 74-59=15, Resulting Numbers: [3, 15] Generated Node #0,0,0: 65:[3, 15] Operation: 74-59=15 Moving to Node #0,0,0 Current State: 65:[3, 15], Operations: ['25+49=74', '74-59=15'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,65 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
[ 72, 20, 24, 23 ]
48
[ "23-20=3", "72/3=24", "24+24=48" ]
Current State: 48:[72, 20, 24, 23], Operations: [] Exploring Operation: 23-20=3, Resulting Numbers: [72, 24, 3] Generated Node #2: [72, 24, 3] from Operation: 23-20=3 Current State: 48:[72, 24, 3], Operations: ['23-20=3'] Exploring Operation: 72/3=24, Resulting Numbers: [24, 24] Generated Node #3: [24, 24] from Operation: 72/3=24 Current State: 48:[24, 24], Operations: ['23-20=3', '72/3=24'] Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[72, 20, 24, 23], Operations: [] Exploring Operation: 72-20=52, Resulting Numbers: [24, 23, 52] Generated Node #0,0: 48:[24, 23, 52] Operation: 72-20=52 Moving to Node #0,0 Current State: 48:[24, 23, 52], Operations: ['72-20=52'] Exploring Operation: 24+23=47, Resulting Numbers: [52, 47] Generated Node #0,0,0: 48:[52, 47] Operation: 24+23=47 Moving to Node #0,0,0 Current State: 48:[52, 47], Operations: ['72-20=52', '24+23=47'] Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,48 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 54, 77, 29, 72 ]
12
[ "77-54=23", "29-23=6", "72/6=12" ]
Current State: 12:[54, 77, 29, 72], Operations: [] Exploring Operation: 77-54=23, Resulting Numbers: [29, 72, 23] Generated Node #2: [29, 72, 23] from Operation: 77-54=23 Current State: 12:[29, 72, 23], Operations: ['77-54=23'] Exploring Operation: 29-23=6, Resulting Numbers: [72, 6] Generated Node #3: [72, 6] from Operation: 29-23=6 Current State: 12:[72, 6], Operations: ['77-54=23', '29-23=6'] Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[54, 77, 29, 72], Operations: [] Exploring Operation: 77-54=23, Resulting Numbers: [29, 72, 23] Generated Node #0,0: 12:[29, 72, 23] Operation: 77-54=23 Exploring Operation: 77-72=5, Resulting Numbers: [54, 29, 5] Generated Node #0,1: 12:[54, 29, 5] Operation: 77-72=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[54, 29, 5], Operations: ['77-72=5'] Exploring Operation: 54-5=49, Resulting Numbers: [29, 49] Generated Node #0,1,0: 12:[29, 49] Operation: 54-5=49 Exploring Operation: 54-29=25, Resulting Numbers: [5, 25] Generated Node #0,1,1: 12:[5, 25] Operation: 54-29=25 Moving to Node #0,1,1 Current State: 12:[5, 25], Operations: ['77-72=5', '54-29=25'] Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[29, 49], Operations: ['77-72=5', '54-5=49'] Exploring Operation: 29+49=78, Resulting Numbers: [78] 78,12 unequal: No Solution Exploring Operation: 49-29=20, Resulting Numbers: [20] 20,12 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: 12:[29, 72, 23], Operations: ['77-54=23'] Exploring Operation: 72-29=43, Resulting Numbers: [23, 43] Generated Node #0,0,0: 12:[23, 43] Operation: 72-29=43 Exploring Operation: 72-23=49, Resulting Numbers: [29, 49] Generated Node #0,0,1: 12:[29, 49] Operation: 72-23=49 Moving to Node #0,0,0 Current State: 12:[23, 43], Operations: ['77-54=23', '72-29=43'] Exploring Operation: 23+43=66, Resulting Numbers: [66] 66,12 unequal: No Solution Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[29, 49], Operations: ['77-54=23', '72-23=49'] Exploring Operation: 49-29=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 29+49=78, Resulting Numbers: [78] 78,12 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
[ 43, 54, 86, 4 ]
79
[ "54-43=11", "86+4=90", "90-11=79" ]
Current State: 79:[43, 54, 86, 4], Operations: [] Exploring Operation: 54-43=11, Resulting Numbers: [86, 4, 11] Generated Node #2: [86, 4, 11] from Operation: 54-43=11 Current State: 79:[86, 4, 11], Operations: ['54-43=11'] Exploring Operation: 86+4=90, Resulting Numbers: [11, 90] Generated Node #3: [11, 90] from Operation: 86+4=90 Current State: 79:[11, 90], Operations: ['54-43=11', '86+4=90'] Exploring Operation: 90-11=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[43, 54, 86, 4], Operations: [] Exploring Operation: 43-4=39, Resulting Numbers: [54, 86, 39] Generated Node #0,0: 79:[54, 86, 39] Operation: 43-4=39 Exploring Operation: 43+4=47, Resulting Numbers: [54, 86, 47] Generated Node #0,1: 79:[54, 86, 47] Operation: 43+4=47 Exploring Operation: 86-4=82, Resulting Numbers: [43, 54, 82] Generated Node #0,2: 79:[43, 54, 82] Operation: 86-4=82 Exploring Operation: 54+4=58, Resulting Numbers: [43, 86, 58] Generated Node #0,3: 79:[43, 86, 58] Operation: 54+4=58 Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[54, 86, 47], Operations: ['43+4=47'] Exploring Operation: 54-47=7, Resulting Numbers: [86, 7] Generated Node #0,1,0: 79:[86, 7] Operation: 54-47=7 Exploring Operation: 54+47=101, Resulting Numbers: [86, 101] Generated Node #0,1,1: 79:[86, 101] Operation: 54+47=101 Exploring Operation: 86-47=39, Resulting Numbers: [54, 39] Generated Node #0,1,2: 79:[54, 39] Operation: 86-47=39 Exploring Operation: 86-54=32, Resulting Numbers: [47, 32] Generated Node #0,1,3: 79:[47, 32] Operation: 86-54=32 Moving to Node #0,1,1 Current State: 79:[86, 101], Operations: ['43+4=47', '54+47=101'] Exploring Operation: 86*101=8686, Resulting Numbers: [8686] 8686,79 unequal: No Solution Exploring Operation: 101-86=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 86+101=187, Resulting Numbers: [187] 187,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[54, 39], Operations: ['43+4=47', '86-47=39'] Exploring Operation: 54*39=2106, Resulting Numbers: [2106] 2106,79 unequal: No Solution Exploring Operation: 54+39=93, Resulting Numbers: [93] 93,79 unequal: No Solution Exploring Operation: 54-39=15, Resulting Numbers: [15] 15,79 unequal: No Solution Moving to Node #0,1,3 Current State: 79:[47, 32], Operations: ['43+4=47', '86-54=32'] Exploring Operation: 47+32=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[43, 54, 86, 4], Operations: [] Exploring Operation: 43+4=47, Resulting Numbers: [54, 86, 47] Generated Node #0,1: 79:[54, 86, 47] Operation: 43+4=47 Moving to Node #0,1 Current State: 79:[54, 86, 47], Operations: ['43+4=47'] Exploring Operation: 86-54=32, Resulting Numbers: [47, 32] Generated Node #0,1,3: 79:[47, 32] Operation: 86-54=32 Moving to Node #0,1,3 Current State: 79:[47, 32], Operations: ['43+4=47', '86-54=32'] Exploring Operation: 47+32=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 31, 48, 34, 93 ]
50
[ "31*48=1488", "1488/93=16", "34+16=50" ]
Current State: 50:[31, 48, 34, 93], Operations: [] Exploring Operation: 31*48=1488, Resulting Numbers: [34, 93, 1488] Generated Node #2: [34, 93, 1488] from Operation: 31*48=1488 Current State: 50:[34, 93, 1488], Operations: ['31*48=1488'] Exploring Operation: 1488/93=16, Resulting Numbers: [34, 16] Generated Node #3: [34, 16] from Operation: 1488/93=16 Current State: 50:[34, 16], Operations: ['31*48=1488', '1488/93=16'] Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[31, 48, 34, 93], Operations: [] Exploring Operation: 93/31=3, Resulting Numbers: [48, 34, 3] Generated Node #0,0: 50:[48, 34, 3] Operation: 93/31=3 Exploring Operation: 93-48=45, Resulting Numbers: [31, 34, 45] Generated Node #0,1: 50:[31, 34, 45] Operation: 93-48=45 Exploring Operation: 93-34=59, Resulting Numbers: [31, 48, 59] Generated Node #0,2: 50:[31, 48, 59] Operation: 93-34=59 Moving to Node #0,0 Current State: 50:[48, 34, 3], Operations: ['93/31=3'] Exploring Operation: 48-34=14, Resulting Numbers: [3, 14] Generated Node #0,0,0: 50:[3, 14] Operation: 48-34=14 Exploring Operation: 48+3=51, Resulting Numbers: [34, 51] Generated Node #0,0,1: 50:[34, 51] Operation: 48+3=51 Exploring Operation: 34-3=31, Resulting Numbers: [48, 31] Generated Node #0,0,2: 50:[48, 31] Operation: 34-3=31 Moving to Node #0,2 Current State: 50:[31, 48, 59], Operations: ['93-34=59'] Exploring Operation: 59-48=11, Resulting Numbers: [31, 11] Generated Node #0,2,0: 50:[31, 11] Operation: 59-48=11 Exploring Operation: 59-31=28, Resulting Numbers: [48, 28] Generated Node #0,2,1: 50:[48, 28] Operation: 59-31=28 Exploring Operation: 48-31=17, Resulting Numbers: [59, 17] Generated Node #0,2,2: 50:[59, 17] Operation: 48-31=17 Moving to Node #0,1 Current State: 50:[31, 34, 45], Operations: ['93-48=45'] Exploring Operation: 45-31=14, Resulting Numbers: [34, 14] Generated Node #0,1,0: 50:[34, 14] Operation: 45-31=14 Exploring Operation: 34-31=3, Resulting Numbers: [45, 3] Generated Node #0,1,1: 50:[45, 3] Operation: 34-31=3 Exploring Operation: 45-34=11, Resulting Numbers: [31, 11] Generated Node #0,1,2: 50:[31, 11] Operation: 45-34=11 Moving to Node #0,0,0 Current State: 50:[3, 14], Operations: ['93/31=3', '48-34=14'] Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,50 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,50 unequal: No Solution Moving to Node #0,2,1 Current State: 50:[48, 28], Operations: ['93-34=59', '59-31=28'] Exploring Operation: 48-28=20, Resulting Numbers: [20] 20,50 unequal: No Solution Exploring Operation: 48+28=76, Resulting Numbers: [76] 76,50 unequal: No Solution Exploring Operation: 48*28=1344, Resulting Numbers: [1344] 1344,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[45, 3], Operations: ['93-48=45', '34-31=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,50 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,50 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,50 unequal: No Solution Moving to Node #0,2,0 Current State: 50:[31, 11], Operations: ['93-34=59', '59-48=11'] Exploring Operation: 31*11=341, Resulting Numbers: [341] 341,50 unequal: No Solution Exploring Operation: 31+11=42, Resulting Numbers: [42] 42,50 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,50 unequal: No Solution Moving to Node #0,1,2 Current State: 50:[31, 11], Operations: ['93-48=45', '45-34=11'] Exploring Operation: 31*11=341, Resulting Numbers: [341] 341,50 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,50 unequal: No Solution Exploring Operation: 31+11=42, Resulting Numbers: [42] 42,50 unequal: No Solution Moving to Node #0,0,2 Current State: 50:[48, 31], Operations: ['93/31=3', '34-3=31'] Exploring Operation: 48+31=79, Resulting Numbers: [79] 79,50 unequal: No Solution Exploring Operation: 48-31=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 48*31=1488, Resulting Numbers: [1488] 1488,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[34, 51], Operations: ['93/31=3', '48+3=51'] Exploring Operation: 34*51=1734, Resulting Numbers: [1734] 1734,50 unequal: No Solution Exploring Operation: 34+51=85, Resulting Numbers: [85] 85,50 unequal: No Solution Exploring Operation: 51-34=17, Resulting Numbers: [17] 17,50 unequal: No Solution Moving to Node #0,1,0 Current State: 50:[34, 14], Operations: ['93-48=45', '45-31=14'] Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,50 unequal: No Solution Exploring Operation: 34*14=476, Resulting Numbers: [476] 476,50 unequal: No Solution Exploring Operation: 34+14=48, Resulting Numbers: [48] 48,50 unequal: No Solution Moving to Node #0,2,2 Current State: 50:[59, 17], Operations: ['93-34=59', '48-31=17'] Exploring Operation: 59-17=42, Resulting Numbers: [42] 42,50 unequal: No Solution Exploring Operation: 59+17=76, Resulting Numbers: [76] 76,50 unequal: No Solution Exploring Operation: 59*17=1003, Resulting Numbers: [1003] 1003,50 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 58, 38, 76, 78 ]
40
[ "58-38=20", "78-76=2", "20*2=40" ]
Current State: 40:[58, 38, 76, 78], Operations: [] Exploring Operation: 58-38=20, Resulting Numbers: [76, 78, 20] Generated Node #2: [76, 78, 20] from Operation: 58-38=20 Current State: 40:[76, 78, 20], Operations: ['58-38=20'] Exploring Operation: 78-76=2, Resulting Numbers: [20, 2] Generated Node #3: [20, 2] from Operation: 78-76=2 Current State: 40:[20, 2], Operations: ['58-38=20', '78-76=2'] Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[58, 38, 76, 78], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [58, 38, 2] Generated Node #0,0: 40:[58, 38, 2] Operation: 78-76=2 Exploring Operation: 78-38=40, Resulting Numbers: [58, 76, 40] Generated Node #0,1: 40:[58, 76, 40] Operation: 78-38=40 Exploring Operation: 78-58=20, Resulting Numbers: [38, 76, 20] Generated Node #0,2: 40:[38, 76, 20] Operation: 78-58=20 Exploring Operation: 76-58=18, Resulting Numbers: [38, 78, 18] Generated Node #0,3: 40:[38, 78, 18] Operation: 76-58=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[58, 38, 2], Operations: ['78-76=2'] Exploring Operation: 58/2=29, Resulting Numbers: [38, 29] Generated Node #0,0,0: 40:[38, 29] Operation: 58/2=29 Exploring Operation: 58-2=56, Resulting Numbers: [38, 56] Generated Node #0,0,1: 40:[38, 56] Operation: 58-2=56 Exploring Operation: 38+2=40, Resulting Numbers: [58, 40] Generated Node #0,0,2: 40:[58, 40] Operation: 38+2=40 Exploring Operation: 58-38=20, Resulting Numbers: [2, 20] Generated Node #0,0,3: 40:[2, 20] Operation: 58-38=20 Moving to Node #0,0,3 Current State: 40:[2, 20], Operations: ['78-76=2', '58-38=20'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[58, 38, 76, 78], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [58, 38, 2] Generated Node #0,0: 40:[58, 38, 2] Operation: 78-76=2 Moving to Node #0,0 Current State: 40:[58, 38, 2], Operations: ['78-76=2'] Exploring Operation: 58-38=20, Resulting Numbers: [2, 20] Generated Node #0,0,3: 40:[2, 20] Operation: 58-38=20 Moving to Node #0,0,3 Current State: 40:[2, 20], Operations: ['78-76=2', '58-38=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 32, 10, 7, 18 ]
78
[ "10-7=3", "32*3=96", "96-18=78" ]
Current State: 78:[32, 10, 7, 18], Operations: [] Exploring Operation: 10-7=3, Resulting Numbers: [32, 18, 3] Generated Node #2: [32, 18, 3] from Operation: 10-7=3 Current State: 78:[32, 18, 3], Operations: ['10-7=3'] Exploring Operation: 32*3=96, Resulting Numbers: [18, 96] Generated Node #3: [18, 96] from Operation: 32*3=96 Current State: 78:[18, 96], Operations: ['10-7=3', '32*3=96'] Exploring Operation: 96-18=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[32, 10, 7, 18], Operations: [] Exploring Operation: 32+7=39, Resulting Numbers: [10, 18, 39] Generated Node #0,0: 78:[10, 18, 39] Operation: 32+7=39 Exploring Operation: 32-18=14, Resulting Numbers: [10, 7, 14] Generated Node #0,1: 78:[10, 7, 14] Operation: 32-18=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[10, 7, 14], Operations: ['32-18=14'] Exploring Operation: 10-7=3, Resulting Numbers: [14, 3] Generated Node #0,1,0: 78:[14, 3] Operation: 10-7=3 Exploring Operation: 14-10=4, Resulting Numbers: [7, 4] Generated Node #0,1,1: 78:[7, 4] Operation: 14-10=4 Moving to Node #0,1,0 Current State: 78:[14, 3], Operations: ['32-18=14', '10-7=3'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[7, 4], Operations: ['32-18=14', '14-10=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,78 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: 78:[10, 18, 39], Operations: ['32+7=39'] Exploring Operation: 10+18=28, Resulting Numbers: [39, 28] Generated Node #0,0,0: 78:[39, 28] Operation: 10+18=28 Exploring Operation: 18-10=8, Resulting Numbers: [39, 8] Generated Node #0,0,1: 78:[39, 8] Operation: 18-10=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 78:[39, 28], Operations: ['32+7=39', '10+18=28'] Exploring Operation: 39-28=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 39+28=67, Resulting Numbers: [67] 67,78 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: 78:[39, 8], Operations: ['32+7=39', '18-10=8'] Exploring Operation: 39+8=47, Resulting Numbers: [47] 47,78 unequal: No Solution Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,78 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
[ 1, 39, 44, 5 ]
25
[ "1*39=39", "44-39=5", "5*5=25" ]
Current State: 25:[1, 39, 44, 5], Operations: [] Exploring Operation: 1*39=39, Resulting Numbers: [44, 5, 39] Generated Node #2: [44, 5, 39] from Operation: 1*39=39 Current State: 25:[44, 5, 39], Operations: ['1*39=39'] Exploring Operation: 44-39=5, Resulting Numbers: [5, 5] Generated Node #3: [5, 5] from Operation: 44-39=5 Current State: 25:[5, 5], Operations: ['1*39=39', '44-39=5'] Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[1, 39, 44, 5], Operations: [] Exploring Operation: 39-5=34, Resulting Numbers: [1, 44, 34] Generated Node #0,0: 25:[1, 44, 34] Operation: 39-5=34 Exploring Operation: 44-1=43, Resulting Numbers: [39, 5, 43] Generated Node #0,1: 25:[39, 5, 43] Operation: 44-1=43 Exploring Operation: 44-5=39, Resulting Numbers: [1, 39, 39] Generated Node #0,2: 25:[1, 39, 39] Operation: 44-5=39 Exploring Operation: 39-1=38, Resulting Numbers: [44, 5, 38] Generated Node #0,3: 25:[44, 5, 38] Operation: 39-1=38 Exploring Operation: 44-39=5, Resulting Numbers: [1, 5, 5] Generated Node #0,4: 25:[1, 5, 5] Operation: 44-39=5 Start Sub Search at level 1: Moving to Node #0,4 Current State: 25:[1, 5, 5], Operations: ['44-39=5'] Exploring Operation: 1+5=6, Resulting Numbers: [5, 6] Generated Node #0,4,0: 25:[5, 6] Operation: 1+5=6 Exploring Operation: 1*5=5, Resulting Numbers: [5, 5] Generated Node #0,4,1: 25:[5, 5] Operation: 1*5=5 Exploring Operation: 1*5=5, Resulting Numbers: [5, 5] Generated Node #0,4,2: 25:[5, 5] Operation: 1*5=5 Exploring Operation: 5/1=5, Resulting Numbers: [5, 5] Generated Node #0,4,3: 25:[5, 5] Operation: 5/1=5 Exploring Operation: 5/1=5, Resulting Numbers: [5, 5] Generated Node #0,4,4: 25:[5, 5] Operation: 5/1=5 Moving to Node #0,4,1 Current State: 25:[5, 5], Operations: ['44-39=5', '1*5=5'] Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,25 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[1, 39, 44, 5], Operations: [] Exploring Operation: 44-39=5, Resulting Numbers: [1, 5, 5] Generated Node #0,4: 25:[1, 5, 5] Operation: 44-39=5 Moving to Node #0,4 Current State: 25:[1, 5, 5], Operations: ['44-39=5'] Exploring Operation: 1*5=5, Resulting Numbers: [5, 5] Generated Node #0,4,1: 25:[5, 5] Operation: 1*5=5 Moving to Node #0,4,1 Current State: 25:[5, 5], Operations: ['44-39=5', '1*5=5'] Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 63, 99, 97, 98 ]
61
[ "99+97=196", "196/98=2", "63-2=61" ]
Current State: 61:[63, 99, 97, 98], Operations: [] Exploring Operation: 99+97=196, Resulting Numbers: [63, 98, 196] Generated Node #2: [63, 98, 196] from Operation: 99+97=196 Current State: 61:[63, 98, 196], Operations: ['99+97=196'] Exploring Operation: 196/98=2, Resulting Numbers: [63, 2] Generated Node #3: [63, 2] from Operation: 196/98=2 Current State: 61:[63, 2], Operations: ['99+97=196', '196/98=2'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[63, 99, 97, 98], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [63, 97, 1] Generated Node #0,0: 61:[63, 97, 1] Operation: 99-98=1 Exploring Operation: 99-97=2, Resulting Numbers: [63, 98, 2] Generated Node #0,1: 61:[63, 98, 2] Operation: 99-97=2 Exploring Operation: 98-63=35, Resulting Numbers: [99, 97, 35] Generated Node #0,2: 61:[99, 97, 35] Operation: 98-63=35 Exploring Operation: 99-63=36, Resulting Numbers: [97, 98, 36] Generated Node #0,3: 61:[97, 98, 36] Operation: 99-63=36 Moving to Node #0,0 Current State: 61:[63, 97, 1], Operations: ['99-98=1'] Exploring Operation: 97-1=96, Resulting Numbers: [63, 96] Generated Node #0,0,0: 61:[63, 96] Operation: 97-1=96 Exploring Operation: 63/1=63, Resulting Numbers: [97, 63] Generated Node #0,0,1: 61:[97, 63] Operation: 63/1=63 Exploring Operation: 63*1=63, Resulting Numbers: [97, 63] Generated Node #0,0,2: 61:[97, 63] Operation: 63*1=63 Exploring Operation: 63-1=62, Resulting Numbers: [97, 62] Generated Node #0,0,3: 61:[97, 62] Operation: 63-1=62 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[63, 96], Operations: ['99-98=1', '97-1=96'] Exploring Operation: 96-63=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 63+96=159, Resulting Numbers: [159] 159,61 unequal: No Solution Exploring Operation: 63*96=6048, Resulting Numbers: [6048] 6048,61 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: 61:[97, 62], Operations: ['99-98=1', '63-1=62'] Exploring Operation: 97*62=6014, Resulting Numbers: [6014] 6014,61 unequal: No Solution Exploring Operation: 97-62=35, Resulting Numbers: [35] 35,61 unequal: No Solution Exploring Operation: 97+62=159, Resulting Numbers: [159] 159,61 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: 61:[97, 63], Operations: ['99-98=1', '63/1=63'] Exploring Operation: 97*63=6111, Resulting Numbers: [6111] 6111,61 unequal: No Solution Exploring Operation: 97-63=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 97+63=160, Resulting Numbers: [160] 160,61 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: 61:[97, 63], Operations: ['99-98=1', '63*1=63'] Exploring Operation: 97*63=6111, Resulting Numbers: [6111] 6111,61 unequal: No Solution Exploring Operation: 97+63=160, Resulting Numbers: [160] 160,61 unequal: No Solution Exploring Operation: 97-63=34, Resulting Numbers: [34] 34,61 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: 61:[97, 98, 36], Operations: ['99-63=36'] Exploring Operation: 97-36=61, Resulting Numbers: [98, 61] Generated Node #0,3,0: 61:[98, 61] Operation: 97-36=61 Exploring Operation: 97+36=133, Resulting Numbers: [98, 133] Generated Node #0,3,1: 61:[98, 133] Operation: 97+36=133 Exploring Operation: 98-36=62, Resulting Numbers: [97, 62] Generated Node #0,3,2: 61:[97, 62] Operation: 98-36=62 Exploring Operation: 98-97=1, Resulting Numbers: [36, 1] Generated Node #0,3,3: 61:[36, 1] Operation: 98-97=1 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 61:[98, 61], Operations: ['99-63=36', '97-36=61'] Exploring Operation: 98*61=5978, Resulting Numbers: [5978] 5978,61 unequal: No Solution Exploring Operation: 98-61=37, Resulting Numbers: [37] 37,61 unequal: No Solution Exploring Operation: 98+61=159, Resulting Numbers: [159] 159,61 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: 61:[97, 62], Operations: ['99-63=36', '98-36=62'] Exploring Operation: 97+62=159, Resulting Numbers: [159] 159,61 unequal: No Solution Exploring Operation: 97*62=6014, Resulting Numbers: [6014] 6014,61 unequal: No Solution Exploring Operation: 97-62=35, Resulting Numbers: [35] 35,61 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: 61:[36, 1], Operations: ['99-63=36', '98-97=1'] Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,61 unequal: No Solution Exploring Operation: 36*1=36, Resulting Numbers: [36] 36,61 unequal: No Solution Exploring Operation: 36+1=37, Resulting Numbers: [37] 37,61 unequal: No Solution Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,61 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: 61:[98, 133], Operations: ['99-63=36', '97+36=133'] Exploring Operation: 98+133=231, Resulting Numbers: [231] 231,61 unequal: No Solution Exploring Operation: 133-98=35, Resulting Numbers: [35] 35,61 unequal: No Solution Exploring Operation: 98*133=13034, Resulting Numbers: [13034] 13034,61 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: 61:[63, 98, 2], Operations: ['99-97=2'] Exploring Operation: 63+2=65, Resulting Numbers: [98, 65] Generated Node #0,1,0: 61:[98, 65] Operation: 63+2=65 Exploring Operation: 98-2=96, Resulting Numbers: [63, 96] Generated Node #0,1,1: 61:[63, 96] Operation: 98-2=96 Exploring Operation: 63-2=61, Resulting Numbers: [98, 61] Generated Node #0,1,2: 61:[98, 61] Operation: 63-2=61 Exploring Operation: 98/2=49, Resulting Numbers: [63, 49] Generated Node #0,1,3: 61:[63, 49] Operation: 98/2=49 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 61:[63, 49], Operations: ['99-97=2', '98/2=49'] Exploring Operation: 63*49=3087, Resulting Numbers: [3087] 3087,61 unequal: No Solution Exploring Operation: 63+49=112, Resulting Numbers: [112] 112,61 unequal: No Solution Exploring Operation: 63-49=14, Resulting Numbers: [14] 14,61 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: 61:[63, 96], Operations: ['99-97=2', '98-2=96'] Exploring Operation: 96-63=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 63+96=159, Resulting Numbers: [159] 159,61 unequal: No Solution Exploring Operation: 63*96=6048, Resulting Numbers: [6048] 6048,61 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: 61:[98, 61], Operations: ['99-97=2', '63-2=61'] Exploring Operation: 98*61=5978, Resulting Numbers: [5978] 5978,61 unequal: No Solution Exploring Operation: 98+61=159, Resulting Numbers: [159] 159,61 unequal: No Solution Exploring Operation: 98-61=37, Resulting Numbers: [37] 37,61 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: 61:[98, 65], Operations: ['99-97=2', '63+2=65'] Exploring Operation: 98+65=163, Resulting Numbers: [163] 163,61 unequal: No Solution Exploring Operation: 98-65=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 98*65=6370, Resulting Numbers: [6370] 6370,61 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: 61:[99, 97, 35], Operations: ['98-63=35'] Exploring Operation: 99-97=2, Resulting Numbers: [35, 2] Generated Node #0,2,0: 61:[35, 2] Operation: 99-97=2 Exploring Operation: 99-35=64, Resulting Numbers: [97, 64] Generated Node #0,2,1: 61:[97, 64] Operation: 99-35=64 Exploring Operation: 97-35=62, Resulting Numbers: [99, 62] Generated Node #0,2,2: 61:[99, 62] Operation: 97-35=62 Exploring Operation: 99+35=134, Resulting Numbers: [97, 134] Generated Node #0,2,3: 61:[97, 134] Operation: 99+35=134 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 61:[97, 64], Operations: ['98-63=35', '99-35=64'] Exploring Operation: 97*64=6208, Resulting Numbers: [6208] 6208,61 unequal: No Solution Exploring Operation: 97+64=161, Resulting Numbers: [161] 161,61 unequal: No Solution Exploring Operation: 97-64=33, Resulting Numbers: [33] 33,61 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: 61:[99, 62], Operations: ['98-63=35', '97-35=62'] Exploring Operation: 99*62=6138, Resulting Numbers: [6138] 6138,61 unequal: No Solution Exploring Operation: 99-62=37, Resulting Numbers: [37] 37,61 unequal: No Solution Exploring Operation: 99+62=161, Resulting Numbers: [161] 161,61 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: 61:[35, 2], Operations: ['98-63=35', '99-97=2'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,61 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,61 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: 61:[97, 134], Operations: ['98-63=35', '99+35=134'] Exploring Operation: 97+134=231, Resulting Numbers: [231] 231,61 unequal: No Solution Exploring Operation: 97*134=12998, Resulting Numbers: [12998] 12998,61 unequal: No Solution Exploring Operation: 134-97=37, Resulting Numbers: [37] 37,61 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
[ 37, 8, 78, 5 ]
51
[ "78-8=70", "70/5=14", "37+14=51" ]
Current State: 51:[37, 8, 78, 5], Operations: [] Exploring Operation: 78-8=70, Resulting Numbers: [37, 5, 70] Generated Node #2: [37, 5, 70] from Operation: 78-8=70 Current State: 51:[37, 5, 70], Operations: ['78-8=70'] Exploring Operation: 70/5=14, Resulting Numbers: [37, 14] Generated Node #3: [37, 14] from Operation: 70/5=14 Current State: 51:[37, 14], Operations: ['78-8=70', '70/5=14'] Exploring Operation: 37+14=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[37, 8, 78, 5], Operations: [] Exploring Operation: 78-37=41, Resulting Numbers: [8, 5, 41] Generated Node #0,0: 51:[8, 5, 41] Operation: 78-37=41 Moving to Node #0,0 Current State: 51:[8, 5, 41], Operations: ['78-37=41'] Exploring Operation: 8+41=49, Resulting Numbers: [5, 49] Generated Node #0,0,0: 51:[5, 49] Operation: 8+41=49 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[5, 49], Operations: ['78-37=41', '8+41=49'] Exploring Operation: 5+49=54, Resulting Numbers: [54] 54,51 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
[ 45, 96, 90, 23 ]
71
[ "45*96=4320", "4320/90=48", "23+48=71" ]
Current State: 71:[45, 96, 90, 23], Operations: [] Exploring Operation: 45*96=4320, Resulting Numbers: [90, 23, 4320] Generated Node #2: [90, 23, 4320] from Operation: 45*96=4320 Current State: 71:[90, 23, 4320], Operations: ['45*96=4320'] Exploring Operation: 4320/90=48, Resulting Numbers: [23, 48] Generated Node #3: [23, 48] from Operation: 4320/90=48 Current State: 71:[23, 48], Operations: ['45*96=4320', '4320/90=48'] Exploring Operation: 23+48=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[45, 96, 90, 23], Operations: [] Exploring Operation: 45+23=68, Resulting Numbers: [96, 90, 68] Generated Node #0,0: 71:[96, 90, 68] Operation: 45+23=68 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[96, 90, 68], Operations: ['45+23=68'] Exploring Operation: 96-68=28, Resulting Numbers: [90, 28] Generated Node #0,0,0: 71:[90, 28] Operation: 96-68=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[90, 28], Operations: ['45+23=68', '96-68=28'] Exploring Operation: 90-28=62, Resulting Numbers: [62] 62,71 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 No solution found.
0
hs_1
sum_heuristic
[ 93, 27, 69, 33 ]
11
[ "93-27=66", "69-66=3", "33/3=11" ]
Current State: 11:[93, 27, 69, 33], Operations: [] Exploring Operation: 93-27=66, Resulting Numbers: [69, 33, 66] Generated Node #2: [69, 33, 66] from Operation: 93-27=66 Current State: 11:[69, 33, 66], Operations: ['93-27=66'] Exploring Operation: 69-66=3, Resulting Numbers: [33, 3] Generated Node #3: [33, 3] from Operation: 69-66=3 Current State: 11:[33, 3], Operations: ['93-27=66', '69-66=3'] Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[93, 27, 69, 33], Operations: [] Exploring Operation: 93-27=66, Resulting Numbers: [69, 33, 66] Generated Node #0,0: 11:[69, 33, 66] Operation: 93-27=66 Exploring Operation: 69-33=36, Resulting Numbers: [93, 27, 36] Generated Node #0,1: 11:[93, 27, 36] Operation: 69-33=36 Exploring Operation: 93-33=60, Resulting Numbers: [27, 69, 60] Generated Node #0,2: 11:[27, 69, 60] Operation: 93-33=60 Exploring Operation: 93-69=24, Resulting Numbers: [27, 33, 24] Generated Node #0,3: 11:[27, 33, 24] Operation: 93-69=24 Moving to Node #0,3 Current State: 11:[27, 33, 24], Operations: ['93-69=24'] Exploring Operation: 33-27=6, Resulting Numbers: [24, 6] Generated Node #0,3,0: 11:[24, 6] Operation: 33-27=6 Exploring Operation: 27-24=3, Resulting Numbers: [33, 3] Generated Node #0,3,1: 11:[33, 3] Operation: 27-24=3 Exploring Operation: 33-24=9, Resulting Numbers: [27, 9] Generated Node #0,3,2: 11:[27, 9] Operation: 33-24=9 Exploring Operation: 27+33=60, Resulting Numbers: [24, 60] Generated Node #0,3,3: 11:[24, 60] Operation: 27+33=60 Moving to Node #0,2 Current State: 11:[27, 69, 60], Operations: ['93-33=60'] Exploring Operation: 27+69=96, Resulting Numbers: [60, 96] Generated Node #0,2,0: 11:[60, 96] Operation: 27+69=96 Exploring Operation: 69-27=42, Resulting Numbers: [60, 42] Generated Node #0,2,1: 11:[60, 42] Operation: 69-27=42 Exploring Operation: 60-27=33, Resulting Numbers: [69, 33] Generated Node #0,2,2: 11:[69, 33] Operation: 60-27=33 Exploring Operation: 69-60=9, Resulting Numbers: [27, 9] Generated Node #0,2,3: 11:[27, 9] Operation: 69-60=9 Moving to Node #0,1 Current State: 11:[93, 27, 36], Operations: ['69-33=36'] Exploring Operation: 36-27=9, Resulting Numbers: [93, 9] Generated Node #0,1,0: 11:[93, 9] Operation: 36-27=9 Exploring Operation: 93-27=66, Resulting Numbers: [36, 66] Generated Node #0,1,1: 11:[36, 66] Operation: 93-27=66 Exploring Operation: 93+27=120, Resulting Numbers: [36, 120] Generated Node #0,1,2: 11:[36, 120] Operation: 93+27=120 Exploring Operation: 93-36=57, Resulting Numbers: [27, 57] Generated Node #0,1,3: 11:[27, 57] Operation: 93-36=57 Moving to Node #0,0 Current State: 11:[69, 33, 66], Operations: ['93-27=66'] Exploring Operation: 66-33=33, Resulting Numbers: [69, 33] Generated Node #0,0,0: 11:[69, 33] Operation: 66-33=33 Exploring Operation: 69-33=36, Resulting Numbers: [66, 36] Generated Node #0,0,1: 11:[66, 36] Operation: 69-33=36 Exploring Operation: 69-66=3, Resulting Numbers: [33, 3] Generated Node #0,0,2: 11:[33, 3] Operation: 69-66=3 Exploring Operation: 66/33=2, Resulting Numbers: [69, 2] Generated Node #0,0,3: 11:[69, 2] Operation: 66/33=2 Moving to Node #0,3,0 Current State: 11:[24, 6], Operations: ['93-69=24', '33-27=6'] Exploring Operation: 24+6=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 24*6=144, Resulting Numbers: [144] 144,11 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,11 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,11 unequal: No Solution Moving to Node #0,3,2 Current State: 11:[27, 9], Operations: ['93-69=24', '33-24=9'] Exploring Operation: 27+9=36, Resulting Numbers: [36] 36,11 unequal: No Solution Exploring Operation: 27*9=243, Resulting Numbers: [243] 243,11 unequal: No Solution Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,11 unequal: No Solution Moving to Node #0,2,3 Current State: 11:[27, 9], Operations: ['93-33=60', '69-60=9'] Exploring Operation: 27+9=36, Resulting Numbers: [36] 36,11 unequal: No Solution Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 27*9=243, Resulting Numbers: [243] 243,11 unequal: No Solution Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,11 unequal: No Solution Moving to Node #0,3,1 Current State: 11:[33, 3], Operations: ['93-69=24', '27-24=3'] Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,11 unequal: No Solution Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,11 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[93, 27, 69, 33], Operations: [] Exploring Operation: 93-69=24, Resulting Numbers: [27, 33, 24] Generated Node #0,3: 11:[27, 33, 24] Operation: 93-69=24 Moving to Node #0,3 Current State: 11:[27, 33, 24], Operations: ['93-69=24'] Exploring Operation: 27-24=3, Resulting Numbers: [33, 3] Generated Node #0,3,1: 11:[33, 3] Operation: 27-24=3 Moving to Node #0,3,1 Current State: 11:[33, 3], Operations: ['93-69=24', '27-24=3'] Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
0.966146
hs_4
mult_heuristic
[ 64, 98, 7, 63 ]
36
[ "98-64=34", "7+63=70", "70-34=36" ]
Current State: 36:[64, 98, 7, 63], Operations: [] Exploring Operation: 98-64=34, Resulting Numbers: [7, 63, 34] Generated Node #2: [7, 63, 34] from Operation: 98-64=34 Current State: 36:[7, 63, 34], Operations: ['98-64=34'] Exploring Operation: 7+63=70, Resulting Numbers: [34, 70] Generated Node #3: [34, 70] from Operation: 7+63=70 Current State: 36:[34, 70], Operations: ['98-64=34', '7+63=70'] Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[64, 98, 7, 63], Operations: [] Exploring Operation: 98-63=35, Resulting Numbers: [64, 7, 35] Generated Node #0,0: 36:[64, 7, 35] Operation: 98-63=35 Exploring Operation: 98-64=34, Resulting Numbers: [7, 63, 34] Generated Node #0,1: 36:[7, 63, 34] Operation: 98-64=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[64, 7, 35], Operations: ['98-63=35'] Exploring Operation: 64-7=57, Resulting Numbers: [35, 57] Generated Node #0,0,0: 36:[35, 57] Operation: 64-7=57 Exploring Operation: 64-35=29, Resulting Numbers: [7, 29] Generated Node #0,0,1: 36:[7, 29] Operation: 64-35=29 Moving to Node #0,0,1 Current State: 36:[7, 29], Operations: ['98-63=35', '64-35=29'] Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,36 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[64, 98, 7, 63], Operations: [] Exploring Operation: 98-63=35, Resulting Numbers: [64, 7, 35] Generated Node #0,0: 36:[64, 7, 35] Operation: 98-63=35 Moving to Node #0,0 Current State: 36:[64, 7, 35], Operations: ['98-63=35'] Exploring Operation: 64-35=29, Resulting Numbers: [7, 29] Generated Node #0,0,1: 36:[7, 29] Operation: 64-35=29 Moving to Node #0,0,1 Current State: 36:[7, 29], Operations: ['98-63=35', '64-35=29'] Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 68, 4, 4, 30 ]
52
[ "68/4=17", "30-17=13", "4*13=52" ]
Current State: 52:[68, 4, 4, 30], Operations: [] Exploring Operation: 68/4=17, Resulting Numbers: [30, 17] Generated Node #2: [30, 17] from Operation: 68/4=17 Current State: 52:[30, 17], Operations: ['68/4=17'] Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,52 equal: Goal Reached Exploring Operation: 4*13=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[68, 4, 4, 30], Operations: [] Exploring Operation: 68/4=17, Resulting Numbers: [4, 30, 17] Generated Node #0,0: 52:[4, 30, 17] Operation: 68/4=17 Exploring Operation: 68/4=17, Resulting Numbers: [4, 30, 17] Generated Node #0,1: 52:[4, 30, 17] Operation: 68/4=17 Exploring Operation: 68-30=38, Resulting Numbers: [4, 4, 38] Generated Node #0,2: 52:[4, 4, 38] Operation: 68-30=38 Moving to Node #0,0 Current State: 52:[4, 30, 17], Operations: ['68/4=17'] Exploring Operation: 30-17=13, Resulting Numbers: [4, 13] Generated Node #0,0,0: 52:[4, 13] Operation: 30-17=13 Exploring Operation: 17-4=13, Resulting Numbers: [30, 13] Generated Node #0,0,1: 52:[30, 13] Operation: 17-4=13 Exploring Operation: 30-4=26, Resulting Numbers: [17, 26] Generated Node #0,0,2: 52:[17, 26] Operation: 30-4=26 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[4, 13], Operations: ['68/4=17', '30-17=13'] Exploring Operation: 4+13=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 4*13=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[68, 4, 4, 30], Operations: [] Exploring Operation: 68/4=17, Resulting Numbers: [4, 30, 17] Generated Node #0,0: 52:[4, 30, 17] Operation: 68/4=17 Moving to Node #0,0 Current State: 52:[4, 30, 17], Operations: ['68/4=17'] Exploring Operation: 30-17=13, Resulting Numbers: [4, 13] Generated Node #0,0,0: 52:[4, 13] Operation: 30-17=13 Moving to Node #0,0,0 Current State: 52:[4, 13], Operations: ['68/4=17', '30-17=13'] Exploring Operation: 4*13=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 62, 48, 72, 40 ]
33
[ "62-40=22", "72*22=1584", "1584/48=33" ]
Current State: 33:[62, 48, 72, 40], Operations: [] Exploring Operation: 62-40=22, Resulting Numbers: [48, 72, 22] Generated Node #2: [48, 72, 22] from Operation: 62-40=22 Current State: 33:[48, 72, 22], Operations: ['62-40=22'] Exploring Operation: 72*22=1584, Resulting Numbers: [48, 1584] Generated Node #3: [48, 1584] from Operation: 72*22=1584 Current State: 33:[48, 1584], Operations: ['62-40=22', '72*22=1584'] Exploring Operation: 1584/48=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[62, 48, 72, 40], Operations: [] Exploring Operation: 72-62=10, Resulting Numbers: [48, 40, 10] Generated Node #0,0: 33:[48, 40, 10] Operation: 72-62=10 Exploring Operation: 72-40=32, Resulting Numbers: [62, 48, 32] Generated Node #0,1: 33:[62, 48, 32] Operation: 72-40=32 Exploring Operation: 72-48=24, Resulting Numbers: [62, 40, 24] Generated Node #0,2: 33:[62, 40, 24] Operation: 72-48=24 Moving to Node #0,0 Current State: 33:[48, 40, 10], Operations: ['72-62=10'] Exploring Operation: 48-40=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 33:[10, 8] Operation: 48-40=8 Exploring Operation: 48-10=38, Resulting Numbers: [40, 38] Generated Node #0,0,1: 33:[40, 38] Operation: 48-10=38 Exploring Operation: 40/10=4, Resulting Numbers: [48, 4] Generated Node #0,0,2: 33:[48, 4] Operation: 40/10=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[10, 8], Operations: ['72-62=10', '48-40=8'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,33 unequal: No Solution Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,33 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: 33:[40, 38], Operations: ['72-62=10', '48-10=38'] Exploring Operation: 40*38=1520, Resulting Numbers: [1520] 1520,33 unequal: No Solution Exploring Operation: 40-38=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 40+38=78, Resulting Numbers: [78] 78,33 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: 33:[48, 4], Operations: ['72-62=10', '40/10=4'] Exploring Operation: 48+4=52, Resulting Numbers: [52] 52,33 unequal: No Solution Exploring Operation: 48/4=12, Resulting Numbers: [12] 12,33 unequal: No Solution Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,33 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: 33:[62, 48, 32], Operations: ['72-40=32'] Exploring Operation: 48-32=16, Resulting Numbers: [62, 16] Generated Node #0,1,0: 33:[62, 16] Operation: 48-32=16 Exploring Operation: 62-48=14, Resulting Numbers: [32, 14] Generated Node #0,1,1: 33:[32, 14] Operation: 62-48=14 Exploring Operation: 62-32=30, Resulting Numbers: [48, 30] Generated Node #0,1,2: 33:[48, 30] Operation: 62-32=30 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 33:[32, 14], Operations: ['72-40=32', '62-48=14'] Exploring Operation: 32*14=448, Resulting Numbers: [448] 448,33 unequal: No Solution Exploring Operation: 32+14=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,33 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: 33:[48, 30], Operations: ['72-40=32', '62-32=30'] Exploring Operation: 48+30=78, Resulting Numbers: [78] 78,33 unequal: No Solution Exploring Operation: 48*30=1440, Resulting Numbers: [1440] 1440,33 unequal: No Solution Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,33 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: 33:[62, 16], Operations: ['72-40=32', '48-32=16'] Exploring Operation: 62+16=78, Resulting Numbers: [78] 78,33 unequal: No Solution Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 62*16=992, Resulting Numbers: [992] 992,33 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: 33:[62, 40, 24], Operations: ['72-48=24'] Exploring Operation: 62-24=38, Resulting Numbers: [40, 38] Generated Node #0,2,0: 33:[40, 38] Operation: 62-24=38 Exploring Operation: 40-24=16, Resulting Numbers: [62, 16] Generated Node #0,2,1: 33:[62, 16] Operation: 40-24=16 Exploring Operation: 62-40=22, Resulting Numbers: [24, 22] Generated Node #0,2,2: 33:[24, 22] Operation: 62-40=22 Moving to Node #0,2,0 Current State: 33:[40, 38], Operations: ['72-48=24', '62-24=38'] Exploring Operation: 40+38=78, Resulting Numbers: [78] 78,33 unequal: No Solution Exploring Operation: 40*38=1520, Resulting Numbers: [1520] 1520,33 unequal: No Solution Exploring Operation: 40-38=2, Resulting Numbers: [2] 2,33 unequal: No Solution Moving to Node #0,2,2 Current State: 33:[24, 22], Operations: ['72-48=24', '62-40=22'] Exploring Operation: 24*22=528, Resulting Numbers: [528] 528,33 unequal: No Solution Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,33 unequal: No Solution Moving to Node #0,2,1 Current State: 33:[62, 16], Operations: ['72-48=24', '40-24=16'] Exploring Operation: 62*16=992, Resulting Numbers: [992] 992,33 unequal: No Solution Exploring Operation: 62+16=78, Resulting Numbers: [78] 78,33 unequal: No Solution Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,33 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 6, 4, 47, 44 ]
39
[ "4+44=48", "48/6=8", "47-8=39" ]
Current State: 39:[6, 4, 47, 44], Operations: [] Exploring Operation: 4+44=48, Resulting Numbers: [6, 47, 48] Generated Node #2: [6, 47, 48] from Operation: 4+44=48 Current State: 39:[6, 47, 48], Operations: ['4+44=48'] Exploring Operation: 48/6=8, Resulting Numbers: [47, 8] Generated Node #3: [47, 8] from Operation: 48/6=8 Current State: 39:[47, 8], Operations: ['4+44=48', '48/6=8'] Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[6, 4, 47, 44], Operations: [] Exploring Operation: 47-44=3, Resulting Numbers: [6, 4, 3] Generated Node #0,0: 39:[6, 4, 3] Operation: 47-44=3 Exploring Operation: 47-6=41, Resulting Numbers: [4, 44, 41] Generated Node #0,1: 39:[4, 44, 41] Operation: 47-6=41 Exploring Operation: 44-6=38, Resulting Numbers: [4, 47, 38] Generated Node #0,2: 39:[4, 47, 38] Operation: 44-6=38 Exploring Operation: 47-4=43, Resulting Numbers: [6, 44, 43] Generated Node #0,3: 39:[6, 44, 43] Operation: 47-4=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[6, 4, 3], Operations: ['47-44=3'] Exploring Operation: 6-3=3, Resulting Numbers: [4, 3] Generated Node #0,0,0: 39:[4, 3] Operation: 6-3=3 Exploring Operation: 6-4=2, Resulting Numbers: [3, 2] Generated Node #0,0,1: 39:[3, 2] Operation: 6-4=2 Exploring Operation: 6+4=10, Resulting Numbers: [3, 10] Generated Node #0,0,2: 39:[3, 10] Operation: 6+4=10 Exploring Operation: 6/3=2, Resulting Numbers: [4, 2] Generated Node #0,0,3: 39:[4, 2] Operation: 6/3=2 Moving to Node #0,0,0 Current State: 39:[4, 3], Operations: ['47-44=3', '6-3=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[3, 2], Operations: ['47-44=3', '6-4=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[4, 2], Operations: ['47-44=3', '6/3=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,39 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[3, 10], Operations: ['47-44=3', '6+4=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,39 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,39 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:[4, 44, 41], Operations: ['47-6=41'] Exploring Operation: 44-41=3, Resulting Numbers: [4, 3] Generated Node #0,1,0: 39:[4, 3] Operation: 44-41=3 Exploring Operation: 44/4=11, Resulting Numbers: [41, 11] Generated Node #0,1,1: 39:[41, 11] Operation: 44/4=11 Exploring Operation: 41-4=37, Resulting Numbers: [44, 37] Generated Node #0,1,2: 39:[44, 37] Operation: 41-4=37 Exploring Operation: 44-4=40, Resulting Numbers: [41, 40] Generated Node #0,1,3: 39:[41, 40] Operation: 44-4=40 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 39:[4, 3], Operations: ['47-6=41', '44-41=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,39 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 #0,1,3 Current State: 39:[41, 40], Operations: ['47-6=41', '44-4=40'] Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,39 unequal: No Solution Exploring Operation: 41*40=1640, Resulting Numbers: [1640] 1640,39 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 #0,1,1 Current State: 39:[41, 11], Operations: ['47-6=41', '44/4=11'] Exploring Operation: 41+11=52, Resulting Numbers: [52] 52,39 unequal: No Solution Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,39 unequal: No Solution Exploring Operation: 41*11=451, Resulting Numbers: [451] 451,39 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 #0,1,2 Current State: 39:[44, 37], Operations: ['47-6=41', '41-4=37'] Exploring Operation: 44*37=1628, Resulting Numbers: [1628] 1628,39 unequal: No Solution Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,39 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 #0,2 Current State: 39:[4, 47, 38], Operations: ['44-6=38'] Exploring Operation: 4+47=51, Resulting Numbers: [38, 51] Generated Node #0,2,0: 39:[38, 51] Operation: 4+47=51 Exploring Operation: 47-38=9, Resulting Numbers: [4, 9] Generated Node #0,2,1: 39:[4, 9] Operation: 47-38=9 Exploring Operation: 4+38=42, Resulting Numbers: [47, 42] Generated Node #0,2,2: 39:[47, 42] Operation: 4+38=42 Exploring Operation: 47-4=43, Resulting Numbers: [38, 43] Generated Node #0,2,3: 39:[38, 43] Operation: 47-4=43 Moving to Node #0,2,1 Current State: 39:[4, 9], Operations: ['44-6=38', '47-38=9'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,39 unequal: No Solution Moving to Node #0,2,3 Current State: 39:[38, 43], Operations: ['44-6=38', '47-4=43'] Exploring Operation: 43-38=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 38+43=81, Resulting Numbers: [81] 81,39 unequal: No Solution Exploring Operation: 38*43=1634, Resulting Numbers: [1634] 1634,39 unequal: No Solution Moving to Node #0,2,2 Current State: 39:[47, 42], Operations: ['44-6=38', '4+38=42'] Exploring Operation: 47*42=1974, Resulting Numbers: [1974] 1974,39 unequal: No Solution Exploring Operation: 47-42=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 47+42=89, Resulting Numbers: [89] 89,39 unequal: No Solution Moving to Node #0,2,0 Current State: 39:[38, 51], Operations: ['44-6=38', '4+47=51'] Exploring Operation: 38*51=1938, Resulting Numbers: [1938] 1938,39 unequal: No Solution Exploring Operation: 51-38=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 38+51=89, Resulting Numbers: [89] 89,39 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 #0,3 Current State: 39:[6, 44, 43], Operations: ['47-4=43'] Exploring Operation: 44-6=38, Resulting Numbers: [43, 38] Generated Node #0,3,0: 39:[43, 38] Operation: 44-6=38 Exploring Operation: 6+44=50, Resulting Numbers: [43, 50] Generated Node #0,3,1: 39:[43, 50] Operation: 6+44=50 Exploring Operation: 44-43=1, Resulting Numbers: [6, 1] Generated Node #0,3,2: 39:[6, 1] Operation: 44-43=1 Exploring Operation: 43-6=37, Resulting Numbers: [44, 37] Generated Node #0,3,3: 39:[44, 37] Operation: 43-6=37 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 39:[43, 38], Operations: ['47-4=43', '44-6=38'] Exploring Operation: 43-38=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 43+38=81, Resulting Numbers: [81] 81,39 unequal: No Solution Exploring Operation: 43*38=1634, Resulting Numbers: [1634] 1634,39 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 #0,3,2 Current State: 39:[6, 1], Operations: ['47-4=43', '44-43=1'] Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,39 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 #0,3,3 Current State: 39:[44, 37], Operations: ['47-4=43', '43-6=37'] Exploring Operation: 44*37=1628, Resulting Numbers: [1628] 1628,39 unequal: No Solution Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,39 unequal: No Solution Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,39 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 #0,3,1 Current State: 39:[43, 50], Operations: ['47-4=43', '6+44=50'] Exploring Operation: 50-43=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 43+50=93, Resulting Numbers: [93] 93,39 unequal: No Solution Exploring Operation: 43*50=2150, Resulting Numbers: [2150] 2150,39 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 No solution found.
0
hs_4
mult_heuristic
[ 7, 55, 2, 48 ]
27
[ "48-7=41", "2*41=82", "82-55=27" ]
Current State: 27:[7, 55, 2, 48], Operations: [] Exploring Operation: 48-7=41, Resulting Numbers: [55, 2, 41] Generated Node #2: [55, 2, 41] from Operation: 48-7=41 Current State: 27:[55, 2, 41], Operations: ['48-7=41'] Exploring Operation: 2*41=82, Resulting Numbers: [55, 82] Generated Node #3: [55, 82] from Operation: 2*41=82 Current State: 27:[55, 82], Operations: ['48-7=41', '2*41=82'] Exploring Operation: 82-55=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[7, 55, 2, 48], Operations: [] Exploring Operation: 48/2=24, Resulting Numbers: [7, 55, 24] Generated Node #0,0: 27:[7, 55, 24] Operation: 48/2=24 Exploring Operation: 55-48=7, Resulting Numbers: [7, 2, 7] Generated Node #0,1: 27:[7, 2, 7] Operation: 55-48=7 Exploring Operation: 48-7=41, Resulting Numbers: [55, 2, 41] Generated Node #0,2: 27:[55, 2, 41] Operation: 48-7=41 Exploring Operation: 7+2=9, Resulting Numbers: [55, 48, 9] Generated Node #0,3: 27:[55, 48, 9] Operation: 7+2=9 Exploring Operation: 55-7=48, Resulting Numbers: [2, 48, 48] Generated Node #0,4: 27:[2, 48, 48] Operation: 55-7=48 Moving to Node #0,1 Current State: 27:[7, 2, 7], Operations: ['55-48=7'] Exploring Operation: 7-7=0, Resulting Numbers: [2, 0] Generated Node #0,1,0: 27:[2, 0] Operation: 7-7=0 Exploring Operation: 7+2=9, Resulting Numbers: [7, 9] Generated Node #0,1,1: 27:[7, 9] Operation: 7+2=9 Exploring Operation: 7/7=1, Resulting Numbers: [2, 1] Generated Node #0,1,2: 27:[2, 1] Operation: 7/7=1 Exploring Operation: 7-2=5, Resulting Numbers: [7, 5] Generated Node #0,1,3: 27:[7, 5] Operation: 7-2=5 Exploring Operation: 2+7=9, Resulting Numbers: [7, 9] Generated Node #0,1,4: 27:[7, 9] Operation: 2+7=9 Moving to Node #0,0 Current State: 27:[7, 55, 24], Operations: ['48/2=24'] Exploring Operation: 7+55=62, Resulting Numbers: [24, 62] Generated Node #0,0,0: 27:[24, 62] Operation: 7+55=62 Exploring Operation: 24-7=17, Resulting Numbers: [55, 17] Generated Node #0,0,1: 27:[55, 17] Operation: 24-7=17 Exploring Operation: 7+24=31, Resulting Numbers: [55, 31] Generated Node #0,0,2: 27:[55, 31] Operation: 7+24=31 Exploring Operation: 55-7=48, Resulting Numbers: [24, 48] Generated Node #0,0,3: 27:[24, 48] Operation: 55-7=48 Exploring Operation: 55-24=31, Resulting Numbers: [7, 31] Generated Node #0,0,4: 27:[7, 31] Operation: 55-24=31 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 27:[7, 31], Operations: ['48/2=24', '55-24=31'] Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,27 unequal: No Solution Exploring Operation: 7*31=217, Resulting Numbers: [217] 217,27 unequal: No Solution Exploring Operation: 7+31=38, Resulting Numbers: [38] 38,27 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: 27:[24, 48], Operations: ['48/2=24', '55-7=48'] Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,27 unequal: No Solution Exploring Operation: 24*48=1152, Resulting Numbers: [1152] 1152,27 unequal: No Solution Exploring Operation: 24+48=72, Resulting Numbers: [72] 72,27 unequal: No Solution Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,27 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: 27:[55, 31], Operations: ['48/2=24', '7+24=31'] Exploring Operation: 55*31=1705, Resulting Numbers: [1705] 1705,27 unequal: No Solution Exploring Operation: 55+31=86, Resulting Numbers: [86] 86,27 unequal: No Solution Exploring Operation: 55-31=24, Resulting Numbers: [24] 24,27 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: 27:[55, 17], Operations: ['48/2=24', '24-7=17'] Exploring Operation: 55+17=72, Resulting Numbers: [72] 72,27 unequal: No Solution Exploring Operation: 55-17=38, Resulting Numbers: [38] 38,27 unequal: No Solution Exploring Operation: 55*17=935, Resulting Numbers: [935] 935,27 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: 27:[24, 62], Operations: ['48/2=24', '7+55=62'] Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,27 unequal: No Solution Exploring Operation: 24*62=1488, Resulting Numbers: [1488] 1488,27 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,27 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: 27:[55, 2, 41], Operations: ['48-7=41'] Exploring Operation: 55-2=53, Resulting Numbers: [41, 53] Generated Node #0,2,0: 27:[41, 53] Operation: 55-2=53 Exploring Operation: 41-2=39, Resulting Numbers: [55, 39] Generated Node #0,2,1: 27:[55, 39] Operation: 41-2=39 Exploring Operation: 2+41=43, Resulting Numbers: [55, 43] Generated Node #0,2,2: 27:[55, 43] Operation: 2+41=43 Exploring Operation: 55-41=14, Resulting Numbers: [2, 14] Generated Node #0,2,3: 27:[2, 14] Operation: 55-41=14 Exploring Operation: 55+2=57, Resulting Numbers: [41, 57] Generated Node #0,2,4: 27:[41, 57] Operation: 55+2=57 Moving to Node #0,4 Current State: 27:[2, 48, 48], Operations: ['55-7=48'] Exploring Operation: 48/2=24, Resulting Numbers: [48, 24] Generated Node #0,4,0: 27:[48, 24] Operation: 48/2=24 Exploring Operation: 48-2=46, Resulting Numbers: [48, 46] Generated Node #0,4,1: 27:[48, 46] Operation: 48-2=46 Exploring Operation: 48/2=24, Resulting Numbers: [48, 24] Generated Node #0,4,2: 27:[48, 24] Operation: 48/2=24 Exploring Operation: 48/48=1, Resulting Numbers: [2, 1] Generated Node #0,4,3: 27:[2, 1] Operation: 48/48=1 Exploring Operation: 48-48=0, Resulting Numbers: [2, 0] Generated Node #0,4,4: 27:[2, 0] Operation: 48-48=0 Moving to Node #0,3 Current State: 27:[55, 48, 9], Operations: ['7+2=9'] Exploring Operation: 55+9=64, Resulting Numbers: [48, 64] Generated Node #0,3,0: 27:[48, 64] Operation: 55+9=64 Exploring Operation: 48+9=57, Resulting Numbers: [55, 57] Generated Node #0,3,1: 27:[55, 57] Operation: 48+9=57 Exploring Operation: 55-48=7, Resulting Numbers: [9, 7] Generated Node #0,3,2: 27:[9, 7] Operation: 55-48=7 Exploring Operation: 55-9=46, Resulting Numbers: [48, 46] Generated Node #0,3,3: 27:[48, 46] Operation: 55-9=46 Exploring Operation: 48-9=39, Resulting Numbers: [55, 39] Generated Node #0,3,4: 27:[55, 39] Operation: 48-9=39 Moving to Node #0,1,1 Current State: 27:[7, 9], Operations: ['55-48=7', '7+2=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,27 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,27 unequal: No Solution Moving to Node #0,1,4 Current State: 27:[7, 9], Operations: ['55-48=7', '2+7=9'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,27 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,27 unequal: No Solution Moving to Node #0,3,2 Current State: 27:[9, 7], Operations: ['7+2=9', '55-48=7'] Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,27 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,27 unequal: No Solution Moving to Node #0,1,2 Current State: 27:[2, 1], Operations: ['55-48=7', '7/7=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,27 unequal: No Solution Moving to Node #0,4,3 Current State: 27:[2, 1], Operations: ['55-7=48', '48/48=1'] Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,27 unequal: No Solution Moving to Node #0,4,4 Current State: 27:[2, 0], Operations: ['55-7=48', '48-48=0'] Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,27 unequal: No Solution Moving to Node #0,1,3 Current State: 27:[7, 5], Operations: ['55-48=7', '7-2=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,27 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,27 unequal: No Solution Moving to Node #0,1,0 Current State: 27:[2, 0], Operations: ['55-48=7', '7-7=0'] Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,27 unequal: No Solution Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,27 unequal: No Solution Moving to Node #0,2,3 Current State: 27:[2, 14], Operations: ['48-7=41', '55-41=14'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,27 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,27 unequal: No Solution Moving to Node #0,4,2 Current State: 27:[48, 24], Operations: ['55-7=48', '48/2=24'] Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,27 unequal: No Solution Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 48+24=72, Resulting Numbers: [72] 72,27 unequal: No Solution Exploring Operation: 48*24=1152, Resulting Numbers: [1152] 1152,27 unequal: No Solution Moving to Node #0,4,0 Current State: 27:[48, 24], Operations: ['55-7=48', '48/2=24'] Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,27 unequal: No Solution Exploring Operation: 48*24=1152, Resulting Numbers: [1152] 1152,27 unequal: No Solution Exploring Operation: 48+24=72, Resulting Numbers: [72] 72,27 unequal: No Solution Moving to Node #0,2,1 Current State: 27:[55, 39], Operations: ['48-7=41', '41-2=39'] Exploring Operation: 55+39=94, Resulting Numbers: [94] 94,27 unequal: No Solution Exploring Operation: 55-39=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 55*39=2145, Resulting Numbers: [2145] 2145,27 unequal: No Solution Moving to Node #0,3,4 Current State: 27:[55, 39], Operations: ['7+2=9', '48-9=39'] Exploring Operation: 55+39=94, Resulting Numbers: [94] 94,27 unequal: No Solution Exploring Operation: 55*39=2145, Resulting Numbers: [2145] 2145,27 unequal: No Solution Exploring Operation: 55-39=16, Resulting Numbers: [16] 16,27 unequal: No Solution Moving to Node #0,4,1 Current State: 27:[48, 46], Operations: ['55-7=48', '48-2=46'] Exploring Operation: 48+46=94, Resulting Numbers: [94] 94,27 unequal: No Solution Exploring Operation: 48-46=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 48*46=2208, Resulting Numbers: [2208] 2208,27 unequal: No Solution Moving to Node #0,3,3 Current State: 27:[48, 46], Operations: ['7+2=9', '55-9=46'] Exploring Operation: 48*46=2208, Resulting Numbers: [2208] 2208,27 unequal: No Solution Exploring Operation: 48-46=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 48+46=94, Resulting Numbers: [94] 94,27 unequal: No Solution Moving to Node #0,2,0 Current State: 27:[41, 53], Operations: ['48-7=41', '55-2=53'] Exploring Operation: 41+53=94, Resulting Numbers: [94] 94,27 unequal: No Solution Exploring Operation: 41*53=2173, Resulting Numbers: [2173] 2173,27 unequal: No Solution Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,27 unequal: No Solution Moving to Node #0,2,2 Current State: 27:[55, 43], Operations: ['48-7=41', '2+41=43'] Exploring Operation: 55*43=2365, Resulting Numbers: [2365] 2365,27 unequal: No Solution Exploring Operation: 55+43=98, Resulting Numbers: [98] 98,27 unequal: No Solution Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,27 unequal: No Solution Moving to Node #0,2,4 Current State: 27:[41, 57], Operations: ['48-7=41', '55+2=57'] Exploring Operation: 41*57=2337, Resulting Numbers: [2337] 2337,27 unequal: No Solution Exploring Operation: 41+57=98, Resulting Numbers: [98] 98,27 unequal: No Solution Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,27 unequal: No Solution Moving to Node #0,3,0 Current State: 27:[48, 64], Operations: ['7+2=9', '55+9=64'] Exploring Operation: 48*64=3072, Resulting Numbers: [3072] 3072,27 unequal: No Solution Exploring Operation: 48+64=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 64-48=16, Resulting Numbers: [16] 16,27 unequal: No Solution Moving to Node #0,3,1 Current State: 27:[55, 57], Operations: ['7+2=9', '48+9=57'] Exploring Operation: 57-55=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 55*57=3135, Resulting Numbers: [3135] 3135,27 unequal: No Solution Exploring Operation: 55+57=112, Resulting Numbers: [112] 112,27 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 58, 61, 37, 22 ]
60
[ "58+61=119", "37+22=59", "119-59=60" ]
Current State: 60:[58, 61, 37, 22], Operations: [] Exploring Operation: 58+61=119, Resulting Numbers: [37, 22, 119] Generated Node #2: [37, 22, 119] from Operation: 58+61=119 Current State: 60:[37, 22, 119], Operations: ['58+61=119'] Exploring Operation: 37+22=59, Resulting Numbers: [119, 59] Generated Node #3: [119, 59] from Operation: 37+22=59 Current State: 60:[119, 59], Operations: ['58+61=119', '37+22=59'] Exploring Operation: 119-59=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[58, 61, 37, 22], Operations: [] Exploring Operation: 37-22=15, Resulting Numbers: [58, 61, 15] Generated Node #0,0: 60:[58, 61, 15] Operation: 37-22=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[58, 61, 15], Operations: ['37-22=15'] Exploring Operation: 61-58=3, Resulting Numbers: [15, 3] Generated Node #0,0,0: 60:[15, 3] Operation: 61-58=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[15, 3], Operations: ['37-22=15', '61-58=3'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,60 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
sum_heuristic
[ 63, 12, 21, 7 ]
59
[ "12*7=84", "84/21=4", "63-4=59" ]
Current State: 59:[63, 12, 21, 7], Operations: [] Exploring Operation: 12*7=84, Resulting Numbers: [63, 21, 84] Generated Node #2: [63, 21, 84] from Operation: 12*7=84 Current State: 59:[63, 21, 84], Operations: ['12*7=84'] Exploring Operation: 84/21=4, Resulting Numbers: [63, 4] Generated Node #3: [63, 4] from Operation: 84/21=4 Current State: 59:[63, 4], Operations: ['12*7=84', '84/21=4'] Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[63, 12, 21, 7], Operations: [] Exploring Operation: 63-7=56, Resulting Numbers: [12, 21, 56] Generated Node #0,0: 59:[12, 21, 56] Operation: 63-7=56 Exploring Operation: 21+7=28, Resulting Numbers: [63, 12, 28] Generated Node #0,1: 59:[63, 12, 28] Operation: 21+7=28 Exploring Operation: 12*7=84, Resulting Numbers: [63, 21, 84] Generated Node #0,2: 59:[63, 21, 84] Operation: 12*7=84 Exploring Operation: 12+21=33, Resulting Numbers: [63, 7, 33] Generated Node #0,3: 59:[63, 7, 33] Operation: 12+21=33 Exploring Operation: 12+7=19, Resulting Numbers: [63, 21, 19] Generated Node #0,4: 59:[63, 21, 19] Operation: 12+7=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[63, 21, 84], Operations: ['12*7=84'] Exploring Operation: 21+84=105, Resulting Numbers: [63, 105] Generated Node #0,2,0: 59:[63, 105] Operation: 21+84=105 Exploring Operation: 84-21=63, Resulting Numbers: [63, 63] Generated Node #0,2,1: 59:[63, 63] Operation: 84-21=63 Exploring Operation: 84/21=4, Resulting Numbers: [63, 4] Generated Node #0,2,2: 59:[63, 4] Operation: 84/21=4 Exploring Operation: 63-21=42, Resulting Numbers: [84, 42] Generated Node #0,2,3: 59:[84, 42] Operation: 63-21=42 Exploring Operation: 63+21=84, Resulting Numbers: [84, 84] Generated Node #0,2,4: 59:[84, 84] Operation: 63+21=84 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 59:[63, 63], Operations: ['12*7=84', '84-21=63'] Exploring Operation: 63+63=126, Resulting Numbers: [126] 126,59 unequal: No Solution Exploring Operation: 63/63=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 63*63=3969, Resulting Numbers: [3969] 3969,59 unequal: No Solution Exploring Operation: 63-63=0, Resulting Numbers: [0] 0,59 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: 59:[84, 42], Operations: ['12*7=84', '63-21=42'] Exploring Operation: 84-42=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 84*42=3528, Resulting Numbers: [3528] 3528,59 unequal: No Solution Exploring Operation: 84/42=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 84+42=126, Resulting Numbers: [126] 126,59 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: 59:[63, 105], Operations: ['12*7=84', '21+84=105'] Exploring Operation: 63+105=168, Resulting Numbers: [168] 168,59 unequal: No Solution Exploring Operation: 63*105=6615, Resulting Numbers: [6615] 6615,59 unequal: No Solution Exploring Operation: 105-63=42, Resulting Numbers: [42] 42,59 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: 59:[84, 84], Operations: ['12*7=84', '63+21=84'] Exploring Operation: 84+84=168, Resulting Numbers: [168] 168,59 unequal: No Solution Exploring Operation: 84*84=7056, Resulting Numbers: [7056] 7056,59 unequal: No Solution Exploring Operation: 84/84=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 84-84=0, Resulting Numbers: [0] 0,59 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: 59:[63, 4], Operations: ['12*7=84', '84/21=4'] Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,59 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[63, 12, 21, 7], Operations: [] Exploring Operation: 12*7=84, Resulting Numbers: [63, 21, 84] Generated Node #0,2: 59:[63, 21, 84] Operation: 12*7=84 Moving to Node #0,2 Current State: 59:[63, 21, 84], Operations: ['12*7=84'] Exploring Operation: 84/21=4, Resulting Numbers: [63, 4] Generated Node #0,2,2: 59:[63, 4] Operation: 84/21=4 Moving to Node #0,2,2 Current State: 59:[63, 4], Operations: ['12*7=84', '84/21=4'] Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_5
sum_heuristic
[ 15, 80, 40, 80 ]
54
[ "15+40=55", "80/80=1", "55-1=54" ]
Current State: 54:[15, 80, 40, 80], Operations: [] Exploring Operation: 15+40=55, Resulting Numbers: [80, 80, 55] Generated Node #2: [80, 80, 55] from Operation: 15+40=55 Current State: 54:[80, 80, 55], Operations: ['15+40=55'] Exploring Operation: 80/80=1, Resulting Numbers: [55, 1] Generated Node #3: [55, 1] from Operation: 80/80=1 Current State: 54:[55, 1], Operations: ['15+40=55', '80/80=1'] Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[15, 80, 40, 80], Operations: [] Exploring Operation: 80/80=1, Resulting Numbers: [15, 40, 1] Generated Node #0,0: 54:[15, 40, 1] Operation: 80/80=1 Exploring Operation: 80-80=0, Resulting Numbers: [15, 40, 0] Generated Node #0,1: 54:[15, 40, 0] Operation: 80-80=0 Exploring Operation: 80/40=2, Resulting Numbers: [15, 80, 2] Generated Node #0,2: 54:[15, 80, 2] Operation: 80/40=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[15, 40, 1], Operations: ['80/80=1'] Exploring Operation: 15+40=55, Resulting Numbers: [1, 55] Generated Node #0,0,0: 54:[1, 55] Operation: 15+40=55 Exploring Operation: 15+1=16, Resulting Numbers: [40, 16] Generated Node #0,0,1: 54:[40, 16] Operation: 15+1=16 Exploring Operation: 40-15=25, Resulting Numbers: [1, 25] Generated Node #0,0,2: 54:[1, 25] Operation: 40-15=25 Moving to Node #0,0,0 Current State: 54:[1, 55], Operations: ['80/80=1', '15+40=55'] Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[15, 80, 40, 80], Operations: [] Exploring Operation: 80/80=1, Resulting Numbers: [15, 40, 1] Generated Node #0,0: 54:[15, 40, 1] Operation: 80/80=1 Moving to Node #0,0 Current State: 54:[15, 40, 1], Operations: ['80/80=1'] Exploring Operation: 15+40=55, Resulting Numbers: [1, 55] Generated Node #0,0,0: 54:[1, 55] Operation: 15+40=55 Moving to Node #0,0,0 Current State: 54:[1, 55], Operations: ['80/80=1', '15+40=55'] Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 97, 97, 63, 87 ]
87
[ "97-97=0", "63*0=0", "87+0=87" ]
Current State: 87:[97, 97, 63, 87], Operations: [] Exploring Operation: 97-97=0, Resulting Numbers: [63, 87, 0] Generated Node #2: [63, 87, 0] from Operation: 97-97=0 Current State: 87:[63, 87, 0], Operations: ['97-97=0'] Exploring Operation: 63*0=0, Resulting Numbers: [87, 0] Generated Node #3: [87, 0] from Operation: 63*0=0 Current State: 87:[87, 0], Operations: ['97-97=0', '63*0=0'] Exploring Operation: 87+0=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[97, 97, 63, 87], Operations: [] Exploring Operation: 87-63=24, Resulting Numbers: [97, 97, 24] Generated Node #0,0: 87:[97, 97, 24] Operation: 87-63=24 Exploring Operation: 97-63=34, Resulting Numbers: [97, 87, 34] Generated Node #0,1: 87:[97, 87, 34] Operation: 97-63=34 Exploring Operation: 97-63=34, Resulting Numbers: [97, 87, 34] Generated Node #0,2: 87:[97, 87, 34] Operation: 97-63=34 Exploring Operation: 97-97=0, Resulting Numbers: [63, 87, 0] Generated Node #0,3: 87:[63, 87, 0] Operation: 97-97=0 Exploring Operation: 97/97=1, Resulting Numbers: [63, 87, 1] Generated Node #0,4: 87:[63, 87, 1] Operation: 97/97=1 Moving to Node #0,1 Current State: 87:[97, 87, 34], Operations: ['97-63=34'] Exploring Operation: 97-34=63, Resulting Numbers: [87, 63] Generated Node #0,1,0: 87:[87, 63] Operation: 97-34=63 Exploring Operation: 87+34=121, Resulting Numbers: [97, 121] Generated Node #0,1,1: 87:[97, 121] Operation: 87+34=121 Exploring Operation: 97-87=10, Resulting Numbers: [34, 10] Generated Node #0,1,2: 87:[34, 10] Operation: 97-87=10 Exploring Operation: 87-34=53, Resulting Numbers: [97, 53] Generated Node #0,1,3: 87:[97, 53] Operation: 87-34=53 Exploring Operation: 97+34=131, Resulting Numbers: [87, 131] Generated Node #0,1,4: 87:[87, 131] Operation: 97+34=131 Moving to Node #0,2 Current State: 87:[97, 87, 34], Operations: ['97-63=34'] Exploring Operation: 97+34=131, Resulting Numbers: [87, 131] Generated Node #0,2,0: 87:[87, 131] Operation: 97+34=131 Exploring Operation: 97-34=63, Resulting Numbers: [87, 63] Generated Node #0,2,1: 87:[87, 63] Operation: 97-34=63 Exploring Operation: 87-34=53, Resulting Numbers: [97, 53] Generated Node #0,2,2: 87:[97, 53] Operation: 87-34=53 Exploring Operation: 97-87=10, Resulting Numbers: [34, 10] Generated Node #0,2,3: 87:[34, 10] Operation: 97-87=10 Exploring Operation: 87+34=121, Resulting Numbers: [97, 121] Generated Node #0,2,4: 87:[97, 121] Operation: 87+34=121 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 87:[34, 10], Operations: ['97-63=34', '97-87=10'] Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,87 unequal: No Solution Exploring Operation: 34*10=340, Resulting Numbers: [340] 340,87 unequal: No Solution Exploring Operation: 34+10=44, Resulting Numbers: [44] 44,87 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: 87:[87, 63], Operations: ['97-63=34', '97-34=63'] Exploring Operation: 87+63=150, Resulting Numbers: [150] 150,87 unequal: No Solution Exploring Operation: 87*63=5481, Resulting Numbers: [5481] 5481,87 unequal: No Solution Exploring Operation: 87-63=24, Resulting Numbers: [24] 24,87 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: 87:[97, 53], Operations: ['97-63=34', '87-34=53'] Exploring Operation: 97*53=5141, Resulting Numbers: [5141] 5141,87 unequal: No Solution Exploring Operation: 97-53=44, Resulting Numbers: [44] 44,87 unequal: No Solution Exploring Operation: 97+53=150, Resulting Numbers: [150] 150,87 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: 87:[87, 131], Operations: ['97-63=34', '97+34=131'] Exploring Operation: 131-87=44, Resulting Numbers: [44] 44,87 unequal: No Solution Exploring Operation: 87*131=11397, Resulting Numbers: [11397] 11397,87 unequal: No Solution Exploring Operation: 87+131=218, Resulting Numbers: [218] 218,87 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: 87:[97, 121], Operations: ['97-63=34', '87+34=121'] Exploring Operation: 97+121=218, Resulting Numbers: [218] 218,87 unequal: No Solution Exploring Operation: 121-97=24, Resulting Numbers: [24] 24,87 unequal: No Solution Exploring Operation: 97*121=11737, Resulting Numbers: [11737] 11737,87 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: 87:[97, 97, 24], Operations: ['87-63=24'] Exploring Operation: 97+24=121, Resulting Numbers: [97, 121] Generated Node #0,0,0: 87:[97, 121] Operation: 97+24=121 Exploring Operation: 97-24=73, Resulting Numbers: [97, 73] Generated Node #0,0,1: 87:[97, 73] Operation: 97-24=73 Exploring Operation: 97/97=1, Resulting Numbers: [24, 1] Generated Node #0,0,2: 87:[24, 1] Operation: 97/97=1 Exploring Operation: 97-24=73, Resulting Numbers: [97, 73] Generated Node #0,0,3: 87:[97, 73] Operation: 97-24=73 Exploring Operation: 97-97=0, Resulting Numbers: [24, 0] Generated Node #0,0,4: 87:[24, 0] Operation: 97-97=0 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 87:[24, 1], Operations: ['87-63=24', '97/97=1'] Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,87 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,87 unequal: No Solution Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,87 unequal: No Solution Exploring Operation: 24*1=24, Resulting Numbers: [24] 24,87 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: 87:[24, 0], Operations: ['87-63=24', '97-97=0'] Exploring Operation: 24-0=24, Resulting Numbers: [24] 24,87 unequal: No Solution Exploring Operation: 24*0=0, Resulting Numbers: [0] 0,87 unequal: No Solution Exploring Operation: 24+0=24, Resulting Numbers: [24] 24,87 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: 87:[97, 73], Operations: ['87-63=24', '97-24=73'] Exploring Operation: 97*73=7081, Resulting Numbers: [7081] 7081,87 unequal: No Solution Exploring Operation: 97+73=170, Resulting Numbers: [170] 170,87 unequal: No Solution Exploring Operation: 97-73=24, Resulting Numbers: [24] 24,87 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: 87:[97, 73], Operations: ['87-63=24', '97-24=73'] Exploring Operation: 97-73=24, Resulting Numbers: [24] 24,87 unequal: No Solution Exploring Operation: 97*73=7081, Resulting Numbers: [7081] 7081,87 unequal: No Solution Exploring Operation: 97+73=170, Resulting Numbers: [170] 170,87 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: 87:[97, 121], Operations: ['87-63=24', '97+24=121'] Exploring Operation: 121-97=24, Resulting Numbers: [24] 24,87 unequal: No Solution Exploring Operation: 97*121=11737, Resulting Numbers: [11737] 11737,87 unequal: No Solution Exploring Operation: 97+121=218, Resulting Numbers: [218] 218,87 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: 87:[63, 87, 1], Operations: ['97/97=1'] Exploring Operation: 87*1=87, Resulting Numbers: [63, 87] Generated Node #0,4,0: 87:[63, 87] Operation: 87*1=87 Exploring Operation: 87-63=24, Resulting Numbers: [1, 24] Generated Node #0,4,1: 87:[1, 24] Operation: 87-63=24 Exploring Operation: 63/1=63, Resulting Numbers: [87, 63] Generated Node #0,4,2: 87:[87, 63] Operation: 63/1=63 Exploring Operation: 63+1=64, Resulting Numbers: [87, 64] Generated Node #0,4,3: 87:[87, 64] Operation: 63+1=64 Exploring Operation: 63*1=63, Resulting Numbers: [87, 63] Generated Node #0,4,4: 87:[87, 63] Operation: 63*1=63 Moving to Node #0,3 Current State: 87:[63, 87, 0], Operations: ['97-97=0'] Exploring Operation: 87-63=24, Resulting Numbers: [0, 24] Generated Node #0,3,0: 87:[0, 24] Operation: 87-63=24 Exploring Operation: 87+0=87, Resulting Numbers: [63, 87] Generated Node #0,3,1: 87:[63, 87] Operation: 87+0=87 Exploring Operation: 63-0=63, Resulting Numbers: [87, 63] Generated Node #0,3,2: 87:[87, 63] Operation: 63-0=63 Exploring Operation: 63*0=0, Resulting Numbers: [87, 0] Generated Node #0,3,3: 87:[87, 0] Operation: 63*0=0 Exploring Operation: 63+0=63, Resulting Numbers: [87, 63] Generated Node #0,3,4: 87:[87, 63] Operation: 63+0=63 Moving to Node #0,3,3 Current State: 87:[87, 0], Operations: ['97-97=0', '63*0=0'] Exploring Operation: 87+0=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[97, 97, 63, 87], Operations: [] Exploring Operation: 97-97=0, Resulting Numbers: [63, 87, 0] Generated Node #0,3: 87:[63, 87, 0] Operation: 97-97=0 Moving to Node #0,3 Current State: 87:[63, 87, 0], Operations: ['97-97=0'] Exploring Operation: 63*0=0, Resulting Numbers: [87, 0] Generated Node #0,3,3: 87:[87, 0] Operation: 63*0=0 Moving to Node #0,3,3 Current State: 87:[87, 0], Operations: ['97-97=0', '63*0=0'] Exploring Operation: 87+0=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
0.942708
hs_5
sum_heuristic
[ 32, 9, 34, 45 ]
12
[ "32-9=23", "45-34=11", "23-11=12" ]
Current State: 12:[32, 9, 34, 45], Operations: [] Exploring Operation: 32-9=23, Resulting Numbers: [34, 45, 23] Generated Node #2: [34, 45, 23] from Operation: 32-9=23 Current State: 12:[34, 45, 23], Operations: ['32-9=23'] Exploring Operation: 45-34=11, Resulting Numbers: [23, 11] Generated Node #3: [23, 11] from Operation: 45-34=11 Current State: 12:[23, 11], Operations: ['32-9=23', '45-34=11'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[32, 9, 34, 45], Operations: [] Exploring Operation: 45-34=11, Resulting Numbers: [32, 9, 11] Generated Node #0,0: 12:[32, 9, 11] Operation: 45-34=11 Exploring Operation: 45-32=13, Resulting Numbers: [9, 34, 13] Generated Node #0,1: 12:[9, 34, 13] Operation: 45-32=13 Moving to Node #0,0 Current State: 12:[32, 9, 11], Operations: ['45-34=11'] Exploring Operation: 32-11=21, Resulting Numbers: [9, 21] Generated Node #0,0,0: 12:[9, 21] Operation: 32-11=21 Exploring Operation: 32-9=23, Resulting Numbers: [11, 23] Generated Node #0,0,1: 12:[11, 23] Operation: 32-9=23 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[9, 21], Operations: ['45-34=11', '32-11=21'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[32, 9, 34, 45], Operations: [] Exploring Operation: 45-34=11, Resulting Numbers: [32, 9, 11] Generated Node #0,0: 12:[32, 9, 11] Operation: 45-34=11 Moving to Node #0,0 Current State: 12:[32, 9, 11], Operations: ['45-34=11'] Exploring Operation: 32-11=21, Resulting Numbers: [9, 21] Generated Node #0,0,0: 12:[9, 21] Operation: 32-11=21 Moving to Node #0,0,0 Current State: 12:[9, 21], Operations: ['45-34=11', '32-11=21'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 24, 72, 37, 2 ]
85
[ "24+72=96", "96/2=48", "37+48=85" ]
Current State: 85:[24, 72, 37, 2], Operations: [] Exploring Operation: 24+72=96, Resulting Numbers: [37, 2, 96] Generated Node #2: [37, 2, 96] from Operation: 24+72=96 Current State: 85:[37, 2, 96], Operations: ['24+72=96'] Exploring Operation: 96/2=48, Resulting Numbers: [37, 48] Generated Node #3: [37, 48] from Operation: 96/2=48 Current State: 85:[37, 48], Operations: ['24+72=96', '96/2=48'] Exploring Operation: 37+48=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[24, 72, 37, 2], Operations: [] Exploring Operation: 24+72=96, Resulting Numbers: [37, 2, 96] Generated Node #0,0: 85:[37, 2, 96] Operation: 24+72=96 Exploring Operation: 37*2=74, Resulting Numbers: [24, 72, 74] Generated Node #0,1: 85:[24, 72, 74] Operation: 37*2=74 Exploring Operation: 72-37=35, Resulting Numbers: [24, 2, 35] Generated Node #0,2: 85:[24, 2, 35] Operation: 72-37=35 Exploring Operation: 37-24=13, Resulting Numbers: [72, 2, 13] Generated Node #0,3: 85:[72, 2, 13] Operation: 37-24=13 Exploring Operation: 72/24=3, Resulting Numbers: [37, 2, 3] Generated Node #0,4: 85:[37, 2, 3] Operation: 72/24=3 Moving to Node #0,3 Current State: 85:[72, 2, 13], Operations: ['37-24=13'] Exploring Operation: 72+13=85, Resulting Numbers: [2, 85] Generated Node #0,3,0: 85:[2, 85] Operation: 72+13=85 Exploring Operation: 2+13=15, Resulting Numbers: [72, 15] Generated Node #0,3,1: 85:[72, 15] Operation: 2+13=15 Exploring Operation: 13-2=11, Resulting Numbers: [72, 11] Generated Node #0,3,2: 85:[72, 11] Operation: 13-2=11 Exploring Operation: 72-2=70, Resulting Numbers: [13, 70] Generated Node #0,3,3: 85:[13, 70] Operation: 72-2=70 Exploring Operation: 72+2=74, Resulting Numbers: [13, 74] Generated Node #0,3,4: 85:[13, 74] Operation: 72+2=74 Moving to Node #0,4 Current State: 85:[37, 2, 3], Operations: ['72/24=3'] Exploring Operation: 37-3=34, Resulting Numbers: [2, 34] Generated Node #0,4,0: 85:[2, 34] Operation: 37-3=34 Exploring Operation: 37-2=35, Resulting Numbers: [3, 35] Generated Node #0,4,1: 85:[3, 35] Operation: 37-2=35 Exploring Operation: 37*2=74, Resulting Numbers: [3, 74] Generated Node #0,4,2: 85:[3, 74] Operation: 37*2=74 Exploring Operation: 2+3=5, Resulting Numbers: [37, 5] Generated Node #0,4,3: 85:[37, 5] Operation: 2+3=5 Exploring Operation: 2*3=6, Resulting Numbers: [37, 6] Generated Node #0,4,4: 85:[37, 6] Operation: 2*3=6 Moving to Node #0,2 Current State: 85:[24, 2, 35], Operations: ['72-37=35'] Exploring Operation: 24/2=12, Resulting Numbers: [35, 12] Generated Node #0,2,0: 85:[35, 12] Operation: 24/2=12 Exploring Operation: 2*35=70, Resulting Numbers: [24, 70] Generated Node #0,2,1: 85:[24, 70] Operation: 2*35=70 Exploring Operation: 35-24=11, Resulting Numbers: [2, 11] Generated Node #0,2,2: 85:[2, 11] Operation: 35-24=11 Exploring Operation: 35-2=33, Resulting Numbers: [24, 33] Generated Node #0,2,3: 85:[24, 33] Operation: 35-2=33 Exploring Operation: 24-2=22, Resulting Numbers: [35, 22] Generated Node #0,2,4: 85:[35, 22] Operation: 24-2=22 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 85:[2, 11], Operations: ['72-37=35', '35-24=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,85 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,85 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: 85:[24, 70], Operations: ['72-37=35', '2*35=70'] Exploring Operation: 70-24=46, Resulting Numbers: [46] 46,85 unequal: No Solution Exploring Operation: 24*70=1680, Resulting Numbers: [1680] 1680,85 unequal: No Solution Exploring Operation: 24+70=94, Resulting Numbers: [94] 94,85 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: 85:[35, 12], Operations: ['72-37=35', '24/2=12'] Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,85 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,85 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: 85:[24, 33], Operations: ['72-37=35', '35-2=33'] Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,85 unequal: No Solution Exploring Operation: 24+33=57, Resulting Numbers: [57] 57,85 unequal: No Solution Exploring Operation: 24*33=792, Resulting Numbers: [792] 792,85 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: 85:[35, 22], Operations: ['72-37=35', '24-2=22'] Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,85 unequal: No Solution Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,85 unequal: No Solution Exploring Operation: 35*22=770, Resulting Numbers: [770] 770,85 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: 85:[24, 72, 74], Operations: ['37*2=74'] Exploring Operation: 72-24=48, Resulting Numbers: [74, 48] Generated Node #0,1,0: 85:[74, 48] Operation: 72-24=48 Exploring Operation: 24+72=96, Resulting Numbers: [74, 96] Generated Node #0,1,1: 85:[74, 96] Operation: 24+72=96 Exploring Operation: 24+74=98, Resulting Numbers: [72, 98] Generated Node #0,1,2: 85:[72, 98] Operation: 24+74=98 Exploring Operation: 72/24=3, Resulting Numbers: [74, 3] Generated Node #0,1,3: 85:[74, 3] Operation: 72/24=3 Exploring Operation: 74-72=2, Resulting Numbers: [24, 2] Generated Node #0,1,4: 85:[24, 2] Operation: 74-72=2 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 85:[24, 2], Operations: ['37*2=74', '74-72=2'] Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,85 unequal: No Solution Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,85 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: 85:[74, 3], Operations: ['37*2=74', '72/24=3'] Exploring Operation: 74+3=77, Resulting Numbers: [77] 77,85 unequal: No Solution Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,85 unequal: No Solution Exploring Operation: 74*3=222, Resulting Numbers: [222] 222,85 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: 85:[74, 96], Operations: ['37*2=74', '24+72=96'] Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 74+96=170, Resulting Numbers: [170] 170,85 unequal: No Solution Exploring Operation: 74*96=7104, Resulting Numbers: [7104] 7104,85 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: 85:[72, 98], Operations: ['37*2=74', '24+74=98'] Exploring Operation: 72*98=7056, Resulting Numbers: [7056] 7056,85 unequal: No Solution Exploring Operation: 98-72=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 72+98=170, Resulting Numbers: [170] 170,85 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: 85:[74, 48], Operations: ['37*2=74', '72-24=48'] Exploring Operation: 74+48=122, Resulting Numbers: [122] 122,85 unequal: No Solution Exploring Operation: 74*48=3552, Resulting Numbers: [3552] 3552,85 unequal: No Solution Exploring Operation: 74-48=26, Resulting Numbers: [26] 26,85 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: 85:[37, 2, 96], Operations: ['24+72=96'] Exploring Operation: 96-37=59, Resulting Numbers: [2, 59] Generated Node #0,0,0: 85:[2, 59] Operation: 96-37=59 Exploring Operation: 37*2=74, Resulting Numbers: [96, 74] Generated Node #0,0,1: 85:[96, 74] Operation: 37*2=74 Exploring Operation: 96-2=94, Resulting Numbers: [37, 94] Generated Node #0,0,2: 85:[37, 94] Operation: 96-2=94 Exploring Operation: 37-2=35, Resulting Numbers: [96, 35] Generated Node #0,0,3: 85:[96, 35] Operation: 37-2=35 Exploring Operation: 37+2=39, Resulting Numbers: [96, 39] Generated Node #0,0,4: 85:[96, 39] Operation: 37+2=39 Moving to Node #0,3,0 Current State: 85:[2, 85], Operations: ['37-24=13', '72+13=85'] Exploring Operation: 2+85=87, Resulting Numbers: [87] 87,85 unequal: No Solution Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,85 unequal: No Solution Exploring Operation: 2*85=170, Resulting Numbers: [170] 170,85 unequal: No Solution Moving to Node #0,4,2 Current State: 85:[3, 74], Operations: ['72/24=3', '37*2=74'] Exploring Operation: 3*74=222, Resulting Numbers: [222] 222,85 unequal: No Solution Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,85 unequal: No Solution Exploring Operation: 3+74=77, Resulting Numbers: [77] 77,85 unequal: No Solution Moving to Node #0,3,4 Current State: 85:[13, 74], Operations: ['37-24=13', '72+2=74'] Exploring Operation: 13+74=87, Resulting Numbers: [87] 87,85 unequal: No Solution Exploring Operation: 13*74=962, Resulting Numbers: [962] 962,85 unequal: No Solution Exploring Operation: 74-13=61, Resulting Numbers: [61] 61,85 unequal: No Solution Moving to Node #0,3,1 Current State: 85:[72, 15], Operations: ['37-24=13', '2+13=15'] Exploring Operation: 72+15=87, Resulting Numbers: [87] 87,85 unequal: No Solution Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,85 unequal: No Solution Exploring Operation: 72*15=1080, Resulting Numbers: [1080] 1080,85 unequal: No Solution Moving to Node #0,3,3 Current State: 85:[13, 70], Operations: ['37-24=13', '72-2=70'] Exploring Operation: 70-13=57, Resulting Numbers: [57] 57,85 unequal: No Solution Exploring Operation: 13*70=910, Resulting Numbers: [910] 910,85 unequal: No Solution Exploring Operation: 13+70=83, Resulting Numbers: [83] 83,85 unequal: No Solution Moving to Node #0,3,2 Current State: 85:[72, 11], Operations: ['37-24=13', '13-2=11'] Exploring Operation: 72+11=83, Resulting Numbers: [83] 83,85 unequal: No Solution Exploring Operation: 72-11=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 72*11=792, Resulting Numbers: [792] 792,85 unequal: No Solution Moving to Node #0,4,0 Current State: 85:[2, 34], Operations: ['72/24=3', '37-3=34'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,85 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,85 unequal: No Solution Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,85 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,85 unequal: No Solution Moving to Node #0,4,3 Current State: 85:[37, 5], Operations: ['72/24=3', '2+3=5'] Exploring Operation: 37+5=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 37*5=185, Resulting Numbers: [185] 185,85 unequal: No Solution Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,85 unequal: No Solution Moving to Node #0,4,1 Current State: 85:[3, 35], Operations: ['72/24=3', '37-2=35'] Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,85 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,85 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,85 unequal: No Solution Moving to Node #0,4,4 Current State: 85:[37, 6], Operations: ['72/24=3', '2*3=6'] Exploring Operation: 37*6=222, Resulting Numbers: [222] 222,85 unequal: No Solution Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,85 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[96, 74], Operations: ['24+72=96', '37*2=74'] Exploring Operation: 96+74=170, Resulting Numbers: [170] 170,85 unequal: No Solution Exploring Operation: 96*74=7104, Resulting Numbers: [7104] 7104,85 unequal: No Solution Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[96, 35], Operations: ['24+72=96', '37-2=35'] Exploring Operation: 96-35=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 96*35=3360, Resulting Numbers: [3360] 3360,85 unequal: No Solution Exploring Operation: 96+35=131, Resulting Numbers: [131] 131,85 unequal: No Solution Moving to Node #0,0,2 Current State: 85:[37, 94], Operations: ['24+72=96', '96-2=94'] Exploring Operation: 94-37=57, Resulting Numbers: [57] 57,85 unequal: No Solution Exploring Operation: 37+94=131, Resulting Numbers: [131] 131,85 unequal: No Solution Exploring Operation: 37*94=3478, Resulting Numbers: [3478] 3478,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[2, 59], Operations: ['24+72=96', '96-37=59'] Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,85 unequal: No Solution Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,85 unequal: No Solution Moving to Node #0,0,4 Current State: 85:[96, 39], Operations: ['24+72=96', '37+2=39'] Exploring Operation: 96-39=57, Resulting Numbers: [57] 57,85 unequal: No Solution Exploring Operation: 96+39=135, Resulting Numbers: [135] 135,85 unequal: No Solution Exploring Operation: 96*39=3744, Resulting Numbers: [3744] 3744,85 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 57, 32, 19, 59 ]
37
[ "57*32=1824", "1824/19=96", "96-59=37" ]
Current State: 37:[57, 32, 19, 59], Operations: [] Exploring Operation: 57*32=1824, Resulting Numbers: [19, 59, 1824] Generated Node #2: [19, 59, 1824] from Operation: 57*32=1824 Current State: 37:[19, 59, 1824], Operations: ['57*32=1824'] Exploring Operation: 1824/19=96, Resulting Numbers: [59, 96] Generated Node #3: [59, 96] from Operation: 1824/19=96 Current State: 37:[59, 96], Operations: ['57*32=1824', '1824/19=96'] Exploring Operation: 96-59=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[57, 32, 19, 59], Operations: [] Exploring Operation: 59-19=40, Resulting Numbers: [57, 32, 40] Generated Node #0,0: 37:[57, 32, 40] Operation: 59-19=40 Exploring Operation: 57-19=38, Resulting Numbers: [32, 59, 38] Generated Node #0,1: 37:[32, 59, 38] Operation: 57-19=38 Moving to Node #0,0 Current State: 37:[57, 32, 40], Operations: ['59-19=40'] Exploring Operation: 57-32=25, Resulting Numbers: [40, 25] Generated Node #0,0,0: 37:[40, 25] Operation: 57-32=25 Exploring Operation: 57-40=17, Resulting Numbers: [32, 17] Generated Node #0,0,1: 37:[32, 17] Operation: 57-40=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[40, 25], Operations: ['59-19=40', '57-32=25'] Exploring Operation: 40+25=65, Resulting Numbers: [65] 65,37 unequal: No Solution Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,37 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: 37:[32, 17], Operations: ['59-19=40', '57-40=17'] Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,37 unequal: No Solution Exploring Operation: 32+17=49, Resulting Numbers: [49] 49,37 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: 37:[32, 59, 38], Operations: ['57-19=38'] Exploring Operation: 59-32=27, Resulting Numbers: [38, 27] Generated Node #0,1,0: 37:[38, 27] Operation: 59-32=27 Exploring Operation: 59-38=21, Resulting Numbers: [32, 21] Generated Node #0,1,1: 37:[32, 21] Operation: 59-38=21 Moving to Node #0,1,0 Current State: 37:[38, 27], Operations: ['57-19=38', '59-32=27'] Exploring Operation: 38+27=65, Resulting Numbers: [65] 65,37 unequal: No Solution Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[32, 21], Operations: ['57-19=38', '59-38=21'] Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 32+21=53, Resulting Numbers: [53] 53,37 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 4, 18, 48, 19 ]
15
[ "18-4=14", "48-19=29", "29-14=15" ]
Current State: 15:[4, 18, 48, 19], Operations: [] Exploring Operation: 18-4=14, Resulting Numbers: [48, 19, 14] Generated Node #2: [48, 19, 14] from Operation: 18-4=14 Current State: 15:[48, 19, 14], Operations: ['18-4=14'] Exploring Operation: 48-19=29, Resulting Numbers: [14, 29] Generated Node #3: [14, 29] from Operation: 48-19=29 Current State: 15:[14, 29], Operations: ['18-4=14', '48-19=29'] Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[4, 18, 48, 19], Operations: [] Exploring Operation: 48/4=12, Resulting Numbers: [18, 19, 12] Generated Node #0,0: 15:[18, 19, 12] Operation: 48/4=12 Moving to Node #0,0 Current State: 15:[18, 19, 12], Operations: ['48/4=12'] Exploring Operation: 19-18=1, Resulting Numbers: [12, 1] Generated Node #0,0,0: 15:[12, 1] Operation: 19-18=1 Moving to Node #0,0,0 Current State: 15:[12, 1], Operations: ['48/4=12', '19-18=1'] Exploring Operation: 12+1=13, Resulting Numbers: [13] 13,15 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 61, 18, 36, 82 ]
33
[ "61+18=79", "82-36=46", "79-46=33" ]
Current State: 33:[61, 18, 36, 82], Operations: [] Exploring Operation: 61+18=79, Resulting Numbers: [36, 82, 79] Generated Node #2: [36, 82, 79] from Operation: 61+18=79 Current State: 33:[36, 82, 79], Operations: ['61+18=79'] Exploring Operation: 82-36=46, Resulting Numbers: [79, 46] Generated Node #3: [79, 46] from Operation: 82-36=46 Current State: 33:[79, 46], Operations: ['61+18=79', '82-36=46'] Exploring Operation: 79-46=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[61, 18, 36, 82], Operations: [] Exploring Operation: 82-61=21, Resulting Numbers: [18, 36, 21] Generated Node #0,0: 33:[18, 36, 21] Operation: 82-61=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[18, 36, 21], Operations: ['82-61=21'] Exploring Operation: 21-18=3, Resulting Numbers: [36, 3] Generated Node #0,0,0: 33:[36, 3] Operation: 21-18=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 33:[36, 3], Operations: ['82-61=21', '21-18=3'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[61, 18, 36, 82], Operations: [] Exploring Operation: 82-61=21, Resulting Numbers: [18, 36, 21] Generated Node #0,0: 33:[18, 36, 21] Operation: 82-61=21 Moving to Node #0,0 Current State: 33:[18, 36, 21], Operations: ['82-61=21'] Exploring Operation: 21-18=3, Resulting Numbers: [36, 3] Generated Node #0,0,0: 33:[36, 3] Operation: 21-18=3 Moving to Node #0,0,0 Current State: 33:[36, 3], Operations: ['82-61=21', '21-18=3'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 90, 94, 84, 3 ]
91
[ "94-90=4", "84+3=87", "4+87=91" ]
Current State: 91:[90, 94, 84, 3], Operations: [] Exploring Operation: 94-90=4, Resulting Numbers: [84, 3, 4] Generated Node #2: [84, 3, 4] from Operation: 94-90=4 Current State: 91:[84, 3, 4], Operations: ['94-90=4'] Exploring Operation: 84+3=87, Resulting Numbers: [4, 87] Generated Node #3: [4, 87] from Operation: 84+3=87 Current State: 91:[4, 87], Operations: ['94-90=4', '84+3=87'] Exploring Operation: 4+87=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[90, 94, 84, 3], Operations: [] Exploring Operation: 90-84=6, Resulting Numbers: [94, 3, 6] Generated Node #0,0: 91:[94, 3, 6] Operation: 90-84=6 Exploring Operation: 94-84=10, Resulting Numbers: [90, 3, 10] Generated Node #0,1: 91:[90, 3, 10] Operation: 94-84=10 Moving to Node #0,0 Current State: 91:[94, 3, 6], Operations: ['90-84=6'] Exploring Operation: 94-3=91, Resulting Numbers: [6, 91] Generated Node #0,0,0: 91:[6, 91] Operation: 94-3=91 Exploring Operation: 3+6=9, Resulting Numbers: [94, 9] Generated Node #0,0,1: 91:[94, 9] Operation: 3+6=9 Moving to Node #0,1 Current State: 91:[90, 3, 10], Operations: ['94-84=10'] Exploring Operation: 3+10=13, Resulting Numbers: [90, 13] Generated Node #0,1,0: 91:[90, 13] Operation: 3+10=13 Exploring Operation: 10-3=7, Resulting Numbers: [90, 7] Generated Node #0,1,1: 91:[90, 7] Operation: 10-3=7 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 91:[90, 13], Operations: ['94-84=10', '3+10=13'] Exploring Operation: 90+13=103, Resulting Numbers: [103] 103,91 unequal: No Solution Exploring Operation: 90-13=77, Resulting Numbers: [77] 77,91 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: 91:[90, 7], Operations: ['94-84=10', '10-3=7'] Exploring Operation: 90+7=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,91 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: 91:[6, 91], Operations: ['90-84=6', '94-3=91'] Exploring Operation: 91-6=85, Resulting Numbers: [85] 85,91 unequal: No Solution Exploring Operation: 6+91=97, Resulting Numbers: [97] 97,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[94, 9], Operations: ['90-84=6', '3+6=9'] Exploring Operation: 94-9=85, Resulting Numbers: [85] 85,91 unequal: No Solution Exploring Operation: 94+9=103, Resulting Numbers: [103] 103,91 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 86, 9, 33, 22 ]
43
[ "33-9=24", "24-22=2", "86/2=43" ]
Current State: 43:[86, 9, 33, 22], Operations: [] Exploring Operation: 33-9=24, Resulting Numbers: [86, 22, 24] Generated Node #2: [86, 22, 24] from Operation: 33-9=24 Current State: 43:[86, 22, 24], Operations: ['33-9=24'] Exploring Operation: 24-22=2, Resulting Numbers: [86, 2] Generated Node #3: [86, 2] from Operation: 24-22=2 Current State: 43:[86, 2], Operations: ['33-9=24', '24-22=2'] Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[86, 9, 33, 22], Operations: [] Exploring Operation: 86-22=64, Resulting Numbers: [9, 33, 64] Generated Node #0,0: 43:[9, 33, 64] Operation: 86-22=64 Exploring Operation: 86-33=53, Resulting Numbers: [9, 22, 53] Generated Node #0,1: 43:[9, 22, 53] Operation: 86-33=53 Exploring Operation: 86-9=77, Resulting Numbers: [33, 22, 77] Generated Node #0,2: 43:[33, 22, 77] Operation: 86-9=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[9, 33, 64], Operations: ['86-22=64'] Exploring Operation: 33-9=24, Resulting Numbers: [64, 24] Generated Node #0,0,0: 43:[64, 24] Operation: 33-9=24 Exploring Operation: 9+33=42, Resulting Numbers: [64, 42] Generated Node #0,0,1: 43:[64, 42] Operation: 9+33=42 Exploring Operation: 64-9=55, Resulting Numbers: [33, 55] Generated Node #0,0,2: 43:[33, 55] Operation: 64-9=55 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 43:[64, 42], Operations: ['86-22=64', '9+33=42'] Exploring Operation: 64*42=2688, Resulting Numbers: [2688] 2688,43 unequal: No Solution Exploring Operation: 64+42=106, Resulting Numbers: [106] 106,43 unequal: No Solution Exploring Operation: 64-42=22, Resulting Numbers: [22] 22,43 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: 43:[33, 55], Operations: ['86-22=64', '64-9=55'] Exploring Operation: 33+55=88, Resulting Numbers: [88] 88,43 unequal: No Solution Exploring Operation: 55-33=22, Resulting Numbers: [22] 22,43 unequal: No Solution Exploring Operation: 33*55=1815, Resulting Numbers: [1815] 1815,43 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: 43:[64, 24], Operations: ['86-22=64', '33-9=24'] Exploring Operation: 64*24=1536, Resulting Numbers: [1536] 1536,43 unequal: No Solution Exploring Operation: 64-24=40, Resulting Numbers: [40] 40,43 unequal: No Solution Exploring Operation: 64+24=88, Resulting Numbers: [88] 88,43 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: 43:[9, 22, 53], Operations: ['86-33=53'] Exploring Operation: 9+22=31, Resulting Numbers: [53, 31] Generated Node #0,1,0: 43:[53, 31] Operation: 9+22=31 Exploring Operation: 22-9=13, Resulting Numbers: [53, 13] Generated Node #0,1,1: 43:[53, 13] Operation: 22-9=13 Exploring Operation: 53-9=44, Resulting Numbers: [22, 44] Generated Node #0,1,2: 43:[22, 44] Operation: 53-9=44 Moving to Node #0,1,0 Current State: 43:[53, 31], Operations: ['86-33=53', '9+22=31'] Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,43 unequal: No Solution Exploring Operation: 53*31=1643, Resulting Numbers: [1643] 1643,43 unequal: No Solution Exploring Operation: 53+31=84, Resulting Numbers: [84] 84,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[22, 44], Operations: ['86-33=53', '53-9=44'] Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,43 unequal: No Solution Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[53, 13], Operations: ['86-33=53', '22-9=13'] Exploring Operation: 53+13=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 53*13=689, Resulting Numbers: [689] 689,43 unequal: No Solution Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,43 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: 43:[33, 22, 77], Operations: ['86-9=77'] Exploring Operation: 77-33=44, Resulting Numbers: [22, 44] Generated Node #0,2,0: 43:[22, 44] Operation: 77-33=44 Exploring Operation: 77-22=55, Resulting Numbers: [33, 55] Generated Node #0,2,1: 43:[33, 55] Operation: 77-22=55 Exploring Operation: 33+22=55, Resulting Numbers: [77, 55] Generated Node #0,2,2: 43:[77, 55] Operation: 33+22=55 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 43:[22, 44], Operations: ['86-9=77', '77-33=44'] Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,43 unequal: No Solution Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,43 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: 43:[33, 55], Operations: ['86-9=77', '77-22=55'] Exploring Operation: 33+55=88, Resulting Numbers: [88] 88,43 unequal: No Solution Exploring Operation: 33*55=1815, Resulting Numbers: [1815] 1815,43 unequal: No Solution Exploring Operation: 55-33=22, Resulting Numbers: [22] 22,43 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: 43:[77, 55], Operations: ['86-9=77', '33+22=55'] Exploring Operation: 77+55=132, Resulting Numbers: [132] 132,43 unequal: No Solution Exploring Operation: 77-55=22, Resulting Numbers: [22] 22,43 unequal: No Solution Exploring Operation: 77*55=4235, Resulting Numbers: [4235] 4235,43 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
[ 66, 2, 14, 20 ]
12
[ "66-14=52", "2*20=40", "52-40=12" ]
Current State: 12:[66, 2, 14, 20], Operations: [] Exploring Operation: 66-14=52, Resulting Numbers: [2, 20, 52] Generated Node #2: [2, 20, 52] from Operation: 66-14=52 Current State: 12:[2, 20, 52], Operations: ['66-14=52'] Exploring Operation: 2*20=40, Resulting Numbers: [52, 40] Generated Node #3: [52, 40] from Operation: 2*20=40 Current State: 12:[52, 40], Operations: ['66-14=52', '2*20=40'] Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[66, 2, 14, 20], Operations: [] Exploring Operation: 66/2=33, Resulting Numbers: [14, 20, 33] Generated Node #0,0: 12:[14, 20, 33] Operation: 66/2=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[14, 20, 33], Operations: ['66/2=33'] Exploring Operation: 33-20=13, Resulting Numbers: [14, 13] Generated Node #0,0,0: 12:[14, 13] Operation: 33-20=13 Moving to Node #0,0,0 Current State: 12:[14, 13], Operations: ['66/2=33', '33-20=13'] Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,12 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
[ 37, 14, 6, 69 ]
98
[ "37-14=23", "6+69=75", "23+75=98" ]
Current State: 98:[37, 14, 6, 69], Operations: [] Exploring Operation: 37-14=23, Resulting Numbers: [6, 69, 23] Generated Node #2: [6, 69, 23] from Operation: 37-14=23 Current State: 98:[6, 69, 23], Operations: ['37-14=23'] Exploring Operation: 6+69=75, Resulting Numbers: [23, 75] Generated Node #3: [23, 75] from Operation: 6+69=75 Current State: 98:[23, 75], Operations: ['37-14=23', '6+69=75'] Exploring Operation: 23+75=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[37, 14, 6, 69], Operations: [] Exploring Operation: 69-14=55, Resulting Numbers: [37, 6, 55] Generated Node #0,0: 98:[37, 6, 55] Operation: 69-14=55 Exploring Operation: 37+14=51, Resulting Numbers: [6, 69, 51] Generated Node #0,1: 98:[6, 69, 51] Operation: 37+14=51 Exploring Operation: 69-37=32, Resulting Numbers: [14, 6, 32] Generated Node #0,2: 98:[14, 6, 32] Operation: 69-37=32 Exploring Operation: 37+69=106, Resulting Numbers: [14, 6, 106] Generated Node #0,3: 98:[14, 6, 106] Operation: 37+69=106 Start Sub Search at level 1: Moving to Node #0,3 Current State: 98:[14, 6, 106], Operations: ['37+69=106'] Exploring Operation: 14+6=20, Resulting Numbers: [106, 20] Generated Node #0,3,0: 98:[106, 20] Operation: 14+6=20 Exploring Operation: 106-6=100, Resulting Numbers: [14, 100] Generated Node #0,3,1: 98:[14, 100] Operation: 106-6=100 Exploring Operation: 106-14=92, Resulting Numbers: [6, 92] Generated Node #0,3,2: 98:[6, 92] Operation: 106-14=92 Exploring Operation: 14-6=8, Resulting Numbers: [106, 8] Generated Node #0,3,3: 98:[106, 8] Operation: 14-6=8 Moving to Node #0,3,1 Current State: 98:[14, 100], Operations: ['37+69=106', '106-6=100'] Exploring Operation: 100-14=86, Resulting Numbers: [86] 86,98 unequal: No Solution Exploring Operation: 14*100=1400, Resulting Numbers: [1400] 1400,98 unequal: No Solution Exploring Operation: 14+100=114, Resulting Numbers: [114] 114,98 unequal: No Solution Moving to Node #0,3,2 Current State: 98:[6, 92], Operations: ['37+69=106', '106-14=92'] Exploring Operation: 6+92=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[37, 14, 6, 69], Operations: [] Exploring Operation: 37+69=106, Resulting Numbers: [14, 6, 106] Generated Node #0,3: 98:[14, 6, 106] Operation: 37+69=106 Moving to Node #0,3 Current State: 98:[14, 6, 106], Operations: ['37+69=106'] Exploring Operation: 106-14=92, Resulting Numbers: [6, 92] Generated Node #0,3,2: 98:[6, 92] Operation: 106-14=92 Moving to Node #0,3,2 Current State: 98:[6, 92], Operations: ['37+69=106', '106-14=92'] Exploring Operation: 6+92=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 17, 75, 68, 13 ]
58
[ "68/17=4", "75-13=62", "62-4=58" ]
Current State: 58:[17, 75, 68, 13], Operations: [] Exploring Operation: 68/17=4, Resulting Numbers: [75, 13, 4] Generated Node #2: [75, 13, 4] from Operation: 68/17=4 Current State: 58:[75, 13, 4], Operations: ['68/17=4'] Exploring Operation: 75-13=62, Resulting Numbers: [4, 62] Generated Node #3: [4, 62] from Operation: 75-13=62 Current State: 58:[4, 62], Operations: ['68/17=4', '75-13=62'] Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[17, 75, 68, 13], Operations: [] Exploring Operation: 17+13=30, Resulting Numbers: [75, 68, 30] Generated Node #0,0: 58:[75, 68, 30] Operation: 17+13=30 Exploring Operation: 75-17=58, Resulting Numbers: [68, 13, 58] Generated Node #0,1: 58:[68, 13, 58] Operation: 75-17=58 Exploring Operation: 75-68=7, Resulting Numbers: [17, 13, 7] Generated Node #0,2: 58:[17, 13, 7] Operation: 75-68=7 Exploring Operation: 75-13=62, Resulting Numbers: [17, 68, 62] Generated Node #0,3: 58:[17, 68, 62] Operation: 75-13=62 Moving to Node #0,1 Current State: 58:[68, 13, 58], Operations: ['75-17=58'] Exploring Operation: 13+58=71, Resulting Numbers: [68, 71] Generated Node #0,1,0: 58:[68, 71] Operation: 13+58=71 Exploring Operation: 68-13=55, Resulting Numbers: [58, 55] Generated Node #0,1,1: 58:[58, 55] Operation: 68-13=55 Exploring Operation: 68-58=10, Resulting Numbers: [13, 10] Generated Node #0,1,2: 58:[13, 10] Operation: 68-58=10 Exploring Operation: 68+13=81, Resulting Numbers: [58, 81] Generated Node #0,1,3: 58:[58, 81] Operation: 68+13=81 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 58:[58, 55], Operations: ['75-17=58', '68-13=55'] Exploring Operation: 58-55=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 58*55=3190, Resulting Numbers: [3190] 3190,58 unequal: No Solution Exploring Operation: 58+55=113, Resulting Numbers: [113] 113,58 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: 58:[13, 10], Operations: ['75-17=58', '68-58=10'] Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,58 unequal: No Solution Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,58 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,58 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: 58:[68, 71], Operations: ['75-17=58', '13+58=71'] Exploring Operation: 71-68=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 68*71=4828, Resulting Numbers: [4828] 4828,58 unequal: No Solution Exploring Operation: 68+71=139, Resulting Numbers: [139] 139,58 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: 58:[58, 81], Operations: ['75-17=58', '68+13=81'] Exploring Operation: 58+81=139, Resulting Numbers: [139] 139,58 unequal: No Solution Exploring Operation: 58*81=4698, Resulting Numbers: [4698] 4698,58 unequal: No Solution Exploring Operation: 81-58=23, Resulting Numbers: [23] 23,58 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: 58:[17, 68, 62], Operations: ['75-13=62'] Exploring Operation: 68-17=51, Resulting Numbers: [62, 51] Generated Node #0,3,0: 58:[62, 51] Operation: 68-17=51 Exploring Operation: 68-62=6, Resulting Numbers: [17, 6] Generated Node #0,3,1: 58:[17, 6] Operation: 68-62=6 Exploring Operation: 68/17=4, Resulting Numbers: [62, 4] Generated Node #0,3,2: 58:[62, 4] Operation: 68/17=4 Exploring Operation: 62-17=45, Resulting Numbers: [68, 45] Generated Node #0,3,3: 58:[68, 45] Operation: 62-17=45 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 58:[62, 4], Operations: ['75-13=62', '68/17=4'] Exploring Operation: 62*4=248, Resulting Numbers: [248] 248,58 unequal: No Solution Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[17, 75, 68, 13], Operations: [] Exploring Operation: 75-13=62, Resulting Numbers: [17, 68, 62] Generated Node #0,3: 58:[17, 68, 62] Operation: 75-13=62 Moving to Node #0,3 Current State: 58:[17, 68, 62], Operations: ['75-13=62'] Exploring Operation: 68/17=4, Resulting Numbers: [62, 4] Generated Node #0,3,2: 58:[62, 4] Operation: 68/17=4 Moving to Node #0,3,2 Current State: 58:[62, 4], Operations: ['75-13=62', '68/17=4'] Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 54, 10, 37, 30 ]
32
[ "37-10=27", "54/27=2", "30+2=32" ]
Current State: 32:[54, 10, 37, 30], Operations: [] Exploring Operation: 37-10=27, Resulting Numbers: [54, 30, 27] Generated Node #2: [54, 30, 27] from Operation: 37-10=27 Current State: 32:[54, 30, 27], Operations: ['37-10=27'] Exploring Operation: 54/27=2, Resulting Numbers: [30, 2] Generated Node #3: [30, 2] from Operation: 54/27=2 Current State: 32:[30, 2], Operations: ['37-10=27', '54/27=2'] Exploring Operation: 30+2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[54, 10, 37, 30], Operations: [] Exploring Operation: 54-30=24, Resulting Numbers: [10, 37, 24] Generated Node #0,0: 32:[10, 37, 24] Operation: 54-30=24 Exploring Operation: 54-37=17, Resulting Numbers: [10, 30, 17] Generated Node #0,1: 32:[10, 30, 17] Operation: 54-37=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[10, 30, 17], Operations: ['54-37=17'] Exploring Operation: 17-10=7, Resulting Numbers: [30, 7] Generated Node #0,1,0: 32:[30, 7] Operation: 17-10=7 Exploring Operation: 30/10=3, Resulting Numbers: [17, 3] Generated Node #0,1,1: 32:[17, 3] Operation: 30/10=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 32:[17, 3], Operations: ['54-37=17', '30/10=3'] Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,32 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,32 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: 32:[30, 7], Operations: ['54-37=17', '17-10=7'] Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,32 unequal: No Solution Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,32 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: 32:[10, 37, 24], Operations: ['54-30=24'] Exploring Operation: 37-24=13, Resulting Numbers: [10, 13] Generated Node #0,0,0: 32:[10, 13] Operation: 37-24=13 Exploring Operation: 10+24=34, Resulting Numbers: [37, 34] Generated Node #0,0,1: 32:[37, 34] Operation: 10+24=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[10, 13], Operations: ['54-30=24', '37-24=13'] Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,32 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,32 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: 32:[37, 34], Operations: ['54-30=24', '10+24=34'] Exploring Operation: 37+34=71, Resulting Numbers: [71] 71,32 unequal: No Solution Exploring Operation: 37-34=3, Resulting Numbers: [3] 3,32 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
[ 88, 15, 88, 18 ]
94
[ "88+88=176", "15*18=270", "270-176=94" ]
Current State: 94:[88, 15, 88, 18], Operations: [] Exploring Operation: 88+88=176, Resulting Numbers: [15, 18, 176] Generated Node #2: [15, 18, 176] from Operation: 88+88=176 Current State: 94:[15, 18, 176], Operations: ['88+88=176'] Exploring Operation: 15*18=270, Resulting Numbers: [176, 270] Generated Node #3: [176, 270] from Operation: 15*18=270 Current State: 94:[176, 270], Operations: ['88+88=176', '15*18=270'] Exploring Operation: 270-176=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[88, 15, 88, 18], Operations: [] Exploring Operation: 18-15=3, Resulting Numbers: [88, 88, 3] Generated Node #0,0: 94:[88, 88, 3] Operation: 18-15=3 Exploring Operation: 15+18=33, Resulting Numbers: [88, 88, 33] Generated Node #0,1: 94:[88, 88, 33] Operation: 15+18=33 Exploring Operation: 88/88=1, Resulting Numbers: [15, 18, 1] Generated Node #0,2: 94:[15, 18, 1] Operation: 88/88=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[88, 88, 3], Operations: ['18-15=3'] Exploring Operation: 88/88=1, Resulting Numbers: [3, 1] Generated Node #0,0,0: 94:[3, 1] Operation: 88/88=1 Exploring Operation: 88-88=0, Resulting Numbers: [3, 0] Generated Node #0,0,1: 94:[3, 0] Operation: 88-88=0 Exploring Operation: 88+3=91, Resulting Numbers: [88, 91] Generated Node #0,0,2: 94:[88, 91] Operation: 88+3=91 Moving to Node #0,0,0 Current State: 94:[3, 1], Operations: ['18-15=3', '88/88=1'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[3, 0], Operations: ['18-15=3', '88-88=0'] Exploring Operation: 3-0=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 3*0=0, Resulting Numbers: [0] 0,94 unequal: No Solution Exploring Operation: 3+0=3, Resulting Numbers: [3] 3,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[88, 91], Operations: ['18-15=3', '88+3=91'] Exploring Operation: 88+91=179, Resulting Numbers: [179] 179,94 unequal: No Solution Exploring Operation: 91-88=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 88*91=8008, Resulting Numbers: [8008] 8008,94 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 #0,1 Current State: 94:[88, 88, 33], Operations: ['15+18=33'] Exploring Operation: 88-33=55, Resulting Numbers: [88, 55] Generated Node #0,1,0: 94:[88, 55] Operation: 88-33=55 Exploring Operation: 88-33=55, Resulting Numbers: [88, 55] Generated Node #0,1,1: 94:[88, 55] Operation: 88-33=55 Exploring Operation: 88/88=1, Resulting Numbers: [33, 1] Generated Node #0,1,2: 94:[33, 1] Operation: 88/88=1 Moving to Node #0,1,0 Current State: 94:[88, 55], Operations: ['15+18=33', '88-33=55'] Exploring Operation: 88+55=143, Resulting Numbers: [143] 143,94 unequal: No Solution Exploring Operation: 88*55=4840, Resulting Numbers: [4840] 4840,94 unequal: No Solution Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[88, 55], Operations: ['15+18=33', '88-33=55'] Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,94 unequal: No Solution Exploring Operation: 88+55=143, Resulting Numbers: [143] 143,94 unequal: No Solution Exploring Operation: 88*55=4840, Resulting Numbers: [4840] 4840,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[33, 1], Operations: ['15+18=33', '88/88=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,94 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,94 unequal: No Solution Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,94 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 #0,2 Current State: 94:[15, 18, 1], Operations: ['88/88=1'] Exploring Operation: 15-1=14, Resulting Numbers: [18, 14] Generated Node #0,2,0: 94:[18, 14] Operation: 15-1=14 Exploring Operation: 18-15=3, Resulting Numbers: [1, 3] Generated Node #0,2,1: 94:[1, 3] Operation: 18-15=3 Exploring Operation: 15+18=33, Resulting Numbers: [1, 33] Generated Node #0,2,2: 94:[1, 33] Operation: 15+18=33 Moving to Node #0,2,1 Current State: 94:[1, 3], Operations: ['88/88=1', '18-15=3'] Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[1, 33], Operations: ['88/88=1', '15+18=33'] Exploring Operation: 1*33=33, Resulting Numbers: [33] 33,94 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,94 unequal: No Solution Exploring Operation: 1+33=34, Resulting Numbers: [34] 34,94 unequal: No Solution Moving to Node #0,2,0 Current State: 94:[18, 14], Operations: ['88/88=1', '15-1=14'] Exploring Operation: 18+14=32, Resulting Numbers: [32] 32,94 unequal: No Solution Exploring Operation: 18*14=252, Resulting Numbers: [252] 252,94 unequal: No Solution Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 16, 52, 5, 20 ]
17
[ "16+52=68", "20/5=4", "68/4=17" ]
Current State: 17:[16, 52, 5, 20], Operations: [] Exploring Operation: 16+52=68, Resulting Numbers: [5, 20, 68] Generated Node #2: [5, 20, 68] from Operation: 16+52=68 Current State: 17:[5, 20, 68], Operations: ['16+52=68'] Exploring Operation: 20/5=4, Resulting Numbers: [68, 4] Generated Node #3: [68, 4] from Operation: 20/5=4 Current State: 17:[68, 4], Operations: ['16+52=68', '20/5=4'] Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[16, 52, 5, 20], Operations: [] Exploring Operation: 52-20=32, Resulting Numbers: [16, 5, 32] Generated Node #0,0: 17:[16, 5, 32] Operation: 52-20=32 Exploring Operation: 16+5=21, Resulting Numbers: [52, 20, 21] Generated Node #0,1: 17:[52, 20, 21] Operation: 16+5=21 Exploring Operation: 52-16=36, Resulting Numbers: [5, 20, 36] Generated Node #0,2: 17:[5, 20, 36] Operation: 52-16=36 Exploring Operation: 52-5=47, Resulting Numbers: [16, 20, 47] Generated Node #0,3: 17:[16, 20, 47] Operation: 52-5=47 Exploring Operation: 20-5=15, Resulting Numbers: [16, 52, 15] Generated Node #0,4: 17:[16, 52, 15] Operation: 20-5=15 Moving to Node #0,0 Current State: 17:[16, 5, 32], Operations: ['52-20=32'] Exploring Operation: 16-5=11, Resulting Numbers: [32, 11] Generated Node #0,0,0: 17:[32, 11] Operation: 16-5=11 Exploring Operation: 32-5=27, Resulting Numbers: [16, 27] Generated Node #0,0,1: 17:[16, 27] Operation: 32-5=27 Exploring Operation: 16+5=21, Resulting Numbers: [32, 21] Generated Node #0,0,2: 17:[32, 21] Operation: 16+5=21 Exploring Operation: 32-16=16, Resulting Numbers: [5, 16] Generated Node #0,0,3: 17:[5, 16] Operation: 32-16=16 Exploring Operation: 5+32=37, Resulting Numbers: [16, 37] Generated Node #0,0,4: 17:[16, 37] Operation: 5+32=37 Moving to Node #0,3 Current State: 17:[16, 20, 47], Operations: ['52-5=47'] Exploring Operation: 47-20=27, Resulting Numbers: [16, 27] Generated Node #0,3,0: 17:[16, 27] Operation: 47-20=27 Exploring Operation: 47-16=31, Resulting Numbers: [20, 31] Generated Node #0,3,1: 17:[20, 31] Operation: 47-16=31 Exploring Operation: 16+47=63, Resulting Numbers: [20, 63] Generated Node #0,3,2: 17:[20, 63] Operation: 16+47=63 Exploring Operation: 20-16=4, Resulting Numbers: [47, 4] Generated Node #0,3,3: 17:[47, 4] Operation: 20-16=4 Exploring Operation: 16+20=36, Resulting Numbers: [47, 36] Generated Node #0,3,4: 17:[47, 36] Operation: 16+20=36 Moving to Node #0,2 Current State: 17:[5, 20, 36], Operations: ['52-16=36'] Exploring Operation: 5+36=41, Resulting Numbers: [20, 41] Generated Node #0,2,0: 17:[20, 41] Operation: 5+36=41 Exploring Operation: 36-5=31, Resulting Numbers: [20, 31] Generated Node #0,2,1: 17:[20, 31] Operation: 36-5=31 Exploring Operation: 5+20=25, Resulting Numbers: [36, 25] Generated Node #0,2,2: 17:[36, 25] Operation: 5+20=25 Exploring Operation: 36-20=16, Resulting Numbers: [5, 16] Generated Node #0,2,3: 17:[5, 16] Operation: 36-20=16 Exploring Operation: 20-5=15, Resulting Numbers: [36, 15] Generated Node #0,2,4: 17:[36, 15] Operation: 20-5=15 Moving to Node #0,4 Current State: 17:[16, 52, 15], Operations: ['20-5=15'] Exploring Operation: 52-16=36, Resulting Numbers: [15, 36] Generated Node #0,4,0: 17:[15, 36] Operation: 52-16=36 Exploring Operation: 52-15=37, Resulting Numbers: [16, 37] Generated Node #0,4,1: 17:[16, 37] Operation: 52-15=37 Exploring Operation: 52+15=67, Resulting Numbers: [16, 67] Generated Node #0,4,2: 17:[16, 67] Operation: 52+15=67 Exploring Operation: 16+15=31, Resulting Numbers: [52, 31] Generated Node #0,4,3: 17:[52, 31] Operation: 16+15=31 Exploring Operation: 16-15=1, Resulting Numbers: [52, 1] Generated Node #0,4,4: 17:[52, 1] Operation: 16-15=1 Moving to Node #0,1 Current State: 17:[52, 20, 21], Operations: ['16+5=21'] Exploring Operation: 52-20=32, Resulting Numbers: [21, 32] Generated Node #0,1,0: 17:[21, 32] Operation: 52-20=32 Exploring Operation: 21-20=1, Resulting Numbers: [52, 1] Generated Node #0,1,1: 17:[52, 1] Operation: 21-20=1 Exploring Operation: 52-21=31, Resulting Numbers: [20, 31] Generated Node #0,1,2: 17:[20, 31] Operation: 52-21=31 Exploring Operation: 52+21=73, Resulting Numbers: [20, 73] Generated Node #0,1,3: 17:[20, 73] Operation: 52+21=73 Exploring Operation: 52+20=72, Resulting Numbers: [21, 72] Generated Node #0,1,4: 17:[21, 72] Operation: 52+20=72 Moving to Node #0,0,1 Current State: 17:[16, 27], Operations: ['52-20=32', '32-5=27'] Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 16*27=432, Resulting Numbers: [432] 432,17 unequal: No Solution Exploring Operation: 16+27=43, Resulting Numbers: [43] 43,17 unequal: No Solution Moving to Node #0,3,0 Current State: 17:[16, 27], Operations: ['52-5=47', '47-20=27'] Exploring Operation: 16+27=43, Resulting Numbers: [43] 43,17 unequal: No Solution Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 16*27=432, Resulting Numbers: [432] 432,17 unequal: No Solution Moving to Node #0,0,3 Current State: 17:[5, 16], Operations: ['52-20=32', '32-16=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,17 unequal: No Solution Moving to Node #0,2,3 Current State: 17:[5, 16], Operations: ['52-16=36', '36-20=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,17 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,17 unequal: No Solution Moving to Node #0,3,1 Current State: 17:[20, 31], Operations: ['52-5=47', '47-16=31'] Exploring Operation: 20*31=620, Resulting Numbers: [620] 620,17 unequal: No Solution Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,17 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[20, 31], Operations: ['52-16=36', '36-5=31'] Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,17 unequal: No Solution Exploring Operation: 20*31=620, Resulting Numbers: [620] 620,17 unequal: No Solution Moving to Node #0,1,2 Current State: 17:[20, 31], Operations: ['16+5=21', '52-21=31'] Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,17 unequal: No Solution Exploring Operation: 20*31=620, Resulting Numbers: [620] 620,17 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[32, 21], Operations: ['52-20=32', '16+5=21'] Exploring Operation: 32*21=672, Resulting Numbers: [672] 672,17 unequal: No Solution Exploring Operation: 32+21=53, Resulting Numbers: [53] 53,17 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[21, 32], Operations: ['16+5=21', '52-20=32'] Exploring Operation: 21+32=53, Resulting Numbers: [53] 53,17 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 21*32=672, Resulting Numbers: [672] 672,17 unequal: No Solution Moving to Node #0,2,4 Current State: 17:[36, 15], Operations: ['52-16=36', '20-5=15'] Exploring Operation: 36+15=51, Resulting Numbers: [51] 51,17 unequal: No Solution Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 36*15=540, Resulting Numbers: [540] 540,17 unequal: No Solution Moving to Node #0,4,1 Current State: 17:[16, 37], Operations: ['20-5=15', '52-15=37'] Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 16*37=592, Resulting Numbers: [592] 592,17 unequal: No Solution Exploring Operation: 16+37=53, Resulting Numbers: [53] 53,17 unequal: No Solution Moving to Node #0,0,4 Current State: 17:[16, 37], Operations: ['52-20=32', '5+32=37'] Exploring Operation: 16+37=53, Resulting Numbers: [53] 53,17 unequal: No Solution Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 16*37=592, Resulting Numbers: [592] 592,17 unequal: No Solution Moving to Node #0,0,0 Current State: 17:[32, 11], Operations: ['52-20=32', '16-5=11'] Exploring Operation: 32*11=352, Resulting Numbers: [352] 352,17 unequal: No Solution Exploring Operation: 32+11=43, Resulting Numbers: [43] 43,17 unequal: No Solution Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,17 unequal: No Solution Moving to Node #0,4,0 Current State: 17:[15, 36], Operations: ['20-5=15', '52-16=36'] Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 15+36=51, Resulting Numbers: [51] 51,17 unequal: No Solution Exploring Operation: 15*36=540, Resulting Numbers: [540] 540,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[36, 25], Operations: ['52-16=36', '5+20=25'] Exploring Operation: 36-25=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 36+25=61, Resulting Numbers: [61] 61,17 unequal: No Solution Exploring Operation: 36*25=900, Resulting Numbers: [900] 900,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[20, 41], Operations: ['52-16=36', '5+36=41'] Exploring Operation: 20*41=820, Resulting Numbers: [820] 820,17 unequal: No Solution Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 20+41=61, Resulting Numbers: [61] 61,17 unequal: No Solution Moving to Node #0,3,3 Current State: 17:[47, 4], Operations: ['52-5=47', '20-16=4'] Exploring Operation: 47*4=188, Resulting Numbers: [188] 188,17 unequal: No Solution Exploring Operation: 47+4=51, Resulting Numbers: [51] 51,17 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,17 unequal: No Solution Moving to Node #0,3,4 Current State: 17:[47, 36], Operations: ['52-5=47', '16+20=36'] Exploring Operation: 47-36=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 47+36=83, Resulting Numbers: [83] 83,17 unequal: No Solution Exploring Operation: 47*36=1692, Resulting Numbers: [1692] 1692,17 unequal: No Solution Moving to Node #0,4,3 Current State: 17:[52, 31], Operations: ['20-5=15', '16+15=31'] Exploring Operation: 52+31=83, Resulting Numbers: [83] 83,17 unequal: No Solution Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 52*31=1612, Resulting Numbers: [1612] 1612,17 unequal: No Solution Moving to Node #0,3,2 Current State: 17:[20, 63], Operations: ['52-5=47', '16+47=63'] Exploring Operation: 20+63=83, Resulting Numbers: [83] 83,17 unequal: No Solution Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,17 unequal: No Solution Exploring Operation: 20*63=1260, Resulting Numbers: [1260] 1260,17 unequal: No Solution Moving to Node #0,4,2 Current State: 17:[16, 67], Operations: ['20-5=15', '52+15=67'] Exploring Operation: 16+67=83, Resulting Numbers: [83] 83,17 unequal: No Solution Exploring Operation: 16*67=1072, Resulting Numbers: [1072] 1072,17 unequal: No Solution Exploring Operation: 67-16=51, Resulting Numbers: [51] 51,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[52, 1], Operations: ['16+5=21', '21-20=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 52+1=53, Resulting Numbers: [53] 53,17 unequal: No Solution Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,17 unequal: No Solution Moving to Node #0,4,4 Current State: 17:[52, 1], Operations: ['20-5=15', '16-15=1'] Exploring Operation: 52+1=53, Resulting Numbers: [53] 53,17 unequal: No Solution Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,17 unequal: No Solution Moving to Node #0,1,4 Current State: 17:[21, 72], Operations: ['16+5=21', '52+20=72'] Exploring Operation: 72-21=51, Resulting Numbers: [51] 51,17 unequal: No Solution Exploring Operation: 21+72=93, Resulting Numbers: [93] 93,17 unequal: No Solution Exploring Operation: 21*72=1512, Resulting Numbers: [1512] 1512,17 unequal: No Solution Moving to Node #0,1,3 Current State: 17:[20, 73], Operations: ['16+5=21', '52+21=73'] Exploring Operation: 20+73=93, Resulting Numbers: [93] 93,17 unequal: No Solution Exploring Operation: 73-20=53, Resulting Numbers: [53] 53,17 unequal: No Solution Exploring Operation: 20*73=1460, Resulting Numbers: [1460] 1460,17 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 44, 84, 81, 40 ]
12
[ "44-40=4", "84-81=3", "4*3=12" ]
Current State: 12:[44, 84, 81, 40], Operations: [] Exploring Operation: 44-40=4, Resulting Numbers: [84, 81, 4] Generated Node #2: [84, 81, 4] from Operation: 44-40=4 Current State: 12:[84, 81, 4], Operations: ['44-40=4'] Exploring Operation: 84-81=3, Resulting Numbers: [4, 3] Generated Node #3: [4, 3] from Operation: 84-81=3 Current State: 12:[4, 3], Operations: ['44-40=4', '84-81=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[44, 84, 81, 40], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [44, 40, 3] Generated Node #0,0: 12:[44, 40, 3] Operation: 84-81=3 Exploring Operation: 84-44=40, Resulting Numbers: [81, 40, 40] Generated Node #0,1: 12:[81, 40, 40] Operation: 84-44=40 Moving to Node #0,0 Current State: 12:[44, 40, 3], Operations: ['84-81=3'] Exploring Operation: 44-3=41, Resulting Numbers: [40, 41] Generated Node #0,0,0: 12:[40, 41] Operation: 44-3=41 Exploring Operation: 44-40=4, Resulting Numbers: [3, 4] Generated Node #0,0,1: 12:[3, 4] Operation: 44-40=4 Moving to Node #0,1 Current State: 12:[81, 40, 40], Operations: ['84-44=40'] Exploring Operation: 81-40=41, Resulting Numbers: [40, 41] Generated Node #0,1,0: 12:[40, 41] Operation: 81-40=41 Exploring Operation: 81-40=41, Resulting Numbers: [40, 41] Generated Node #0,1,1: 12:[40, 41] Operation: 81-40=41 Moving to Node #0,0,1 Current State: 12:[3, 4], Operations: ['84-81=3', '44-40=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,12 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[44, 84, 81, 40], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [44, 40, 3] Generated Node #0,0: 12:[44, 40, 3] Operation: 84-81=3 Moving to Node #0,0 Current State: 12:[44, 40, 3], Operations: ['84-81=3'] Exploring Operation: 44-40=4, Resulting Numbers: [3, 4] Generated Node #0,0,1: 12:[3, 4] Operation: 44-40=4 Moving to Node #0,0,1 Current State: 12:[3, 4], Operations: ['84-81=3', '44-40=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.989583
hs_2
sum_heuristic
[ 2, 39, 26, 27 ]
81
[ "2*39=78", "78/26=3", "27*3=81" ]
Current State: 81:[2, 39, 26, 27], Operations: [] Exploring Operation: 2*39=78, Resulting Numbers: [26, 27, 78] Generated Node #2: [26, 27, 78] from Operation: 2*39=78 Current State: 81:[26, 27, 78], Operations: ['2*39=78'] Exploring Operation: 78/26=3, Resulting Numbers: [27, 3] Generated Node #3: [27, 3] from Operation: 78/26=3 Current State: 81:[27, 3], Operations: ['2*39=78', '78/26=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[2, 39, 26, 27], Operations: [] Exploring Operation: 39-26=13, Resulting Numbers: [2, 27, 13] Generated Node #0,0: 81:[2, 27, 13] Operation: 39-26=13 Exploring Operation: 2*39=78, Resulting Numbers: [26, 27, 78] Generated Node #0,1: 81:[26, 27, 78] Operation: 2*39=78 Moving to Node #0,1 Current State: 81:[26, 27, 78], Operations: ['2*39=78'] Exploring Operation: 27-26=1, Resulting Numbers: [78, 1] Generated Node #0,1,0: 81:[78, 1] Operation: 27-26=1 Exploring Operation: 78/26=3, Resulting Numbers: [27, 3] Generated Node #0,1,1: 81:[27, 3] Operation: 78/26=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 81:[27, 3], Operations: ['2*39=78', '78/26=3'] Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,81 unequal: No Solution Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[2, 39, 26, 27], Operations: [] Exploring Operation: 2*39=78, Resulting Numbers: [26, 27, 78] Generated Node #0,1: 81:[26, 27, 78] Operation: 2*39=78 Moving to Node #0,1 Current State: 81:[26, 27, 78], Operations: ['2*39=78'] Exploring Operation: 78/26=3, Resulting Numbers: [27, 3] Generated Node #0,1,1: 81:[27, 3] Operation: 78/26=3 Moving to Node #0,1,1 Current State: 81:[27, 3], Operations: ['2*39=78', '78/26=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 4, 84, 14, 1 ]
35
[ "84/4=21", "14*1=14", "21+14=35" ]
Current State: 35:[4, 84, 14, 1], Operations: [] Exploring Operation: 84/4=21, Resulting Numbers: [14, 1, 21] Generated Node #2: [14, 1, 21] from Operation: 84/4=21 Current State: 35:[14, 1, 21], Operations: ['84/4=21'] Exploring Operation: 14*1=14, Resulting Numbers: [21, 14] Generated Node #3: [21, 14] from Operation: 14*1=14 Current State: 35:[21, 14], Operations: ['84/4=21', '14*1=14'] Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[4, 84, 14, 1], Operations: [] Exploring Operation: 84-14=70, Resulting Numbers: [4, 1, 70] Generated Node #0,0: 35:[4, 1, 70] Operation: 84-14=70 Exploring Operation: 84/14=6, Resulting Numbers: [4, 1, 6] Generated Node #0,1: 35:[4, 1, 6] Operation: 84/14=6 Exploring Operation: 84-4=80, Resulting Numbers: [14, 1, 80] Generated Node #0,2: 35:[14, 1, 80] Operation: 84-4=80 Exploring Operation: 84/4=21, Resulting Numbers: [14, 1, 21] Generated Node #0,3: 35:[14, 1, 21] Operation: 84/4=21 Moving to Node #0,1 Current State: 35:[4, 1, 6], Operations: ['84/14=6'] Exploring Operation: 4*1=4, Resulting Numbers: [6, 4] Generated Node #0,1,0: 35:[6, 4] Operation: 4*1=4 Exploring Operation: 6-1=5, Resulting Numbers: [4, 5] Generated Node #0,1,1: 35:[4, 5] Operation: 6-1=5 Exploring Operation: 1+6=7, Resulting Numbers: [4, 7] Generated Node #0,1,2: 35:[4, 7] Operation: 1+6=7 Exploring Operation: 4+1=5, Resulting Numbers: [6, 5] Generated Node #0,1,3: 35:[6, 5] Operation: 4+1=5 Moving to Node #0,3 Current State: 35:[14, 1, 21], Operations: ['84/4=21'] Exploring Operation: 14-1=13, Resulting Numbers: [21, 13] Generated Node #0,3,0: 35:[21, 13] Operation: 14-1=13 Exploring Operation: 1+21=22, Resulting Numbers: [14, 22] Generated Node #0,3,1: 35:[14, 22] Operation: 1+21=22 Exploring Operation: 21-14=7, Resulting Numbers: [1, 7] Generated Node #0,3,2: 35:[1, 7] Operation: 21-14=7 Exploring Operation: 14+21=35, Resulting Numbers: [1, 35] Generated Node #0,3,3: 35:[1, 35] Operation: 14+21=35 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 35:[1, 7], Operations: ['84/4=21', '21-14=7'] Exploring Operation: 1+7=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 1*7=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,35 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: 35:[1, 35], Operations: ['84/4=21', '14+21=35'] Exploring Operation: 35-1=34, Resulting Numbers: [34] 34,35 unequal: No Solution Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[4, 84, 14, 1], Operations: [] Exploring Operation: 84/4=21, Resulting Numbers: [14, 1, 21] Generated Node #0,3: 35:[14, 1, 21] Operation: 84/4=21 Moving to Node #0,3 Current State: 35:[14, 1, 21], Operations: ['84/4=21'] Exploring Operation: 14+21=35, Resulting Numbers: [1, 35] Generated Node #0,3,3: 35:[1, 35] Operation: 14+21=35 Moving to Node #0,3,3 Current State: 35:[1, 35], Operations: ['84/4=21', '14+21=35'] Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
sum_heuristic
[ 16, 14, 16, 40 ]
86
[ "16+14=30", "16+40=56", "30+56=86" ]
Current State: 86:[16, 14, 16, 40], Operations: [] Exploring Operation: 16+14=30, Resulting Numbers: [40, 30] Generated Node #2: [40, 30] from Operation: 16+14=30 Current State: 86:[40, 30], Operations: ['16+14=30'] Exploring Operation: 16+40=56, Resulting Numbers: [30, 56] Generated Node #3: [30, 56] from Operation: 16+40=56 Current State: 86:[30, 56], Operations: ['16+14=30', '16+40=56'] Exploring Operation: 30+56=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[16, 14, 16, 40], Operations: [] Exploring Operation: 16+16=32, Resulting Numbers: [14, 40, 32] Generated Node #0,0: 86:[14, 40, 32] Operation: 16+16=32 Exploring Operation: 16-16=0, Resulting Numbers: [14, 40, 0] Generated Node #0,1: 86:[14, 40, 0] Operation: 16-16=0 Exploring Operation: 16-14=2, Resulting Numbers: [16, 40, 2] Generated Node #0,2: 86:[16, 40, 2] Operation: 16-14=2 Exploring Operation: 16/16=1, Resulting Numbers: [14, 40, 1] Generated Node #0,3: 86:[14, 40, 1] Operation: 16/16=1 Exploring Operation: 16-14=2, Resulting Numbers: [16, 40, 2] Generated Node #0,4: 86:[16, 40, 2] Operation: 16-14=2 Moving to Node #0,3 Current State: 86:[14, 40, 1], Operations: ['16/16=1'] Exploring Operation: 14-1=13, Resulting Numbers: [40, 13] Generated Node #0,3,0: 86:[40, 13] Operation: 14-1=13 Exploring Operation: 14+40=54, Resulting Numbers: [1, 54] Generated Node #0,3,1: 86:[1, 54] Operation: 14+40=54 Exploring Operation: 14/1=14, Resulting Numbers: [40, 14] Generated Node #0,3,2: 86:[40, 14] Operation: 14/1=14 Exploring Operation: 40+1=41, Resulting Numbers: [14, 41] Generated Node #0,3,3: 86:[14, 41] Operation: 40+1=41 Exploring Operation: 14*1=14, Resulting Numbers: [40, 14] Generated Node #0,3,4: 86:[40, 14] Operation: 14*1=14 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 86:[1, 54], Operations: ['16/16=1', '14+40=54'] Exploring Operation: 1*54=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 54/1=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,86 unequal: No Solution Exploring Operation: 1+54=55, Resulting Numbers: [55] 55,86 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: 86:[40, 13], Operations: ['16/16=1', '14-1=13'] Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,86 unequal: No Solution Exploring Operation: 40*13=520, Resulting Numbers: [520] 520,86 unequal: No Solution Exploring Operation: 40+13=53, Resulting Numbers: [53] 53,86 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: 86:[14, 41], Operations: ['16/16=1', '40+1=41'] Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,86 unequal: No Solution Exploring Operation: 14*41=574, Resulting Numbers: [574] 574,86 unequal: No Solution Exploring Operation: 14+41=55, Resulting Numbers: [55] 55,86 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: 86:[40, 14], Operations: ['16/16=1', '14/1=14'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,86 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: 86:[40, 14], Operations: ['16/16=1', '14*1=14'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,86 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,86 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: 86:[16, 40, 2], Operations: ['16-14=2'] Exploring Operation: 40+2=42, Resulting Numbers: [16, 42] Generated Node #0,2,0: 86:[16, 42] Operation: 40+2=42 Exploring Operation: 16/2=8, Resulting Numbers: [40, 8] Generated Node #0,2,1: 86:[40, 8] Operation: 16/2=8 Exploring Operation: 16-2=14, Resulting Numbers: [40, 14] Generated Node #0,2,2: 86:[40, 14] Operation: 16-2=14 Exploring Operation: 16*2=32, Resulting Numbers: [40, 32] Generated Node #0,2,3: 86:[40, 32] Operation: 16*2=32 Exploring Operation: 16+40=56, Resulting Numbers: [2, 56] Generated Node #0,2,4: 86:[2, 56] Operation: 16+40=56 Moving to Node #0,1 Current State: 86:[14, 40, 0], Operations: ['16-16=0'] Exploring Operation: 14*0=0, Resulting Numbers: [40, 0] Generated Node #0,1,0: 86:[40, 0] Operation: 14*0=0 Exploring Operation: 14+0=14, Resulting Numbers: [40, 14] Generated Node #0,1,1: 86:[40, 14] Operation: 14+0=14 Exploring Operation: 40*0=0, Resulting Numbers: [14, 0] Generated Node #0,1,2: 86:[14, 0] Operation: 40*0=0 Exploring Operation: 14+40=54, Resulting Numbers: [0, 54] Generated Node #0,1,3: 86:[0, 54] Operation: 14+40=54 Exploring Operation: 14-0=14, Resulting Numbers: [40, 14] Generated Node #0,1,4: 86:[40, 14] Operation: 14-0=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[40, 0], Operations: ['16-16=0', '14*0=0'] Exploring Operation: 40+0=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 40*0=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 40-0=40, Resulting Numbers: [40] 40,86 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: 86:[0, 54], Operations: ['16-16=0', '14+40=54'] Exploring Operation: 0*54=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 0+54=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 54-0=54, Resulting Numbers: [54] 54,86 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: 86:[14, 0], Operations: ['16-16=0', '40*0=0'] Exploring Operation: 14*0=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 14+0=14, Resulting Numbers: [14] 14,86 unequal: No Solution Exploring Operation: 14-0=14, Resulting Numbers: [14] 14,86 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: 86:[40, 14], Operations: ['16-16=0', '14+0=14'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,86 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: 86:[40, 14], Operations: ['16-16=0', '14-0=14'] Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,86 unequal: No Solution Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,86 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: 86:[16, 40, 2], Operations: ['16-14=2'] Exploring Operation: 40+2=42, Resulting Numbers: [16, 42] Generated Node #0,4,0: 86:[16, 42] Operation: 40+2=42 Exploring Operation: 16-2=14, Resulting Numbers: [40, 14] Generated Node #0,4,1: 86:[40, 14] Operation: 16-2=14 Exploring Operation: 16+40=56, Resulting Numbers: [2, 56] Generated Node #0,4,2: 86:[2, 56] Operation: 16+40=56 Exploring Operation: 16/2=8, Resulting Numbers: [40, 8] Generated Node #0,4,3: 86:[40, 8] Operation: 16/2=8 Exploring Operation: 16*2=32, Resulting Numbers: [40, 32] Generated Node #0,4,4: 86:[40, 32] Operation: 16*2=32 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 86:[40, 8], Operations: ['16-14=2', '16/2=8'] Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,86 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 40*8=320, Resulting Numbers: [320] 320,86 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: 86:[2, 56], Operations: ['16-14=2', '16+40=56'] Exploring Operation: 2*56=112, Resulting Numbers: [112] 112,86 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,86 unequal: No Solution Exploring Operation: 2+56=58, Resulting Numbers: [58] 58,86 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: 86:[40, 32], Operations: ['16-14=2', '16*2=32'] Exploring Operation: 40*32=1280, Resulting Numbers: [1280] 1280,86 unequal: No Solution Exploring Operation: 40+32=72, Resulting Numbers: [72] 72,86 unequal: No Solution Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,86 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: 86:[16, 42], Operations: ['16-14=2', '40+2=42'] Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 16+42=58, Resulting Numbers: [58] 58,86 unequal: No Solution Exploring Operation: 16*42=672, Resulting Numbers: [672] 672,86 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: 86:[40, 14], Operations: ['16-14=2', '16-2=14'] Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,86 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,86 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: 86:[14, 40, 32], Operations: ['16+16=32'] Exploring Operation: 14+32=46, Resulting Numbers: [40, 46] Generated Node #0,0,0: 86:[40, 46] Operation: 14+32=46 Exploring Operation: 40+32=72, Resulting Numbers: [14, 72] Generated Node #0,0,1: 86:[14, 72] Operation: 40+32=72 Exploring Operation: 32-14=18, Resulting Numbers: [40, 18] Generated Node #0,0,2: 86:[40, 18] Operation: 32-14=18 Exploring Operation: 40-32=8, Resulting Numbers: [14, 8] Generated Node #0,0,3: 86:[14, 8] Operation: 40-32=8 Exploring Operation: 14+40=54, Resulting Numbers: [32, 54] Generated Node #0,0,4: 86:[32, 54] Operation: 14+40=54 Moving to Node #0,0,0 Current State: 86:[40, 46], Operations: ['16+16=32', '14+32=46'] Exploring Operation: 40*46=1840, Resulting Numbers: [1840] 1840,86 unequal: No Solution Exploring Operation: 46-40=6, Resulting Numbers: [6] 6,86 unequal: No Solution Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[16, 14, 16, 40], Operations: [] Exploring Operation: 16+16=32, Resulting Numbers: [14, 40, 32] Generated Node #0,0: 86:[14, 40, 32] Operation: 16+16=32 Moving to Node #0,0 Current State: 86:[14, 40, 32], Operations: ['16+16=32'] Exploring Operation: 14+32=46, Resulting Numbers: [40, 46] Generated Node #0,0,0: 86:[40, 46] Operation: 14+32=46 Moving to Node #0,0,0 Current State: 86:[40, 46], Operations: ['16+16=32', '14+32=46'] Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
0.926215
hs_5
sum_heuristic
[ 40, 30, 32, 42 ]
92
[ "42-40=2", "30*2=60", "32+60=92" ]
Current State: 92:[40, 30, 32, 42], Operations: [] Exploring Operation: 42-40=2, Resulting Numbers: [30, 32, 2] Generated Node #2: [30, 32, 2] from Operation: 42-40=2 Current State: 92:[30, 32, 2], Operations: ['42-40=2'] Exploring Operation: 30*2=60, Resulting Numbers: [32, 60] Generated Node #3: [32, 60] from Operation: 30*2=60 Current State: 92:[32, 60], Operations: ['42-40=2', '30*2=60'] Exploring Operation: 32+60=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[40, 30, 32, 42], Operations: [] Exploring Operation: 32-30=2, Resulting Numbers: [40, 42, 2] Generated Node #0,0: 92:[40, 42, 2] Operation: 32-30=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[40, 42, 2], Operations: ['32-30=2'] Exploring Operation: 42-40=2, Resulting Numbers: [2, 2] Generated Node #0,0,0: 92:[2, 2] Operation: 42-40=2 Moving to Node #0,0,0 Current State: 92:[2, 2], Operations: ['32-30=2', '42-40=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,92 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
[ 26, 4, 74, 98 ]
95
[ "4+74=78", "78/26=3", "98-3=95" ]
Current State: 95:[26, 4, 74, 98], Operations: [] Exploring Operation: 4+74=78, Resulting Numbers: [26, 98, 78] Generated Node #2: [26, 98, 78] from Operation: 4+74=78 Current State: 95:[26, 98, 78], Operations: ['4+74=78'] Exploring Operation: 78/26=3, Resulting Numbers: [98, 3] Generated Node #3: [98, 3] from Operation: 78/26=3 Current State: 95:[98, 3], Operations: ['4+74=78', '78/26=3'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[26, 4, 74, 98], Operations: [] Exploring Operation: 4+74=78, Resulting Numbers: [26, 98, 78] Generated Node #0,0: 95:[26, 98, 78] Operation: 4+74=78 Exploring Operation: 26+74=100, Resulting Numbers: [4, 98, 100] Generated Node #0,1: 95:[4, 98, 100] Operation: 26+74=100 Exploring Operation: 26-4=22, Resulting Numbers: [74, 98, 22] Generated Node #0,2: 95:[74, 98, 22] Operation: 26-4=22 Exploring Operation: 98-74=24, Resulting Numbers: [26, 4, 24] Generated Node #0,3: 95:[26, 4, 24] Operation: 98-74=24 Moving to Node #0,1 Current State: 95:[4, 98, 100], Operations: ['26+74=100'] Exploring Operation: 100-4=96, Resulting Numbers: [98, 96] Generated Node #0,1,0: 95:[98, 96] Operation: 100-4=96 Exploring Operation: 100-98=2, Resulting Numbers: [4, 2] Generated Node #0,1,1: 95:[4, 2] Operation: 100-98=2 Exploring Operation: 100/4=25, Resulting Numbers: [98, 25] Generated Node #0,1,2: 95:[98, 25] Operation: 100/4=25 Exploring Operation: 98-4=94, Resulting Numbers: [100, 94] Generated Node #0,1,3: 95:[100, 94] Operation: 98-4=94 Moving to Node #0,3 Current State: 95:[26, 4, 24], Operations: ['98-74=24'] Exploring Operation: 26-4=22, Resulting Numbers: [24, 22] Generated Node #0,3,0: 95:[24, 22] Operation: 26-4=22 Exploring Operation: 4*24=96, Resulting Numbers: [26, 96] Generated Node #0,3,1: 95:[26, 96] Operation: 4*24=96 Exploring Operation: 26-24=2, Resulting Numbers: [4, 2] Generated Node #0,3,2: 95:[4, 2] Operation: 26-24=2 Exploring Operation: 24-4=20, Resulting Numbers: [26, 20] Generated Node #0,3,3: 95:[26, 20] Operation: 24-4=20 Moving to Node #0,2 Current State: 95:[74, 98, 22], Operations: ['26-4=22'] Exploring Operation: 98-74=24, Resulting Numbers: [22, 24] Generated Node #0,2,0: 95:[22, 24] Operation: 98-74=24 Exploring Operation: 74-22=52, Resulting Numbers: [98, 52] Generated Node #0,2,1: 95:[98, 52] Operation: 74-22=52 Exploring Operation: 74+22=96, Resulting Numbers: [98, 96] Generated Node #0,2,2: 95:[98, 96] Operation: 74+22=96 Exploring Operation: 98-22=76, Resulting Numbers: [74, 76] Generated Node #0,2,3: 95:[74, 76] Operation: 98-22=76 Moving to Node #0,0 Current State: 95:[26, 98, 78], Operations: ['4+74=78'] Exploring Operation: 78-26=52, Resulting Numbers: [98, 52] Generated Node #0,0,0: 95:[98, 52] Operation: 78-26=52 Exploring Operation: 26+78=104, Resulting Numbers: [98, 104] Generated Node #0,0,1: 95:[98, 104] Operation: 26+78=104 Exploring Operation: 78/26=3, Resulting Numbers: [98, 3] Generated Node #0,0,2: 95:[98, 3] Operation: 78/26=3 Exploring Operation: 98-78=20, Resulting Numbers: [26, 20] Generated Node #0,0,3: 95:[26, 20] Operation: 98-78=20 Moving to Node #0,1,0 Current State: 95:[98, 96], Operations: ['26+74=100', '100-4=96'] Exploring Operation: 98+96=194, Resulting Numbers: [194] 194,95 unequal: No Solution Exploring Operation: 98-96=2, Resulting Numbers: [2] 2,95 unequal: No Solution Exploring Operation: 98*96=9408, Resulting Numbers: [9408] 9408,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[4, 2], Operations: ['26+74=100', '100-98=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,95 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,95 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,95 unequal: No Solution Moving to Node #0,3,2 Current State: 95:[4, 2], Operations: ['98-74=24', '26-24=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,95 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,95 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,95 unequal: No Solution Moving to Node #0,2,2 Current State: 95:[98, 96], Operations: ['26-4=22', '74+22=96'] Exploring Operation: 98-96=2, Resulting Numbers: [2] 2,95 unequal: No Solution Exploring Operation: 98*96=9408, Resulting Numbers: [9408] 9408,95 unequal: No Solution Exploring Operation: 98+96=194, Resulting Numbers: [194] 194,95 unequal: No Solution Moving to Node #0,0,2 Current State: 95:[98, 3], Operations: ['4+74=78', '78/26=3'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[26, 4, 74, 98], Operations: [] Exploring Operation: 4+74=78, Resulting Numbers: [26, 98, 78] Generated Node #0,0: 95:[26, 98, 78] Operation: 4+74=78 Moving to Node #0,0 Current State: 95:[26, 98, 78], Operations: ['4+74=78'] Exploring Operation: 78/26=3, Resulting Numbers: [98, 3] Generated Node #0,0,2: 95:[98, 3] Operation: 78/26=3 Moving to Node #0,0,2 Current State: 95:[98, 3], Operations: ['4+74=78', '78/26=3'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
0.966146
hs_4
sum_heuristic
[ 92, 18, 50, 65 ]
95
[ "92+18=110", "65-50=15", "110-15=95" ]
Current State: 95:[92, 18, 50, 65], Operations: [] Exploring Operation: 92+18=110, Resulting Numbers: [50, 65, 110] Generated Node #2: [50, 65, 110] from Operation: 92+18=110 Current State: 95:[50, 65, 110], Operations: ['92+18=110'] Exploring Operation: 65-50=15, Resulting Numbers: [110, 15] Generated Node #3: [110, 15] from Operation: 65-50=15 Current State: 95:[110, 15], Operations: ['92+18=110', '65-50=15'] Exploring Operation: 110-15=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[92, 18, 50, 65], Operations: [] Exploring Operation: 65-50=15, Resulting Numbers: [92, 18, 15] Generated Node #0,0: 95:[92, 18, 15] Operation: 65-50=15 Moving to Node #0,0 Current State: 95:[92, 18, 15], Operations: ['65-50=15'] Exploring Operation: 18-15=3, Resulting Numbers: [92, 3] Generated Node #0,0,0: 95:[92, 3] Operation: 18-15=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[92, 3], Operations: ['65-50=15', '18-15=3'] Exploring Operation: 92+3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[92, 18, 50, 65], Operations: [] Exploring Operation: 65-50=15, Resulting Numbers: [92, 18, 15] Generated Node #0,0: 95:[92, 18, 15] Operation: 65-50=15 Moving to Node #0,0 Current State: 95:[92, 18, 15], Operations: ['65-50=15'] Exploring Operation: 18-15=3, Resulting Numbers: [92, 3] Generated Node #0,0,0: 95:[92, 3] Operation: 18-15=3 Moving to Node #0,0,0 Current State: 95:[92, 3], Operations: ['65-50=15', '18-15=3'] Exploring Operation: 92+3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 68, 93, 60, 50 ]
85
[ "93-68=25", "60+50=110", "110-25=85" ]
Current State: 85:[68, 93, 60, 50], Operations: [] Exploring Operation: 93-68=25, Resulting Numbers: [60, 50, 25] Generated Node #2: [60, 50, 25] from Operation: 93-68=25 Current State: 85:[60, 50, 25], Operations: ['93-68=25'] Exploring Operation: 60+50=110, Resulting Numbers: [25, 110] Generated Node #3: [25, 110] from Operation: 60+50=110 Current State: 85:[25, 110], Operations: ['93-68=25', '60+50=110'] Exploring Operation: 110-25=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[68, 93, 60, 50], Operations: [] Exploring Operation: 60-50=10, Resulting Numbers: [68, 93, 10] Generated Node #0,0: 85:[68, 93, 10] Operation: 60-50=10 Exploring Operation: 68-50=18, Resulting Numbers: [93, 60, 18] Generated Node #0,1: 85:[93, 60, 18] Operation: 68-50=18 Moving to Node #0,0 Current State: 85:[68, 93, 10], Operations: ['60-50=10'] Exploring Operation: 93-68=25, Resulting Numbers: [10, 25] Generated Node #0,0,0: 85:[10, 25] Operation: 93-68=25 Exploring Operation: 68+10=78, Resulting Numbers: [93, 78] Generated Node #0,0,1: 85:[93, 78] Operation: 68+10=78 Moving to Node #0,1 Current State: 85:[93, 60, 18], Operations: ['68-50=18'] Exploring Operation: 93-60=33, Resulting Numbers: [18, 33] Generated Node #0,1,0: 85:[18, 33] Operation: 93-60=33 Exploring Operation: 60+18=78, Resulting Numbers: [93, 78] Generated Node #0,1,1: 85:[93, 78] Operation: 60+18=78 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 85:[93, 78], Operations: ['68-50=18', '60+18=78'] Exploring Operation: 93-78=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 93+78=171, Resulting Numbers: [171] 171,85 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: 85:[18, 33], Operations: ['68-50=18', '93-60=33'] Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,85 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,85 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: 85:[10, 25], Operations: ['60-50=10', '93-68=25'] Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,85 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[93, 78], Operations: ['60-50=10', '68+10=78'] Exploring Operation: 93-78=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 93+78=171, Resulting Numbers: [171] 171,85 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 93, 47, 87, 87 ]
47
[ "93-47=46", "87/87=1", "46+1=47" ]
Current State: 47:[93, 47, 87, 87], Operations: [] Exploring Operation: 93-47=46, Resulting Numbers: [87, 87, 46] Generated Node #2: [87, 87, 46] from Operation: 93-47=46 Current State: 47:[87, 87, 46], Operations: ['93-47=46'] Exploring Operation: 87/87=1, Resulting Numbers: [46, 1] Generated Node #3: [46, 1] from Operation: 87/87=1 Current State: 47:[46, 1], Operations: ['93-47=46', '87/87=1'] Exploring Operation: 46+1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[93, 47, 87, 87], Operations: [] Exploring Operation: 93-47=46, Resulting Numbers: [87, 87, 46] Generated Node #0,0: 47:[87, 87, 46] Operation: 93-47=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[87, 87, 46], Operations: ['93-47=46'] Exploring Operation: 87-46=41, Resulting Numbers: [87, 41] Generated Node #0,0,0: 47:[87, 41] Operation: 87-46=41 Moving to Node #0,0,0 Current State: 47:[87, 41], Operations: ['93-47=46', '87-46=41'] Exploring Operation: 87-41=46, Resulting Numbers: [46] 46,47 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
[ 39, 44, 87, 34 ]
30
[ "39+44=83", "87-34=53", "83-53=30" ]
Current State: 30:[39, 44, 87, 34], Operations: [] Exploring Operation: 39+44=83, Resulting Numbers: [87, 34, 83] Generated Node #2: [87, 34, 83] from Operation: 39+44=83 Current State: 30:[87, 34, 83], Operations: ['39+44=83'] Exploring Operation: 87-34=53, Resulting Numbers: [83, 53] Generated Node #3: [83, 53] from Operation: 87-34=53 Current State: 30:[83, 53], Operations: ['39+44=83', '87-34=53'] Exploring Operation: 83-53=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[39, 44, 87, 34], Operations: [] Exploring Operation: 87-39=48, Resulting Numbers: [44, 34, 48] Generated Node #0,0: 30:[44, 34, 48] Operation: 87-39=48 Exploring Operation: 44-39=5, Resulting Numbers: [87, 34, 5] Generated Node #0,1: 30:[87, 34, 5] Operation: 44-39=5 Exploring Operation: 87-34=53, Resulting Numbers: [39, 44, 53] Generated Node #0,2: 30:[39, 44, 53] Operation: 87-34=53 Exploring Operation: 87-44=43, Resulting Numbers: [39, 34, 43] Generated Node #0,3: 30:[39, 34, 43] Operation: 87-44=43 Start Sub Search at level 1: Moving to Node #0,3 Current State: 30:[39, 34, 43], Operations: ['87-44=43'] Exploring Operation: 39-34=5, Resulting Numbers: [43, 5] Generated Node #0,3,0: 30:[43, 5] Operation: 39-34=5 Exploring Operation: 39+34=73, Resulting Numbers: [43, 73] Generated Node #0,3,1: 30:[43, 73] Operation: 39+34=73 Exploring Operation: 43-34=9, Resulting Numbers: [39, 9] Generated Node #0,3,2: 30:[39, 9] Operation: 43-34=9 Exploring Operation: 43-39=4, Resulting Numbers: [34, 4] Generated Node #0,3,3: 30:[34, 4] Operation: 43-39=4 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 30:[34, 4], Operations: ['87-44=43', '43-39=4'] Exploring Operation: 34*4=136, Resulting Numbers: [136] 136,30 unequal: No Solution Exploring Operation: 34+4=38, Resulting Numbers: [38] 38,30 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[39, 44, 87, 34], Operations: [] Exploring Operation: 87-44=43, Resulting Numbers: [39, 34, 43] Generated Node #0,3: 30:[39, 34, 43] Operation: 87-44=43 Moving to Node #0,3 Current State: 30:[39, 34, 43], Operations: ['87-44=43'] Exploring Operation: 43-39=4, Resulting Numbers: [34, 4] Generated Node #0,3,3: 30:[34, 4] Operation: 43-39=4 Moving to Node #0,3,3 Current State: 30:[34, 4], Operations: ['87-44=43', '43-39=4'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 9, 91, 82, 62 ]
75
[ "82+62=144", "144/9=16", "91-16=75" ]
Current State: 75:[9, 91, 82, 62], Operations: [] Exploring Operation: 82+62=144, Resulting Numbers: [9, 91, 144] Generated Node #2: [9, 91, 144] from Operation: 82+62=144 Current State: 75:[9, 91, 144], Operations: ['82+62=144'] Exploring Operation: 144/9=16, Resulting Numbers: [91, 16] Generated Node #3: [91, 16] from Operation: 144/9=16 Current State: 75:[91, 16], Operations: ['82+62=144', '144/9=16'] Exploring Operation: 91-16=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[9, 91, 82, 62], Operations: [] Exploring Operation: 91-62=29, Resulting Numbers: [9, 82, 29] Generated Node #0,0: 75:[9, 82, 29] Operation: 91-62=29 Exploring Operation: 82-62=20, Resulting Numbers: [9, 91, 20] Generated Node #0,1: 75:[9, 91, 20] Operation: 82-62=20 Exploring Operation: 91-82=9, Resulting Numbers: [9, 62, 9] Generated Node #0,2: 75:[9, 62, 9] Operation: 91-82=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[9, 82, 29], Operations: ['91-62=29'] Exploring Operation: 9+82=91, Resulting Numbers: [29, 91] Generated Node #0,0,0: 75:[29, 91] Operation: 9+82=91 Exploring Operation: 29-9=20, Resulting Numbers: [82, 20] Generated Node #0,0,1: 75:[82, 20] Operation: 29-9=20 Exploring Operation: 82-9=73, Resulting Numbers: [29, 73] Generated Node #0,0,2: 75:[29, 73] Operation: 82-9=73 Moving to Node #0,0,2 Current State: 75:[29, 73], Operations: ['91-62=29', '82-9=73'] Exploring Operation: 29*73=2117, Resulting Numbers: [2117] 2117,75 unequal: No Solution Exploring Operation: 73-29=44, Resulting Numbers: [44] 44,75 unequal: No Solution Exploring Operation: 29+73=102, Resulting Numbers: [102] 102,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[82, 20], Operations: ['91-62=29', '29-9=20'] Exploring Operation: 82-20=62, Resulting Numbers: [62] 62,75 unequal: No Solution Exploring Operation: 82+20=102, Resulting Numbers: [102] 102,75 unequal: No Solution Exploring Operation: 82*20=1640, Resulting Numbers: [1640] 1640,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[29, 91], Operations: ['91-62=29', '9+82=91'] Exploring Operation: 29*91=2639, Resulting Numbers: [2639] 2639,75 unequal: No Solution Exploring Operation: 29+91=120, Resulting Numbers: [120] 120,75 unequal: No Solution Exploring Operation: 91-29=62, Resulting Numbers: [62] 62,75 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: 75:[9, 62, 9], Operations: ['91-82=9'] Exploring Operation: 9+62=71, Resulting Numbers: [9, 71] Generated Node #0,2,0: 75:[9, 71] Operation: 9+62=71 Exploring Operation: 62+9=71, Resulting Numbers: [9, 71] Generated Node #0,2,1: 75:[9, 71] Operation: 62+9=71 Exploring Operation: 9/9=1, Resulting Numbers: [62, 1] Generated Node #0,2,2: 75:[62, 1] Operation: 9/9=1 Moving to Node #0,2,0 Current State: 75:[9, 71], Operations: ['91-82=9', '9+62=71'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,75 unequal: No Solution Exploring Operation: 9*71=639, Resulting Numbers: [639] 639,75 unequal: No Solution Exploring Operation: 9+71=80, Resulting Numbers: [80] 80,75 unequal: No Solution Moving to Node #0,2,1 Current State: 75:[9, 71], Operations: ['91-82=9', '62+9=71'] Exploring Operation: 9+71=80, Resulting Numbers: [80] 80,75 unequal: No Solution Exploring Operation: 9*71=639, Resulting Numbers: [639] 639,75 unequal: No Solution Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,75 unequal: No Solution Moving to Node #0,2,2 Current State: 75:[62, 1], Operations: ['91-82=9', '9/9=1'] Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,75 unequal: No Solution Exploring Operation: 62*1=62, Resulting Numbers: [62] 62,75 unequal: No Solution Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,75 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: 75:[9, 91, 20], Operations: ['82-62=20'] Exploring Operation: 91-20=71, Resulting Numbers: [9, 71] Generated Node #0,1,0: 75:[9, 71] Operation: 91-20=71 Exploring Operation: 9+20=29, Resulting Numbers: [91, 29] Generated Node #0,1,1: 75:[91, 29] Operation: 9+20=29 Exploring Operation: 91-9=82, Resulting Numbers: [20, 82] Generated Node #0,1,2: 75:[20, 82] Operation: 91-9=82 Moving to Node #0,1,0 Current State: 75:[9, 71], Operations: ['82-62=20', '91-20=71'] Exploring Operation: 9+71=80, Resulting Numbers: [80] 80,75 unequal: No Solution Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,75 unequal: No Solution Exploring Operation: 9*71=639, Resulting Numbers: [639] 639,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[20, 82], Operations: ['82-62=20', '91-9=82'] Exploring Operation: 20+82=102, Resulting Numbers: [102] 102,75 unequal: No Solution Exploring Operation: 82-20=62, Resulting Numbers: [62] 62,75 unequal: No Solution Exploring Operation: 20*82=1640, Resulting Numbers: [1640] 1640,75 unequal: No Solution Moving to Node #0,1,1 Current State: 75:[91, 29], Operations: ['82-62=20', '9+20=29'] Exploring Operation: 91+29=120, Resulting Numbers: [120] 120,75 unequal: No Solution Exploring Operation: 91-29=62, Resulting Numbers: [62] 62,75 unequal: No Solution Exploring Operation: 91*29=2639, Resulting Numbers: [2639] 2639,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 18, 86, 81, 20 ]
43
[ "18+86=104", "81-20=61", "104-61=43" ]
Current State: 43:[18, 86, 81, 20], Operations: [] Exploring Operation: 18+86=104, Resulting Numbers: [81, 20, 104] Generated Node #2: [81, 20, 104] from Operation: 18+86=104 Current State: 43:[81, 20, 104], Operations: ['18+86=104'] Exploring Operation: 81-20=61, Resulting Numbers: [104, 61] Generated Node #3: [104, 61] from Operation: 81-20=61 Current State: 43:[104, 61], Operations: ['18+86=104', '81-20=61'] Exploring Operation: 104-61=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[18, 86, 81, 20], Operations: [] Exploring Operation: 81-18=63, Resulting Numbers: [86, 20, 63] Generated Node #0,0: 43:[86, 20, 63] Operation: 81-18=63 Exploring Operation: 18+20=38, Resulting Numbers: [86, 81, 38] Generated Node #0,1: 43:[86, 81, 38] Operation: 18+20=38 Exploring Operation: 86-18=68, Resulting Numbers: [81, 20, 68] Generated Node #0,2: 43:[81, 20, 68] Operation: 86-18=68 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[86, 20, 63], Operations: ['81-18=63'] Exploring Operation: 63-20=43, Resulting Numbers: [86, 43] Generated Node #0,0,0: 43:[86, 43] Operation: 63-20=43 Exploring Operation: 86-20=66, Resulting Numbers: [63, 66] Generated Node #0,0,1: 43:[63, 66] Operation: 86-20=66 Exploring Operation: 86-63=23, Resulting Numbers: [20, 23] Generated Node #0,0,2: 43:[20, 23] Operation: 86-63=23 Moving to Node #0,0,0 Current State: 43:[86, 43], Operations: ['81-18=63', '63-20=43'] Exploring Operation: 86/43=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 86+43=129, Resulting Numbers: [129] 129,43 unequal: No Solution Exploring Operation: 86-43=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[18, 86, 81, 20], Operations: [] Exploring Operation: 81-18=63, Resulting Numbers: [86, 20, 63] Generated Node #0,0: 43:[86, 20, 63] Operation: 81-18=63 Moving to Node #0,0 Current State: 43:[86, 20, 63], Operations: ['81-18=63'] Exploring Operation: 63-20=43, Resulting Numbers: [86, 43] Generated Node #0,0,0: 43:[86, 43] Operation: 63-20=43 Moving to Node #0,0,0 Current State: 43:[86, 43], Operations: ['81-18=63', '63-20=43'] Exploring Operation: 86-43=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 60, 3, 66, 70 ]
79
[ "60-3=57", "66+70=136", "136-57=79" ]
Current State: 79:[60, 3, 66, 70], Operations: [] Exploring Operation: 60-3=57, Resulting Numbers: [66, 70, 57] Generated Node #2: [66, 70, 57] from Operation: 60-3=57 Current State: 79:[66, 70, 57], Operations: ['60-3=57'] Exploring Operation: 66+70=136, Resulting Numbers: [57, 136] Generated Node #3: [57, 136] from Operation: 66+70=136 Current State: 79:[57, 136], Operations: ['60-3=57', '66+70=136'] Exploring Operation: 136-57=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[60, 3, 66, 70], Operations: [] Exploring Operation: 60+3=63, Resulting Numbers: [66, 70, 63] Generated Node #0,0: 79:[66, 70, 63] Operation: 60+3=63 Exploring Operation: 3+66=69, Resulting Numbers: [60, 70, 69] Generated Node #0,1: 79:[60, 70, 69] Operation: 3+66=69 Exploring Operation: 60-3=57, Resulting Numbers: [66, 70, 57] Generated Node #0,2: 79:[66, 70, 57] Operation: 60-3=57 Exploring Operation: 3+70=73, Resulting Numbers: [60, 66, 73] Generated Node #0,3: 79:[60, 66, 73] Operation: 3+70=73 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[66, 70, 63], Operations: ['60+3=63'] Exploring Operation: 66+63=129, Resulting Numbers: [70, 129] Generated Node #0,0,0: 79:[70, 129] Operation: 66+63=129 Exploring Operation: 66-63=3, Resulting Numbers: [70, 3] Generated Node #0,0,1: 79:[70, 3] Operation: 66-63=3 Exploring Operation: 70+63=133, Resulting Numbers: [66, 133] Generated Node #0,0,2: 79:[66, 133] Operation: 70+63=133 Exploring Operation: 66+70=136, Resulting Numbers: [63, 136] Generated Node #0,0,3: 79:[63, 136] Operation: 66+70=136 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[70, 129], Operations: ['60+3=63', '66+63=129'] Exploring Operation: 70*129=9030, Resulting Numbers: [9030] 9030,79 unequal: No Solution Exploring Operation: 129-70=59, Resulting Numbers: [59] 59,79 unequal: No Solution Exploring Operation: 70+129=199, Resulting Numbers: [199] 199,79 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: 79:[66, 133], Operations: ['60+3=63', '70+63=133'] Exploring Operation: 133-66=67, Resulting Numbers: [67] 67,79 unequal: No Solution Exploring Operation: 66*133=8778, Resulting Numbers: [8778] 8778,79 unequal: No Solution Exploring Operation: 66+133=199, Resulting Numbers: [199] 199,79 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: 79:[63, 136], Operations: ['60+3=63', '66+70=136'] Exploring Operation: 63+136=199, Resulting Numbers: [199] 199,79 unequal: No Solution Exploring Operation: 63*136=8568, Resulting Numbers: [8568] 8568,79 unequal: No Solution Exploring Operation: 136-63=73, Resulting Numbers: [73] 73,79 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: 79:[70, 3], Operations: ['60+3=63', '66-63=3'] Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,79 unequal: No Solution Exploring Operation: 70+3=73, Resulting Numbers: [73] 73,79 unequal: No Solution Exploring Operation: 70*3=210, Resulting Numbers: [210] 210,79 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: 79:[60, 70, 69], Operations: ['3+66=69'] Exploring Operation: 69-60=9, Resulting Numbers: [70, 9] Generated Node #0,1,0: 79:[70, 9] Operation: 69-60=9 Exploring Operation: 60+70=130, Resulting Numbers: [69, 130] Generated Node #0,1,1: 79:[69, 130] Operation: 60+70=130 Exploring Operation: 60+69=129, Resulting Numbers: [70, 129] Generated Node #0,1,2: 79:[70, 129] Operation: 60+69=129 Exploring Operation: 70-60=10, Resulting Numbers: [69, 10] Generated Node #0,1,3: 79:[69, 10] Operation: 70-60=10 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 79:[70, 129], Operations: ['3+66=69', '60+69=129'] Exploring Operation: 129-70=59, Resulting Numbers: [59] 59,79 unequal: No Solution Exploring Operation: 70+129=199, Resulting Numbers: [199] 199,79 unequal: No Solution Exploring Operation: 70*129=9030, Resulting Numbers: [9030] 9030,79 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: 79:[69, 130], Operations: ['3+66=69', '60+70=130'] Exploring Operation: 69*130=8970, Resulting Numbers: [8970] 8970,79 unequal: No Solution Exploring Operation: 69+130=199, Resulting Numbers: [199] 199,79 unequal: No Solution Exploring Operation: 130-69=61, Resulting Numbers: [61] 61,79 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: 79:[70, 9], Operations: ['3+66=69', '69-60=9'] Exploring Operation: 70*9=630, Resulting Numbers: [630] 630,79 unequal: No Solution Exploring Operation: 70+9=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[60, 3, 66, 70], Operations: [] Exploring Operation: 3+66=69, Resulting Numbers: [60, 70, 69] Generated Node #0,1: 79:[60, 70, 69] Operation: 3+66=69 Moving to Node #0,1 Current State: 79:[60, 70, 69], Operations: ['3+66=69'] Exploring Operation: 69-60=9, Resulting Numbers: [70, 9] Generated Node #0,1,0: 79:[70, 9] Operation: 69-60=9 Moving to Node #0,1,0 Current State: 79:[70, 9], Operations: ['3+66=69', '69-60=9'] Exploring Operation: 70+9=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_4
mult_heuristic
[ 13, 89, 29, 55 ]
38
[ "13*89=1157", "1157-55=1102", "1102/29=38" ]
Current State: 38:[13, 89, 29, 55], Operations: [] Exploring Operation: 13*89=1157, Resulting Numbers: [29, 55, 1157] Generated Node #2: [29, 55, 1157] from Operation: 13*89=1157 Current State: 38:[29, 55, 1157], Operations: ['13*89=1157'] Exploring Operation: 1157-55=1102, Resulting Numbers: [29, 1102] Generated Node #3: [29, 1102] from Operation: 1157-55=1102 Current State: 38:[29, 1102], Operations: ['13*89=1157', '1157-55=1102'] Exploring Operation: 1102/29=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[13, 89, 29, 55], Operations: [] Exploring Operation: 89-13=76, Resulting Numbers: [29, 55, 76] Generated Node #0,0: 38:[29, 55, 76] Operation: 89-13=76 Exploring Operation: 89-29=60, Resulting Numbers: [13, 55, 60] Generated Node #0,1: 38:[13, 55, 60] Operation: 89-29=60 Exploring Operation: 89-55=34, Resulting Numbers: [13, 29, 34] Generated Node #0,2: 38:[13, 29, 34] Operation: 89-55=34 Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[13, 29, 34], Operations: ['89-55=34'] Exploring Operation: 29-13=16, Resulting Numbers: [34, 16] Generated Node #0,2,0: 38:[34, 16] Operation: 29-13=16 Exploring Operation: 13+29=42, Resulting Numbers: [34, 42] Generated Node #0,2,1: 38:[34, 42] Operation: 13+29=42 Exploring Operation: 34-29=5, Resulting Numbers: [13, 5] Generated Node #0,2,2: 38:[13, 5] Operation: 34-29=5 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 38:[34, 16], Operations: ['89-55=34', '29-13=16'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,38 unequal: No Solution Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,38 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: 38:[34, 42], Operations: ['89-55=34', '13+29=42'] Exploring Operation: 34+42=76, Resulting Numbers: [76] 76,38 unequal: No Solution Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 34*42=1428, Resulting Numbers: [1428] 1428,38 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: 38:[13, 5], Operations: ['89-55=34', '34-29=5'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,38 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: 38:[13, 55, 60], Operations: ['89-29=60'] Exploring Operation: 60-55=5, Resulting Numbers: [13, 5] Generated Node #0,1,0: 38:[13, 5] Operation: 60-55=5 Exploring Operation: 60-13=47, Resulting Numbers: [55, 47] Generated Node #0,1,1: 38:[55, 47] Operation: 60-13=47 Exploring Operation: 55-13=42, Resulting Numbers: [60, 42] Generated Node #0,1,2: 38:[60, 42] Operation: 55-13=42 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 38:[13, 5], Operations: ['89-29=60', '60-55=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,38 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: 38:[55, 47], Operations: ['89-29=60', '60-13=47'] Exploring Operation: 55-47=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 55+47=102, Resulting Numbers: [102] 102,38 unequal: No Solution Exploring Operation: 55*47=2585, Resulting Numbers: [2585] 2585,38 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: 38:[60, 42], Operations: ['89-29=60', '55-13=42'] Exploring Operation: 60*42=2520, Resulting Numbers: [2520] 2520,38 unequal: No Solution Exploring Operation: 60-42=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 60+42=102, Resulting Numbers: [102] 102,38 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: 38:[29, 55, 76], Operations: ['89-13=76'] Exploring Operation: 76-29=47, Resulting Numbers: [55, 47] Generated Node #0,0,0: 38:[55, 47] Operation: 76-29=47 Exploring Operation: 76-55=21, Resulting Numbers: [29, 21] Generated Node #0,0,1: 38:[29, 21] Operation: 76-55=21 Exploring Operation: 55-29=26, Resulting Numbers: [76, 26] Generated Node #0,0,2: 38:[76, 26] Operation: 55-29=26 Moving to Node #0,0,1 Current State: 38:[29, 21], Operations: ['89-13=76', '76-55=21'] Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 29+21=50, Resulting Numbers: [50] 50,38 unequal: No Solution Exploring Operation: 29*21=609, Resulting Numbers: [609] 609,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[55, 47], Operations: ['89-13=76', '76-29=47'] Exploring Operation: 55-47=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 55+47=102, Resulting Numbers: [102] 102,38 unequal: No Solution Exploring Operation: 55*47=2585, Resulting Numbers: [2585] 2585,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[76, 26], Operations: ['89-13=76', '55-29=26'] Exploring Operation: 76+26=102, Resulting Numbers: [102] 102,38 unequal: No Solution Exploring Operation: 76*26=1976, Resulting Numbers: [1976] 1976,38 unequal: No Solution Exploring Operation: 76-26=50, Resulting Numbers: [50] 50,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 38, 87, 48, 62 ]
15
[ "38+87=125", "48+62=110", "125-110=15" ]
Current State: 15:[38, 87, 48, 62], Operations: [] Exploring Operation: 38+87=125, Resulting Numbers: [48, 62, 125] Generated Node #2: [48, 62, 125] from Operation: 38+87=125 Current State: 15:[48, 62, 125], Operations: ['38+87=125'] Exploring Operation: 48+62=110, Resulting Numbers: [125, 110] Generated Node #3: [125, 110] from Operation: 48+62=110 Current State: 15:[125, 110], Operations: ['38+87=125', '48+62=110'] Exploring Operation: 125-110=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[38, 87, 48, 62], Operations: [] Exploring Operation: 87-62=25, Resulting Numbers: [38, 48, 25] Generated Node #0,0: 15:[38, 48, 25] Operation: 87-62=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[38, 48, 25], Operations: ['87-62=25'] Exploring Operation: 48-38=10, Resulting Numbers: [25, 10] Generated Node #0,0,0: 15:[25, 10] Operation: 48-38=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[25, 10], Operations: ['87-62=25', '48-38=10'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[38, 87, 48, 62], Operations: [] Exploring Operation: 87-62=25, Resulting Numbers: [38, 48, 25] Generated Node #0,0: 15:[38, 48, 25] Operation: 87-62=25 Moving to Node #0,0 Current State: 15:[38, 48, 25], Operations: ['87-62=25'] Exploring Operation: 48-38=10, Resulting Numbers: [25, 10] Generated Node #0,0,0: 15:[25, 10] Operation: 48-38=10 Moving to Node #0,0,0 Current State: 15:[25, 10], Operations: ['87-62=25', '48-38=10'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 14, 87, 5, 9 ]
97
[ "14+87=101", "9-5=4", "101-4=97" ]
Current State: 97:[14, 87, 5, 9], Operations: [] Exploring Operation: 14+87=101, Resulting Numbers: [5, 9, 101] Generated Node #2: [5, 9, 101] from Operation: 14+87=101 Current State: 97:[5, 9, 101], Operations: ['14+87=101'] Exploring Operation: 9-5=4, Resulting Numbers: [101, 4] Generated Node #3: [101, 4] from Operation: 9-5=4 Current State: 97:[101, 4], Operations: ['14+87=101', '9-5=4'] Exploring Operation: 101-4=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[14, 87, 5, 9], Operations: [] Exploring Operation: 14*9=126, Resulting Numbers: [87, 5, 126] Generated Node #0,0: 97:[87, 5, 126] Operation: 14*9=126 Exploring Operation: 14*5=70, Resulting Numbers: [87, 9, 70] Generated Node #0,1: 97:[87, 9, 70] Operation: 14*5=70 Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[87, 9, 70], Operations: ['14*5=70'] Exploring Operation: 87+9=96, Resulting Numbers: [70, 96] Generated Node #0,1,0: 97:[70, 96] Operation: 87+9=96 Exploring Operation: 9+70=79, Resulting Numbers: [87, 79] Generated Node #0,1,1: 97:[87, 79] Operation: 9+70=79 Moving to Node #0,1,0 Current State: 97:[70, 96], Operations: ['14*5=70', '87+9=96'] Exploring Operation: 96-70=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 70+96=166, Resulting Numbers: [166] 166,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[87, 79], Operations: ['14*5=70', '9+70=79'] Exploring Operation: 87+79=166, Resulting Numbers: [166] 166,97 unequal: No Solution Exploring Operation: 87-79=8, Resulting Numbers: [8] 8,97 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: 97:[87, 5, 126], Operations: ['14*9=126'] Exploring Operation: 87+5=92, Resulting Numbers: [126, 92] Generated Node #0,0,0: 97:[126, 92] Operation: 87+5=92 Exploring Operation: 126-5=121, Resulting Numbers: [87, 121] Generated Node #0,0,1: 97:[87, 121] Operation: 126-5=121 Moving to Node #0,0,0 Current State: 97:[126, 92], Operations: ['14*9=126', '87+5=92'] Exploring Operation: 126-92=34, Resulting Numbers: [34] 34,97 unequal: No Solution Exploring Operation: 126+92=218, Resulting Numbers: [218] 218,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[87, 121], Operations: ['14*9=126', '126-5=121'] Exploring Operation: 121-87=34, Resulting Numbers: [34] 34,97 unequal: No Solution Exploring Operation: 87+121=208, Resulting Numbers: [208] 208,97 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
[ 77, 88, 79, 24 ]
66
[ "88-77=11", "79-24=55", "11+55=66" ]
Current State: 66:[77, 88, 79, 24], Operations: [] Exploring Operation: 88-77=11, Resulting Numbers: [79, 24, 11] Generated Node #2: [79, 24, 11] from Operation: 88-77=11 Current State: 66:[79, 24, 11], Operations: ['88-77=11'] Exploring Operation: 79-24=55, Resulting Numbers: [11, 55] Generated Node #3: [11, 55] from Operation: 79-24=55 Current State: 66:[11, 55], Operations: ['88-77=11', '79-24=55'] Exploring Operation: 11+55=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[77, 88, 79, 24], Operations: [] Exploring Operation: 88-77=11, Resulting Numbers: [79, 24, 11] Generated Node #0,0: 66:[79, 24, 11] Operation: 88-77=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[79, 24, 11], Operations: ['88-77=11'] Exploring Operation: 79-11=68, Resulting Numbers: [24, 68] Generated Node #0,0,0: 66:[24, 68] Operation: 79-11=68 Moving to Node #0,0,0 Current State: 66:[24, 68], Operations: ['88-77=11', '79-11=68'] Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,66 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
[ 37, 40, 79, 34 ]
77
[ "40+34=74", "74/37=2", "79-2=77" ]
Current State: 77:[37, 40, 79, 34], Operations: [] Exploring Operation: 40+34=74, Resulting Numbers: [37, 79, 74] Generated Node #2: [37, 79, 74] from Operation: 40+34=74 Current State: 77:[37, 79, 74], Operations: ['40+34=74'] Exploring Operation: 74/37=2, Resulting Numbers: [79, 2] Generated Node #3: [79, 2] from Operation: 74/37=2 Current State: 77:[79, 2], Operations: ['40+34=74', '74/37=2'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[37, 40, 79, 34], Operations: [] Exploring Operation: 37+40=77, Resulting Numbers: [79, 34, 77] Generated Node #0,0: 77:[79, 34, 77] Operation: 37+40=77 Exploring Operation: 40-37=3, Resulting Numbers: [79, 34, 3] Generated Node #0,1: 77:[79, 34, 3] Operation: 40-37=3 Exploring Operation: 37-34=3, Resulting Numbers: [40, 79, 3] Generated Node #0,2: 77:[40, 79, 3] Operation: 37-34=3 Exploring Operation: 40-34=6, Resulting Numbers: [37, 79, 6] Generated Node #0,3: 77:[37, 79, 6] Operation: 40-34=6 Exploring Operation: 40+34=74, Resulting Numbers: [37, 79, 74] Generated Node #0,4: 77:[37, 79, 74] Operation: 40+34=74 Moving to Node #0,0 Current State: 77:[79, 34, 77], Operations: ['37+40=77'] Exploring Operation: 79-34=45, Resulting Numbers: [77, 45] Generated Node #0,0,0: 77:[77, 45] Operation: 79-34=45 Exploring Operation: 34+77=111, Resulting Numbers: [79, 111] Generated Node #0,0,1: 77:[79, 111] Operation: 34+77=111 Exploring Operation: 79+34=113, Resulting Numbers: [77, 113] Generated Node #0,0,2: 77:[77, 113] Operation: 79+34=113 Exploring Operation: 79-77=2, Resulting Numbers: [34, 2] Generated Node #0,0,3: 77:[34, 2] Operation: 79-77=2 Exploring Operation: 77-34=43, Resulting Numbers: [79, 43] Generated Node #0,0,4: 77:[79, 43] Operation: 77-34=43 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 77:[34, 2], Operations: ['37+40=77', '79-77=2'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,77 unequal: No Solution Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,77 unequal: No Solution Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,77 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,77 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: 77:[77, 45], Operations: ['37+40=77', '79-34=45'] Exploring Operation: 77*45=3465, Resulting Numbers: [3465] 3465,77 unequal: No Solution Exploring Operation: 77+45=122, Resulting Numbers: [122] 122,77 unequal: No Solution Exploring Operation: 77-45=32, Resulting Numbers: [32] 32,77 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: 77:[79, 43], Operations: ['37+40=77', '77-34=43'] Exploring Operation: 79+43=122, Resulting Numbers: [122] 122,77 unequal: No Solution Exploring Operation: 79-43=36, Resulting Numbers: [36] 36,77 unequal: No Solution Exploring Operation: 79*43=3397, Resulting Numbers: [3397] 3397,77 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: 77:[79, 111], Operations: ['37+40=77', '34+77=111'] Exploring Operation: 79+111=190, Resulting Numbers: [190] 190,77 unequal: No Solution Exploring Operation: 111-79=32, Resulting Numbers: [32] 32,77 unequal: No Solution Exploring Operation: 79*111=8769, Resulting Numbers: [8769] 8769,77 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: 77:[77, 113], Operations: ['37+40=77', '79+34=113'] Exploring Operation: 77*113=8701, Resulting Numbers: [8701] 8701,77 unequal: No Solution Exploring Operation: 77+113=190, Resulting Numbers: [190] 190,77 unequal: No Solution Exploring Operation: 113-77=36, Resulting Numbers: [36] 36,77 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: 77:[37, 79, 6], Operations: ['40-34=6'] Exploring Operation: 37-6=31, Resulting Numbers: [79, 31] Generated Node #0,3,0: 77:[79, 31] Operation: 37-6=31 Exploring Operation: 79-37=42, Resulting Numbers: [6, 42] Generated Node #0,3,1: 77:[6, 42] Operation: 79-37=42 Exploring Operation: 79-6=73, Resulting Numbers: [37, 73] Generated Node #0,3,2: 77:[37, 73] Operation: 79-6=73 Exploring Operation: 37+6=43, Resulting Numbers: [79, 43] Generated Node #0,3,3: 77:[79, 43] Operation: 37+6=43 Exploring Operation: 79+6=85, Resulting Numbers: [37, 85] Generated Node #0,3,4: 77:[37, 85] Operation: 79+6=85 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 77:[79, 31], Operations: ['40-34=6', '37-6=31'] Exploring Operation: 79+31=110, Resulting Numbers: [110] 110,77 unequal: No Solution Exploring Operation: 79-31=48, Resulting Numbers: [48] 48,77 unequal: No Solution Exploring Operation: 79*31=2449, Resulting Numbers: [2449] 2449,77 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: 77:[37, 73], Operations: ['40-34=6', '79-6=73'] Exploring Operation: 37*73=2701, Resulting Numbers: [2701] 2701,77 unequal: No Solution Exploring Operation: 73-37=36, Resulting Numbers: [36] 36,77 unequal: No Solution Exploring Operation: 37+73=110, Resulting Numbers: [110] 110,77 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: 77:[6, 42], Operations: ['40-34=6', '79-37=42'] Exploring Operation: 6+42=48, Resulting Numbers: [48] 48,77 unequal: No Solution Exploring Operation: 6*42=252, Resulting Numbers: [252] 252,77 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,77 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: 77:[79, 43], Operations: ['40-34=6', '37+6=43'] Exploring Operation: 79*43=3397, Resulting Numbers: [3397] 3397,77 unequal: No Solution Exploring Operation: 79+43=122, Resulting Numbers: [122] 122,77 unequal: No Solution Exploring Operation: 79-43=36, Resulting Numbers: [36] 36,77 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: 77:[37, 85], Operations: ['40-34=6', '79+6=85'] Exploring Operation: 37*85=3145, Resulting Numbers: [3145] 3145,77 unequal: No Solution Exploring Operation: 37+85=122, Resulting Numbers: [122] 122,77 unequal: No Solution Exploring Operation: 85-37=48, Resulting Numbers: [48] 48,77 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: 77:[79, 34, 3], Operations: ['40-37=3'] Exploring Operation: 34-3=31, Resulting Numbers: [79, 31] Generated Node #0,1,0: 77:[79, 31] Operation: 34-3=31 Exploring Operation: 79-3=76, Resulting Numbers: [34, 76] Generated Node #0,1,1: 77:[34, 76] Operation: 79-3=76 Exploring Operation: 34+3=37, Resulting Numbers: [79, 37] Generated Node #0,1,2: 77:[79, 37] Operation: 34+3=37 Exploring Operation: 34*3=102, Resulting Numbers: [79, 102] Generated Node #0,1,3: 77:[79, 102] Operation: 34*3=102 Exploring Operation: 79+3=82, Resulting Numbers: [34, 82] Generated Node #0,1,4: 77:[34, 82] Operation: 79+3=82 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 77:[79, 31], Operations: ['40-37=3', '34-3=31'] Exploring Operation: 79-31=48, Resulting Numbers: [48] 48,77 unequal: No Solution Exploring Operation: 79*31=2449, Resulting Numbers: [2449] 2449,77 unequal: No Solution Exploring Operation: 79+31=110, Resulting Numbers: [110] 110,77 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: 77:[34, 76], Operations: ['40-37=3', '79-3=76'] Exploring Operation: 34*76=2584, Resulting Numbers: [2584] 2584,77 unequal: No Solution Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,77 unequal: No Solution Exploring Operation: 34+76=110, Resulting Numbers: [110] 110,77 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: 77:[79, 102], Operations: ['40-37=3', '34*3=102'] Exploring Operation: 79*102=8058, Resulting Numbers: [8058] 8058,77 unequal: No Solution Exploring Operation: 102-79=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 79+102=181, Resulting Numbers: [181] 181,77 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: 77:[79, 37], Operations: ['40-37=3', '34+3=37'] Exploring Operation: 79+37=116, Resulting Numbers: [116] 116,77 unequal: No Solution Exploring Operation: 79-37=42, Resulting Numbers: [42] 42,77 unequal: No Solution Exploring Operation: 79*37=2923, Resulting Numbers: [2923] 2923,77 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: 77:[34, 82], Operations: ['40-37=3', '79+3=82'] Exploring Operation: 82-34=48, Resulting Numbers: [48] 48,77 unequal: No Solution Exploring Operation: 34*82=2788, Resulting Numbers: [2788] 2788,77 unequal: No Solution Exploring Operation: 34+82=116, Resulting Numbers: [116] 116,77 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: 77:[37, 79, 74], Operations: ['40+34=74'] Exploring Operation: 74/37=2, Resulting Numbers: [79, 2] Generated Node #0,4,0: 77:[79, 2] Operation: 74/37=2 Exploring Operation: 37+74=111, Resulting Numbers: [79, 111] Generated Node #0,4,1: 77:[79, 111] Operation: 37+74=111 Exploring Operation: 79-37=42, Resulting Numbers: [74, 42] Generated Node #0,4,2: 77:[74, 42] Operation: 79-37=42 Exploring Operation: 79-74=5, Resulting Numbers: [37, 5] Generated Node #0,4,3: 77:[37, 5] Operation: 79-74=5 Exploring Operation: 74-37=37, Resulting Numbers: [79, 37] Generated Node #0,4,4: 77:[79, 37] Operation: 74-37=37 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 77:[79, 2], Operations: ['40+34=74', '74/37=2'] Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,77 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[37, 40, 79, 34], Operations: [] Exploring Operation: 40+34=74, Resulting Numbers: [37, 79, 74] Generated Node #0,4: 77:[37, 79, 74] Operation: 40+34=74 Moving to Node #0,4 Current State: 77:[37, 79, 74], Operations: ['40+34=74'] Exploring Operation: 74/37=2, Resulting Numbers: [79, 2] Generated Node #0,4,0: 77:[79, 2] Operation: 74/37=2 Moving to Node #0,4,0 Current State: 77:[79, 2], Operations: ['40+34=74', '74/37=2'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.932292
hs_5
mult_heuristic
[ 11, 57, 6, 6 ]
67
[ "11+57=68", "6/6=1", "68-1=67" ]
Current State: 67:[11, 57, 6, 6], Operations: [] Exploring Operation: 11+57=68, Resulting Numbers: [6, 6, 68] Generated Node #2: [6, 6, 68] from Operation: 11+57=68 Current State: 67:[6, 6, 68], Operations: ['11+57=68'] Exploring Operation: 6/6=1, Resulting Numbers: [68, 1] Generated Node #3: [68, 1] from Operation: 6/6=1 Current State: 67:[68, 1], Operations: ['11+57=68', '6/6=1'] Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[11, 57, 6, 6], Operations: [] Exploring Operation: 11*6=66, Resulting Numbers: [57, 6, 66] Generated Node #0,0: 67:[57, 6, 66] Operation: 11*6=66 Exploring Operation: 11+6=17, Resulting Numbers: [57, 6, 17] Generated Node #0,1: 67:[57, 6, 17] Operation: 11+6=17 Exploring Operation: 6*6=36, Resulting Numbers: [11, 57, 36] Generated Node #0,2: 67:[11, 57, 36] Operation: 6*6=36 Exploring Operation: 11+6=17, Resulting Numbers: [57, 6, 17] Generated Node #0,3: 67:[57, 6, 17] Operation: 11+6=17 Exploring Operation: 11*6=66, Resulting Numbers: [57, 6, 66] Generated Node #0,4: 67:[57, 6, 66] Operation: 11*6=66 Moving to Node #0,0 Current State: 67:[57, 6, 66], Operations: ['11*6=66'] Exploring Operation: 66-6=60, Resulting Numbers: [57, 60] Generated Node #0,0,0: 67:[57, 60] Operation: 66-6=60 Exploring Operation: 57-6=51, Resulting Numbers: [66, 51] Generated Node #0,0,1: 67:[66, 51] Operation: 57-6=51 Exploring Operation: 6+66=72, Resulting Numbers: [57, 72] Generated Node #0,0,2: 67:[57, 72] Operation: 6+66=72 Exploring Operation: 66/6=11, Resulting Numbers: [57, 11] Generated Node #0,0,3: 67:[57, 11] Operation: 66/6=11 Exploring Operation: 57+6=63, Resulting Numbers: [66, 63] Generated Node #0,0,4: 67:[66, 63] Operation: 57+6=63 Moving to Node #0,4 Current State: 67:[57, 6, 66], Operations: ['11*6=66'] Exploring Operation: 66/6=11, Resulting Numbers: [57, 11] Generated Node #0,4,0: 67:[57, 11] Operation: 66/6=11 Exploring Operation: 57-6=51, Resulting Numbers: [66, 51] Generated Node #0,4,1: 67:[66, 51] Operation: 57-6=51 Exploring Operation: 66-6=60, Resulting Numbers: [57, 60] Generated Node #0,4,2: 67:[57, 60] Operation: 66-6=60 Exploring Operation: 6+66=72, Resulting Numbers: [57, 72] Generated Node #0,4,3: 67:[57, 72] Operation: 6+66=72 Exploring Operation: 57+6=63, Resulting Numbers: [66, 63] Generated Node #0,4,4: 67:[66, 63] Operation: 57+6=63 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 67:[66, 63], Operations: ['11*6=66', '57+6=63'] Exploring Operation: 66-63=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 66*63=4158, Resulting Numbers: [4158] 4158,67 unequal: No Solution Exploring Operation: 66+63=129, Resulting Numbers: [129] 129,67 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 #0,4,3 Current State: 67:[57, 72], Operations: ['11*6=66', '6+66=72'] Exploring Operation: 72-57=15, Resulting Numbers: [15] 15,67 unequal: No Solution Exploring Operation: 57+72=129, Resulting Numbers: [129] 129,67 unequal: No Solution Exploring Operation: 57*72=4104, Resulting Numbers: [4104] 4104,67 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 #0,4,1 Current State: 67:[66, 51], Operations: ['11*6=66', '57-6=51'] Exploring Operation: 66+51=117, Resulting Numbers: [117] 117,67 unequal: No Solution Exploring Operation: 66-51=15, Resulting Numbers: [15] 15,67 unequal: No Solution Exploring Operation: 66*51=3366, Resulting Numbers: [3366] 3366,67 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 #0,4,2 Current State: 67:[57, 60], Operations: ['11*6=66', '66-6=60'] Exploring Operation: 60-57=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 57+60=117, Resulting Numbers: [117] 117,67 unequal: No Solution Exploring Operation: 57*60=3420, Resulting Numbers: [3420] 3420,67 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 #0,4,0 Current State: 67:[57, 11], Operations: ['11*6=66', '66/6=11'] Exploring Operation: 57-11=46, Resulting Numbers: [46] 46,67 unequal: No Solution Exploring Operation: 57+11=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 57*11=627, Resulting Numbers: [627] 627,67 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: 67:[11, 57, 36], Operations: ['6*6=36'] Exploring Operation: 57-11=46, Resulting Numbers: [36, 46] Generated Node #0,2,0: 67:[36, 46] Operation: 57-11=46 Exploring Operation: 11+57=68, Resulting Numbers: [36, 68] Generated Node #0,2,1: 67:[36, 68] Operation: 11+57=68 Exploring Operation: 11+36=47, Resulting Numbers: [57, 47] Generated Node #0,2,2: 67:[57, 47] Operation: 11+36=47 Exploring Operation: 36-11=25, Resulting Numbers: [57, 25] Generated Node #0,2,3: 67:[57, 25] Operation: 36-11=25 Exploring Operation: 57+36=93, Resulting Numbers: [11, 93] Generated Node #0,2,4: 67:[11, 93] Operation: 57+36=93 Moving to Node #0,1 Current State: 67:[57, 6, 17], Operations: ['11+6=17'] Exploring Operation: 57-6=51, Resulting Numbers: [17, 51] Generated Node #0,1,0: 67:[17, 51] Operation: 57-6=51 Exploring Operation: 6*17=102, Resulting Numbers: [57, 102] Generated Node #0,1,1: 67:[57, 102] Operation: 6*17=102 Exploring Operation: 57+6=63, Resulting Numbers: [17, 63] Generated Node #0,1,2: 67:[17, 63] Operation: 57+6=63 Exploring Operation: 6+17=23, Resulting Numbers: [57, 23] Generated Node #0,1,3: 67:[57, 23] Operation: 6+17=23 Exploring Operation: 17-6=11, Resulting Numbers: [57, 11] Generated Node #0,1,4: 67:[57, 11] Operation: 17-6=11 Moving to Node #0,3 Current State: 67:[57, 6, 17], Operations: ['11+6=17'] Exploring Operation: 57+6=63, Resulting Numbers: [17, 63] Generated Node #0,3,0: 67:[17, 63] Operation: 57+6=63 Exploring Operation: 6+17=23, Resulting Numbers: [57, 23] Generated Node #0,3,1: 67:[57, 23] Operation: 6+17=23 Exploring Operation: 17-6=11, Resulting Numbers: [57, 11] Generated Node #0,3,2: 67:[57, 11] Operation: 17-6=11 Exploring Operation: 6*17=102, Resulting Numbers: [57, 102] Generated Node #0,3,3: 67:[57, 102] Operation: 6*17=102 Exploring Operation: 57-6=51, Resulting Numbers: [17, 51] Generated Node #0,3,4: 67:[17, 51] Operation: 57-6=51 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 67:[57, 102], Operations: ['11+6=17', '6*17=102'] Exploring Operation: 102-57=45, Resulting Numbers: [45] 45,67 unequal: No Solution Exploring Operation: 57*102=5814, Resulting Numbers: [5814] 5814,67 unequal: No Solution Exploring Operation: 57+102=159, Resulting Numbers: [159] 159,67 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 #0,3,0 Current State: 67:[17, 63], Operations: ['11+6=17', '57+6=63'] Exploring Operation: 17+63=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 17*63=1071, Resulting Numbers: [1071] 1071,67 unequal: No Solution Exploring Operation: 63-17=46, Resulting Numbers: [46] 46,67 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 #0,3,1 Current State: 67:[57, 23], Operations: ['11+6=17', '6+17=23'] Exploring Operation: 57*23=1311, Resulting Numbers: [1311] 1311,67 unequal: No Solution Exploring Operation: 57+23=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,67 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 #0,3,2 Current State: 67:[57, 11], Operations: ['11+6=17', '17-6=11'] Exploring Operation: 57-11=46, Resulting Numbers: [46] 46,67 unequal: No Solution Exploring Operation: 57+11=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 57*11=627, Resulting Numbers: [627] 627,67 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 #0,3,4 Current State: 67:[17, 51], Operations: ['11+6=17', '57-6=51'] Exploring Operation: 17*51=867, Resulting Numbers: [867] 867,67 unequal: No Solution Exploring Operation: 51/17=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 17+51=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 51-17=34, Resulting Numbers: [34] 34,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,4 Current State: 67:[66, 63], Operations: ['11*6=66', '57+6=63'] Exploring Operation: 66*63=4158, Resulting Numbers: [4158] 4158,67 unequal: No Solution Exploring Operation: 66+63=129, Resulting Numbers: [129] 129,67 unequal: No Solution Exploring Operation: 66-63=3, Resulting Numbers: [3] 3,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[57, 72], Operations: ['11*6=66', '6+66=72'] Exploring Operation: 72-57=15, Resulting Numbers: [15] 15,67 unequal: No Solution Exploring Operation: 57+72=129, Resulting Numbers: [129] 129,67 unequal: No Solution Exploring Operation: 57*72=4104, Resulting Numbers: [4104] 4104,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[57, 60], Operations: ['11*6=66', '66-6=60'] Exploring Operation: 57+60=117, Resulting Numbers: [117] 117,67 unequal: No Solution Exploring Operation: 60-57=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 57*60=3420, Resulting Numbers: [3420] 3420,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[66, 51], Operations: ['11*6=66', '57-6=51'] Exploring Operation: 66*51=3366, Resulting Numbers: [3366] 3366,67 unequal: No Solution Exploring Operation: 66+51=117, Resulting Numbers: [117] 117,67 unequal: No Solution Exploring Operation: 66-51=15, Resulting Numbers: [15] 15,67 unequal: No Solution Moving to Node #0,2,2 Current State: 67:[57, 47], Operations: ['6*6=36', '11+36=47'] Exploring Operation: 57*47=2679, Resulting Numbers: [2679] 2679,67 unequal: No Solution Exploring Operation: 57+47=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 57-47=10, Resulting Numbers: [10] 10,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[36, 68], Operations: ['6*6=36', '11+57=68'] Exploring Operation: 36*68=2448, Resulting Numbers: [2448] 2448,67 unequal: No Solution Exploring Operation: 36+68=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 68-36=32, Resulting Numbers: [32] 32,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[57, 102], Operations: ['11+6=17', '6*17=102'] Exploring Operation: 102-57=45, Resulting Numbers: [45] 45,67 unequal: No Solution Exploring Operation: 57+102=159, Resulting Numbers: [159] 159,67 unequal: No Solution Exploring Operation: 57*102=5814, Resulting Numbers: [5814] 5814,67 unequal: No Solution Moving to Node #0,2,3 Current State: 67:[57, 25], Operations: ['6*6=36', '36-11=25'] Exploring Operation: 57+25=82, Resulting Numbers: [82] 82,67 unequal: No Solution Exploring Operation: 57*25=1425, Resulting Numbers: [1425] 1425,67 unequal: No Solution Exploring Operation: 57-25=32, Resulting Numbers: [32] 32,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[36, 46], Operations: ['6*6=36', '57-11=46'] Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,67 unequal: No Solution Exploring Operation: 36*46=1656, Resulting Numbers: [1656] 1656,67 unequal: No Solution Exploring Operation: 36+46=82, Resulting Numbers: [82] 82,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[17, 63], Operations: ['11+6=17', '57+6=63'] Exploring Operation: 63-17=46, Resulting Numbers: [46] 46,67 unequal: No Solution Exploring Operation: 17+63=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 17*63=1071, Resulting Numbers: [1071] 1071,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[57, 23], Operations: ['11+6=17', '6+17=23'] Exploring Operation: 57+23=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 57*23=1311, Resulting Numbers: [1311] 1311,67 unequal: No Solution Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[17, 51], Operations: ['11+6=17', '57-6=51'] Exploring Operation: 17+51=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 17*51=867, Resulting Numbers: [867] 867,67 unequal: No Solution Exploring Operation: 51/17=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 51-17=34, Resulting Numbers: [34] 34,67 unequal: No Solution Moving to Node #0,0,3 Current State: 67:[57, 11], Operations: ['11*6=66', '66/6=11'] Exploring Operation: 57-11=46, Resulting Numbers: [46] 46,67 unequal: No Solution Exploring Operation: 57*11=627, Resulting Numbers: [627] 627,67 unequal: No Solution Exploring Operation: 57+11=68, Resulting Numbers: [68] 68,67 unequal: No Solution Moving to Node #0,1,4 Current State: 67:[57, 11], Operations: ['11+6=17', '17-6=11'] Exploring Operation: 57+11=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 57*11=627, Resulting Numbers: [627] 627,67 unequal: No Solution Exploring Operation: 57-11=46, Resulting Numbers: [46] 46,67 unequal: No Solution Moving to Node #0,2,4 Current State: 67:[11, 93], Operations: ['6*6=36', '57+36=93'] Exploring Operation: 11+93=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 93-11=82, Resulting Numbers: [82] 82,67 unequal: No Solution Exploring Operation: 11*93=1023, Resulting Numbers: [1023] 1023,67 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 54, 53, 40, 7 ]
46
[ "54-53=1", "40+7=47", "47-1=46" ]
Current State: 46:[54, 53, 40, 7], Operations: [] Exploring Operation: 54-53=1, Resulting Numbers: [40, 7, 1] Generated Node #2: [40, 7, 1] from Operation: 54-53=1 Current State: 46:[40, 7, 1], Operations: ['54-53=1'] Exploring Operation: 40+7=47, Resulting Numbers: [1, 47] Generated Node #3: [1, 47] from Operation: 40+7=47 Current State: 46:[1, 47], Operations: ['54-53=1', '40+7=47'] Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[54, 53, 40, 7], Operations: [] Exploring Operation: 54-7=47, Resulting Numbers: [53, 40, 47] Generated Node #0,0: 46:[53, 40, 47] Operation: 54-7=47 Exploring Operation: 53-7=46, Resulting Numbers: [54, 40, 46] Generated Node #0,1: 46:[54, 40, 46] Operation: 53-7=46 Exploring Operation: 54-53=1, Resulting Numbers: [40, 7, 1] Generated Node #0,2: 46:[40, 7, 1] Operation: 54-53=1 Exploring Operation: 40+7=47, Resulting Numbers: [54, 53, 47] Generated Node #0,3: 46:[54, 53, 47] Operation: 40+7=47 Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[40, 7, 1], Operations: ['54-53=1'] Exploring Operation: 40-7=33, Resulting Numbers: [1, 33] Generated Node #0,2,0: 46:[1, 33] Operation: 40-7=33 Exploring Operation: 7-1=6, Resulting Numbers: [40, 6] Generated Node #0,2,1: 46:[40, 6] Operation: 7-1=6 Exploring Operation: 40+7=47, Resulting Numbers: [1, 47] Generated Node #0,2,2: 46:[1, 47] Operation: 40+7=47 Exploring Operation: 40+1=41, Resulting Numbers: [7, 41] Generated Node #0,2,3: 46:[7, 41] Operation: 40+1=41 Moving to Node #0,2,2 Current State: 46:[1, 47], Operations: ['54-53=1', '40+7=47'] Exploring Operation: 1*47=47, Resulting Numbers: [47] 47,46 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[54, 53, 40, 7], Operations: [] Exploring Operation: 54-53=1, Resulting Numbers: [40, 7, 1] Generated Node #0,2: 46:[40, 7, 1] Operation: 54-53=1 Moving to Node #0,2 Current State: 46:[40, 7, 1], Operations: ['54-53=1'] Exploring Operation: 40+7=47, Resulting Numbers: [1, 47] Generated Node #0,2,2: 46:[1, 47] Operation: 40+7=47 Moving to Node #0,2,2 Current State: 46:[1, 47], Operations: ['54-53=1', '40+7=47'] Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 87, 84, 73, 44 ]
32
[ "87-84=3", "73-44=29", "3+29=32" ]
Current State: 32:[87, 84, 73, 44], Operations: [] Exploring Operation: 87-84=3, Resulting Numbers: [73, 44, 3] Generated Node #2: [73, 44, 3] from Operation: 87-84=3 Current State: 32:[73, 44, 3], Operations: ['87-84=3'] Exploring Operation: 73-44=29, Resulting Numbers: [3, 29] Generated Node #3: [3, 29] from Operation: 73-44=29 Current State: 32:[3, 29], Operations: ['87-84=3', '73-44=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[87, 84, 73, 44], Operations: [] Exploring Operation: 84-73=11, Resulting Numbers: [87, 44, 11] Generated Node #0,0: 32:[87, 44, 11] Operation: 84-73=11 Exploring Operation: 84-44=40, Resulting Numbers: [87, 73, 40] Generated Node #0,1: 32:[87, 73, 40] Operation: 84-44=40 Exploring Operation: 87-44=43, Resulting Numbers: [84, 73, 43] Generated Node #0,2: 32:[84, 73, 43] Operation: 87-44=43 Exploring Operation: 87-84=3, Resulting Numbers: [73, 44, 3] Generated Node #0,3: 32:[73, 44, 3] Operation: 87-84=3 Exploring Operation: 87-73=14, Resulting Numbers: [84, 44, 14] Generated Node #0,4: 32:[84, 44, 14] Operation: 87-73=14 Moving to Node #0,3 Current State: 32:[73, 44, 3], Operations: ['87-84=3'] Exploring Operation: 44+3=47, Resulting Numbers: [73, 47] Generated Node #0,3,0: 32:[73, 47] Operation: 44+3=47 Exploring Operation: 73-44=29, Resulting Numbers: [3, 29] Generated Node #0,3,1: 32:[3, 29] Operation: 73-44=29 Exploring Operation: 73-3=70, Resulting Numbers: [44, 70] Generated Node #0,3,2: 32:[44, 70] Operation: 73-3=70 Exploring Operation: 73+3=76, Resulting Numbers: [44, 76] Generated Node #0,3,3: 32:[44, 76] Operation: 73+3=76 Exploring Operation: 44-3=41, Resulting Numbers: [73, 41] Generated Node #0,3,4: 32:[73, 41] Operation: 44-3=41 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 32:[3, 29], Operations: ['87-84=3', '73-44=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,32 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[87, 84, 73, 44], Operations: [] Exploring Operation: 87-84=3, Resulting Numbers: [73, 44, 3] Generated Node #0,3: 32:[73, 44, 3] Operation: 87-84=3 Moving to Node #0,3 Current State: 32:[73, 44, 3], Operations: ['87-84=3'] Exploring Operation: 73-44=29, Resulting Numbers: [3, 29] Generated Node #0,3,1: 32:[3, 29] Operation: 73-44=29 Moving to Node #0,3,1 Current State: 32:[3, 29], Operations: ['87-84=3', '73-44=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 38, 61, 88, 18 ]
54
[ "38+88=126", "126/18=7", "61-7=54" ]
Current State: 54:[38, 61, 88, 18], Operations: [] Exploring Operation: 38+88=126, Resulting Numbers: [61, 18, 126] Generated Node #2: [61, 18, 126] from Operation: 38+88=126 Current State: 54:[61, 18, 126], Operations: ['38+88=126'] Exploring Operation: 126/18=7, Resulting Numbers: [61, 7] Generated Node #3: [61, 7] from Operation: 126/18=7 Current State: 54:[61, 7], Operations: ['38+88=126', '126/18=7'] Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[38, 61, 88, 18], Operations: [] Exploring Operation: 88-61=27, Resulting Numbers: [38, 18, 27] Generated Node #0,0: 54:[38, 18, 27] Operation: 88-61=27 Exploring Operation: 88-38=50, Resulting Numbers: [61, 18, 50] Generated Node #0,1: 54:[61, 18, 50] Operation: 88-38=50 Exploring Operation: 88-18=70, Resulting Numbers: [38, 61, 70] Generated Node #0,2: 54:[38, 61, 70] Operation: 88-18=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[38, 18, 27], Operations: ['88-61=27'] Exploring Operation: 38-27=11, Resulting Numbers: [18, 11] Generated Node #0,0,0: 54:[18, 11] Operation: 38-27=11 Exploring Operation: 38+18=56, Resulting Numbers: [27, 56] Generated Node #0,0,1: 54:[27, 56] Operation: 38+18=56 Exploring Operation: 38-18=20, Resulting Numbers: [27, 20] Generated Node #0,0,2: 54:[27, 20] Operation: 38-18=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[18, 11], Operations: ['88-61=27', '38-27=11'] Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 18*11=198, Resulting Numbers: [198] 198,54 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: 54:[27, 56], Operations: ['88-61=27', '38+18=56'] Exploring Operation: 56-27=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 27+56=83, Resulting Numbers: [83] 83,54 unequal: No Solution Exploring Operation: 27*56=1512, Resulting Numbers: [1512] 1512,54 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: 54:[27, 20], Operations: ['88-61=27', '38-18=20'] Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 27+20=47, Resulting Numbers: [47] 47,54 unequal: No Solution Exploring Operation: 27*20=540, Resulting Numbers: [540] 540,54 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: 54:[61, 18, 50], Operations: ['88-38=50'] Exploring Operation: 61-50=11, Resulting Numbers: [18, 11] Generated Node #0,1,0: 54:[18, 11] Operation: 61-50=11 Exploring Operation: 50-18=32, Resulting Numbers: [61, 32] Generated Node #0,1,1: 54:[61, 32] Operation: 50-18=32 Exploring Operation: 61-18=43, Resulting Numbers: [50, 43] Generated Node #0,1,2: 54:[50, 43] Operation: 61-18=43 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 54:[18, 11], Operations: ['88-38=50', '61-50=11'] Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 18*11=198, Resulting Numbers: [198] 198,54 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: 54:[61, 32], Operations: ['88-38=50', '50-18=32'] Exploring Operation: 61*32=1952, Resulting Numbers: [1952] 1952,54 unequal: No Solution Exploring Operation: 61-32=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 61+32=93, Resulting Numbers: [93] 93,54 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: 54:[50, 43], Operations: ['88-38=50', '61-18=43'] Exploring Operation: 50*43=2150, Resulting Numbers: [2150] 2150,54 unequal: No Solution Exploring Operation: 50-43=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 50+43=93, Resulting Numbers: [93] 93,54 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: 54:[38, 61, 70], Operations: ['88-18=70'] Exploring Operation: 70-38=32, Resulting Numbers: [61, 32] Generated Node #0,2,0: 54:[61, 32] Operation: 70-38=32 Exploring Operation: 70-61=9, Resulting Numbers: [38, 9] Generated Node #0,2,1: 54:[38, 9] Operation: 70-61=9 Exploring Operation: 61-38=23, Resulting Numbers: [70, 23] Generated Node #0,2,2: 54:[70, 23] Operation: 61-38=23 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 54:[38, 9], Operations: ['88-18=70', '70-61=9'] Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 38*9=342, Resulting Numbers: [342] 342,54 unequal: No Solution Exploring Operation: 38+9=47, Resulting Numbers: [47] 47,54 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: 54:[61, 32], Operations: ['88-18=70', '70-38=32'] Exploring Operation: 61-32=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 61*32=1952, Resulting Numbers: [1952] 1952,54 unequal: No Solution Exploring Operation: 61+32=93, Resulting Numbers: [93] 93,54 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: 54:[70, 23], Operations: ['88-18=70', '61-38=23'] Exploring Operation: 70-23=47, Resulting Numbers: [47] 47,54 unequal: No Solution Exploring Operation: 70+23=93, Resulting Numbers: [93] 93,54 unequal: No Solution Exploring Operation: 70*23=1610, Resulting Numbers: [1610] 1610,54 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
[ 80, 93, 76, 44 ]
82
[ "80-76=4", "44/4=11", "93-11=82" ]
Current State: 82:[80, 93, 76, 44], Operations: [] Exploring Operation: 80-76=4, Resulting Numbers: [93, 44, 4] Generated Node #2: [93, 44, 4] from Operation: 80-76=4 Current State: 82:[93, 44, 4], Operations: ['80-76=4'] Exploring Operation: 44/4=11, Resulting Numbers: [93, 11] Generated Node #3: [93, 11] from Operation: 44/4=11 Current State: 82:[93, 11], Operations: ['80-76=4', '44/4=11'] Exploring Operation: 93-11=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[80, 93, 76, 44], Operations: [] Exploring Operation: 80-76=4, Resulting Numbers: [93, 44, 4] Generated Node #0,0: 82:[93, 44, 4] Operation: 80-76=4 Moving to Node #0,0 Current State: 82:[93, 44, 4], Operations: ['80-76=4'] Exploring Operation: 93-44=49, Resulting Numbers: [4, 49] Generated Node #0,0,0: 82:[4, 49] Operation: 93-44=49 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 82:[4, 49], Operations: ['80-76=4', '93-44=49'] Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,82 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
[ 76, 19, 12, 6 ]
54
[ "76/19=4", "12*4=48", "6+48=54" ]
Current State: 54:[76, 19, 12, 6], Operations: [] Exploring Operation: 76/19=4, Resulting Numbers: [12, 6, 4] Generated Node #2: [12, 6, 4] from Operation: 76/19=4 Current State: 54:[12, 6, 4], Operations: ['76/19=4'] Exploring Operation: 12*4=48, Resulting Numbers: [6, 48] Generated Node #3: [6, 48] from Operation: 12*4=48 Current State: 54:[6, 48], Operations: ['76/19=4', '12*4=48'] Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[76, 19, 12, 6], Operations: [] Exploring Operation: 76/19=4, Resulting Numbers: [12, 6, 4] Generated Node #0,0: 54:[12, 6, 4] Operation: 76/19=4 Moving to Node #0,0 Current State: 54:[12, 6, 4], Operations: ['76/19=4'] Exploring Operation: 12/4=3, Resulting Numbers: [6, 3] Generated Node #0,0,0: 54:[6, 3] Operation: 12/4=3 Moving to Node #0,0,0 Current State: 54:[6, 3], Operations: ['76/19=4', '12/4=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,54 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 36, 72, 7, 4 ]
61
[ "36+7=43", "72/4=18", "43+18=61" ]
Current State: 61:[36, 72, 7, 4], Operations: [] Exploring Operation: 36+7=43, Resulting Numbers: [72, 4, 43] Generated Node #2: [72, 4, 43] from Operation: 36+7=43 Current State: 61:[72, 4, 43], Operations: ['36+7=43'] Exploring Operation: 72/4=18, Resulting Numbers: [43, 18] Generated Node #3: [43, 18] from Operation: 72/4=18 Current State: 61:[43, 18], Operations: ['36+7=43', '72/4=18'] Exploring Operation: 43+18=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[36, 72, 7, 4], Operations: [] Exploring Operation: 36+7=43, Resulting Numbers: [72, 4, 43] Generated Node #0,0: 61:[72, 4, 43] Operation: 36+7=43 Exploring Operation: 7*4=28, Resulting Numbers: [36, 72, 28] Generated Node #0,1: 61:[36, 72, 28] Operation: 7*4=28 Exploring Operation: 36+4=40, Resulting Numbers: [72, 7, 40] Generated Node #0,2: 61:[72, 7, 40] Operation: 36+4=40 Moving to Node #0,1 Current State: 61:[36, 72, 28], Operations: ['7*4=28'] Exploring Operation: 36+28=64, Resulting Numbers: [72, 64] Generated Node #0,1,0: 61:[72, 64] Operation: 36+28=64 Exploring Operation: 72-28=44, Resulting Numbers: [36, 44] Generated Node #0,1,1: 61:[36, 44] Operation: 72-28=44 Exploring Operation: 72-36=36, Resulting Numbers: [28, 36] Generated Node #0,1,2: 61:[28, 36] Operation: 72-36=36 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 61:[72, 64], Operations: ['7*4=28', '36+28=64'] Exploring Operation: 72*64=4608, Resulting Numbers: [4608] 4608,61 unequal: No Solution Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 72+64=136, Resulting Numbers: [136] 136,61 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: 61:[36, 44], Operations: ['7*4=28', '72-28=44'] Exploring Operation: 36+44=80, Resulting Numbers: [80] 80,61 unequal: No Solution Exploring Operation: 36*44=1584, Resulting Numbers: [1584] 1584,61 unequal: No Solution Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,61 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: 61:[28, 36], Operations: ['7*4=28', '72-36=36'] Exploring Operation: 28+36=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 28*36=1008, Resulting Numbers: [1008] 1008,61 unequal: No Solution Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,61 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: 61:[72, 4, 43], Operations: ['36+7=43'] Exploring Operation: 72+4=76, Resulting Numbers: [43, 76] Generated Node #0,0,0: 61:[43, 76] Operation: 72+4=76 Exploring Operation: 72-4=68, Resulting Numbers: [43, 68] Generated Node #0,0,1: 61:[43, 68] Operation: 72-4=68 Exploring Operation: 4+43=47, Resulting Numbers: [72, 47] Generated Node #0,0,2: 61:[72, 47] Operation: 4+43=47 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[43, 68], Operations: ['36+7=43', '72-4=68'] Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,61 unequal: No Solution Exploring Operation: 43+68=111, Resulting Numbers: [111] 111,61 unequal: No Solution Exploring Operation: 43*68=2924, Resulting Numbers: [2924] 2924,61 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: 61:[72, 47], Operations: ['36+7=43', '4+43=47'] Exploring Operation: 72*47=3384, Resulting Numbers: [3384] 3384,61 unequal: No Solution Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,61 unequal: No Solution Exploring Operation: 72+47=119, Resulting Numbers: [119] 119,61 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: 61:[43, 76], Operations: ['36+7=43', '72+4=76'] Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 43*76=3268, Resulting Numbers: [3268] 3268,61 unequal: No Solution Exploring Operation: 43+76=119, Resulting Numbers: [119] 119,61 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: 61:[72, 7, 40], Operations: ['36+4=40'] Exploring Operation: 72-7=65, Resulting Numbers: [40, 65] Generated Node #0,2,0: 61:[40, 65] Operation: 72-7=65 Exploring Operation: 72+7=79, Resulting Numbers: [40, 79] Generated Node #0,2,1: 61:[40, 79] Operation: 72+7=79 Exploring Operation: 7+40=47, Resulting Numbers: [72, 47] Generated Node #0,2,2: 61:[72, 47] Operation: 7+40=47 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[40, 65], Operations: ['36+4=40', '72-7=65'] Exploring Operation: 65-40=25, Resulting Numbers: [25] 25,61 unequal: No Solution Exploring Operation: 40*65=2600, Resulting Numbers: [2600] 2600,61 unequal: No Solution Exploring Operation: 40+65=105, Resulting Numbers: [105] 105,61 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: 61:[72, 47], Operations: ['36+4=40', '7+40=47'] Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,61 unequal: No Solution Exploring Operation: 72*47=3384, Resulting Numbers: [3384] 3384,61 unequal: No Solution Exploring Operation: 72+47=119, Resulting Numbers: [119] 119,61 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: 61:[40, 79], Operations: ['36+4=40', '72+7=79'] Exploring Operation: 40+79=119, Resulting Numbers: [119] 119,61 unequal: No Solution Exploring Operation: 79-40=39, Resulting Numbers: [39] 39,61 unequal: No Solution Exploring Operation: 40*79=3160, Resulting Numbers: [3160] 3160,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 82, 33, 57, 3 ]
30
[ "82-33=49", "57/3=19", "49-19=30" ]
Current State: 30:[82, 33, 57, 3], Operations: [] Exploring Operation: 82-33=49, Resulting Numbers: [57, 3, 49] Generated Node #2: [57, 3, 49] from Operation: 82-33=49 Current State: 30:[57, 3, 49], Operations: ['82-33=49'] Exploring Operation: 57/3=19, Resulting Numbers: [49, 19] Generated Node #3: [49, 19] from Operation: 57/3=19 Current State: 30:[49, 19], Operations: ['82-33=49', '57/3=19'] Exploring Operation: 49-19=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[82, 33, 57, 3], Operations: [] Exploring Operation: 82-57=25, Resulting Numbers: [33, 3, 25] Generated Node #0,0: 30:[33, 3, 25] Operation: 82-57=25 Moving to Node #0,0 Current State: 30:[33, 3, 25], Operations: ['82-57=25'] Exploring Operation: 33-25=8, Resulting Numbers: [3, 8] Generated Node #0,0,0: 30:[3, 8] Operation: 33-25=8 Moving to Node #0,0,0 Current State: 30:[3, 8], Operations: ['82-57=25', '33-25=8'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,30 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 5, 12, 24, 5 ]
55
[ "24-12=12", "5*12=60", "60-5=55" ]
Current State: 55:[5, 12, 24, 5], Operations: [] Exploring Operation: 24-12=12, Resulting Numbers: [5, 5, 12] Generated Node #2: [5, 5, 12] from Operation: 24-12=12 Current State: 55:[5, 5, 12], Operations: ['24-12=12'] Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,55 equal: Goal Reached Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[5, 12, 24, 5], Operations: [] Exploring Operation: 24/12=2, Resulting Numbers: [5, 5, 2] Generated Node #0,0: 55:[5, 5, 2] Operation: 24/12=2 Exploring Operation: 24-12=12, Resulting Numbers: [5, 5, 12] Generated Node #0,1: 55:[5, 5, 12] Operation: 24-12=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[5, 5, 12], Operations: ['24-12=12'] Exploring Operation: 12-5=7, Resulting Numbers: [5, 7] Generated Node #0,1,0: 55:[5, 7] Operation: 12-5=7 Exploring Operation: 5+5=10, Resulting Numbers: [12, 10] Generated Node #0,1,1: 55:[12, 10] Operation: 5+5=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[5, 7], Operations: ['24-12=12', '12-5=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,55 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: 55:[12, 10], Operations: ['24-12=12', '5+5=10'] Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,55 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: 55:[5, 5, 2], Operations: ['24/12=2'] Exploring Operation: 5*2=10, Resulting Numbers: [5, 10] Generated Node #0,0,0: 55:[5, 10] Operation: 5*2=10 Exploring Operation: 5*2=10, Resulting Numbers: [5, 10] Generated Node #0,0,1: 55:[5, 10] Operation: 5*2=10 Moving to Node #0,0,0 Current State: 55:[5, 10], Operations: ['24/12=2', '5*2=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[5, 10], Operations: ['24/12=2', '5*2=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 26, 22, 80, 35 ]
93
[ "26+22=48", "80-35=45", "48+45=93" ]
Current State: 93:[26, 22, 80, 35], Operations: [] Exploring Operation: 26+22=48, Resulting Numbers: [80, 35, 48] Generated Node #2: [80, 35, 48] from Operation: 26+22=48 Current State: 93:[80, 35, 48], Operations: ['26+22=48'] Exploring Operation: 80-35=45, Resulting Numbers: [48, 45] Generated Node #3: [48, 45] from Operation: 80-35=45 Current State: 93:[48, 45], Operations: ['26+22=48', '80-35=45'] Exploring Operation: 48+45=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[26, 22, 80, 35], Operations: [] Exploring Operation: 35-26=9, Resulting Numbers: [22, 80, 9] Generated Node #0,0: 93:[22, 80, 9] Operation: 35-26=9 Exploring Operation: 26+80=106, Resulting Numbers: [22, 35, 106] Generated Node #0,1: 93:[22, 35, 106] Operation: 26+80=106 Exploring Operation: 22+80=102, Resulting Numbers: [26, 35, 102] Generated Node #0,2: 93:[26, 35, 102] Operation: 22+80=102 Exploring Operation: 26-22=4, Resulting Numbers: [80, 35, 4] Generated Node #0,3: 93:[80, 35, 4] Operation: 26-22=4 Moving to Node #0,2 Current State: 93:[26, 35, 102], Operations: ['22+80=102'] Exploring Operation: 102-35=67, Resulting Numbers: [26, 67] Generated Node #0,2,0: 93:[26, 67] Operation: 102-35=67 Exploring Operation: 35-26=9, Resulting Numbers: [102, 9] Generated Node #0,2,1: 93:[102, 9] Operation: 35-26=9 Exploring Operation: 102-26=76, Resulting Numbers: [35, 76] Generated Node #0,2,2: 93:[35, 76] Operation: 102-26=76 Exploring Operation: 26+35=61, Resulting Numbers: [102, 61] Generated Node #0,2,3: 93:[102, 61] Operation: 26+35=61 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 93:[102, 9], Operations: ['22+80=102', '35-26=9'] Exploring Operation: 102*9=918, Resulting Numbers: [918] 918,93 unequal: No Solution Exploring Operation: 102-9=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[26, 22, 80, 35], Operations: [] Exploring Operation: 22+80=102, Resulting Numbers: [26, 35, 102] Generated Node #0,2: 93:[26, 35, 102] Operation: 22+80=102 Moving to Node #0,2 Current State: 93:[26, 35, 102], Operations: ['22+80=102'] Exploring Operation: 35-26=9, Resulting Numbers: [102, 9] Generated Node #0,2,1: 93:[102, 9] Operation: 35-26=9 Moving to Node #0,2,1 Current State: 93:[102, 9], Operations: ['22+80=102', '35-26=9'] Exploring Operation: 102-9=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 89, 2, 12, 34 ]
86
[ "89-12=77", "77-34=43", "2*43=86" ]
Current State: 86:[89, 2, 12, 34], Operations: [] Exploring Operation: 89-12=77, Resulting Numbers: [2, 34, 77] Generated Node #2: [2, 34, 77] from Operation: 89-12=77 Current State: 86:[2, 34, 77], Operations: ['89-12=77'] Exploring Operation: 77-34=43, Resulting Numbers: [2, 43] Generated Node #3: [2, 43] from Operation: 77-34=43 Current State: 86:[2, 43], Operations: ['89-12=77', '77-34=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[89, 2, 12, 34], Operations: [] Exploring Operation: 12+34=46, Resulting Numbers: [89, 2, 46] Generated Node #0,0: 86:[89, 2, 46] Operation: 12+34=46 Exploring Operation: 12/2=6, Resulting Numbers: [89, 34, 6] Generated Node #0,1: 86:[89, 34, 6] Operation: 12/2=6 Moving to Node #0,0 Current State: 86:[89, 2, 46], Operations: ['12+34=46'] Exploring Operation: 89-2=87, Resulting Numbers: [46, 87] Generated Node #0,0,0: 86:[46, 87] Operation: 89-2=87 Exploring Operation: 89-46=43, Resulting Numbers: [2, 43] Generated Node #0,0,1: 86:[2, 43] Operation: 89-46=43 Moving to Node #0,1 Current State: 86:[89, 34, 6], Operations: ['12/2=6'] Exploring Operation: 34+6=40, Resulting Numbers: [89, 40] Generated Node #0,1,0: 86:[89, 40] Operation: 34+6=40 Exploring Operation: 89-6=83, Resulting Numbers: [34, 83] Generated Node #0,1,1: 86:[34, 83] Operation: 89-6=83 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[89, 40], Operations: ['12/2=6', '34+6=40'] Exploring Operation: 89-40=49, Resulting Numbers: [49] 49,86 unequal: No Solution Exploring Operation: 89+40=129, Resulting Numbers: [129] 129,86 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: 86:[34, 83], Operations: ['12/2=6', '89-6=83'] Exploring Operation: 34+83=117, Resulting Numbers: [117] 117,86 unequal: No Solution Exploring Operation: 83-34=49, Resulting Numbers: [49] 49,86 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: 86:[2, 43], Operations: ['12+34=46', '89-46=43'] Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,86 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[89, 2, 12, 34], Operations: [] Exploring Operation: 12+34=46, Resulting Numbers: [89, 2, 46] Generated Node #0,0: 86:[89, 2, 46] Operation: 12+34=46 Moving to Node #0,0 Current State: 86:[89, 2, 46], Operations: ['12+34=46'] Exploring Operation: 89-46=43, Resulting Numbers: [2, 43] Generated Node #0,0,1: 86:[2, 43] Operation: 89-46=43 Moving to Node #0,0,1 Current State: 86:[2, 43], Operations: ['12+34=46', '89-46=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 74, 80, 41, 66 ]
47
[ "74+80=154", "41+66=107", "154-107=47" ]
Current State: 47:[74, 80, 41, 66], Operations: [] Exploring Operation: 74+80=154, Resulting Numbers: [41, 66, 154] Generated Node #2: [41, 66, 154] from Operation: 74+80=154 Current State: 47:[41, 66, 154], Operations: ['74+80=154'] Exploring Operation: 41+66=107, Resulting Numbers: [154, 107] Generated Node #3: [154, 107] from Operation: 41+66=107 Current State: 47:[154, 107], Operations: ['74+80=154', '41+66=107'] Exploring Operation: 154-107=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[74, 80, 41, 66], Operations: [] Exploring Operation: 80-41=39, Resulting Numbers: [74, 66, 39] Generated Node #0,0: 47:[74, 66, 39] Operation: 80-41=39 Exploring Operation: 74-41=33, Resulting Numbers: [80, 66, 33] Generated Node #0,1: 47:[80, 66, 33] Operation: 74-41=33 Exploring Operation: 80-74=6, Resulting Numbers: [41, 66, 6] Generated Node #0,2: 47:[41, 66, 6] Operation: 80-74=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[74, 66, 39], Operations: ['80-41=39'] Exploring Operation: 74-39=35, Resulting Numbers: [66, 35] Generated Node #0,0,0: 47:[66, 35] Operation: 74-39=35 Exploring Operation: 74-66=8, Resulting Numbers: [39, 8] Generated Node #0,0,1: 47:[39, 8] Operation: 74-66=8 Exploring Operation: 66-39=27, Resulting Numbers: [74, 27] Generated Node #0,0,2: 47:[74, 27] Operation: 66-39=27 Moving to Node #0,0,0 Current State: 47:[66, 35], Operations: ['80-41=39', '74-39=35'] Exploring Operation: 66+35=101, Resulting Numbers: [101] 101,47 unequal: No Solution Exploring Operation: 66-35=31, Resulting Numbers: [31] 31,47 unequal: No Solution Exploring Operation: 66*35=2310, Resulting Numbers: [2310] 2310,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[39, 8], Operations: ['80-41=39', '74-66=8'] Exploring Operation: 39*8=312, Resulting Numbers: [312] 312,47 unequal: No Solution Exploring Operation: 39+8=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[74, 80, 41, 66], Operations: [] Exploring Operation: 80-41=39, Resulting Numbers: [74, 66, 39] Generated Node #0,0: 47:[74, 66, 39] Operation: 80-41=39 Moving to Node #0,0 Current State: 47:[74, 66, 39], Operations: ['80-41=39'] Exploring Operation: 74-66=8, Resulting Numbers: [39, 8] Generated Node #0,0,1: 47:[39, 8] Operation: 74-66=8 Moving to Node #0,0,1 Current State: 47:[39, 8], Operations: ['80-41=39', '74-66=8'] Exploring Operation: 39+8=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 50, 52, 37, 7 ]
67
[ "52-50=2", "37*2=74", "74-7=67" ]
Current State: 67:[50, 52, 37, 7], Operations: [] Exploring Operation: 52-50=2, Resulting Numbers: [37, 7, 2] Generated Node #2: [37, 7, 2] from Operation: 52-50=2 Current State: 67:[37, 7, 2], Operations: ['52-50=2'] Exploring Operation: 37*2=74, Resulting Numbers: [7, 74] Generated Node #3: [7, 74] from Operation: 37*2=74 Current State: 67:[7, 74], Operations: ['52-50=2', '37*2=74'] Exploring Operation: 74-7=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[50, 52, 37, 7], Operations: [] Exploring Operation: 50+7=57, Resulting Numbers: [52, 37, 57] Generated Node #0,0: 67:[52, 37, 57] Operation: 50+7=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[52, 37, 57], Operations: ['50+7=57'] Exploring Operation: 52+37=89, Resulting Numbers: [57, 89] Generated Node #0,0,0: 67:[57, 89] Operation: 52+37=89 Moving to Node #0,0,0 Current State: 67:[57, 89], Operations: ['50+7=57', '52+37=89'] Exploring Operation: 89-57=32, Resulting Numbers: [32] 32,67 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
[ 20, 59, 3, 44 ]
86
[ "59-20=39", "3+44=47", "39+47=86" ]
Current State: 86:[20, 59, 3, 44], Operations: [] Exploring Operation: 59-20=39, Resulting Numbers: [3, 44, 39] Generated Node #2: [3, 44, 39] from Operation: 59-20=39 Current State: 86:[3, 44, 39], Operations: ['59-20=39'] Exploring Operation: 3+44=47, Resulting Numbers: [39, 47] Generated Node #3: [39, 47] from Operation: 3+44=47 Current State: 86:[39, 47], Operations: ['59-20=39', '3+44=47'] Exploring Operation: 39+47=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[20, 59, 3, 44], Operations: [] Exploring Operation: 59-20=39, Resulting Numbers: [3, 44, 39] Generated Node #0,0: 86:[3, 44, 39] Operation: 59-20=39 Moving to Node #0,0 Current State: 86:[3, 44, 39], Operations: ['59-20=39'] Exploring Operation: 3+39=42, Resulting Numbers: [44, 42] Generated Node #0,0,0: 86:[44, 42] Operation: 3+39=42 Moving to Node #0,0,0 Current State: 86:[44, 42], Operations: ['59-20=39', '3+39=42'] Exploring Operation: 44+42=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[20, 59, 3, 44], Operations: [] Exploring Operation: 59-20=39, Resulting Numbers: [3, 44, 39] Generated Node #0,0: 86:[3, 44, 39] Operation: 59-20=39 Moving to Node #0,0 Current State: 86:[3, 44, 39], Operations: ['59-20=39'] Exploring Operation: 3+39=42, Resulting Numbers: [44, 42] Generated Node #0,0,0: 86:[44, 42] Operation: 3+39=42 Moving to Node #0,0,0 Current State: 86:[44, 42], Operations: ['59-20=39', '3+39=42'] Exploring Operation: 44+42=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 79, 52, 25, 26 ]
56
[ "79+25=104", "104/26=4", "52+4=56" ]
Current State: 56:[79, 52, 25, 26], Operations: [] Exploring Operation: 79+25=104, Resulting Numbers: [52, 26, 104] Generated Node #2: [52, 26, 104] from Operation: 79+25=104 Current State: 56:[52, 26, 104], Operations: ['79+25=104'] Exploring Operation: 104/26=4, Resulting Numbers: [52, 4] Generated Node #3: [52, 4] from Operation: 104/26=4 Current State: 56:[52, 4], Operations: ['79+25=104', '104/26=4'] Exploring Operation: 52+4=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[79, 52, 25, 26], Operations: [] Exploring Operation: 79-25=54, Resulting Numbers: [52, 26, 54] Generated Node #0,0: 56:[52, 26, 54] Operation: 79-25=54 Exploring Operation: 79-52=27, Resulting Numbers: [25, 26, 27] Generated Node #0,1: 56:[25, 26, 27] Operation: 79-52=27 Moving to Node #0,1 Current State: 56:[25, 26, 27], Operations: ['79-52=27'] Exploring Operation: 27-25=2, Resulting Numbers: [26, 2] Generated Node #0,1,0: 56:[26, 2] Operation: 27-25=2 Exploring Operation: 26-25=1, Resulting Numbers: [27, 1] Generated Node #0,1,1: 56:[27, 1] Operation: 26-25=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 56:[26, 2], Operations: ['79-52=27', '27-25=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,56 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,56 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: 56:[27, 1], Operations: ['79-52=27', '26-25=1'] Exploring Operation: 27+1=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,56 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: 56:[52, 26, 54], Operations: ['79-25=54'] Exploring Operation: 52/26=2, Resulting Numbers: [54, 2] Generated Node #0,0,0: 56:[54, 2] Operation: 52/26=2 Exploring Operation: 54-52=2, Resulting Numbers: [26, 2] Generated Node #0,0,1: 56:[26, 2] Operation: 54-52=2 Moving to Node #0,0,0 Current State: 56:[54, 2], Operations: ['79-25=54', '52/26=2'] Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,56 unequal: No Solution Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[79, 52, 25, 26], Operations: [] Exploring Operation: 79-25=54, Resulting Numbers: [52, 26, 54] Generated Node #0,0: 56:[52, 26, 54] Operation: 79-25=54 Moving to Node #0,0 Current State: 56:[52, 26, 54], Operations: ['79-25=54'] Exploring Operation: 52/26=2, Resulting Numbers: [54, 2] Generated Node #0,0,0: 56:[54, 2] Operation: 52/26=2 Moving to Node #0,0,0 Current State: 56:[54, 2], Operations: ['79-25=54', '52/26=2'] Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 2, 13, 83, 47 ]
52
[ "83+47=130", "130/2=65", "65-13=52" ]
Current State: 52:[2, 13, 83, 47], Operations: [] Exploring Operation: 83+47=130, Resulting Numbers: [2, 13, 130] Generated Node #2: [2, 13, 130] from Operation: 83+47=130 Current State: 52:[2, 13, 130], Operations: ['83+47=130'] Exploring Operation: 130/2=65, Resulting Numbers: [13, 65] Generated Node #3: [13, 65] from Operation: 130/2=65 Current State: 52:[13, 65], Operations: ['83+47=130', '130/2=65'] Exploring Operation: 65-13=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[2, 13, 83, 47], Operations: [] Exploring Operation: 83-47=36, Resulting Numbers: [2, 13, 36] Generated Node #0,0: 52:[2, 13, 36] Operation: 83-47=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[2, 13, 36], Operations: ['83-47=36'] Exploring Operation: 13+36=49, Resulting Numbers: [2, 49] Generated Node #0,0,0: 52:[2, 49] Operation: 13+36=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[2, 49], Operations: ['83-47=36', '13+36=49'] Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,52 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
[ 11, 9, 75, 97 ]
73
[ "11*9=99", "75+97=172", "172-99=73" ]
Current State: 73:[11, 9, 75, 97], Operations: [] Exploring Operation: 11*9=99, Resulting Numbers: [75, 97, 99] Generated Node #2: [75, 97, 99] from Operation: 11*9=99 Current State: 73:[75, 97, 99], Operations: ['11*9=99'] Exploring Operation: 75+97=172, Resulting Numbers: [99, 172] Generated Node #3: [99, 172] from Operation: 75+97=172 Current State: 73:[99, 172], Operations: ['11*9=99', '75+97=172'] Exploring Operation: 172-99=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[11, 9, 75, 97], Operations: [] Exploring Operation: 11+9=20, Resulting Numbers: [75, 97, 20] Generated Node #0,0: 73:[75, 97, 20] Operation: 11+9=20 Exploring Operation: 11*9=99, Resulting Numbers: [75, 97, 99] Generated Node #0,1: 73:[75, 97, 99] Operation: 11*9=99 Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[75, 97, 99], Operations: ['11*9=99'] Exploring Operation: 99-97=2, Resulting Numbers: [75, 2] Generated Node #0,1,0: 73:[75, 2] Operation: 99-97=2 Exploring Operation: 99-75=24, Resulting Numbers: [97, 24] Generated Node #0,1,1: 73:[97, 24] Operation: 99-75=24 Moving to Node #0,1,0 Current State: 73:[75, 2], Operations: ['11*9=99', '99-97=2'] Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[11, 9, 75, 97], Operations: [] Exploring Operation: 11*9=99, Resulting Numbers: [75, 97, 99] Generated Node #0,1: 73:[75, 97, 99] Operation: 11*9=99 Moving to Node #0,1 Current State: 73:[75, 97, 99], Operations: ['11*9=99'] Exploring Operation: 99-97=2, Resulting Numbers: [75, 2] Generated Node #0,1,0: 73:[75, 2] Operation: 99-97=2 Moving to Node #0,1,0 Current State: 73:[75, 2], Operations: ['11*9=99', '99-97=2'] Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic