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, 27, 20, 2 ]
33
[ "19+27=46", "20+46=66", "66/2=33" ]
Current State: 33:[19, 27, 20, 2], Operations: [] Exploring Operation: 19+27=46, Resulting Numbers: [20, 2, 46] Generated Node #2: [20, 2, 46] from Operation: 19+27=46 Current State: 33:[20, 2, 46], Operations: ['19+27=46'] Exploring Operation: 20+46=66, Resulting Numbers: [2, 66] Generated Node #3: [2, 66] from Operation: 20+46=66 Current State: 33:[2, 66], Operations: ['19+27=46', '20+46=66'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[19, 27, 20, 2], Operations: [] Exploring Operation: 27-19=8, Resulting Numbers: [20, 2, 8] Generated Node #0,0: 33:[20, 2, 8] Operation: 27-19=8 Exploring Operation: 19+20=39, Resulting Numbers: [27, 2, 39] Generated Node #0,1: 33:[27, 2, 39] Operation: 19+20=39 Exploring Operation: 20/2=10, Resulting Numbers: [19, 27, 10] Generated Node #0,2: 33:[19, 27, 10] Operation: 20/2=10 Exploring Operation: 20-19=1, Resulting Numbers: [27, 2, 1] Generated Node #0,3: 33:[27, 2, 1] Operation: 20-19=1 Exploring Operation: 27-20=7, Resulting Numbers: [19, 2, 7] Generated Node #0,4: 33:[19, 2, 7] Operation: 27-20=7 Start Sub Search at level 1: Moving to Node #0,3 Current State: 33:[27, 2, 1], Operations: ['20-19=1'] Exploring Operation: 27+1=28, Resulting Numbers: [2, 28] Generated Node #0,3,0: 33:[2, 28] Operation: 27+1=28 Exploring Operation: 27/1=27, Resulting Numbers: [2, 27] Generated Node #0,3,1: 33:[2, 27] Operation: 27/1=27 Exploring Operation: 27+2=29, Resulting Numbers: [1, 29] Generated Node #0,3,2: 33:[1, 29] Operation: 27+2=29 Exploring Operation: 2+1=3, Resulting Numbers: [27, 3] Generated Node #0,3,3: 33:[27, 3] Operation: 2+1=3 Exploring Operation: 27*1=27, Resulting Numbers: [2, 27] Generated Node #0,3,4: 33:[2, 27] Operation: 27*1=27 Moving to Node #0,3,0 Current State: 33:[2, 28], Operations: ['20-19=1', '27+1=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,33 unequal: No Solution Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,33 unequal: No Solution Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,33 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,33 unequal: No Solution Moving to Node #0,3,3 Current State: 33:[27, 3], Operations: ['20-19=1', '2+1=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,33 unequal: No Solution Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,33 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,33 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,33 unequal: No Solution Moving to Node #0,3,2 Current State: 33:[1, 29], Operations: ['20-19=1', '27+2=29'] Exploring Operation: 29/1=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 1*29=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 29-1=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 1+29=30, Resulting Numbers: [30] 30,33 unequal: No Solution Moving to Node #0,3,1 Current State: 33:[2, 27], Operations: ['20-19=1', '27/1=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,33 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,33 unequal: No Solution Moving to Node #0,3,4 Current State: 33:[2, 27], Operations: ['20-19=1', '27*1=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,33 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,33 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 Current State: 33:[20, 2, 8], Operations: ['27-19=8'] Exploring Operation: 20*2=40, Resulting Numbers: [8, 40] Generated Node #0,0,0: 33:[8, 40] Operation: 20*2=40 Exploring Operation: 20-2=18, Resulting Numbers: [8, 18] Generated Node #0,0,1: 33:[8, 18] Operation: 20-2=18 Exploring Operation: 20-8=12, Resulting Numbers: [2, 12] Generated Node #0,0,2: 33:[2, 12] Operation: 20-8=12 Exploring Operation: 20/2=10, Resulting Numbers: [8, 10] Generated Node #0,0,3: 33:[8, 10] Operation: 20/2=10 Exploring Operation: 20+8=28, Resulting Numbers: [2, 28] Generated Node #0,0,4: 33:[2, 28] Operation: 20+8=28 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 33:[2, 12], Operations: ['27-19=8', '20-8=12'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,33 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: 33:[8, 10], Operations: ['27-19=8', '20/2=10'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,33 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,33 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: 33:[2, 28], Operations: ['27-19=8', '20+8=28'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,33 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,33 unequal: No Solution Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,33 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: 33:[8, 40], Operations: ['27-19=8', '20*2=40'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,33 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,33 unequal: No Solution Exploring Operation: 8*40=320, Resulting Numbers: [320] 320,33 unequal: No Solution Exploring Operation: 8+40=48, Resulting Numbers: [48] 48,33 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: 33:[8, 18], Operations: ['27-19=8', '20-2=18'] Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,33 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,33 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: 33:[27, 2, 39], Operations: ['19+20=39'] Exploring Operation: 39-27=12, Resulting Numbers: [2, 12] Generated Node #0,1,0: 33:[2, 12] Operation: 39-27=12 Exploring Operation: 39-2=37, Resulting Numbers: [27, 37] Generated Node #0,1,1: 33:[27, 37] Operation: 39-2=37 Exploring Operation: 27-2=25, Resulting Numbers: [39, 25] Generated Node #0,1,2: 33:[39, 25] Operation: 27-2=25 Exploring Operation: 27+2=29, Resulting Numbers: [39, 29] Generated Node #0,1,3: 33:[39, 29] Operation: 27+2=29 Exploring Operation: 2+39=41, Resulting Numbers: [27, 41] Generated Node #0,1,4: 33:[27, 41] Operation: 2+39=41 Moving to Node #0,1,0 Current State: 33:[2, 12], Operations: ['19+20=39', '39-27=12'] Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,33 unequal: No Solution Moving to Node #0,1,3 Current State: 33:[39, 29], Operations: ['19+20=39', '27+2=29'] Exploring Operation: 39-29=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 39+29=68, Resulting Numbers: [68] 68,33 unequal: No Solution Exploring Operation: 39*29=1131, Resulting Numbers: [1131] 1131,33 unequal: No Solution Moving to Node #0,1,1 Current State: 33:[27, 37], Operations: ['19+20=39', '39-2=37'] Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 27+37=64, Resulting Numbers: [64] 64,33 unequal: No Solution Exploring Operation: 27*37=999, Resulting Numbers: [999] 999,33 unequal: No Solution Moving to Node #0,1,2 Current State: 33:[39, 25], Operations: ['19+20=39', '27-2=25'] Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 39*25=975, Resulting Numbers: [975] 975,33 unequal: No Solution Exploring Operation: 39+25=64, Resulting Numbers: [64] 64,33 unequal: No Solution Moving to Node #0,1,4 Current State: 33:[27, 41], Operations: ['19+20=39', '2+39=41'] Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,33 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,33 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 #0,4 Current State: 33:[19, 2, 7], Operations: ['27-20=7'] Exploring Operation: 19-7=12, Resulting Numbers: [2, 12] Generated Node #0,4,0: 33:[2, 12] Operation: 19-7=12 Exploring Operation: 19+7=26, Resulting Numbers: [2, 26] Generated Node #0,4,1: 33:[2, 26] Operation: 19+7=26 Exploring Operation: 19*2=38, Resulting Numbers: [7, 38] Generated Node #0,4,2: 33:[7, 38] Operation: 19*2=38 Exploring Operation: 19-2=17, Resulting Numbers: [7, 17] Generated Node #0,4,3: 33:[7, 17] Operation: 19-2=17 Exploring Operation: 2+7=9, Resulting Numbers: [19, 9] Generated Node #0,4,4: 33:[19, 9] Operation: 2+7=9 Moving to Node #0,4,0 Current State: 33:[2, 12], Operations: ['27-20=7', '19-7=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,33 unequal: No Solution Moving to Node #0,4,1 Current State: 33:[2, 26], Operations: ['27-20=7', '19+7=26'] Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,33 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,33 unequal: No Solution Moving to Node #0,4,2 Current State: 33:[7, 38], Operations: ['27-20=7', '19*2=38'] Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,33 unequal: No Solution Exploring Operation: 7+38=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 7*38=266, Resulting Numbers: [266] 266,33 unequal: No Solution Moving to Node #0,4,3 Current State: 33:[7, 17], Operations: ['27-20=7', '19-2=17'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,33 unequal: No Solution Moving to Node #0,4,4 Current State: 33:[19, 9], Operations: ['27-20=7', '2+7=9'] Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,33 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,33 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 #0,2 Current State: 33:[19, 27, 10], Operations: ['20/2=10'] Exploring Operation: 19+27=46, Resulting Numbers: [10, 46] Generated Node #0,2,0: 33:[10, 46] Operation: 19+27=46 Exploring Operation: 19+10=29, Resulting Numbers: [27, 29] Generated Node #0,2,1: 33:[27, 29] Operation: 19+10=29 Exploring Operation: 19-10=9, Resulting Numbers: [27, 9] Generated Node #0,2,2: 33:[27, 9] Operation: 19-10=9 Exploring Operation: 27-19=8, Resulting Numbers: [10, 8] Generated Node #0,2,3: 33:[10, 8] Operation: 27-19=8 Exploring Operation: 27+10=37, Resulting Numbers: [19, 37] Generated Node #0,2,4: 33:[19, 37] Operation: 27+10=37 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 33:[10, 8], Operations: ['20/2=10', '27-19=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,33 unequal: No Solution Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,33 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,33 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: 33:[27, 9], Operations: ['20/2=10', '19-10=9'] Exploring Operation: 27*9=243, Resulting Numbers: [243] 243,33 unequal: No Solution Exploring Operation: 27+9=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,33 unequal: No Solution Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,33 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: 33:[27, 29], Operations: ['20/2=10', '19+10=29'] Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,33 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,33 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: 33:[19, 37], Operations: ['20/2=10', '27+10=37'] Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,33 unequal: No Solution Exploring Operation: 19*37=703, Resulting Numbers: [703] 703,33 unequal: No Solution Exploring Operation: 19+37=56, Resulting Numbers: [56] 56,33 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: 33:[10, 46], Operations: ['20/2=10', '19+27=46'] Exploring Operation: 10*46=460, Resulting Numbers: [460] 460,33 unequal: No Solution Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 10+46=56, Resulting Numbers: [56] 56,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 98, 92, 13, 79 ]
98
[ "98+92=190", "13+79=92", "190-92=98" ]
Current State: 98:[98, 92, 13, 79], Operations: [] Exploring Operation: 98+92=190, Resulting Numbers: [13, 79, 190] Generated Node #2: [13, 79, 190] from Operation: 98+92=190 Current State: 98:[13, 79, 190], Operations: ['98+92=190'] Exploring Operation: 13+79=92, Resulting Numbers: [190, 92] Generated Node #3: [190, 92] from Operation: 13+79=92 Current State: 98:[190, 92], Operations: ['98+92=190', '13+79=92'] Exploring Operation: 190-92=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[98, 92, 13, 79], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [98, 13, 13] Generated Node #0,0: 98:[98, 13, 13] Operation: 92-79=13 Exploring Operation: 98-79=19, Resulting Numbers: [92, 13, 19] Generated Node #0,1: 98:[92, 13, 19] Operation: 98-79=19 Exploring Operation: 13+79=92, Resulting Numbers: [98, 92, 92] Generated Node #0,2: 98:[98, 92, 92] Operation: 13+79=92 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[98, 13, 13], Operations: ['92-79=13'] Exploring Operation: 13-13=0, Resulting Numbers: [98, 0] Generated Node #0,0,0: 98:[98, 0] Operation: 13-13=0 Exploring Operation: 13+13=26, Resulting Numbers: [98, 26] Generated Node #0,0,1: 98:[98, 26] Operation: 13+13=26 Exploring Operation: 13/13=1, Resulting Numbers: [98, 1] Generated Node #0,0,2: 98:[98, 1] Operation: 13/13=1 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 98:[98, 1], Operations: ['92-79=13', '13/13=1'] Exploring Operation: 98+1=99, Resulting Numbers: [99] 99,98 unequal: No Solution Exploring Operation: 98/1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[98, 92, 13, 79], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [98, 13, 13] Generated Node #0,0: 98:[98, 13, 13] Operation: 92-79=13 Moving to Node #0,0 Current State: 98:[98, 13, 13], Operations: ['92-79=13'] Exploring Operation: 13/13=1, Resulting Numbers: [98, 1] Generated Node #0,0,2: 98:[98, 1] Operation: 13/13=1 Moving to Node #0,0,2 Current State: 98:[98, 1], Operations: ['92-79=13', '13/13=1'] Exploring Operation: 98/1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 4, 90, 75, 87 ]
82
[ "4+90=94", "87-75=12", "94-12=82" ]
Current State: 82:[4, 90, 75, 87], Operations: [] Exploring Operation: 4+90=94, Resulting Numbers: [75, 87, 94] Generated Node #2: [75, 87, 94] from Operation: 4+90=94 Current State: 82:[75, 87, 94], Operations: ['4+90=94'] Exploring Operation: 87-75=12, Resulting Numbers: [94, 12] Generated Node #3: [94, 12] from Operation: 87-75=12 Current State: 82:[94, 12], Operations: ['4+90=94', '87-75=12'] Exploring Operation: 94-12=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[4, 90, 75, 87], Operations: [] Exploring Operation: 90-4=86, Resulting Numbers: [75, 87, 86] Generated Node #0,0: 82:[75, 87, 86] Operation: 90-4=86 Exploring Operation: 90-87=3, Resulting Numbers: [4, 75, 3] Generated Node #0,1: 82:[4, 75, 3] Operation: 90-87=3 Moving to Node #0,1 Current State: 82:[4, 75, 3], Operations: ['90-87=3'] Exploring Operation: 75+3=78, Resulting Numbers: [4, 78] Generated Node #0,1,0: 82:[4, 78] Operation: 75+3=78 Exploring Operation: 4+75=79, Resulting Numbers: [3, 79] Generated Node #0,1,1: 82:[3, 79] Operation: 4+75=79 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 82:[3, 79], Operations: ['90-87=3', '4+75=79'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,82 unequal: No Solution Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[4, 90, 75, 87], Operations: [] Exploring Operation: 90-87=3, Resulting Numbers: [4, 75, 3] Generated Node #0,1: 82:[4, 75, 3] Operation: 90-87=3 Moving to Node #0,1 Current State: 82:[4, 75, 3], Operations: ['90-87=3'] Exploring Operation: 4+75=79, Resulting Numbers: [3, 79] Generated Node #0,1,1: 82:[3, 79] Operation: 4+75=79 Moving to Node #0,1,1 Current State: 82:[3, 79], Operations: ['90-87=3', '4+75=79'] Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 81, 98, 77, 14 ]
88
[ "81+98=179", "77+14=91", "179-91=88" ]
Current State: 88:[81, 98, 77, 14], Operations: [] Exploring Operation: 81+98=179, Resulting Numbers: [77, 14, 179] Generated Node #2: [77, 14, 179] from Operation: 81+98=179 Current State: 88:[77, 14, 179], Operations: ['81+98=179'] Exploring Operation: 77+14=91, Resulting Numbers: [179, 91] Generated Node #3: [179, 91] from Operation: 77+14=91 Current State: 88:[179, 91], Operations: ['81+98=179', '77+14=91'] Exploring Operation: 179-91=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[81, 98, 77, 14], Operations: [] Exploring Operation: 98-81=17, Resulting Numbers: [77, 14, 17] Generated Node #0,0: 88:[77, 14, 17] Operation: 98-81=17 Exploring Operation: 98-77=21, Resulting Numbers: [81, 14, 21] Generated Node #0,1: 88:[81, 14, 21] Operation: 98-77=21 Exploring Operation: 81-77=4, Resulting Numbers: [98, 14, 4] Generated Node #0,2: 88:[98, 14, 4] Operation: 81-77=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[81, 14, 21], Operations: ['98-77=21'] Exploring Operation: 14+21=35, Resulting Numbers: [81, 35] Generated Node #0,1,0: 88:[81, 35] Operation: 14+21=35 Exploring Operation: 81+14=95, Resulting Numbers: [21, 95] Generated Node #0,1,1: 88:[21, 95] Operation: 81+14=95 Exploring Operation: 21-14=7, Resulting Numbers: [81, 7] Generated Node #0,1,2: 88:[81, 7] Operation: 21-14=7 Moving to Node #0,1,1 Current State: 88:[21, 95], Operations: ['98-77=21', '81+14=95'] Exploring Operation: 21*95=1995, Resulting Numbers: [1995] 1995,88 unequal: No Solution Exploring Operation: 21+95=116, Resulting Numbers: [116] 116,88 unequal: No Solution Exploring Operation: 95-21=74, Resulting Numbers: [74] 74,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[81, 7], Operations: ['98-77=21', '21-14=7'] Exploring Operation: 81+7=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[81, 98, 77, 14], Operations: [] Exploring Operation: 98-77=21, Resulting Numbers: [81, 14, 21] Generated Node #0,1: 88:[81, 14, 21] Operation: 98-77=21 Moving to Node #0,1 Current State: 88:[81, 14, 21], Operations: ['98-77=21'] Exploring Operation: 21-14=7, Resulting Numbers: [81, 7] Generated Node #0,1,2: 88:[81, 7] Operation: 21-14=7 Moving to Node #0,1,2 Current State: 88:[81, 7], Operations: ['98-77=21', '21-14=7'] Exploring Operation: 81+7=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 88, 67, 90, 48 ]
29
[ "90-88=2", "48*2=96", "96-67=29" ]
Current State: 29:[88, 67, 90, 48], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [67, 48, 2] Generated Node #2: [67, 48, 2] from Operation: 90-88=2 Current State: 29:[67, 48, 2], Operations: ['90-88=2'] Exploring Operation: 48*2=96, Resulting Numbers: [67, 96] Generated Node #3: [67, 96] from Operation: 48*2=96 Current State: 29:[67, 96], Operations: ['90-88=2', '48*2=96'] Exploring Operation: 96-67=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[88, 67, 90, 48], Operations: [] Exploring Operation: 90-67=23, Resulting Numbers: [88, 48, 23] Generated Node #0,0: 29:[88, 48, 23] Operation: 90-67=23 Exploring Operation: 88-67=21, Resulting Numbers: [90, 48, 21] Generated Node #0,1: 29:[90, 48, 21] Operation: 88-67=21 Exploring Operation: 90-88=2, Resulting Numbers: [67, 48, 2] Generated Node #0,2: 29:[67, 48, 2] Operation: 90-88=2 Moving to Node #0,0 Current State: 29:[88, 48, 23], Operations: ['90-67=23'] Exploring Operation: 48-23=25, Resulting Numbers: [88, 25] Generated Node #0,0,0: 29:[88, 25] Operation: 48-23=25 Exploring Operation: 88-48=40, Resulting Numbers: [23, 40] Generated Node #0,0,1: 29:[23, 40] Operation: 88-48=40 Exploring Operation: 88-23=65, Resulting Numbers: [48, 65] Generated Node #0,0,2: 29:[48, 65] Operation: 88-23=65 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 29:[23, 40], Operations: ['90-67=23', '88-48=40'] Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 23*40=920, Resulting Numbers: [920] 920,29 unequal: No Solution Exploring Operation: 23+40=63, Resulting Numbers: [63] 63,29 unequal: No Solution No 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: 29:[48, 65], Operations: ['90-67=23', '88-23=65'] Exploring Operation: 48*65=3120, Resulting Numbers: [3120] 3120,29 unequal: No Solution Exploring Operation: 65-48=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 48+65=113, Resulting Numbers: [113] 113,29 unequal: No Solution No 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: 29:[88, 25], Operations: ['90-67=23', '48-23=25'] Exploring Operation: 88+25=113, Resulting Numbers: [113] 113,29 unequal: No Solution Exploring Operation: 88-25=63, Resulting Numbers: [63] 63,29 unequal: No Solution Exploring Operation: 88*25=2200, Resulting Numbers: [2200] 2200,29 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: 29:[67, 48, 2], Operations: ['90-88=2'] Exploring Operation: 67-2=65, Resulting Numbers: [48, 65] Generated Node #0,2,0: 29:[48, 65] Operation: 67-2=65 Exploring Operation: 48/2=24, Resulting Numbers: [67, 24] Generated Node #0,2,1: 29:[67, 24] Operation: 48/2=24 Exploring Operation: 67-48=19, Resulting Numbers: [2, 19] Generated Node #0,2,2: 29:[2, 19] Operation: 67-48=19 Moving to Node #0,1 Current State: 29:[90, 48, 21], Operations: ['88-67=21'] Exploring Operation: 48-21=27, Resulting Numbers: [90, 27] Generated Node #0,1,0: 29:[90, 27] Operation: 48-21=27 Exploring Operation: 90-48=42, Resulting Numbers: [21, 42] Generated Node #0,1,1: 29:[21, 42] Operation: 90-48=42 Exploring Operation: 90-21=69, Resulting Numbers: [48, 69] Generated Node #0,1,2: 29:[48, 69] Operation: 90-21=69 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 29:[21, 42], Operations: ['88-67=21', '90-48=42'] Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,29 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,29 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,29 unequal: No Solution No 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: 29:[48, 69], Operations: ['88-67=21', '90-21=69'] Exploring Operation: 48*69=3312, Resulting Numbers: [3312] 3312,29 unequal: No Solution Exploring Operation: 69-48=21, Resulting Numbers: [21] 21,29 unequal: No Solution Exploring Operation: 48+69=117, Resulting Numbers: [117] 117,29 unequal: No Solution No 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: 29:[90, 27], Operations: ['88-67=21', '48-21=27'] Exploring Operation: 90+27=117, Resulting Numbers: [117] 117,29 unequal: No Solution Exploring Operation: 90*27=2430, Resulting Numbers: [2430] 2430,29 unequal: No Solution Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 29:[2, 19], Operations: ['90-88=2', '67-48=19'] Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,29 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[67, 24], Operations: ['90-88=2', '48/2=24'] Exploring Operation: 67+24=91, Resulting Numbers: [91] 91,29 unequal: No Solution Exploring Operation: 67*24=1608, Resulting Numbers: [1608] 1608,29 unequal: No Solution Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,29 unequal: No Solution Moving to Node #0,2,0 Current State: 29:[48, 65], Operations: ['90-88=2', '67-2=65'] Exploring Operation: 48*65=3120, Resulting Numbers: [3120] 3120,29 unequal: No Solution Exploring Operation: 65-48=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 48+65=113, Resulting Numbers: [113] 113,29 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 94, 97, 98, 74 ]
92
[ "98-94=4", "97-74=23", "4*23=92" ]
Current State: 92:[94, 97, 98, 74], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [97, 74, 4] Generated Node #2: [97, 74, 4] from Operation: 98-94=4 Current State: 92:[97, 74, 4], Operations: ['98-94=4'] Exploring Operation: 97-74=23, Resulting Numbers: [4, 23] Generated Node #3: [4, 23] from Operation: 97-74=23 Current State: 92:[4, 23], Operations: ['98-94=4', '97-74=23'] Exploring Operation: 4*23=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[94, 97, 98, 74], Operations: [] Exploring Operation: 98-74=24, Resulting Numbers: [94, 97, 24] Generated Node #0,0: 92:[94, 97, 24] Operation: 98-74=24 Exploring Operation: 94-74=20, Resulting Numbers: [97, 98, 20] Generated Node #0,1: 92:[97, 98, 20] Operation: 94-74=20 Exploring Operation: 97-74=23, Resulting Numbers: [94, 98, 23] Generated Node #0,2: 92:[94, 98, 23] Operation: 97-74=23 Exploring Operation: 98-97=1, Resulting Numbers: [94, 74, 1] Generated Node #0,3: 92:[94, 74, 1] Operation: 98-97=1 Moving to Node #0,0 Current State: 92:[94, 97, 24], Operations: ['98-74=24'] Exploring Operation: 97-94=3, Resulting Numbers: [24, 3] Generated Node #0,0,0: 92:[24, 3] Operation: 97-94=3 Exploring Operation: 97-24=73, Resulting Numbers: [94, 73] Generated Node #0,0,1: 92:[94, 73] Operation: 97-24=73 Exploring Operation: 94-24=70, Resulting Numbers: [97, 70] Generated Node #0,0,2: 92:[97, 70] Operation: 94-24=70 Exploring Operation: 94+24=118, Resulting Numbers: [97, 118] Generated Node #0,0,3: 92:[97, 118] Operation: 94+24=118 Moving to Node #0,2 Current State: 92:[94, 98, 23], Operations: ['97-74=23'] Exploring Operation: 98-23=75, Resulting Numbers: [94, 75] Generated Node #0,2,0: 92:[94, 75] Operation: 98-23=75 Exploring Operation: 94-23=71, Resulting Numbers: [98, 71] Generated Node #0,2,1: 92:[98, 71] Operation: 94-23=71 Exploring Operation: 94+23=117, Resulting Numbers: [98, 117] Generated Node #0,2,2: 92:[98, 117] Operation: 94+23=117 Exploring Operation: 98-94=4, Resulting Numbers: [23, 4] Generated Node #0,2,3: 92:[23, 4] Operation: 98-94=4 Moving to Node #0,1 Current State: 92:[97, 98, 20], Operations: ['94-74=20'] Exploring Operation: 97+20=117, Resulting Numbers: [98, 117] Generated Node #0,1,0: 92:[98, 117] Operation: 97+20=117 Exploring Operation: 98-20=78, Resulting Numbers: [97, 78] Generated Node #0,1,1: 92:[97, 78] Operation: 98-20=78 Exploring Operation: 98-97=1, Resulting Numbers: [20, 1] Generated Node #0,1,2: 92:[20, 1] Operation: 98-97=1 Exploring Operation: 97-20=77, Resulting Numbers: [98, 77] Generated Node #0,1,3: 92:[98, 77] Operation: 97-20=77 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 92:[20, 1], Operations: ['94-74=20', '98-97=1'] Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,92 unequal: No Solution Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,92 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,92 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[97, 78], Operations: ['94-74=20', '98-20=78'] Exploring Operation: 97-78=19, Resulting Numbers: [19] 19,92 unequal: No Solution Exploring Operation: 97*78=7566, Resulting Numbers: [7566] 7566,92 unequal: No Solution Exploring Operation: 97+78=175, Resulting Numbers: [175] 175,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 92:[98, 77], Operations: ['94-74=20', '97-20=77'] Exploring Operation: 98+77=175, Resulting Numbers: [175] 175,92 unequal: No Solution Exploring Operation: 98*77=7546, Resulting Numbers: [7546] 7546,92 unequal: No Solution Exploring Operation: 98-77=21, Resulting Numbers: [21] 21,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[98, 117], Operations: ['94-74=20', '97+20=117'] Exploring Operation: 98+117=215, Resulting Numbers: [215] 215,92 unequal: No Solution Exploring Operation: 98*117=11466, Resulting Numbers: [11466] 11466,92 unequal: No Solution Exploring Operation: 117-98=19, Resulting Numbers: [19] 19,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 92:[94, 74, 1], Operations: ['98-97=1'] Exploring Operation: 94-74=20, Resulting Numbers: [1, 20] Generated Node #0,3,0: 92:[1, 20] Operation: 94-74=20 Exploring Operation: 94-1=93, Resulting Numbers: [74, 93] Generated Node #0,3,1: 92:[74, 93] Operation: 94-1=93 Exploring Operation: 74+1=75, Resulting Numbers: [94, 75] Generated Node #0,3,2: 92:[94, 75] Operation: 74+1=75 Exploring Operation: 94*1=94, Resulting Numbers: [74, 94] Generated Node #0,3,3: 92:[74, 94] Operation: 94*1=94 Moving to Node #0,2,3 Current State: 92:[23, 4], Operations: ['97-74=23', '98-94=4'] Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,92 unequal: No Solution Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[94, 97, 98, 74], Operations: [] Exploring Operation: 97-74=23, Resulting Numbers: [94, 98, 23] Generated Node #0,2: 92:[94, 98, 23] Operation: 97-74=23 Moving to Node #0,2 Current State: 92:[94, 98, 23], Operations: ['97-74=23'] Exploring Operation: 98-94=4, Resulting Numbers: [23, 4] Generated Node #0,2,3: 92:[23, 4] Operation: 98-94=4 Moving to Node #0,2,3 Current State: 92:[23, 4], Operations: ['97-74=23', '98-94=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
0.965278
hs_4
mult_heuristic
[ 62, 4, 33, 98 ]
24
[ "98-62=36", "36/4=9", "33-9=24" ]
Current State: 24:[62, 4, 33, 98], Operations: [] Exploring Operation: 98-62=36, Resulting Numbers: [4, 33, 36] Generated Node #2: [4, 33, 36] from Operation: 98-62=36 Current State: 24:[4, 33, 36], Operations: ['98-62=36'] Exploring Operation: 36/4=9, Resulting Numbers: [33, 9] Generated Node #3: [33, 9] from Operation: 36/4=9 Current State: 24:[33, 9], Operations: ['98-62=36', '36/4=9'] Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[62, 4, 33, 98], Operations: [] Exploring Operation: 98-62=36, Resulting Numbers: [4, 33, 36] Generated Node #0,0: 24:[4, 33, 36] Operation: 98-62=36 Exploring Operation: 62-33=29, Resulting Numbers: [4, 98, 29] Generated Node #0,1: 24:[4, 98, 29] Operation: 62-33=29 Exploring Operation: 98-33=65, Resulting Numbers: [62, 4, 65] Generated Node #0,2: 24:[62, 4, 65] Operation: 98-33=65 Moving to Node #0,0 Current State: 24:[4, 33, 36], Operations: ['98-62=36'] Exploring Operation: 36/4=9, Resulting Numbers: [33, 9] Generated Node #0,0,0: 24:[33, 9] Operation: 36/4=9 Exploring Operation: 36-33=3, Resulting Numbers: [4, 3] Generated Node #0,0,1: 24:[4, 3] Operation: 36-33=3 Exploring Operation: 33-4=29, Resulting Numbers: [36, 29] Generated Node #0,0,2: 24:[36, 29] Operation: 33-4=29 Moving to Node #0,1 Current State: 24:[4, 98, 29], Operations: ['62-33=29'] Exploring Operation: 98-4=94, Resulting Numbers: [29, 94] Generated Node #0,1,0: 24:[29, 94] Operation: 98-4=94 Exploring Operation: 29-4=25, Resulting Numbers: [98, 25] Generated Node #0,1,1: 24:[98, 25] Operation: 29-4=25 Exploring Operation: 98-29=69, Resulting Numbers: [4, 69] Generated Node #0,1,2: 24:[4, 69] Operation: 98-29=69 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[4, 69], Operations: ['62-33=29', '98-29=69'] Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,24 unequal: No Solution Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,24 unequal: No Solution Exploring Operation: 4*69=276, Resulting Numbers: [276] 276,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[29, 94], Operations: ['62-33=29', '98-4=94'] Exploring Operation: 29+94=123, Resulting Numbers: [123] 123,24 unequal: No Solution Exploring Operation: 94-29=65, Resulting Numbers: [65] 65,24 unequal: No Solution Exploring Operation: 29*94=2726, Resulting Numbers: [2726] 2726,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 24:[98, 25], Operations: ['62-33=29', '29-4=25'] Exploring Operation: 98+25=123, Resulting Numbers: [123] 123,24 unequal: No Solution Exploring Operation: 98*25=2450, Resulting Numbers: [2450] 2450,24 unequal: No Solution Exploring Operation: 98-25=73, Resulting Numbers: [73] 73,24 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: 24:[62, 4, 65], Operations: ['98-33=65'] Exploring Operation: 65-4=61, Resulting Numbers: [62, 61] Generated Node #0,2,0: 24:[62, 61] Operation: 65-4=61 Exploring Operation: 65-62=3, Resulting Numbers: [4, 3] Generated Node #0,2,1: 24:[4, 3] Operation: 65-62=3 Exploring Operation: 62-4=58, Resulting Numbers: [65, 58] Generated Node #0,2,2: 24:[65, 58] Operation: 62-4=58 Moving to Node #0,0,1 Current State: 24:[4, 3], Operations: ['98-62=36', '36-33=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,24 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,24 unequal: No Solution Moving to Node #0,2,1 Current State: 24:[4, 3], Operations: ['98-33=65', '65-62=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,24 unequal: No Solution Moving to Node #0,0,0 Current State: 24:[33, 9], Operations: ['98-62=36', '36/4=9'] Exploring Operation: 33+9=42, Resulting Numbers: [42] 42,24 unequal: No Solution Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[62, 4, 33, 98], Operations: [] Exploring Operation: 98-62=36, Resulting Numbers: [4, 33, 36] Generated Node #0,0: 24:[4, 33, 36] Operation: 98-62=36 Moving to Node #0,0 Current State: 24:[4, 33, 36], Operations: ['98-62=36'] Exploring Operation: 36/4=9, Resulting Numbers: [33, 9] Generated Node #0,0,0: 24:[33, 9] Operation: 36/4=9 Moving to Node #0,0,0 Current State: 24:[33, 9], Operations: ['98-62=36', '36/4=9'] Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
0.971354
hs_3
sum_heuristic
[ 11, 62, 13, 15 ]
94
[ "13-11=2", "62-15=47", "2*47=94" ]
Current State: 94:[11, 62, 13, 15], Operations: [] Exploring Operation: 13-11=2, Resulting Numbers: [62, 15, 2] Generated Node #2: [62, 15, 2] from Operation: 13-11=2 Current State: 94:[62, 15, 2], Operations: ['13-11=2'] Exploring Operation: 62-15=47, Resulting Numbers: [2, 47] Generated Node #3: [2, 47] from Operation: 62-15=47 Current State: 94:[2, 47], Operations: ['13-11=2', '62-15=47'] Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[11, 62, 13, 15], Operations: [] Exploring Operation: 62-15=47, Resulting Numbers: [11, 13, 47] Generated Node #0,0: 94:[11, 13, 47] Operation: 62-15=47 Moving to Node #0,0 Current State: 94:[11, 13, 47], Operations: ['62-15=47'] Exploring Operation: 13-11=2, Resulting Numbers: [47, 2] Generated Node #0,0,0: 94:[47, 2] Operation: 13-11=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[47, 2], Operations: ['62-15=47', '13-11=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[11, 62, 13, 15], Operations: [] Exploring Operation: 62-15=47, Resulting Numbers: [11, 13, 47] Generated Node #0,0: 94:[11, 13, 47] Operation: 62-15=47 Moving to Node #0,0 Current State: 94:[11, 13, 47], Operations: ['62-15=47'] Exploring Operation: 13-11=2, Resulting Numbers: [47, 2] Generated Node #0,0,0: 94:[47, 2] Operation: 13-11=2 Moving to Node #0,0,0 Current State: 94:[47, 2], Operations: ['62-15=47', '13-11=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 7, 48, 16, 26 ]
97
[ "7+48=55", "16+26=42", "55+42=97" ]
Current State: 97:[7, 48, 16, 26], Operations: [] Exploring Operation: 7+48=55, Resulting Numbers: [16, 26, 55] Generated Node #2: [16, 26, 55] from Operation: 7+48=55 Current State: 97:[16, 26, 55], Operations: ['7+48=55'] Exploring Operation: 16+26=42, Resulting Numbers: [55, 42] Generated Node #3: [55, 42] from Operation: 16+26=42 Current State: 97:[55, 42], Operations: ['7+48=55', '16+26=42'] Exploring Operation: 55+42=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[7, 48, 16, 26], Operations: [] Exploring Operation: 7*16=112, Resulting Numbers: [48, 26, 112] Generated Node #0,0: 97:[48, 26, 112] Operation: 7*16=112 Moving to Node #0,0 Current State: 97:[48, 26, 112], Operations: ['7*16=112'] Exploring Operation: 48+26=74, Resulting Numbers: [112, 74] Generated Node #0,0,0: 97:[112, 74] Operation: 48+26=74 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[112, 74], Operations: ['7*16=112', '48+26=74'] Exploring Operation: 112-74=38, Resulting Numbers: [38] 38,97 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
[ 76, 69, 4, 61 ]
44
[ "69-61=8", "4*8=32", "76-32=44" ]
Current State: 44:[76, 69, 4, 61], Operations: [] Exploring Operation: 69-61=8, Resulting Numbers: [76, 4, 8] Generated Node #2: [76, 4, 8] from Operation: 69-61=8 Current State: 44:[76, 4, 8], Operations: ['69-61=8'] Exploring Operation: 4*8=32, Resulting Numbers: [76, 32] Generated Node #3: [76, 32] from Operation: 4*8=32 Current State: 44:[76, 32], Operations: ['69-61=8', '4*8=32'] Exploring Operation: 76-32=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[76, 69, 4, 61], Operations: [] Exploring Operation: 76-69=7, Resulting Numbers: [4, 61, 7] Generated Node #0,0: 44:[4, 61, 7] Operation: 76-69=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[4, 61, 7], Operations: ['76-69=7'] Exploring Operation: 61-7=54, Resulting Numbers: [4, 54] Generated Node #0,0,0: 44:[4, 54] Operation: 61-7=54 Moving to Node #0,0,0 Current State: 44:[4, 54], Operations: ['76-69=7', '61-7=54'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,44 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
[ 24, 67, 78, 10 ]
86
[ "78-67=11", "10*11=110", "110-24=86" ]
Current State: 86:[24, 67, 78, 10], Operations: [] Exploring Operation: 78-67=11, Resulting Numbers: [24, 10, 11] Generated Node #2: [24, 10, 11] from Operation: 78-67=11 Current State: 86:[24, 10, 11], Operations: ['78-67=11'] Exploring Operation: 10*11=110, Resulting Numbers: [24, 110] Generated Node #3: [24, 110] from Operation: 10*11=110 Current State: 86:[24, 110], Operations: ['78-67=11', '10*11=110'] Exploring Operation: 110-24=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[24, 67, 78, 10], Operations: [] Exploring Operation: 24+67=91, Resulting Numbers: [78, 10, 91] Generated Node #0,0: 86:[78, 10, 91] Operation: 24+67=91 Exploring Operation: 78-67=11, Resulting Numbers: [24, 10, 11] Generated Node #0,1: 86:[24, 10, 11] Operation: 78-67=11 Exploring Operation: 67-24=43, Resulting Numbers: [78, 10, 43] Generated Node #0,2: 86:[78, 10, 43] Operation: 67-24=43 Exploring Operation: 67+10=77, Resulting Numbers: [24, 78, 77] Generated Node #0,3: 86:[24, 78, 77] Operation: 67+10=77 Exploring Operation: 24+10=34, Resulting Numbers: [67, 78, 34] Generated Node #0,4: 86:[67, 78, 34] Operation: 24+10=34 Moving to Node #0,2 Current State: 86:[78, 10, 43], Operations: ['67-24=43'] Exploring Operation: 78-43=35, Resulting Numbers: [10, 35] Generated Node #0,2,0: 86:[10, 35] Operation: 78-43=35 Exploring Operation: 43-10=33, Resulting Numbers: [78, 33] Generated Node #0,2,1: 86:[78, 33] Operation: 43-10=33 Exploring Operation: 10+43=53, Resulting Numbers: [78, 53] Generated Node #0,2,2: 86:[78, 53] Operation: 10+43=53 Exploring Operation: 78+10=88, Resulting Numbers: [43, 88] Generated Node #0,2,3: 86:[43, 88] Operation: 78+10=88 Exploring Operation: 78-10=68, Resulting Numbers: [43, 68] Generated Node #0,2,4: 86:[43, 68] Operation: 78-10=68 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 86:[43, 88], Operations: ['67-24=43', '78+10=88'] Exploring Operation: 43+88=131, Resulting Numbers: [131] 131,86 unequal: No Solution Exploring Operation: 43*88=3784, Resulting Numbers: [3784] 3784,86 unequal: No Solution Exploring Operation: 88-43=45, Resulting Numbers: [45] 45,86 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 #0,2,0 Current State: 86:[10, 35], Operations: ['67-24=43', '78-43=35'] Exploring Operation: 10+35=45, Resulting Numbers: [45] 45,86 unequal: No Solution Exploring Operation: 35-10=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 10*35=350, Resulting Numbers: [350] 350,86 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 #0,2,1 Current State: 86:[78, 33], Operations: ['67-24=43', '43-10=33'] Exploring Operation: 78-33=45, Resulting Numbers: [45] 45,86 unequal: No Solution Exploring Operation: 78*33=2574, Resulting Numbers: [2574] 2574,86 unequal: No Solution Exploring Operation: 78+33=111, Resulting Numbers: [111] 111,86 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 #0,2,2 Current State: 86:[78, 53], Operations: ['67-24=43', '10+43=53'] Exploring Operation: 78+53=131, Resulting Numbers: [131] 131,86 unequal: No Solution Exploring Operation: 78*53=4134, Resulting Numbers: [4134] 4134,86 unequal: No Solution Exploring Operation: 78-53=25, Resulting Numbers: [25] 25,86 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 #0,2,4 Current State: 86:[43, 68], Operations: ['67-24=43', '78-10=68'] Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 43+68=111, Resulting Numbers: [111] 111,86 unequal: No Solution Exploring Operation: 43*68=2924, Resulting Numbers: [2924] 2924,86 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:[78, 10, 91], Operations: ['24+67=91'] Exploring Operation: 91-10=81, Resulting Numbers: [78, 81] Generated Node #0,0,0: 86:[78, 81] Operation: 91-10=81 Exploring Operation: 10+91=101, Resulting Numbers: [78, 101] Generated Node #0,0,1: 86:[78, 101] Operation: 10+91=101 Exploring Operation: 78-10=68, Resulting Numbers: [91, 68] Generated Node #0,0,2: 86:[91, 68] Operation: 78-10=68 Exploring Operation: 91-78=13, Resulting Numbers: [10, 13] Generated Node #0,0,3: 86:[10, 13] Operation: 91-78=13 Exploring Operation: 78+10=88, Resulting Numbers: [91, 88] Generated Node #0,0,4: 86:[91, 88] Operation: 78+10=88 Moving to Node #0,1 Current State: 86:[24, 10, 11], Operations: ['78-67=11'] Exploring Operation: 24-10=14, Resulting Numbers: [11, 14] Generated Node #0,1,0: 86:[11, 14] Operation: 24-10=14 Exploring Operation: 24-11=13, Resulting Numbers: [10, 13] Generated Node #0,1,1: 86:[10, 13] Operation: 24-11=13 Exploring Operation: 24+11=35, Resulting Numbers: [10, 35] Generated Node #0,1,2: 86:[10, 35] Operation: 24+11=35 Exploring Operation: 24+10=34, Resulting Numbers: [11, 34] Generated Node #0,1,3: 86:[11, 34] Operation: 24+10=34 Exploring Operation: 11-10=1, Resulting Numbers: [24, 1] Generated Node #0,1,4: 86:[24, 1] Operation: 11-10=1 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[10, 35], Operations: ['78-67=11', '24+11=35'] Exploring Operation: 35-10=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 10+35=45, Resulting Numbers: [45] 45,86 unequal: No Solution Exploring Operation: 10*35=350, Resulting Numbers: [350] 350,86 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:[11, 34], Operations: ['78-67=11', '24+10=34'] Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,86 unequal: No Solution Exploring Operation: 11+34=45, Resulting Numbers: [45] 45,86 unequal: No Solution Exploring Operation: 11*34=374, Resulting Numbers: [374] 374,86 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:[10, 13], Operations: ['78-67=11', '24-11=13'] Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,86 unequal: No Solution Exploring Operation: 10*13=130, Resulting Numbers: [130] 130,86 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,86 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:[24, 1], Operations: ['78-67=11', '11-10=1'] Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,86 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,86 unequal: No Solution Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 24*1=24, Resulting Numbers: [24] 24,86 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 #0,1,0 Current State: 86:[11, 14], Operations: ['78-67=11', '24-10=14'] Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,86 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,86 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: 86:[24, 78, 77], Operations: ['67+10=77'] Exploring Operation: 24+77=101, Resulting Numbers: [78, 101] Generated Node #0,3,0: 86:[78, 101] Operation: 24+77=101 Exploring Operation: 77-24=53, Resulting Numbers: [78, 53] Generated Node #0,3,1: 86:[78, 53] Operation: 77-24=53 Exploring Operation: 78-77=1, Resulting Numbers: [24, 1] Generated Node #0,3,2: 86:[24, 1] Operation: 78-77=1 Exploring Operation: 24+78=102, Resulting Numbers: [77, 102] Generated Node #0,3,3: 86:[77, 102] Operation: 24+78=102 Exploring Operation: 78-24=54, Resulting Numbers: [77, 54] Generated Node #0,3,4: 86:[77, 54] Operation: 78-24=54 Moving to Node #0,4 Current State: 86:[67, 78, 34], Operations: ['24+10=34'] Exploring Operation: 67+34=101, Resulting Numbers: [78, 101] Generated Node #0,4,0: 86:[78, 101] Operation: 67+34=101 Exploring Operation: 78-34=44, Resulting Numbers: [67, 44] Generated Node #0,4,1: 86:[67, 44] Operation: 78-34=44 Exploring Operation: 78+34=112, Resulting Numbers: [67, 112] Generated Node #0,4,2: 86:[67, 112] Operation: 78+34=112 Exploring Operation: 67-34=33, Resulting Numbers: [78, 33] Generated Node #0,4,3: 86:[78, 33] Operation: 67-34=33 Exploring Operation: 78-67=11, Resulting Numbers: [34, 11] Generated Node #0,4,4: 86:[34, 11] Operation: 78-67=11 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 86:[78, 33], Operations: ['24+10=34', '67-34=33'] Exploring Operation: 78*33=2574, Resulting Numbers: [2574] 2574,86 unequal: No Solution Exploring Operation: 78+33=111, Resulting Numbers: [111] 111,86 unequal: No Solution Exploring Operation: 78-33=45, Resulting Numbers: [45] 45,86 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:[34, 11], Operations: ['24+10=34', '78-67=11'] Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,86 unequal: No Solution Exploring Operation: 34+11=45, Resulting Numbers: [45] 45,86 unequal: No Solution Exploring Operation: 34*11=374, Resulting Numbers: [374] 374,86 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:[67, 44], Operations: ['24+10=34', '78-34=44'] Exploring Operation: 67-44=23, Resulting Numbers: [23] 23,86 unequal: No Solution Exploring Operation: 67+44=111, Resulting Numbers: [111] 111,86 unequal: No Solution Exploring Operation: 67*44=2948, Resulting Numbers: [2948] 2948,86 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:[78, 101], Operations: ['24+10=34', '67+34=101'] Exploring Operation: 78*101=7878, Resulting Numbers: [7878] 7878,86 unequal: No Solution Exploring Operation: 101-78=23, Resulting Numbers: [23] 23,86 unequal: No Solution Exploring Operation: 78+101=179, Resulting Numbers: [179] 179,86 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:[67, 112], Operations: ['24+10=34', '78+34=112'] Exploring Operation: 112-67=45, Resulting Numbers: [45] 45,86 unequal: No Solution Exploring Operation: 67+112=179, Resulting Numbers: [179] 179,86 unequal: No Solution Exploring Operation: 67*112=7504, Resulting Numbers: [7504] 7504,86 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: 86:[91, 88], Operations: ['24+67=91', '78+10=88'] Exploring Operation: 91-88=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 91+88=179, Resulting Numbers: [179] 179,86 unequal: No Solution Exploring Operation: 91*88=8008, Resulting Numbers: [8008] 8008,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[78, 81], Operations: ['24+67=91', '91-10=81'] Exploring Operation: 78*81=6318, Resulting Numbers: [6318] 6318,86 unequal: No Solution Exploring Operation: 81-78=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 78+81=159, Resulting Numbers: [159] 159,86 unequal: No Solution Moving to Node #0,3,1 Current State: 86:[78, 53], Operations: ['67+10=77', '77-24=53'] Exploring Operation: 78*53=4134, Resulting Numbers: [4134] 4134,86 unequal: No Solution Exploring Operation: 78-53=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 78+53=131, Resulting Numbers: [131] 131,86 unequal: No Solution Moving to Node #0,0,3 Current State: 86:[10, 13], Operations: ['24+67=91', '91-78=13'] Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,86 unequal: No Solution Exploring Operation: 10*13=130, Resulting Numbers: [130] 130,86 unequal: No Solution Moving to Node #0,3,2 Current State: 86:[24, 1], Operations: ['67+10=77', '78-77=1'] Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 24*1=24, Resulting Numbers: [24] 24,86 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,86 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,86 unequal: No Solution Moving to Node #0,3,4 Current State: 86:[77, 54], Operations: ['67+10=77', '78-24=54'] Exploring Operation: 77*54=4158, Resulting Numbers: [4158] 4158,86 unequal: No Solution Exploring Operation: 77+54=131, Resulting Numbers: [131] 131,86 unequal: No Solution Exploring Operation: 77-54=23, Resulting Numbers: [23] 23,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[78, 101], Operations: ['24+67=91', '10+91=101'] Exploring Operation: 101-78=23, Resulting Numbers: [23] 23,86 unequal: No Solution Exploring Operation: 78+101=179, Resulting Numbers: [179] 179,86 unequal: No Solution Exploring Operation: 78*101=7878, Resulting Numbers: [7878] 7878,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[91, 68], Operations: ['24+67=91', '78-10=68'] Exploring Operation: 91-68=23, Resulting Numbers: [23] 23,86 unequal: No Solution Exploring Operation: 91+68=159, Resulting Numbers: [159] 159,86 unequal: No Solution Exploring Operation: 91*68=6188, Resulting Numbers: [6188] 6188,86 unequal: No Solution Moving to Node #0,3,0 Current State: 86:[78, 101], Operations: ['67+10=77', '24+77=101'] Exploring Operation: 78*101=7878, Resulting Numbers: [7878] 7878,86 unequal: No Solution Exploring Operation: 78+101=179, Resulting Numbers: [179] 179,86 unequal: No Solution Exploring Operation: 101-78=23, Resulting Numbers: [23] 23,86 unequal: No Solution Moving to Node #0,3,3 Current State: 86:[77, 102], Operations: ['67+10=77', '24+78=102'] Exploring Operation: 77*102=7854, Resulting Numbers: [7854] 7854,86 unequal: No Solution Exploring Operation: 102-77=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 77+102=179, Resulting Numbers: [179] 179,86 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 36, 56, 64, 77 ]
79
[ "36+56=92", "77-64=13", "92-13=79" ]
Current State: 79:[36, 56, 64, 77], Operations: [] Exploring Operation: 36+56=92, Resulting Numbers: [64, 77, 92] Generated Node #2: [64, 77, 92] from Operation: 36+56=92 Current State: 79:[64, 77, 92], Operations: ['36+56=92'] Exploring Operation: 77-64=13, Resulting Numbers: [92, 13] Generated Node #3: [92, 13] from Operation: 77-64=13 Current State: 79:[92, 13], Operations: ['36+56=92', '77-64=13'] Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[36, 56, 64, 77], Operations: [] Exploring Operation: 56-36=20, Resulting Numbers: [64, 77, 20] Generated Node #0,0: 79:[64, 77, 20] Operation: 56-36=20 Exploring Operation: 64-36=28, Resulting Numbers: [56, 77, 28] Generated Node #0,1: 79:[56, 77, 28] Operation: 64-36=28 Exploring Operation: 36+56=92, Resulting Numbers: [64, 77, 92] Generated Node #0,2: 79:[64, 77, 92] Operation: 36+56=92 Exploring Operation: 36+64=100, Resulting Numbers: [56, 77, 100] Generated Node #0,3: 79:[56, 77, 100] Operation: 36+64=100 Exploring Operation: 36+77=113, Resulting Numbers: [56, 64, 113] Generated Node #0,4: 79:[56, 64, 113] Operation: 36+77=113 Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[64, 77, 92], Operations: ['36+56=92'] Exploring Operation: 92-64=28, Resulting Numbers: [77, 28] Generated Node #0,2,0: 79:[77, 28] Operation: 92-64=28 Exploring Operation: 64+92=156, Resulting Numbers: [77, 156] Generated Node #0,2,1: 79:[77, 156] Operation: 64+92=156 Exploring Operation: 92-77=15, Resulting Numbers: [64, 15] Generated Node #0,2,2: 79:[64, 15] Operation: 92-77=15 Exploring Operation: 77-64=13, Resulting Numbers: [92, 13] Generated Node #0,2,3: 79:[92, 13] Operation: 77-64=13 Exploring Operation: 64+77=141, Resulting Numbers: [92, 141] Generated Node #0,2,4: 79:[92, 141] Operation: 64+77=141 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 79:[77, 28], Operations: ['36+56=92', '92-64=28'] Exploring Operation: 77-28=49, Resulting Numbers: [49] 49,79 unequal: No Solution Exploring Operation: 77*28=2156, Resulting Numbers: [2156] 2156,79 unequal: No Solution Exploring Operation: 77+28=105, Resulting Numbers: [105] 105,79 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 #0,2,4 Current State: 79:[92, 141], Operations: ['36+56=92', '64+77=141'] Exploring Operation: 92+141=233, Resulting Numbers: [233] 233,79 unequal: No Solution Exploring Operation: 141-92=49, Resulting Numbers: [49] 49,79 unequal: No Solution Exploring Operation: 92*141=12972, Resulting Numbers: [12972] 12972,79 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 #0,2,1 Current State: 79:[77, 156], Operations: ['36+56=92', '64+92=156'] Exploring Operation: 77*156=12012, Resulting Numbers: [12012] 12012,79 unequal: No Solution Exploring Operation: 156-77=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[36, 56, 64, 77], Operations: [] Exploring Operation: 36+56=92, Resulting Numbers: [64, 77, 92] Generated Node #0,2: 79:[64, 77, 92] Operation: 36+56=92 Moving to Node #0,2 Current State: 79:[64, 77, 92], Operations: ['36+56=92'] Exploring Operation: 64+92=156, Resulting Numbers: [77, 156] Generated Node #0,2,1: 79:[77, 156] Operation: 64+92=156 Moving to Node #0,2,1 Current State: 79:[77, 156], Operations: ['36+56=92', '64+92=156'] Exploring Operation: 156-77=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 88, 18, 33, 85 ]
87
[ "88-85=3", "18*3=54", "33+54=87" ]
Current State: 87:[88, 18, 33, 85], Operations: [] Exploring Operation: 88-85=3, Resulting Numbers: [18, 33, 3] Generated Node #2: [18, 33, 3] from Operation: 88-85=3 Current State: 87:[18, 33, 3], Operations: ['88-85=3'] Exploring Operation: 18*3=54, Resulting Numbers: [33, 54] Generated Node #3: [33, 54] from Operation: 18*3=54 Current State: 87:[33, 54], Operations: ['88-85=3', '18*3=54'] Exploring Operation: 33+54=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[88, 18, 33, 85], Operations: [] Exploring Operation: 88-18=70, Resulting Numbers: [33, 85, 70] Generated Node #0,0: 87:[33, 85, 70] Operation: 88-18=70 Exploring Operation: 18+85=103, Resulting Numbers: [88, 33, 103] Generated Node #0,1: 87:[88, 33, 103] Operation: 18+85=103 Exploring Operation: 88-85=3, Resulting Numbers: [18, 33, 3] Generated Node #0,2: 87:[18, 33, 3] Operation: 88-85=3 Exploring Operation: 33-18=15, Resulting Numbers: [88, 85, 15] Generated Node #0,3: 87:[88, 85, 15] Operation: 33-18=15 Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[18, 33, 3], Operations: ['88-85=3'] Exploring Operation: 33-18=15, Resulting Numbers: [3, 15] Generated Node #0,2,0: 87:[3, 15] Operation: 33-18=15 Exploring Operation: 18+3=21, Resulting Numbers: [33, 21] Generated Node #0,2,1: 87:[33, 21] Operation: 18+3=21 Exploring Operation: 18/3=6, Resulting Numbers: [33, 6] Generated Node #0,2,2: 87:[33, 6] Operation: 18/3=6 Exploring Operation: 33-3=30, Resulting Numbers: [18, 30] Generated Node #0,2,3: 87:[18, 30] Operation: 33-3=30 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 87:[33, 6], Operations: ['88-85=3', '18/3=6'] Exploring Operation: 33+6=39, Resulting Numbers: [39] 39,87 unequal: No Solution Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,87 unequal: No Solution Exploring Operation: 33*6=198, Resulting Numbers: [198] 198,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 87:[3, 15], Operations: ['88-85=3', '33-18=15'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,87 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 87:[33, 21], Operations: ['88-85=3', '18+3=21'] Exploring Operation: 33*21=693, Resulting Numbers: [693] 693,87 unequal: No Solution Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 87:[18, 30], Operations: ['88-85=3', '33-3=30'] Exploring Operation: 18+30=48, Resulting Numbers: [48] 48,87 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 18*30=540, Resulting Numbers: [540] 540,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 87:[88, 85, 15], Operations: ['33-18=15'] Exploring Operation: 88+15=103, Resulting Numbers: [85, 103] Generated Node #0,3,0: 87:[85, 103] Operation: 88+15=103 Exploring Operation: 85+15=100, Resulting Numbers: [88, 100] Generated Node #0,3,1: 87:[88, 100] Operation: 85+15=100 Exploring Operation: 88-85=3, Resulting Numbers: [15, 3] Generated Node #0,3,2: 87:[15, 3] Operation: 88-85=3 Exploring Operation: 88-15=73, Resulting Numbers: [85, 73] Generated Node #0,3,3: 87:[85, 73] Operation: 88-15=73 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 87:[15, 3], Operations: ['33-18=15', '88-85=3'] Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,87 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 87:[88, 100], Operations: ['33-18=15', '85+15=100'] Exploring Operation: 100-88=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 88+100=188, Resulting Numbers: [188] 188,87 unequal: No Solution Exploring Operation: 88*100=8800, Resulting Numbers: [8800] 8800,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 87:[85, 73], Operations: ['33-18=15', '88-15=73'] Exploring Operation: 85-73=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 85*73=6205, Resulting Numbers: [6205] 6205,87 unequal: No Solution Exploring Operation: 85+73=158, Resulting Numbers: [158] 158,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 87:[85, 103], Operations: ['33-18=15', '88+15=103'] Exploring Operation: 85*103=8755, Resulting Numbers: [8755] 8755,87 unequal: No Solution Exploring Operation: 85+103=188, Resulting Numbers: [188] 188,87 unequal: No Solution Exploring Operation: 103-85=18, Resulting Numbers: [18] 18,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[88, 33, 103], Operations: ['18+85=103'] Exploring Operation: 88-33=55, Resulting Numbers: [103, 55] Generated Node #0,1,0: 87:[103, 55] Operation: 88-33=55 Exploring Operation: 88+33=121, Resulting Numbers: [103, 121] Generated Node #0,1,1: 87:[103, 121] Operation: 88+33=121 Exploring Operation: 103-33=70, Resulting Numbers: [88, 70] Generated Node #0,1,2: 87:[88, 70] Operation: 103-33=70 Exploring Operation: 103-88=15, Resulting Numbers: [33, 15] Generated Node #0,1,3: 87:[33, 15] Operation: 103-88=15 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 87:[33, 15], Operations: ['18+85=103', '103-88=15'] Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,87 unequal: No Solution Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 87:[88, 70], Operations: ['18+85=103', '103-33=70'] Exploring Operation: 88-70=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 88*70=6160, Resulting Numbers: [6160] 6160,87 unequal: No Solution Exploring Operation: 88+70=158, Resulting Numbers: [158] 158,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[103, 55], Operations: ['18+85=103', '88-33=55'] Exploring Operation: 103*55=5665, Resulting Numbers: [5665] 5665,87 unequal: No Solution Exploring Operation: 103-55=48, Resulting Numbers: [48] 48,87 unequal: No Solution Exploring Operation: 103+55=158, Resulting Numbers: [158] 158,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[103, 121], Operations: ['18+85=103', '88+33=121'] Exploring Operation: 121-103=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 103+121=224, Resulting Numbers: [224] 224,87 unequal: No Solution Exploring Operation: 103*121=12463, Resulting Numbers: [12463] 12463,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[33, 85, 70], Operations: ['88-18=70'] Exploring Operation: 85-70=15, Resulting Numbers: [33, 15] Generated Node #0,0,0: 87:[33, 15] Operation: 85-70=15 Exploring Operation: 85-33=52, Resulting Numbers: [70, 52] Generated Node #0,0,1: 87:[70, 52] Operation: 85-33=52 Exploring Operation: 70-33=37, Resulting Numbers: [85, 37] Generated Node #0,0,2: 87:[85, 37] Operation: 70-33=37 Exploring Operation: 33+70=103, Resulting Numbers: [85, 103] Generated Node #0,0,3: 87:[85, 103] Operation: 33+70=103 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 87:[85, 37], Operations: ['88-18=70', '70-33=37'] Exploring Operation: 85+37=122, Resulting Numbers: [122] 122,87 unequal: No Solution Exploring Operation: 85*37=3145, Resulting Numbers: [3145] 3145,87 unequal: No Solution Exploring Operation: 85-37=48, Resulting Numbers: [48] 48,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[33, 15], Operations: ['88-18=70', '85-70=15'] Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,87 unequal: No Solution Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 87:[85, 103], Operations: ['88-18=70', '33+70=103'] Exploring Operation: 85*103=8755, Resulting Numbers: [8755] 8755,87 unequal: No Solution Exploring Operation: 85+103=188, Resulting Numbers: [188] 188,87 unequal: No Solution Exploring Operation: 103-85=18, Resulting Numbers: [18] 18,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[70, 52], Operations: ['88-18=70', '85-33=52'] Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 70*52=3640, Resulting Numbers: [3640] 3640,87 unequal: No Solution Exploring Operation: 70+52=122, Resulting Numbers: [122] 122,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 19, 27, 8, 17 ]
57
[ "19*27=513", "17-8=9", "513/9=57" ]
Current State: 57:[19, 27, 8, 17], Operations: [] Exploring Operation: 19*27=513, Resulting Numbers: [8, 17, 513] Generated Node #2: [8, 17, 513] from Operation: 19*27=513 Current State: 57:[8, 17, 513], Operations: ['19*27=513'] Exploring Operation: 17-8=9, Resulting Numbers: [513, 9] Generated Node #3: [513, 9] from Operation: 17-8=9 Current State: 57:[513, 9], Operations: ['19*27=513', '17-8=9'] Exploring Operation: 513/9=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[19, 27, 8, 17], Operations: [] Exploring Operation: 27-8=19, Resulting Numbers: [19, 17, 19] Generated Node #0,0: 57:[19, 17, 19] Operation: 27-8=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[19, 17, 19], Operations: ['27-8=19'] Exploring Operation: 19-17=2, Resulting Numbers: [19, 2] Generated Node #0,0,0: 57:[19, 2] Operation: 19-17=2 Moving to Node #0,0,0 Current State: 57:[19, 2], Operations: ['27-8=19', '19-17=2'] Exploring Operation: 19+2=21, Resulting Numbers: [21] 21,57 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
[ 85, 90, 73, 14 ]
54
[ "90-85=5", "73-14=59", "59-5=54" ]
Current State: 54:[85, 90, 73, 14], Operations: [] Exploring Operation: 90-85=5, Resulting Numbers: [73, 14, 5] Generated Node #2: [73, 14, 5] from Operation: 90-85=5 Current State: 54:[73, 14, 5], Operations: ['90-85=5'] Exploring Operation: 73-14=59, Resulting Numbers: [5, 59] Generated Node #3: [5, 59] from Operation: 73-14=59 Current State: 54:[5, 59], Operations: ['90-85=5', '73-14=59'] Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[85, 90, 73, 14], Operations: [] Exploring Operation: 85-14=71, Resulting Numbers: [90, 73, 71] Generated Node #0,0: 54:[90, 73, 71] Operation: 85-14=71 Exploring Operation: 90-73=17, Resulting Numbers: [85, 14, 17] Generated Node #0,1: 54:[85, 14, 17] Operation: 90-73=17 Exploring Operation: 90-14=76, Resulting Numbers: [85, 73, 76] Generated Node #0,2: 54:[85, 73, 76] Operation: 90-14=76 Exploring Operation: 85-73=12, Resulting Numbers: [90, 14, 12] Generated Node #0,3: 54:[90, 14, 12] Operation: 85-73=12 Exploring Operation: 90-85=5, Resulting Numbers: [73, 14, 5] Generated Node #0,4: 54:[73, 14, 5] Operation: 90-85=5 Start Sub Search at level 1: Moving to Node #0,4 Current State: 54:[73, 14, 5], Operations: ['90-85=5'] Exploring Operation: 73-14=59, Resulting Numbers: [5, 59] Generated Node #0,4,0: 54:[5, 59] Operation: 73-14=59 Exploring Operation: 73+5=78, Resulting Numbers: [14, 78] Generated Node #0,4,1: 54:[14, 78] Operation: 73+5=78 Exploring Operation: 73-5=68, Resulting Numbers: [14, 68] Generated Node #0,4,2: 54:[14, 68] Operation: 73-5=68 Exploring Operation: 14-5=9, Resulting Numbers: [73, 9] Generated Node #0,4,3: 54:[73, 9] Operation: 14-5=9 Exploring Operation: 14+5=19, Resulting Numbers: [73, 19] Generated Node #0,4,4: 54:[73, 19] Operation: 14+5=19 Moving to Node #0,4,0 Current State: 54:[5, 59], Operations: ['90-85=5', '73-14=59'] Exploring Operation: 5*59=295, Resulting Numbers: [295] 295,54 unequal: No Solution Exploring Operation: 5+59=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[85, 90, 73, 14], Operations: [] Exploring Operation: 90-85=5, Resulting Numbers: [73, 14, 5] Generated Node #0,4: 54:[73, 14, 5] Operation: 90-85=5 Moving to Node #0,4 Current State: 54:[73, 14, 5], Operations: ['90-85=5'] Exploring Operation: 73-14=59, Resulting Numbers: [5, 59] Generated Node #0,4,0: 54:[5, 59] Operation: 73-14=59 Moving to Node #0,4,0 Current State: 54:[5, 59], Operations: ['90-85=5', '73-14=59'] Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 25, 43, 17, 21 ]
72
[ "25+43=68", "21-17=4", "68+4=72" ]
Current State: 72:[25, 43, 17, 21], Operations: [] Exploring Operation: 25+43=68, Resulting Numbers: [17, 21, 68] Generated Node #2: [17, 21, 68] from Operation: 25+43=68 Current State: 72:[17, 21, 68], Operations: ['25+43=68'] Exploring Operation: 21-17=4, Resulting Numbers: [68, 4] Generated Node #3: [68, 4] from Operation: 21-17=4 Current State: 72:[68, 4], Operations: ['25+43=68', '21-17=4'] Exploring Operation: 68+4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[25, 43, 17, 21], Operations: [] Exploring Operation: 25+43=68, Resulting Numbers: [17, 21, 68] Generated Node #0,0: 72:[17, 21, 68] Operation: 25+43=68 Exploring Operation: 43-25=18, Resulting Numbers: [17, 21, 18] Generated Node #0,1: 72:[17, 21, 18] Operation: 43-25=18 Exploring Operation: 43-21=22, Resulting Numbers: [25, 17, 22] Generated Node #0,2: 72:[25, 17, 22] Operation: 43-21=22 Exploring Operation: 43-17=26, Resulting Numbers: [25, 21, 26] Generated Node #0,3: 72:[25, 21, 26] Operation: 43-17=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[17, 21, 18], Operations: ['43-25=18'] Exploring Operation: 21-18=3, Resulting Numbers: [17, 3] Generated Node #0,1,0: 72:[17, 3] Operation: 21-18=3 Exploring Operation: 17+18=35, Resulting Numbers: [21, 35] Generated Node #0,1,1: 72:[21, 35] Operation: 17+18=35 Exploring Operation: 17+21=38, Resulting Numbers: [18, 38] Generated Node #0,1,2: 72:[18, 38] Operation: 17+21=38 Exploring Operation: 21-17=4, Resulting Numbers: [18, 4] Generated Node #0,1,3: 72:[18, 4] Operation: 21-17=4 Moving to Node #0,1,3 Current State: 72:[18, 4], Operations: ['43-25=18', '21-17=4'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[25, 43, 17, 21], Operations: [] Exploring Operation: 43-25=18, Resulting Numbers: [17, 21, 18] Generated Node #0,1: 72:[17, 21, 18] Operation: 43-25=18 Moving to Node #0,1 Current State: 72:[17, 21, 18], Operations: ['43-25=18'] Exploring Operation: 21-17=4, Resulting Numbers: [18, 4] Generated Node #0,1,3: 72:[18, 4] Operation: 21-17=4 Moving to Node #0,1,3 Current State: 72:[18, 4], Operations: ['43-25=18', '21-17=4'] Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 12, 5, 40, 33 ]
10
[ "12+5=17", "40-33=7", "17-7=10" ]
Current State: 10:[12, 5, 40, 33], Operations: [] Exploring Operation: 12+5=17, Resulting Numbers: [40, 33, 17] Generated Node #2: [40, 33, 17] from Operation: 12+5=17 Current State: 10:[40, 33, 17], Operations: ['12+5=17'] Exploring Operation: 40-33=7, Resulting Numbers: [17, 7] Generated Node #3: [17, 7] from Operation: 40-33=7 Current State: 10:[17, 7], Operations: ['12+5=17', '40-33=7'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[12, 5, 40, 33], Operations: [] Exploring Operation: 40-33=7, Resulting Numbers: [12, 5, 7] Generated Node #0,0: 10:[12, 5, 7] Operation: 40-33=7 Moving to Node #0,0 Current State: 10:[12, 5, 7], Operations: ['40-33=7'] Exploring Operation: 12-7=5, Resulting Numbers: [5, 5] Generated Node #0,0,0: 10:[5, 5] Operation: 12-7=5 Moving to Node #0,0,0 Current State: 10:[5, 5], Operations: ['40-33=7', '12-7=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[12, 5, 40, 33], Operations: [] Exploring Operation: 40-33=7, Resulting Numbers: [12, 5, 7] Generated Node #0,0: 10:[12, 5, 7] Operation: 40-33=7 Moving to Node #0,0 Current State: 10:[12, 5, 7], Operations: ['40-33=7'] Exploring Operation: 12-7=5, Resulting Numbers: [5, 5] Generated Node #0,0,0: 10:[5, 5] Operation: 12-7=5 Moving to Node #0,0,0 Current State: 10:[5, 5], Operations: ['40-33=7', '12-7=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 20, 80, 67, 73 ]
87
[ "67+73=140", "140/20=7", "80+7=87" ]
Current State: 87:[20, 80, 67, 73], Operations: [] Exploring Operation: 67+73=140, Resulting Numbers: [20, 80, 140] Generated Node #2: [20, 80, 140] from Operation: 67+73=140 Current State: 87:[20, 80, 140], Operations: ['67+73=140'] Exploring Operation: 140/20=7, Resulting Numbers: [80, 7] Generated Node #3: [80, 7] from Operation: 140/20=7 Current State: 87:[80, 7], Operations: ['67+73=140', '140/20=7'] Exploring Operation: 80+7=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[20, 80, 67, 73], Operations: [] Exploring Operation: 20+67=87, Resulting Numbers: [80, 73, 87] Generated Node #0,0: 87:[80, 73, 87] Operation: 20+67=87 Exploring Operation: 73-67=6, Resulting Numbers: [20, 80, 6] Generated Node #0,1: 87:[20, 80, 6] Operation: 73-67=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[20, 80, 6], Operations: ['73-67=6'] Exploring Operation: 80/20=4, Resulting Numbers: [6, 4] Generated Node #0,1,0: 87:[6, 4] Operation: 80/20=4 Exploring Operation: 20+6=26, Resulting Numbers: [80, 26] Generated Node #0,1,1: 87:[80, 26] Operation: 20+6=26 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[6, 4], Operations: ['73-67=6', '80/20=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,87 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[80, 26], Operations: ['73-67=6', '20+6=26'] Exploring Operation: 80+26=106, Resulting Numbers: [106] 106,87 unequal: No Solution Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[80, 73, 87], Operations: ['20+67=87'] Exploring Operation: 87-80=7, Resulting Numbers: [73, 7] Generated Node #0,0,0: 87:[73, 7] Operation: 87-80=7 Exploring Operation: 80-73=7, Resulting Numbers: [87, 7] Generated Node #0,0,1: 87:[87, 7] Operation: 80-73=7 Moving to Node #0,0,1 Current State: 87:[87, 7], Operations: ['20+67=87', '80-73=7'] Exploring Operation: 87-7=80, Resulting Numbers: [80] 80,87 unequal: No Solution Exploring Operation: 87+7=94, Resulting Numbers: [94] 94,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[73, 7], Operations: ['20+67=87', '87-80=7'] Exploring Operation: 73-7=66, Resulting Numbers: [66] 66,87 unequal: No Solution Exploring Operation: 73+7=80, Resulting Numbers: [80] 80,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 4, 14, 8, 54 ]
94
[ "8/4=2", "54*2=108", "108-14=94" ]
Current State: 94:[4, 14, 8, 54], Operations: [] Exploring Operation: 8/4=2, Resulting Numbers: [14, 54, 2] Generated Node #2: [14, 54, 2] from Operation: 8/4=2 Current State: 94:[14, 54, 2], Operations: ['8/4=2'] Exploring Operation: 54*2=108, Resulting Numbers: [14, 108] Generated Node #3: [14, 108] from Operation: 54*2=108 Current State: 94:[14, 108], Operations: ['8/4=2', '54*2=108'] Exploring Operation: 108-14=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[4, 14, 8, 54], Operations: [] Exploring Operation: 14-8=6, Resulting Numbers: [4, 54, 6] Generated Node #0,0: 94:[4, 54, 6] Operation: 14-8=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[4, 54, 6], Operations: ['14-8=6'] Exploring Operation: 54-6=48, Resulting Numbers: [4, 48] Generated Node #0,0,0: 94:[4, 48] Operation: 54-6=48 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[4, 48], Operations: ['14-8=6', '54-6=48'] Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,94 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
[ 17, 57, 37, 54 ]
60
[ "37-17=20", "57-54=3", "20*3=60" ]
Current State: 60:[17, 57, 37, 54], Operations: [] Exploring Operation: 37-17=20, Resulting Numbers: [57, 54, 20] Generated Node #2: [57, 54, 20] from Operation: 37-17=20 Current State: 60:[57, 54, 20], Operations: ['37-17=20'] Exploring Operation: 57-54=3, Resulting Numbers: [20, 3] Generated Node #3: [20, 3] from Operation: 57-54=3 Current State: 60:[20, 3], Operations: ['37-17=20', '57-54=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[17, 57, 37, 54], Operations: [] Exploring Operation: 37-17=20, Resulting Numbers: [57, 54, 20] Generated Node #0,0: 60:[57, 54, 20] Operation: 37-17=20 Exploring Operation: 54-37=17, Resulting Numbers: [17, 57, 17] Generated Node #0,1: 60:[17, 57, 17] Operation: 54-37=17 Exploring Operation: 57-37=20, Resulting Numbers: [17, 54, 20] Generated Node #0,2: 60:[17, 54, 20] Operation: 57-37=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 60:[17, 57, 17], Operations: ['54-37=17'] Exploring Operation: 17/17=1, Resulting Numbers: [57, 1] Generated Node #0,1,0: 60:[57, 1] Operation: 17/17=1 Exploring Operation: 17+17=34, Resulting Numbers: [57, 34] Generated Node #0,1,1: 60:[57, 34] Operation: 17+17=34 Exploring Operation: 17-17=0, Resulting Numbers: [57, 0] Generated Node #0,1,2: 60:[57, 0] Operation: 17-17=0 Moving to Node #0,1,0 Current State: 60:[57, 1], Operations: ['54-37=17', '17/17=1'] Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,60 unequal: No Solution Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,60 unequal: No Solution Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,60 unequal: No Solution Moving to Node #0,1,2 Current State: 60:[57, 0], Operations: ['54-37=17', '17-17=0'] Exploring Operation: 57*0=0, Resulting Numbers: [0] 0,60 unequal: No Solution Exploring Operation: 57-0=57, Resulting Numbers: [57] 57,60 unequal: No Solution Exploring Operation: 57+0=57, Resulting Numbers: [57] 57,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[57, 34], Operations: ['54-37=17', '17+17=34'] Exploring Operation: 57*34=1938, Resulting Numbers: [1938] 1938,60 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 57+34=91, Resulting Numbers: [91] 91,60 unequal: No Solution No 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: 60:[17, 54, 20], Operations: ['57-37=20'] Exploring Operation: 54-20=34, Resulting Numbers: [17, 34] Generated Node #0,2,0: 60:[17, 34] Operation: 54-20=34 Exploring Operation: 20-17=3, Resulting Numbers: [54, 3] Generated Node #0,2,1: 60:[54, 3] Operation: 20-17=3 Exploring Operation: 54-17=37, Resulting Numbers: [20, 37] Generated Node #0,2,2: 60:[20, 37] Operation: 54-17=37 Moving to Node #0,2,0 Current State: 60:[17, 34], Operations: ['57-37=20', '54-20=34'] Exploring Operation: 17+34=51, Resulting Numbers: [51] 51,60 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,60 unequal: No Solution Moving to Node #0,2,1 Current State: 60:[54, 3], Operations: ['57-37=20', '20-17=3'] Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,60 unequal: No Solution Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,60 unequal: No Solution Moving to Node #0,2,2 Current State: 60:[20, 37], Operations: ['57-37=20', '54-17=37'] Exploring Operation: 20+37=57, Resulting Numbers: [57] 57,60 unequal: No Solution Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 20*37=740, Resulting Numbers: [740] 740,60 unequal: No Solution No 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: 60:[57, 54, 20], Operations: ['37-17=20'] Exploring Operation: 57-20=37, Resulting Numbers: [54, 37] Generated Node #0,0,0: 60:[54, 37] Operation: 57-20=37 Exploring Operation: 54-20=34, Resulting Numbers: [57, 34] Generated Node #0,0,1: 60:[57, 34] Operation: 54-20=34 Exploring Operation: 57-54=3, Resulting Numbers: [20, 3] Generated Node #0,0,2: 60:[20, 3] Operation: 57-54=3 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 60:[20, 3], Operations: ['37-17=20', '57-54=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[17, 57, 37, 54], Operations: [] Exploring Operation: 37-17=20, Resulting Numbers: [57, 54, 20] Generated Node #0,0: 60:[57, 54, 20] Operation: 37-17=20 Moving to Node #0,0 Current State: 60:[57, 54, 20], Operations: ['37-17=20'] Exploring Operation: 57-54=3, Resulting Numbers: [20, 3] Generated Node #0,0,2: 60:[20, 3] Operation: 57-54=3 Moving to Node #0,0,2 Current State: 60:[20, 3], Operations: ['37-17=20', '57-54=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_3
sum_heuristic
[ 76, 89, 74, 8 ]
99
[ "76+89=165", "74-8=66", "165-66=99" ]
Current State: 99:[76, 89, 74, 8], Operations: [] Exploring Operation: 76+89=165, Resulting Numbers: [74, 8, 165] Generated Node #2: [74, 8, 165] from Operation: 76+89=165 Current State: 99:[74, 8, 165], Operations: ['76+89=165'] Exploring Operation: 74-8=66, Resulting Numbers: [165, 66] Generated Node #3: [165, 66] from Operation: 74-8=66 Current State: 99:[165, 66], Operations: ['76+89=165', '74-8=66'] Exploring Operation: 165-66=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[76, 89, 74, 8], Operations: [] Exploring Operation: 89-76=13, Resulting Numbers: [74, 8, 13] Generated Node #0,0: 99:[74, 8, 13] Operation: 89-76=13 Exploring Operation: 76-74=2, Resulting Numbers: [89, 8, 2] Generated Node #0,1: 99:[89, 8, 2] Operation: 76-74=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[89, 8, 2], Operations: ['76-74=2'] Exploring Operation: 89+8=97, Resulting Numbers: [2, 97] Generated Node #0,1,0: 99:[2, 97] Operation: 89+8=97 Exploring Operation: 89+2=91, Resulting Numbers: [8, 91] Generated Node #0,1,1: 99:[8, 91] Operation: 89+2=91 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 99:[2, 97], Operations: ['76-74=2', '89+8=97'] Exploring Operation: 2+97=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[76, 89, 74, 8], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [89, 8, 2] Generated Node #0,1: 99:[89, 8, 2] Operation: 76-74=2 Moving to Node #0,1 Current State: 99:[89, 8, 2], Operations: ['76-74=2'] Exploring Operation: 89+8=97, Resulting Numbers: [2, 97] Generated Node #0,1,0: 99:[2, 97] Operation: 89+8=97 Moving to Node #0,1,0 Current State: 99:[2, 97], Operations: ['76-74=2', '89+8=97'] Exploring Operation: 2+97=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 10, 15, 25, 95 ]
95
[ "10+15=25", "25+95=120", "120-25=95" ]
Current State: 95:[10, 15, 25, 95], Operations: [] Exploring Operation: 10+15=25, Resulting Numbers: [25, 95, 25] Generated Node #2: [25, 95, 25] from Operation: 10+15=25 Current State: 95:[25, 95, 25], Operations: ['10+15=25'] Exploring Operation: 25+95=120, Resulting Numbers: [120] 120,95 equal: Goal Reached Exploring Operation: 120-25=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[10, 15, 25, 95], Operations: [] Exploring Operation: 15-10=5, Resulting Numbers: [25, 95, 5] Generated Node #0,0: 95:[25, 95, 5] Operation: 15-10=5 Moving to Node #0,0 Current State: 95:[25, 95, 5], Operations: ['15-10=5'] Exploring Operation: 25/5=5, Resulting Numbers: [95, 5] Generated Node #0,0,0: 95:[95, 5] Operation: 25/5=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[95, 5], Operations: ['15-10=5', '25/5=5'] Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,95 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
[ 6, 38, 33, 70 ]
51
[ "38+70=108", "108/6=18", "33+18=51" ]
Current State: 51:[6, 38, 33, 70], Operations: [] Exploring Operation: 38+70=108, Resulting Numbers: [6, 33, 108] Generated Node #2: [6, 33, 108] from Operation: 38+70=108 Current State: 51:[6, 33, 108], Operations: ['38+70=108'] Exploring Operation: 108/6=18, Resulting Numbers: [33, 18] Generated Node #3: [33, 18] from Operation: 108/6=18 Current State: 51:[33, 18], Operations: ['38+70=108', '108/6=18'] Exploring Operation: 33+18=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[6, 38, 33, 70], Operations: [] Exploring Operation: 70-33=37, Resulting Numbers: [6, 38, 37] Generated Node #0,0: 51:[6, 38, 37] Operation: 70-33=37 Exploring Operation: 38-33=5, Resulting Numbers: [6, 70, 5] Generated Node #0,1: 51:[6, 70, 5] Operation: 38-33=5 Moving to Node #0,1 Current State: 51:[6, 70, 5], Operations: ['38-33=5'] Exploring Operation: 70-6=64, Resulting Numbers: [5, 64] Generated Node #0,1,0: 51:[5, 64] Operation: 70-6=64 Exploring Operation: 70/5=14, Resulting Numbers: [6, 14] Generated Node #0,1,1: 51:[6, 14] Operation: 70/5=14 Moving to Node #0,0 Current State: 51:[6, 38, 37], Operations: ['70-33=37'] Exploring Operation: 38-37=1, Resulting Numbers: [6, 1] Generated Node #0,0,0: 51:[6, 1] Operation: 38-37=1 Exploring Operation: 6+38=44, Resulting Numbers: [37, 44] Generated Node #0,0,1: 51:[37, 44] Operation: 6+38=44 Moving to Node #0,0,0 Current State: 51:[6, 1], Operations: ['70-33=37', '38-37=1'] Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,51 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[6, 14], Operations: ['38-33=5', '70/5=14'] Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[5, 64], Operations: ['38-33=5', '70-6=64'] Exploring Operation: 64-5=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 5+64=69, Resulting Numbers: [69] 69,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[37, 44], Operations: ['70-33=37', '6+38=44'] Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,51 unequal: No Solution Exploring Operation: 37+44=81, Resulting Numbers: [81] 81,51 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 55, 22, 26, 12 ]
63
[ "55+22=77", "26-12=14", "77-14=63" ]
Current State: 63:[55, 22, 26, 12], Operations: [] Exploring Operation: 55+22=77, Resulting Numbers: [26, 12, 77] Generated Node #2: [26, 12, 77] from Operation: 55+22=77 Current State: 63:[26, 12, 77], Operations: ['55+22=77'] Exploring Operation: 26-12=14, Resulting Numbers: [77, 14] Generated Node #3: [77, 14] from Operation: 26-12=14 Current State: 63:[77, 14], Operations: ['55+22=77', '26-12=14'] Exploring Operation: 77-14=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[55, 22, 26, 12], Operations: [] Exploring Operation: 22-12=10, Resulting Numbers: [55, 26, 10] Generated Node #0,0: 63:[55, 26, 10] Operation: 22-12=10 Exploring Operation: 26-12=14, Resulting Numbers: [55, 22, 14] Generated Node #0,1: 63:[55, 22, 14] Operation: 26-12=14 Exploring Operation: 55+12=67, Resulting Numbers: [22, 26, 67] Generated Node #0,2: 63:[22, 26, 67] Operation: 55+12=67 Exploring Operation: 55-26=29, Resulting Numbers: [22, 12, 29] Generated Node #0,3: 63:[22, 12, 29] Operation: 55-26=29 Exploring Operation: 26-22=4, Resulting Numbers: [55, 12, 4] Generated Node #0,4: 63:[55, 12, 4] Operation: 26-22=4 Moving to Node #0,2 Current State: 63:[22, 26, 67], Operations: ['55+12=67'] Exploring Operation: 67-22=45, Resulting Numbers: [26, 45] Generated Node #0,2,0: 63:[26, 45] Operation: 67-22=45 Exploring Operation: 67-26=41, Resulting Numbers: [22, 41] Generated Node #0,2,1: 63:[22, 41] Operation: 67-26=41 Exploring Operation: 22+26=48, Resulting Numbers: [67, 48] Generated Node #0,2,2: 63:[67, 48] Operation: 22+26=48 Exploring Operation: 22+67=89, Resulting Numbers: [26, 89] Generated Node #0,2,3: 63:[26, 89] Operation: 22+67=89 Exploring Operation: 26-22=4, Resulting Numbers: [67, 4] Generated Node #0,2,4: 63:[67, 4] Operation: 26-22=4 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 63:[67, 4], Operations: ['55+12=67', '26-22=4'] Exploring Operation: 67+4=71, Resulting Numbers: [71] 71,63 unequal: No Solution Exploring Operation: 67*4=268, Resulting Numbers: [268] 268,63 unequal: No Solution Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[55, 22, 26, 12], Operations: [] Exploring Operation: 55+12=67, Resulting Numbers: [22, 26, 67] Generated Node #0,2: 63:[22, 26, 67] Operation: 55+12=67 Moving to Node #0,2 Current State: 63:[22, 26, 67], Operations: ['55+12=67'] Exploring Operation: 26-22=4, Resulting Numbers: [67, 4] Generated Node #0,2,4: 63:[67, 4] Operation: 26-22=4 Moving to Node #0,2,4 Current State: 63:[67, 4], Operations: ['55+12=67', '26-22=4'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 32, 6, 96, 10 ]
20
[ "32*6=192", "192/96=2", "10*2=20" ]
Current State: 20:[32, 6, 96, 10], Operations: [] Exploring Operation: 32*6=192, Resulting Numbers: [96, 10, 192] Generated Node #2: [96, 10, 192] from Operation: 32*6=192 Current State: 20:[96, 10, 192], Operations: ['32*6=192'] Exploring Operation: 192/96=2, Resulting Numbers: [10, 2] Generated Node #3: [10, 2] from Operation: 192/96=2 Current State: 20:[10, 2], Operations: ['32*6=192', '192/96=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[32, 6, 96, 10], Operations: [] Exploring Operation: 96/32=3, Resulting Numbers: [6, 10, 3] Generated Node #0,0: 20:[6, 10, 3] Operation: 96/32=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[6, 10, 3], Operations: ['96/32=3'] Exploring Operation: 6/3=2, Resulting Numbers: [10, 2] Generated Node #0,0,0: 20:[10, 2] Operation: 6/3=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 20:[10, 2], Operations: ['96/32=3', '6/3=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[32, 6, 96, 10], Operations: [] Exploring Operation: 96/32=3, Resulting Numbers: [6, 10, 3] Generated Node #0,0: 20:[6, 10, 3] Operation: 96/32=3 Moving to Node #0,0 Current State: 20:[6, 10, 3], Operations: ['96/32=3'] Exploring Operation: 6/3=2, Resulting Numbers: [10, 2] Generated Node #0,0,0: 20:[10, 2] Operation: 6/3=2 Moving to Node #0,0,0 Current State: 20:[10, 2], Operations: ['96/32=3', '6/3=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 84, 80, 56, 72 ]
87
[ "80-56=24", "72/24=3", "84+3=87" ]
Current State: 87:[84, 80, 56, 72], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [84, 72, 24] Generated Node #2: [84, 72, 24] from Operation: 80-56=24 Current State: 87:[84, 72, 24], Operations: ['80-56=24'] Exploring Operation: 72/24=3, Resulting Numbers: [84, 3] Generated Node #3: [84, 3] from Operation: 72/24=3 Current State: 87:[84, 3], Operations: ['80-56=24', '72/24=3'] Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[84, 80, 56, 72], Operations: [] Exploring Operation: 84-56=28, Resulting Numbers: [80, 72, 28] Generated Node #0,0: 87:[80, 72, 28] Operation: 84-56=28 Exploring Operation: 72-56=16, Resulting Numbers: [84, 80, 16] Generated Node #0,1: 87:[84, 80, 16] Operation: 72-56=16 Exploring Operation: 80-56=24, Resulting Numbers: [84, 72, 24] Generated Node #0,2: 87:[84, 72, 24] Operation: 80-56=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[80, 72, 28], Operations: ['84-56=28'] Exploring Operation: 80-72=8, Resulting Numbers: [28, 8] Generated Node #0,0,0: 87:[28, 8] Operation: 80-72=8 Exploring Operation: 72+28=100, Resulting Numbers: [80, 100] Generated Node #0,0,1: 87:[80, 100] Operation: 72+28=100 Exploring Operation: 72-28=44, Resulting Numbers: [80, 44] Generated Node #0,0,2: 87:[80, 44] Operation: 72-28=44 Moving to Node #0,0,0 Current State: 87:[28, 8], Operations: ['84-56=28', '80-72=8'] Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 28*8=224, Resulting Numbers: [224] 224,87 unequal: No Solution Moving to Node #0,0,1 Current State: 87:[80, 100], Operations: ['84-56=28', '72+28=100'] Exploring Operation: 80+100=180, Resulting Numbers: [180] 180,87 unequal: No Solution Exploring Operation: 80*100=8000, Resulting Numbers: [8000] 8000,87 unequal: No Solution Exploring Operation: 100-80=20, Resulting Numbers: [20] 20,87 unequal: No Solution Moving to Node #0,0,2 Current State: 87:[80, 44], Operations: ['84-56=28', '72-28=44'] Exploring Operation: 80-44=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 80*44=3520, Resulting Numbers: [3520] 3520,87 unequal: No Solution Exploring Operation: 80+44=124, Resulting Numbers: [124] 124,87 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 #0,1 Current State: 87:[84, 80, 16], Operations: ['72-56=16'] Exploring Operation: 80/16=5, Resulting Numbers: [84, 5] Generated Node #0,1,0: 87:[84, 5] Operation: 80/16=5 Exploring Operation: 80+16=96, Resulting Numbers: [84, 96] Generated Node #0,1,1: 87:[84, 96] Operation: 80+16=96 Exploring Operation: 84-80=4, Resulting Numbers: [16, 4] Generated Node #0,1,2: 87:[16, 4] Operation: 84-80=4 Moving to Node #0,1,0 Current State: 87:[84, 5], Operations: ['72-56=16', '80/16=5'] Exploring Operation: 84*5=420, Resulting Numbers: [420] 420,87 unequal: No Solution Exploring Operation: 84-5=79, Resulting Numbers: [79] 79,87 unequal: No Solution Exploring Operation: 84+5=89, Resulting Numbers: [89] 89,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[84, 96], Operations: ['72-56=16', '80+16=96'] Exploring Operation: 84*96=8064, Resulting Numbers: [8064] 8064,87 unequal: No Solution Exploring Operation: 96-84=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 84+96=180, Resulting Numbers: [180] 180,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[16, 4], Operations: ['72-56=16', '84-80=4'] Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,87 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,87 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 Current State: 87:[84, 72, 24], Operations: ['80-56=24'] Exploring Operation: 84-72=12, Resulting Numbers: [24, 12] Generated Node #0,2,0: 87:[24, 12] Operation: 84-72=12 Exploring Operation: 72/24=3, Resulting Numbers: [84, 3] Generated Node #0,2,1: 87:[84, 3] Operation: 72/24=3 Exploring Operation: 72+24=96, Resulting Numbers: [84, 96] Generated Node #0,2,2: 87:[84, 96] Operation: 72+24=96 Moving to Node #0,2,1 Current State: 87:[84, 3], Operations: ['80-56=24', '72/24=3'] Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[84, 80, 56, 72], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [84, 72, 24] Generated Node #0,2: 87:[84, 72, 24] Operation: 80-56=24 Moving to Node #0,2 Current State: 87:[84, 72, 24], Operations: ['80-56=24'] Exploring Operation: 72/24=3, Resulting Numbers: [84, 3] Generated Node #0,2,1: 87:[84, 3] Operation: 72/24=3 Moving to Node #0,2,1 Current State: 87:[84, 3], Operations: ['80-56=24', '72/24=3'] Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_3
sum_heuristic
[ 6, 33, 4, 33 ]
68
[ "6+33=39", "33-4=29", "39+29=68" ]
Current State: 68:[6, 33, 4, 33], Operations: [] Exploring Operation: 6+33=39, Resulting Numbers: [4, 39] Generated Node #2: [4, 39] from Operation: 6+33=39 Current State: 68:[4, 39], Operations: ['6+33=39'] Exploring Operation: 33-4=29, Resulting Numbers: [39, 29] Generated Node #3: [39, 29] from Operation: 33-4=29 Current State: 68:[39, 29], Operations: ['6+33=39', '33-4=29'] Exploring Operation: 39+29=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[6, 33, 4, 33], Operations: [] Exploring Operation: 6-4=2, Resulting Numbers: [33, 33, 2] Generated Node #0,0: 68:[33, 33, 2] Operation: 6-4=2 Moving to Node #0,0 Current State: 68:[33, 33, 2], Operations: ['6-4=2'] Exploring Operation: 33/33=1, Resulting Numbers: [2, 1] Generated Node #0,0,0: 68:[2, 1] Operation: 33/33=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[2, 1], Operations: ['6-4=2', '33/33=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,68 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
[ 15, 53, 98, 40 ]
97
[ "53-40=13", "15*13=195", "195-98=97" ]
Current State: 97:[15, 53, 98, 40], Operations: [] Exploring Operation: 53-40=13, Resulting Numbers: [15, 98, 13] Generated Node #2: [15, 98, 13] from Operation: 53-40=13 Current State: 97:[15, 98, 13], Operations: ['53-40=13'] Exploring Operation: 15*13=195, Resulting Numbers: [98, 195] Generated Node #3: [98, 195] from Operation: 15*13=195 Current State: 97:[98, 195], Operations: ['53-40=13', '15*13=195'] Exploring Operation: 195-98=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[15, 53, 98, 40], Operations: [] Exploring Operation: 98-15=83, Resulting Numbers: [53, 40, 83] Generated Node #0,0: 97:[53, 40, 83] Operation: 98-15=83 Exploring Operation: 53+40=93, Resulting Numbers: [15, 98, 93] Generated Node #0,1: 97:[15, 98, 93] Operation: 53+40=93 Exploring Operation: 15+40=55, Resulting Numbers: [53, 98, 55] Generated Node #0,2: 97:[53, 98, 55] Operation: 15+40=55 Exploring Operation: 15+53=68, Resulting Numbers: [98, 40, 68] Generated Node #0,3: 97:[98, 40, 68] Operation: 15+53=68 Moving to Node #0,1 Current State: 97:[15, 98, 93], Operations: ['53+40=93'] Exploring Operation: 98-15=83, Resulting Numbers: [93, 83] Generated Node #0,1,0: 97:[93, 83] Operation: 98-15=83 Exploring Operation: 93-15=78, Resulting Numbers: [98, 78] Generated Node #0,1,1: 97:[98, 78] Operation: 93-15=78 Exploring Operation: 15+93=108, Resulting Numbers: [98, 108] Generated Node #0,1,2: 97:[98, 108] Operation: 15+93=108 Exploring Operation: 15+98=113, Resulting Numbers: [93, 113] Generated Node #0,1,3: 97:[93, 113] Operation: 15+98=113 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 97:[98, 108], Operations: ['53+40=93', '15+93=108'] Exploring Operation: 98*108=10584, Resulting Numbers: [10584] 10584,97 unequal: No Solution Exploring Operation: 108-98=10, Resulting Numbers: [10] 10,97 unequal: No Solution Exploring Operation: 98+108=206, Resulting Numbers: [206] 206,97 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 #0,1,0 Current State: 97:[93, 83], Operations: ['53+40=93', '98-15=83'] Exploring Operation: 93+83=176, Resulting Numbers: [176] 176,97 unequal: No Solution Exploring Operation: 93*83=7719, Resulting Numbers: [7719] 7719,97 unequal: No Solution Exploring Operation: 93-83=10, Resulting Numbers: [10] 10,97 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 #0,1,1 Current State: 97:[98, 78], Operations: ['53+40=93', '93-15=78'] Exploring Operation: 98*78=7644, Resulting Numbers: [7644] 7644,97 unequal: No Solution Exploring Operation: 98-78=20, Resulting Numbers: [20] 20,97 unequal: No Solution Exploring Operation: 98+78=176, Resulting Numbers: [176] 176,97 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 #0,1,3 Current State: 97:[93, 113], Operations: ['53+40=93', '15+98=113'] Exploring Operation: 113-93=20, Resulting Numbers: [20] 20,97 unequal: No Solution Exploring Operation: 93+113=206, Resulting Numbers: [206] 206,97 unequal: No Solution Exploring Operation: 93*113=10509, Resulting Numbers: [10509] 10509,97 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: 97:[98, 40, 68], Operations: ['15+53=68'] Exploring Operation: 98+40=138, Resulting Numbers: [68, 138] Generated Node #0,3,0: 97:[68, 138] Operation: 98+40=138 Exploring Operation: 68-40=28, Resulting Numbers: [98, 28] Generated Node #0,3,1: 97:[98, 28] Operation: 68-40=28 Exploring Operation: 40+68=108, Resulting Numbers: [98, 108] Generated Node #0,3,2: 97:[98, 108] Operation: 40+68=108 Exploring Operation: 98-40=58, Resulting Numbers: [68, 58] Generated Node #0,3,3: 97:[68, 58] Operation: 98-40=58 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 97:[98, 108], Operations: ['15+53=68', '40+68=108'] Exploring Operation: 108-98=10, Resulting Numbers: [10] 10,97 unequal: No Solution Exploring Operation: 98*108=10584, Resulting Numbers: [10584] 10584,97 unequal: No Solution Exploring Operation: 98+108=206, Resulting Numbers: [206] 206,97 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 #0,3,3 Current State: 97:[68, 58], Operations: ['15+53=68', '98-40=58'] Exploring Operation: 68*58=3944, Resulting Numbers: [3944] 3944,97 unequal: No Solution Exploring Operation: 68-58=10, Resulting Numbers: [10] 10,97 unequal: No Solution Exploring Operation: 68+58=126, Resulting Numbers: [126] 126,97 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 #0,3,0 Current State: 97:[68, 138], Operations: ['15+53=68', '98+40=138'] Exploring Operation: 68*138=9384, Resulting Numbers: [9384] 9384,97 unequal: No Solution Exploring Operation: 138-68=70, Resulting Numbers: [70] 70,97 unequal: No Solution Exploring Operation: 68+138=206, Resulting Numbers: [206] 206,97 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 #0,3,1 Current State: 97:[98, 28], Operations: ['15+53=68', '68-40=28'] Exploring Operation: 98+28=126, Resulting Numbers: [126] 126,97 unequal: No Solution Exploring Operation: 98*28=2744, Resulting Numbers: [2744] 2744,97 unequal: No Solution Exploring Operation: 98-28=70, Resulting Numbers: [70] 70,97 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: 97:[53, 98, 55], Operations: ['15+40=55'] Exploring Operation: 53+55=108, Resulting Numbers: [98, 108] Generated Node #0,2,0: 97:[98, 108] Operation: 53+55=108 Exploring Operation: 98-53=45, Resulting Numbers: [55, 45] Generated Node #0,2,1: 97:[55, 45] Operation: 98-53=45 Exploring Operation: 53+98=151, Resulting Numbers: [55, 151] Generated Node #0,2,2: 97:[55, 151] Operation: 53+98=151 Exploring Operation: 55-53=2, Resulting Numbers: [98, 2] Generated Node #0,2,3: 97:[98, 2] Operation: 55-53=2 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[98, 108], Operations: ['15+40=55', '53+55=108'] Exploring Operation: 98+108=206, Resulting Numbers: [206] 206,97 unequal: No Solution Exploring Operation: 108-98=10, Resulting Numbers: [10] 10,97 unequal: No Solution Exploring Operation: 98*108=10584, Resulting Numbers: [10584] 10584,97 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 #0,2,1 Current State: 97:[55, 45], Operations: ['15+40=55', '98-53=45'] Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,97 unequal: No Solution Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,97 unequal: No Solution Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,97 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 #0,2,2 Current State: 97:[55, 151], Operations: ['15+40=55', '53+98=151'] Exploring Operation: 55*151=8305, Resulting Numbers: [8305] 8305,97 unequal: No Solution Exploring Operation: 55+151=206, Resulting Numbers: [206] 206,97 unequal: No Solution Exploring Operation: 151-55=96, Resulting Numbers: [96] 96,97 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 #0,2,3 Current State: 97:[98, 2], Operations: ['15+40=55', '55-53=2'] Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,97 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,97 unequal: No Solution Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,97 unequal: No Solution Exploring Operation: 98*2=196, Resulting Numbers: [196] 196,97 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: 97:[53, 40, 83], Operations: ['98-15=83'] Exploring Operation: 53+40=93, Resulting Numbers: [83, 93] Generated Node #0,0,0: 97:[83, 93] Operation: 53+40=93 Exploring Operation: 40+83=123, Resulting Numbers: [53, 123] Generated Node #0,0,1: 97:[53, 123] Operation: 40+83=123 Exploring Operation: 53+83=136, Resulting Numbers: [40, 136] Generated Node #0,0,2: 97:[40, 136] Operation: 53+83=136 Exploring Operation: 53-40=13, Resulting Numbers: [83, 13] Generated Node #0,0,3: 97:[83, 13] Operation: 53-40=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[83, 93], Operations: ['98-15=83', '53+40=93'] Exploring Operation: 83*93=7719, Resulting Numbers: [7719] 7719,97 unequal: No Solution Exploring Operation: 93-83=10, Resulting Numbers: [10] 10,97 unequal: No Solution Exploring Operation: 83+93=176, Resulting Numbers: [176] 176,97 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 #0,0,1 Current State: 97:[53, 123], Operations: ['98-15=83', '40+83=123'] Exploring Operation: 53*123=6519, Resulting Numbers: [6519] 6519,97 unequal: No Solution Exploring Operation: 53+123=176, Resulting Numbers: [176] 176,97 unequal: No Solution Exploring Operation: 123-53=70, Resulting Numbers: [70] 70,97 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 #0,0,2 Current State: 97:[40, 136], Operations: ['98-15=83', '53+83=136'] Exploring Operation: 40+136=176, Resulting Numbers: [176] 176,97 unequal: No Solution Exploring Operation: 136-40=96, Resulting Numbers: [96] 96,97 unequal: No Solution Exploring Operation: 40*136=5440, Resulting Numbers: [5440] 5440,97 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 #0,0,3 Current State: 97:[83, 13], Operations: ['98-15=83', '53-40=13'] Exploring Operation: 83-13=70, Resulting Numbers: [70] 70,97 unequal: No Solution Exploring Operation: 83*13=1079, Resulting Numbers: [1079] 1079,97 unequal: No Solution Exploring Operation: 83+13=96, Resulting Numbers: [96] 96,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 93, 54, 55, 89 ]
73
[ "93-54=39", "89-55=34", "39+34=73" ]
Current State: 73:[93, 54, 55, 89], Operations: [] Exploring Operation: 93-54=39, Resulting Numbers: [55, 89, 39] Generated Node #2: [55, 89, 39] from Operation: 93-54=39 Current State: 73:[55, 89, 39], Operations: ['93-54=39'] Exploring Operation: 89-55=34, Resulting Numbers: [39, 34] Generated Node #3: [39, 34] from Operation: 89-55=34 Current State: 73:[39, 34], Operations: ['93-54=39', '89-55=34'] Exploring Operation: 39+34=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[93, 54, 55, 89], Operations: [] Exploring Operation: 93-55=38, Resulting Numbers: [54, 89, 38] Generated Node #0,0: 73:[54, 89, 38] Operation: 93-55=38 Exploring Operation: 93-54=39, Resulting Numbers: [55, 89, 39] Generated Node #0,1: 73:[55, 89, 39] Operation: 93-54=39 Exploring Operation: 54+55=109, Resulting Numbers: [93, 89, 109] Generated Node #0,2: 73:[93, 89, 109] Operation: 54+55=109 Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[55, 89, 39], Operations: ['93-54=39'] Exploring Operation: 89-55=34, Resulting Numbers: [39, 34] Generated Node #0,1,0: 73:[39, 34] Operation: 89-55=34 Exploring Operation: 89-39=50, Resulting Numbers: [55, 50] Generated Node #0,1,1: 73:[55, 50] Operation: 89-39=50 Exploring Operation: 55+39=94, Resulting Numbers: [89, 94] Generated Node #0,1,2: 73:[89, 94] Operation: 55+39=94 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 73:[89, 94], Operations: ['93-54=39', '55+39=94'] Exploring Operation: 89*94=8366, Resulting Numbers: [8366] 8366,73 unequal: No Solution Exploring Operation: 94-89=5, Resulting Numbers: [5] 5,73 unequal: No Solution Exploring Operation: 89+94=183, Resulting Numbers: [183] 183,73 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: 73:[55, 50], Operations: ['93-54=39', '89-39=50'] Exploring Operation: 55*50=2750, Resulting Numbers: [2750] 2750,73 unequal: No Solution Exploring Operation: 55+50=105, Resulting Numbers: [105] 105,73 unequal: No Solution Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,73 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: 73:[39, 34], Operations: ['93-54=39', '89-55=34'] Exploring Operation: 39*34=1326, Resulting Numbers: [1326] 1326,73 unequal: No Solution Exploring Operation: 39-34=5, Resulting Numbers: [5] 5,73 unequal: No Solution Exploring Operation: 39+34=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[93, 54, 55, 89], Operations: [] Exploring Operation: 93-54=39, Resulting Numbers: [55, 89, 39] Generated Node #0,1: 73:[55, 89, 39] Operation: 93-54=39 Moving to Node #0,1 Current State: 73:[55, 89, 39], Operations: ['93-54=39'] Exploring Operation: 89-55=34, Resulting Numbers: [39, 34] Generated Node #0,1,0: 73:[39, 34] Operation: 89-55=34 Moving to Node #0,1,0 Current State: 73:[39, 34], Operations: ['93-54=39', '89-55=34'] Exploring Operation: 39+34=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_3
mult_heuristic
[ 7, 75, 97, 25 ]
87
[ "97-7=90", "75/25=3", "90-3=87" ]
Current State: 87:[7, 75, 97, 25], Operations: [] Exploring Operation: 97-7=90, Resulting Numbers: [75, 25, 90] Generated Node #2: [75, 25, 90] from Operation: 97-7=90 Current State: 87:[75, 25, 90], Operations: ['97-7=90'] Exploring Operation: 75/25=3, Resulting Numbers: [90, 3] Generated Node #3: [90, 3] from Operation: 75/25=3 Current State: 87:[90, 3], Operations: ['97-7=90', '75/25=3'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[7, 75, 97, 25], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [7, 97, 3] Generated Node #0,0: 87:[7, 97, 3] Operation: 75/25=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[7, 97, 3], Operations: ['75/25=3'] Exploring Operation: 97-7=90, Resulting Numbers: [3, 90] Generated Node #0,0,0: 87:[3, 90] Operation: 97-7=90 Moving to Node #0,0,0 Current State: 87:[3, 90], Operations: ['75/25=3', '97-7=90'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[7, 75, 97, 25], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [7, 97, 3] Generated Node #0,0: 87:[7, 97, 3] Operation: 75/25=3 Moving to Node #0,0 Current State: 87:[7, 97, 3], Operations: ['75/25=3'] Exploring Operation: 97-7=90, Resulting Numbers: [3, 90] Generated Node #0,0,0: 87:[3, 90] Operation: 97-7=90 Moving to Node #0,0,0 Current State: 87:[3, 90], Operations: ['75/25=3', '97-7=90'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 68, 34, 33, 68 ]
33
[ "68/34=2", "68-33=35", "35-2=33" ]
Current State: 33:[68, 34, 33, 68], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [33, 2] Generated Node #2: [33, 2] from Operation: 68/34=2 Current State: 33:[33, 2], Operations: ['68/34=2'] Exploring Operation: 68-33=35, Resulting Numbers: [2, 35] Generated Node #3: [2, 35] from Operation: 68-33=35 Current State: 33:[2, 35], Operations: ['68/34=2', '68-33=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[68, 34, 33, 68], Operations: [] Exploring Operation: 68/68=1, Resulting Numbers: [34, 33, 1] Generated Node #0,0: 33:[34, 33, 1] Operation: 68/68=1 Exploring Operation: 68/34=2, Resulting Numbers: [33, 68, 2] Generated Node #0,1: 33:[33, 68, 2] Operation: 68/34=2 Exploring Operation: 68-34=34, Resulting Numbers: [33, 68, 34] Generated Node #0,2: 33:[33, 68, 34] Operation: 68-34=34 Exploring Operation: 68-68=0, Resulting Numbers: [34, 33, 0] Generated Node #0,3: 33:[34, 33, 0] Operation: 68-68=0 Moving to Node #0,0 Current State: 33:[34, 33, 1], Operations: ['68/68=1'] Exploring Operation: 34/1=34, Resulting Numbers: [33, 34] Generated Node #0,0,0: 33:[33, 34] Operation: 34/1=34 Exploring Operation: 33*1=33, Resulting Numbers: [34, 33] Generated Node #0,0,1: 33:[34, 33] Operation: 33*1=33 Exploring Operation: 34-1=33, Resulting Numbers: [33, 33] Generated Node #0,0,2: 33:[33, 33] Operation: 34-1=33 Exploring Operation: 34*1=34, Resulting Numbers: [33, 34] Generated Node #0,0,3: 33:[33, 34] Operation: 34*1=34 Moving to Node #0,3 Current State: 33:[34, 33, 0], Operations: ['68-68=0'] Exploring Operation: 34+0=34, Resulting Numbers: [33, 34] Generated Node #0,3,0: 33:[33, 34] Operation: 34+0=34 Exploring Operation: 34-0=34, Resulting Numbers: [33, 34] Generated Node #0,3,1: 33:[33, 34] Operation: 34-0=34 Exploring Operation: 33-0=33, Resulting Numbers: [34, 33] Generated Node #0,3,2: 33:[34, 33] Operation: 33-0=33 Exploring Operation: 33+0=33, Resulting Numbers: [34, 33] Generated Node #0,3,3: 33:[34, 33] Operation: 33+0=33 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 33:[33, 34], Operations: ['68-68=0', '34+0=34'] Exploring Operation: 33*34=1122, Resulting Numbers: [1122] 1122,33 unequal: No Solution Exploring Operation: 33+34=67, Resulting Numbers: [67] 67,33 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,33 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 #0,3,1 Current State: 33:[33, 34], Operations: ['68-68=0', '34-0=34'] Exploring Operation: 33+34=67, Resulting Numbers: [67] 67,33 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 33*34=1122, Resulting Numbers: [1122] 1122,33 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 #0,3,2 Current State: 33:[34, 33], Operations: ['68-68=0', '33-0=33'] Exploring Operation: 34*33=1122, Resulting Numbers: [1122] 1122,33 unequal: No Solution Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,33 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,33 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 #0,3,3 Current State: 33:[34, 33], Operations: ['68-68=0', '33+0=33'] Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,33 unequal: No Solution Exploring Operation: 34*33=1122, Resulting Numbers: [1122] 1122,33 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:[33, 68, 34], Operations: ['68-34=34'] Exploring Operation: 68-34=34, Resulting Numbers: [33, 34] Generated Node #0,2,0: 33:[33, 34] Operation: 68-34=34 Exploring Operation: 68/34=2, Resulting Numbers: [33, 2] Generated Node #0,2,1: 33:[33, 2] Operation: 68/34=2 Exploring Operation: 34-33=1, Resulting Numbers: [68, 1] Generated Node #0,2,2: 33:[68, 1] Operation: 34-33=1 Exploring Operation: 68-33=35, Resulting Numbers: [34, 35] Generated Node #0,2,3: 33:[34, 35] Operation: 68-33=35 Moving to Node #0,1 Current State: 33:[33, 68, 2], Operations: ['68/34=2'] Exploring Operation: 68-2=66, Resulting Numbers: [33, 66] Generated Node #0,1,0: 33:[33, 66] Operation: 68-2=66 Exploring Operation: 33+2=35, Resulting Numbers: [68, 35] Generated Node #0,1,1: 33:[68, 35] Operation: 33+2=35 Exploring Operation: 68/2=34, Resulting Numbers: [33, 34] Generated Node #0,1,2: 33:[33, 34] Operation: 68/2=34 Exploring Operation: 68-33=35, Resulting Numbers: [2, 35] Generated Node #0,1,3: 33:[2, 35] Operation: 68-33=35 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 33:[33, 34], Operations: ['68/34=2', '68/2=34'] Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 33+34=67, Resulting Numbers: [67] 67,33 unequal: No Solution Exploring Operation: 33*34=1122, Resulting Numbers: [1122] 1122,33 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 #0,1,3 Current State: 33:[2, 35], Operations: ['68/34=2', '68-33=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,33 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,33 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[68, 34, 33, 68], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [33, 68, 2] Generated Node #0,1: 33:[33, 68, 2] Operation: 68/34=2 Moving to Node #0,1 Current State: 33:[33, 68, 2], Operations: ['68/34=2'] Exploring Operation: 68-33=35, Resulting Numbers: [2, 35] Generated Node #0,1,3: 33:[2, 35] Operation: 68-33=35 Moving to Node #0,1,3 Current State: 33:[2, 35], Operations: ['68/34=2', '68-33=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_4
mult_heuristic
[ 73, 54, 76, 1 ]
19
[ "76-73=3", "54/3=18", "1+18=19" ]
Current State: 19:[73, 54, 76, 1], Operations: [] Exploring Operation: 76-73=3, Resulting Numbers: [54, 1, 3] Generated Node #2: [54, 1, 3] from Operation: 76-73=3 Current State: 19:[54, 1, 3], Operations: ['76-73=3'] Exploring Operation: 54/3=18, Resulting Numbers: [1, 18] Generated Node #3: [1, 18] from Operation: 54/3=18 Current State: 19:[1, 18], Operations: ['76-73=3', '54/3=18'] Exploring Operation: 1+18=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[73, 54, 76, 1], Operations: [] Exploring Operation: 76-54=22, Resulting Numbers: [73, 1, 22] Generated Node #0,0: 19:[73, 1, 22] Operation: 76-54=22 Exploring Operation: 54-1=53, Resulting Numbers: [73, 76, 53] Generated Node #0,1: 19:[73, 76, 53] Operation: 54-1=53 Exploring Operation: 73-1=72, Resulting Numbers: [54, 76, 72] Generated Node #0,2: 19:[54, 76, 72] Operation: 73-1=72 Exploring Operation: 73-54=19, Resulting Numbers: [76, 1, 19] Generated Node #0,3: 19:[76, 1, 19] Operation: 73-54=19 Exploring Operation: 76-73=3, Resulting Numbers: [54, 1, 3] Generated Node #0,4: 19:[54, 1, 3] Operation: 76-73=3 Start Sub Search at level 1: Moving to Node #0,4 Current State: 19:[54, 1, 3], Operations: ['76-73=3'] Exploring Operation: 54-1=53, Resulting Numbers: [3, 53] Generated Node #0,4,0: 19:[3, 53] Operation: 54-1=53 Exploring Operation: 54-3=51, Resulting Numbers: [1, 51] Generated Node #0,4,1: 19:[1, 51] Operation: 54-3=51 Exploring Operation: 1+3=4, Resulting Numbers: [54, 4] Generated Node #0,4,2: 19:[54, 4] Operation: 1+3=4 Exploring Operation: 54/3=18, Resulting Numbers: [1, 18] Generated Node #0,4,3: 19:[1, 18] Operation: 54/3=18 Exploring Operation: 54*1=54, Resulting Numbers: [3, 54] Generated Node #0,4,4: 19:[3, 54] Operation: 54*1=54 Moving to Node #0,4,3 Current State: 19:[1, 18], Operations: ['76-73=3', '54/3=18'] Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,19 unequal: No Solution Exploring Operation: 1*18=18, Resulting Numbers: [18] 18,19 unequal: No Solution Exploring Operation: 1+18=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[73, 54, 76, 1], Operations: [] Exploring Operation: 76-73=3, Resulting Numbers: [54, 1, 3] Generated Node #0,4: 19:[54, 1, 3] Operation: 76-73=3 Moving to Node #0,4 Current State: 19:[54, 1, 3], Operations: ['76-73=3'] Exploring Operation: 54/3=18, Resulting Numbers: [1, 18] Generated Node #0,4,3: 19:[1, 18] Operation: 54/3=18 Moving to Node #0,4,3 Current State: 19:[1, 18], Operations: ['76-73=3', '54/3=18'] Exploring Operation: 1+18=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 60, 40, 76, 39 ]
15
[ "60+40=100", "76+39=115", "115-100=15" ]
Current State: 15:[60, 40, 76, 39], Operations: [] Exploring Operation: 60+40=100, Resulting Numbers: [76, 39, 100] Generated Node #2: [76, 39, 100] from Operation: 60+40=100 Current State: 15:[76, 39, 100], Operations: ['60+40=100'] Exploring Operation: 76+39=115, Resulting Numbers: [100, 115] Generated Node #3: [100, 115] from Operation: 76+39=115 Current State: 15:[100, 115], Operations: ['60+40=100', '76+39=115'] Exploring Operation: 115-100=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[60, 40, 76, 39], Operations: [] Exploring Operation: 76-60=16, Resulting Numbers: [40, 39, 16] Generated Node #0,0: 15:[40, 39, 16] Operation: 76-60=16 Moving to Node #0,0 Current State: 15:[40, 39, 16], Operations: ['76-60=16'] Exploring Operation: 40-39=1, Resulting Numbers: [16, 1] Generated Node #0,0,0: 15:[16, 1] Operation: 40-39=1 Moving to Node #0,0,0 Current State: 15:[16, 1], Operations: ['76-60=16', '40-39=1'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[60, 40, 76, 39], Operations: [] Exploring Operation: 76-60=16, Resulting Numbers: [40, 39, 16] Generated Node #0,0: 15:[40, 39, 16] Operation: 76-60=16 Moving to Node #0,0 Current State: 15:[40, 39, 16], Operations: ['76-60=16'] Exploring Operation: 40-39=1, Resulting Numbers: [16, 1] Generated Node #0,0,0: 15:[16, 1] Operation: 40-39=1 Moving to Node #0,0,0 Current State: 15:[16, 1], Operations: ['76-60=16', '40-39=1'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 78, 14, 60, 93 ]
60
[ "78+14=92", "93-92=1", "60*1=60" ]
Current State: 60:[78, 14, 60, 93], Operations: [] Exploring Operation: 78+14=92, Resulting Numbers: [60, 93, 92] Generated Node #2: [60, 93, 92] from Operation: 78+14=92 Current State: 60:[60, 93, 92], Operations: ['78+14=92'] Exploring Operation: 93-92=1, Resulting Numbers: [60, 1] Generated Node #3: [60, 1] from Operation: 93-92=1 Current State: 60:[60, 1], Operations: ['78+14=92', '93-92=1'] Exploring Operation: 60*1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[78, 14, 60, 93], Operations: [] Exploring Operation: 93-78=15, Resulting Numbers: [14, 60, 15] Generated Node #0,0: 60:[14, 60, 15] Operation: 93-78=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[14, 60, 15], Operations: ['93-78=15'] Exploring Operation: 14+15=29, Resulting Numbers: [60, 29] Generated Node #0,0,0: 60:[60, 29] Operation: 14+15=29 Moving to Node #0,0,0 Current State: 60:[60, 29], Operations: ['93-78=15', '14+15=29'] Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,60 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
[ 99, 66, 88, 57 ]
99
[ "99-88=11", "66-57=9", "11*9=99" ]
Current State: 99:[99, 66, 88, 57], Operations: [] Exploring Operation: 99-88=11, Resulting Numbers: [66, 57, 11] Generated Node #2: [66, 57, 11] from Operation: 99-88=11 Current State: 99:[66, 57, 11], Operations: ['99-88=11'] Exploring Operation: 66-57=9, Resulting Numbers: [11, 9] Generated Node #3: [11, 9] from Operation: 66-57=9 Current State: 99:[11, 9], Operations: ['99-88=11', '66-57=9'] Exploring Operation: 11*9=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[99, 66, 88, 57], Operations: [] Exploring Operation: 88-66=22, Resulting Numbers: [99, 57, 22] Generated Node #0,0: 99:[99, 57, 22] Operation: 88-66=22 Exploring Operation: 66-57=9, Resulting Numbers: [99, 88, 9] Generated Node #0,1: 99:[99, 88, 9] Operation: 66-57=9 Exploring Operation: 99-66=33, Resulting Numbers: [88, 57, 33] Generated Node #0,2: 99:[88, 57, 33] Operation: 99-66=33 Exploring Operation: 66+57=123, Resulting Numbers: [99, 88, 123] Generated Node #0,3: 99:[99, 88, 123] Operation: 66+57=123 Moving to Node #0,1 Current State: 99:[99, 88, 9], Operations: ['66-57=9'] Exploring Operation: 99+9=108, Resulting Numbers: [88, 108] Generated Node #0,1,0: 99:[88, 108] Operation: 99+9=108 Exploring Operation: 88+9=97, Resulting Numbers: [99, 97] Generated Node #0,1,1: 99:[99, 97] Operation: 88+9=97 Exploring Operation: 99-88=11, Resulting Numbers: [9, 11] Generated Node #0,1,2: 99:[9, 11] Operation: 99-88=11 Exploring Operation: 99/9=11, Resulting Numbers: [88, 11] Generated Node #0,1,3: 99:[88, 11] Operation: 99/9=11 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 99:[9, 11], Operations: ['66-57=9', '99-88=11'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,99 unequal: No Solution Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,99 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[99, 66, 88, 57], Operations: [] Exploring Operation: 66-57=9, Resulting Numbers: [99, 88, 9] Generated Node #0,1: 99:[99, 88, 9] Operation: 66-57=9 Moving to Node #0,1 Current State: 99:[99, 88, 9], Operations: ['66-57=9'] Exploring Operation: 99-88=11, Resulting Numbers: [9, 11] Generated Node #0,1,2: 99:[9, 11] Operation: 99-88=11 Moving to Node #0,1,2 Current State: 99:[9, 11], Operations: ['66-57=9', '99-88=11'] Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 84, 56, 35, 92 ]
99
[ "84-56=28", "35+92=127", "127-28=99" ]
Current State: 99:[84, 56, 35, 92], Operations: [] Exploring Operation: 84-56=28, Resulting Numbers: [35, 92, 28] Generated Node #2: [35, 92, 28] from Operation: 84-56=28 Current State: 99:[35, 92, 28], Operations: ['84-56=28'] Exploring Operation: 35+92=127, Resulting Numbers: [28, 127] Generated Node #3: [28, 127] from Operation: 35+92=127 Current State: 99:[28, 127], Operations: ['84-56=28', '35+92=127'] Exploring Operation: 127-28=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[84, 56, 35, 92], Operations: [] Exploring Operation: 56+35=91, Resulting Numbers: [84, 92, 91] Generated Node #0,0: 99:[84, 92, 91] Operation: 56+35=91 Exploring Operation: 84-56=28, Resulting Numbers: [35, 92, 28] Generated Node #0,1: 99:[35, 92, 28] Operation: 84-56=28 Exploring Operation: 92-84=8, Resulting Numbers: [56, 35, 8] Generated Node #0,2: 99:[56, 35, 8] Operation: 92-84=8 Exploring Operation: 92-56=36, Resulting Numbers: [84, 35, 36] Generated Node #0,3: 99:[84, 35, 36] Operation: 92-56=36 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[35, 92, 28], Operations: ['84-56=28'] Exploring Operation: 92+28=120, Resulting Numbers: [35, 120] Generated Node #0,1,0: 99:[35, 120] Operation: 92+28=120 Exploring Operation: 35-28=7, Resulting Numbers: [92, 7] Generated Node #0,1,1: 99:[92, 7] Operation: 35-28=7 Exploring Operation: 92-35=57, Resulting Numbers: [28, 57] Generated Node #0,1,2: 99:[28, 57] Operation: 92-35=57 Exploring Operation: 35+92=127, Resulting Numbers: [28, 127] Generated Node #0,1,3: 99:[28, 127] Operation: 35+92=127 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 99:[92, 7], Operations: ['84-56=28', '35-28=7'] Exploring Operation: 92+7=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[84, 56, 35, 92], Operations: [] Exploring Operation: 84-56=28, Resulting Numbers: [35, 92, 28] Generated Node #0,1: 99:[35, 92, 28] Operation: 84-56=28 Moving to Node #0,1 Current State: 99:[35, 92, 28], Operations: ['84-56=28'] Exploring Operation: 35-28=7, Resulting Numbers: [92, 7] Generated Node #0,1,1: 99:[92, 7] Operation: 35-28=7 Moving to Node #0,1,1 Current State: 99:[92, 7], Operations: ['84-56=28', '35-28=7'] Exploring Operation: 92+7=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 68, 48, 94, 45 ]
54
[ "68+94=162", "48-45=3", "162/3=54" ]
Current State: 54:[68, 48, 94, 45], Operations: [] Exploring Operation: 68+94=162, Resulting Numbers: [48, 45, 162] Generated Node #2: [48, 45, 162] from Operation: 68+94=162 Current State: 54:[48, 45, 162], Operations: ['68+94=162'] Exploring Operation: 48-45=3, Resulting Numbers: [162, 3] Generated Node #3: [162, 3] from Operation: 48-45=3 Current State: 54:[162, 3], Operations: ['68+94=162', '48-45=3'] Exploring Operation: 162/3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[68, 48, 94, 45], Operations: [] Exploring Operation: 94-68=26, Resulting Numbers: [48, 45, 26] Generated Node #0,0: 54:[48, 45, 26] Operation: 94-68=26 Exploring Operation: 94-45=49, Resulting Numbers: [68, 48, 49] Generated Node #0,1: 54:[68, 48, 49] Operation: 94-45=49 Moving to Node #0,0 Current State: 54:[48, 45, 26], Operations: ['94-68=26'] Exploring Operation: 48-45=3, Resulting Numbers: [26, 3] Generated Node #0,0,0: 54:[26, 3] Operation: 48-45=3 Exploring Operation: 45-26=19, Resulting Numbers: [48, 19] Generated Node #0,0,1: 54:[48, 19] Operation: 45-26=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[26, 3], Operations: ['94-68=26', '48-45=3'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,54 unequal: No Solution Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[48, 19], Operations: ['94-68=26', '45-26=19'] Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 48+19=67, Resulting Numbers: [67] 67,54 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: 54:[68, 48, 49], Operations: ['94-45=49'] Exploring Operation: 68-49=19, Resulting Numbers: [48, 19] Generated Node #0,1,0: 54:[48, 19] Operation: 68-49=19 Exploring Operation: 68-48=20, Resulting Numbers: [49, 20] Generated Node #0,1,1: 54:[49, 20] Operation: 68-48=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 54:[48, 19], Operations: ['94-45=49', '68-49=19'] Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 48+19=67, Resulting Numbers: [67] 67,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 54:[49, 20], Operations: ['94-45=49', '68-48=20'] Exploring Operation: 49+20=69, Resulting Numbers: [69] 69,54 unequal: No Solution Exploring Operation: 49-20=29, Resulting Numbers: [29] 29,54 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
[ 97, 59, 53, 5 ]
20
[ "97-59=38", "53+5=58", "58-38=20" ]
Current State: 20:[97, 59, 53, 5], Operations: [] Exploring Operation: 97-59=38, Resulting Numbers: [53, 5, 38] Generated Node #2: [53, 5, 38] from Operation: 97-59=38 Current State: 20:[53, 5, 38], Operations: ['97-59=38'] Exploring Operation: 53+5=58, Resulting Numbers: [38, 58] Generated Node #3: [38, 58] from Operation: 53+5=58 Current State: 20:[38, 58], Operations: ['97-59=38', '53+5=58'] Exploring Operation: 58-38=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[97, 59, 53, 5], Operations: [] Exploring Operation: 97-53=44, Resulting Numbers: [59, 5, 44] Generated Node #0,0: 20:[59, 5, 44] Operation: 97-53=44 Exploring Operation: 97-59=38, Resulting Numbers: [53, 5, 38] Generated Node #0,1: 20:[53, 5, 38] Operation: 97-59=38 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[53, 5, 38], Operations: ['97-59=38'] Exploring Operation: 53-38=15, Resulting Numbers: [5, 15] Generated Node #0,1,0: 20:[5, 15] Operation: 53-38=15 Exploring Operation: 53-5=48, Resulting Numbers: [38, 48] Generated Node #0,1,1: 20:[38, 48] Operation: 53-5=48 Moving to Node #0,1,0 Current State: 20:[5, 15], Operations: ['97-59=38', '53-38=15'] Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[97, 59, 53, 5], Operations: [] Exploring Operation: 97-59=38, Resulting Numbers: [53, 5, 38] Generated Node #0,1: 20:[53, 5, 38] Operation: 97-59=38 Moving to Node #0,1 Current State: 20:[53, 5, 38], Operations: ['97-59=38'] Exploring Operation: 53-38=15, Resulting Numbers: [5, 15] Generated Node #0,1,0: 20:[5, 15] Operation: 53-38=15 Moving to Node #0,1,0 Current State: 20:[5, 15], Operations: ['97-59=38', '53-38=15'] Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 47, 16, 84, 2 ]
22
[ "47-16=31", "2*31=62", "84-62=22" ]
Current State: 22:[47, 16, 84, 2], Operations: [] Exploring Operation: 47-16=31, Resulting Numbers: [84, 2, 31] Generated Node #2: [84, 2, 31] from Operation: 47-16=31 Current State: 22:[84, 2, 31], Operations: ['47-16=31'] Exploring Operation: 2*31=62, Resulting Numbers: [84, 62] Generated Node #3: [84, 62] from Operation: 2*31=62 Current State: 22:[84, 62], Operations: ['47-16=31', '2*31=62'] Exploring Operation: 84-62=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[47, 16, 84, 2], Operations: [] Exploring Operation: 84-16=68, Resulting Numbers: [47, 2, 68] Generated Node #0,0: 22:[47, 2, 68] Operation: 84-16=68 Exploring Operation: 84-47=37, Resulting Numbers: [16, 2, 37] Generated Node #0,1: 22:[16, 2, 37] Operation: 84-47=37 Exploring Operation: 84/2=42, Resulting Numbers: [47, 16, 42] Generated Node #0,2: 22:[47, 16, 42] Operation: 84/2=42 Exploring Operation: 47-16=31, Resulting Numbers: [84, 2, 31] Generated Node #0,3: 22:[84, 2, 31] Operation: 47-16=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[16, 2, 37], Operations: ['84-47=37'] Exploring Operation: 16-2=14, Resulting Numbers: [37, 14] Generated Node #0,1,0: 22:[37, 14] Operation: 16-2=14 Exploring Operation: 16/2=8, Resulting Numbers: [37, 8] Generated Node #0,1,1: 22:[37, 8] Operation: 16/2=8 Exploring Operation: 37-2=35, Resulting Numbers: [16, 35] Generated Node #0,1,2: 22:[16, 35] Operation: 37-2=35 Exploring Operation: 37-16=21, Resulting Numbers: [2, 21] Generated Node #0,1,3: 22:[2, 21] Operation: 37-16=21 Moving to Node #0,1,3 Current State: 22:[2, 21], Operations: ['84-47=37', '37-16=21'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,22 unequal: No Solution Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[37, 8], Operations: ['84-47=37', '16/2=8'] Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 37+8=45, Resulting Numbers: [45] 45,22 unequal: No Solution Exploring Operation: 37*8=296, Resulting Numbers: [296] 296,22 unequal: No Solution Moving to Node #0,1,0 Current State: 22:[37, 14], Operations: ['84-47=37', '16-2=14'] Exploring Operation: 37*14=518, Resulting Numbers: [518] 518,22 unequal: No Solution Exploring Operation: 37+14=51, Resulting Numbers: [51] 51,22 unequal: No Solution Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[16, 35], Operations: ['84-47=37', '37-2=35'] Exploring Operation: 16+35=51, Resulting Numbers: [51] 51,22 unequal: No Solution Exploring Operation: 16*35=560, Resulting Numbers: [560] 560,22 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,22 unequal: No Solution No 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: 22:[47, 16, 42], Operations: ['84/2=42'] Exploring Operation: 47-42=5, Resulting Numbers: [16, 5] Generated Node #0,2,0: 22:[16, 5] Operation: 47-42=5 Exploring Operation: 47-16=31, Resulting Numbers: [42, 31] Generated Node #0,2,1: 22:[42, 31] Operation: 47-16=31 Exploring Operation: 47+16=63, Resulting Numbers: [42, 63] Generated Node #0,2,2: 22:[42, 63] Operation: 47+16=63 Exploring Operation: 42-16=26, Resulting Numbers: [47, 26] Generated Node #0,2,3: 22:[47, 26] Operation: 42-16=26 Moving to Node #0,2,0 Current State: 22:[16, 5], Operations: ['84/2=42', '47-42=5'] Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,22 unequal: No Solution Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,22 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,22 unequal: No Solution Moving to Node #0,2,3 Current State: 22:[47, 26], Operations: ['84/2=42', '42-16=26'] Exploring Operation: 47+26=73, Resulting Numbers: [73] 73,22 unequal: No Solution Exploring Operation: 47-26=21, Resulting Numbers: [21] 21,22 unequal: No Solution Exploring Operation: 47*26=1222, Resulting Numbers: [1222] 1222,22 unequal: No Solution Moving to Node #0,2,1 Current State: 22:[42, 31], Operations: ['84/2=42', '47-16=31'] Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 42+31=73, Resulting Numbers: [73] 73,22 unequal: No Solution Exploring Operation: 42*31=1302, Resulting Numbers: [1302] 1302,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[42, 63], Operations: ['84/2=42', '47+16=63'] Exploring Operation: 63-42=21, Resulting Numbers: [21] 21,22 unequal: No Solution Exploring Operation: 42*63=2646, Resulting Numbers: [2646] 2646,22 unequal: No Solution Exploring Operation: 42+63=105, Resulting Numbers: [105] 105,22 unequal: No Solution No 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: 22:[47, 2, 68], Operations: ['84-16=68'] Exploring Operation: 47-2=45, Resulting Numbers: [68, 45] Generated Node #0,0,0: 22:[68, 45] Operation: 47-2=45 Exploring Operation: 68-2=66, Resulting Numbers: [47, 66] Generated Node #0,0,1: 22:[47, 66] Operation: 68-2=66 Exploring Operation: 68/2=34, Resulting Numbers: [47, 34] Generated Node #0,0,2: 22:[47, 34] Operation: 68/2=34 Exploring Operation: 68-47=21, Resulting Numbers: [2, 21] Generated Node #0,0,3: 22:[2, 21] Operation: 68-47=21 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 22:[2, 21], Operations: ['84-16=68', '68-47=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,22 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: 22:[47, 34], Operations: ['84-16=68', '68/2=34'] Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,22 unequal: No Solution Exploring Operation: 47+34=81, Resulting Numbers: [81] 81,22 unequal: No Solution Exploring Operation: 47*34=1598, Resulting Numbers: [1598] 1598,22 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: 22:[68, 45], Operations: ['84-16=68', '47-2=45'] Exploring Operation: 68-45=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 68*45=3060, Resulting Numbers: [3060] 3060,22 unequal: No Solution Exploring Operation: 68+45=113, Resulting Numbers: [113] 113,22 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: 22:[47, 66], Operations: ['84-16=68', '68-2=66'] Exploring Operation: 47+66=113, Resulting Numbers: [113] 113,22 unequal: No Solution Exploring Operation: 47*66=3102, Resulting Numbers: [3102] 3102,22 unequal: No Solution Exploring Operation: 66-47=19, Resulting Numbers: [19] 19,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 22:[84, 2, 31], Operations: ['47-16=31'] Exploring Operation: 84/2=42, Resulting Numbers: [31, 42] Generated Node #0,3,0: 22:[31, 42] Operation: 84/2=42 Exploring Operation: 31-2=29, Resulting Numbers: [84, 29] Generated Node #0,3,1: 22:[84, 29] Operation: 31-2=29 Exploring Operation: 84-2=82, Resulting Numbers: [31, 82] Generated Node #0,3,2: 22:[31, 82] Operation: 84-2=82 Exploring Operation: 84-31=53, Resulting Numbers: [2, 53] Generated Node #0,3,3: 22:[2, 53] Operation: 84-31=53 Moving to Node #0,3,0 Current State: 22:[31, 42], Operations: ['47-16=31', '84/2=42'] Exploring Operation: 31*42=1302, Resulting Numbers: [1302] 1302,22 unequal: No Solution Exploring Operation: 31+42=73, Resulting Numbers: [73] 73,22 unequal: No Solution Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,22 unequal: No Solution Moving to Node #0,3,3 Current State: 22:[2, 53], Operations: ['47-16=31', '84-31=53'] Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,22 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,22 unequal: No Solution Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,22 unequal: No Solution Moving to Node #0,3,2 Current State: 22:[31, 82], Operations: ['47-16=31', '84-2=82'] Exploring Operation: 31+82=113, Resulting Numbers: [113] 113,22 unequal: No Solution Exploring Operation: 31*82=2542, Resulting Numbers: [2542] 2542,22 unequal: No Solution Exploring Operation: 82-31=51, Resulting Numbers: [51] 51,22 unequal: No Solution Moving to Node #0,3,1 Current State: 22:[84, 29], Operations: ['47-16=31', '31-2=29'] Exploring Operation: 84-29=55, Resulting Numbers: [55] 55,22 unequal: No Solution Exploring Operation: 84*29=2436, Resulting Numbers: [2436] 2436,22 unequal: No Solution Exploring Operation: 84+29=113, Resulting Numbers: [113] 113,22 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
[ 11, 59, 20, 19 ]
69
[ "11+59=70", "20-19=1", "70-1=69" ]
Current State: 69:[11, 59, 20, 19], Operations: [] Exploring Operation: 11+59=70, Resulting Numbers: [20, 19, 70] Generated Node #2: [20, 19, 70] from Operation: 11+59=70 Current State: 69:[20, 19, 70], Operations: ['11+59=70'] Exploring Operation: 20-19=1, Resulting Numbers: [70, 1] Generated Node #3: [70, 1] from Operation: 20-19=1 Current State: 69:[70, 1], Operations: ['11+59=70', '20-19=1'] Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[11, 59, 20, 19], Operations: [] Exploring Operation: 20-11=9, Resulting Numbers: [59, 19, 9] Generated Node #0,0: 69:[59, 19, 9] Operation: 20-11=9 Exploring Operation: 11+59=70, Resulting Numbers: [20, 19, 70] Generated Node #0,1: 69:[20, 19, 70] Operation: 11+59=70 Exploring Operation: 19-11=8, Resulting Numbers: [59, 20, 8] Generated Node #0,2: 69:[59, 20, 8] Operation: 19-11=8 Exploring Operation: 11+19=30, Resulting Numbers: [59, 20, 30] Generated Node #0,3: 69:[59, 20, 30] Operation: 11+19=30 Moving to Node #0,1 Current State: 69:[20, 19, 70], Operations: ['11+59=70'] Exploring Operation: 70-20=50, Resulting Numbers: [19, 50] Generated Node #0,1,0: 69:[19, 50] Operation: 70-20=50 Exploring Operation: 20-19=1, Resulting Numbers: [70, 1] Generated Node #0,1,1: 69:[70, 1] Operation: 20-19=1 Exploring Operation: 20+19=39, Resulting Numbers: [70, 39] Generated Node #0,1,2: 69:[70, 39] Operation: 20+19=39 Exploring Operation: 70-19=51, Resulting Numbers: [20, 51] Generated Node #0,1,3: 69:[20, 51] Operation: 70-19=51 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[70, 1], Operations: ['11+59=70', '20-19=1'] Exploring Operation: 70+1=71, Resulting Numbers: [71] 71,69 unequal: No Solution Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,69 unequal: No Solution Exploring Operation: 70*1=70, Resulting Numbers: [70] 70,69 unequal: No Solution Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[11, 59, 20, 19], Operations: [] Exploring Operation: 11+59=70, Resulting Numbers: [20, 19, 70] Generated Node #0,1: 69:[20, 19, 70] Operation: 11+59=70 Moving to Node #0,1 Current State: 69:[20, 19, 70], Operations: ['11+59=70'] Exploring Operation: 20-19=1, Resulting Numbers: [70, 1] Generated Node #0,1,1: 69:[70, 1] Operation: 20-19=1 Moving to Node #0,1,1 Current State: 69:[70, 1], Operations: ['11+59=70', '20-19=1'] Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 21, 27, 9, 41 ]
22
[ "21*27=567", "567/9=63", "63-41=22" ]
Current State: 22:[21, 27, 9, 41], Operations: [] Exploring Operation: 21*27=567, Resulting Numbers: [9, 41, 567] Generated Node #2: [9, 41, 567] from Operation: 21*27=567 Current State: 22:[9, 41, 567], Operations: ['21*27=567'] Exploring Operation: 567/9=63, Resulting Numbers: [41, 63] Generated Node #3: [41, 63] from Operation: 567/9=63 Current State: 22:[41, 63], Operations: ['21*27=567', '567/9=63'] Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[21, 27, 9, 41], Operations: [] Exploring Operation: 41-21=20, Resulting Numbers: [27, 9, 20] Generated Node #0,0: 22:[27, 9, 20] Operation: 41-21=20 Exploring Operation: 41-27=14, Resulting Numbers: [21, 9, 14] Generated Node #0,1: 22:[21, 9, 14] Operation: 41-27=14 Exploring Operation: 41-9=32, Resulting Numbers: [21, 27, 32] Generated Node #0,2: 22:[21, 27, 32] Operation: 41-9=32 Exploring Operation: 27-9=18, Resulting Numbers: [21, 41, 18] Generated Node #0,3: 22:[21, 41, 18] Operation: 27-9=18 Exploring Operation: 27/9=3, Resulting Numbers: [21, 41, 3] Generated Node #0,4: 22:[21, 41, 3] Operation: 27/9=3 Moving to Node #0,1 Current State: 22:[21, 9, 14], Operations: ['41-27=14'] Exploring Operation: 9+14=23, Resulting Numbers: [21, 23] Generated Node #0,1,0: 22:[21, 23] Operation: 9+14=23 Exploring Operation: 21-9=12, Resulting Numbers: [14, 12] Generated Node #0,1,1: 22:[14, 12] Operation: 21-9=12 Exploring Operation: 14-9=5, Resulting Numbers: [21, 5] Generated Node #0,1,2: 22:[21, 5] Operation: 14-9=5 Exploring Operation: 21-14=7, Resulting Numbers: [9, 7] Generated Node #0,1,3: 22:[9, 7] Operation: 21-14=7 Exploring Operation: 21+9=30, Resulting Numbers: [14, 30] Generated Node #0,1,4: 22:[14, 30] Operation: 21+9=30 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[21, 23], Operations: ['41-27=14', '9+14=23'] Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 21*23=483, Resulting Numbers: [483] 483,22 unequal: No Solution Exploring Operation: 21+23=44, Resulting Numbers: [44] 44,22 unequal: No Solution No 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: 22:[14, 12], Operations: ['41-27=14', '21-9=12'] Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,22 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,22 unequal: No Solution No 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: 22:[21, 5], Operations: ['41-27=14', '14-9=5'] Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,22 unequal: No Solution Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,22 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,22 unequal: No Solution No 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: 22:[9, 7], Operations: ['41-27=14', '21-14=7'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,22 unequal: No Solution Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,22 unequal: No Solution No 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: 22:[14, 30], Operations: ['41-27=14', '21+9=30'] Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,22 unequal: No Solution Exploring Operation: 14*30=420, Resulting Numbers: [420] 420,22 unequal: No Solution Exploring Operation: 14+30=44, Resulting Numbers: [44] 44,22 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: 22:[27, 9, 20], Operations: ['41-21=20'] Exploring Operation: 9+20=29, Resulting Numbers: [27, 29] Generated Node #0,0,0: 22:[27, 29] Operation: 9+20=29 Exploring Operation: 20-9=11, Resulting Numbers: [27, 11] Generated Node #0,0,1: 22:[27, 11] Operation: 20-9=11 Exploring Operation: 27-9=18, Resulting Numbers: [20, 18] Generated Node #0,0,2: 22:[20, 18] Operation: 27-9=18 Exploring Operation: 27/9=3, Resulting Numbers: [20, 3] Generated Node #0,0,3: 22:[20, 3] Operation: 27/9=3 Exploring Operation: 27-20=7, Resulting Numbers: [9, 7] Generated Node #0,0,4: 22:[9, 7] Operation: 27-20=7 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 22:[20, 3], Operations: ['41-21=20', '27/9=3'] Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,22 unequal: No Solution Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,22 unequal: No Solution No 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: 22:[27, 11], Operations: ['41-21=20', '20-9=11'] Exploring Operation: 27+11=38, Resulting Numbers: [38] 38,22 unequal: No Solution Exploring Operation: 27*11=297, Resulting Numbers: [297] 297,22 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,22 unequal: No Solution No 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: 22:[20, 18], Operations: ['41-21=20', '27-9=18'] Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,22 unequal: No Solution Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,22 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,22 unequal: No Solution No 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: 22:[9, 7], Operations: ['41-21=20', '27-20=7'] Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,22 unequal: No Solution No 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: 22:[27, 29], Operations: ['41-21=20', '9+20=29'] Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,22 unequal: No Solution Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,22 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: 22:[21, 27, 32], Operations: ['41-9=32'] Exploring Operation: 21+32=53, Resulting Numbers: [27, 53] Generated Node #0,2,0: 22:[27, 53] Operation: 21+32=53 Exploring Operation: 27-21=6, Resulting Numbers: [32, 6] Generated Node #0,2,1: 22:[32, 6] Operation: 27-21=6 Exploring Operation: 32-21=11, Resulting Numbers: [27, 11] Generated Node #0,2,2: 22:[27, 11] Operation: 32-21=11 Exploring Operation: 21+27=48, Resulting Numbers: [32, 48] Generated Node #0,2,3: 22:[32, 48] Operation: 21+27=48 Exploring Operation: 32-27=5, Resulting Numbers: [21, 5] Generated Node #0,2,4: 22:[21, 5] Operation: 32-27=5 Moving to Node #0,4 Current State: 22:[21, 41, 3], Operations: ['27/9=3'] Exploring Operation: 21/3=7, Resulting Numbers: [41, 7] Generated Node #0,4,0: 22:[41, 7] Operation: 21/3=7 Exploring Operation: 41-21=20, Resulting Numbers: [3, 20] Generated Node #0,4,1: 22:[3, 20] Operation: 41-21=20 Exploring Operation: 41-3=38, Resulting Numbers: [21, 38] Generated Node #0,4,2: 22:[21, 38] Operation: 41-3=38 Exploring Operation: 21+3=24, Resulting Numbers: [41, 24] Generated Node #0,4,3: 22:[41, 24] Operation: 21+3=24 Exploring Operation: 21-3=18, Resulting Numbers: [41, 18] Generated Node #0,4,4: 22:[41, 18] Operation: 21-3=18 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 22:[3, 20], Operations: ['27/9=3', '41-21=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,22 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,22 unequal: No Solution No 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: 22:[21, 38], Operations: ['27/9=3', '41-3=38'] Exploring Operation: 21+38=59, Resulting Numbers: [59] 59,22 unequal: No Solution Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,22 unequal: No Solution Exploring Operation: 21*38=798, Resulting Numbers: [798] 798,22 unequal: No Solution No 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: 22:[41, 24], Operations: ['27/9=3', '21+3=24'] Exploring Operation: 41*24=984, Resulting Numbers: [984] 984,22 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,22 unequal: No Solution Exploring Operation: 41+24=65, Resulting Numbers: [65] 65,22 unequal: No Solution No 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: 22:[41, 7], Operations: ['27/9=3', '21/3=7'] Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,22 unequal: No Solution Exploring Operation: 41*7=287, Resulting Numbers: [287] 287,22 unequal: No Solution Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,22 unequal: No Solution No 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: 22:[41, 18], Operations: ['27/9=3', '21-3=18'] Exploring Operation: 41+18=59, Resulting Numbers: [59] 59,22 unequal: No Solution Exploring Operation: 41-18=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 41*18=738, Resulting Numbers: [738] 738,22 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: 22:[21, 41, 18], Operations: ['27-9=18'] Exploring Operation: 21-18=3, Resulting Numbers: [41, 3] Generated Node #0,3,0: 22:[41, 3] Operation: 21-18=3 Exploring Operation: 41-18=23, Resulting Numbers: [21, 23] Generated Node #0,3,1: 22:[21, 23] Operation: 41-18=23 Exploring Operation: 41-21=20, Resulting Numbers: [18, 20] Generated Node #0,3,2: 22:[18, 20] Operation: 41-21=20 Exploring Operation: 41+18=59, Resulting Numbers: [21, 59] Generated Node #0,3,3: 22:[21, 59] Operation: 41+18=59 Exploring Operation: 21+18=39, Resulting Numbers: [41, 39] Generated Node #0,3,4: 22:[41, 39] Operation: 21+18=39 Moving to Node #0,3,1 Current State: 22:[21, 23], Operations: ['27-9=18', '41-18=23'] Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 21+23=44, Resulting Numbers: [44] 44,22 unequal: No Solution Exploring Operation: 21*23=483, Resulting Numbers: [483] 483,22 unequal: No Solution Moving to Node #0,2,4 Current State: 22:[21, 5], Operations: ['41-9=32', '32-27=5'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,22 unequal: No Solution Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,22 unequal: No Solution Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[27, 11], Operations: ['41-9=32', '32-21=11'] Exploring Operation: 27+11=38, Resulting Numbers: [38] 38,22 unequal: No Solution Exploring Operation: 27*11=297, Resulting Numbers: [297] 297,22 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,22 unequal: No Solution Moving to Node #0,3,2 Current State: 22:[18, 20], Operations: ['27-9=18', '41-21=20'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 18*20=360, Resulting Numbers: [360] 360,22 unequal: No Solution Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,22 unequal: No Solution Moving to Node #0,2,1 Current State: 22:[32, 6], Operations: ['41-9=32', '27-21=6'] Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,22 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,22 unequal: No Solution Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,22 unequal: No Solution Moving to Node #0,3,0 Current State: 22:[41, 3], Operations: ['27-9=18', '21-18=3'] Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,22 unequal: No Solution Exploring Operation: 41*3=123, Resulting Numbers: [123] 123,22 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,22 unequal: No Solution Moving to Node #0,3,4 Current State: 22:[41, 39], Operations: ['27-9=18', '21+18=39'] Exploring Operation: 41*39=1599, Resulting Numbers: [1599] 1599,22 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,22 unequal: No Solution Moving to Node #0,2,3 Current State: 22:[32, 48], Operations: ['41-9=32', '21+27=48'] Exploring Operation: 32+48=80, Resulting Numbers: [80] 80,22 unequal: No Solution Exploring Operation: 32*48=1536, Resulting Numbers: [1536] 1536,22 unequal: No Solution Exploring Operation: 48-32=16, Resulting Numbers: [16] 16,22 unequal: No Solution Moving to Node #0,2,0 Current State: 22:[27, 53], Operations: ['41-9=32', '21+32=53'] Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,22 unequal: No Solution Exploring Operation: 27+53=80, Resulting Numbers: [80] 80,22 unequal: No Solution Exploring Operation: 27*53=1431, Resulting Numbers: [1431] 1431,22 unequal: No Solution Moving to Node #0,3,3 Current State: 22:[21, 59], Operations: ['27-9=18', '41+18=59'] Exploring Operation: 21+59=80, Resulting Numbers: [80] 80,22 unequal: No Solution Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,22 unequal: No Solution Exploring Operation: 21*59=1239, Resulting Numbers: [1239] 1239,22 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 14, 47, 27, 94 ]
11
[ "27-14=13", "94/47=2", "13-2=11" ]
Current State: 11:[14, 47, 27, 94], Operations: [] Exploring Operation: 27-14=13, Resulting Numbers: [47, 94, 13] Generated Node #2: [47, 94, 13] from Operation: 27-14=13 Current State: 11:[47, 94, 13], Operations: ['27-14=13'] Exploring Operation: 94/47=2, Resulting Numbers: [13, 2] Generated Node #3: [13, 2] from Operation: 94/47=2 Current State: 11:[13, 2], Operations: ['27-14=13', '94/47=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[14, 47, 27, 94], Operations: [] Exploring Operation: 94-47=47, Resulting Numbers: [14, 27, 47] Generated Node #0,0: 11:[14, 27, 47] Operation: 94-47=47 Exploring Operation: 94/47=2, Resulting Numbers: [14, 27, 2] Generated Node #0,1: 11:[14, 27, 2] Operation: 94/47=2 Exploring Operation: 94-27=67, Resulting Numbers: [14, 47, 67] Generated Node #0,2: 11:[14, 47, 67] Operation: 94-27=67 Exploring Operation: 47-27=20, Resulting Numbers: [14, 94, 20] Generated Node #0,3: 11:[14, 94, 20] Operation: 47-27=20 Moving to Node #0,1 Current State: 11:[14, 27, 2], Operations: ['94/47=2'] Exploring Operation: 14-2=12, Resulting Numbers: [27, 12] Generated Node #0,1,0: 11:[27, 12] Operation: 14-2=12 Exploring Operation: 14/2=7, Resulting Numbers: [27, 7] Generated Node #0,1,1: 11:[27, 7] Operation: 14/2=7 Exploring Operation: 27-14=13, Resulting Numbers: [2, 13] Generated Node #0,1,2: 11:[2, 13] Operation: 27-14=13 Exploring Operation: 27-2=25, Resulting Numbers: [14, 25] Generated Node #0,1,3: 11:[14, 25] Operation: 27-2=25 Moving to Node #0,0 Current State: 11:[14, 27, 47], Operations: ['94-47=47'] Exploring Operation: 14+27=41, Resulting Numbers: [47, 41] Generated Node #0,0,0: 11:[47, 41] Operation: 14+27=41 Exploring Operation: 47-27=20, Resulting Numbers: [14, 20] Generated Node #0,0,1: 11:[14, 20] Operation: 47-27=20 Exploring Operation: 27-14=13, Resulting Numbers: [47, 13] Generated Node #0,0,2: 11:[47, 13] Operation: 27-14=13 Exploring Operation: 47-14=33, Resulting Numbers: [27, 33] Generated Node #0,0,3: 11:[27, 33] Operation: 47-14=33 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 11:[14, 20], Operations: ['94-47=47', '47-27=20'] Exploring Operation: 14*20=280, Resulting Numbers: [280] 280,11 unequal: No Solution Exploring Operation: 14+20=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 11:[47, 13], Operations: ['94-47=47', '27-14=13'] Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 47+13=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 47*13=611, Resulting Numbers: [611] 611,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 11:[27, 33], Operations: ['94-47=47', '47-14=33'] Exploring Operation: 27*33=891, Resulting Numbers: [891] 891,11 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 27+33=60, Resulting Numbers: [60] 60,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[47, 41], Operations: ['94-47=47', '14+27=41'] Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 47*41=1927, Resulting Numbers: [1927] 1927,11 unequal: No Solution Exploring Operation: 47+41=88, Resulting Numbers: [88] 88,11 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: 11:[14, 94, 20], Operations: ['47-27=20'] Exploring Operation: 94-14=80, Resulting Numbers: [20, 80] Generated Node #0,3,0: 11:[20, 80] Operation: 94-14=80 Exploring Operation: 94-20=74, Resulting Numbers: [14, 74] Generated Node #0,3,1: 11:[14, 74] Operation: 94-20=74 Exploring Operation: 20-14=6, Resulting Numbers: [94, 6] Generated Node #0,3,2: 11:[94, 6] Operation: 20-14=6 Exploring Operation: 14+94=108, Resulting Numbers: [20, 108] Generated Node #0,3,3: 11:[20, 108] Operation: 14+94=108 Moving to Node #0,2 Current State: 11:[14, 47, 67], Operations: ['94-27=67'] Exploring Operation: 47-14=33, Resulting Numbers: [67, 33] Generated Node #0,2,0: 11:[67, 33] Operation: 47-14=33 Exploring Operation: 14+47=61, Resulting Numbers: [67, 61] Generated Node #0,2,1: 11:[67, 61] Operation: 14+47=61 Exploring Operation: 67-14=53, Resulting Numbers: [47, 53] Generated Node #0,2,2: 11:[47, 53] Operation: 67-14=53 Exploring Operation: 67-47=20, Resulting Numbers: [14, 20] Generated Node #0,2,3: 11:[14, 20] Operation: 67-47=20 Moving to Node #0,1,2 Current State: 11:[2, 13], Operations: ['94/47=2', '27-14=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[14, 47, 27, 94], Operations: [] Exploring Operation: 94/47=2, Resulting Numbers: [14, 27, 2] Generated Node #0,1: 11:[14, 27, 2] Operation: 94/47=2 Moving to Node #0,1 Current State: 11:[14, 27, 2], Operations: ['94/47=2'] Exploring Operation: 27-14=13, Resulting Numbers: [2, 13] Generated Node #0,1,2: 11:[2, 13] Operation: 27-14=13 Moving to Node #0,1,2 Current State: 11:[2, 13], Operations: ['94/47=2', '27-14=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
0.967882
hs_4
sum_heuristic
[ 17, 48, 59, 23 ]
29
[ "17+48=65", "59-23=36", "65-36=29" ]
Current State: 29:[17, 48, 59, 23], Operations: [] Exploring Operation: 17+48=65, Resulting Numbers: [59, 23, 65] Generated Node #2: [59, 23, 65] from Operation: 17+48=65 Current State: 29:[59, 23, 65], Operations: ['17+48=65'] Exploring Operation: 59-23=36, Resulting Numbers: [65, 36] Generated Node #3: [65, 36] from Operation: 59-23=36 Current State: 29:[65, 36], Operations: ['17+48=65', '59-23=36'] Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[17, 48, 59, 23], Operations: [] Exploring Operation: 48-17=31, Resulting Numbers: [59, 23, 31] Generated Node #0,0: 29:[59, 23, 31] Operation: 48-17=31 Exploring Operation: 59-17=42, Resulting Numbers: [48, 23, 42] Generated Node #0,1: 29:[48, 23, 42] Operation: 59-17=42 Exploring Operation: 59-23=36, Resulting Numbers: [17, 48, 36] Generated Node #0,2: 29:[17, 48, 36] Operation: 59-23=36 Exploring Operation: 59-48=11, Resulting Numbers: [17, 23, 11] Generated Node #0,3: 29:[17, 23, 11] Operation: 59-48=11 Start Sub Search at level 1: Moving to Node #0,3 Current State: 29:[17, 23, 11], Operations: ['59-48=11'] Exploring Operation: 17+23=40, Resulting Numbers: [11, 40] Generated Node #0,3,0: 29:[11, 40] Operation: 17+23=40 Exploring Operation: 17-11=6, Resulting Numbers: [23, 6] Generated Node #0,3,1: 29:[23, 6] Operation: 17-11=6 Exploring Operation: 23+11=34, Resulting Numbers: [17, 34] Generated Node #0,3,2: 29:[17, 34] Operation: 23+11=34 Exploring Operation: 17+11=28, Resulting Numbers: [23, 28] Generated Node #0,3,3: 29:[23, 28] Operation: 17+11=28 Moving to Node #0,3,3 Current State: 29:[23, 28], Operations: ['59-48=11', '17+11=28'] Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,29 unequal: No Solution Exploring Operation: 23+28=51, Resulting Numbers: [51] 51,29 unequal: No Solution Exploring Operation: 23*28=644, Resulting Numbers: [644] 644,29 unequal: No Solution Moving to Node #0,3,2 Current State: 29:[17, 34], Operations: ['59-48=11', '23+11=34'] Exploring Operation: 17*34=578, Resulting Numbers: [578] 578,29 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 17+34=51, Resulting Numbers: [51] 51,29 unequal: No Solution Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,29 unequal: No Solution Moving to Node #0,3,1 Current State: 29:[23, 6], Operations: ['59-48=11', '17-11=6'] Exploring Operation: 23*6=138, Resulting Numbers: [138] 138,29 unequal: No Solution Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[17, 48, 59, 23], Operations: [] Exploring Operation: 59-48=11, Resulting Numbers: [17, 23, 11] Generated Node #0,3: 29:[17, 23, 11] Operation: 59-48=11 Moving to Node #0,3 Current State: 29:[17, 23, 11], Operations: ['59-48=11'] Exploring Operation: 17-11=6, Resulting Numbers: [23, 6] Generated Node #0,3,1: 29:[23, 6] Operation: 17-11=6 Moving to Node #0,3,1 Current State: 29:[23, 6], Operations: ['59-48=11', '17-11=6'] Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 68, 83, 31, 38 ]
65
[ "83+31=114", "114/38=3", "68-3=65" ]
Current State: 65:[68, 83, 31, 38], Operations: [] Exploring Operation: 83+31=114, Resulting Numbers: [68, 38, 114] Generated Node #2: [68, 38, 114] from Operation: 83+31=114 Current State: 65:[68, 38, 114], Operations: ['83+31=114'] Exploring Operation: 114/38=3, Resulting Numbers: [68, 3] Generated Node #3: [68, 3] from Operation: 114/38=3 Current State: 65:[68, 3], Operations: ['83+31=114', '114/38=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[68, 83, 31, 38], Operations: [] Exploring Operation: 31+38=69, Resulting Numbers: [68, 83, 69] Generated Node #0,0: 65:[68, 83, 69] Operation: 31+38=69 Exploring Operation: 83-31=52, Resulting Numbers: [68, 38, 52] Generated Node #0,1: 65:[68, 38, 52] Operation: 83-31=52 Exploring Operation: 83-38=45, Resulting Numbers: [68, 31, 45] Generated Node #0,2: 65:[68, 31, 45] Operation: 83-38=45 Exploring Operation: 83-68=15, Resulting Numbers: [31, 38, 15] Generated Node #0,3: 65:[31, 38, 15] Operation: 83-68=15 Exploring Operation: 38-31=7, Resulting Numbers: [68, 83, 7] Generated Node #0,4: 65:[68, 83, 7] Operation: 38-31=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 65:[68, 83, 7], Operations: ['38-31=7'] Exploring Operation: 83-68=15, Resulting Numbers: [7, 15] Generated Node #0,4,0: 65:[7, 15] Operation: 83-68=15 Exploring Operation: 83+7=90, Resulting Numbers: [68, 90] Generated Node #0,4,1: 65:[68, 90] Operation: 83+7=90 Exploring Operation: 83-7=76, Resulting Numbers: [68, 76] Generated Node #0,4,2: 65:[68, 76] Operation: 83-7=76 Exploring Operation: 68-7=61, Resulting Numbers: [83, 61] Generated Node #0,4,3: 65:[83, 61] Operation: 68-7=61 Exploring Operation: 68+7=75, Resulting Numbers: [83, 75] Generated Node #0,4,4: 65:[83, 75] Operation: 68+7=75 Moving to Node #0,4,0 Current State: 65:[7, 15], Operations: ['38-31=7', '83-68=15'] Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 7*15=105, Resulting Numbers: [105] 105,65 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,65 unequal: No Solution Moving to Node #0,4,2 Current State: 65:[68, 76], Operations: ['38-31=7', '83-7=76'] Exploring Operation: 68*76=5168, Resulting Numbers: [5168] 5168,65 unequal: No Solution Exploring Operation: 68+76=144, Resulting Numbers: [144] 144,65 unequal: No Solution Exploring Operation: 76-68=8, Resulting Numbers: [8] 8,65 unequal: No Solution Moving to Node #0,4,3 Current State: 65:[83, 61], Operations: ['38-31=7', '68-7=61'] Exploring Operation: 83+61=144, Resulting Numbers: [144] 144,65 unequal: No Solution Exploring Operation: 83-61=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 83*61=5063, Resulting Numbers: [5063] 5063,65 unequal: No Solution Moving to Node #0,4,1 Current State: 65:[68, 90], Operations: ['38-31=7', '83+7=90'] Exploring Operation: 68+90=158, Resulting Numbers: [158] 158,65 unequal: No Solution Exploring Operation: 68*90=6120, Resulting Numbers: [6120] 6120,65 unequal: No Solution Exploring Operation: 90-68=22, Resulting Numbers: [22] 22,65 unequal: No Solution Moving to Node #0,4,4 Current State: 65:[83, 75], Operations: ['38-31=7', '68+7=75'] Exploring Operation: 83+75=158, Resulting Numbers: [158] 158,65 unequal: No Solution Exploring Operation: 83*75=6225, Resulting Numbers: [6225] 6225,65 unequal: No Solution Exploring Operation: 83-75=8, Resulting Numbers: [8] 8,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[68, 83, 69], Operations: ['31+38=69'] Exploring Operation: 68+83=151, Resulting Numbers: [69, 151] Generated Node #0,0,0: 65:[69, 151] Operation: 68+83=151 Exploring Operation: 83-69=14, Resulting Numbers: [68, 14] Generated Node #0,0,1: 65:[68, 14] Operation: 83-69=14 Exploring Operation: 68+69=137, Resulting Numbers: [83, 137] Generated Node #0,0,2: 65:[83, 137] Operation: 68+69=137 Exploring Operation: 69-68=1, Resulting Numbers: [83, 1] Generated Node #0,0,3: 65:[83, 1] Operation: 69-68=1 Exploring Operation: 83-68=15, Resulting Numbers: [69, 15] Generated Node #0,0,4: 65:[69, 15] Operation: 83-68=15 Moving to Node #0,0,1 Current State: 65:[68, 14], Operations: ['31+38=69', '83-69=14'] Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 68+14=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 68*14=952, Resulting Numbers: [952] 952,65 unequal: No Solution Moving to Node #0,0,4 Current State: 65:[69, 15], Operations: ['31+38=69', '83-68=15'] Exploring Operation: 69*15=1035, Resulting Numbers: [1035] 1035,65 unequal: No Solution Exploring Operation: 69-15=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 69+15=84, Resulting Numbers: [84] 84,65 unequal: No Solution Moving to Node #0,0,3 Current State: 65:[83, 1], Operations: ['31+38=69', '69-68=1'] Exploring Operation: 83*1=83, Resulting Numbers: [83] 83,65 unequal: No Solution Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 83/1=83, Resulting Numbers: [83] 83,65 unequal: No Solution Exploring Operation: 83+1=84, Resulting Numbers: [84] 84,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[69, 151], Operations: ['31+38=69', '68+83=151'] Exploring Operation: 69*151=10419, Resulting Numbers: [10419] 10419,65 unequal: No Solution Exploring Operation: 151-69=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 69+151=220, Resulting Numbers: [220] 220,65 unequal: No Solution Moving to Node #0,0,2 Current State: 65:[83, 137], Operations: ['31+38=69', '68+69=137'] Exploring Operation: 83*137=11371, Resulting Numbers: [11371] 11371,65 unequal: No Solution Exploring Operation: 83+137=220, Resulting Numbers: [220] 220,65 unequal: No Solution Exploring Operation: 137-83=54, Resulting Numbers: [54] 54,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[68, 38, 52], Operations: ['83-31=52'] Exploring Operation: 68-52=16, Resulting Numbers: [38, 16] Generated Node #0,1,0: 65:[38, 16] Operation: 68-52=16 Exploring Operation: 52-38=14, Resulting Numbers: [68, 14] Generated Node #0,1,1: 65:[68, 14] Operation: 52-38=14 Exploring Operation: 38+52=90, Resulting Numbers: [68, 90] Generated Node #0,1,2: 65:[68, 90] Operation: 38+52=90 Exploring Operation: 68-38=30, Resulting Numbers: [52, 30] Generated Node #0,1,3: 65:[52, 30] Operation: 68-38=30 Exploring Operation: 68+38=106, Resulting Numbers: [52, 106] Generated Node #0,1,4: 65:[52, 106] Operation: 68+38=106 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 65:[68, 14], Operations: ['83-31=52', '52-38=14'] Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 68+14=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 68*14=952, Resulting Numbers: [952] 952,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 65:[38, 16], Operations: ['83-31=52', '68-52=16'] Exploring Operation: 38*16=608, Resulting Numbers: [608] 608,65 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 38+16=54, Resulting Numbers: [54] 54,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 65:[68, 90], Operations: ['83-31=52', '38+52=90'] Exploring Operation: 68+90=158, Resulting Numbers: [158] 158,65 unequal: No Solution Exploring Operation: 90-68=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 68*90=6120, Resulting Numbers: [6120] 6120,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 65:[52, 30], Operations: ['83-31=52', '68-38=30'] Exploring Operation: 52-30=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 52*30=1560, Resulting Numbers: [1560] 1560,65 unequal: No Solution Exploring Operation: 52+30=82, Resulting Numbers: [82] 82,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 65:[52, 106], Operations: ['83-31=52', '68+38=106'] Exploring Operation: 106-52=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 52*106=5512, Resulting Numbers: [5512] 5512,65 unequal: No Solution Exploring Operation: 52+106=158, Resulting Numbers: [158] 158,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[68, 31, 45], Operations: ['83-38=45'] Exploring Operation: 31+45=76, Resulting Numbers: [68, 76] Generated Node #0,2,0: 65:[68, 76] Operation: 31+45=76 Exploring Operation: 68-45=23, Resulting Numbers: [31, 23] Generated Node #0,2,1: 65:[31, 23] Operation: 68-45=23 Exploring Operation: 68+31=99, Resulting Numbers: [45, 99] Generated Node #0,2,2: 65:[45, 99] Operation: 68+31=99 Exploring Operation: 45-31=14, Resulting Numbers: [68, 14] Generated Node #0,2,3: 65:[68, 14] Operation: 45-31=14 Exploring Operation: 68-31=37, Resulting Numbers: [45, 37] Generated Node #0,2,4: 65:[45, 37] Operation: 68-31=37 Moving to Node #0,2,3 Current State: 65:[68, 14], Operations: ['83-38=45', '45-31=14'] Exploring Operation: 68+14=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 68*14=952, Resulting Numbers: [952] 952,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[68, 76], Operations: ['83-38=45', '31+45=76'] Exploring Operation: 68*76=5168, Resulting Numbers: [5168] 5168,65 unequal: No Solution Exploring Operation: 76-68=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 68+76=144, Resulting Numbers: [144] 144,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[31, 23], Operations: ['83-38=45', '68-45=23'] Exploring Operation: 31*23=713, Resulting Numbers: [713] 713,65 unequal: No Solution Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,65 unequal: No Solution Moving to Node #0,2,4 Current State: 65:[45, 37], Operations: ['83-38=45', '68-31=37'] Exploring Operation: 45+37=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 45-37=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 45*37=1665, Resulting Numbers: [1665] 1665,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[45, 99], Operations: ['83-38=45', '68+31=99'] Exploring Operation: 45*99=4455, Resulting Numbers: [4455] 4455,65 unequal: No Solution Exploring Operation: 45+99=144, Resulting Numbers: [144] 144,65 unequal: No Solution Exploring Operation: 99-45=54, Resulting Numbers: [54] 54,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 65:[31, 38, 15], Operations: ['83-68=15'] Exploring Operation: 38-31=7, Resulting Numbers: [15, 7] Generated Node #0,3,0: 65:[15, 7] Operation: 38-31=7 Exploring Operation: 38+15=53, Resulting Numbers: [31, 53] Generated Node #0,3,1: 65:[31, 53] Operation: 38+15=53 Exploring Operation: 38-15=23, Resulting Numbers: [31, 23] Generated Node #0,3,2: 65:[31, 23] Operation: 38-15=23 Exploring Operation: 31-15=16, Resulting Numbers: [38, 16] Generated Node #0,3,3: 65:[38, 16] Operation: 31-15=16 Exploring Operation: 31+38=69, Resulting Numbers: [15, 69] Generated Node #0,3,4: 65:[15, 69] Operation: 31+38=69 Moving to Node #0,3,0 Current State: 65:[15, 7], Operations: ['83-68=15', '38-31=7'] Exploring Operation: 15*7=105, Resulting Numbers: [105] 105,65 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,65 unequal: No Solution Moving to Node #0,3,4 Current State: 65:[15, 69], Operations: ['83-68=15', '31+38=69'] Exploring Operation: 15+69=84, Resulting Numbers: [84] 84,65 unequal: No Solution Exploring Operation: 69-15=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 15*69=1035, Resulting Numbers: [1035] 1035,65 unequal: No Solution Moving to Node #0,3,2 Current State: 65:[31, 23], Operations: ['83-68=15', '38-15=23'] Exploring Operation: 31*23=713, Resulting Numbers: [713] 713,65 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,65 unequal: No Solution Moving to Node #0,3,3 Current State: 65:[38, 16], Operations: ['83-68=15', '31-15=16'] Exploring Operation: 38+16=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 38*16=608, Resulting Numbers: [608] 608,65 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,65 unequal: No Solution Moving to Node #0,3,1 Current State: 65:[31, 53], Operations: ['83-68=15', '38+15=53'] Exploring Operation: 31*53=1643, Resulting Numbers: [1643] 1643,65 unequal: No Solution Exploring Operation: 31+53=84, Resulting Numbers: [84] 84,65 unequal: No Solution Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,65 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
[ 39, 33, 17, 1 ]
37
[ "33+1=34", "34/17=2", "39-2=37" ]
Current State: 37:[39, 33, 17, 1], Operations: [] Exploring Operation: 33+1=34, Resulting Numbers: [39, 17, 34] Generated Node #2: [39, 17, 34] from Operation: 33+1=34 Current State: 37:[39, 17, 34], Operations: ['33+1=34'] Exploring Operation: 34/17=2, Resulting Numbers: [39, 2] Generated Node #3: [39, 2] from Operation: 34/17=2 Current State: 37:[39, 2], Operations: ['33+1=34', '34/17=2'] Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[39, 33, 17, 1], Operations: [] Exploring Operation: 39-1=38, Resulting Numbers: [33, 17, 38] Generated Node #0,0: 37:[33, 17, 38] Operation: 39-1=38 Exploring Operation: 33+1=34, Resulting Numbers: [39, 17, 34] Generated Node #0,1: 37:[39, 17, 34] Operation: 33+1=34 Exploring Operation: 17+1=18, Resulting Numbers: [39, 33, 18] Generated Node #0,2: 37:[39, 33, 18] Operation: 17+1=18 Moving to Node #0,0 Current State: 37:[33, 17, 38], Operations: ['39-1=38'] Exploring Operation: 33+17=50, Resulting Numbers: [38, 50] Generated Node #0,0,0: 37:[38, 50] Operation: 33+17=50 Exploring Operation: 33-17=16, Resulting Numbers: [38, 16] Generated Node #0,0,1: 37:[38, 16] Operation: 33-17=16 Exploring Operation: 38-17=21, Resulting Numbers: [33, 21] Generated Node #0,0,2: 37:[33, 21] Operation: 38-17=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[38, 50], Operations: ['39-1=38', '33+17=50'] Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 38+50=88, Resulting Numbers: [88] 88,37 unequal: No Solution Exploring Operation: 38*50=1900, Resulting Numbers: [1900] 1900,37 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 #0,0,2 Current State: 37:[33, 21], Operations: ['39-1=38', '38-17=21'] Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,37 unequal: No Solution Exploring Operation: 33*21=693, Resulting Numbers: [693] 693,37 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,37 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:[38, 16], Operations: ['39-1=38', '33-17=16'] Exploring Operation: 38+16=54, Resulting Numbers: [54] 54,37 unequal: No Solution Exploring Operation: 38*16=608, Resulting Numbers: [608] 608,37 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,37 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:[39, 17, 34], Operations: ['33+1=34'] Exploring Operation: 17+34=51, Resulting Numbers: [39, 51] Generated Node #0,1,0: 37:[39, 51] Operation: 17+34=51 Exploring Operation: 39-17=22, Resulting Numbers: [34, 22] Generated Node #0,1,1: 37:[34, 22] Operation: 39-17=22 Exploring Operation: 39+17=56, Resulting Numbers: [34, 56] Generated Node #0,1,2: 37:[34, 56] Operation: 39+17=56 Moving to Node #0,2 Current State: 37:[39, 33, 18], Operations: ['17+1=18'] Exploring Operation: 39-18=21, Resulting Numbers: [33, 21] Generated Node #0,2,0: 37:[33, 21] Operation: 39-18=21 Exploring Operation: 33+18=51, Resulting Numbers: [39, 51] Generated Node #0,2,1: 37:[39, 51] Operation: 33+18=51 Exploring Operation: 39+18=57, Resulting Numbers: [33, 57] Generated Node #0,2,2: 37:[33, 57] Operation: 39+18=57 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 37:[39, 51], Operations: ['17+1=18', '33+18=51'] Exploring Operation: 39*51=1989, Resulting Numbers: [1989] 1989,37 unequal: No Solution Exploring Operation: 39+51=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 51-39=12, Resulting Numbers: [12] 12,37 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 #0,2,0 Current State: 37:[33, 21], Operations: ['17+1=18', '39-18=21'] Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,37 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 33*21=693, Resulting Numbers: [693] 693,37 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 #0,2,2 Current State: 37:[33, 57], Operations: ['17+1=18', '39+18=57'] Exploring Operation: 33*57=1881, Resulting Numbers: [1881] 1881,37 unequal: No Solution Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,37 unequal: No Solution Exploring Operation: 33+57=90, Resulting Numbers: [90] 90,37 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: 37:[39, 51], Operations: ['33+1=34', '17+34=51'] Exploring Operation: 51-39=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 39*51=1989, Resulting Numbers: [1989] 1989,37 unequal: No Solution Exploring Operation: 39+51=90, Resulting Numbers: [90] 90,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[34, 22], Operations: ['33+1=34', '39-17=22'] Exploring Operation: 34*22=748, Resulting Numbers: [748] 748,37 unequal: No Solution Exploring Operation: 34+22=56, Resulting Numbers: [56] 56,37 unequal: No Solution Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[34, 56], Operations: ['33+1=34', '39+17=56'] Exploring Operation: 34+56=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 56-34=22, Resulting Numbers: [22] 22,37 unequal: No Solution Exploring Operation: 34*56=1904, Resulting Numbers: [1904] 1904,37 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 53, 75, 13, 1 ]
35
[ "75-53=22", "13*1=13", "22+13=35" ]
Current State: 35:[53, 75, 13, 1], Operations: [] Exploring Operation: 75-53=22, Resulting Numbers: [13, 1, 22] Generated Node #2: [13, 1, 22] from Operation: 75-53=22 Current State: 35:[13, 1, 22], Operations: ['75-53=22'] Exploring Operation: 13*1=13, Resulting Numbers: [22, 13] Generated Node #3: [22, 13] from Operation: 13*1=13 Current State: 35:[22, 13], Operations: ['75-53=22', '13*1=13'] Exploring Operation: 22+13=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[53, 75, 13, 1], Operations: [] Exploring Operation: 75-53=22, Resulting Numbers: [13, 1, 22] Generated Node #0,0: 35:[13, 1, 22] Operation: 75-53=22 Exploring Operation: 53-13=40, Resulting Numbers: [75, 1, 40] Generated Node #0,1: 35:[75, 1, 40] Operation: 53-13=40 Exploring Operation: 75-13=62, Resulting Numbers: [53, 1, 62] Generated Node #0,2: 35:[53, 1, 62] Operation: 75-13=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[13, 1, 22], Operations: ['75-53=22'] Exploring Operation: 22-13=9, Resulting Numbers: [1, 9] Generated Node #0,0,0: 35:[1, 9] Operation: 22-13=9 Exploring Operation: 13+22=35, Resulting Numbers: [1, 35] Generated Node #0,0,1: 35:[1, 35] Operation: 13+22=35 Exploring Operation: 13-1=12, Resulting Numbers: [22, 12] Generated Node #0,0,2: 35:[22, 12] Operation: 13-1=12 Moving to Node #0,0,1 Current State: 35:[1, 35], Operations: ['75-53=22', '13+22=35'] Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[53, 75, 13, 1], Operations: [] Exploring Operation: 75-53=22, Resulting Numbers: [13, 1, 22] Generated Node #0,0: 35:[13, 1, 22] Operation: 75-53=22 Moving to Node #0,0 Current State: 35:[13, 1, 22], Operations: ['75-53=22'] Exploring Operation: 13+22=35, Resulting Numbers: [1, 35] Generated Node #0,0,1: 35:[1, 35] Operation: 13+22=35 Moving to Node #0,0,1 Current State: 35:[1, 35], Operations: ['75-53=22', '13+22=35'] Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 4, 72, 92, 39 ]
80
[ "72+92=164", "164/4=41", "39+41=80" ]
Current State: 80:[4, 72, 92, 39], Operations: [] Exploring Operation: 72+92=164, Resulting Numbers: [4, 39, 164] Generated Node #2: [4, 39, 164] from Operation: 72+92=164 Current State: 80:[4, 39, 164], Operations: ['72+92=164'] Exploring Operation: 164/4=41, Resulting Numbers: [39, 41] Generated Node #3: [39, 41] from Operation: 164/4=41 Current State: 80:[39, 41], Operations: ['72+92=164', '164/4=41'] Exploring Operation: 39+41=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[4, 72, 92, 39], Operations: [] Exploring Operation: 92/4=23, Resulting Numbers: [72, 39, 23] Generated Node #0,0: 80:[72, 39, 23] Operation: 92/4=23 Exploring Operation: 92-72=20, Resulting Numbers: [4, 39, 20] Generated Node #0,1: 80:[4, 39, 20] Operation: 92-72=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[4, 39, 20], Operations: ['92-72=20'] Exploring Operation: 4*20=80, Resulting Numbers: [39, 80] Generated Node #0,1,0: 80:[39, 80] Operation: 4*20=80 Exploring Operation: 20-4=16, Resulting Numbers: [39, 16] Generated Node #0,1,1: 80:[39, 16] Operation: 20-4=16 Moving to Node #0,1,0 Current State: 80:[39, 80], Operations: ['92-72=20', '4*20=80'] Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,80 unequal: No Solution Exploring Operation: 39+80=119, Resulting Numbers: [119] 119,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[39, 16], Operations: ['92-72=20', '20-4=16'] Exploring Operation: 39+16=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 39-16=23, Resulting Numbers: [23] 23,80 unequal: No Solution No 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: 80:[72, 39, 23], Operations: ['92/4=23'] Exploring Operation: 39-23=16, Resulting Numbers: [72, 16] Generated Node #0,0,0: 80:[72, 16] Operation: 39-23=16 Exploring Operation: 72-39=33, Resulting Numbers: [23, 33] Generated Node #0,0,1: 80:[23, 33] Operation: 72-39=33 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[72, 16], Operations: ['92/4=23', '39-23=16'] Exploring Operation: 72+16=88, Resulting Numbers: [88] 88,80 unequal: No Solution Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,80 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: 80:[23, 33], Operations: ['92/4=23', '72-39=33'] Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 23+33=56, Resulting Numbers: [56] 56,80 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
[ 38, 15, 75, 96 ]
53
[ "96-38=58", "75/15=5", "58-5=53" ]
Current State: 53:[38, 15, 75, 96], Operations: [] Exploring Operation: 96-38=58, Resulting Numbers: [15, 75, 58] Generated Node #2: [15, 75, 58] from Operation: 96-38=58 Current State: 53:[15, 75, 58], Operations: ['96-38=58'] Exploring Operation: 75/15=5, Resulting Numbers: [58, 5] Generated Node #3: [58, 5] from Operation: 75/15=5 Current State: 53:[58, 5], Operations: ['96-38=58', '75/15=5'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[38, 15, 75, 96], Operations: [] Exploring Operation: 96-38=58, Resulting Numbers: [15, 75, 58] Generated Node #0,0: 53:[15, 75, 58] Operation: 96-38=58 Exploring Operation: 96-15=81, Resulting Numbers: [38, 75, 81] Generated Node #0,1: 53:[38, 75, 81] Operation: 96-15=81 Exploring Operation: 96-75=21, Resulting Numbers: [38, 15, 21] Generated Node #0,2: 53:[38, 15, 21] Operation: 96-75=21 Exploring Operation: 38+15=53, Resulting Numbers: [75, 96, 53] Generated Node #0,3: 53:[75, 96, 53] Operation: 38+15=53 Exploring Operation: 75-15=60, Resulting Numbers: [38, 96, 60] Generated Node #0,4: 53:[38, 96, 60] Operation: 75-15=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[15, 75, 58], Operations: ['96-38=58'] Exploring Operation: 15+58=73, Resulting Numbers: [75, 73] Generated Node #0,0,0: 53:[75, 73] Operation: 15+58=73 Exploring Operation: 58-15=43, Resulting Numbers: [75, 43] Generated Node #0,0,1: 53:[75, 43] Operation: 58-15=43 Exploring Operation: 75/15=5, Resulting Numbers: [58, 5] Generated Node #0,0,2: 53:[58, 5] Operation: 75/15=5 Exploring Operation: 75-15=60, Resulting Numbers: [58, 60] Generated Node #0,0,3: 53:[58, 60] Operation: 75-15=60 Exploring Operation: 15+75=90, Resulting Numbers: [58, 90] Generated Node #0,0,4: 53:[58, 90] Operation: 15+75=90 Moving to Node #0,0,3 Current State: 53:[58, 60], Operations: ['96-38=58', '75-15=60'] Exploring Operation: 58*60=3480, Resulting Numbers: [3480] 3480,53 unequal: No Solution Exploring Operation: 60-58=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 58+60=118, Resulting Numbers: [118] 118,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[75, 43], Operations: ['96-38=58', '58-15=43'] Exploring Operation: 75+43=118, Resulting Numbers: [118] 118,53 unequal: No Solution Exploring Operation: 75*43=3225, Resulting Numbers: [3225] 3225,53 unequal: No Solution Exploring Operation: 75-43=32, Resulting Numbers: [32] 32,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[75, 73], Operations: ['96-38=58', '15+58=73'] Exploring Operation: 75-73=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 75*73=5475, Resulting Numbers: [5475] 5475,53 unequal: No Solution Exploring Operation: 75+73=148, Resulting Numbers: [148] 148,53 unequal: No Solution Moving to Node #0,0,4 Current State: 53:[58, 90], Operations: ['96-38=58', '15+75=90'] Exploring Operation: 58+90=148, Resulting Numbers: [148] 148,53 unequal: No Solution Exploring Operation: 90-58=32, Resulting Numbers: [32] 32,53 unequal: No Solution Exploring Operation: 58*90=5220, Resulting Numbers: [5220] 5220,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[58, 5], Operations: ['96-38=58', '75/15=5'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[38, 15, 75, 96], Operations: [] Exploring Operation: 96-38=58, Resulting Numbers: [15, 75, 58] Generated Node #0,0: 53:[15, 75, 58] Operation: 96-38=58 Moving to Node #0,0 Current State: 53:[15, 75, 58], Operations: ['96-38=58'] Exploring Operation: 75/15=5, Resulting Numbers: [58, 5] Generated Node #0,0,2: 53:[58, 5] Operation: 75/15=5 Moving to Node #0,0,2 Current State: 53:[58, 5], Operations: ['96-38=58', '75/15=5'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_5
mult_heuristic
[ 9, 8, 10, 27 ]
45
[ "9+27=36", "10*36=360", "360/8=45" ]
Current State: 45:[9, 8, 10, 27], Operations: [] Exploring Operation: 9+27=36, Resulting Numbers: [8, 10, 36] Generated Node #2: [8, 10, 36] from Operation: 9+27=36 Current State: 45:[8, 10, 36], Operations: ['9+27=36'] Exploring Operation: 10*36=360, Resulting Numbers: [8, 360] Generated Node #3: [8, 360] from Operation: 10*36=360 Current State: 45:[8, 360], Operations: ['9+27=36', '10*36=360'] Exploring Operation: 360/8=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[9, 8, 10, 27], Operations: [] Exploring Operation: 27/9=3, Resulting Numbers: [8, 10, 3] Generated Node #0,0: 45:[8, 10, 3] Operation: 27/9=3 Exploring Operation: 27-8=19, Resulting Numbers: [9, 10, 19] Generated Node #0,1: 45:[9, 10, 19] Operation: 27-8=19 Exploring Operation: 27-9=18, Resulting Numbers: [8, 10, 18] Generated Node #0,2: 45:[8, 10, 18] Operation: 27-9=18 Exploring Operation: 27-10=17, Resulting Numbers: [9, 8, 17] Generated Node #0,3: 45:[9, 8, 17] Operation: 27-10=17 Moving to Node #0,0 Current State: 45:[8, 10, 3], Operations: ['27/9=3'] Exploring Operation: 8+10=18, Resulting Numbers: [3, 18] Generated Node #0,0,0: 45:[3, 18] Operation: 8+10=18 Exploring Operation: 10-8=2, Resulting Numbers: [3, 2] Generated Node #0,0,1: 45:[3, 2] Operation: 10-8=2 Exploring Operation: 8-3=5, Resulting Numbers: [10, 5] Generated Node #0,0,2: 45:[10, 5] Operation: 8-3=5 Exploring Operation: 8+3=11, Resulting Numbers: [10, 11] Generated Node #0,0,3: 45:[10, 11] Operation: 8+3=11 Moving to Node #0,3 Current State: 45:[9, 8, 17], Operations: ['27-10=17'] Exploring Operation: 17-9=8, Resulting Numbers: [8, 8] Generated Node #0,3,0: 45:[8, 8] Operation: 17-9=8 Exploring Operation: 9+8=17, Resulting Numbers: [17, 17] Generated Node #0,3,1: 45:[17, 17] Operation: 9+8=17 Exploring Operation: 17-8=9, Resulting Numbers: [9, 9] Generated Node #0,3,2: 45:[9, 9] Operation: 17-8=9 Exploring Operation: 9-8=1, Resulting Numbers: [17, 1] Generated Node #0,3,3: 45:[17, 1] Operation: 9-8=1 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 45:[9, 9], Operations: ['27-10=17', '17-8=9'] Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,45 unequal: No Solution Exploring Operation: 9*9=81, Resulting Numbers: [81] 81,45 unequal: No Solution Exploring Operation: 9-9=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 9/9=1, Resulting Numbers: [1] 1,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 45:[8, 8], Operations: ['27-10=17', '17-9=8'] Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 45:[17, 17], Operations: ['27-10=17', '9+8=17'] Exploring Operation: 17/17=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 17-17=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 17*17=289, Resulting Numbers: [289] 289,45 unequal: No Solution Exploring Operation: 17+17=34, Resulting Numbers: [34] 34,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 45:[17, 1], Operations: ['27-10=17', '9-8=1'] Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,45 unequal: No Solution Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,45 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,45 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: 45:[8, 10, 18], Operations: ['27-9=18'] Exploring Operation: 10-8=2, Resulting Numbers: [18, 2] Generated Node #0,2,0: 45:[18, 2] Operation: 10-8=2 Exploring Operation: 18-8=10, Resulting Numbers: [10, 10] Generated Node #0,2,1: 45:[10, 10] Operation: 18-8=10 Exploring Operation: 8+10=18, Resulting Numbers: [18, 18] Generated Node #0,2,2: 45:[18, 18] Operation: 8+10=18 Exploring Operation: 18-10=8, Resulting Numbers: [8, 8] Generated Node #0,2,3: 45:[8, 8] Operation: 18-10=8 Moving to Node #0,1 Current State: 45:[9, 10, 19], Operations: ['27-8=19'] Exploring Operation: 10-9=1, Resulting Numbers: [19, 1] Generated Node #0,1,0: 45:[19, 1] Operation: 10-9=1 Exploring Operation: 19-10=9, Resulting Numbers: [9, 9] Generated Node #0,1,1: 45:[9, 9] Operation: 19-10=9 Exploring Operation: 19-9=10, Resulting Numbers: [10, 10] Generated Node #0,1,2: 45:[10, 10] Operation: 19-9=10 Exploring Operation: 9+10=19, Resulting Numbers: [19, 19] Generated Node #0,1,3: 45:[19, 19] Operation: 9+10=19 Moving to Node #0,1,1 Current State: 45:[9, 9], Operations: ['27-8=19', '19-10=9'] Exploring Operation: 9-9=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 9*9=81, Resulting Numbers: [81] 81,45 unequal: No Solution Exploring Operation: 9/9=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[3, 2], Operations: ['27/9=3', '10-8=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[10, 5], Operations: ['27/9=3', '8-3=5'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 10*5=50, Resulting Numbers: [50] 50,45 unequal: No Solution Exploring Operation: 10+5=15, Resulting Numbers: [15] 15,45 unequal: No Solution Moving to Node #0,2,3 Current State: 45:[8, 8], Operations: ['27-9=18', '18-10=8'] Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,45 unequal: No Solution Moving to Node #0,2,1 Current State: 45:[10, 10], Operations: ['27-9=18', '18-8=10'] Exploring Operation: 10+10=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 10/10=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 10-10=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,45 unequal: No Solution Moving to Node #0,1,2 Current State: 45:[10, 10], Operations: ['27-8=19', '19-9=10'] Exploring Operation: 10+10=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 10-10=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 10/10=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[3, 18], Operations: ['27/9=3', '8+10=18'] Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,45 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,45 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,45 unequal: No Solution Moving to Node #0,0,3 Current State: 45:[10, 11], Operations: ['27/9=3', '8+3=11'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,45 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,45 unequal: No Solution Moving to Node #0,2,0 Current State: 45:[18, 2], Operations: ['27-9=18', '10-8=2'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,45 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,45 unequal: No Solution Moving to Node #0,2,2 Current State: 45:[18, 18], Operations: ['27-9=18', '8+10=18'] Exploring Operation: 18-18=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,45 unequal: No Solution Exploring Operation: 18*18=324, Resulting Numbers: [324] 324,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[19, 1], Operations: ['27-8=19', '10-9=1'] Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,45 unequal: No Solution Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,45 unequal: No Solution Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,45 unequal: No Solution Moving to Node #0,1,3 Current State: 45:[19, 19], Operations: ['27-8=19', '9+10=19'] Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 19*19=361, Resulting Numbers: [361] 361,45 unequal: No Solution Exploring Operation: 19-19=0, Resulting Numbers: [0] 0,45 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 14, 3, 19, 65 ]
34
[ "14+19=33", "3*33=99", "99-65=34" ]
Current State: 34:[14, 3, 19, 65], Operations: [] Exploring Operation: 14+19=33, Resulting Numbers: [3, 65, 33] Generated Node #2: [3, 65, 33] from Operation: 14+19=33 Current State: 34:[3, 65, 33], Operations: ['14+19=33'] Exploring Operation: 3*33=99, Resulting Numbers: [65, 99] Generated Node #3: [65, 99] from Operation: 3*33=99 Current State: 34:[65, 99], Operations: ['14+19=33', '3*33=99'] Exploring Operation: 99-65=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[14, 3, 19, 65], Operations: [] Exploring Operation: 65-14=51, Resulting Numbers: [3, 19, 51] Generated Node #0,0: 34:[3, 19, 51] Operation: 65-14=51 Exploring Operation: 65-19=46, Resulting Numbers: [14, 3, 46] Generated Node #0,1: 34:[14, 3, 46] Operation: 65-19=46 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[14, 3, 46], Operations: ['65-19=46'] Exploring Operation: 14+3=17, Resulting Numbers: [46, 17] Generated Node #0,1,0: 34:[46, 17] Operation: 14+3=17 Exploring Operation: 46-14=32, Resulting Numbers: [3, 32] Generated Node #0,1,1: 34:[3, 32] Operation: 46-14=32 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 34:[3, 32], Operations: ['65-19=46', '46-14=32'] Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,34 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 34:[46, 17], Operations: ['65-19=46', '14+3=17'] Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,34 unequal: No Solution Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,34 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: 34:[3, 19, 51], Operations: ['65-14=51'] Exploring Operation: 51/3=17, Resulting Numbers: [19, 17] Generated Node #0,0,0: 34:[19, 17] Operation: 51/3=17 Exploring Operation: 51-19=32, Resulting Numbers: [3, 32] Generated Node #0,0,1: 34:[3, 32] Operation: 51-19=32 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[19, 17], Operations: ['65-14=51', '51/3=17'] Exploring Operation: 19+17=36, Resulting Numbers: [36] 36,34 unequal: No Solution Exploring Operation: 19-17=2, Resulting Numbers: [2] 2,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 34:[3, 32], Operations: ['65-14=51', '51-19=32'] Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,34 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,34 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
[ 22, 69, 10, 44 ]
81
[ "69-22=47", "44-10=34", "47+34=81" ]
Current State: 81:[22, 69, 10, 44], Operations: [] Exploring Operation: 69-22=47, Resulting Numbers: [10, 44, 47] Generated Node #2: [10, 44, 47] from Operation: 69-22=47 Current State: 81:[10, 44, 47], Operations: ['69-22=47'] Exploring Operation: 44-10=34, Resulting Numbers: [47, 34] Generated Node #3: [47, 34] from Operation: 44-10=34 Current State: 81:[47, 34], Operations: ['69-22=47', '44-10=34'] Exploring Operation: 47+34=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[22, 69, 10, 44], Operations: [] Exploring Operation: 69-44=25, Resulting Numbers: [22, 10, 25] Generated Node #0,0: 81:[22, 10, 25] Operation: 69-44=25 Exploring Operation: 69+10=79, Resulting Numbers: [22, 44, 79] Generated Node #0,1: 81:[22, 44, 79] Operation: 69+10=79 Exploring Operation: 44-10=34, Resulting Numbers: [22, 69, 34] Generated Node #0,2: 81:[22, 69, 34] Operation: 44-10=34 Exploring Operation: 44/22=2, Resulting Numbers: [69, 10, 2] Generated Node #0,3: 81:[69, 10, 2] Operation: 44/22=2 Exploring Operation: 44-22=22, Resulting Numbers: [69, 10, 22] Generated Node #0,4: 81:[69, 10, 22] Operation: 44-22=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[22, 10, 25], Operations: ['69-44=25'] Exploring Operation: 22+10=32, Resulting Numbers: [25, 32] Generated Node #0,0,0: 81:[25, 32] Operation: 22+10=32 Exploring Operation: 10+25=35, Resulting Numbers: [22, 35] Generated Node #0,0,1: 81:[22, 35] Operation: 10+25=35 Exploring Operation: 25-10=15, Resulting Numbers: [22, 15] Generated Node #0,0,2: 81:[22, 15] Operation: 25-10=15 Exploring Operation: 25-22=3, Resulting Numbers: [10, 3] Generated Node #0,0,3: 81:[10, 3] Operation: 25-22=3 Exploring Operation: 22-10=12, Resulting Numbers: [25, 12] Generated Node #0,0,4: 81:[25, 12] Operation: 22-10=12 Moving to Node #0,0,3 Current State: 81:[10, 3], Operations: ['69-44=25', '25-22=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,81 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,81 unequal: No Solution Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,81 unequal: No Solution Moving to Node #0,0,4 Current State: 81:[25, 12], Operations: ['69-44=25', '22-10=12'] Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,81 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,81 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[25, 32], Operations: ['69-44=25', '22+10=32'] Exploring Operation: 25*32=800, Resulting Numbers: [800] 800,81 unequal: No Solution Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,81 unequal: No Solution Exploring Operation: 25+32=57, Resulting Numbers: [57] 57,81 unequal: No Solution Moving to Node #0,0,2 Current State: 81:[22, 15], Operations: ['69-44=25', '25-10=15'] Exploring Operation: 22+15=37, Resulting Numbers: [37] 37,81 unequal: No Solution Exploring Operation: 22*15=330, Resulting Numbers: [330] 330,81 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[22, 35], Operations: ['69-44=25', '10+25=35'] Exploring Operation: 22+35=57, Resulting Numbers: [57] 57,81 unequal: No Solution Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,81 unequal: No Solution Exploring Operation: 22*35=770, Resulting Numbers: [770] 770,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 81:[69, 10, 2], Operations: ['44/22=2'] Exploring Operation: 69+2=71, Resulting Numbers: [10, 71] Generated Node #0,3,0: 81:[10, 71] Operation: 69+2=71 Exploring Operation: 69-2=67, Resulting Numbers: [10, 67] Generated Node #0,3,1: 81:[10, 67] Operation: 69-2=67 Exploring Operation: 69+10=79, Resulting Numbers: [2, 79] Generated Node #0,3,2: 81:[2, 79] Operation: 69+10=79 Exploring Operation: 10/2=5, Resulting Numbers: [69, 5] Generated Node #0,3,3: 81:[69, 5] Operation: 10/2=5 Exploring Operation: 10-2=8, Resulting Numbers: [69, 8] Generated Node #0,3,4: 81:[69, 8] Operation: 10-2=8 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 81:[2, 79], Operations: ['44/22=2', '69+10=79'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,81 unequal: No Solution Exploring Operation: 2*79=158, Resulting Numbers: [158] 158,81 unequal: No Solution Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[22, 69, 10, 44], Operations: [] Exploring Operation: 44/22=2, Resulting Numbers: [69, 10, 2] Generated Node #0,3: 81:[69, 10, 2] Operation: 44/22=2 Moving to Node #0,3 Current State: 81:[69, 10, 2], Operations: ['44/22=2'] Exploring Operation: 69+10=79, Resulting Numbers: [2, 79] Generated Node #0,3,2: 81:[2, 79] Operation: 69+10=79 Moving to Node #0,3,2 Current State: 81:[2, 79], Operations: ['44/22=2', '69+10=79'] Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_5
mult_heuristic
[ 64, 12, 38, 57 ]
95
[ "64+12=76", "57-38=19", "76+19=95" ]
Current State: 95:[64, 12, 38, 57], Operations: [] Exploring Operation: 64+12=76, Resulting Numbers: [38, 57, 76] Generated Node #2: [38, 57, 76] from Operation: 64+12=76 Current State: 95:[38, 57, 76], Operations: ['64+12=76'] Exploring Operation: 57-38=19, Resulting Numbers: [76, 19] Generated Node #3: [76, 19] from Operation: 57-38=19 Current State: 95:[76, 19], Operations: ['64+12=76', '57-38=19'] Exploring Operation: 76+19=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[64, 12, 38, 57], Operations: [] Exploring Operation: 38+57=95, Resulting Numbers: [64, 12, 95] Generated Node #0,0: 95:[64, 12, 95] Operation: 38+57=95 Exploring Operation: 57-38=19, Resulting Numbers: [64, 12, 19] Generated Node #0,1: 95:[64, 12, 19] Operation: 57-38=19 Exploring Operation: 64+38=102, Resulting Numbers: [12, 57, 102] Generated Node #0,2: 95:[12, 57, 102] Operation: 64+38=102 Exploring Operation: 64-57=7, Resulting Numbers: [12, 38, 7] Generated Node #0,3: 95:[12, 38, 7] Operation: 64-57=7 Moving to Node #0,3 Current State: 95:[12, 38, 7], Operations: ['64-57=7'] Exploring Operation: 38-7=31, Resulting Numbers: [12, 31] Generated Node #0,3,0: 95:[12, 31] Operation: 38-7=31 Exploring Operation: 38-12=26, Resulting Numbers: [7, 26] Generated Node #0,3,1: 95:[7, 26] Operation: 38-12=26 Exploring Operation: 12+7=19, Resulting Numbers: [38, 19] Generated Node #0,3,2: 95:[38, 19] Operation: 12+7=19 Exploring Operation: 12-7=5, Resulting Numbers: [38, 5] Generated Node #0,3,3: 95:[38, 5] Operation: 12-7=5 Moving to Node #0,1 Current State: 95:[64, 12, 19], Operations: ['57-38=19'] Exploring Operation: 64+19=83, Resulting Numbers: [12, 83] Generated Node #0,1,0: 95:[12, 83] Operation: 64+19=83 Exploring Operation: 64-19=45, Resulting Numbers: [12, 45] Generated Node #0,1,1: 95:[12, 45] Operation: 64-19=45 Exploring Operation: 64+12=76, Resulting Numbers: [19, 76] Generated Node #0,1,2: 95:[19, 76] Operation: 64+12=76 Exploring Operation: 64-12=52, Resulting Numbers: [19, 52] Generated Node #0,1,3: 95:[19, 52] Operation: 64-12=52 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 95:[12, 83], Operations: ['57-38=19', '64+19=83'] Exploring Operation: 12+83=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[64, 12, 38, 57], Operations: [] Exploring Operation: 57-38=19, Resulting Numbers: [64, 12, 19] Generated Node #0,1: 95:[64, 12, 19] Operation: 57-38=19 Moving to Node #0,1 Current State: 95:[64, 12, 19], Operations: ['57-38=19'] Exploring Operation: 64+19=83, Resulting Numbers: [12, 83] Generated Node #0,1,0: 95:[12, 83] Operation: 64+19=83 Moving to Node #0,1,0 Current State: 95:[12, 83], Operations: ['57-38=19', '64+19=83'] Exploring Operation: 12+83=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 1, 7, 64, 32 ]
39
[ "1*7=7", "64-32=32", "7+32=39" ]
Current State: 39:[1, 7, 64, 32], Operations: [] Exploring Operation: 1*7=7, Resulting Numbers: [64, 32, 7] Generated Node #2: [64, 32, 7] from Operation: 1*7=7 Current State: 39:[64, 32, 7], Operations: ['1*7=7'] Exploring Operation: 64-32=32, Resulting Numbers: [7, 32] Generated Node #3: [7, 32] from Operation: 64-32=32 Current State: 39:[7, 32], Operations: ['1*7=7', '64-32=32'] Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[1, 7, 64, 32], Operations: [] Exploring Operation: 7+32=39, Resulting Numbers: [1, 64, 39] Generated Node #0,0: 39:[1, 64, 39] Operation: 7+32=39 Exploring Operation: 64-7=57, Resulting Numbers: [1, 32, 57] Generated Node #0,1: 39:[1, 32, 57] Operation: 64-7=57 Exploring Operation: 64-32=32, Resulting Numbers: [1, 7, 32] Generated Node #0,2: 39:[1, 7, 32] Operation: 64-32=32 Exploring Operation: 64/32=2, Resulting Numbers: [1, 7, 2] Generated Node #0,3: 39:[1, 7, 2] Operation: 64/32=2 Moving to Node #0,3 Current State: 39:[1, 7, 2], Operations: ['64/32=2'] Exploring Operation: 7-2=5, Resulting Numbers: [1, 5] Generated Node #0,3,0: 39:[1, 5] Operation: 7-2=5 Exploring Operation: 1+2=3, Resulting Numbers: [7, 3] Generated Node #0,3,1: 39:[7, 3] Operation: 1+2=3 Exploring Operation: 7-1=6, Resulting Numbers: [2, 6] Generated Node #0,3,2: 39:[2, 6] Operation: 7-1=6 Exploring Operation: 7*2=14, Resulting Numbers: [1, 14] Generated Node #0,3,3: 39:[1, 14] Operation: 7*2=14 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 39:[1, 14], Operations: ['64/32=2', '7*2=14'] Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,39 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,39 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 #0,3,0 Current State: 39:[1, 5], Operations: ['64/32=2', '7-2=5'] Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,39 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 #0,3,1 Current State: 39:[7, 3], Operations: ['64/32=2', '1+2=3'] Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,39 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 #0,3,2 Current State: 39:[2, 6], Operations: ['64/32=2', '7-1=6'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,39 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,39 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: 39:[1, 7, 32], Operations: ['64-32=32'] Exploring Operation: 1*7=7, Resulting Numbers: [32, 7] Generated Node #0,2,0: 39:[32, 7] Operation: 1*7=7 Exploring Operation: 1+32=33, Resulting Numbers: [7, 33] Generated Node #0,2,1: 39:[7, 33] Operation: 1+32=33 Exploring Operation: 7-1=6, Resulting Numbers: [32, 6] Generated Node #0,2,2: 39:[32, 6] Operation: 7-1=6 Exploring Operation: 7+32=39, Resulting Numbers: [1, 39] Generated Node #0,2,3: 39:[1, 39] Operation: 7+32=39 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 39:[1, 39], Operations: ['64-32=32', '7+32=39'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[1, 7, 64, 32], Operations: [] Exploring Operation: 64-32=32, Resulting Numbers: [1, 7, 32] Generated Node #0,2: 39:[1, 7, 32] Operation: 64-32=32 Moving to Node #0,2 Current State: 39:[1, 7, 32], Operations: ['64-32=32'] Exploring Operation: 7+32=39, Resulting Numbers: [1, 39] Generated Node #0,2,3: 39:[1, 39] Operation: 7+32=39 Moving to Node #0,2,3 Current State: 39:[1, 39], Operations: ['64-32=32', '7+32=39'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
sum_heuristic
[ 78, 9, 73, 27 ]
18
[ "78-73=5", "9*5=45", "45-27=18" ]
Current State: 18:[78, 9, 73, 27], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [9, 27, 5] Generated Node #2: [9, 27, 5] from Operation: 78-73=5 Current State: 18:[9, 27, 5], Operations: ['78-73=5'] Exploring Operation: 9*5=45, Resulting Numbers: [27, 45] Generated Node #3: [27, 45] from Operation: 9*5=45 Current State: 18:[27, 45], Operations: ['78-73=5', '9*5=45'] Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[78, 9, 73, 27], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [9, 27, 5] Generated Node #0,0: 18:[9, 27, 5] Operation: 78-73=5 Exploring Operation: 78-9=69, Resulting Numbers: [73, 27, 69] Generated Node #0,1: 18:[73, 27, 69] Operation: 78-9=69 Exploring Operation: 78-27=51, Resulting Numbers: [9, 73, 51] Generated Node #0,2: 18:[9, 73, 51] Operation: 78-27=51 Exploring Operation: 73-27=46, Resulting Numbers: [78, 9, 46] Generated Node #0,3: 18:[78, 9, 46] Operation: 73-27=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[9, 27, 5], Operations: ['78-73=5'] Exploring Operation: 9-5=4, Resulting Numbers: [27, 4] Generated Node #0,0,0: 18:[27, 4] Operation: 9-5=4 Exploring Operation: 27-5=22, Resulting Numbers: [9, 22] Generated Node #0,0,1: 18:[9, 22] Operation: 27-5=22 Exploring Operation: 27-9=18, Resulting Numbers: [5, 18] Generated Node #0,0,2: 18:[5, 18] Operation: 27-9=18 Exploring Operation: 27/9=3, Resulting Numbers: [5, 3] Generated Node #0,0,3: 18:[5, 3] Operation: 27/9=3 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 18:[5, 18], Operations: ['78-73=5', '27-9=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,18 unequal: No Solution Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,18 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: 18:[5, 3], Operations: ['78-73=5', '27/9=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,18 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,18 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: 18:[9, 22], Operations: ['78-73=5', '27-5=22'] Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,18 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,18 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: 18:[27, 4], Operations: ['78-73=5', '9-5=4'] Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 27*4=108, Resulting Numbers: [108] 108,18 unequal: No Solution Exploring Operation: 27+4=31, Resulting Numbers: [31] 31,18 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: 18:[9, 73, 51], Operations: ['78-27=51'] Exploring Operation: 73-51=22, Resulting Numbers: [9, 22] Generated Node #0,2,0: 18:[9, 22] Operation: 73-51=22 Exploring Operation: 9+73=82, Resulting Numbers: [51, 82] Generated Node #0,2,1: 18:[51, 82] Operation: 9+73=82 Exploring Operation: 51-9=42, Resulting Numbers: [73, 42] Generated Node #0,2,2: 18:[73, 42] Operation: 51-9=42 Exploring Operation: 73-9=64, Resulting Numbers: [51, 64] Generated Node #0,2,3: 18:[51, 64] Operation: 73-9=64 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 18:[9, 22], Operations: ['78-27=51', '73-51=22'] Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,18 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,18 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,18 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: 18:[73, 42], Operations: ['78-27=51', '51-9=42'] Exploring Operation: 73*42=3066, Resulting Numbers: [3066] 3066,18 unequal: No Solution Exploring Operation: 73+42=115, Resulting Numbers: [115] 115,18 unequal: No Solution Exploring Operation: 73-42=31, Resulting Numbers: [31] 31,18 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: 18:[51, 64], Operations: ['78-27=51', '73-9=64'] Exploring Operation: 51+64=115, Resulting Numbers: [115] 115,18 unequal: No Solution Exploring Operation: 51*64=3264, Resulting Numbers: [3264] 3264,18 unequal: No Solution Exploring Operation: 64-51=13, Resulting Numbers: [13] 13,18 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: 18:[51, 82], Operations: ['78-27=51', '9+73=82'] Exploring Operation: 82-51=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 51*82=4182, Resulting Numbers: [4182] 4182,18 unequal: No Solution Exploring Operation: 51+82=133, Resulting Numbers: [133] 133,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 18:[78, 9, 46], Operations: ['73-27=46'] Exploring Operation: 78+9=87, Resulting Numbers: [46, 87] Generated Node #0,3,0: 18:[46, 87] Operation: 78+9=87 Exploring Operation: 78-46=32, Resulting Numbers: [9, 32] Generated Node #0,3,1: 18:[9, 32] Operation: 78-46=32 Exploring Operation: 78-9=69, Resulting Numbers: [46, 69] Generated Node #0,3,2: 18:[46, 69] Operation: 78-9=69 Exploring Operation: 46-9=37, Resulting Numbers: [78, 37] Generated Node #0,3,3: 18:[78, 37] Operation: 46-9=37 Moving to Node #0,3,1 Current State: 18:[9, 32], Operations: ['73-27=46', '78-46=32'] Exploring Operation: 9*32=288, Resulting Numbers: [288] 288,18 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 9+32=41, Resulting Numbers: [41] 41,18 unequal: No Solution Moving to Node #0,3,3 Current State: 18:[78, 37], Operations: ['73-27=46', '46-9=37'] Exploring Operation: 78+37=115, Resulting Numbers: [115] 115,18 unequal: No Solution Exploring Operation: 78-37=41, Resulting Numbers: [41] 41,18 unequal: No Solution Exploring Operation: 78*37=2886, Resulting Numbers: [2886] 2886,18 unequal: No Solution Moving to Node #0,3,2 Current State: 18:[46, 69], Operations: ['73-27=46', '78-9=69'] Exploring Operation: 46*69=3174, Resulting Numbers: [3174] 3174,18 unequal: No Solution Exploring Operation: 69-46=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 46+69=115, Resulting Numbers: [115] 115,18 unequal: No Solution Moving to Node #0,3,0 Current State: 18:[46, 87], Operations: ['73-27=46', '78+9=87'] Exploring Operation: 46+87=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 46*87=4002, Resulting Numbers: [4002] 4002,18 unequal: No Solution Exploring Operation: 87-46=41, Resulting Numbers: [41] 41,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[73, 27, 69], Operations: ['78-9=69'] Exploring Operation: 73+27=100, Resulting Numbers: [69, 100] Generated Node #0,1,0: 18:[69, 100] Operation: 73+27=100 Exploring Operation: 73-69=4, Resulting Numbers: [27, 4] Generated Node #0,1,1: 18:[27, 4] Operation: 73-69=4 Exploring Operation: 73-27=46, Resulting Numbers: [69, 46] Generated Node #0,1,2: 18:[69, 46] Operation: 73-27=46 Exploring Operation: 69-27=42, Resulting Numbers: [73, 42] Generated Node #0,1,3: 18:[73, 42] Operation: 69-27=42 Moving to Node #0,1,1 Current State: 18:[27, 4], Operations: ['78-9=69', '73-69=4'] Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 27*4=108, Resulting Numbers: [108] 108,18 unequal: No Solution Exploring Operation: 27+4=31, Resulting Numbers: [31] 31,18 unequal: No Solution Moving to Node #0,1,3 Current State: 18:[73, 42], Operations: ['78-9=69', '69-27=42'] Exploring Operation: 73+42=115, Resulting Numbers: [115] 115,18 unequal: No Solution Exploring Operation: 73-42=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 73*42=3066, Resulting Numbers: [3066] 3066,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[69, 46], Operations: ['78-9=69', '73-27=46'] Exploring Operation: 69-46=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 69*46=3174, Resulting Numbers: [3174] 3174,18 unequal: No Solution Exploring Operation: 69+46=115, Resulting Numbers: [115] 115,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[69, 100], Operations: ['78-9=69', '73+27=100'] Exploring Operation: 69*100=6900, Resulting Numbers: [6900] 6900,18 unequal: No Solution Exploring Operation: 100-69=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 69+100=169, Resulting Numbers: [169] 169,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 12, 6, 90, 15 ]
22
[ "90-6=84", "84/12=7", "15+7=22" ]
Current State: 22:[12, 6, 90, 15], Operations: [] Exploring Operation: 90-6=84, Resulting Numbers: [12, 15, 84] Generated Node #2: [12, 15, 84] from Operation: 90-6=84 Current State: 22:[12, 15, 84], Operations: ['90-6=84'] Exploring Operation: 84/12=7, Resulting Numbers: [15, 7] Generated Node #3: [15, 7] from Operation: 84/12=7 Current State: 22:[15, 7], Operations: ['90-6=84', '84/12=7'] Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[12, 6, 90, 15], Operations: [] Exploring Operation: 90/6=15, Resulting Numbers: [12, 15, 15] Generated Node #0,0: 22:[12, 15, 15] Operation: 90/6=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[12, 15, 15], Operations: ['90/6=15'] Exploring Operation: 15/15=1, Resulting Numbers: [12, 1] Generated Node #0,0,0: 22:[12, 1] Operation: 15/15=1 Moving to Node #0,0,0 Current State: 22:[12, 1], Operations: ['90/6=15', '15/15=1'] Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,22 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
[ 8, 10, 15, 48 ]
78
[ "10-8=2", "15*2=30", "48+30=78" ]
Current State: 78:[8, 10, 15, 48], Operations: [] Exploring Operation: 10-8=2, Resulting Numbers: [15, 48, 2] Generated Node #2: [15, 48, 2] from Operation: 10-8=2 Current State: 78:[15, 48, 2], Operations: ['10-8=2'] Exploring Operation: 15*2=30, Resulting Numbers: [48, 30] Generated Node #3: [48, 30] from Operation: 15*2=30 Current State: 78:[48, 30], Operations: ['10-8=2', '15*2=30'] Exploring Operation: 48+30=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[8, 10, 15, 48], Operations: [] Exploring Operation: 48-10=38, Resulting Numbers: [8, 15, 38] Generated Node #0,0: 78:[8, 15, 38] Operation: 48-10=38 Exploring Operation: 48-15=33, Resulting Numbers: [8, 10, 33] Generated Node #0,1: 78:[8, 10, 33] Operation: 48-15=33 Exploring Operation: 10-8=2, Resulting Numbers: [15, 48, 2] Generated Node #0,2: 78:[15, 48, 2] Operation: 10-8=2 Exploring Operation: 48/8=6, Resulting Numbers: [10, 15, 6] Generated Node #0,3: 78:[10, 15, 6] Operation: 48/8=6 Exploring Operation: 48-8=40, Resulting Numbers: [10, 15, 40] Generated Node #0,4: 78:[10, 15, 40] Operation: 48-8=40 Moving to Node #0,0 Current State: 78:[8, 15, 38], Operations: ['48-10=38'] Exploring Operation: 15-8=7, Resulting Numbers: [38, 7] Generated Node #0,0,0: 78:[38, 7] Operation: 15-8=7 Exploring Operation: 38-8=30, Resulting Numbers: [15, 30] Generated Node #0,0,1: 78:[15, 30] Operation: 38-8=30 Exploring Operation: 38-15=23, Resulting Numbers: [8, 23] Generated Node #0,0,2: 78:[8, 23] Operation: 38-15=23 Exploring Operation: 8+15=23, Resulting Numbers: [38, 23] Generated Node #0,0,3: 78:[38, 23] Operation: 8+15=23 Exploring Operation: 8+38=46, Resulting Numbers: [15, 46] Generated Node #0,0,4: 78:[15, 46] Operation: 8+38=46 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[38, 7], Operations: ['48-10=38', '15-8=7'] Exploring Operation: 38+7=45, Resulting Numbers: [45] 45,78 unequal: No Solution Exploring Operation: 38*7=266, Resulting Numbers: [266] 266,78 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,78 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 #0,0,3 Current State: 78:[38, 23], Operations: ['48-10=38', '8+15=23'] Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 38+23=61, Resulting Numbers: [61] 61,78 unequal: No Solution Exploring Operation: 38*23=874, Resulting Numbers: [874] 874,78 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 #0,0,2 Current State: 78:[8, 23], Operations: ['48-10=38', '38-15=23'] Exploring Operation: 8+23=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 8*23=184, Resulting Numbers: [184] 184,78 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 #0,0,1 Current State: 78:[15, 30], Operations: ['48-10=38', '38-8=30'] Exploring Operation: 15*30=450, Resulting Numbers: [450] 450,78 unequal: No Solution Exploring Operation: 15+30=45, Resulting Numbers: [45] 45,78 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,78 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 #0,0,4 Current State: 78:[15, 46], Operations: ['48-10=38', '8+38=46'] Exploring Operation: 15+46=61, Resulting Numbers: [61] 61,78 unequal: No Solution Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 15*46=690, Resulting Numbers: [690] 690,78 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: 78:[10, 15, 6], Operations: ['48/8=6'] Exploring Operation: 15-6=9, Resulting Numbers: [10, 9] Generated Node #0,3,0: 78:[10, 9] Operation: 15-6=9 Exploring Operation: 15-10=5, Resulting Numbers: [6, 5] Generated Node #0,3,1: 78:[6, 5] Operation: 15-10=5 Exploring Operation: 10-6=4, Resulting Numbers: [15, 4] Generated Node #0,3,2: 78:[15, 4] Operation: 10-6=4 Exploring Operation: 10+6=16, Resulting Numbers: [15, 16] Generated Node #0,3,3: 78:[15, 16] Operation: 10+6=16 Exploring Operation: 10+15=25, Resulting Numbers: [6, 25] Generated Node #0,3,4: 78:[6, 25] Operation: 10+15=25 Moving to Node #0,4 Current State: 78:[10, 15, 40], Operations: ['48-8=40'] Exploring Operation: 40/10=4, Resulting Numbers: [15, 4] Generated Node #0,4,0: 78:[15, 4] Operation: 40/10=4 Exploring Operation: 40-10=30, Resulting Numbers: [15, 30] Generated Node #0,4,1: 78:[15, 30] Operation: 40-10=30 Exploring Operation: 15-10=5, Resulting Numbers: [40, 5] Generated Node #0,4,2: 78:[40, 5] Operation: 15-10=5 Exploring Operation: 10+15=25, Resulting Numbers: [40, 25] Generated Node #0,4,3: 78:[40, 25] Operation: 10+15=25 Exploring Operation: 40-15=25, Resulting Numbers: [10, 25] Generated Node #0,4,4: 78:[10, 25] Operation: 40-15=25 Moving to Node #0,1 Current State: 78:[8, 10, 33], Operations: ['48-15=33'] Exploring Operation: 10-8=2, Resulting Numbers: [33, 2] Generated Node #0,1,0: 78:[33, 2] Operation: 10-8=2 Exploring Operation: 33-8=25, Resulting Numbers: [10, 25] Generated Node #0,1,1: 78:[10, 25] Operation: 33-8=25 Exploring Operation: 33-10=23, Resulting Numbers: [8, 23] Generated Node #0,1,2: 78:[8, 23] Operation: 33-10=23 Exploring Operation: 8+33=41, Resulting Numbers: [10, 41] Generated Node #0,1,3: 78:[10, 41] Operation: 8+33=41 Exploring Operation: 10+33=43, Resulting Numbers: [8, 43] Generated Node #0,1,4: 78:[8, 43] Operation: 10+33=43 Moving to Node #0,2 Current State: 78:[15, 48, 2], Operations: ['10-8=2'] Exploring Operation: 48-2=46, Resulting Numbers: [15, 46] Generated Node #0,2,0: 78:[15, 46] Operation: 48-2=46 Exploring Operation: 15+2=17, Resulting Numbers: [48, 17] Generated Node #0,2,1: 78:[48, 17] Operation: 15+2=17 Exploring Operation: 48-15=33, Resulting Numbers: [2, 33] Generated Node #0,2,2: 78:[2, 33] Operation: 48-15=33 Exploring Operation: 48/2=24, Resulting Numbers: [15, 24] Generated Node #0,2,3: 78:[15, 24] Operation: 48/2=24 Exploring Operation: 15-2=13, Resulting Numbers: [48, 13] Generated Node #0,2,4: 78:[48, 13] Operation: 15-2=13 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 78:[15, 24], Operations: ['10-8=2', '48/2=24'] Exploring Operation: 15*24=360, Resulting Numbers: [360] 360,78 unequal: No Solution Exploring Operation: 15+24=39, Resulting Numbers: [39] 39,78 unequal: No Solution Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,78 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 #0,2,2 Current State: 78:[2, 33], Operations: ['10-8=2', '48-15=33'] Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,78 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,78 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 #0,2,0 Current State: 78:[15, 46], Operations: ['10-8=2', '48-2=46'] Exploring Operation: 15+46=61, Resulting Numbers: [61] 61,78 unequal: No Solution Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 15*46=690, Resulting Numbers: [690] 690,78 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 #0,2,4 Current State: 78:[48, 13], Operations: ['10-8=2', '15-2=13'] Exploring Operation: 48*13=624, Resulting Numbers: [624] 624,78 unequal: No Solution Exploring Operation: 48+13=61, Resulting Numbers: [61] 61,78 unequal: No Solution Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,78 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 #0,2,1 Current State: 78:[48, 17], Operations: ['10-8=2', '15+2=17'] Exploring Operation: 48+17=65, Resulting Numbers: [65] 65,78 unequal: No Solution Exploring Operation: 48*17=816, Resulting Numbers: [816] 816,78 unequal: No Solution Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 78:[6, 5], Operations: ['48/8=6', '15-10=5'] Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,78 unequal: No Solution Moving to Node #0,3,4 Current State: 78:[6, 25], Operations: ['48/8=6', '10+15=25'] Exploring Operation: 6*25=150, Resulting Numbers: [150] 150,78 unequal: No Solution Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,78 unequal: No Solution Moving to Node #0,4,2 Current State: 78:[40, 5], Operations: ['48-8=40', '15-10=5'] Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,78 unequal: No Solution Exploring Operation: 40+5=45, Resulting Numbers: [45] 45,78 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,78 unequal: No Solution Exploring Operation: 40*5=200, Resulting Numbers: [200] 200,78 unequal: No Solution Moving to Node #0,4,3 Current State: 78:[40, 25], Operations: ['48-8=40', '10+15=25'] Exploring Operation: 40*25=1000, Resulting Numbers: [1000] 1000,78 unequal: No Solution Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 40+25=65, Resulting Numbers: [65] 65,78 unequal: No Solution Moving to Node #0,3,2 Current State: 78:[15, 4], Operations: ['48/8=6', '10-6=4'] Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,78 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,78 unequal: No Solution Moving to Node #0,4,0 Current State: 78:[15, 4], Operations: ['48-8=40', '40/10=4'] Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,78 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[10, 25], Operations: ['48-15=33', '33-8=25'] Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,78 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,78 unequal: No Solution Moving to Node #0,4,4 Current State: 78:[10, 25], Operations: ['48-8=40', '40-15=25'] Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,78 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,78 unequal: No Solution Moving to Node #0,1,2 Current State: 78:[8, 23], Operations: ['48-15=33', '33-10=23'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 8*23=184, Resulting Numbers: [184] 184,78 unequal: No Solution Exploring Operation: 8+23=31, Resulting Numbers: [31] 31,78 unequal: No Solution Moving to Node #0,1,3 Current State: 78:[10, 41], Operations: ['48-15=33', '8+33=41'] Exploring Operation: 10*41=410, Resulting Numbers: [410] 410,78 unequal: No Solution Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,78 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,78 unequal: No Solution Moving to Node #0,3,3 Current State: 78:[15, 16], Operations: ['48/8=6', '10+6=16'] Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,78 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,78 unequal: No Solution Moving to Node #0,1,4 Current State: 78:[8, 43], Operations: ['48-15=33', '10+33=43'] Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,78 unequal: No Solution Exploring Operation: 8*43=344, Resulting Numbers: [344] 344,78 unequal: No Solution Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[33, 2], Operations: ['48-15=33', '10-8=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,78 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,78 unequal: No Solution Moving to Node #0,4,1 Current State: 78:[15, 30], Operations: ['48-8=40', '40-10=30'] Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,78 unequal: No Solution Exploring Operation: 15*30=450, Resulting Numbers: [450] 450,78 unequal: No Solution Exploring Operation: 15+30=45, Resulting Numbers: [45] 45,78 unequal: No Solution Moving to Node #0,3,0 Current State: 78:[10, 9], Operations: ['48/8=6', '15-6=9'] Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,78 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,78 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 63, 33, 14, 61 ]
40
[ "63-61=2", "14/2=7", "33+7=40" ]
Current State: 40:[63, 33, 14, 61], Operations: [] Exploring Operation: 63-61=2, Resulting Numbers: [33, 14, 2] Generated Node #2: [33, 14, 2] from Operation: 63-61=2 Current State: 40:[33, 14, 2], Operations: ['63-61=2'] Exploring Operation: 14/2=7, Resulting Numbers: [33, 7] Generated Node #3: [33, 7] from Operation: 14/2=7 Current State: 40:[33, 7], Operations: ['63-61=2', '14/2=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[63, 33, 14, 61], Operations: [] Exploring Operation: 63-61=2, Resulting Numbers: [33, 14, 2] Generated Node #0,0: 40:[33, 14, 2] Operation: 63-61=2 Exploring Operation: 63-33=30, Resulting Numbers: [14, 61, 30] Generated Node #0,1: 40:[14, 61, 30] Operation: 63-33=30 Exploring Operation: 61-14=47, Resulting Numbers: [63, 33, 47] Generated Node #0,2: 40:[63, 33, 47] Operation: 61-14=47 Exploring Operation: 61-33=28, Resulting Numbers: [63, 14, 28] Generated Node #0,3: 40:[63, 14, 28] Operation: 61-33=28 Exploring Operation: 63-14=49, Resulting Numbers: [33, 61, 49] Generated Node #0,4: 40:[33, 61, 49] Operation: 63-14=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[33, 14, 2], Operations: ['63-61=2'] Exploring Operation: 14-2=12, Resulting Numbers: [33, 12] Generated Node #0,0,0: 40:[33, 12] Operation: 14-2=12 Exploring Operation: 33+14=47, Resulting Numbers: [2, 47] Generated Node #0,0,1: 40:[2, 47] Operation: 33+14=47 Exploring Operation: 33+2=35, Resulting Numbers: [14, 35] Generated Node #0,0,2: 40:[14, 35] Operation: 33+2=35 Exploring Operation: 14/2=7, Resulting Numbers: [33, 7] Generated Node #0,0,3: 40:[33, 7] Operation: 14/2=7 Exploring Operation: 33-14=19, Resulting Numbers: [2, 19] Generated Node #0,0,4: 40:[2, 19] Operation: 33-14=19 Moving to Node #0,0,4 Current State: 40:[2, 19], Operations: ['63-61=2', '33-14=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,40 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[2, 47], Operations: ['63-61=2', '33+14=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,40 unequal: No Solution Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,40 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,40 unequal: No Solution Moving to Node #0,0,3 Current State: 40:[33, 7], Operations: ['63-61=2', '14/2=7'] Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,40 unequal: No Solution Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[63, 33, 14, 61], Operations: [] Exploring Operation: 63-61=2, Resulting Numbers: [33, 14, 2] Generated Node #0,0: 40:[33, 14, 2] Operation: 63-61=2 Moving to Node #0,0 Current State: 40:[33, 14, 2], Operations: ['63-61=2'] Exploring Operation: 14/2=7, Resulting Numbers: [33, 7] Generated Node #0,0,3: 40:[33, 7] Operation: 14/2=7 Moving to Node #0,0,3 Current State: 40:[33, 7], Operations: ['63-61=2', '14/2=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 92, 25, 27, 68 ]
58
[ "27-25=2", "68/2=34", "92-34=58" ]
Current State: 58:[92, 25, 27, 68], Operations: [] Exploring Operation: 27-25=2, Resulting Numbers: [92, 68, 2] Generated Node #2: [92, 68, 2] from Operation: 27-25=2 Current State: 58:[92, 68, 2], Operations: ['27-25=2'] Exploring Operation: 68/2=34, Resulting Numbers: [92, 34] Generated Node #3: [92, 34] from Operation: 68/2=34 Current State: 58:[92, 34], Operations: ['27-25=2', '68/2=34'] Exploring Operation: 92-34=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[92, 25, 27, 68], Operations: [] Exploring Operation: 92-25=67, Resulting Numbers: [27, 68, 67] Generated Node #0,0: 58:[27, 68, 67] Operation: 92-25=67 Exploring Operation: 92-68=24, Resulting Numbers: [25, 27, 24] Generated Node #0,1: 58:[25, 27, 24] Operation: 92-68=24 Moving to Node #0,1 Current State: 58:[25, 27, 24], Operations: ['92-68=24'] Exploring Operation: 25-24=1, Resulting Numbers: [27, 1] Generated Node #0,1,0: 58:[27, 1] Operation: 25-24=1 Exploring Operation: 27-25=2, Resulting Numbers: [24, 2] Generated Node #0,1,1: 58:[24, 2] Operation: 27-25=2 Moving to Node #0,0 Current State: 58:[27, 68, 67], Operations: ['92-25=67'] Exploring Operation: 68-27=41, Resulting Numbers: [67, 41] Generated Node #0,0,0: 58:[67, 41] Operation: 68-27=41 Exploring Operation: 68-67=1, Resulting Numbers: [27, 1] Generated Node #0,0,1: 58:[27, 1] Operation: 68-67=1 Moving to Node #0,1,0 Current State: 58:[27, 1], Operations: ['92-68=24', '25-24=1'] Exploring Operation: 27+1=28, Resulting Numbers: [28] 28,58 unequal: No Solution Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,58 unequal: No Solution Moving to Node #0,0,1 Current State: 58:[27, 1], Operations: ['92-25=67', '68-67=1'] Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 27+1=28, Resulting Numbers: [28] 28,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[24, 2], Operations: ['92-68=24', '27-25=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,58 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,58 unequal: No Solution Moving to Node #0,0,0 Current State: 58:[67, 41], Operations: ['92-25=67', '68-27=41'] Exploring Operation: 67-41=26, Resulting Numbers: [26] 26,58 unequal: No Solution Exploring Operation: 67+41=108, Resulting Numbers: [108] 108,58 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 2, 32, 72, 88 ]
72
[ "2*88=176", "32+72=104", "176-104=72" ]
Current State: 72:[2, 32, 72, 88], Operations: [] Exploring Operation: 2*88=176, Resulting Numbers: [32, 72, 176] Generated Node #2: [32, 72, 176] from Operation: 2*88=176 Current State: 72:[32, 72, 176], Operations: ['2*88=176'] Exploring Operation: 32+72=104, Resulting Numbers: [176, 104] Generated Node #3: [176, 104] from Operation: 32+72=104 Current State: 72:[176, 104], Operations: ['2*88=176', '32+72=104'] Exploring Operation: 176-104=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[2, 32, 72, 88], Operations: [] Exploring Operation: 88-72=16, Resulting Numbers: [2, 32, 16] Generated Node #0,0: 72:[2, 32, 16] Operation: 88-72=16 Exploring Operation: 88-32=56, Resulting Numbers: [2, 72, 56] Generated Node #0,1: 72:[2, 72, 56] Operation: 88-32=56 Exploring Operation: 88/2=44, Resulting Numbers: [32, 72, 44] Generated Node #0,2: 72:[32, 72, 44] Operation: 88/2=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[2, 32, 16], Operations: ['88-72=16'] Exploring Operation: 2+32=34, Resulting Numbers: [16, 34] Generated Node #0,0,0: 72:[16, 34] Operation: 2+32=34 Exploring Operation: 32-16=16, Resulting Numbers: [2, 16] Generated Node #0,0,1: 72:[2, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [2, 2] Generated Node #0,0,2: 72:[2, 2] Operation: 32/16=2 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 72:[2, 2], Operations: ['88-72=16', '32/16=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,72 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 72:[2, 16], Operations: ['88-72=16', '32-16=16'] Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[16, 34], Operations: ['88-72=16', '2+32=34'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 16*34=544, Resulting Numbers: [544] 544,72 unequal: No Solution Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[32, 72, 44], Operations: ['88/2=44'] Exploring Operation: 72-44=28, Resulting Numbers: [32, 28] Generated Node #0,2,0: 72:[32, 28] Operation: 72-44=28 Exploring Operation: 32+44=76, Resulting Numbers: [72, 76] Generated Node #0,2,1: 72:[72, 76] Operation: 32+44=76 Exploring Operation: 44-32=12, Resulting Numbers: [72, 12] Generated Node #0,2,2: 72:[72, 12] Operation: 44-32=12 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 72:[72, 12], Operations: ['88/2=44', '44-32=12'] Exploring Operation: 72/12=6, Resulting Numbers: [6] 6,72 unequal: No Solution Exploring Operation: 72-12=60, Resulting Numbers: [60] 60,72 unequal: No Solution Exploring Operation: 72+12=84, Resulting Numbers: [84] 84,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 72:[72, 76], Operations: ['88/2=44', '32+44=76'] Exploring Operation: 72+76=148, Resulting Numbers: [148] 148,72 unequal: No Solution Exploring Operation: 76-72=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 72*76=5472, Resulting Numbers: [5472] 5472,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 72:[32, 28], Operations: ['88/2=44', '72-44=28'] Exploring Operation: 32*28=896, Resulting Numbers: [896] 896,72 unequal: No Solution Exploring Operation: 32+28=60, Resulting Numbers: [60] 60,72 unequal: No Solution Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[2, 72, 56], Operations: ['88-32=56'] Exploring Operation: 2+56=58, Resulting Numbers: [72, 58] Generated Node #0,1,0: 72:[72, 58] Operation: 2+56=58 Exploring Operation: 56/2=28, Resulting Numbers: [72, 28] Generated Node #0,1,1: 72:[72, 28] Operation: 56/2=28 Exploring Operation: 72-56=16, Resulting Numbers: [2, 16] Generated Node #0,1,2: 72:[2, 16] Operation: 72-56=16 Moving to Node #0,1,2 Current State: 72:[2, 16], Operations: ['88-32=56', '72-56=16'] Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[72, 28], Operations: ['88-32=56', '56/2=28'] Exploring Operation: 72*28=2016, Resulting Numbers: [2016] 2016,72 unequal: No Solution Exploring Operation: 72+28=100, Resulting Numbers: [100] 100,72 unequal: No Solution Exploring Operation: 72-28=44, Resulting Numbers: [44] 44,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[72, 58], Operations: ['88-32=56', '2+56=58'] Exploring Operation: 72-58=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 72+58=130, Resulting Numbers: [130] 130,72 unequal: No Solution Exploring Operation: 72*58=4176, Resulting Numbers: [4176] 4176,72 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
[ 6, 60, 12, 65 ]
75
[ "12-6=6", "60/6=10", "65+10=75" ]
Current State: 75:[6, 60, 12, 65], Operations: [] Exploring Operation: 12-6=6, Resulting Numbers: [60, 65, 6] Generated Node #2: [60, 65, 6] from Operation: 12-6=6 Current State: 75:[60, 65, 6], Operations: ['12-6=6'] Exploring Operation: 60/6=10, Resulting Numbers: [65, 10] Generated Node #3: [65, 10] from Operation: 60/6=10 Current State: 75:[65, 10], Operations: ['12-6=6', '60/6=10'] Exploring Operation: 65+10=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[6, 60, 12, 65], Operations: [] Exploring Operation: 60+12=72, Resulting Numbers: [6, 65, 72] Generated Node #0,0: 75:[6, 65, 72] Operation: 60+12=72 Exploring Operation: 60/12=5, Resulting Numbers: [6, 65, 5] Generated Node #0,1: 75:[6, 65, 5] Operation: 60/12=5 Exploring Operation: 65-60=5, Resulting Numbers: [6, 12, 5] Generated Node #0,2: 75:[6, 12, 5] Operation: 65-60=5 Exploring Operation: 60/6=10, Resulting Numbers: [12, 65, 10] Generated Node #0,3: 75:[12, 65, 10] Operation: 60/6=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[6, 12, 5], Operations: ['65-60=5'] Exploring Operation: 6+12=18, Resulting Numbers: [5, 18] Generated Node #0,2,0: 75:[5, 18] Operation: 6+12=18 Exploring Operation: 6*12=72, Resulting Numbers: [5, 72] Generated Node #0,2,1: 75:[5, 72] Operation: 6*12=72 Exploring Operation: 12-6=6, Resulting Numbers: [5, 6] Generated Node #0,2,2: 75:[5, 6] Operation: 12-6=6 Exploring Operation: 12/6=2, Resulting Numbers: [5, 2] Generated Node #0,2,3: 75:[5, 2] Operation: 12/6=2 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 75:[5, 6], Operations: ['65-60=5', '12-6=6'] Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,75 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,75 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: 75:[5, 2], Operations: ['65-60=5', '12/6=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,75 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: 75:[5, 18], Operations: ['65-60=5', '6+12=18'] Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,75 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,75 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: 75:[5, 72], Operations: ['65-60=5', '6*12=72'] Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,75 unequal: No Solution Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,75 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,75 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: 75:[6, 65, 5], Operations: ['60/12=5'] Exploring Operation: 6-5=1, Resulting Numbers: [65, 1] Generated Node #0,1,0: 75:[65, 1] Operation: 6-5=1 Exploring Operation: 65/5=13, Resulting Numbers: [6, 13] Generated Node #0,1,1: 75:[6, 13] Operation: 65/5=13 Exploring Operation: 6+65=71, Resulting Numbers: [5, 71] Generated Node #0,1,2: 75:[5, 71] Operation: 6+65=71 Exploring Operation: 65+5=70, Resulting Numbers: [6, 70] Generated Node #0,1,3: 75:[6, 70] Operation: 65+5=70 Moving to Node #0,1,1 Current State: 75:[6, 13], Operations: ['60/12=5', '65/5=13'] Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,75 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[5, 71], Operations: ['60/12=5', '6+65=71'] Exploring Operation: 5*71=355, Resulting Numbers: [355] 355,75 unequal: No Solution Exploring Operation: 71-5=66, Resulting Numbers: [66] 66,75 unequal: No Solution Exploring Operation: 5+71=76, Resulting Numbers: [76] 76,75 unequal: No Solution Moving to Node #0,1,3 Current State: 75:[6, 70], Operations: ['60/12=5', '65+5=70'] Exploring Operation: 6+70=76, Resulting Numbers: [76] 76,75 unequal: No Solution Exploring Operation: 70-6=64, Resulting Numbers: [64] 64,75 unequal: No Solution Exploring Operation: 6*70=420, Resulting Numbers: [420] 420,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[65, 1], Operations: ['60/12=5', '6-5=1'] Exploring Operation: 65*1=65, Resulting Numbers: [65] 65,75 unequal: No Solution Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,75 unequal: No Solution Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,75 unequal: No Solution Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,75 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 #0,0 Current State: 75:[6, 65, 72], Operations: ['60+12=72'] Exploring Operation: 72/6=12, Resulting Numbers: [65, 12] Generated Node #0,0,0: 75:[65, 12] Operation: 72/6=12 Exploring Operation: 72-65=7, Resulting Numbers: [6, 7] Generated Node #0,0,1: 75:[6, 7] Operation: 72-65=7 Exploring Operation: 6+72=78, Resulting Numbers: [65, 78] Generated Node #0,0,2: 75:[65, 78] Operation: 6+72=78 Exploring Operation: 6+65=71, Resulting Numbers: [72, 71] Generated Node #0,0,3: 75:[72, 71] Operation: 6+65=71 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 75:[6, 7], Operations: ['60+12=72', '72-65=7'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,75 unequal: No Solution Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,75 unequal: No Solution Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,75 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: 75:[72, 71], Operations: ['60+12=72', '6+65=71'] Exploring Operation: 72-71=1, Resulting Numbers: [1] 1,75 unequal: No Solution Exploring Operation: 72+71=143, Resulting Numbers: [143] 143,75 unequal: No Solution Exploring Operation: 72*71=5112, Resulting Numbers: [5112] 5112,75 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: 75:[65, 12], Operations: ['60+12=72', '72/6=12'] Exploring Operation: 65*12=780, Resulting Numbers: [780] 780,75 unequal: No Solution Exploring Operation: 65+12=77, Resulting Numbers: [77] 77,75 unequal: No Solution Exploring Operation: 65-12=53, Resulting Numbers: [53] 53,75 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: 75:[65, 78], Operations: ['60+12=72', '6+72=78'] Exploring Operation: 65*78=5070, Resulting Numbers: [5070] 5070,75 unequal: No Solution Exploring Operation: 78-65=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 65+78=143, Resulting Numbers: [143] 143,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 75:[12, 65, 10], Operations: ['60/6=10'] Exploring Operation: 12+65=77, Resulting Numbers: [10, 77] Generated Node #0,3,0: 75:[10, 77] Operation: 12+65=77 Exploring Operation: 12-10=2, Resulting Numbers: [65, 2] Generated Node #0,3,1: 75:[65, 2] Operation: 12-10=2 Exploring Operation: 65+10=75, Resulting Numbers: [12, 75] Generated Node #0,3,2: 75:[12, 75] Operation: 65+10=75 Exploring Operation: 12+10=22, Resulting Numbers: [65, 22] Generated Node #0,3,3: 75:[65, 22] Operation: 12+10=22 Moving to Node #0,3,2 Current State: 75:[12, 75], Operations: ['60/6=10', '65+10=75'] Exploring Operation: 75-12=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 12*75=900, Resulting Numbers: [900] 900,75 unequal: No Solution Exploring Operation: 12+75=87, Resulting Numbers: [87] 87,75 unequal: No Solution Moving to Node #0,3,0 Current State: 75:[10, 77], Operations: ['60/6=10', '12+65=77'] Exploring Operation: 77-10=67, Resulting Numbers: [67] 67,75 unequal: No Solution Exploring Operation: 10*77=770, Resulting Numbers: [770] 770,75 unequal: No Solution Exploring Operation: 10+77=87, Resulting Numbers: [87] 87,75 unequal: No Solution Moving to Node #0,3,1 Current State: 75:[65, 2], Operations: ['60/6=10', '12-10=2'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 65*2=130, Resulting Numbers: [130] 130,75 unequal: No Solution Exploring Operation: 65+2=67, Resulting Numbers: [67] 67,75 unequal: No Solution Moving to Node #0,3,3 Current State: 75:[65, 22], Operations: ['60/6=10', '12+10=22'] Exploring Operation: 65-22=43, Resulting Numbers: [43] 43,75 unequal: No Solution Exploring Operation: 65*22=1430, Resulting Numbers: [1430] 1430,75 unequal: No Solution Exploring Operation: 65+22=87, Resulting Numbers: [87] 87,75 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
[ 16, 26, 65, 77 ]
54
[ "16+26=42", "77-65=12", "42+12=54" ]
Current State: 54:[16, 26, 65, 77], Operations: [] Exploring Operation: 16+26=42, Resulting Numbers: [65, 77, 42] Generated Node #2: [65, 77, 42] from Operation: 16+26=42 Current State: 54:[65, 77, 42], Operations: ['16+26=42'] Exploring Operation: 77-65=12, Resulting Numbers: [42, 12] Generated Node #3: [42, 12] from Operation: 77-65=12 Current State: 54:[42, 12], Operations: ['16+26=42', '77-65=12'] Exploring Operation: 42+12=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[16, 26, 65, 77], Operations: [] Exploring Operation: 65-16=49, Resulting Numbers: [26, 77, 49] Generated Node #0,0: 54:[26, 77, 49] Operation: 65-16=49 Exploring Operation: 77-26=51, Resulting Numbers: [16, 65, 51] Generated Node #0,1: 54:[16, 65, 51] Operation: 77-26=51 Exploring Operation: 26-16=10, Resulting Numbers: [65, 77, 10] Generated Node #0,2: 54:[65, 77, 10] Operation: 26-16=10 Exploring Operation: 77-65=12, Resulting Numbers: [16, 26, 12] Generated Node #0,3: 54:[16, 26, 12] Operation: 77-65=12 Exploring Operation: 77-16=61, Resulting Numbers: [26, 65, 61] Generated Node #0,4: 54:[26, 65, 61] Operation: 77-16=61 Start Sub Search at level 1: Moving to Node #0,3 Current State: 54:[16, 26, 12], Operations: ['77-65=12'] Exploring Operation: 26-12=14, Resulting Numbers: [16, 14] Generated Node #0,3,0: 54:[16, 14] Operation: 26-12=14 Exploring Operation: 26+12=38, Resulting Numbers: [16, 38] Generated Node #0,3,1: 54:[16, 38] Operation: 26+12=38 Exploring Operation: 16+12=28, Resulting Numbers: [26, 28] Generated Node #0,3,2: 54:[26, 28] Operation: 16+12=28 Exploring Operation: 16-12=4, Resulting Numbers: [26, 4] Generated Node #0,3,3: 54:[26, 4] Operation: 16-12=4 Exploring Operation: 26-16=10, Resulting Numbers: [12, 10] Generated Node #0,3,4: 54:[12, 10] Operation: 26-16=10 Moving to Node #0,3,2 Current State: 54:[26, 28], Operations: ['77-65=12', '16+12=28'] Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[16, 26, 65, 77], Operations: [] Exploring Operation: 77-65=12, Resulting Numbers: [16, 26, 12] Generated Node #0,3: 54:[16, 26, 12] Operation: 77-65=12 Moving to Node #0,3 Current State: 54:[16, 26, 12], Operations: ['77-65=12'] Exploring Operation: 16+12=28, Resulting Numbers: [26, 28] Generated Node #0,3,2: 54:[26, 28] Operation: 16+12=28 Moving to Node #0,3,2 Current State: 54:[26, 28], Operations: ['77-65=12', '16+12=28'] Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 87, 82, 2, 66 ]
73
[ "87-82=5", "2+66=68", "5+68=73" ]
Current State: 73:[87, 82, 2, 66], Operations: [] Exploring Operation: 87-82=5, Resulting Numbers: [2, 66, 5] Generated Node #2: [2, 66, 5] from Operation: 87-82=5 Current State: 73:[2, 66, 5], Operations: ['87-82=5'] Exploring Operation: 2+66=68, Resulting Numbers: [5, 68] Generated Node #3: [5, 68] from Operation: 2+66=68 Current State: 73:[5, 68], Operations: ['87-82=5', '2+66=68'] Exploring Operation: 5+68=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[87, 82, 2, 66], Operations: [] Exploring Operation: 82-2=80, Resulting Numbers: [87, 66, 80] Generated Node #0,0: 73:[87, 66, 80] Operation: 82-2=80 Exploring Operation: 2+66=68, Resulting Numbers: [87, 82, 68] Generated Node #0,1: 73:[87, 82, 68] Operation: 2+66=68 Exploring Operation: 87+2=89, Resulting Numbers: [82, 66, 89] Generated Node #0,2: 73:[82, 66, 89] Operation: 87+2=89 Exploring Operation: 87-2=85, Resulting Numbers: [82, 66, 85] Generated Node #0,3: 73:[82, 66, 85] Operation: 87-2=85 Exploring Operation: 82+2=84, Resulting Numbers: [87, 66, 84] Generated Node #0,4: 73:[87, 66, 84] Operation: 82+2=84 Moving to Node #0,0 Current State: 73:[87, 66, 80], Operations: ['82-2=80'] Exploring Operation: 80-66=14, Resulting Numbers: [87, 14] Generated Node #0,0,0: 73:[87, 14] Operation: 80-66=14 Exploring Operation: 87-66=21, Resulting Numbers: [80, 21] Generated Node #0,0,1: 73:[80, 21] Operation: 87-66=21 Exploring Operation: 66+80=146, Resulting Numbers: [87, 146] Generated Node #0,0,2: 73:[87, 146] Operation: 66+80=146 Exploring Operation: 87-80=7, Resulting Numbers: [66, 7] Generated Node #0,0,3: 73:[66, 7] Operation: 87-80=7 Exploring Operation: 87+66=153, Resulting Numbers: [80, 153] Generated Node #0,0,4: 73:[80, 153] Operation: 87+66=153 Moving to Node #0,3 Current State: 73:[82, 66, 85], Operations: ['87-2=85'] Exploring Operation: 66+85=151, Resulting Numbers: [82, 151] Generated Node #0,3,0: 73:[82, 151] Operation: 66+85=151 Exploring Operation: 82+66=148, Resulting Numbers: [85, 148] Generated Node #0,3,1: 73:[85, 148] Operation: 82+66=148 Exploring Operation: 85-66=19, Resulting Numbers: [82, 19] Generated Node #0,3,2: 73:[82, 19] Operation: 85-66=19 Exploring Operation: 85-82=3, Resulting Numbers: [66, 3] Generated Node #0,3,3: 73:[66, 3] Operation: 85-82=3 Exploring Operation: 82-66=16, Resulting Numbers: [85, 16] Generated Node #0,3,4: 73:[85, 16] Operation: 82-66=16 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 73:[82, 19], Operations: ['87-2=85', '85-66=19'] Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 82*19=1558, Resulting Numbers: [1558] 1558,73 unequal: No Solution Exploring Operation: 82+19=101, Resulting Numbers: [101] 101,73 unequal: No Solution No 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: 73:[85, 16], Operations: ['87-2=85', '82-66=16'] Exploring Operation: 85+16=101, Resulting Numbers: [101] 101,73 unequal: No Solution Exploring Operation: 85*16=1360, Resulting Numbers: [1360] 1360,73 unequal: No Solution Exploring Operation: 85-16=69, Resulting Numbers: [69] 69,73 unequal: No Solution No 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: 73:[66, 3], Operations: ['87-2=85', '85-82=3'] Exploring Operation: 66+3=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 66-3=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 66*3=198, Resulting Numbers: [198] 198,73 unequal: No Solution Exploring Operation: 66/3=22, Resulting Numbers: [22] 22,73 unequal: No Solution No 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: 73:[82, 151], Operations: ['87-2=85', '66+85=151'] Exploring Operation: 82*151=12382, Resulting Numbers: [12382] 12382,73 unequal: No Solution Exploring Operation: 82+151=233, Resulting Numbers: [233] 233,73 unequal: No Solution Exploring Operation: 151-82=69, Resulting Numbers: [69] 69,73 unequal: No Solution No 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: 73:[85, 148], Operations: ['87-2=85', '82+66=148'] Exploring Operation: 85+148=233, Resulting Numbers: [233] 233,73 unequal: No Solution Exploring Operation: 85*148=12580, Resulting Numbers: [12580] 12580,73 unequal: No Solution Exploring Operation: 148-85=63, Resulting Numbers: [63] 63,73 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: 73:[87, 82, 68], Operations: ['2+66=68'] Exploring Operation: 82-68=14, Resulting Numbers: [87, 14] Generated Node #0,1,0: 73:[87, 14] Operation: 82-68=14 Exploring Operation: 87-68=19, Resulting Numbers: [82, 19] Generated Node #0,1,1: 73:[82, 19] Operation: 87-68=19 Exploring Operation: 87-82=5, Resulting Numbers: [68, 5] Generated Node #0,1,2: 73:[68, 5] Operation: 87-82=5 Exploring Operation: 87+68=155, Resulting Numbers: [82, 155] Generated Node #0,1,3: 73:[82, 155] Operation: 87+68=155 Exploring Operation: 82+68=150, Resulting Numbers: [87, 150] Generated Node #0,1,4: 73:[87, 150] Operation: 82+68=150 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[82, 19], Operations: ['2+66=68', '87-68=19'] Exploring Operation: 82+19=101, Resulting Numbers: [101] 101,73 unequal: No Solution Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 82*19=1558, Resulting Numbers: [1558] 1558,73 unequal: No Solution No 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: 73:[87, 14], Operations: ['2+66=68', '82-68=14'] Exploring Operation: 87*14=1218, Resulting Numbers: [1218] 1218,73 unequal: No Solution Exploring Operation: 87+14=101, Resulting Numbers: [101] 101,73 unequal: No Solution Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[87, 82, 2, 66], Operations: [] Exploring Operation: 2+66=68, Resulting Numbers: [87, 82, 68] Generated Node #0,1: 73:[87, 82, 68] Operation: 2+66=68 Moving to Node #0,1 Current State: 73:[87, 82, 68], Operations: ['2+66=68'] Exploring Operation: 82-68=14, Resulting Numbers: [87, 14] Generated Node #0,1,0: 73:[87, 14] Operation: 82-68=14 Moving to Node #0,1,0 Current State: 73:[87, 14], Operations: ['2+66=68', '82-68=14'] Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.960069
hs_5
mult_heuristic
[ 92, 6, 56, 79 ]
73
[ "92-56=36", "36/6=6", "79-6=73" ]
Current State: 73:[92, 6, 56, 79], Operations: [] Exploring Operation: 92-56=36, Resulting Numbers: [6, 79, 36] Generated Node #2: [6, 79, 36] from Operation: 92-56=36 Current State: 73:[6, 79, 36], Operations: ['92-56=36'] Exploring Operation: 36/6=6, Resulting Numbers: [79, 6] Generated Node #3: [79, 6] from Operation: 36/6=6 Current State: 73:[79, 6], Operations: ['92-56=36', '36/6=6'] Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[92, 6, 56, 79], Operations: [] Exploring Operation: 92-6=86, Resulting Numbers: [56, 79, 86] Generated Node #0,0: 73:[56, 79, 86] Operation: 92-6=86 Exploring Operation: 6+56=62, Resulting Numbers: [92, 79, 62] Generated Node #0,1: 73:[92, 79, 62] Operation: 6+56=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[56, 79, 86], Operations: ['92-6=86'] Exploring Operation: 79-56=23, Resulting Numbers: [86, 23] Generated Node #0,0,0: 73:[86, 23] Operation: 79-56=23 Exploring Operation: 86-56=30, Resulting Numbers: [79, 30] Generated Node #0,0,1: 73:[79, 30] Operation: 86-56=30 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[79, 30], Operations: ['92-6=86', '86-56=30'] Exploring Operation: 79-30=49, Resulting Numbers: [49] 49,73 unequal: No Solution Exploring Operation: 79+30=109, Resulting Numbers: [109] 109,73 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: 73:[86, 23], Operations: ['92-6=86', '79-56=23'] Exploring Operation: 86+23=109, Resulting Numbers: [109] 109,73 unequal: No Solution Exploring Operation: 86-23=63, Resulting Numbers: [63] 63,73 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: 73:[92, 79, 62], Operations: ['6+56=62'] Exploring Operation: 92-62=30, Resulting Numbers: [79, 30] Generated Node #0,1,0: 73:[79, 30] Operation: 92-62=30 Exploring Operation: 92-79=13, Resulting Numbers: [62, 13] Generated Node #0,1,1: 73:[62, 13] Operation: 92-79=13 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[79, 30], Operations: ['6+56=62', '92-62=30'] Exploring Operation: 79+30=109, Resulting Numbers: [109] 109,73 unequal: No Solution Exploring Operation: 79-30=49, Resulting Numbers: [49] 49,73 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: 73:[62, 13], Operations: ['6+56=62', '92-79=13'] Exploring Operation: 62+13=75, Resulting Numbers: [75] 75,73 unequal: No Solution Exploring Operation: 62-13=49, Resulting Numbers: [49] 49,73 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
[ 4, 6, 10, 37 ]
83
[ "4*10=40", "6+37=43", "40+43=83" ]
Current State: 83:[4, 6, 10, 37], Operations: [] Exploring Operation: 4*10=40, Resulting Numbers: [6, 37, 40] Generated Node #2: [6, 37, 40] from Operation: 4*10=40 Current State: 83:[6, 37, 40], Operations: ['4*10=40'] Exploring Operation: 6+37=43, Resulting Numbers: [40, 43] Generated Node #3: [40, 43] from Operation: 6+37=43 Current State: 83:[40, 43], Operations: ['4*10=40', '6+37=43'] Exploring Operation: 40+43=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[4, 6, 10, 37], Operations: [] Exploring Operation: 6*10=60, Resulting Numbers: [4, 37, 60] Generated Node #0,0: 83:[4, 37, 60] Operation: 6*10=60 Exploring Operation: 4*10=40, Resulting Numbers: [6, 37, 40] Generated Node #0,1: 83:[6, 37, 40] Operation: 4*10=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[4, 37, 60], Operations: ['6*10=60'] Exploring Operation: 4+37=41, Resulting Numbers: [60, 41] Generated Node #0,0,0: 83:[60, 41] Operation: 4+37=41 Exploring Operation: 4+60=64, Resulting Numbers: [37, 64] Generated Node #0,0,1: 83:[37, 64] Operation: 4+60=64 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[60, 41], Operations: ['6*10=60', '4+37=41'] Exploring Operation: 60-41=19, Resulting Numbers: [19] 19,83 unequal: No Solution Exploring Operation: 60+41=101, Resulting Numbers: [101] 101,83 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 #0,0,1 Current State: 83:[37, 64], Operations: ['6*10=60', '4+60=64'] Exploring Operation: 37+64=101, Resulting Numbers: [101] 101,83 unequal: No Solution Exploring Operation: 64-37=27, Resulting Numbers: [27] 27,83 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 #0,1 Current State: 83:[6, 37, 40], Operations: ['4*10=40'] Exploring Operation: 6+40=46, Resulting Numbers: [37, 46] Generated Node #0,1,0: 83:[37, 46] Operation: 6+40=46 Exploring Operation: 6+37=43, Resulting Numbers: [40, 43] Generated Node #0,1,1: 83:[40, 43] Operation: 6+37=43 Moving to Node #0,1,0 Current State: 83:[37, 46], Operations: ['4*10=40', '6+40=46'] Exploring Operation: 37+46=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[4, 6, 10, 37], Operations: [] Exploring Operation: 4*10=40, Resulting Numbers: [6, 37, 40] Generated Node #0,1: 83:[6, 37, 40] Operation: 4*10=40 Moving to Node #0,1 Current State: 83:[6, 37, 40], Operations: ['4*10=40'] Exploring Operation: 6+40=46, Resulting Numbers: [37, 46] Generated Node #0,1,0: 83:[37, 46] Operation: 6+40=46 Moving to Node #0,1,0 Current State: 83:[37, 46], Operations: ['4*10=40', '6+40=46'] Exploring Operation: 37+46=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 82, 4, 23, 41 ]
16
[ "82+23=105", "105-41=64", "64/4=16" ]
Current State: 16:[82, 4, 23, 41], Operations: [] Exploring Operation: 82+23=105, Resulting Numbers: [4, 41, 105] Generated Node #2: [4, 41, 105] from Operation: 82+23=105 Current State: 16:[4, 41, 105], Operations: ['82+23=105'] Exploring Operation: 105-41=64, Resulting Numbers: [4, 64] Generated Node #3: [4, 64] from Operation: 105-41=64 Current State: 16:[4, 64], Operations: ['82+23=105', '105-41=64'] Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[82, 4, 23, 41], Operations: [] Exploring Operation: 82-41=41, Resulting Numbers: [4, 23, 41] Generated Node #0,0: 16:[4, 23, 41] Operation: 82-41=41 Exploring Operation: 82/41=2, Resulting Numbers: [4, 23, 2] Generated Node #0,1: 16:[4, 23, 2] Operation: 82/41=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[4, 23, 2], Operations: ['82/41=2'] Exploring Operation: 23-4=19, Resulting Numbers: [2, 19] Generated Node #0,1,0: 16:[2, 19] Operation: 23-4=19 Exploring Operation: 23-2=21, Resulting Numbers: [4, 21] Generated Node #0,1,1: 16:[4, 21] Operation: 23-2=21 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[2, 19], Operations: ['82/41=2', '23-4=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,16 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[4, 21], Operations: ['82/41=2', '23-2=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[4, 23, 41], Operations: ['82-41=41'] Exploring Operation: 41-23=18, Resulting Numbers: [4, 18] Generated Node #0,0,0: 16:[4, 18] Operation: 41-23=18 Exploring Operation: 23-4=19, Resulting Numbers: [41, 19] Generated Node #0,0,1: 16:[41, 19] Operation: 23-4=19 Moving to Node #0,0,0 Current State: 16:[4, 18], Operations: ['82-41=41', '41-23=18'] Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[41, 19], Operations: ['82-41=41', '23-4=19'] Exploring Operation: 41-19=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 41+19=60, Resulting Numbers: [60] 60,16 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
[ 64, 19, 11, 16 ]
31
[ "19-16=3", "11*3=33", "64-33=31" ]
Current State: 31:[64, 19, 11, 16], Operations: [] Exploring Operation: 19-16=3, Resulting Numbers: [64, 11, 3] Generated Node #2: [64, 11, 3] from Operation: 19-16=3 Current State: 31:[64, 11, 3], Operations: ['19-16=3'] Exploring Operation: 11*3=33, Resulting Numbers: [64, 33] Generated Node #3: [64, 33] from Operation: 11*3=33 Current State: 31:[64, 33], Operations: ['19-16=3', '11*3=33'] Exploring Operation: 64-33=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[64, 19, 11, 16], Operations: [] Exploring Operation: 64-19=45, Resulting Numbers: [11, 16, 45] Generated Node #0,0: 31:[11, 16, 45] Operation: 64-19=45 Exploring Operation: 64-11=53, Resulting Numbers: [19, 16, 53] Generated Node #0,1: 31:[19, 16, 53] Operation: 64-11=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[11, 16, 45], Operations: ['64-19=45'] Exploring Operation: 11+16=27, Resulting Numbers: [45, 27] Generated Node #0,0,0: 31:[45, 27] Operation: 11+16=27 Exploring Operation: 45-11=34, Resulting Numbers: [16, 34] Generated Node #0,0,1: 31:[16, 34] Operation: 45-11=34 Moving to Node #0,0,0 Current State: 31:[45, 27], Operations: ['64-19=45', '11+16=27'] Exploring Operation: 45+27=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[16, 34], Operations: ['64-19=45', '45-11=34'] Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[19, 16, 53], Operations: ['64-11=53'] Exploring Operation: 53-19=34, Resulting Numbers: [16, 34] Generated Node #0,1,0: 31:[16, 34] Operation: 53-19=34 Exploring Operation: 53-16=37, Resulting Numbers: [19, 37] Generated Node #0,1,1: 31:[19, 37] Operation: 53-16=37 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 31:[16, 34], Operations: ['64-11=53', '53-19=34'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,31 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: 31:[19, 37], Operations: ['64-11=53', '53-16=37'] Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 19+37=56, Resulting Numbers: [56] 56,31 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
[ 83, 84, 58, 41 ]
29
[ "83-41=42", "84/42=2", "58/2=29" ]
Current State: 29:[83, 84, 58, 41], Operations: [] Exploring Operation: 83-41=42, Resulting Numbers: [84, 58, 42] Generated Node #2: [84, 58, 42] from Operation: 83-41=42 Current State: 29:[84, 58, 42], Operations: ['83-41=42'] Exploring Operation: 84/42=2, Resulting Numbers: [58, 2] Generated Node #3: [58, 2] from Operation: 84/42=2 Current State: 29:[58, 2], Operations: ['83-41=42', '84/42=2'] Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[83, 84, 58, 41], Operations: [] Exploring Operation: 84-83=1, Resulting Numbers: [58, 41, 1] Generated Node #0,0: 29:[58, 41, 1] Operation: 84-83=1 Exploring Operation: 84-58=26, Resulting Numbers: [83, 41, 26] Generated Node #0,1: 29:[83, 41, 26] Operation: 84-58=26 Moving to Node #0,0 Current State: 29:[58, 41, 1], Operations: ['84-83=1'] Exploring Operation: 58-41=17, Resulting Numbers: [1, 17] Generated Node #0,0,0: 29:[1, 17] Operation: 58-41=17 Exploring Operation: 58-1=57, Resulting Numbers: [41, 57] Generated Node #0,0,1: 29:[41, 57] Operation: 58-1=57 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[1, 17], Operations: ['84-83=1', '58-41=17'] Exploring Operation: 1+17=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 1*17=17, Resulting Numbers: [17] 17,29 unequal: No Solution No 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: 29:[41, 57], Operations: ['84-83=1', '58-1=57'] Exploring Operation: 41+57=98, Resulting Numbers: [98] 98,29 unequal: No Solution Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,29 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: 29:[83, 41, 26], Operations: ['84-58=26'] Exploring Operation: 83-26=57, Resulting Numbers: [41, 57] Generated Node #0,1,0: 29:[41, 57] Operation: 83-26=57 Exploring Operation: 83-41=42, Resulting Numbers: [26, 42] Generated Node #0,1,1: 29:[26, 42] Operation: 83-41=42 Moving to Node #0,1,1 Current State: 29:[26, 42], Operations: ['84-58=26', '83-41=42'] Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,29 unequal: No Solution Exploring Operation: 26+42=68, Resulting Numbers: [68] 68,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[41, 57], Operations: ['84-58=26', '83-26=57'] Exploring Operation: 41+57=98, Resulting Numbers: [98] 98,29 unequal: No Solution Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,29 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 38, 72, 4, 30 ]
35
[ "38+72=110", "30+110=140", "140/4=35" ]
Current State: 35:[38, 72, 4, 30], Operations: [] Exploring Operation: 38+72=110, Resulting Numbers: [4, 30, 110] Generated Node #2: [4, 30, 110] from Operation: 38+72=110 Current State: 35:[4, 30, 110], Operations: ['38+72=110'] Exploring Operation: 30+110=140, Resulting Numbers: [4, 140] Generated Node #3: [4, 140] from Operation: 30+110=140 Current State: 35:[4, 140], Operations: ['38+72=110', '30+110=140'] Exploring Operation: 140/4=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[38, 72, 4, 30], Operations: [] Exploring Operation: 72/4=18, Resulting Numbers: [38, 30, 18] Generated Node #0,0: 35:[38, 30, 18] Operation: 72/4=18 Exploring Operation: 72-30=42, Resulting Numbers: [38, 4, 42] Generated Node #0,1: 35:[38, 4, 42] Operation: 72-30=42 Exploring Operation: 72-38=34, Resulting Numbers: [4, 30, 34] Generated Node #0,2: 35:[4, 30, 34] Operation: 72-38=34 Exploring Operation: 38-30=8, Resulting Numbers: [72, 4, 8] Generated Node #0,3: 35:[72, 4, 8] Operation: 38-30=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[4, 30, 34], Operations: ['72-38=34'] Exploring Operation: 30-4=26, Resulting Numbers: [34, 26] Generated Node #0,2,0: 35:[34, 26] Operation: 30-4=26 Exploring Operation: 34-30=4, Resulting Numbers: [4, 4] Generated Node #0,2,1: 35:[4, 4] Operation: 34-30=4 Exploring Operation: 4+30=34, Resulting Numbers: [34, 34] Generated Node #0,2,2: 35:[34, 34] Operation: 4+30=34 Exploring Operation: 4+34=38, Resulting Numbers: [30, 38] Generated Node #0,2,3: 35:[30, 38] Operation: 4+34=38 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 35:[4, 4], Operations: ['72-38=34', '34-30=4'] Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,35 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: 35:[34, 34], Operations: ['72-38=34', '4+30=34'] Exploring Operation: 34/34=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 34*34=1156, Resulting Numbers: [1156] 1156,35 unequal: No Solution Exploring Operation: 34-34=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 34+34=68, Resulting Numbers: [68] 68,35 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: 35:[30, 38], Operations: ['72-38=34', '4+34=38'] Exploring Operation: 30+38=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 30*38=1140, Resulting Numbers: [1140] 1140,35 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: 35:[34, 26], Operations: ['72-38=34', '30-4=26'] Exploring Operation: 34*26=884, Resulting Numbers: [884] 884,35 unequal: No Solution Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 34+26=60, Resulting Numbers: [60] 60,35 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: 35:[38, 4, 42], Operations: ['72-30=42'] Exploring Operation: 42-38=4, Resulting Numbers: [4, 4] Generated Node #0,1,0: 35:[4, 4] Operation: 42-38=4 Exploring Operation: 42-4=38, Resulting Numbers: [38, 38] Generated Node #0,1,1: 35:[38, 38] Operation: 42-4=38 Exploring Operation: 38-4=34, Resulting Numbers: [42, 34] Generated Node #0,1,2: 35:[42, 34] Operation: 38-4=34 Exploring Operation: 38+4=42, Resulting Numbers: [42, 42] Generated Node #0,1,3: 35:[42, 42] Operation: 38+4=42 Moving to Node #0,1,0 Current State: 35:[4, 4], Operations: ['72-30=42', '42-38=4'] Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[38, 38], Operations: ['72-30=42', '42-4=38'] Exploring Operation: 38*38=1444, Resulting Numbers: [1444] 1444,35 unequal: No Solution Exploring Operation: 38/38=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 38+38=76, Resulting Numbers: [76] 76,35 unequal: No Solution Exploring Operation: 38-38=0, Resulting Numbers: [0] 0,35 unequal: No Solution Moving to Node #0,1,2 Current State: 35:[42, 34], Operations: ['72-30=42', '38-4=34'] Exploring Operation: 42+34=76, Resulting Numbers: [76] 76,35 unequal: No Solution Exploring Operation: 42*34=1428, Resulting Numbers: [1428] 1428,35 unequal: No Solution Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,35 unequal: No Solution Moving to Node #0,1,3 Current State: 35:[42, 42], Operations: ['72-30=42', '38+4=42'] Exploring Operation: 42+42=84, Resulting Numbers: [84] 84,35 unequal: No Solution Exploring Operation: 42/42=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 42*42=1764, Resulting Numbers: [1764] 1764,35 unequal: No Solution Exploring Operation: 42-42=0, Resulting Numbers: [0] 0,35 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 #0,0 Current State: 35:[38, 30, 18], Operations: ['72/4=18'] Exploring Operation: 38-30=8, Resulting Numbers: [18, 8] Generated Node #0,0,0: 35:[18, 8] Operation: 38-30=8 Exploring Operation: 30+18=48, Resulting Numbers: [38, 48] Generated Node #0,0,1: 35:[38, 48] Operation: 30+18=48 Exploring Operation: 38-18=20, Resulting Numbers: [30, 20] Generated Node #0,0,2: 35:[30, 20] Operation: 38-18=20 Exploring Operation: 30-18=12, Resulting Numbers: [38, 12] Generated Node #0,0,3: 35:[38, 12] Operation: 30-18=12 Moving to Node #0,0,3 Current State: 35:[38, 12], Operations: ['72/4=18', '30-18=12'] Exploring Operation: 38-12=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 38*12=456, Resulting Numbers: [456] 456,35 unequal: No Solution Exploring Operation: 38+12=50, Resulting Numbers: [50] 50,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[18, 8], Operations: ['72/4=18', '38-30=8'] Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,35 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[38, 48], Operations: ['72/4=18', '30+18=48'] Exploring Operation: 38+48=86, Resulting Numbers: [86] 86,35 unequal: No Solution Exploring Operation: 38*48=1824, Resulting Numbers: [1824] 1824,35 unequal: No Solution Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,35 unequal: No Solution Moving to Node #0,0,2 Current State: 35:[30, 20], Operations: ['72/4=18', '38-18=20'] Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,35 unequal: No Solution Exploring Operation: 30*20=600, Resulting Numbers: [600] 600,35 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,35 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 Current State: 35:[72, 4, 8], Operations: ['38-30=8'] Exploring Operation: 72-8=64, Resulting Numbers: [4, 64] Generated Node #0,3,0: 35:[4, 64] Operation: 72-8=64 Exploring Operation: 72-4=68, Resulting Numbers: [8, 68] Generated Node #0,3,1: 35:[8, 68] Operation: 72-4=68 Exploring Operation: 72/4=18, Resulting Numbers: [8, 18] Generated Node #0,3,2: 35:[8, 18] Operation: 72/4=18 Exploring Operation: 72/8=9, Resulting Numbers: [4, 9] Generated Node #0,3,3: 35:[4, 9] Operation: 72/8=9 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 35:[4, 9], Operations: ['38-30=8', '72/8=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,35 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,35 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: 35:[8, 18], Operations: ['38-30=8', '72/4=18'] Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,35 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,35 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: 35:[4, 64], Operations: ['38-30=8', '72-8=64'] Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 4*64=256, Resulting Numbers: [256] 256,35 unequal: No Solution Exploring Operation: 4+64=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,35 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: 35:[8, 68], Operations: ['38-30=8', '72-4=68'] Exploring Operation: 68-8=60, Resulting Numbers: [60] 60,35 unequal: No Solution Exploring Operation: 8*68=544, Resulting Numbers: [544] 544,35 unequal: No Solution Exploring Operation: 8+68=76, Resulting Numbers: [76] 76,35 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
[ 55, 84, 52, 34 ]
57
[ "84-55=29", "52+34=86", "86-29=57" ]
Current State: 57:[55, 84, 52, 34], Operations: [] Exploring Operation: 84-55=29, Resulting Numbers: [52, 34, 29] Generated Node #2: [52, 34, 29] from Operation: 84-55=29 Current State: 57:[52, 34, 29], Operations: ['84-55=29'] Exploring Operation: 52+34=86, Resulting Numbers: [29, 86] Generated Node #3: [29, 86] from Operation: 52+34=86 Current State: 57:[29, 86], Operations: ['84-55=29', '52+34=86'] Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[55, 84, 52, 34], Operations: [] Exploring Operation: 84-55=29, Resulting Numbers: [52, 34, 29] Generated Node #0,0: 57:[52, 34, 29] Operation: 84-55=29 Exploring Operation: 84-52=32, Resulting Numbers: [55, 34, 32] Generated Node #0,1: 57:[55, 34, 32] Operation: 84-52=32 Exploring Operation: 84-34=50, Resulting Numbers: [55, 52, 50] Generated Node #0,2: 57:[55, 52, 50] Operation: 84-34=50 Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[55, 52, 50], Operations: ['84-34=50'] Exploring Operation: 52-50=2, Resulting Numbers: [55, 2] Generated Node #0,2,0: 57:[55, 2] Operation: 52-50=2 Exploring Operation: 55-50=5, Resulting Numbers: [52, 5] Generated Node #0,2,1: 57:[52, 5] Operation: 55-50=5 Exploring Operation: 55-52=3, Resulting Numbers: [50, 3] Generated Node #0,2,2: 57:[50, 3] Operation: 55-52=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 57:[55, 2], Operations: ['84-34=50', '52-50=2'] Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[55, 84, 52, 34], Operations: [] Exploring Operation: 84-34=50, Resulting Numbers: [55, 52, 50] Generated Node #0,2: 57:[55, 52, 50] Operation: 84-34=50 Moving to Node #0,2 Current State: 57:[55, 52, 50], Operations: ['84-34=50'] Exploring Operation: 52-50=2, Resulting Numbers: [55, 2] Generated Node #0,2,0: 57:[55, 2] Operation: 52-50=2 Moving to Node #0,2,0 Current State: 57:[55, 2], Operations: ['84-34=50', '52-50=2'] Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 35, 70, 28, 55 ]
69
[ "70/35=2", "28/2=14", "55+14=69" ]
Current State: 69:[35, 70, 28, 55], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [28, 55, 2] Generated Node #2: [28, 55, 2] from Operation: 70/35=2 Current State: 69:[28, 55, 2], Operations: ['70/35=2'] Exploring Operation: 28/2=14, Resulting Numbers: [55, 14] Generated Node #3: [55, 14] from Operation: 28/2=14 Current State: 69:[55, 14], Operations: ['70/35=2', '28/2=14'] Exploring Operation: 55+14=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[35, 70, 28, 55], Operations: [] Exploring Operation: 55-35=20, Resulting Numbers: [70, 28, 20] Generated Node #0,0: 69:[70, 28, 20] Operation: 55-35=20 Moving to Node #0,0 Current State: 69:[70, 28, 20], Operations: ['55-35=20'] Exploring Operation: 28-20=8, Resulting Numbers: [70, 8] Generated Node #0,0,0: 69:[70, 8] Operation: 28-20=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[70, 8], Operations: ['55-35=20', '28-20=8'] Exploring Operation: 70-8=62, Resulting Numbers: [62] 62,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 10, 16, 16, 53 ]
42
[ "53-10=43", "16/16=1", "43-1=42" ]
Current State: 42:[10, 16, 16, 53], Operations: [] Exploring Operation: 53-10=43, Resulting Numbers: [16, 16, 43] Generated Node #2: [16, 16, 43] from Operation: 53-10=43 Current State: 42:[16, 16, 43], Operations: ['53-10=43'] Exploring Operation: 16/16=1, Resulting Numbers: [43, 1] Generated Node #3: [43, 1] from Operation: 16/16=1 Current State: 42:[43, 1], Operations: ['53-10=43', '16/16=1'] Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[10, 16, 16, 53], Operations: [] Exploring Operation: 53-10=43, Resulting Numbers: [16, 16, 43] Generated Node #0,0: 42:[16, 16, 43] Operation: 53-10=43 Exploring Operation: 16-10=6, Resulting Numbers: [16, 53, 6] Generated Node #0,1: 42:[16, 53, 6] Operation: 16-10=6 Exploring Operation: 53-16=37, Resulting Numbers: [10, 16, 37] Generated Node #0,2: 42:[10, 16, 37] Operation: 53-16=37 Exploring Operation: 16-10=6, Resulting Numbers: [16, 53, 6] Generated Node #0,3: 42:[16, 53, 6] Operation: 16-10=6 Exploring Operation: 53-16=37, Resulting Numbers: [10, 16, 37] Generated Node #0,4: 42:[10, 16, 37] Operation: 53-16=37 Moving to Node #0,0 Current State: 42:[16, 16, 43], Operations: ['53-10=43'] Exploring Operation: 16+16=32, Resulting Numbers: [43, 32] Generated Node #0,0,0: 42:[43, 32] Operation: 16+16=32 Exploring Operation: 43-16=27, Resulting Numbers: [16, 27] Generated Node #0,0,1: 42:[16, 27] Operation: 43-16=27 Exploring Operation: 16/16=1, Resulting Numbers: [43, 1] Generated Node #0,0,2: 42:[43, 1] Operation: 16/16=1 Exploring Operation: 16-16=0, Resulting Numbers: [43, 0] Generated Node #0,0,3: 42:[43, 0] Operation: 16-16=0 Exploring Operation: 43-16=27, Resulting Numbers: [16, 27] Generated Node #0,0,4: 42:[16, 27] Operation: 43-16=27 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 42:[43, 1], Operations: ['53-10=43', '16/16=1'] Exploring Operation: 43+1=44, Resulting Numbers: [44] 44,42 unequal: No Solution Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,42 unequal: No Solution Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[10, 16, 16, 53], Operations: [] Exploring Operation: 53-10=43, Resulting Numbers: [16, 16, 43] Generated Node #0,0: 42:[16, 16, 43] Operation: 53-10=43 Moving to Node #0,0 Current State: 42:[16, 16, 43], Operations: ['53-10=43'] Exploring Operation: 16/16=1, Resulting Numbers: [43, 1] Generated Node #0,0,2: 42:[43, 1] Operation: 16/16=1 Moving to Node #0,0,2 Current State: 42:[43, 1], Operations: ['53-10=43', '16/16=1'] Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 8, 35, 70, 94 ]
90
[ "8*35=280", "280/70=4", "94-4=90" ]
Current State: 90:[8, 35, 70, 94], Operations: [] Exploring Operation: 8*35=280, Resulting Numbers: [70, 94, 280] Generated Node #2: [70, 94, 280] from Operation: 8*35=280 Current State: 90:[70, 94, 280], Operations: ['8*35=280'] Exploring Operation: 280/70=4, Resulting Numbers: [94, 4] Generated Node #3: [94, 4] from Operation: 280/70=4 Current State: 90:[94, 4], Operations: ['8*35=280', '280/70=4'] Exploring Operation: 94-4=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[8, 35, 70, 94], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [8, 94, 2] Generated Node #0,0: 90:[8, 94, 2] Operation: 70/35=2 Exploring Operation: 70-35=35, Resulting Numbers: [8, 94, 35] Generated Node #0,1: 90:[8, 94, 35] Operation: 70-35=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[8, 94, 2], Operations: ['70/35=2'] Exploring Operation: 94-2=92, Resulting Numbers: [8, 92] Generated Node #0,0,0: 90:[8, 92] Operation: 94-2=92 Exploring Operation: 94/2=47, Resulting Numbers: [8, 47] Generated Node #0,0,1: 90:[8, 47] Operation: 94/2=47 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[8, 92], Operations: ['70/35=2', '94-2=92'] Exploring Operation: 8+92=100, Resulting Numbers: [100] 100,90 unequal: No Solution Exploring Operation: 92-8=84, Resulting Numbers: [84] 84,90 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: 90:[8, 47], Operations: ['70/35=2', '94/2=47'] Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,90 unequal: No Solution Exploring Operation: 8+47=55, Resulting Numbers: [55] 55,90 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: 90:[8, 94, 35], Operations: ['70-35=35'] Exploring Operation: 35-8=27, Resulting Numbers: [94, 27] Generated Node #0,1,0: 90:[94, 27] Operation: 35-8=27 Exploring Operation: 8+35=43, Resulting Numbers: [94, 43] Generated Node #0,1,1: 90:[94, 43] Operation: 8+35=43 Moving to Node #0,1,1 Current State: 90:[94, 43], Operations: ['70-35=35', '8+35=43'] Exploring Operation: 94+43=137, Resulting Numbers: [137] 137,90 unequal: No Solution Exploring Operation: 94-43=51, Resulting Numbers: [51] 51,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[94, 27], Operations: ['70-35=35', '35-8=27'] Exploring Operation: 94-27=67, Resulting Numbers: [67] 67,90 unequal: No Solution Exploring Operation: 94+27=121, Resulting Numbers: [121] 121,90 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
[ 6, 26, 74, 40 ]
24
[ "6+74=80", "80/40=2", "26-2=24" ]
Current State: 24:[6, 26, 74, 40], Operations: [] Exploring Operation: 6+74=80, Resulting Numbers: [26, 40, 80] Generated Node #2: [26, 40, 80] from Operation: 6+74=80 Current State: 24:[26, 40, 80], Operations: ['6+74=80'] Exploring Operation: 80/40=2, Resulting Numbers: [26, 2] Generated Node #3: [26, 2] from Operation: 80/40=2 Current State: 24:[26, 2], Operations: ['6+74=80', '80/40=2'] Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[6, 26, 74, 40], Operations: [] Exploring Operation: 74-26=48, Resulting Numbers: [6, 40, 48] Generated Node #0,0: 24:[6, 40, 48] Operation: 74-26=48 Exploring Operation: 74-40=34, Resulting Numbers: [6, 26, 34] Generated Node #0,1: 24:[6, 26, 34] Operation: 74-40=34 Exploring Operation: 40-26=14, Resulting Numbers: [6, 74, 14] Generated Node #0,2: 24:[6, 74, 14] Operation: 40-26=14 Exploring Operation: 40-6=34, Resulting Numbers: [26, 74, 34] Generated Node #0,3: 24:[26, 74, 34] Operation: 40-6=34 Exploring Operation: 74-6=68, Resulting Numbers: [26, 40, 68] Generated Node #0,4: 24:[26, 40, 68] Operation: 74-6=68 Moving to Node #0,1 Current State: 24:[6, 26, 34], Operations: ['74-40=34'] Exploring Operation: 34-6=28, Resulting Numbers: [26, 28] Generated Node #0,1,0: 24:[26, 28] Operation: 34-6=28 Exploring Operation: 6+26=32, Resulting Numbers: [34, 32] Generated Node #0,1,1: 24:[34, 32] Operation: 6+26=32 Exploring Operation: 26-6=20, Resulting Numbers: [34, 20] Generated Node #0,1,2: 24:[34, 20] Operation: 26-6=20 Exploring Operation: 6+34=40, Resulting Numbers: [26, 40] Generated Node #0,1,3: 24:[26, 40] Operation: 6+34=40 Exploring Operation: 34-26=8, Resulting Numbers: [6, 8] Generated Node #0,1,4: 24:[6, 8] Operation: 34-26=8 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 24:[6, 8], Operations: ['74-40=34', '34-26=8'] Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,24 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[26, 28], Operations: ['74-40=34', '34-6=28'] Exploring Operation: 26*28=728, Resulting Numbers: [728] 728,24 unequal: No Solution Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[34, 20], Operations: ['74-40=34', '26-6=20'] Exploring Operation: 34+20=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 34*20=680, Resulting Numbers: [680] 680,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 24:[34, 32], Operations: ['74-40=34', '6+26=32'] Exploring Operation: 34*32=1088, Resulting Numbers: [1088] 1088,24 unequal: No Solution Exploring Operation: 34+32=66, Resulting Numbers: [66] 66,24 unequal: No Solution Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 24:[26, 40], Operations: ['74-40=34', '6+34=40'] Exploring Operation: 26+40=66, Resulting Numbers: [66] 66,24 unequal: No Solution Exploring Operation: 26*40=1040, Resulting Numbers: [1040] 1040,24 unequal: No Solution Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 24:[6, 40, 48], Operations: ['74-26=48'] Exploring Operation: 48-40=8, Resulting Numbers: [6, 8] Generated Node #0,0,0: 24:[6, 8] Operation: 48-40=8 Exploring Operation: 48/6=8, Resulting Numbers: [40, 8] Generated Node #0,0,1: 24:[40, 8] Operation: 48/6=8 Exploring Operation: 48-6=42, Resulting Numbers: [40, 42] Generated Node #0,0,2: 24:[40, 42] Operation: 48-6=42 Exploring Operation: 40-6=34, Resulting Numbers: [48, 34] Generated Node #0,0,3: 24:[48, 34] Operation: 40-6=34 Exploring Operation: 6+40=46, Resulting Numbers: [48, 46] Generated Node #0,0,4: 24:[48, 46] Operation: 6+40=46 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 24:[6, 8], Operations: ['74-26=48', '48-40=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[40, 8], Operations: ['74-26=48', '48/6=8'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 40*8=320, Resulting Numbers: [320] 320,24 unequal: No Solution Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,24 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 24:[40, 42], Operations: ['74-26=48', '48-6=42'] Exploring Operation: 40*42=1680, Resulting Numbers: [1680] 1680,24 unequal: No Solution Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 40+42=82, Resulting Numbers: [82] 82,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 24:[48, 34], Operations: ['74-26=48', '40-6=34'] Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 48+34=82, Resulting Numbers: [82] 82,24 unequal: No Solution Exploring Operation: 48*34=1632, Resulting Numbers: [1632] 1632,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 24:[48, 46], Operations: ['74-26=48', '6+40=46'] Exploring Operation: 48-46=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 48*46=2208, Resulting Numbers: [2208] 2208,24 unequal: No Solution Exploring Operation: 48+46=94, Resulting Numbers: [94] 94,24 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: 24:[6, 74, 14], Operations: ['40-26=14'] Exploring Operation: 74-6=68, Resulting Numbers: [14, 68] Generated Node #0,2,0: 24:[14, 68] Operation: 74-6=68 Exploring Operation: 74-14=60, Resulting Numbers: [6, 60] Generated Node #0,2,1: 24:[6, 60] Operation: 74-14=60 Exploring Operation: 14-6=8, Resulting Numbers: [74, 8] Generated Node #0,2,2: 24:[74, 8] Operation: 14-6=8 Exploring Operation: 6+14=20, Resulting Numbers: [74, 20] Generated Node #0,2,3: 24:[74, 20] Operation: 6+14=20 Exploring Operation: 6+74=80, Resulting Numbers: [14, 80] Generated Node #0,2,4: 24:[14, 80] Operation: 6+74=80 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 24:[6, 60], Operations: ['40-26=14', '74-14=60'] Exploring Operation: 6+60=66, Resulting Numbers: [66] 66,24 unequal: No Solution Exploring Operation: 6*60=360, Resulting Numbers: [360] 360,24 unequal: No Solution Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 24:[14, 68], Operations: ['40-26=14', '74-6=68'] Exploring Operation: 14*68=952, Resulting Numbers: [952] 952,24 unequal: No Solution Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 14+68=82, Resulting Numbers: [82] 82,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 24:[74, 8], Operations: ['40-26=14', '14-6=8'] Exploring Operation: 74+8=82, Resulting Numbers: [82] 82,24 unequal: No Solution Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,24 unequal: No Solution Exploring Operation: 74*8=592, Resulting Numbers: [592] 592,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 24:[74, 20], Operations: ['40-26=14', '6+14=20'] Exploring Operation: 74+20=94, Resulting Numbers: [94] 94,24 unequal: No Solution Exploring Operation: 74*20=1480, Resulting Numbers: [1480] 1480,24 unequal: No Solution Exploring Operation: 74-20=54, Resulting Numbers: [54] 54,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 24:[14, 80], Operations: ['40-26=14', '6+74=80'] Exploring Operation: 14+80=94, Resulting Numbers: [94] 94,24 unequal: No Solution Exploring Operation: 14*80=1120, Resulting Numbers: [1120] 1120,24 unequal: No Solution Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,24 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: 24:[26, 74, 34], Operations: ['40-6=34'] Exploring Operation: 74-34=40, Resulting Numbers: [26, 40] Generated Node #0,3,0: 24:[26, 40] Operation: 74-34=40 Exploring Operation: 74-26=48, Resulting Numbers: [34, 48] Generated Node #0,3,1: 24:[34, 48] Operation: 74-26=48 Exploring Operation: 26+34=60, Resulting Numbers: [74, 60] Generated Node #0,3,2: 24:[74, 60] Operation: 26+34=60 Exploring Operation: 26+74=100, Resulting Numbers: [34, 100] Generated Node #0,3,3: 24:[34, 100] Operation: 26+74=100 Exploring Operation: 34-26=8, Resulting Numbers: [74, 8] Generated Node #0,3,4: 24:[74, 8] Operation: 34-26=8 Moving to Node #0,4 Current State: 24:[26, 40, 68], Operations: ['74-6=68'] Exploring Operation: 68-40=28, Resulting Numbers: [26, 28] Generated Node #0,4,0: 24:[26, 28] Operation: 68-40=28 Exploring Operation: 68-26=42, Resulting Numbers: [40, 42] Generated Node #0,4,1: 24:[40, 42] Operation: 68-26=42 Exploring Operation: 26+40=66, Resulting Numbers: [68, 66] Generated Node #0,4,2: 24:[68, 66] Operation: 26+40=66 Exploring Operation: 40-26=14, Resulting Numbers: [68, 14] Generated Node #0,4,3: 24:[68, 14] Operation: 40-26=14 Exploring Operation: 26+68=94, Resulting Numbers: [40, 94] Generated Node #0,4,4: 24:[40, 94] Operation: 26+68=94 Moving to Node #0,4,0 Current State: 24:[26, 28], Operations: ['74-6=68', '68-40=28'] Exploring Operation: 26*28=728, Resulting Numbers: [728] 728,24 unequal: No Solution Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,24 unequal: No Solution Moving to Node #0,3,0 Current State: 24:[26, 40], Operations: ['40-6=34', '74-34=40'] Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 26+40=66, Resulting Numbers: [66] 66,24 unequal: No Solution Exploring Operation: 26*40=1040, Resulting Numbers: [1040] 1040,24 unequal: No Solution Moving to Node #0,4,1 Current State: 24:[40, 42], Operations: ['74-6=68', '68-26=42'] Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 40+42=82, Resulting Numbers: [82] 82,24 unequal: No Solution Exploring Operation: 40*42=1680, Resulting Numbers: [1680] 1680,24 unequal: No Solution Moving to Node #0,3,1 Current State: 24:[34, 48], Operations: ['40-6=34', '74-26=48'] Exploring Operation: 34+48=82, Resulting Numbers: [82] 82,24 unequal: No Solution Exploring Operation: 34*48=1632, Resulting Numbers: [1632] 1632,24 unequal: No Solution Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,24 unequal: No Solution Moving to Node #0,4,3 Current State: 24:[68, 14], Operations: ['74-6=68', '40-26=14'] Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 68+14=82, Resulting Numbers: [82] 82,24 unequal: No Solution Exploring Operation: 68*14=952, Resulting Numbers: [952] 952,24 unequal: No Solution Moving to Node #0,3,4 Current State: 24:[74, 8], Operations: ['40-6=34', '34-26=8'] Exploring Operation: 74*8=592, Resulting Numbers: [592] 592,24 unequal: No Solution Exploring Operation: 74+8=82, Resulting Numbers: [82] 82,24 unequal: No Solution Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,24 unequal: No Solution Moving to Node #0,4,2 Current State: 24:[68, 66], Operations: ['74-6=68', '26+40=66'] Exploring Operation: 68*66=4488, Resulting Numbers: [4488] 4488,24 unequal: No Solution Exploring Operation: 68+66=134, Resulting Numbers: [134] 134,24 unequal: No Solution Exploring Operation: 68-66=2, Resulting Numbers: [2] 2,24 unequal: No Solution Moving to Node #0,4,4 Current State: 24:[40, 94], Operations: ['74-6=68', '26+68=94'] Exploring Operation: 40+94=134, Resulting Numbers: [134] 134,24 unequal: No Solution Exploring Operation: 94-40=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 40*94=3760, Resulting Numbers: [3760] 3760,24 unequal: No Solution Moving to Node #0,3,3 Current State: 24:[34, 100], Operations: ['40-6=34', '26+74=100'] Exploring Operation: 34+100=134, Resulting Numbers: [134] 134,24 unequal: No Solution Exploring Operation: 34*100=3400, Resulting Numbers: [3400] 3400,24 unequal: No Solution Exploring Operation: 100-34=66, Resulting Numbers: [66] 66,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[74, 60], Operations: ['40-6=34', '26+34=60'] Exploring Operation: 74+60=134, Resulting Numbers: [134] 134,24 unequal: No Solution Exploring Operation: 74-60=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 74*60=4440, Resulting Numbers: [4440] 4440,24 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 50, 5, 4, 21 ]
96
[ "50-5=45", "45-21=24", "4*24=96" ]
Current State: 96:[50, 5, 4, 21], Operations: [] Exploring Operation: 50-5=45, Resulting Numbers: [4, 21, 45] Generated Node #2: [4, 21, 45] from Operation: 50-5=45 Current State: 96:[4, 21, 45], Operations: ['50-5=45'] Exploring Operation: 45-21=24, Resulting Numbers: [4, 24] Generated Node #3: [4, 24] from Operation: 45-21=24 Current State: 96:[4, 24], Operations: ['50-5=45', '45-21=24'] Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[50, 5, 4, 21], Operations: [] Exploring Operation: 50-21=29, Resulting Numbers: [5, 4, 29] Generated Node #0,0: 96:[5, 4, 29] Operation: 50-21=29 Exploring Operation: 21-5=16, Resulting Numbers: [50, 4, 16] Generated Node #0,1: 96:[50, 4, 16] Operation: 21-5=16 Moving to Node #0,1 Current State: 96:[50, 4, 16], Operations: ['21-5=16'] Exploring Operation: 50-16=34, Resulting Numbers: [4, 34] Generated Node #0,1,0: 96:[4, 34] Operation: 50-16=34 Exploring Operation: 50-4=46, Resulting Numbers: [16, 46] Generated Node #0,1,1: 96:[16, 46] Operation: 50-4=46 Moving to Node #0,0 Current State: 96:[5, 4, 29], Operations: ['50-21=29'] Exploring Operation: 29-5=24, Resulting Numbers: [4, 24] Generated Node #0,0,0: 96:[4, 24] Operation: 29-5=24 Exploring Operation: 5+29=34, Resulting Numbers: [4, 34] Generated Node #0,0,1: 96:[4, 34] Operation: 5+29=34 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[4, 24], Operations: ['50-21=29', '29-5=24'] Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,96 unequal: No Solution Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[50, 5, 4, 21], Operations: [] Exploring Operation: 50-21=29, Resulting Numbers: [5, 4, 29] Generated Node #0,0: 96:[5, 4, 29] Operation: 50-21=29 Moving to Node #0,0 Current State: 96:[5, 4, 29], Operations: ['50-21=29'] Exploring Operation: 29-5=24, Resulting Numbers: [4, 24] Generated Node #0,0,0: 96:[4, 24] Operation: 29-5=24 Moving to Node #0,0,0 Current State: 96:[4, 24], Operations: ['50-21=29', '29-5=24'] Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 18, 9, 28, 61 ]
24
[ "18-9=9", "61-28=33", "33-9=24" ]
Current State: 24:[18, 9, 28, 61], Operations: [] Exploring Operation: 18-9=9, Resulting Numbers: [28, 61, 9] Generated Node #2: [28, 61, 9] from Operation: 18-9=9 Current State: 24:[28, 61, 9], Operations: ['18-9=9'] Exploring Operation: 61-28=33, Resulting Numbers: [9, 33] Generated Node #3: [9, 33] from Operation: 61-28=33 Current State: 24:[9, 33], Operations: ['18-9=9', '61-28=33'] Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[18, 9, 28, 61], Operations: [] Exploring Operation: 61-28=33, Resulting Numbers: [18, 9, 33] Generated Node #0,0: 24:[18, 9, 33] Operation: 61-28=33 Exploring Operation: 61-18=43, Resulting Numbers: [9, 28, 43] Generated Node #0,1: 24:[9, 28, 43] Operation: 61-18=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[18, 9, 33], Operations: ['61-28=33'] Exploring Operation: 33-9=24, Resulting Numbers: [18, 24] Generated Node #0,0,0: 24:[18, 24] Operation: 33-9=24 Exploring Operation: 33-18=15, Resulting Numbers: [9, 15] Generated Node #0,0,1: 24:[9, 15] Operation: 33-18=15 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 24:[9, 15], Operations: ['61-28=33', '33-18=15'] Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[18, 9, 28, 61], Operations: [] Exploring Operation: 61-28=33, Resulting Numbers: [18, 9, 33] Generated Node #0,0: 24:[18, 9, 33] Operation: 61-28=33 Moving to Node #0,0 Current State: 24:[18, 9, 33], Operations: ['61-28=33'] Exploring Operation: 33-18=15, Resulting Numbers: [9, 15] Generated Node #0,0,1: 24:[9, 15] Operation: 33-18=15 Moving to Node #0,0,1 Current State: 24:[9, 15], Operations: ['61-28=33', '33-18=15'] Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 1, 58, 13, 3 ]
68
[ "1*58=58", "13-3=10", "58+10=68" ]
Current State: 68:[1, 58, 13, 3], Operations: [] Exploring Operation: 1*58=58, Resulting Numbers: [13, 3, 58] Generated Node #2: [13, 3, 58] from Operation: 1*58=58 Current State: 68:[13, 3, 58], Operations: ['1*58=58'] Exploring Operation: 13-3=10, Resulting Numbers: [58, 10] Generated Node #3: [58, 10] from Operation: 13-3=10 Current State: 68:[58, 10], Operations: ['1*58=58', '13-3=10'] Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[1, 58, 13, 3], Operations: [] Exploring Operation: 13+3=16, Resulting Numbers: [1, 58, 16] Generated Node #0,0: 68:[1, 58, 16] Operation: 13+3=16 Exploring Operation: 58+3=61, Resulting Numbers: [1, 13, 61] Generated Node #0,1: 68:[1, 13, 61] Operation: 58+3=61 Exploring Operation: 58+13=71, Resulting Numbers: [1, 3, 71] Generated Node #0,2: 68:[1, 3, 71] Operation: 58+13=71 Moving to Node #0,2 Current State: 68:[1, 3, 71], Operations: ['58+13=71'] Exploring Operation: 1+3=4, Resulting Numbers: [71, 4] Generated Node #0,2,0: 68:[71, 4] Operation: 1+3=4 Exploring Operation: 71-3=68, Resulting Numbers: [1, 68] Generated Node #0,2,1: 68:[1, 68] Operation: 71-3=68 Exploring Operation: 3-1=2, Resulting Numbers: [71, 2] Generated Node #0,2,2: 68:[71, 2] Operation: 3-1=2 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 68:[1, 68], Operations: ['58+13=71', '71-3=68'] Exploring Operation: 1+68=69, Resulting Numbers: [69] 69,68 unequal: No Solution Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[1, 58, 13, 3], Operations: [] Exploring Operation: 58+13=71, Resulting Numbers: [1, 3, 71] Generated Node #0,2: 68:[1, 3, 71] Operation: 58+13=71 Moving to Node #0,2 Current State: 68:[1, 3, 71], Operations: ['58+13=71'] Exploring Operation: 71-3=68, Resulting Numbers: [1, 68] Generated Node #0,2,1: 68:[1, 68] Operation: 71-3=68 Moving to Node #0,2,1 Current State: 68:[1, 68], Operations: ['58+13=71', '71-3=68'] Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 90, 78, 45, 50 ]
72
[ "78*45=3510", "90+3510=3600", "3600/50=72" ]
Current State: 72:[90, 78, 45, 50], Operations: [] Exploring Operation: 78*45=3510, Resulting Numbers: [90, 50, 3510] Generated Node #2: [90, 50, 3510] from Operation: 78*45=3510 Current State: 72:[90, 50, 3510], Operations: ['78*45=3510'] Exploring Operation: 90+3510=3600, Resulting Numbers: [50, 3600] Generated Node #3: [50, 3600] from Operation: 90+3510=3600 Current State: 72:[50, 3600], Operations: ['78*45=3510', '90+3510=3600'] Exploring Operation: 3600/50=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[90, 78, 45, 50], Operations: [] Exploring Operation: 90-50=40, Resulting Numbers: [78, 45, 40] Generated Node #0,0: 72:[78, 45, 40] Operation: 90-50=40 Moving to Node #0,0 Current State: 72:[78, 45, 40], Operations: ['90-50=40'] Exploring Operation: 78-45=33, Resulting Numbers: [40, 33] Generated Node #0,0,0: 72:[40, 33] Operation: 78-45=33 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[40, 33], Operations: ['90-50=40', '78-45=33'] Exploring Operation: 40+33=73, Resulting Numbers: [73] 73,72 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
[ 42, 84, 60, 7 ]
95
[ "84-42=42", "60-7=53", "42+53=95" ]
Current State: 95:[42, 84, 60, 7], Operations: [] Exploring Operation: 84-42=42, Resulting Numbers: [60, 7, 42] Generated Node #2: [60, 7, 42] from Operation: 84-42=42 Current State: 95:[60, 7, 42], Operations: ['84-42=42'] Exploring Operation: 60-7=53, Resulting Numbers: [42, 53] Generated Node #3: [42, 53] from Operation: 60-7=53 Current State: 95:[42, 53], Operations: ['84-42=42', '60-7=53'] Exploring Operation: 42+53=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[42, 84, 60, 7], Operations: [] Exploring Operation: 84-60=24, Resulting Numbers: [42, 7, 24] Generated Node #0,0: 95:[42, 7, 24] Operation: 84-60=24 Exploring Operation: 60-42=18, Resulting Numbers: [84, 7, 18] Generated Node #0,1: 95:[84, 7, 18] Operation: 60-42=18 Exploring Operation: 42+60=102, Resulting Numbers: [84, 7, 102] Generated Node #0,2: 95:[84, 7, 102] Operation: 42+60=102 Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[84, 7, 18], Operations: ['60-42=18'] Exploring Operation: 84+7=91, Resulting Numbers: [18, 91] Generated Node #0,1,0: 95:[18, 91] Operation: 84+7=91 Exploring Operation: 84+18=102, Resulting Numbers: [7, 102] Generated Node #0,1,1: 95:[7, 102] Operation: 84+18=102 Exploring Operation: 84/7=12, Resulting Numbers: [18, 12] Generated Node #0,1,2: 95:[18, 12] Operation: 84/7=12 Moving to Node #0,1,0 Current State: 95:[18, 91], Operations: ['60-42=18', '84+7=91'] Exploring Operation: 18*91=1638, Resulting Numbers: [1638] 1638,95 unequal: No Solution Exploring Operation: 91-18=73, Resulting Numbers: [73] 73,95 unequal: No Solution Exploring Operation: 18+91=109, Resulting Numbers: [109] 109,95 unequal: No Solution Moving to Node #0,1,2 Current State: 95:[18, 12], Operations: ['60-42=18', '84/7=12'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,95 unequal: No Solution Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,95 unequal: No Solution Exploring Operation: 18*12=216, Resulting Numbers: [216] 216,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[7, 102], Operations: ['60-42=18', '84+18=102'] Exploring Operation: 102-7=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[42, 84, 60, 7], Operations: [] Exploring Operation: 60-42=18, Resulting Numbers: [84, 7, 18] Generated Node #0,1: 95:[84, 7, 18] Operation: 60-42=18 Moving to Node #0,1 Current State: 95:[84, 7, 18], Operations: ['60-42=18'] Exploring Operation: 84+18=102, Resulting Numbers: [7, 102] Generated Node #0,1,1: 95:[7, 102] Operation: 84+18=102 Moving to Node #0,1,1 Current State: 95:[7, 102], Operations: ['60-42=18', '84+18=102'] Exploring Operation: 102-7=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 79, 30, 3, 65 ]
38
[ "79-30=49", "65+49=114", "114/3=38" ]
Current State: 38:[79, 30, 3, 65], Operations: [] Exploring Operation: 79-30=49, Resulting Numbers: [3, 65, 49] Generated Node #2: [3, 65, 49] from Operation: 79-30=49 Current State: 38:[3, 65, 49], Operations: ['79-30=49'] Exploring Operation: 65+49=114, Resulting Numbers: [3, 114] Generated Node #3: [3, 114] from Operation: 65+49=114 Current State: 38:[3, 114], Operations: ['79-30=49', '65+49=114'] Exploring Operation: 114/3=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[79, 30, 3, 65], Operations: [] Exploring Operation: 79-65=14, Resulting Numbers: [30, 3, 14] Generated Node #0,0: 38:[30, 3, 14] Operation: 79-65=14 Exploring Operation: 79-30=49, Resulting Numbers: [3, 65, 49] Generated Node #0,1: 38:[3, 65, 49] Operation: 79-30=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[30, 3, 14], Operations: ['79-65=14'] Exploring Operation: 30+14=44, Resulting Numbers: [3, 44] Generated Node #0,0,0: 38:[3, 44] Operation: 30+14=44 Exploring Operation: 30-14=16, Resulting Numbers: [3, 16] Generated Node #0,0,1: 38:[3, 16] Operation: 30-14=16 Moving to Node #0,0,1 Current State: 38:[3, 16], Operations: ['79-65=14', '30-14=16'] Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[3, 44], Operations: ['79-65=14', '30+14=44'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,38 unequal: No Solution Exploring Operation: 3+44=47, Resulting Numbers: [47] 47,38 unequal: No Solution No 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:[3, 65, 49], Operations: ['79-30=49'] Exploring Operation: 65-3=62, Resulting Numbers: [49, 62] Generated Node #0,1,0: 38:[49, 62] Operation: 65-3=62 Exploring Operation: 65-49=16, Resulting Numbers: [3, 16] Generated Node #0,1,1: 38:[3, 16] Operation: 65-49=16 Moving to Node #0,1,1 Current State: 38:[3, 16], Operations: ['79-30=49', '65-49=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,38 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[49, 62], Operations: ['79-30=49', '65-3=62'] Exploring Operation: 49+62=111, Resulting Numbers: [111] 111,38 unequal: No Solution Exploring Operation: 62-49=13, Resulting Numbers: [13] 13,38 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
[ 18, 42, 7, 32 ]
40
[ "32-18=14", "14/7=2", "42-2=40" ]
Current State: 40:[18, 42, 7, 32], Operations: [] Exploring Operation: 32-18=14, Resulting Numbers: [42, 7, 14] Generated Node #2: [42, 7, 14] from Operation: 32-18=14 Current State: 40:[42, 7, 14], Operations: ['32-18=14'] Exploring Operation: 14/7=2, Resulting Numbers: [42, 2] Generated Node #3: [42, 2] from Operation: 14/7=2 Current State: 40:[42, 2], Operations: ['32-18=14', '14/7=2'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[18, 42, 7, 32], Operations: [] Exploring Operation: 7+32=39, Resulting Numbers: [18, 42, 39] Generated Node #0,0: 40:[18, 42, 39] Operation: 7+32=39 Exploring Operation: 42-32=10, Resulting Numbers: [18, 7, 10] Generated Node #0,1: 40:[18, 7, 10] Operation: 42-32=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[18, 7, 10], Operations: ['42-32=10'] Exploring Operation: 18-7=11, Resulting Numbers: [10, 11] Generated Node #0,1,0: 40:[10, 11] Operation: 18-7=11 Exploring Operation: 18-10=8, Resulting Numbers: [7, 8] Generated Node #0,1,1: 40:[7, 8] Operation: 18-10=8 Moving to Node #0,1,0 Current State: 40:[10, 11], Operations: ['42-32=10', '18-7=11'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,40 unequal: No Solution Moving to Node #0,1,1 Current State: 40:[7, 8], Operations: ['42-32=10', '18-10=8'] Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,40 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,40 unequal: No Solution No 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: 40:[18, 42, 39], Operations: ['7+32=39'] Exploring Operation: 42-39=3, Resulting Numbers: [18, 3] Generated Node #0,0,0: 40:[18, 3] Operation: 42-39=3 Exploring Operation: 39-18=21, Resulting Numbers: [42, 21] Generated Node #0,0,1: 40:[42, 21] Operation: 39-18=21 Moving to Node #0,0,0 Current State: 40:[18, 3], Operations: ['7+32=39', '42-39=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,40 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[42, 21], Operations: ['7+32=39', '39-18=21'] Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,40 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
[ 89, 38, 75, 89 ]
65
[ "89-38=51", "89-75=14", "51+14=65" ]
Current State: 65:[89, 38, 75, 89], Operations: [] Exploring Operation: 89-38=51, Resulting Numbers: [75, 51] Generated Node #2: [75, 51] from Operation: 89-38=51 Current State: 65:[75, 51], Operations: ['89-38=51'] Exploring Operation: 89-75=14, Resulting Numbers: [51, 14] Generated Node #3: [51, 14] from Operation: 89-75=14 Current State: 65:[51, 14], Operations: ['89-38=51', '89-75=14'] Exploring Operation: 51+14=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[89, 38, 75, 89], Operations: [] Exploring Operation: 89/89=1, Resulting Numbers: [38, 75, 1] Generated Node #0,0: 65:[38, 75, 1] Operation: 89/89=1 Exploring Operation: 89-89=0, Resulting Numbers: [38, 75, 0] Generated Node #0,1: 65:[38, 75, 0] Operation: 89-89=0 Exploring Operation: 89-38=51, Resulting Numbers: [75, 89, 51] Generated Node #0,2: 65:[75, 89, 51] Operation: 89-38=51 Exploring Operation: 89-38=51, Resulting Numbers: [89, 75, 51] Generated Node #0,3: 65:[89, 75, 51] Operation: 89-38=51 Exploring Operation: 89-75=14, Resulting Numbers: [38, 89, 14] Generated Node #0,4: 65:[38, 89, 14] Operation: 89-75=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[38, 75, 1], Operations: ['89/89=1'] Exploring Operation: 75-1=74, Resulting Numbers: [38, 74] Generated Node #0,0,0: 65:[38, 74] Operation: 75-1=74 Exploring Operation: 75-38=37, Resulting Numbers: [1, 37] Generated Node #0,0,1: 65:[1, 37] Operation: 75-38=37 Exploring Operation: 38-1=37, Resulting Numbers: [75, 37] Generated Node #0,0,2: 65:[75, 37] Operation: 38-1=37 Exploring Operation: 38*1=38, Resulting Numbers: [75, 38] Generated Node #0,0,3: 65:[75, 38] Operation: 38*1=38 Exploring Operation: 38/1=38, Resulting Numbers: [75, 38] Generated Node #0,0,4: 65:[75, 38] Operation: 38/1=38 Moving to Node #0,0,1 Current State: 65:[1, 37], Operations: ['89/89=1', '75-38=37'] Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,65 unequal: No Solution Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,65 unequal: No Solution Exploring Operation: 1*37=37, Resulting Numbers: [37] 37,65 unequal: No Solution Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,65 unequal: No Solution Moving to Node #0,0,2 Current State: 65:[75, 37], Operations: ['89/89=1', '38-1=37'] Exploring Operation: 75+37=112, Resulting Numbers: [112] 112,65 unequal: No Solution Exploring Operation: 75*37=2775, Resulting Numbers: [2775] 2775,65 unequal: No Solution Exploring Operation: 75-37=38, Resulting Numbers: [38] 38,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[38, 74], Operations: ['89/89=1', '75-1=74'] Exploring Operation: 38*74=2812, Resulting Numbers: [2812] 2812,65 unequal: No Solution Exploring Operation: 74-38=36, Resulting Numbers: [36] 36,65 unequal: No Solution Exploring Operation: 38+74=112, Resulting Numbers: [112] 112,65 unequal: No Solution Moving to Node #0,0,3 Current State: 65:[75, 38], Operations: ['89/89=1', '38*1=38'] Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,65 unequal: No Solution Exploring Operation: 75*38=2850, Resulting Numbers: [2850] 2850,65 unequal: No Solution Exploring Operation: 75+38=113, Resulting Numbers: [113] 113,65 unequal: No Solution Moving to Node #0,0,4 Current State: 65:[75, 38], Operations: ['89/89=1', '38/1=38'] Exploring Operation: 75*38=2850, Resulting Numbers: [2850] 2850,65 unequal: No Solution Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,65 unequal: No Solution Exploring Operation: 75+38=113, Resulting Numbers: [113] 113,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[38, 75, 0], Operations: ['89-89=0'] Exploring Operation: 38*0=0, Resulting Numbers: [75, 0] Generated Node #0,1,0: 65:[75, 0] Operation: 38*0=0 Exploring Operation: 38-0=38, Resulting Numbers: [75, 38] Generated Node #0,1,1: 65:[75, 38] Operation: 38-0=38 Exploring Operation: 75-38=37, Resulting Numbers: [0, 37] Generated Node #0,1,2: 65:[0, 37] Operation: 75-38=37 Exploring Operation: 38+0=38, Resulting Numbers: [75, 38] Generated Node #0,1,3: 65:[75, 38] Operation: 38+0=38 Exploring Operation: 75*0=0, Resulting Numbers: [38, 0] Generated Node #0,1,4: 65:[38, 0] Operation: 75*0=0 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 65:[75, 0], Operations: ['89-89=0', '38*0=0'] Exploring Operation: 75+0=75, Resulting Numbers: [75] 75,65 unequal: No Solution Exploring Operation: 75-0=75, Resulting Numbers: [75] 75,65 unequal: No Solution Exploring Operation: 75*0=0, Resulting Numbers: [0] 0,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 65:[0, 37], Operations: ['89-89=0', '75-38=37'] Exploring Operation: 0*37=0, Resulting Numbers: [0] 0,65 unequal: No Solution Exploring Operation: 0+37=37, Resulting Numbers: [37] 37,65 unequal: No Solution Exploring Operation: 37-0=37, Resulting Numbers: [37] 37,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 65:[38, 0], Operations: ['89-89=0', '75*0=0'] Exploring Operation: 38*0=0, Resulting Numbers: [0] 0,65 unequal: No Solution Exploring Operation: 38+0=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 38-0=38, Resulting Numbers: [38] 38,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 65:[75, 38], Operations: ['89-89=0', '38-0=38'] Exploring Operation: 75+38=113, Resulting Numbers: [113] 113,65 unequal: No Solution Exploring Operation: 75*38=2850, Resulting Numbers: [2850] 2850,65 unequal: No Solution Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 65:[75, 38], Operations: ['89-89=0', '38+0=38'] Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,65 unequal: No Solution Exploring Operation: 75*38=2850, Resulting Numbers: [2850] 2850,65 unequal: No Solution Exploring Operation: 75+38=113, Resulting Numbers: [113] 113,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[75, 89, 51], Operations: ['89-38=51'] Exploring Operation: 75-51=24, Resulting Numbers: [89, 24] Generated Node #0,2,0: 65:[89, 24] Operation: 75-51=24 Exploring Operation: 89+51=140, Resulting Numbers: [75, 140] Generated Node #0,2,1: 65:[75, 140] Operation: 89+51=140 Exploring Operation: 89-51=38, Resulting Numbers: [75, 38] Generated Node #0,2,2: 65:[75, 38] Operation: 89-51=38 Exploring Operation: 89-75=14, Resulting Numbers: [51, 14] Generated Node #0,2,3: 65:[51, 14] Operation: 89-75=14 Exploring Operation: 75+51=126, Resulting Numbers: [89, 126] Generated Node #0,2,4: 65:[89, 126] Operation: 75+51=126 Moving to Node #0,2,3 Current State: 65:[51, 14], Operations: ['89-38=51', '89-75=14'] Exploring Operation: 51*14=714, Resulting Numbers: [714] 714,65 unequal: No Solution Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,65 unequal: No Solution Exploring Operation: 51+14=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[89, 38, 75, 89], Operations: [] Exploring Operation: 89-38=51, Resulting Numbers: [75, 89, 51] Generated Node #0,2: 65:[75, 89, 51] Operation: 89-38=51 Moving to Node #0,2 Current State: 65:[75, 89, 51], Operations: ['89-38=51'] Exploring Operation: 89-75=14, Resulting Numbers: [51, 14] Generated Node #0,2,3: 65:[51, 14] Operation: 89-75=14 Moving to Node #0,2,3 Current State: 65:[51, 14], Operations: ['89-38=51', '89-75=14'] Exploring Operation: 51+14=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.949653
hs_5
sum_heuristic
[ 49, 69, 79, 78 ]
19
[ "69-49=20", "79-78=1", "20-1=19" ]
Current State: 19:[49, 69, 79, 78], Operations: [] Exploring Operation: 69-49=20, Resulting Numbers: [79, 78, 20] Generated Node #2: [79, 78, 20] from Operation: 69-49=20 Current State: 19:[79, 78, 20], Operations: ['69-49=20'] Exploring Operation: 79-78=1, Resulting Numbers: [20, 1] Generated Node #3: [20, 1] from Operation: 79-78=1 Current State: 19:[20, 1], Operations: ['69-49=20', '79-78=1'] Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[49, 69, 79, 78], Operations: [] Exploring Operation: 79-69=10, Resulting Numbers: [49, 78, 10] Generated Node #0,0: 19:[49, 78, 10] Operation: 79-69=10 Exploring Operation: 78-69=9, Resulting Numbers: [49, 79, 9] Generated Node #0,1: 19:[49, 79, 9] Operation: 78-69=9 Exploring Operation: 79-78=1, Resulting Numbers: [49, 69, 1] Generated Node #0,2: 19:[49, 69, 1] Operation: 79-78=1 Exploring Operation: 69-49=20, Resulting Numbers: [79, 78, 20] Generated Node #0,3: 19:[79, 78, 20] Operation: 69-49=20 Moving to Node #0,0 Current State: 19:[49, 78, 10], Operations: ['79-69=10'] Exploring Operation: 78-10=68, Resulting Numbers: [49, 68] Generated Node #0,0,0: 19:[49, 68] Operation: 78-10=68 Exploring Operation: 49-10=39, Resulting Numbers: [78, 39] Generated Node #0,0,1: 19:[78, 39] Operation: 49-10=39 Exploring Operation: 78-49=29, Resulting Numbers: [10, 29] Generated Node #0,0,2: 19:[10, 29] Operation: 78-49=29 Exploring Operation: 49+10=59, Resulting Numbers: [78, 59] Generated Node #0,0,3: 19:[78, 59] Operation: 49+10=59 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 19:[10, 29], Operations: ['79-69=10', '78-49=29'] Exploring Operation: 10+29=39, Resulting Numbers: [39] 39,19 unequal: No Solution Exploring Operation: 10*29=290, Resulting Numbers: [290] 290,19 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[49, 69, 79, 78], Operations: [] Exploring Operation: 79-69=10, Resulting Numbers: [49, 78, 10] Generated Node #0,0: 19:[49, 78, 10] Operation: 79-69=10 Moving to Node #0,0 Current State: 19:[49, 78, 10], Operations: ['79-69=10'] Exploring Operation: 78-49=29, Resulting Numbers: [10, 29] Generated Node #0,0,2: 19:[10, 29] Operation: 78-49=29 Moving to Node #0,0,2 Current State: 19:[10, 29], Operations: ['79-69=10', '78-49=29'] Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 6, 79, 4, 44 ]
57
[ "6-4=2", "44/2=22", "79-22=57" ]
Current State: 57:[6, 79, 4, 44], Operations: [] Exploring Operation: 6-4=2, Resulting Numbers: [79, 44, 2] Generated Node #2: [79, 44, 2] from Operation: 6-4=2 Current State: 57:[79, 44, 2], Operations: ['6-4=2'] Exploring Operation: 44/2=22, Resulting Numbers: [79, 22] Generated Node #3: [79, 22] from Operation: 44/2=22 Current State: 57:[79, 22], Operations: ['6-4=2', '44/2=22'] Exploring Operation: 79-22=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[6, 79, 4, 44], Operations: [] Exploring Operation: 79-44=35, Resulting Numbers: [6, 4, 35] Generated Node #0,0: 57:[6, 4, 35] Operation: 79-44=35 Moving to Node #0,0 Current State: 57:[6, 4, 35], Operations: ['79-44=35'] Exploring Operation: 35-6=29, Resulting Numbers: [4, 29] Generated Node #0,0,0: 57:[4, 29] Operation: 35-6=29 Moving to Node #0,0,0 Current State: 57:[4, 29], Operations: ['79-44=35', '35-6=29'] Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,57 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 6, 77, 97, 75 ]
89
[ "6+77=83", "97+75=172", "172-83=89" ]
Current State: 89:[6, 77, 97, 75], Operations: [] Exploring Operation: 6+77=83, Resulting Numbers: [97, 75, 83] Generated Node #2: [97, 75, 83] from Operation: 6+77=83 Current State: 89:[97, 75, 83], Operations: ['6+77=83'] Exploring Operation: 97+75=172, Resulting Numbers: [83, 172] Generated Node #3: [83, 172] from Operation: 97+75=172 Current State: 89:[83, 172], Operations: ['6+77=83', '97+75=172'] Exploring Operation: 172-83=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[6, 77, 97, 75], Operations: [] Exploring Operation: 6+77=83, Resulting Numbers: [97, 75, 83] Generated Node #0,0: 89:[97, 75, 83] Operation: 6+77=83 Exploring Operation: 6+75=81, Resulting Numbers: [77, 97, 81] Generated Node #0,1: 89:[77, 97, 81] Operation: 6+75=81 Exploring Operation: 6+97=103, Resulting Numbers: [77, 75, 103] Generated Node #0,2: 89:[77, 75, 103] Operation: 6+97=103 Exploring Operation: 77-6=71, Resulting Numbers: [97, 75, 71] Generated Node #0,3: 89:[97, 75, 71] Operation: 77-6=71 Exploring Operation: 97-6=91, Resulting Numbers: [77, 75, 91] Generated Node #0,4: 89:[77, 75, 91] Operation: 97-6=91 Moving to Node #0,0 Current State: 89:[97, 75, 83], Operations: ['6+77=83'] Exploring Operation: 97-83=14, Resulting Numbers: [75, 14] Generated Node #0,0,0: 89:[75, 14] Operation: 97-83=14 Exploring Operation: 97+75=172, Resulting Numbers: [83, 172] Generated Node #0,0,1: 89:[83, 172] Operation: 97+75=172 Exploring Operation: 83-75=8, Resulting Numbers: [97, 8] Generated Node #0,0,2: 89:[97, 8] Operation: 83-75=8 Exploring Operation: 75+83=158, Resulting Numbers: [97, 158] Generated Node #0,0,3: 89:[97, 158] Operation: 75+83=158 Exploring Operation: 97-75=22, Resulting Numbers: [83, 22] Generated Node #0,0,4: 89:[83, 22] Operation: 97-75=22 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 89:[83, 22], Operations: ['6+77=83', '97-75=22'] Exploring Operation: 83-22=61, Resulting Numbers: [61] 61,89 unequal: No Solution Exploring Operation: 83*22=1826, Resulting Numbers: [1826] 1826,89 unequal: No Solution Exploring Operation: 83+22=105, Resulting Numbers: [105] 105,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 89:[97, 158], Operations: ['6+77=83', '75+83=158'] Exploring Operation: 97+158=255, Resulting Numbers: [255] 255,89 unequal: No Solution Exploring Operation: 97*158=15326, Resulting Numbers: [15326] 15326,89 unequal: No Solution Exploring Operation: 158-97=61, Resulting Numbers: [61] 61,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[75, 14], Operations: ['6+77=83', '97-83=14'] Exploring Operation: 75-14=61, Resulting Numbers: [61] 61,89 unequal: No Solution Exploring Operation: 75*14=1050, Resulting Numbers: [1050] 1050,89 unequal: No Solution Exploring Operation: 75+14=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[6, 77, 97, 75], Operations: [] Exploring Operation: 6+77=83, Resulting Numbers: [97, 75, 83] Generated Node #0,0: 89:[97, 75, 83] Operation: 6+77=83 Moving to Node #0,0 Current State: 89:[97, 75, 83], Operations: ['6+77=83'] Exploring Operation: 97-83=14, Resulting Numbers: [75, 14] Generated Node #0,0,0: 89:[75, 14] Operation: 97-83=14 Moving to Node #0,0,0 Current State: 89:[75, 14], Operations: ['6+77=83', '97-83=14'] Exploring Operation: 75+14=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 21, 57, 8, 19 ]
89
[ "21+57=78", "19-8=11", "78+11=89" ]
Current State: 89:[21, 57, 8, 19], Operations: [] Exploring Operation: 21+57=78, Resulting Numbers: [8, 19, 78] Generated Node #2: [8, 19, 78] from Operation: 21+57=78 Current State: 89:[8, 19, 78], Operations: ['21+57=78'] Exploring Operation: 19-8=11, Resulting Numbers: [78, 11] Generated Node #3: [78, 11] from Operation: 19-8=11 Current State: 89:[78, 11], Operations: ['21+57=78', '19-8=11'] Exploring Operation: 78+11=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[21, 57, 8, 19], Operations: [] Exploring Operation: 21+8=29, Resulting Numbers: [57, 19, 29] Generated Node #0,0: 89:[57, 19, 29] Operation: 21+8=29 Exploring Operation: 21+57=78, Resulting Numbers: [8, 19, 78] Generated Node #0,1: 89:[8, 19, 78] Operation: 21+57=78 Exploring Operation: 21+19=40, Resulting Numbers: [57, 8, 40] Generated Node #0,2: 89:[57, 8, 40] Operation: 21+19=40 Moving to Node #0,0 Current State: 89:[57, 19, 29], Operations: ['21+8=29'] Exploring Operation: 57+29=86, Resulting Numbers: [19, 86] Generated Node #0,0,0: 89:[19, 86] Operation: 57+29=86 Exploring Operation: 57+19=76, Resulting Numbers: [29, 76] Generated Node #0,0,1: 89:[29, 76] Operation: 57+19=76 Exploring Operation: 19+29=48, Resulting Numbers: [57, 48] Generated Node #0,0,2: 89:[57, 48] Operation: 19+29=48 Moving to Node #0,1 Current State: 89:[8, 19, 78], Operations: ['21+57=78'] Exploring Operation: 8+78=86, Resulting Numbers: [19, 86] Generated Node #0,1,0: 89:[19, 86] Operation: 8+78=86 Exploring Operation: 8*19=152, Resulting Numbers: [78, 152] Generated Node #0,1,1: 89:[78, 152] Operation: 8*19=152 Exploring Operation: 8+19=27, Resulting Numbers: [78, 27] Generated Node #0,1,2: 89:[78, 27] Operation: 8+19=27 Moving to Node #0,2 Current State: 89:[57, 8, 40], Operations: ['21+19=40'] Exploring Operation: 8+40=48, Resulting Numbers: [57, 48] Generated Node #0,2,0: 89:[57, 48] Operation: 8+40=48 Exploring Operation: 57-8=49, Resulting Numbers: [40, 49] Generated Node #0,2,1: 89:[40, 49] Operation: 57-8=49 Exploring Operation: 57+8=65, Resulting Numbers: [40, 65] Generated Node #0,2,2: 89:[40, 65] Operation: 57+8=65 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 89:[57, 48], Operations: ['21+19=40', '8+40=48'] Exploring Operation: 57*48=2736, Resulting Numbers: [2736] 2736,89 unequal: No Solution Exploring Operation: 57+48=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 57-48=9, Resulting Numbers: [9] 9,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[40, 65], Operations: ['21+19=40', '57+8=65'] Exploring Operation: 40+65=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 40*65=2600, Resulting Numbers: [2600] 2600,89 unequal: No Solution Exploring Operation: 65-40=25, Resulting Numbers: [25] 25,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 89:[40, 49], Operations: ['21+19=40', '57-8=49'] Exploring Operation: 40*49=1960, Resulting Numbers: [1960] 1960,89 unequal: No Solution Exploring Operation: 49-40=9, Resulting Numbers: [9] 9,89 unequal: No Solution Exploring Operation: 40+49=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[21, 57, 8, 19], Operations: [] Exploring Operation: 21+19=40, Resulting Numbers: [57, 8, 40] Generated Node #0,2: 89:[57, 8, 40] Operation: 21+19=40 Moving to Node #0,2 Current State: 89:[57, 8, 40], Operations: ['21+19=40'] Exploring Operation: 57-8=49, Resulting Numbers: [40, 49] Generated Node #0,2,1: 89:[40, 49] Operation: 57-8=49 Moving to Node #0,2,1 Current State: 89:[40, 49], Operations: ['21+19=40', '57-8=49'] Exploring Operation: 40+49=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
sum_heuristic
[ 38, 49, 33, 50 ]
39
[ "38-33=5", "50/5=10", "49-10=39" ]
Current State: 39:[38, 49, 33, 50], Operations: [] Exploring Operation: 38-33=5, Resulting Numbers: [49, 50, 5] Generated Node #2: [49, 50, 5] from Operation: 38-33=5 Current State: 39:[49, 50, 5], Operations: ['38-33=5'] Exploring Operation: 50/5=10, Resulting Numbers: [49, 10] Generated Node #3: [49, 10] from Operation: 50/5=10 Current State: 39:[49, 10], Operations: ['38-33=5', '50/5=10'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[38, 49, 33, 50], Operations: [] Exploring Operation: 50-49=1, Resulting Numbers: [38, 33, 1] Generated Node #0,0: 39:[38, 33, 1] Operation: 50-49=1 Exploring Operation: 50-33=17, Resulting Numbers: [38, 49, 17] Generated Node #0,1: 39:[38, 49, 17] Operation: 50-33=17 Exploring Operation: 50-38=12, Resulting Numbers: [49, 33, 12] Generated Node #0,2: 39:[49, 33, 12] Operation: 50-38=12 Exploring Operation: 49-33=16, Resulting Numbers: [38, 50, 16] Generated Node #0,3: 39:[38, 50, 16] Operation: 49-33=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[38, 33, 1], Operations: ['50-49=1'] Exploring Operation: 38-33=5, Resulting Numbers: [1, 5] Generated Node #0,0,0: 39:[1, 5] Operation: 38-33=5 Exploring Operation: 38*1=38, Resulting Numbers: [33, 38] Generated Node #0,0,1: 39:[33, 38] Operation: 38*1=38 Exploring Operation: 33+1=34, Resulting Numbers: [38, 34] Generated Node #0,0,2: 39:[38, 34] Operation: 33+1=34 Exploring Operation: 38+1=39, Resulting Numbers: [33, 39] Generated Node #0,0,3: 39:[33, 39] Operation: 38+1=39 Moving to Node #0,0,0 Current State: 39:[1, 5], Operations: ['50-49=1', '38-33=5'] Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[33, 39], Operations: ['50-49=1', '38+1=39'] Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,39 unequal: No Solution Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[38, 34], Operations: ['50-49=1', '33+1=34'] Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 38*34=1292, Resulting Numbers: [1292] 1292,39 unequal: No Solution Exploring Operation: 38+34=72, Resulting Numbers: [72] 72,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[33, 38], Operations: ['50-49=1', '38*1=38'] Exploring Operation: 38-33=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 33*38=1254, Resulting Numbers: [1254] 1254,39 unequal: No Solution Exploring Operation: 33+38=71, Resulting Numbers: [71] 71,39 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:[38, 49, 17], Operations: ['50-33=17'] Exploring Operation: 49-38=11, Resulting Numbers: [17, 11] Generated Node #0,1,0: 39:[17, 11] Operation: 49-38=11 Exploring Operation: 38-17=21, Resulting Numbers: [49, 21] Generated Node #0,1,1: 39:[49, 21] Operation: 38-17=21 Exploring Operation: 38+17=55, Resulting Numbers: [49, 55] Generated Node #0,1,2: 39:[49, 55] Operation: 38+17=55 Exploring Operation: 49-17=32, Resulting Numbers: [38, 32] Generated Node #0,1,3: 39:[38, 32] Operation: 49-17=32 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 39:[17, 11], Operations: ['50-33=17', '49-38=11'] Exploring Operation: 17*11=187, Resulting Numbers: [187] 187,39 unequal: No Solution Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,39 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,39 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:[38, 32], Operations: ['50-33=17', '49-17=32'] Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,39 unequal: No Solution Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,39 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:[49, 21], Operations: ['50-33=17', '38-17=21'] Exploring Operation: 49-21=28, Resulting Numbers: [28] 28,39 unequal: No Solution Exploring Operation: 49+21=70, Resulting Numbers: [70] 70,39 unequal: No Solution Exploring Operation: 49*21=1029, Resulting Numbers: [1029] 1029,39 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:[49, 55], Operations: ['50-33=17', '38+17=55'] Exploring Operation: 55-49=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 49*55=2695, Resulting Numbers: [2695] 2695,39 unequal: No Solution Exploring Operation: 49+55=104, Resulting Numbers: [104] 104,39 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 #0,3 Current State: 39:[38, 50, 16], Operations: ['49-33=16'] Exploring Operation: 50-38=12, Resulting Numbers: [16, 12] Generated Node #0,3,0: 39:[16, 12] Operation: 50-38=12 Exploring Operation: 38+16=54, Resulting Numbers: [50, 54] Generated Node #0,3,1: 39:[50, 54] Operation: 38+16=54 Exploring Operation: 38-16=22, Resulting Numbers: [50, 22] Generated Node #0,3,2: 39:[50, 22] Operation: 38-16=22 Exploring Operation: 50-16=34, Resulting Numbers: [38, 34] Generated Node #0,3,3: 39:[38, 34] Operation: 50-16=34 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 39:[16, 12], Operations: ['49-33=16', '50-38=12'] Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,39 unequal: No Solution Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,39 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:[38, 34], Operations: ['49-33=16', '50-16=34'] Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 38+34=72, Resulting Numbers: [72] 72,39 unequal: No Solution Exploring Operation: 38*34=1292, Resulting Numbers: [1292] 1292,39 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:[50, 22], Operations: ['49-33=16', '38-16=22'] Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,39 unequal: No Solution Exploring Operation: 50*22=1100, Resulting Numbers: [1100] 1100,39 unequal: No Solution Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,39 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:[50, 54], Operations: ['49-33=16', '38+16=54'] Exploring Operation: 50*54=2700, Resulting Numbers: [2700] 2700,39 unequal: No Solution Exploring Operation: 50+54=104, Resulting Numbers: [104] 104,39 unequal: No Solution Exploring Operation: 54-50=4, Resulting Numbers: [4] 4,39 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:[49, 33, 12], Operations: ['50-38=12'] Exploring Operation: 49-12=37, Resulting Numbers: [33, 37] Generated Node #0,2,0: 39:[33, 37] Operation: 49-12=37 Exploring Operation: 33-12=21, Resulting Numbers: [49, 21] Generated Node #0,2,1: 39:[49, 21] Operation: 33-12=21 Exploring Operation: 49-33=16, Resulting Numbers: [12, 16] Generated Node #0,2,2: 39:[12, 16] Operation: 49-33=16 Exploring Operation: 33+12=45, Resulting Numbers: [49, 45] Generated Node #0,2,3: 39:[49, 45] Operation: 33+12=45 Moving to Node #0,2,2 Current State: 39:[12, 16], Operations: ['50-38=12', '49-33=16'] Exploring Operation: 12*16=192, Resulting Numbers: [192] 192,39 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 12+16=28, Resulting Numbers: [28] 28,39 unequal: No Solution Moving to Node #0,2,0 Current State: 39:[33, 37], Operations: ['50-38=12', '49-12=37'] Exploring Operation: 33*37=1221, Resulting Numbers: [1221] 1221,39 unequal: No Solution Exploring Operation: 33+37=70, Resulting Numbers: [70] 70,39 unequal: No Solution Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,39 unequal: No Solution Moving to Node #0,2,3 Current State: 39:[49, 45], Operations: ['50-38=12', '33+12=45'] Exploring Operation: 49-45=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 49+45=94, Resulting Numbers: [94] 94,39 unequal: No Solution Exploring Operation: 49*45=2205, Resulting Numbers: [2205] 2205,39 unequal: No Solution Moving to Node #0,2,1 Current State: 39:[49, 21], Operations: ['50-38=12', '33-12=21'] Exploring Operation: 49-21=28, Resulting Numbers: [28] 28,39 unequal: No Solution Exploring Operation: 49*21=1029, Resulting Numbers: [1029] 1029,39 unequal: No Solution Exploring Operation: 49+21=70, Resulting Numbers: [70] 70,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 77, 50, 15, 79 ]
80
[ "79-77=2", "15*2=30", "50+30=80" ]
Current State: 80:[77, 50, 15, 79], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [50, 15, 2] Generated Node #2: [50, 15, 2] from Operation: 79-77=2 Current State: 80:[50, 15, 2], Operations: ['79-77=2'] Exploring Operation: 15*2=30, Resulting Numbers: [50, 30] Generated Node #3: [50, 30] from Operation: 15*2=30 Current State: 80:[50, 30], Operations: ['79-77=2', '15*2=30'] Exploring Operation: 50+30=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[77, 50, 15, 79], Operations: [] Exploring Operation: 77-50=27, Resulting Numbers: [15, 79, 27] Generated Node #0,0: 80:[15, 79, 27] Operation: 77-50=27 Exploring Operation: 50-15=35, Resulting Numbers: [77, 79, 35] Generated Node #0,1: 80:[77, 79, 35] Operation: 50-15=35 Moving to Node #0,0 Current State: 80:[15, 79, 27], Operations: ['77-50=27'] Exploring Operation: 15+27=42, Resulting Numbers: [79, 42] Generated Node #0,0,0: 80:[79, 42] Operation: 15+27=42 Exploring Operation: 27-15=12, Resulting Numbers: [79, 12] Generated Node #0,0,1: 80:[79, 12] Operation: 27-15=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[79, 42], Operations: ['77-50=27', '15+27=42'] Exploring Operation: 79+42=121, Resulting Numbers: [121] 121,80 unequal: No Solution Exploring Operation: 79-42=37, Resulting Numbers: [37] 37,80 unequal: No Solution No 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: 80:[79, 12], Operations: ['77-50=27', '27-15=12'] Exploring Operation: 79-12=67, Resulting Numbers: [67] 67,80 unequal: No Solution Exploring Operation: 79+12=91, Resulting Numbers: [91] 91,80 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: 80:[77, 79, 35], Operations: ['50-15=35'] Exploring Operation: 77-35=42, Resulting Numbers: [79, 42] Generated Node #0,1,0: 80:[79, 42] Operation: 77-35=42 Exploring Operation: 79-77=2, Resulting Numbers: [35, 2] Generated Node #0,1,1: 80:[35, 2] Operation: 79-77=2 Moving to Node #0,1,0 Current State: 80:[79, 42], Operations: ['50-15=35', '77-35=42'] Exploring Operation: 79+42=121, Resulting Numbers: [121] 121,80 unequal: No Solution Exploring Operation: 79-42=37, Resulting Numbers: [37] 37,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[35, 2], Operations: ['50-15=35', '79-77=2'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,80 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 7, 49, 44, 54 ]
91
[ "49/7=7", "44+54=98", "98-7=91" ]
Current State: 91:[7, 49, 44, 54], Operations: [] Exploring Operation: 49/7=7, Resulting Numbers: [44, 54, 7] Generated Node #2: [44, 54, 7] from Operation: 49/7=7 Current State: 91:[44, 54, 7], Operations: ['49/7=7'] Exploring Operation: 44+54=98, Resulting Numbers: [7, 98] Generated Node #3: [7, 98] from Operation: 44+54=98 Current State: 91:[7, 98], Operations: ['49/7=7', '44+54=98'] Exploring Operation: 98-7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[7, 49, 44, 54], Operations: [] Exploring Operation: 49-44=5, Resulting Numbers: [7, 54, 5] Generated Node #0,0: 91:[7, 54, 5] Operation: 49-44=5 Exploring Operation: 54-44=10, Resulting Numbers: [7, 49, 10] Generated Node #0,1: 91:[7, 49, 10] Operation: 54-44=10 Exploring Operation: 49+44=93, Resulting Numbers: [7, 54, 93] Generated Node #0,2: 91:[7, 54, 93] Operation: 49+44=93 Exploring Operation: 49+54=103, Resulting Numbers: [7, 44, 103] Generated Node #0,3: 91:[7, 44, 103] Operation: 49+54=103 Exploring Operation: 54-49=5, Resulting Numbers: [7, 44, 5] Generated Node #0,4: 91:[7, 44, 5] Operation: 54-49=5 Moving to Node #0,4 Current State: 91:[7, 44, 5], Operations: ['54-49=5'] Exploring Operation: 44+5=49, Resulting Numbers: [7, 49] Generated Node #0,4,0: 91:[7, 49] Operation: 44+5=49 Exploring Operation: 7-5=2, Resulting Numbers: [44, 2] Generated Node #0,4,1: 91:[44, 2] Operation: 7-5=2 Exploring Operation: 7+5=12, Resulting Numbers: [44, 12] Generated Node #0,4,2: 91:[44, 12] Operation: 7+5=12 Exploring Operation: 44-7=37, Resulting Numbers: [5, 37] Generated Node #0,4,3: 91:[5, 37] Operation: 44-7=37 Exploring Operation: 44-5=39, Resulting Numbers: [7, 39] Generated Node #0,4,4: 91:[7, 39] Operation: 44-5=39 Moving to Node #0,1 Current State: 91:[7, 49, 10], Operations: ['54-44=10'] Exploring Operation: 49-7=42, Resulting Numbers: [10, 42] Generated Node #0,1,0: 91:[10, 42] Operation: 49-7=42 Exploring Operation: 7+49=56, Resulting Numbers: [10, 56] Generated Node #0,1,1: 91:[10, 56] Operation: 7+49=56 Exploring Operation: 49/7=7, Resulting Numbers: [10, 7] Generated Node #0,1,2: 91:[10, 7] Operation: 49/7=7 Exploring Operation: 49-10=39, Resulting Numbers: [7, 39] Generated Node #0,1,3: 91:[7, 39] Operation: 49-10=39 Exploring Operation: 49+10=59, Resulting Numbers: [7, 59] Generated Node #0,1,4: 91:[7, 59] Operation: 49+10=59 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 91:[10, 7], Operations: ['54-44=10', '49/7=7'] Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,91 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,91 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,91 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 #0,1,3 Current State: 91:[7, 39], Operations: ['54-44=10', '49-10=39'] Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,91 unequal: No Solution Exploring Operation: 7*39=273, Resulting Numbers: [273] 273,91 unequal: No Solution Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,91 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 #0,1,0 Current State: 91:[10, 42], Operations: ['54-44=10', '49-7=42'] Exploring Operation: 10*42=420, Resulting Numbers: [420] 420,91 unequal: No Solution Exploring Operation: 10+42=52, Resulting Numbers: [52] 52,91 unequal: No Solution Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,91 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 #0,1,4 Current State: 91:[7, 59], Operations: ['54-44=10', '49+10=59'] Exploring Operation: 59-7=52, Resulting Numbers: [52] 52,91 unequal: No Solution Exploring Operation: 7+59=66, Resulting Numbers: [66] 66,91 unequal: No Solution Exploring Operation: 7*59=413, Resulting Numbers: [413] 413,91 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:[10, 56], Operations: ['54-44=10', '7+49=56'] Exploring Operation: 10+56=66, Resulting Numbers: [66] 66,91 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,91 unequal: No Solution Exploring Operation: 10*56=560, Resulting Numbers: [560] 560,91 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: 91:[7, 54, 5], Operations: ['49-44=5'] Exploring Operation: 7+5=12, Resulting Numbers: [54, 12] Generated Node #0,0,0: 91:[54, 12] Operation: 7+5=12 Exploring Operation: 54-7=47, Resulting Numbers: [5, 47] Generated Node #0,0,1: 91:[5, 47] Operation: 54-7=47 Exploring Operation: 7+54=61, Resulting Numbers: [5, 61] Generated Node #0,0,2: 91:[5, 61] Operation: 7+54=61 Exploring Operation: 54+5=59, Resulting Numbers: [7, 59] Generated Node #0,0,3: 91:[7, 59] Operation: 54+5=59 Exploring Operation: 54-5=49, Resulting Numbers: [7, 49] Generated Node #0,0,4: 91:[7, 49] Operation: 54-5=49 Moving to Node #0,2 Current State: 91:[7, 54, 93], Operations: ['49+44=93'] Exploring Operation: 54-7=47, Resulting Numbers: [93, 47] Generated Node #0,2,0: 91:[93, 47] Operation: 54-7=47 Exploring Operation: 7+93=100, Resulting Numbers: [54, 100] Generated Node #0,2,1: 91:[54, 100] Operation: 7+93=100 Exploring Operation: 93-7=86, Resulting Numbers: [54, 86] Generated Node #0,2,2: 91:[54, 86] Operation: 93-7=86 Exploring Operation: 93-54=39, Resulting Numbers: [7, 39] Generated Node #0,2,3: 91:[7, 39] Operation: 93-54=39 Exploring Operation: 7+54=61, Resulting Numbers: [93, 61] Generated Node #0,2,4: 91:[93, 61] Operation: 7+54=61 Moving to Node #0,3 Current State: 91:[7, 44, 103], Operations: ['49+54=103'] Exploring Operation: 7+44=51, Resulting Numbers: [103, 51] Generated Node #0,3,0: 91:[103, 51] Operation: 7+44=51 Exploring Operation: 103-44=59, Resulting Numbers: [7, 59] Generated Node #0,3,1: 91:[7, 59] Operation: 103-44=59 Exploring Operation: 103-7=96, Resulting Numbers: [44, 96] Generated Node #0,3,2: 91:[44, 96] Operation: 103-7=96 Exploring Operation: 7+103=110, Resulting Numbers: [44, 110] Generated Node #0,3,3: 91:[44, 110] Operation: 7+103=110 Exploring Operation: 44-7=37, Resulting Numbers: [103, 37] Generated Node #0,3,4: 91:[103, 37] Operation: 44-7=37 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 91:[7, 59], Operations: ['49+54=103', '103-44=59'] Exploring Operation: 7+59=66, Resulting Numbers: [66] 66,91 unequal: No Solution Exploring Operation: 59-7=52, Resulting Numbers: [52] 52,91 unequal: No Solution Exploring Operation: 7*59=413, Resulting Numbers: [413] 413,91 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 #0,3,2 Current State: 91:[44, 96], Operations: ['49+54=103', '103-7=96'] Exploring Operation: 96-44=52, Resulting Numbers: [52] 52,91 unequal: No Solution Exploring Operation: 44+96=140, Resulting Numbers: [140] 140,91 unequal: No Solution Exploring Operation: 44*96=4224, Resulting Numbers: [4224] 4224,91 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 #0,3,4 Current State: 91:[103, 37], Operations: ['49+54=103', '44-7=37'] Exploring Operation: 103+37=140, Resulting Numbers: [140] 140,91 unequal: No Solution Exploring Operation: 103*37=3811, Resulting Numbers: [3811] 3811,91 unequal: No Solution Exploring Operation: 103-37=66, Resulting Numbers: [66] 66,91 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 #0,3,0 Current State: 91:[103, 51], Operations: ['49+54=103', '7+44=51'] Exploring Operation: 103-51=52, Resulting Numbers: [52] 52,91 unequal: No Solution Exploring Operation: 103*51=5253, Resulting Numbers: [5253] 5253,91 unequal: No Solution Exploring Operation: 103+51=154, Resulting Numbers: [154] 154,91 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 #0,3,3 Current State: 91:[44, 110], Operations: ['49+54=103', '7+103=110'] Exploring Operation: 44*110=4840, Resulting Numbers: [4840] 4840,91 unequal: No Solution Exploring Operation: 44+110=154, Resulting Numbers: [154] 154,91 unequal: No Solution Exploring Operation: 110-44=66, Resulting Numbers: [66] 66,91 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: 91:[5, 37], Operations: ['54-49=5', '44-7=37'] Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,91 unequal: No Solution Exploring Operation: 5*37=185, Resulting Numbers: [185] 185,91 unequal: No Solution Exploring Operation: 5+37=42, Resulting Numbers: [42] 42,91 unequal: No Solution Moving to Node #0,4,4 Current State: 91:[7, 39], Operations: ['54-49=5', '44-5=39'] Exploring Operation: 7*39=273, Resulting Numbers: [273] 273,91 unequal: No Solution Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,91 unequal: No Solution Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,91 unequal: No Solution Moving to Node #0,2,3 Current State: 91:[7, 39], Operations: ['49+44=93', '93-54=39'] Exploring Operation: 7*39=273, Resulting Numbers: [273] 273,91 unequal: No Solution Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,91 unequal: No Solution Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,91 unequal: No Solution Moving to Node #0,4,2 Current State: 91:[44, 12], Operations: ['54-49=5', '7+5=12'] Exploring Operation: 44*12=528, Resulting Numbers: [528] 528,91 unequal: No Solution Exploring Operation: 44+12=56, Resulting Numbers: [56] 56,91 unequal: No Solution Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,91 unequal: No Solution Moving to Node #0,0,3 Current State: 91:[7, 59], Operations: ['49-44=5', '54+5=59'] Exploring Operation: 7*59=413, Resulting Numbers: [413] 413,91 unequal: No Solution Exploring Operation: 7+59=66, Resulting Numbers: [66] 66,91 unequal: No Solution Exploring Operation: 59-7=52, Resulting Numbers: [52] 52,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[5, 61], Operations: ['49-44=5', '7+54=61'] Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,91 unequal: No Solution Exploring Operation: 5+61=66, Resulting Numbers: [66] 66,91 unequal: No Solution Exploring Operation: 5*61=305, Resulting Numbers: [305] 305,91 unequal: No Solution Moving to Node #0,2,4 Current State: 91:[93, 61], Operations: ['49+44=93', '7+54=61'] Exploring Operation: 93-61=32, Resulting Numbers: [32] 32,91 unequal: No Solution Exploring Operation: 93+61=154, Resulting Numbers: [154] 154,91 unequal: No Solution Exploring Operation: 93*61=5673, Resulting Numbers: [5673] 5673,91 unequal: No Solution Moving to Node #0,2,0 Current State: 91:[93, 47], Operations: ['49+44=93', '54-7=47'] Exploring Operation: 93-47=46, Resulting Numbers: [46] 46,91 unequal: No Solution Exploring Operation: 93+47=140, Resulting Numbers: [140] 140,91 unequal: No Solution Exploring Operation: 93*47=4371, Resulting Numbers: [4371] 4371,91 unequal: No Solution Moving to Node #0,0,4 Current State: 91:[7, 49], Operations: ['49-44=5', '54-5=49'] Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,91 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,91 unequal: No Solution Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,91 unequal: No Solution Exploring Operation: 7*49=343, Resulting Numbers: [343] 343,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[5, 47], Operations: ['49-44=5', '54-7=47'] Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,91 unequal: No Solution Exploring Operation: 5*47=235, Resulting Numbers: [235] 235,91 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,91 unequal: No Solution Moving to Node #0,4,1 Current State: 91:[44, 2], Operations: ['54-49=5', '7-5=2'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,91 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,91 unequal: No Solution Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,91 unequal: No Solution Moving to Node #0,4,0 Current State: 91:[7, 49], Operations: ['54-49=5', '44+5=49'] Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,91 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,91 unequal: No Solution Exploring Operation: 7*49=343, Resulting Numbers: [343] 343,91 unequal: No Solution Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,91 unequal: No Solution Moving to Node #0,0,0 Current State: 91:[54, 12], Operations: ['49-44=5', '7+5=12'] Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,91 unequal: No Solution Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,91 unequal: No Solution Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[54, 86], Operations: ['49+44=93', '93-7=86'] Exploring Operation: 54*86=4644, Resulting Numbers: [4644] 4644,91 unequal: No Solution Exploring Operation: 86-54=32, Resulting Numbers: [32] 32,91 unequal: No Solution Exploring Operation: 54+86=140, Resulting Numbers: [140] 140,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[54, 100], Operations: ['49+44=93', '7+93=100'] Exploring Operation: 54*100=5400, Resulting Numbers: [5400] 5400,91 unequal: No Solution Exploring Operation: 100-54=46, Resulting Numbers: [46] 46,91 unequal: No Solution Exploring Operation: 54+100=154, Resulting Numbers: [154] 154,91 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 85, 58, 70, 54 ]
35
[ "85-58=27", "70*27=1890", "1890/54=35" ]
Current State: 35:[85, 58, 70, 54], Operations: [] Exploring Operation: 85-58=27, Resulting Numbers: [70, 54, 27] Generated Node #2: [70, 54, 27] from Operation: 85-58=27 Current State: 35:[70, 54, 27], Operations: ['85-58=27'] Exploring Operation: 70*27=1890, Resulting Numbers: [54, 1890] Generated Node #3: [54, 1890] from Operation: 70*27=1890 Current State: 35:[54, 1890], Operations: ['85-58=27', '70*27=1890'] Exploring Operation: 1890/54=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[85, 58, 70, 54], Operations: [] Exploring Operation: 85-54=31, Resulting Numbers: [58, 70, 31] Generated Node #0,0: 35:[58, 70, 31] Operation: 85-54=31 Exploring Operation: 85-58=27, Resulting Numbers: [70, 54, 27] Generated Node #0,1: 35:[70, 54, 27] Operation: 85-58=27 Exploring Operation: 70-58=12, Resulting Numbers: [85, 54, 12] Generated Node #0,2: 35:[85, 54, 12] Operation: 70-58=12 Exploring Operation: 85-70=15, Resulting Numbers: [58, 54, 15] Generated Node #0,3: 35:[58, 54, 15] Operation: 85-70=15 Start Sub Search at level 1: Moving to Node #0,3 Current State: 35:[58, 54, 15], Operations: ['85-70=15'] Exploring Operation: 58+15=73, Resulting Numbers: [54, 73] Generated Node #0,3,0: 35:[54, 73] Operation: 58+15=73 Exploring Operation: 58-54=4, Resulting Numbers: [15, 4] Generated Node #0,3,1: 35:[15, 4] Operation: 58-54=4 Exploring Operation: 54-15=39, Resulting Numbers: [58, 39] Generated Node #0,3,2: 35:[58, 39] Operation: 54-15=39 Exploring Operation: 58-15=43, Resulting Numbers: [54, 43] Generated Node #0,3,3: 35:[54, 43] Operation: 58-15=43 Moving to Node #0,3,1 Current State: 35:[15, 4], Operations: ['85-70=15', '58-54=4'] Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,35 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,35 unequal: No Solution Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,35 unequal: No Solution Moving to Node #0,3,3 Current State: 35:[54, 43], Operations: ['85-70=15', '58-15=43'] Exploring Operation: 54+43=97, Resulting Numbers: [97] 97,35 unequal: No Solution Exploring Operation: 54*43=2322, Resulting Numbers: [2322] 2322,35 unequal: No Solution Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,35 unequal: No Solution Moving to Node #0,3,2 Current State: 35:[58, 39], Operations: ['85-70=15', '54-15=39'] Exploring Operation: 58-39=19, Resulting Numbers: [19] 19,35 unequal: No Solution Exploring Operation: 58*39=2262, Resulting Numbers: [2262] 2262,35 unequal: No Solution Exploring Operation: 58+39=97, Resulting Numbers: [97] 97,35 unequal: No Solution Moving to Node #0,3,0 Current State: 35:[54, 73], Operations: ['85-70=15', '58+15=73'] Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,35 unequal: No Solution Exploring Operation: 54*73=3942, Resulting Numbers: [3942] 3942,35 unequal: No Solution Exploring Operation: 54+73=127, Resulting Numbers: [127] 127,35 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 #0,0 Current State: 35:[58, 70, 31], Operations: ['85-54=31'] Exploring Operation: 70-58=12, Resulting Numbers: [31, 12] Generated Node #0,0,0: 35:[31, 12] Operation: 70-58=12 Exploring Operation: 70-31=39, Resulting Numbers: [58, 39] Generated Node #0,0,1: 35:[58, 39] Operation: 70-31=39 Exploring Operation: 58-31=27, Resulting Numbers: [70, 27] Generated Node #0,0,2: 35:[70, 27] Operation: 58-31=27 Exploring Operation: 58+31=89, Resulting Numbers: [70, 89] Generated Node #0,0,3: 35:[70, 89] Operation: 58+31=89 Moving to Node #0,0,0 Current State: 35:[31, 12], Operations: ['85-54=31', '70-58=12'] Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,35 unequal: No Solution Exploring Operation: 31*12=372, Resulting Numbers: [372] 372,35 unequal: No Solution Exploring Operation: 31+12=43, Resulting Numbers: [43] 43,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[58, 39], Operations: ['85-54=31', '70-31=39'] Exploring Operation: 58*39=2262, Resulting Numbers: [2262] 2262,35 unequal: No Solution Exploring Operation: 58-39=19, Resulting Numbers: [19] 19,35 unequal: No Solution Exploring Operation: 58+39=97, Resulting Numbers: [97] 97,35 unequal: No Solution Moving to Node #0,0,2 Current State: 35:[70, 27], Operations: ['85-54=31', '58-31=27'] Exploring Operation: 70+27=97, Resulting Numbers: [97] 97,35 unequal: No Solution Exploring Operation: 70-27=43, Resulting Numbers: [43] 43,35 unequal: No Solution Exploring Operation: 70*27=1890, Resulting Numbers: [1890] 1890,35 unequal: No Solution Moving to Node #0,0,3 Current State: 35:[70, 89], Operations: ['85-54=31', '58+31=89'] Exploring Operation: 89-70=19, Resulting Numbers: [19] 19,35 unequal: No Solution Exploring Operation: 70*89=6230, Resulting Numbers: [6230] 6230,35 unequal: No Solution Exploring Operation: 70+89=159, Resulting Numbers: [159] 159,35 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 #0,1 Current State: 35:[70, 54, 27], Operations: ['85-58=27'] Exploring Operation: 70-54=16, Resulting Numbers: [27, 16] Generated Node #0,1,0: 35:[27, 16] Operation: 70-54=16 Exploring Operation: 54/27=2, Resulting Numbers: [70, 2] Generated Node #0,1,1: 35:[70, 2] Operation: 54/27=2 Exploring Operation: 70-27=43, Resulting Numbers: [54, 43] Generated Node #0,1,2: 35:[54, 43] Operation: 70-27=43 Exploring Operation: 54-27=27, Resulting Numbers: [70, 27] Generated Node #0,1,3: 35:[70, 27] Operation: 54-27=27 Moving to Node #0,1,0 Current State: 35:[27, 16], Operations: ['85-58=27', '70-54=16'] Exploring Operation: 27*16=432, Resulting Numbers: [432] 432,35 unequal: No Solution Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,35 unequal: No Solution Exploring Operation: 27+16=43, Resulting Numbers: [43] 43,35 unequal: No Solution Moving to Node #0,1,2 Current State: 35:[54, 43], Operations: ['85-58=27', '70-27=43'] Exploring Operation: 54+43=97, Resulting Numbers: [97] 97,35 unequal: No Solution Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,35 unequal: No Solution Exploring Operation: 54*43=2322, Resulting Numbers: [2322] 2322,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[70, 2], Operations: ['85-58=27', '54/27=2'] Exploring Operation: 70*2=140, Resulting Numbers: [140] 140,35 unequal: No Solution Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,35 unequal: No Solution Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[85, 58, 70, 54], Operations: [] Exploring Operation: 85-58=27, Resulting Numbers: [70, 54, 27] Generated Node #0,1: 35:[70, 54, 27] Operation: 85-58=27 Moving to Node #0,1 Current State: 35:[70, 54, 27], Operations: ['85-58=27'] Exploring Operation: 54/27=2, Resulting Numbers: [70, 2] Generated Node #0,1,1: 35:[70, 2] Operation: 54/27=2 Moving to Node #0,1,1 Current State: 35:[70, 2], Operations: ['85-58=27', '54/27=2'] Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.953993
hs_4
sum_heuristic
[ 42, 53, 4, 63 ]
54
[ "42*63=2646", "53-4=49", "2646/49=54" ]
Current State: 54:[42, 53, 4, 63], Operations: [] Exploring Operation: 42*63=2646, Resulting Numbers: [53, 4, 2646] Generated Node #2: [53, 4, 2646] from Operation: 42*63=2646 Current State: 54:[53, 4, 2646], Operations: ['42*63=2646'] Exploring Operation: 53-4=49, Resulting Numbers: [2646, 49] Generated Node #3: [2646, 49] from Operation: 53-4=49 Current State: 54:[2646, 49], Operations: ['42*63=2646', '53-4=49'] Exploring Operation: 2646/49=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[42, 53, 4, 63], Operations: [] Exploring Operation: 53-42=11, Resulting Numbers: [4, 63, 11] Generated Node #0,0: 54:[4, 63, 11] Operation: 53-42=11 Exploring Operation: 63-53=10, Resulting Numbers: [42, 4, 10] Generated Node #0,1: 54:[42, 4, 10] Operation: 63-53=10 Exploring Operation: 63-42=21, Resulting Numbers: [53, 4, 21] Generated Node #0,2: 54:[53, 4, 21] Operation: 63-42=21 Moving to Node #0,2 Current State: 54:[53, 4, 21], Operations: ['63-42=21'] Exploring Operation: 4+21=25, Resulting Numbers: [53, 25] Generated Node #0,2,0: 54:[53, 25] Operation: 4+21=25 Exploring Operation: 53+4=57, Resulting Numbers: [21, 57] Generated Node #0,2,1: 54:[21, 57] Operation: 53+4=57 Exploring Operation: 21-4=17, Resulting Numbers: [53, 17] Generated Node #0,2,2: 54:[53, 17] Operation: 21-4=17 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 54:[53, 17], Operations: ['63-42=21', '21-4=17'] Exploring Operation: 53*17=901, Resulting Numbers: [901] 901,54 unequal: No Solution Exploring Operation: 53+17=70, Resulting Numbers: [70] 70,54 unequal: No Solution Exploring Operation: 53-17=36, Resulting Numbers: [36] 36,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 54:[53, 25], Operations: ['63-42=21', '4+21=25'] Exploring Operation: 53+25=78, Resulting Numbers: [78] 78,54 unequal: No Solution Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 53*25=1325, Resulting Numbers: [1325] 1325,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 54:[21, 57], Operations: ['63-42=21', '53+4=57'] Exploring Operation: 21+57=78, Resulting Numbers: [78] 78,54 unequal: No Solution Exploring Operation: 57-21=36, Resulting Numbers: [36] 36,54 unequal: No Solution Exploring Operation: 21*57=1197, Resulting Numbers: [1197] 1197,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 54:[4, 63, 11], Operations: ['53-42=11'] Exploring Operation: 63-11=52, Resulting Numbers: [4, 52] Generated Node #0,0,0: 54:[4, 52] Operation: 63-11=52 Exploring Operation: 11-4=7, Resulting Numbers: [63, 7] Generated Node #0,0,1: 54:[63, 7] Operation: 11-4=7 Exploring Operation: 63-4=59, Resulting Numbers: [11, 59] Generated Node #0,0,2: 54:[11, 59] Operation: 63-4=59 Moving to Node #0,1 Current State: 54:[42, 4, 10], Operations: ['63-53=10'] Exploring Operation: 42+4=46, Resulting Numbers: [10, 46] Generated Node #0,1,0: 54:[10, 46] Operation: 42+4=46 Exploring Operation: 42-10=32, Resulting Numbers: [4, 32] Generated Node #0,1,1: 54:[4, 32] Operation: 42-10=32 Exploring Operation: 42+10=52, Resulting Numbers: [4, 52] Generated Node #0,1,2: 54:[4, 52] Operation: 42+10=52 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 54:[4, 52], Operations: ['63-53=10', '42+10=52'] Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 4+52=56, Resulting Numbers: [56] 56,54 unequal: No Solution Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 54:[4, 32], Operations: ['63-53=10', '42-10=32'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,54 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 54:[10, 46], Operations: ['63-53=10', '42+4=46'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,54 unequal: No Solution Exploring Operation: 10+46=56, Resulting Numbers: [56] 56,54 unequal: No Solution Exploring Operation: 10*46=460, Resulting Numbers: [460] 460,54 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: 54:[4, 52], Operations: ['53-42=11', '63-11=52'] Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 4+52=56, Resulting Numbers: [56] 56,54 unequal: No Solution Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[11, 59], Operations: ['53-42=11', '63-4=59'] Exploring Operation: 11*59=649, Resulting Numbers: [649] 649,54 unequal: No Solution Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 11+59=70, Resulting Numbers: [70] 70,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[63, 7], Operations: ['53-42=11', '11-4=7'] Exploring Operation: 63+7=70, Resulting Numbers: [70] 70,54 unequal: No Solution Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,54 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 51, 87, 44, 4 ]
59
[ "51-44=7", "4*7=28", "87-28=59" ]
Current State: 59:[51, 87, 44, 4], Operations: [] Exploring Operation: 51-44=7, Resulting Numbers: [87, 4, 7] Generated Node #2: [87, 4, 7] from Operation: 51-44=7 Current State: 59:[87, 4, 7], Operations: ['51-44=7'] Exploring Operation: 4*7=28, Resulting Numbers: [87, 28] Generated Node #3: [87, 28] from Operation: 4*7=28 Current State: 59:[87, 28], Operations: ['51-44=7', '4*7=28'] Exploring Operation: 87-28=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[51, 87, 44, 4], Operations: [] Exploring Operation: 51-4=47, Resulting Numbers: [87, 44, 47] Generated Node #0,0: 59:[87, 44, 47] Operation: 51-4=47 Exploring Operation: 51+4=55, Resulting Numbers: [87, 44, 55] Generated Node #0,1: 59:[87, 44, 55] Operation: 51+4=55 Exploring Operation: 87-4=83, Resulting Numbers: [51, 44, 83] Generated Node #0,2: 59:[51, 44, 83] Operation: 87-4=83 Exploring Operation: 44+4=48, Resulting Numbers: [51, 87, 48] Generated Node #0,3: 59:[51, 87, 48] Operation: 44+4=48 Moving to Node #0,1 Current State: 59:[87, 44, 55], Operations: ['51+4=55'] Exploring Operation: 44+55=99, Resulting Numbers: [87, 99] Generated Node #0,1,0: 59:[87, 99] Operation: 44+55=99 Exploring Operation: 87+44=131, Resulting Numbers: [55, 131] Generated Node #0,1,1: 59:[55, 131] Operation: 87+44=131 Exploring Operation: 87-55=32, Resulting Numbers: [44, 32] Generated Node #0,1,2: 59:[44, 32] Operation: 87-55=32 Exploring Operation: 87-44=43, Resulting Numbers: [55, 43] Generated Node #0,1,3: 59:[55, 43] Operation: 87-44=43 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 59:[55, 43], Operations: ['51+4=55', '87-44=43'] Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 55*43=2365, Resulting Numbers: [2365] 2365,59 unequal: No Solution Exploring Operation: 55+43=98, Resulting Numbers: [98] 98,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[44, 32], Operations: ['51+4=55', '87-55=32'] Exploring Operation: 44+32=76, Resulting Numbers: [76] 76,59 unequal: No Solution Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 44*32=1408, Resulting Numbers: [1408] 1408,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[87, 99], Operations: ['51+4=55', '44+55=99'] Exploring Operation: 99-87=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 87+99=186, Resulting Numbers: [186] 186,59 unequal: No Solution Exploring Operation: 87*99=8613, Resulting Numbers: [8613] 8613,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[55, 131], Operations: ['51+4=55', '87+44=131'] Exploring Operation: 131-55=76, Resulting Numbers: [76] 76,59 unequal: No Solution Exploring Operation: 55*131=7205, Resulting Numbers: [7205] 7205,59 unequal: No Solution Exploring Operation: 55+131=186, Resulting Numbers: [186] 186,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 59:[51, 87, 48], Operations: ['44+4=48'] Exploring Operation: 87-51=36, Resulting Numbers: [48, 36] Generated Node #0,3,0: 59:[48, 36] Operation: 87-51=36 Exploring Operation: 87-48=39, Resulting Numbers: [51, 39] Generated Node #0,3,1: 59:[51, 39] Operation: 87-48=39 Exploring Operation: 51-48=3, Resulting Numbers: [87, 3] Generated Node #0,3,2: 59:[87, 3] Operation: 51-48=3 Exploring Operation: 51+48=99, Resulting Numbers: [87, 99] Generated Node #0,3,3: 59:[87, 99] Operation: 51+48=99 Moving to Node #0,2 Current State: 59:[51, 44, 83], Operations: ['87-4=83'] Exploring Operation: 51-44=7, Resulting Numbers: [83, 7] Generated Node #0,2,0: 59:[83, 7] Operation: 51-44=7 Exploring Operation: 83-51=32, Resulting Numbers: [44, 32] Generated Node #0,2,1: 59:[44, 32] Operation: 83-51=32 Exploring Operation: 51+44=95, Resulting Numbers: [83, 95] Generated Node #0,2,2: 59:[83, 95] Operation: 51+44=95 Exploring Operation: 83-44=39, Resulting Numbers: [51, 39] Generated Node #0,2,3: 59:[51, 39] Operation: 83-44=39 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 59:[51, 39], Operations: ['87-4=83', '83-44=39'] Exploring Operation: 51-39=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 51+39=90, Resulting Numbers: [90] 90,59 unequal: No Solution Exploring Operation: 51*39=1989, Resulting Numbers: [1989] 1989,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[44, 32], Operations: ['87-4=83', '83-51=32'] Exploring Operation: 44*32=1408, Resulting Numbers: [1408] 1408,59 unequal: No Solution Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 44+32=76, Resulting Numbers: [76] 76,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[83, 95], Operations: ['87-4=83', '51+44=95'] Exploring Operation: 95-83=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 83*95=7885, Resulting Numbers: [7885] 7885,59 unequal: No Solution Exploring Operation: 83+95=178, Resulting Numbers: [178] 178,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[83, 7], Operations: ['87-4=83', '51-44=7'] Exploring Operation: 83+7=90, Resulting Numbers: [90] 90,59 unequal: No Solution Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,59 unequal: No Solution Exploring Operation: 83*7=581, Resulting Numbers: [581] 581,59 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: 59:[87, 44, 47], Operations: ['51-4=47'] Exploring Operation: 87-47=40, Resulting Numbers: [44, 40] Generated Node #0,0,0: 59:[44, 40] Operation: 87-47=40 Exploring Operation: 87-44=43, Resulting Numbers: [47, 43] Generated Node #0,0,1: 59:[47, 43] Operation: 87-44=43 Exploring Operation: 44+47=91, Resulting Numbers: [87, 91] Generated Node #0,0,2: 59:[87, 91] Operation: 44+47=91 Exploring Operation: 87+44=131, Resulting Numbers: [47, 131] Generated Node #0,0,3: 59:[47, 131] Operation: 87+44=131 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[47, 43], Operations: ['51-4=47', '87-44=43'] Exploring Operation: 47-43=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 47*43=2021, Resulting Numbers: [2021] 2021,59 unequal: No Solution Exploring Operation: 47+43=90, Resulting Numbers: [90] 90,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[44, 40], Operations: ['51-4=47', '87-47=40'] Exploring Operation: 44*40=1760, Resulting Numbers: [1760] 1760,59 unequal: No Solution Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 44+40=84, Resulting Numbers: [84] 84,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 59:[87, 91], Operations: ['51-4=47', '44+47=91'] Exploring Operation: 87*91=7917, Resulting Numbers: [7917] 7917,59 unequal: No Solution Exploring Operation: 91-87=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 87+91=178, Resulting Numbers: [178] 178,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 59:[47, 131], Operations: ['51-4=47', '87+44=131'] Exploring Operation: 131-47=84, Resulting Numbers: [84] 84,59 unequal: No Solution Exploring Operation: 47+131=178, Resulting Numbers: [178] 178,59 unequal: No Solution Exploring Operation: 47*131=6157, Resulting Numbers: [6157] 6157,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 59:[51, 39], Operations: ['44+4=48', '87-48=39'] Exploring Operation: 51-39=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 51+39=90, Resulting Numbers: [90] 90,59 unequal: No Solution Exploring Operation: 51*39=1989, Resulting Numbers: [1989] 1989,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[48, 36], Operations: ['44+4=48', '87-51=36'] Exploring Operation: 48*36=1728, Resulting Numbers: [1728] 1728,59 unequal: No Solution Exploring Operation: 48+36=84, Resulting Numbers: [84] 84,59 unequal: No Solution Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[87, 99], Operations: ['44+4=48', '51+48=99'] Exploring Operation: 87+99=186, Resulting Numbers: [186] 186,59 unequal: No Solution Exploring Operation: 87*99=8613, Resulting Numbers: [8613] 8613,59 unequal: No Solution Exploring Operation: 99-87=12, Resulting Numbers: [12] 12,59 unequal: No Solution Moving to Node #0,3,2 Current State: 59:[87, 3], Operations: ['44+4=48', '51-48=3'] Exploring Operation: 87/3=29, Resulting Numbers: [29] 29,59 unequal: No Solution Exploring Operation: 87-3=84, Resulting Numbers: [84] 84,59 unequal: No Solution Exploring Operation: 87*3=261, Resulting Numbers: [261] 261,59 unequal: No Solution Exploring Operation: 87+3=90, Resulting Numbers: [90] 90,59 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 5, 85, 1, 29 ]
51
[ "85-5=80", "1*29=29", "80-29=51" ]
Current State: 51:[5, 85, 1, 29], Operations: [] Exploring Operation: 85-5=80, Resulting Numbers: [1, 29, 80] Generated Node #2: [1, 29, 80] from Operation: 85-5=80 Current State: 51:[1, 29, 80], Operations: ['85-5=80'] Exploring Operation: 1*29=29, Resulting Numbers: [80, 29] Generated Node #3: [80, 29] from Operation: 1*29=29 Current State: 51:[80, 29], Operations: ['85-5=80', '1*29=29'] Exploring Operation: 80-29=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[5, 85, 1, 29], Operations: [] Exploring Operation: 85-29=56, Resulting Numbers: [5, 1, 56] Generated Node #0,0: 51:[5, 1, 56] Operation: 85-29=56 Exploring Operation: 29-5=24, Resulting Numbers: [85, 1, 24] Generated Node #0,1: 51:[85, 1, 24] Operation: 29-5=24 Exploring Operation: 5-1=4, Resulting Numbers: [85, 29, 4] Generated Node #0,2: 51:[85, 29, 4] Operation: 5-1=4 Exploring Operation: 85-5=80, Resulting Numbers: [1, 29, 80] Generated Node #0,3: 51:[1, 29, 80] Operation: 85-5=80 Exploring Operation: 85/5=17, Resulting Numbers: [1, 29, 17] Generated Node #0,4: 51:[1, 29, 17] Operation: 85/5=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[5, 1, 56], Operations: ['85-29=56'] Exploring Operation: 5-1=4, Resulting Numbers: [56, 4] Generated Node #0,0,0: 51:[56, 4] Operation: 5-1=4 Exploring Operation: 56-5=51, Resulting Numbers: [1, 51] Generated Node #0,0,1: 51:[1, 51] Operation: 56-5=51 Exploring Operation: 5/1=5, Resulting Numbers: [56, 5] Generated Node #0,0,2: 51:[56, 5] Operation: 5/1=5 Exploring Operation: 5*1=5, Resulting Numbers: [56, 5] Generated Node #0,0,3: 51:[56, 5] Operation: 5*1=5 Exploring Operation: 56-1=55, Resulting Numbers: [5, 55] Generated Node #0,0,4: 51:[5, 55] Operation: 56-1=55 Moving to Node #0,0,1 Current State: 51:[1, 51], Operations: ['85-29=56', '56-5=51'] Exploring Operation: 1*51=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[5, 85, 1, 29], Operations: [] Exploring Operation: 85-29=56, Resulting Numbers: [5, 1, 56] Generated Node #0,0: 51:[5, 1, 56] Operation: 85-29=56 Moving to Node #0,0 Current State: 51:[5, 1, 56], Operations: ['85-29=56'] Exploring Operation: 56-5=51, Resulting Numbers: [1, 51] Generated Node #0,0,1: 51:[1, 51] Operation: 56-5=51 Moving to Node #0,0,1 Current State: 51:[1, 51], Operations: ['85-29=56', '56-5=51'] Exploring Operation: 1*51=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 12, 44, 88, 66 ]
28
[ "12*88=1056", "1056/66=16", "44-16=28" ]
Current State: 28:[12, 44, 88, 66], Operations: [] Exploring Operation: 12*88=1056, Resulting Numbers: [44, 66, 1056] Generated Node #2: [44, 66, 1056] from Operation: 12*88=1056 Current State: 28:[44, 66, 1056], Operations: ['12*88=1056'] Exploring Operation: 1056/66=16, Resulting Numbers: [44, 16] Generated Node #3: [44, 16] from Operation: 1056/66=16 Current State: 28:[44, 16], Operations: ['12*88=1056', '1056/66=16'] Exploring Operation: 44-16=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[12, 44, 88, 66], Operations: [] Exploring Operation: 88-66=22, Resulting Numbers: [12, 44, 22] Generated Node #0,0: 28:[12, 44, 22] Operation: 88-66=22 Moving to Node #0,0 Current State: 28:[12, 44, 22], Operations: ['88-66=22'] Exploring Operation: 44/22=2, Resulting Numbers: [12, 2] Generated Node #0,0,0: 28:[12, 2] Operation: 44/22=2 Moving to Node #0,0,0 Current State: 28:[12, 2], Operations: ['88-66=22', '44/22=2'] Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,28 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 81, 68, 53, 70 ]
26
[ "81+68=149", "53+70=123", "149-123=26" ]
Current State: 26:[81, 68, 53, 70], Operations: [] Exploring Operation: 81+68=149, Resulting Numbers: [53, 70, 149] Generated Node #2: [53, 70, 149] from Operation: 81+68=149 Current State: 26:[53, 70, 149], Operations: ['81+68=149'] Exploring Operation: 53+70=123, Resulting Numbers: [149, 123] Generated Node #3: [149, 123] from Operation: 53+70=123 Current State: 26:[149, 123], Operations: ['81+68=149', '53+70=123'] Exploring Operation: 149-123=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[81, 68, 53, 70], Operations: [] Exploring Operation: 70-68=2, Resulting Numbers: [81, 53, 2] Generated Node #0,0: 26:[81, 53, 2] Operation: 70-68=2 Exploring Operation: 81-70=11, Resulting Numbers: [68, 53, 11] Generated Node #0,1: 26:[68, 53, 11] Operation: 81-70=11 Exploring Operation: 81-68=13, Resulting Numbers: [53, 70, 13] Generated Node #0,2: 26:[53, 70, 13] Operation: 81-68=13 Moving to Node #0,1 Current State: 26:[68, 53, 11], Operations: ['81-70=11'] Exploring Operation: 68-11=57, Resulting Numbers: [53, 57] Generated Node #0,1,0: 26:[53, 57] Operation: 68-11=57 Exploring Operation: 53-11=42, Resulting Numbers: [68, 42] Generated Node #0,1,1: 26:[68, 42] Operation: 53-11=42 Exploring Operation: 68-53=15, Resulting Numbers: [11, 15] Generated Node #0,1,2: 26:[11, 15] Operation: 68-53=15 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[11, 15], Operations: ['81-70=11', '68-53=15'] Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,26 unequal: No Solution Exploring Operation: 11*15=165, Resulting Numbers: [165] 165,26 unequal: No Solution Exploring Operation: 11+15=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[81, 68, 53, 70], Operations: [] Exploring Operation: 81-70=11, Resulting Numbers: [68, 53, 11] Generated Node #0,1: 26:[68, 53, 11] Operation: 81-70=11 Moving to Node #0,1 Current State: 26:[68, 53, 11], Operations: ['81-70=11'] Exploring Operation: 68-53=15, Resulting Numbers: [11, 15] Generated Node #0,1,2: 26:[11, 15] Operation: 68-53=15 Moving to Node #0,1,2 Current State: 26:[11, 15], Operations: ['81-70=11', '68-53=15'] Exploring Operation: 11+15=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 49, 57, 82, 45 ]
21
[ "49+57=106", "82+45=127", "127-106=21" ]
Current State: 21:[49, 57, 82, 45], Operations: [] Exploring Operation: 49+57=106, Resulting Numbers: [82, 45, 106] Generated Node #2: [82, 45, 106] from Operation: 49+57=106 Current State: 21:[82, 45, 106], Operations: ['49+57=106'] Exploring Operation: 82+45=127, Resulting Numbers: [106, 127] Generated Node #3: [106, 127] from Operation: 82+45=127 Current State: 21:[106, 127], Operations: ['49+57=106', '82+45=127'] Exploring Operation: 127-106=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[49, 57, 82, 45], Operations: [] Exploring Operation: 82-45=37, Resulting Numbers: [49, 57, 37] Generated Node #0,0: 21:[49, 57, 37] Operation: 82-45=37 Exploring Operation: 82-49=33, Resulting Numbers: [57, 45, 33] Generated Node #0,1: 21:[57, 45, 33] Operation: 82-49=33 Exploring Operation: 82-57=25, Resulting Numbers: [49, 45, 25] Generated Node #0,2: 21:[49, 45, 25] Operation: 82-57=25 Exploring Operation: 57-49=8, Resulting Numbers: [82, 45, 8] Generated Node #0,3: 21:[82, 45, 8] Operation: 57-49=8 Moving to Node #0,2 Current State: 21:[49, 45, 25], Operations: ['82-57=25'] Exploring Operation: 49+45=94, Resulting Numbers: [25, 94] Generated Node #0,2,0: 21:[25, 94] Operation: 49+45=94 Exploring Operation: 49-25=24, Resulting Numbers: [45, 24] Generated Node #0,2,1: 21:[45, 24] Operation: 49-25=24 Exploring Operation: 45-25=20, Resulting Numbers: [49, 20] Generated Node #0,2,2: 21:[49, 20] Operation: 45-25=20 Exploring Operation: 49-45=4, Resulting Numbers: [25, 4] Generated Node #0,2,3: 21:[25, 4] Operation: 49-45=4 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 21:[25, 4], Operations: ['82-57=25', '49-45=4'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[49, 57, 82, 45], Operations: [] Exploring Operation: 82-57=25, Resulting Numbers: [49, 45, 25] Generated Node #0,2: 21:[49, 45, 25] Operation: 82-57=25 Moving to Node #0,2 Current State: 21:[49, 45, 25], Operations: ['82-57=25'] Exploring Operation: 49-45=4, Resulting Numbers: [25, 4] Generated Node #0,2,3: 21:[25, 4] Operation: 49-45=4 Moving to Node #0,2,3 Current State: 21:[25, 4], Operations: ['82-57=25', '49-45=4'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 66, 14, 57, 3 ]
49
[ "66/3=22", "14+57=71", "71-22=49" ]
Current State: 49:[66, 14, 57, 3], Operations: [] Exploring Operation: 66/3=22, Resulting Numbers: [14, 57, 22] Generated Node #2: [14, 57, 22] from Operation: 66/3=22 Current State: 49:[14, 57, 22], Operations: ['66/3=22'] Exploring Operation: 14+57=71, Resulting Numbers: [22, 71] Generated Node #3: [22, 71] from Operation: 14+57=71 Current State: 49:[22, 71], Operations: ['66/3=22', '14+57=71'] Exploring Operation: 71-22=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[66, 14, 57, 3], Operations: [] Exploring Operation: 66-14=52, Resulting Numbers: [57, 3, 52] Generated Node #0,0: 49:[57, 3, 52] Operation: 66-14=52 Exploring Operation: 66-57=9, Resulting Numbers: [14, 3, 9] Generated Node #0,1: 49:[14, 3, 9] Operation: 66-57=9 Exploring Operation: 57-14=43, Resulting Numbers: [66, 3, 43] Generated Node #0,2: 49:[66, 3, 43] Operation: 57-14=43 Exploring Operation: 66-3=63, Resulting Numbers: [14, 57, 63] Generated Node #0,3: 49:[14, 57, 63] Operation: 66-3=63 Moving to Node #0,1 Current State: 49:[14, 3, 9], Operations: ['66-57=9'] Exploring Operation: 14-9=5, Resulting Numbers: [3, 5] Generated Node #0,1,0: 49:[3, 5] Operation: 14-9=5 Exploring Operation: 14-3=11, Resulting Numbers: [9, 11] Generated Node #0,1,1: 49:[9, 11] Operation: 14-3=11 Exploring Operation: 14*3=42, Resulting Numbers: [9, 42] Generated Node #0,1,2: 49:[9, 42] Operation: 14*3=42 Exploring Operation: 9-3=6, Resulting Numbers: [14, 6] Generated Node #0,1,3: 49:[14, 6] Operation: 9-3=6 Moving to Node #0,0 Current State: 49:[57, 3, 52], Operations: ['66-14=52'] Exploring Operation: 52-3=49, Resulting Numbers: [57, 49] Generated Node #0,0,0: 49:[57, 49] Operation: 52-3=49 Exploring Operation: 57+3=60, Resulting Numbers: [52, 60] Generated Node #0,0,1: 49:[52, 60] Operation: 57+3=60 Exploring Operation: 57-52=5, Resulting Numbers: [3, 5] Generated Node #0,0,2: 49:[3, 5] Operation: 57-52=5 Exploring Operation: 57-3=54, Resulting Numbers: [52, 54] Generated Node #0,0,3: 49:[52, 54] Operation: 57-3=54 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 49:[3, 5], Operations: ['66-14=52', '57-52=5'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,49 unequal: No Solution No 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: 49:[57, 49], Operations: ['66-14=52', '52-3=49'] Exploring Operation: 57-49=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 57+49=106, Resulting Numbers: [106] 106,49 unequal: No Solution Exploring Operation: 57*49=2793, Resulting Numbers: [2793] 2793,49 unequal: No Solution No 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: 49:[52, 54], Operations: ['66-14=52', '57-3=54'] Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 52+54=106, Resulting Numbers: [106] 106,49 unequal: No Solution Exploring Operation: 52*54=2808, Resulting Numbers: [2808] 2808,49 unequal: No Solution No 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: 49:[52, 60], Operations: ['66-14=52', '57+3=60'] Exploring Operation: 60-52=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 52*60=3120, Resulting Numbers: [3120] 3120,49 unequal: No Solution Exploring Operation: 52+60=112, Resulting Numbers: [112] 112,49 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: 49:[66, 3, 43], Operations: ['57-14=43'] Exploring Operation: 66/3=22, Resulting Numbers: [43, 22] Generated Node #0,2,0: 49:[43, 22] Operation: 66/3=22 Exploring Operation: 66-3=63, Resulting Numbers: [43, 63] Generated Node #0,2,1: 49:[43, 63] Operation: 66-3=63 Exploring Operation: 3+43=46, Resulting Numbers: [66, 46] Generated Node #0,2,2: 49:[66, 46] Operation: 3+43=46 Exploring Operation: 66-43=23, Resulting Numbers: [3, 23] Generated Node #0,2,3: 49:[3, 23] Operation: 66-43=23 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 49:[43, 63], Operations: ['57-14=43', '66-3=63'] Exploring Operation: 63-43=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 43+63=106, Resulting Numbers: [106] 106,49 unequal: No Solution Exploring Operation: 43*63=2709, Resulting Numbers: [2709] 2709,49 unequal: No Solution No 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: 49:[66, 46], Operations: ['57-14=43', '3+43=46'] Exploring Operation: 66-46=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 66*46=3036, Resulting Numbers: [3036] 3036,49 unequal: No Solution Exploring Operation: 66+46=112, Resulting Numbers: [112] 112,49 unequal: No Solution No 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: 49:[3, 23], Operations: ['57-14=43', '66-43=23'] Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,49 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,49 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,49 unequal: No Solution No 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: 49:[43, 22], Operations: ['57-14=43', '66/3=22'] Exploring Operation: 43+22=65, Resulting Numbers: [65] 65,49 unequal: No Solution Exploring Operation: 43*22=946, Resulting Numbers: [946] 946,49 unequal: No Solution Exploring Operation: 43-22=21, Resulting Numbers: [21] 21,49 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: 49:[14, 57, 63], Operations: ['66-3=63'] Exploring Operation: 63-57=6, Resulting Numbers: [14, 6] Generated Node #0,3,0: 49:[14, 6] Operation: 63-57=6 Exploring Operation: 14+57=71, Resulting Numbers: [63, 71] Generated Node #0,3,1: 49:[63, 71] Operation: 14+57=71 Exploring Operation: 57-14=43, Resulting Numbers: [63, 43] Generated Node #0,3,2: 49:[63, 43] Operation: 57-14=43 Exploring Operation: 63-14=49, Resulting Numbers: [57, 49] Generated Node #0,3,3: 49:[57, 49] Operation: 63-14=49 Moving to Node #0,1,0 Current State: 49:[3, 5], Operations: ['66-57=9', '14-9=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,49 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,49 unequal: No Solution Moving to Node #0,1,1 Current State: 49:[9, 11], Operations: ['66-57=9', '14-3=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,49 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,49 unequal: No Solution Moving to Node #0,1,3 Current State: 49:[14, 6], Operations: ['66-57=9', '9-3=6'] Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 14*6=84, Resulting Numbers: [84] 84,49 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,49 unequal: No Solution Moving to Node #0,3,3 Current State: 49:[57, 49], Operations: ['66-3=63', '63-14=49'] Exploring Operation: 57+49=106, Resulting Numbers: [106] 106,49 unequal: No Solution Exploring Operation: 57*49=2793, Resulting Numbers: [2793] 2793,49 unequal: No Solution Exploring Operation: 57-49=8, Resulting Numbers: [8] 8,49 unequal: No Solution Moving to Node #0,3,0 Current State: 49:[14, 6], Operations: ['66-3=63', '63-57=6'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 14*6=84, Resulting Numbers: [84] 84,49 unequal: No Solution Moving to Node #0,1,2 Current State: 49:[9, 42], Operations: ['66-57=9', '14*3=42'] Exploring Operation: 9+42=51, Resulting Numbers: [51] 51,49 unequal: No Solution Exploring Operation: 9*42=378, Resulting Numbers: [378] 378,49 unequal: No Solution Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,49 unequal: No Solution Moving to Node #0,3,2 Current State: 49:[63, 43], Operations: ['66-3=63', '57-14=43'] Exploring Operation: 63+43=106, Resulting Numbers: [106] 106,49 unequal: No Solution Exploring Operation: 63*43=2709, Resulting Numbers: [2709] 2709,49 unequal: No Solution Exploring Operation: 63-43=20, Resulting Numbers: [20] 20,49 unequal: No Solution Moving to Node #0,3,1 Current State: 49:[63, 71], Operations: ['66-3=63', '14+57=71'] Exploring Operation: 63+71=134, Resulting Numbers: [134] 134,49 unequal: No Solution Exploring Operation: 71-63=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 63*71=4473, Resulting Numbers: [4473] 4473,49 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 10, 10, 54, 70 ]
37
[ "54-10=44", "70/10=7", "44-7=37" ]
Current State: 37:[10, 10, 54, 70], Operations: [] Exploring Operation: 54-10=44, Resulting Numbers: [70, 44] Generated Node #2: [70, 44] from Operation: 54-10=44 Current State: 37:[70, 44], Operations: ['54-10=44'] Exploring Operation: 70/10=7, Resulting Numbers: [44, 7] Generated Node #3: [44, 7] from Operation: 70/10=7 Current State: 37:[44, 7], Operations: ['54-10=44', '70/10=7'] Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[10, 10, 54, 70], Operations: [] Exploring Operation: 54-10=44, Resulting Numbers: [10, 70, 44] Generated Node #0,0: 37:[10, 70, 44] Operation: 54-10=44 Exploring Operation: 54-10=44, Resulting Numbers: [10, 70, 44] Generated Node #0,1: 37:[10, 70, 44] Operation: 54-10=44 Exploring Operation: 70-10=60, Resulting Numbers: [10, 54, 60] Generated Node #0,2: 37:[10, 54, 60] Operation: 70-10=60 Exploring Operation: 10+10=20, Resulting Numbers: [54, 70, 20] Generated Node #0,3: 37:[54, 70, 20] Operation: 10+10=20 Exploring Operation: 70-10=60, Resulting Numbers: [10, 54, 60] Generated Node #0,4: 37:[10, 54, 60] Operation: 70-10=60 Moving to Node #0,0 Current State: 37:[10, 70, 44], Operations: ['54-10=44'] Exploring Operation: 44-10=34, Resulting Numbers: [70, 34] Generated Node #0,0,0: 37:[70, 34] Operation: 44-10=34 Exploring Operation: 70-44=26, Resulting Numbers: [10, 26] Generated Node #0,0,1: 37:[10, 26] Operation: 70-44=26 Exploring Operation: 10+70=80, Resulting Numbers: [44, 80] Generated Node #0,0,2: 37:[44, 80] Operation: 10+70=80 Exploring Operation: 70-10=60, Resulting Numbers: [44, 60] Generated Node #0,0,3: 37:[44, 60] Operation: 70-10=60 Exploring Operation: 70/10=7, Resulting Numbers: [44, 7] Generated Node #0,0,4: 37:[44, 7] Operation: 70/10=7 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 37:[44, 60], Operations: ['54-10=44', '70-10=60'] Exploring Operation: 44+60=104, Resulting Numbers: [104] 104,37 unequal: No Solution Exploring Operation: 44*60=2640, Resulting Numbers: [2640] 2640,37 unequal: No Solution Exploring Operation: 60-44=16, Resulting Numbers: [16] 16,37 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 #0,0,0 Current State: 37:[70, 34], Operations: ['54-10=44', '44-10=34'] Exploring Operation: 70*34=2380, Resulting Numbers: [2380] 2380,37 unequal: No Solution Exploring Operation: 70+34=104, Resulting Numbers: [104] 104,37 unequal: No Solution Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,37 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 #0,0,4 Current State: 37:[44, 7], Operations: ['54-10=44', '70/10=7'] Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,37 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[10, 10, 54, 70], Operations: [] Exploring Operation: 54-10=44, Resulting Numbers: [10, 70, 44] Generated Node #0,0: 37:[10, 70, 44] Operation: 54-10=44 Moving to Node #0,0 Current State: 37:[10, 70, 44], Operations: ['54-10=44'] Exploring Operation: 70/10=7, Resulting Numbers: [44, 7] Generated Node #0,0,4: 37:[44, 7] Operation: 70/10=7 Moving to Node #0,0,4 Current State: 37:[44, 7], Operations: ['54-10=44', '70/10=7'] Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 2, 3, 23, 9 ]
77
[ "2*3=6", "9*6=54", "23+54=77" ]
Current State: 77:[2, 3, 23, 9], Operations: [] Exploring Operation: 2*3=6, Resulting Numbers: [23, 9, 6] Generated Node #2: [23, 9, 6] from Operation: 2*3=6 Current State: 77:[23, 9, 6], Operations: ['2*3=6'] Exploring Operation: 9*6=54, Resulting Numbers: [23, 54] Generated Node #3: [23, 54] from Operation: 9*6=54 Current State: 77:[23, 54], Operations: ['2*3=6', '9*6=54'] Exploring Operation: 23+54=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[2, 3, 23, 9], Operations: [] Exploring Operation: 2*3=6, Resulting Numbers: [23, 9, 6] Generated Node #0,0: 77:[23, 9, 6] Operation: 2*3=6 Exploring Operation: 23-9=14, Resulting Numbers: [2, 3, 14] Generated Node #0,1: 77:[2, 3, 14] Operation: 23-9=14 Exploring Operation: 3*23=69, Resulting Numbers: [2, 9, 69] Generated Node #0,2: 77:[2, 9, 69] Operation: 3*23=69 Moving to Node #0,1 Current State: 77:[2, 3, 14], Operations: ['23-9=14'] Exploring Operation: 2+3=5, Resulting Numbers: [14, 5] Generated Node #0,1,0: 77:[14, 5] Operation: 2+3=5 Exploring Operation: 14/2=7, Resulting Numbers: [3, 7] Generated Node #0,1,1: 77:[3, 7] Operation: 14/2=7 Exploring Operation: 2*3=6, Resulting Numbers: [14, 6] Generated Node #0,1,2: 77:[14, 6] Operation: 2*3=6 Moving to Node #0,0 Current State: 77:[23, 9, 6], Operations: ['2*3=6'] Exploring Operation: 23-6=17, Resulting Numbers: [9, 17] Generated Node #0,0,0: 77:[9, 17] Operation: 23-6=17 Exploring Operation: 23-9=14, Resulting Numbers: [6, 14] Generated Node #0,0,1: 77:[6, 14] Operation: 23-9=14 Exploring Operation: 9+6=15, Resulting Numbers: [23, 15] Generated Node #0,0,2: 77:[23, 15] Operation: 9+6=15 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[6, 14], Operations: ['2*3=6', '23-9=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,77 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,77 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:[9, 17], Operations: ['2*3=6', '23-6=17'] Exploring Operation: 9*17=153, Resulting Numbers: [153] 153,77 unequal: No Solution Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,77 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,77 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:[23, 15], Operations: ['2*3=6', '9+6=15'] Exploring Operation: 23*15=345, Resulting Numbers: [345] 345,77 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 23+15=38, Resulting Numbers: [38] 38,77 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: 77:[2, 9, 69], Operations: ['3*23=69'] Exploring Operation: 9-2=7, Resulting Numbers: [69, 7] Generated Node #0,2,0: 77:[69, 7] Operation: 9-2=7 Exploring Operation: 9+69=78, Resulting Numbers: [2, 78] Generated Node #0,2,1: 77:[2, 78] Operation: 9+69=78 Exploring Operation: 2+9=11, Resulting Numbers: [69, 11] Generated Node #0,2,2: 77:[69, 11] Operation: 2+9=11 Moving to Node #0,1,1 Current State: 77:[3, 7], Operations: ['23-9=14', '14/2=7'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,77 unequal: No Solution Moving to Node #0,1,2 Current State: 77:[14, 6], Operations: ['23-9=14', '2*3=6'] Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,77 unequal: No Solution Exploring Operation: 14*6=84, Resulting Numbers: [84] 84,77 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[14, 5], Operations: ['23-9=14', '2+3=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,77 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,77 unequal: No Solution Moving to Node #0,2,1 Current State: 77:[2, 78], Operations: ['3*23=69', '9+69=78'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,77 unequal: No Solution Exploring Operation: 2+78=80, Resulting Numbers: [80] 80,77 unequal: No Solution Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,77 unequal: No Solution Moving to Node #0,2,2 Current State: 77:[69, 11], Operations: ['3*23=69', '2+9=11'] Exploring Operation: 69+11=80, Resulting Numbers: [80] 80,77 unequal: No Solution Exploring Operation: 69*11=759, Resulting Numbers: [759] 759,77 unequal: No Solution Exploring Operation: 69-11=58, Resulting Numbers: [58] 58,77 unequal: No Solution Moving to Node #0,2,0 Current State: 77:[69, 7], Operations: ['3*23=69', '9-2=7'] Exploring Operation: 69*7=483, Resulting Numbers: [483] 483,77 unequal: No Solution Exploring Operation: 69+7=76, Resulting Numbers: [76] 76,77 unequal: No Solution Exploring Operation: 69-7=62, Resulting Numbers: [62] 62,77 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 93, 84, 70, 64 ]
72
[ "93*64=5952", "84*70=5880", "5952-5880=72" ]
Current State: 72:[93, 84, 70, 64], Operations: [] Exploring Operation: 93*64=5952, Resulting Numbers: [84, 70, 5952] Generated Node #2: [84, 70, 5952] from Operation: 93*64=5952 Current State: 72:[84, 70, 5952], Operations: ['93*64=5952'] Exploring Operation: 84*70=5880, Resulting Numbers: [5952, 5880] Generated Node #3: [5952, 5880] from Operation: 84*70=5880 Current State: 72:[5952, 5880], Operations: ['93*64=5952', '84*70=5880'] Exploring Operation: 5952-5880=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[93, 84, 70, 64], Operations: [] Exploring Operation: 93-84=9, Resulting Numbers: [70, 64, 9] Generated Node #0,0: 72:[70, 64, 9] Operation: 93-84=9 Exploring Operation: 93-64=29, Resulting Numbers: [84, 70, 29] Generated Node #0,1: 72:[84, 70, 29] Operation: 93-64=29 Exploring Operation: 93-70=23, Resulting Numbers: [84, 64, 23] Generated Node #0,2: 72:[84, 64, 23] Operation: 93-70=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[70, 64, 9], Operations: ['93-84=9'] Exploring Operation: 64+9=73, Resulting Numbers: [70, 73] Generated Node #0,0,0: 72:[70, 73] Operation: 64+9=73 Exploring Operation: 70+9=79, Resulting Numbers: [64, 79] Generated Node #0,0,1: 72:[64, 79] Operation: 70+9=79 Exploring Operation: 70-64=6, Resulting Numbers: [9, 6] Generated Node #0,0,2: 72:[9, 6] Operation: 70-64=6 Moving to Node #0,0,2 Current State: 72:[9, 6], Operations: ['93-84=9', '70-64=6'] Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,72 unequal: No Solution Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[70, 73], Operations: ['93-84=9', '64+9=73'] Exploring Operation: 70+73=143, Resulting Numbers: [143] 143,72 unequal: No Solution Exploring Operation: 73-70=3, Resulting Numbers: [3] 3,72 unequal: No Solution Exploring Operation: 70*73=5110, Resulting Numbers: [5110] 5110,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[64, 79], Operations: ['93-84=9', '70+9=79'] Exploring Operation: 64*79=5056, Resulting Numbers: [5056] 5056,72 unequal: No Solution Exploring Operation: 64+79=143, Resulting Numbers: [143] 143,72 unequal: No Solution Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[84, 70, 29], Operations: ['93-64=29'] Exploring Operation: 70-29=41, Resulting Numbers: [84, 41] Generated Node #0,1,0: 72:[84, 41] Operation: 70-29=41 Exploring Operation: 84-29=55, Resulting Numbers: [70, 55] Generated Node #0,1,1: 72:[70, 55] Operation: 84-29=55 Exploring Operation: 84-70=14, Resulting Numbers: [29, 14] Generated Node #0,1,2: 72:[29, 14] Operation: 84-70=14 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 72:[29, 14], Operations: ['93-64=29', '84-70=14'] Exploring Operation: 29*14=406, Resulting Numbers: [406] 406,72 unequal: No Solution Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 29+14=43, Resulting Numbers: [43] 43,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 72:[84, 41], Operations: ['93-64=29', '70-29=41'] Exploring Operation: 84+41=125, Resulting Numbers: [125] 125,72 unequal: No Solution Exploring Operation: 84-41=43, Resulting Numbers: [43] 43,72 unequal: No Solution Exploring Operation: 84*41=3444, Resulting Numbers: [3444] 3444,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 72:[70, 55], Operations: ['93-64=29', '84-29=55'] Exploring Operation: 70*55=3850, Resulting Numbers: [3850] 3850,72 unequal: No Solution Exploring Operation: 70-55=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 70+55=125, Resulting Numbers: [125] 125,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[84, 64, 23], Operations: ['93-70=23'] Exploring Operation: 84-64=20, Resulting Numbers: [23, 20] Generated Node #0,2,0: 72:[23, 20] Operation: 84-64=20 Exploring Operation: 64-23=41, Resulting Numbers: [84, 41] Generated Node #0,2,1: 72:[84, 41] Operation: 64-23=41 Exploring Operation: 84-23=61, Resulting Numbers: [64, 61] Generated Node #0,2,2: 72:[64, 61] Operation: 84-23=61 Moving to Node #0,2,0 Current State: 72:[23, 20], Operations: ['93-70=23', '84-64=20'] Exploring Operation: 23+20=43, Resulting Numbers: [43] 43,72 unequal: No Solution Exploring Operation: 23*20=460, Resulting Numbers: [460] 460,72 unequal: No Solution Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[84, 41], Operations: ['93-70=23', '64-23=41'] Exploring Operation: 84*41=3444, Resulting Numbers: [3444] 3444,72 unequal: No Solution Exploring Operation: 84-41=43, Resulting Numbers: [43] 43,72 unequal: No Solution Exploring Operation: 84+41=125, Resulting Numbers: [125] 125,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[64, 61], Operations: ['93-70=23', '84-23=61'] Exploring Operation: 64+61=125, Resulting Numbers: [125] 125,72 unequal: No Solution Exploring Operation: 64*61=3904, Resulting Numbers: [3904] 3904,72 unequal: No Solution Exploring Operation: 64-61=3, Resulting Numbers: [3] 3,72 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
[ 74, 14, 77, 19 ]
61
[ "77-74=3", "14*3=42", "19+42=61" ]
Current State: 61:[74, 14, 77, 19], Operations: [] Exploring Operation: 77-74=3, Resulting Numbers: [14, 19, 3] Generated Node #2: [14, 19, 3] from Operation: 77-74=3 Current State: 61:[14, 19, 3], Operations: ['77-74=3'] Exploring Operation: 14*3=42, Resulting Numbers: [19, 42] Generated Node #3: [19, 42] from Operation: 14*3=42 Current State: 61:[19, 42], Operations: ['77-74=3', '14*3=42'] Exploring Operation: 19+42=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[74, 14, 77, 19], Operations: [] Exploring Operation: 77-14=63, Resulting Numbers: [74, 19, 63] Generated Node #0,0: 61:[74, 19, 63] Operation: 77-14=63 Moving to Node #0,0 Current State: 61:[74, 19, 63], Operations: ['77-14=63'] Exploring Operation: 74-19=55, Resulting Numbers: [63, 55] Generated Node #0,0,0: 61:[63, 55] Operation: 74-19=55 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[63, 55], Operations: ['77-14=63', '74-19=55'] Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,61 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