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
[ 20, 52, 31, 43 ]
43
[ "52-20=32", "32-31=1", "43*1=43" ]
Current State: 43:[20, 52, 31, 43], Operations: [] Exploring Operation: 52-20=32, Resulting Numbers: [31, 43, 32] Generated Node #2: [31, 43, 32] from Operation: 52-20=32 Current State: 43:[31, 43, 32], Operations: ['52-20=32'] Exploring Operation: 32-31=1, Resulting Numbers: [43, 1] Generated Node #3: [43, 1] from Operation: 32-31=1 Current State: 43:[43, 1], Operations: ['52-20=32', '32-31=1'] Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[20, 52, 31, 43], Operations: [] Exploring Operation: 20+31=51, Resulting Numbers: [52, 43, 51] Generated Node #0,0: 43:[52, 43, 51] Operation: 20+31=51 Exploring Operation: 52-20=32, Resulting Numbers: [31, 43, 32] Generated Node #0,1: 43:[31, 43, 32] Operation: 52-20=32 Exploring Operation: 20+52=72, Resulting Numbers: [31, 43, 72] Generated Node #0,2: 43:[31, 43, 72] Operation: 20+52=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[52, 43, 51], Operations: ['20+31=51'] Exploring Operation: 52-51=1, Resulting Numbers: [43, 1] Generated Node #0,0,0: 43:[43, 1] Operation: 52-51=1 Exploring Operation: 52-43=9, Resulting Numbers: [51, 9] Generated Node #0,0,1: 43:[51, 9] Operation: 52-43=9 Exploring Operation: 51-43=8, Resulting Numbers: [52, 8] Generated Node #0,0,2: 43:[52, 8] Operation: 51-43=8 Moving to Node #0,0,0 Current State: 43:[43, 1], Operations: ['20+31=51', '52-51=1'] Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[20, 52, 31, 43], Operations: [] Exploring Operation: 20+31=51, Resulting Numbers: [52, 43, 51] Generated Node #0,0: 43:[52, 43, 51] Operation: 20+31=51 Moving to Node #0,0 Current State: 43:[52, 43, 51], Operations: ['20+31=51'] Exploring Operation: 52-51=1, Resulting Numbers: [43, 1] Generated Node #0,0,0: 43:[43, 1] Operation: 52-51=1 Moving to Node #0,0,0 Current State: 43:[43, 1], Operations: ['20+31=51', '52-51=1'] Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 56, 2, 46, 76 ]
89
[ "56+46=102", "76+102=178", "178/2=89" ]
Current State: 89:[56, 2, 46, 76], Operations: [] Exploring Operation: 56+46=102, Resulting Numbers: [2, 76, 102] Generated Node #2: [2, 76, 102] from Operation: 56+46=102 Current State: 89:[2, 76, 102], Operations: ['56+46=102'] Exploring Operation: 76+102=178, Resulting Numbers: [2, 178] Generated Node #3: [2, 178] from Operation: 76+102=178 Current State: 89:[2, 178], Operations: ['56+46=102', '76+102=178'] Exploring Operation: 178/2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[56, 2, 46, 76], Operations: [] Exploring Operation: 2*46=92, Resulting Numbers: [56, 76, 92] Generated Node #0,0: 89:[56, 76, 92] Operation: 2*46=92 Exploring Operation: 56*2=112, Resulting Numbers: [46, 76, 112] Generated Node #0,1: 89:[46, 76, 112] Operation: 56*2=112 Exploring Operation: 56+2=58, Resulting Numbers: [46, 76, 58] Generated Node #0,2: 89:[46, 76, 58] Operation: 56+2=58 Moving to Node #0,0 Current State: 89:[56, 76, 92], Operations: ['2*46=92'] Exploring Operation: 56+76=132, Resulting Numbers: [92, 132] Generated Node #0,0,0: 89:[92, 132] Operation: 56+76=132 Exploring Operation: 76-56=20, Resulting Numbers: [92, 20] Generated Node #0,0,1: 89:[92, 20] Operation: 76-56=20 Exploring Operation: 92-56=36, Resulting Numbers: [76, 36] Generated Node #0,0,2: 89:[76, 36] Operation: 92-56=36 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[92, 132], Operations: ['2*46=92', '56+76=132'] Exploring Operation: 92*132=12144, Resulting Numbers: [12144] 12144,89 unequal: No Solution Exploring Operation: 92+132=224, Resulting Numbers: [224] 224,89 unequal: No Solution Exploring Operation: 132-92=40, Resulting Numbers: [40] 40,89 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 #0,0,2 Current State: 89:[76, 36], Operations: ['2*46=92', '92-56=36'] Exploring Operation: 76*36=2736, Resulting Numbers: [2736] 2736,89 unequal: No Solution Exploring Operation: 76+36=112, Resulting Numbers: [112] 112,89 unequal: No Solution Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,89 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 #0,0,1 Current State: 89:[92, 20], Operations: ['2*46=92', '76-56=20'] Exploring Operation: 92*20=1840, Resulting Numbers: [1840] 1840,89 unequal: No Solution Exploring Operation: 92+20=112, Resulting Numbers: [112] 112,89 unequal: No Solution Exploring Operation: 92-20=72, Resulting Numbers: [72] 72,89 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: 89:[46, 76, 112], Operations: ['56*2=112'] Exploring Operation: 46+76=122, Resulting Numbers: [112, 122] Generated Node #0,1,0: 89:[112, 122] Operation: 46+76=122 Exploring Operation: 76-46=30, Resulting Numbers: [112, 30] Generated Node #0,1,1: 89:[112, 30] Operation: 76-46=30 Exploring Operation: 112-46=66, Resulting Numbers: [76, 66] Generated Node #0,1,2: 89:[76, 66] Operation: 112-46=66 Moving to Node #0,2 Current State: 89:[46, 76, 58], Operations: ['56+2=58'] Exploring Operation: 46+76=122, Resulting Numbers: [58, 122] Generated Node #0,2,0: 89:[58, 122] Operation: 46+76=122 Exploring Operation: 76+58=134, Resulting Numbers: [46, 134] Generated Node #0,2,1: 89:[46, 134] Operation: 76+58=134 Exploring Operation: 46+58=104, Resulting Numbers: [76, 104] Generated Node #0,2,2: 89:[76, 104] Operation: 46+58=104 Moving to Node #0,2,2 Current State: 89:[76, 104], Operations: ['56+2=58', '46+58=104'] Exploring Operation: 76*104=7904, Resulting Numbers: [7904] 7904,89 unequal: No Solution Exploring Operation: 76+104=180, Resulting Numbers: [180] 180,89 unequal: No Solution Exploring Operation: 104-76=28, Resulting Numbers: [28] 28,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[76, 66], Operations: ['56*2=112', '112-46=66'] Exploring Operation: 76-66=10, Resulting Numbers: [10] 10,89 unequal: No Solution Exploring Operation: 76*66=5016, Resulting Numbers: [5016] 5016,89 unequal: No Solution Exploring Operation: 76+66=142, Resulting Numbers: [142] 142,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[112, 122], Operations: ['56*2=112', '46+76=122'] Exploring Operation: 122-112=10, Resulting Numbers: [10] 10,89 unequal: No Solution Exploring Operation: 112+122=234, Resulting Numbers: [234] 234,89 unequal: No Solution Exploring Operation: 112*122=13664, Resulting Numbers: [13664] 13664,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[58, 122], Operations: ['56+2=58', '46+76=122'] Exploring Operation: 58+122=180, Resulting Numbers: [180] 180,89 unequal: No Solution Exploring Operation: 58*122=7076, Resulting Numbers: [7076] 7076,89 unequal: No Solution Exploring Operation: 122-58=64, Resulting Numbers: [64] 64,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[112, 30], Operations: ['56*2=112', '76-46=30'] Exploring Operation: 112+30=142, Resulting Numbers: [142] 142,89 unequal: No Solution Exploring Operation: 112-30=82, Resulting Numbers: [82] 82,89 unequal: No Solution Exploring Operation: 112*30=3360, Resulting Numbers: [3360] 3360,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[46, 134], Operations: ['56+2=58', '76+58=134'] Exploring Operation: 46+134=180, Resulting Numbers: [180] 180,89 unequal: No Solution Exploring Operation: 46*134=6164, Resulting Numbers: [6164] 6164,89 unequal: No Solution Exploring Operation: 134-46=88, Resulting Numbers: [88] 88,89 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 68, 34, 81, 20 ]
99
[ "68/34=2", "81+20=101", "101-2=99" ]
Current State: 99:[68, 34, 81, 20], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [81, 20, 2] Generated Node #2: [81, 20, 2] from Operation: 68/34=2 Current State: 99:[81, 20, 2], Operations: ['68/34=2'] Exploring Operation: 81+20=101, Resulting Numbers: [2, 101] Generated Node #3: [2, 101] from Operation: 81+20=101 Current State: 99:[2, 101], Operations: ['68/34=2', '81+20=101'] Exploring Operation: 101-2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[68, 34, 81, 20], Operations: [] Exploring Operation: 81-68=13, Resulting Numbers: [34, 20, 13] Generated Node #0,0: 99:[34, 20, 13] Operation: 81-68=13 Exploring Operation: 68-34=34, Resulting Numbers: [81, 20, 34] Generated Node #0,1: 99:[81, 20, 34] Operation: 68-34=34 Exploring Operation: 68/34=2, Resulting Numbers: [81, 20, 2] Generated Node #0,2: 99:[81, 20, 2] Operation: 68/34=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[34, 20, 13], Operations: ['81-68=13'] Exploring Operation: 34-20=14, Resulting Numbers: [13, 14] Generated Node #0,0,0: 99:[13, 14] Operation: 34-20=14 Exploring Operation: 20+13=33, Resulting Numbers: [34, 33] Generated Node #0,0,1: 99:[34, 33] Operation: 20+13=33 Exploring Operation: 20-13=7, Resulting Numbers: [34, 7] Generated Node #0,0,2: 99:[34, 7] Operation: 20-13=7 Moving to Node #0,0,1 Current State: 99:[34, 33], Operations: ['81-68=13', '20+13=33'] Exploring Operation: 34*33=1122, Resulting Numbers: [1122] 1122,99 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[34, 7], Operations: ['81-68=13', '20-13=7'] Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,99 unequal: No Solution Exploring Operation: 34*7=238, Resulting Numbers: [238] 238,99 unequal: No Solution Exploring Operation: 34+7=41, Resulting Numbers: [41] 41,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[13, 14], Operations: ['81-68=13', '34-20=14'] Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,99 unequal: No Solution Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[81, 20, 34], Operations: ['68-34=34'] Exploring Operation: 34-20=14, Resulting Numbers: [81, 14] Generated Node #0,1,0: 99:[81, 14] Operation: 34-20=14 Exploring Operation: 81-34=47, Resulting Numbers: [20, 47] Generated Node #0,1,1: 99:[20, 47] Operation: 81-34=47 Exploring Operation: 81+20=101, Resulting Numbers: [34, 101] Generated Node #0,1,2: 99:[34, 101] Operation: 81+20=101 Moving to Node #0,1,2 Current State: 99:[34, 101], Operations: ['68-34=34', '81+20=101'] Exploring Operation: 34*101=3434, Resulting Numbers: [3434] 3434,99 unequal: No Solution Exploring Operation: 34+101=135, Resulting Numbers: [135] 135,99 unequal: No Solution Exploring Operation: 101-34=67, Resulting Numbers: [67] 67,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[81, 14], Operations: ['68-34=34', '34-20=14'] Exploring Operation: 81-14=67, Resulting Numbers: [67] 67,99 unequal: No Solution Exploring Operation: 81+14=95, Resulting Numbers: [95] 95,99 unequal: No Solution Exploring Operation: 81*14=1134, Resulting Numbers: [1134] 1134,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[20, 47], Operations: ['68-34=34', '81-34=47'] Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,99 unequal: No Solution Exploring Operation: 20*47=940, Resulting Numbers: [940] 940,99 unequal: No Solution Exploring Operation: 20+47=67, Resulting Numbers: [67] 67,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[81, 20, 2], Operations: ['68/34=2'] Exploring Operation: 81+20=101, Resulting Numbers: [2, 101] Generated Node #0,2,0: 99:[2, 101] Operation: 81+20=101 Exploring Operation: 81+2=83, Resulting Numbers: [20, 83] Generated Node #0,2,1: 99:[20, 83] Operation: 81+2=83 Exploring Operation: 20/2=10, Resulting Numbers: [81, 10] Generated Node #0,2,2: 99:[81, 10] Operation: 20/2=10 Moving to Node #0,2,0 Current State: 99:[2, 101], Operations: ['68/34=2', '81+20=101'] Exploring Operation: 2+101=103, Resulting Numbers: [103] 103,99 unequal: No Solution Exploring Operation: 101-2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[68, 34, 81, 20], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [81, 20, 2] Generated Node #0,2: 99:[81, 20, 2] Operation: 68/34=2 Moving to Node #0,2 Current State: 99:[81, 20, 2], Operations: ['68/34=2'] Exploring Operation: 81+20=101, Resulting Numbers: [2, 101] Generated Node #0,2,0: 99:[2, 101] Operation: 81+20=101 Moving to Node #0,2,0 Current State: 99:[2, 101], Operations: ['68/34=2', '81+20=101'] Exploring Operation: 101-2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 31, 11, 88, 52 ]
78
[ "31+11=42", "88-52=36", "42+36=78" ]
Current State: 78:[31, 11, 88, 52], Operations: [] Exploring Operation: 31+11=42, Resulting Numbers: [88, 52, 42] Generated Node #2: [88, 52, 42] from Operation: 31+11=42 Current State: 78:[88, 52, 42], Operations: ['31+11=42'] Exploring Operation: 88-52=36, Resulting Numbers: [42, 36] Generated Node #3: [42, 36] from Operation: 88-52=36 Current State: 78:[42, 36], Operations: ['31+11=42', '88-52=36'] Exploring Operation: 42+36=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[31, 11, 88, 52], Operations: [] Exploring Operation: 88-52=36, Resulting Numbers: [31, 11, 36] Generated Node #0,0: 78:[31, 11, 36] Operation: 88-52=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[31, 11, 36], Operations: ['88-52=36'] Exploring Operation: 36-31=5, Resulting Numbers: [11, 5] Generated Node #0,0,0: 78:[11, 5] Operation: 36-31=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 78:[11, 5], Operations: ['88-52=36', '36-31=5'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 8, 66, 47, 12 ]
77
[ "8*12=96", "66-47=19", "96-19=77" ]
Current State: 77:[8, 66, 47, 12], Operations: [] Exploring Operation: 8*12=96, Resulting Numbers: [66, 47, 96] Generated Node #2: [66, 47, 96] from Operation: 8*12=96 Current State: 77:[66, 47, 96], Operations: ['8*12=96'] Exploring Operation: 66-47=19, Resulting Numbers: [96, 19] Generated Node #3: [96, 19] from Operation: 66-47=19 Current State: 77:[96, 19], Operations: ['8*12=96', '66-47=19'] Exploring Operation: 96-19=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[8, 66, 47, 12], Operations: [] Exploring Operation: 66-47=19, Resulting Numbers: [8, 12, 19] Generated Node #0,0: 77:[8, 12, 19] Operation: 66-47=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[8, 12, 19], Operations: ['66-47=19'] Exploring Operation: 19-8=11, Resulting Numbers: [12, 11] Generated Node #0,0,0: 77:[12, 11] Operation: 19-8=11 Moving to Node #0,0,0 Current State: 77:[12, 11], Operations: ['66-47=19', '19-8=11'] Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,77 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
[ 90, 27, 88, 84 ]
30
[ "90-88=2", "27*2=54", "84-54=30" ]
Current State: 30:[90, 27, 88, 84], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [27, 84, 2] Generated Node #2: [27, 84, 2] from Operation: 90-88=2 Current State: 30:[27, 84, 2], Operations: ['90-88=2'] Exploring Operation: 27*2=54, Resulting Numbers: [84, 54] Generated Node #3: [84, 54] from Operation: 27*2=54 Current State: 30:[84, 54], Operations: ['90-88=2', '27*2=54'] Exploring Operation: 84-54=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[90, 27, 88, 84], Operations: [] Exploring Operation: 88-84=4, Resulting Numbers: [90, 27, 4] Generated Node #0,0: 30:[90, 27, 4] Operation: 88-84=4 Exploring Operation: 90-88=2, Resulting Numbers: [27, 84, 2] Generated Node #0,1: 30:[27, 84, 2] Operation: 90-88=2 Exploring Operation: 90-84=6, Resulting Numbers: [27, 88, 6] Generated Node #0,2: 30:[27, 88, 6] Operation: 90-84=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[27, 84, 2], Operations: ['90-88=2'] Exploring Operation: 84/2=42, Resulting Numbers: [27, 42] Generated Node #0,1,0: 30:[27, 42] Operation: 84/2=42 Exploring Operation: 27+2=29, Resulting Numbers: [84, 29] Generated Node #0,1,1: 30:[84, 29] Operation: 27+2=29 Exploring Operation: 84-27=57, Resulting Numbers: [2, 57] Generated Node #0,1,2: 30:[2, 57] Operation: 84-27=57 Moving to Node #0,1,0 Current State: 30:[27, 42], Operations: ['90-88=2', '84/2=42'] Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 27*42=1134, Resulting Numbers: [1134] 1134,30 unequal: No Solution Exploring Operation: 27+42=69, Resulting Numbers: [69] 69,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[2, 57], Operations: ['90-88=2', '84-27=57'] Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,30 unequal: No Solution Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[84, 29], Operations: ['90-88=2', '27+2=29'] Exploring Operation: 84*29=2436, Resulting Numbers: [2436] 2436,30 unequal: No Solution Exploring Operation: 84-29=55, Resulting Numbers: [55] 55,30 unequal: No Solution Exploring Operation: 84+29=113, Resulting Numbers: [113] 113,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[27, 88, 6], Operations: ['90-84=6'] Exploring Operation: 27+6=33, Resulting Numbers: [88, 33] Generated Node #0,2,0: 30:[88, 33] Operation: 27+6=33 Exploring Operation: 88-6=82, Resulting Numbers: [27, 82] Generated Node #0,2,1: 30:[27, 82] Operation: 88-6=82 Exploring Operation: 88-27=61, Resulting Numbers: [6, 61] Generated Node #0,2,2: 30:[6, 61] Operation: 88-27=61 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 30:[6, 61], Operations: ['90-84=6', '88-27=61'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,30 unequal: No Solution Exploring Operation: 6+61=67, Resulting Numbers: [67] 67,30 unequal: No Solution Exploring Operation: 6*61=366, Resulting Numbers: [366] 366,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 30:[27, 82], Operations: ['90-84=6', '88-6=82'] Exploring Operation: 27*82=2214, Resulting Numbers: [2214] 2214,30 unequal: No Solution Exploring Operation: 82-27=55, Resulting Numbers: [55] 55,30 unequal: No Solution Exploring Operation: 27+82=109, Resulting Numbers: [109] 109,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 30:[88, 33], Operations: ['90-84=6', '27+6=33'] Exploring Operation: 88-33=55, Resulting Numbers: [55] 55,30 unequal: No Solution Exploring Operation: 88+33=121, Resulting Numbers: [121] 121,30 unequal: No Solution Exploring Operation: 88*33=2904, Resulting Numbers: [2904] 2904,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[90, 27, 4], Operations: ['88-84=4'] Exploring Operation: 90-4=86, Resulting Numbers: [27, 86] Generated Node #0,0,0: 30:[27, 86] Operation: 90-4=86 Exploring Operation: 90-27=63, Resulting Numbers: [4, 63] Generated Node #0,0,1: 30:[4, 63] Operation: 90-27=63 Exploring Operation: 27+4=31, Resulting Numbers: [90, 31] Generated Node #0,0,2: 30:[90, 31] Operation: 27+4=31 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[4, 63], Operations: ['88-84=4', '90-27=63'] Exploring Operation: 4*63=252, Resulting Numbers: [252] 252,30 unequal: No Solution Exploring Operation: 4+63=67, Resulting Numbers: [67] 67,30 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[27, 86], Operations: ['88-84=4', '90-4=86'] Exploring Operation: 86-27=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 27*86=2322, Resulting Numbers: [2322] 2322,30 unequal: No Solution Exploring Operation: 27+86=113, Resulting Numbers: [113] 113,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 30:[90, 31], Operations: ['88-84=4', '27+4=31'] Exploring Operation: 90-31=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 90+31=121, Resulting Numbers: [121] 121,30 unequal: No Solution Exploring Operation: 90*31=2790, Resulting Numbers: [2790] 2790,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 66, 15, 25, 76 ]
34
[ "66*25=1650", "1650/15=110", "110-76=34" ]
Current State: 34:[66, 15, 25, 76], Operations: [] Exploring Operation: 66*25=1650, Resulting Numbers: [15, 76, 1650] Generated Node #2: [15, 76, 1650] from Operation: 66*25=1650 Current State: 34:[15, 76, 1650], Operations: ['66*25=1650'] Exploring Operation: 1650/15=110, Resulting Numbers: [76, 110] Generated Node #3: [76, 110] from Operation: 1650/15=110 Current State: 34:[76, 110], Operations: ['66*25=1650', '1650/15=110'] Exploring Operation: 110-76=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[66, 15, 25, 76], Operations: [] Exploring Operation: 76-25=51, Resulting Numbers: [66, 15, 51] Generated Node #0,0: 34:[66, 15, 51] Operation: 76-25=51 Exploring Operation: 66-25=41, Resulting Numbers: [15, 76, 41] Generated Node #0,1: 34:[15, 76, 41] Operation: 66-25=41 Exploring Operation: 76-66=10, Resulting Numbers: [15, 25, 10] Generated Node #0,2: 34:[15, 25, 10] Operation: 76-66=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[15, 25, 10], Operations: ['76-66=10'] Exploring Operation: 25+10=35, Resulting Numbers: [15, 35] Generated Node #0,2,0: 34:[15, 35] Operation: 25+10=35 Exploring Operation: 15-10=5, Resulting Numbers: [25, 5] Generated Node #0,2,1: 34:[25, 5] Operation: 15-10=5 Exploring Operation: 25-10=15, Resulting Numbers: [15, 15] Generated Node #0,2,2: 34:[15, 15] Operation: 25-10=15 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 34:[15, 35], Operations: ['76-66=10', '25+10=35'] Exploring Operation: 15+35=50, Resulting Numbers: [50] 50,34 unequal: No Solution Exploring Operation: 15*35=525, Resulting Numbers: [525] 525,34 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,34 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 #0,2,2 Current State: 34:[15, 15], Operations: ['76-66=10', '25-10=15'] Exploring Operation: 15-15=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 15/15=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,34 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 #0,2,1 Current State: 34:[25, 5], Operations: ['76-66=10', '15-10=5'] Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,34 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,34 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:[66, 15, 51], Operations: ['76-25=51'] Exploring Operation: 51-15=36, Resulting Numbers: [66, 36] Generated Node #0,0,0: 34:[66, 36] Operation: 51-15=36 Exploring Operation: 66-15=51, Resulting Numbers: [51, 51] Generated Node #0,0,1: 34:[51, 51] Operation: 66-15=51 Exploring Operation: 66-51=15, Resulting Numbers: [15, 15] Generated Node #0,0,2: 34:[15, 15] Operation: 66-51=15 Moving to Node #0,0,2 Current State: 34:[15, 15], Operations: ['76-25=51', '66-51=15'] Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,34 unequal: No Solution Exploring Operation: 15-15=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 15/15=1, Resulting Numbers: [1] 1,34 unequal: No Solution Moving to Node #0,0,0 Current State: 34:[66, 36], Operations: ['76-25=51', '51-15=36'] Exploring Operation: 66-36=30, Resulting Numbers: [30] 30,34 unequal: No Solution Exploring Operation: 66+36=102, Resulting Numbers: [102] 102,34 unequal: No Solution Exploring Operation: 66*36=2376, Resulting Numbers: [2376] 2376,34 unequal: No Solution Moving to Node #0,0,1 Current State: 34:[51, 51], Operations: ['76-25=51', '66-15=51'] Exploring Operation: 51+51=102, Resulting Numbers: [102] 102,34 unequal: No Solution Exploring Operation: 51/51=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 51-51=0, Resulting Numbers: [0] 0,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[15, 76, 41], Operations: ['66-25=41'] Exploring Operation: 76-41=35, Resulting Numbers: [15, 35] Generated Node #0,1,0: 34:[15, 35] Operation: 76-41=35 Exploring Operation: 41-15=26, Resulting Numbers: [76, 26] Generated Node #0,1,1: 34:[76, 26] Operation: 41-15=26 Exploring Operation: 76-15=61, Resulting Numbers: [41, 61] Generated Node #0,1,2: 34:[41, 61] Operation: 76-15=61 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 34:[15, 35], Operations: ['66-25=41', '76-41=35'] Exploring Operation: 15+35=50, Resulting Numbers: [50] 50,34 unequal: No Solution Exploring Operation: 15*35=525, Resulting Numbers: [525] 525,34 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,34 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 #0,1,2 Current State: 34:[41, 61], Operations: ['66-25=41', '76-15=61'] Exploring Operation: 61-41=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 41*61=2501, Resulting Numbers: [2501] 2501,34 unequal: No Solution Exploring Operation: 41+61=102, Resulting Numbers: [102] 102,34 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 #0,1,1 Current State: 34:[76, 26], Operations: ['66-25=41', '41-15=26'] Exploring Operation: 76*26=1976, Resulting Numbers: [1976] 1976,34 unequal: No Solution Exploring Operation: 76+26=102, Resulting Numbers: [102] 102,34 unequal: No Solution Exploring Operation: 76-26=50, Resulting Numbers: [50] 50,34 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_3
mult_heuristic
[ 72, 23, 7, 30 ]
58
[ "72+23=95", "7+30=37", "95-37=58" ]
Current State: 58:[72, 23, 7, 30], Operations: [] Exploring Operation: 72+23=95, Resulting Numbers: [7, 30, 95] Generated Node #2: [7, 30, 95] from Operation: 72+23=95 Current State: 58:[7, 30, 95], Operations: ['72+23=95'] Exploring Operation: 7+30=37, Resulting Numbers: [95, 37] Generated Node #3: [95, 37] from Operation: 7+30=37 Current State: 58:[95, 37], Operations: ['72+23=95', '7+30=37'] Exploring Operation: 95-37=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[72, 23, 7, 30], Operations: [] Exploring Operation: 72-7=65, Resulting Numbers: [23, 30, 65] Generated Node #0,0: 58:[23, 30, 65] Operation: 72-7=65 Moving to Node #0,0 Current State: 58:[23, 30, 65], Operations: ['72-7=65'] Exploring Operation: 23+30=53, Resulting Numbers: [65, 53] Generated Node #0,0,0: 58:[65, 53] Operation: 23+30=53 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[65, 53], Operations: ['72-7=65', '23+30=53'] Exploring Operation: 65-53=12, Resulting Numbers: [12] 12,58 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
[ 58, 7, 28, 93 ]
39
[ "93-58=35", "28/7=4", "35+4=39" ]
Current State: 39:[58, 7, 28, 93], Operations: [] Exploring Operation: 93-58=35, Resulting Numbers: [7, 28, 35] Generated Node #2: [7, 28, 35] from Operation: 93-58=35 Current State: 39:[7, 28, 35], Operations: ['93-58=35'] Exploring Operation: 28/7=4, Resulting Numbers: [35, 4] Generated Node #3: [35, 4] from Operation: 28/7=4 Current State: 39:[35, 4], Operations: ['93-58=35', '28/7=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[58, 7, 28, 93], Operations: [] Exploring Operation: 93-58=35, Resulting Numbers: [7, 28, 35] Generated Node #0,0: 39:[7, 28, 35] Operation: 93-58=35 Exploring Operation: 93-28=65, Resulting Numbers: [58, 7, 65] Generated Node #0,1: 39:[58, 7, 65] Operation: 93-28=65 Exploring Operation: 58-28=30, Resulting Numbers: [7, 93, 30] Generated Node #0,2: 39:[7, 93, 30] Operation: 58-28=30 Moving to Node #0,0 Current State: 39:[7, 28, 35], Operations: ['93-58=35'] Exploring Operation: 35-28=7, Resulting Numbers: [7, 7] Generated Node #0,0,0: 39:[7, 7] Operation: 35-28=7 Exploring Operation: 7+28=35, Resulting Numbers: [35, 35] Generated Node #0,0,1: 39:[35, 35] Operation: 7+28=35 Exploring Operation: 28/7=4, Resulting Numbers: [35, 4] Generated Node #0,0,2: 39:[35, 4] Operation: 28/7=4 Moving to Node #0,1 Current State: 39:[58, 7, 65], Operations: ['93-28=65'] Exploring Operation: 65-7=58, Resulting Numbers: [58, 58] Generated Node #0,1,0: 39:[58, 58] Operation: 65-7=58 Exploring Operation: 58-7=51, Resulting Numbers: [65, 51] Generated Node #0,1,1: 39:[65, 51] Operation: 58-7=51 Exploring Operation: 65-58=7, Resulting Numbers: [7, 7] Generated Node #0,1,2: 39:[7, 7] Operation: 65-58=7 Moving to Node #0,2 Current State: 39:[7, 93, 30], Operations: ['58-28=30'] Exploring Operation: 93-30=63, Resulting Numbers: [7, 63] Generated Node #0,2,0: 39:[7, 63] Operation: 93-30=63 Exploring Operation: 93-7=86, Resulting Numbers: [30, 86] Generated Node #0,2,1: 39:[30, 86] Operation: 93-7=86 Exploring Operation: 7+30=37, Resulting Numbers: [93, 37] Generated Node #0,2,2: 39:[93, 37] Operation: 7+30=37 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[7, 63], Operations: ['58-28=30', '93-30=63'] Exploring Operation: 7+63=70, Resulting Numbers: [70] 70,39 unequal: No Solution Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 39:[30, 86], Operations: ['58-28=30', '93-7=86'] Exploring Operation: 86-30=56, Resulting Numbers: [56] 56,39 unequal: No Solution Exploring Operation: 30*86=2580, Resulting Numbers: [2580] 2580,39 unequal: No Solution Exploring Operation: 30+86=116, Resulting Numbers: [116] 116,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 39:[93, 37], Operations: ['58-28=30', '7+30=37'] Exploring Operation: 93+37=130, Resulting Numbers: [130] 130,39 unequal: No Solution Exploring Operation: 93*37=3441, Resulting Numbers: [3441] 3441,39 unequal: No Solution Exploring Operation: 93-37=56, Resulting Numbers: [56] 56,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 39:[35, 4], Operations: ['93-58=35', '28/7=4'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[58, 7, 28, 93], Operations: [] Exploring Operation: 93-58=35, Resulting Numbers: [7, 28, 35] Generated Node #0,0: 39:[7, 28, 35] Operation: 93-58=35 Moving to Node #0,0 Current State: 39:[7, 28, 35], Operations: ['93-58=35'] Exploring Operation: 28/7=4, Resulting Numbers: [35, 4] Generated Node #0,0,2: 39:[35, 4] Operation: 28/7=4 Moving to Node #0,0,2 Current State: 39:[35, 4], Operations: ['93-58=35', '28/7=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
0.976563
hs_3
mult_heuristic
[ 33, 30, 12, 22 ]
73
[ "33+30=63", "22-12=10", "63+10=73" ]
Current State: 73:[33, 30, 12, 22], Operations: [] Exploring Operation: 33+30=63, Resulting Numbers: [12, 22, 63] Generated Node #2: [12, 22, 63] from Operation: 33+30=63 Current State: 73:[12, 22, 63], Operations: ['33+30=63'] Exploring Operation: 22-12=10, Resulting Numbers: [63, 10] Generated Node #3: [63, 10] from Operation: 22-12=10 Current State: 73:[63, 10], Operations: ['33+30=63', '22-12=10'] Exploring Operation: 63+10=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[33, 30, 12, 22], Operations: [] Exploring Operation: 33+12=45, Resulting Numbers: [30, 22, 45] Generated Node #0,0: 73:[30, 22, 45] Operation: 33+12=45 Exploring Operation: 30+12=42, Resulting Numbers: [33, 22, 42] Generated Node #0,1: 73:[33, 22, 42] Operation: 30+12=42 Exploring Operation: 33+22=55, Resulting Numbers: [30, 12, 55] Generated Node #0,2: 73:[30, 12, 55] Operation: 33+22=55 Exploring Operation: 33+30=63, Resulting Numbers: [12, 22, 63] Generated Node #0,3: 73:[12, 22, 63] Operation: 33+30=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[30, 22, 45], Operations: ['33+12=45'] Exploring Operation: 30+45=75, Resulting Numbers: [22, 75] Generated Node #0,0,0: 73:[22, 75] Operation: 30+45=75 Exploring Operation: 30-22=8, Resulting Numbers: [45, 8] Generated Node #0,0,1: 73:[45, 8] Operation: 30-22=8 Exploring Operation: 30+22=52, Resulting Numbers: [45, 52] Generated Node #0,0,2: 73:[45, 52] Operation: 30+22=52 Exploring Operation: 22+45=67, Resulting Numbers: [30, 67] Generated Node #0,0,3: 73:[30, 67] Operation: 22+45=67 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 73:[45, 52], Operations: ['33+12=45', '30+22=52'] Exploring Operation: 45+52=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,73 unequal: No Solution Exploring Operation: 45*52=2340, Resulting Numbers: [2340] 2340,73 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 #0,0,3 Current State: 73:[30, 67], Operations: ['33+12=45', '22+45=67'] Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,73 unequal: No Solution Exploring Operation: 30*67=2010, Resulting Numbers: [2010] 2010,73 unequal: No Solution Exploring Operation: 30+67=97, Resulting Numbers: [97] 97,73 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:[22, 75], Operations: ['33+12=45', '30+45=75'] Exploring Operation: 22+75=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 75-22=53, Resulting Numbers: [53] 53,73 unequal: No Solution Exploring Operation: 22*75=1650, Resulting Numbers: [1650] 1650,73 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 #0,0,1 Current State: 73:[45, 8], Operations: ['33+12=45', '30-22=8'] Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,73 unequal: No Solution Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,73 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,73 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:[33, 22, 42], Operations: ['30+12=42'] Exploring Operation: 33+22=55, Resulting Numbers: [42, 55] Generated Node #0,1,0: 73:[42, 55] Operation: 33+22=55 Exploring Operation: 22+42=64, Resulting Numbers: [33, 64] Generated Node #0,1,1: 73:[33, 64] Operation: 22+42=64 Exploring Operation: 33-22=11, Resulting Numbers: [42, 11] Generated Node #0,1,2: 73:[42, 11] Operation: 33-22=11 Exploring Operation: 33+42=75, Resulting Numbers: [22, 75] Generated Node #0,1,3: 73:[22, 75] Operation: 33+42=75 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[42, 55], Operations: ['30+12=42', '33+22=55'] Exploring Operation: 55-42=13, Resulting Numbers: [13] 13,73 unequal: No Solution Exploring Operation: 42*55=2310, Resulting Numbers: [2310] 2310,73 unequal: No Solution Exploring Operation: 42+55=97, Resulting Numbers: [97] 97,73 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:[33, 64], Operations: ['30+12=42', '22+42=64'] Exploring Operation: 33+64=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 64-33=31, Resulting Numbers: [31] 31,73 unequal: No Solution Exploring Operation: 33*64=2112, Resulting Numbers: [2112] 2112,73 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 #0,1,3 Current State: 73:[22, 75], Operations: ['30+12=42', '33+42=75'] Exploring Operation: 22*75=1650, Resulting Numbers: [1650] 1650,73 unequal: No Solution Exploring Operation: 22+75=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 75-22=53, Resulting Numbers: [53] 53,73 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 #0,1,2 Current State: 73:[42, 11], Operations: ['30+12=42', '33-22=11'] Exploring Operation: 42+11=53, Resulting Numbers: [53] 53,73 unequal: No Solution Exploring Operation: 42*11=462, Resulting Numbers: [462] 462,73 unequal: No Solution Exploring Operation: 42-11=31, Resulting Numbers: [31] 31,73 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 #0,2 Current State: 73:[30, 12, 55], Operations: ['33+22=55'] Exploring Operation: 30-12=18, Resulting Numbers: [55, 18] Generated Node #0,2,0: 73:[55, 18] Operation: 30-12=18 Exploring Operation: 30+12=42, Resulting Numbers: [55, 42] Generated Node #0,2,1: 73:[55, 42] Operation: 30+12=42 Exploring Operation: 30+55=85, Resulting Numbers: [12, 85] Generated Node #0,2,2: 73:[12, 85] Operation: 30+55=85 Exploring Operation: 12+55=67, Resulting Numbers: [30, 67] Generated Node #0,2,3: 73:[30, 67] Operation: 12+55=67 Moving to Node #0,2,1 Current State: 73:[55, 42], Operations: ['33+22=55', '30+12=42'] Exploring Operation: 55-42=13, Resulting Numbers: [13] 13,73 unequal: No Solution Exploring Operation: 55*42=2310, Resulting Numbers: [2310] 2310,73 unequal: No Solution Exploring Operation: 55+42=97, Resulting Numbers: [97] 97,73 unequal: No Solution Moving to Node #0,2,3 Current State: 73:[30, 67], Operations: ['33+22=55', '12+55=67'] Exploring Operation: 30*67=2010, Resulting Numbers: [2010] 2010,73 unequal: No Solution Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,73 unequal: No Solution Exploring Operation: 30+67=97, Resulting Numbers: [97] 97,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[12, 85], Operations: ['33+22=55', '30+55=85'] Exploring Operation: 12*85=1020, Resulting Numbers: [1020] 1020,73 unequal: No Solution Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[33, 30, 12, 22], Operations: [] Exploring Operation: 33+22=55, Resulting Numbers: [30, 12, 55] Generated Node #0,2: 73:[30, 12, 55] Operation: 33+22=55 Moving to Node #0,2 Current State: 73:[30, 12, 55], Operations: ['33+22=55'] Exploring Operation: 30+55=85, Resulting Numbers: [12, 85] Generated Node #0,2,2: 73:[12, 85] Operation: 30+55=85 Moving to Node #0,2,2 Current State: 73:[12, 85], Operations: ['33+22=55', '30+55=85'] Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.954861
hs_4
sum_heuristic
[ 1, 63, 41, 83 ]
22
[ "1+63=64", "83-41=42", "64-42=22" ]
Current State: 22:[1, 63, 41, 83], Operations: [] Exploring Operation: 1+63=64, Resulting Numbers: [41, 83, 64] Generated Node #2: [41, 83, 64] from Operation: 1+63=64 Current State: 22:[41, 83, 64], Operations: ['1+63=64'] Exploring Operation: 83-41=42, Resulting Numbers: [64, 42] Generated Node #3: [64, 42] from Operation: 83-41=42 Current State: 22:[64, 42], Operations: ['1+63=64', '83-41=42'] Exploring Operation: 64-42=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[1, 63, 41, 83], Operations: [] Exploring Operation: 83-63=20, Resulting Numbers: [1, 41, 20] Generated Node #0,0: 22:[1, 41, 20] Operation: 83-63=20 Moving to Node #0,0 Current State: 22:[1, 41, 20], Operations: ['83-63=20'] Exploring Operation: 41-20=21, Resulting Numbers: [1, 21] Generated Node #0,0,0: 22:[1, 21] Operation: 41-20=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[1, 21], Operations: ['83-63=20', '41-20=21'] Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[1, 63, 41, 83], Operations: [] Exploring Operation: 83-63=20, Resulting Numbers: [1, 41, 20] Generated Node #0,0: 22:[1, 41, 20] Operation: 83-63=20 Moving to Node #0,0 Current State: 22:[1, 41, 20], Operations: ['83-63=20'] Exploring Operation: 41-20=21, Resulting Numbers: [1, 21] Generated Node #0,0,0: 22:[1, 21] Operation: 41-20=21 Moving to Node #0,0,0 Current State: 22:[1, 21], Operations: ['83-63=20', '41-20=21'] Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 67, 10, 12, 16 ]
73
[ "67+10=77", "16-12=4", "77-4=73" ]
Current State: 73:[67, 10, 12, 16], Operations: [] Exploring Operation: 67+10=77, Resulting Numbers: [12, 16, 77] Generated Node #2: [12, 16, 77] from Operation: 67+10=77 Current State: 73:[12, 16, 77], Operations: ['67+10=77'] Exploring Operation: 16-12=4, Resulting Numbers: [77, 4] Generated Node #3: [77, 4] from Operation: 16-12=4 Current State: 73:[77, 4], Operations: ['67+10=77', '16-12=4'] Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[67, 10, 12, 16], Operations: [] Exploring Operation: 10*12=120, Resulting Numbers: [67, 16, 120] Generated Node #0,0: 73:[67, 16, 120] Operation: 10*12=120 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[67, 16, 120], Operations: ['10*12=120'] Exploring Operation: 120-16=104, Resulting Numbers: [67, 104] Generated Node #0,0,0: 73:[67, 104] Operation: 120-16=104 Moving to Node #0,0,0 Current State: 73:[67, 104], Operations: ['10*12=120', '120-16=104'] Exploring Operation: 104-67=37, Resulting Numbers: [37] 37,73 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
[ 61, 50, 49, 37 ]
97
[ "61-50=11", "49+37=86", "11+86=97" ]
Current State: 97:[61, 50, 49, 37], Operations: [] Exploring Operation: 61-50=11, Resulting Numbers: [49, 37, 11] Generated Node #2: [49, 37, 11] from Operation: 61-50=11 Current State: 97:[49, 37, 11], Operations: ['61-50=11'] Exploring Operation: 49+37=86, Resulting Numbers: [11, 86] Generated Node #3: [11, 86] from Operation: 49+37=86 Current State: 97:[11, 86], Operations: ['61-50=11', '49+37=86'] Exploring Operation: 11+86=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[61, 50, 49, 37], Operations: [] Exploring Operation: 61+37=98, Resulting Numbers: [50, 49, 98] Generated Node #0,0: 97:[50, 49, 98] Operation: 61+37=98 Exploring Operation: 61+49=110, Resulting Numbers: [50, 37, 110] Generated Node #0,1: 97:[50, 37, 110] Operation: 61+49=110 Exploring Operation: 49+37=86, Resulting Numbers: [61, 50, 86] Generated Node #0,2: 97:[61, 50, 86] Operation: 49+37=86 Exploring Operation: 50+49=99, Resulting Numbers: [61, 37, 99] Generated Node #0,3: 97:[61, 37, 99] Operation: 50+49=99 Exploring Operation: 50+37=87, Resulting Numbers: [61, 49, 87] Generated Node #0,4: 97:[61, 49, 87] Operation: 50+37=87 Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[61, 50, 86], Operations: ['49+37=86'] Exploring Operation: 61+86=147, Resulting Numbers: [50, 147] Generated Node #0,2,0: 97:[50, 147] Operation: 61+86=147 Exploring Operation: 61-50=11, Resulting Numbers: [86, 11] Generated Node #0,2,1: 97:[86, 11] Operation: 61-50=11 Exploring Operation: 50+86=136, Resulting Numbers: [61, 136] Generated Node #0,2,2: 97:[61, 136] Operation: 50+86=136 Exploring Operation: 61+50=111, Resulting Numbers: [86, 111] Generated Node #0,2,3: 97:[86, 111] Operation: 61+50=111 Exploring Operation: 86-50=36, Resulting Numbers: [61, 36] Generated Node #0,2,4: 97:[61, 36] Operation: 86-50=36 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 97:[86, 111], Operations: ['49+37=86', '61+50=111'] Exploring Operation: 86+111=197, Resulting Numbers: [197] 197,97 unequal: No Solution Exploring Operation: 86*111=9546, Resulting Numbers: [9546] 9546,97 unequal: No Solution Exploring Operation: 111-86=25, Resulting Numbers: [25] 25,97 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: 97:[61, 136], Operations: ['49+37=86', '50+86=136'] Exploring Operation: 61+136=197, Resulting Numbers: [197] 197,97 unequal: No Solution Exploring Operation: 136-61=75, Resulting Numbers: [75] 75,97 unequal: No Solution Exploring Operation: 61*136=8296, Resulting Numbers: [8296] 8296,97 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: 97:[50, 147], Operations: ['49+37=86', '61+86=147'] Exploring Operation: 147-50=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[61, 50, 49, 37], Operations: [] Exploring Operation: 49+37=86, Resulting Numbers: [61, 50, 86] Generated Node #0,2: 97:[61, 50, 86] Operation: 49+37=86 Moving to Node #0,2 Current State: 97:[61, 50, 86], Operations: ['49+37=86'] Exploring Operation: 61+86=147, Resulting Numbers: [50, 147] Generated Node #0,2,0: 97:[50, 147] Operation: 61+86=147 Moving to Node #0,2,0 Current State: 97:[50, 147], Operations: ['49+37=86', '61+86=147'] Exploring Operation: 147-50=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 40, 97, 89, 72 ]
14
[ "40+72=112", "97-89=8", "112/8=14" ]
Current State: 14:[40, 97, 89, 72], Operations: [] Exploring Operation: 40+72=112, Resulting Numbers: [97, 89, 112] Generated Node #2: [97, 89, 112] from Operation: 40+72=112 Current State: 14:[97, 89, 112], Operations: ['40+72=112'] Exploring Operation: 97-89=8, Resulting Numbers: [112, 8] Generated Node #3: [112, 8] from Operation: 97-89=8 Current State: 14:[112, 8], Operations: ['40+72=112', '97-89=8'] Exploring Operation: 112/8=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[40, 97, 89, 72], Operations: [] Exploring Operation: 97-72=25, Resulting Numbers: [40, 89, 25] Generated Node #0,0: 14:[40, 89, 25] Operation: 97-72=25 Exploring Operation: 97-89=8, Resulting Numbers: [40, 72, 8] Generated Node #0,1: 14:[40, 72, 8] Operation: 97-89=8 Moving to Node #0,1 Current State: 14:[40, 72, 8], Operations: ['97-89=8'] Exploring Operation: 72-40=32, Resulting Numbers: [8, 32] Generated Node #0,1,0: 14:[8, 32] Operation: 72-40=32 Exploring Operation: 72/8=9, Resulting Numbers: [40, 9] Generated Node #0,1,1: 14:[40, 9] Operation: 72/8=9 Moving to Node #0,0 Current State: 14:[40, 89, 25], Operations: ['97-72=25'] Exploring Operation: 89-40=49, Resulting Numbers: [25, 49] Generated Node #0,0,0: 14:[25, 49] Operation: 89-40=49 Exploring Operation: 40-25=15, Resulting Numbers: [89, 15] Generated Node #0,0,1: 14:[89, 15] Operation: 40-25=15 Moving to Node #0,1,0 Current State: 14:[8, 32], Operations: ['97-89=8', '72-40=32'] Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,14 unequal: No Solution Moving to Node #0,1,1 Current State: 14:[40, 9], Operations: ['97-89=8', '72/8=9'] Exploring Operation: 40+9=49, Resulting Numbers: [49] 49,14 unequal: No Solution Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,14 unequal: No Solution Moving to Node #0,0,0 Current State: 14:[25, 49], Operations: ['97-72=25', '89-40=49'] Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 25+49=74, Resulting Numbers: [74] 74,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[89, 15], Operations: ['97-72=25', '40-25=15'] Exploring Operation: 89+15=104, Resulting Numbers: [104] 104,14 unequal: No Solution Exploring Operation: 89-15=74, Resulting Numbers: [74] 74,14 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 6, 79, 34, 86 ]
99
[ "34+86=120", "120/6=20", "79+20=99" ]
Current State: 99:[6, 79, 34, 86], Operations: [] Exploring Operation: 34+86=120, Resulting Numbers: [6, 79, 120] Generated Node #2: [6, 79, 120] from Operation: 34+86=120 Current State: 99:[6, 79, 120], Operations: ['34+86=120'] Exploring Operation: 120/6=20, Resulting Numbers: [79, 20] Generated Node #3: [79, 20] from Operation: 120/6=20 Current State: 99:[79, 20], Operations: ['34+86=120', '120/6=20'] Exploring Operation: 79+20=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[6, 79, 34, 86], Operations: [] Exploring Operation: 6+86=92, Resulting Numbers: [79, 34, 92] Generated Node #0,0: 99:[79, 34, 92] Operation: 6+86=92 Exploring Operation: 6+79=85, Resulting Numbers: [34, 86, 85] Generated Node #0,1: 99:[34, 86, 85] Operation: 6+79=85 Exploring Operation: 86-79=7, Resulting Numbers: [6, 34, 7] Generated Node #0,2: 99:[6, 34, 7] Operation: 86-79=7 Moving to Node #0,2 Current State: 99:[6, 34, 7], Operations: ['86-79=7'] Exploring Operation: 6+7=13, Resulting Numbers: [34, 13] Generated Node #0,2,0: 99:[34, 13] Operation: 6+7=13 Exploring Operation: 7-6=1, Resulting Numbers: [34, 1] Generated Node #0,2,1: 99:[34, 1] Operation: 7-6=1 Exploring Operation: 34-6=28, Resulting Numbers: [7, 28] Generated Node #0,2,2: 99:[7, 28] Operation: 34-6=28 Moving to Node #0,0 Current State: 99:[79, 34, 92], Operations: ['6+86=92'] Exploring Operation: 79+34=113, Resulting Numbers: [92, 113] Generated Node #0,0,0: 99:[92, 113] Operation: 79+34=113 Exploring Operation: 79-34=45, Resulting Numbers: [92, 45] Generated Node #0,0,1: 99:[92, 45] Operation: 79-34=45 Exploring Operation: 92-79=13, Resulting Numbers: [34, 13] Generated Node #0,0,2: 99:[34, 13] Operation: 92-79=13 Moving to Node #0,1 Current State: 99:[34, 86, 85], Operations: ['6+79=85'] Exploring Operation: 86-34=52, Resulting Numbers: [85, 52] Generated Node #0,1,0: 99:[85, 52] Operation: 86-34=52 Exploring Operation: 85-34=51, Resulting Numbers: [86, 51] Generated Node #0,1,1: 99:[86, 51] Operation: 85-34=51 Exploring Operation: 86-85=1, Resulting Numbers: [34, 1] Generated Node #0,1,2: 99:[34, 1] Operation: 86-85=1 Moving to Node #0,2,0 Current State: 99:[34, 13], Operations: ['86-79=7', '6+7=13'] Exploring Operation: 34+13=47, Resulting Numbers: [47] 47,99 unequal: No Solution Exploring Operation: 34-13=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 34*13=442, Resulting Numbers: [442] 442,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[34, 1], Operations: ['6+79=85', '86-85=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,99 unequal: No Solution Moving to Node #0,2,1 Current State: 99:[34, 1], Operations: ['86-79=7', '7-6=1'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[34, 13], Operations: ['6+86=92', '92-79=13'] Exploring Operation: 34*13=442, Resulting Numbers: [442] 442,99 unequal: No Solution Exploring Operation: 34+13=47, Resulting Numbers: [47] 47,99 unequal: No Solution Exploring Operation: 34-13=21, Resulting Numbers: [21] 21,99 unequal: No Solution Moving to Node #0,2,2 Current State: 99:[7, 28], Operations: ['86-79=7', '34-6=28'] Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,99 unequal: No Solution Exploring Operation: 7+28=35, Resulting Numbers: [35] 35,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[92, 45], Operations: ['6+86=92', '79-34=45'] Exploring Operation: 92-45=47, Resulting Numbers: [47] 47,99 unequal: No Solution Exploring Operation: 92*45=4140, Resulting Numbers: [4140] 4140,99 unequal: No Solution Exploring Operation: 92+45=137, Resulting Numbers: [137] 137,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[92, 113], Operations: ['6+86=92', '79+34=113'] Exploring Operation: 92*113=10396, Resulting Numbers: [10396] 10396,99 unequal: No Solution Exploring Operation: 113-92=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 92+113=205, Resulting Numbers: [205] 205,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[86, 51], Operations: ['6+79=85', '85-34=51'] Exploring Operation: 86*51=4386, Resulting Numbers: [4386] 4386,99 unequal: No Solution Exploring Operation: 86-51=35, Resulting Numbers: [35] 35,99 unequal: No Solution Exploring Operation: 86+51=137, Resulting Numbers: [137] 137,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[85, 52], Operations: ['6+79=85', '86-34=52'] Exploring Operation: 85*52=4420, Resulting Numbers: [4420] 4420,99 unequal: No Solution Exploring Operation: 85-52=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 85+52=137, Resulting Numbers: [137] 137,99 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 67, 92, 77, 46 ]
12
[ "77-67=10", "92/46=2", "10+2=12" ]
Current State: 12:[67, 92, 77, 46], Operations: [] Exploring Operation: 77-67=10, Resulting Numbers: [92, 46, 10] Generated Node #2: [92, 46, 10] from Operation: 77-67=10 Current State: 12:[92, 46, 10], Operations: ['77-67=10'] Exploring Operation: 92/46=2, Resulting Numbers: [10, 2] Generated Node #3: [10, 2] from Operation: 92/46=2 Current State: 12:[10, 2], Operations: ['77-67=10', '92/46=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[67, 92, 77, 46], Operations: [] Exploring Operation: 77-67=10, Resulting Numbers: [92, 46, 10] Generated Node #0,0: 12:[92, 46, 10] Operation: 77-67=10 Exploring Operation: 92-67=25, Resulting Numbers: [77, 46, 25] Generated Node #0,1: 12:[77, 46, 25] Operation: 92-67=25 Exploring Operation: 92-77=15, Resulting Numbers: [67, 46, 15] Generated Node #0,2: 12:[67, 46, 15] Operation: 92-77=15 Moving to Node #0,2 Current State: 12:[67, 46, 15], Operations: ['92-77=15'] Exploring Operation: 67-46=21, Resulting Numbers: [15, 21] Generated Node #0,2,0: 12:[15, 21] Operation: 67-46=21 Exploring Operation: 46-15=31, Resulting Numbers: [67, 31] Generated Node #0,2,1: 12:[67, 31] Operation: 46-15=31 Exploring Operation: 67-15=52, Resulting Numbers: [46, 52] Generated Node #0,2,2: 12:[46, 52] Operation: 67-15=52 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 12:[15, 21], Operations: ['92-77=15', '67-46=21'] Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 15*21=315, Resulting Numbers: [315] 315,12 unequal: No Solution Exploring Operation: 15+21=36, Resulting Numbers: [36] 36,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 12:[67, 31], Operations: ['92-77=15', '46-15=31'] Exploring Operation: 67-31=36, Resulting Numbers: [36] 36,12 unequal: No Solution Exploring Operation: 67*31=2077, Resulting Numbers: [2077] 2077,12 unequal: No Solution Exploring Operation: 67+31=98, Resulting Numbers: [98] 98,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 12:[46, 52], Operations: ['92-77=15', '67-15=52'] Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 46*52=2392, Resulting Numbers: [2392] 2392,12 unequal: No Solution Exploring Operation: 46+52=98, Resulting Numbers: [98] 98,12 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: 12:[77, 46, 25], Operations: ['92-67=25'] Exploring Operation: 77-25=52, Resulting Numbers: [46, 52] Generated Node #0,1,0: 12:[46, 52] Operation: 77-25=52 Exploring Operation: 77-46=31, Resulting Numbers: [25, 31] Generated Node #0,1,1: 12:[25, 31] Operation: 77-46=31 Exploring Operation: 46-25=21, Resulting Numbers: [77, 21] Generated Node #0,1,2: 12:[77, 21] Operation: 46-25=21 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 12:[25, 31], Operations: ['92-67=25', '77-46=31'] Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 25*31=775, Resulting Numbers: [775] 775,12 unequal: No Solution Exploring Operation: 25+31=56, Resulting Numbers: [56] 56,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 12:[46, 52], Operations: ['92-67=25', '77-25=52'] Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 46+52=98, Resulting Numbers: [98] 98,12 unequal: No Solution Exploring Operation: 46*52=2392, Resulting Numbers: [2392] 2392,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 12:[77, 21], Operations: ['92-67=25', '46-25=21'] Exploring Operation: 77+21=98, Resulting Numbers: [98] 98,12 unequal: No Solution Exploring Operation: 77*21=1617, Resulting Numbers: [1617] 1617,12 unequal: No Solution Exploring Operation: 77-21=56, Resulting Numbers: [56] 56,12 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: 12:[92, 46, 10], Operations: ['77-67=10'] Exploring Operation: 92/46=2, Resulting Numbers: [10, 2] Generated Node #0,0,0: 12:[10, 2] Operation: 92/46=2 Exploring Operation: 92-46=46, Resulting Numbers: [10, 46] Generated Node #0,0,1: 12:[10, 46] Operation: 92-46=46 Exploring Operation: 92-10=82, Resulting Numbers: [46, 82] Generated Node #0,0,2: 12:[46, 82] Operation: 92-10=82 Moving to Node #0,0,0 Current State: 12:[10, 2], Operations: ['77-67=10', '92/46=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[67, 92, 77, 46], Operations: [] Exploring Operation: 77-67=10, Resulting Numbers: [92, 46, 10] Generated Node #0,0: 12:[92, 46, 10] Operation: 77-67=10 Moving to Node #0,0 Current State: 12:[92, 46, 10], Operations: ['77-67=10'] Exploring Operation: 92/46=2, Resulting Numbers: [10, 2] Generated Node #0,0,0: 12:[10, 2] Operation: 92/46=2 Moving to Node #0,0,0 Current State: 12:[10, 2], Operations: ['77-67=10', '92/46=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.967882
hs_3
sum_heuristic
[ 92, 2, 69, 81 ]
29
[ "92-69=23", "81-23=58", "58/2=29" ]
Current State: 29:[92, 2, 69, 81], Operations: [] Exploring Operation: 92-69=23, Resulting Numbers: [2, 81, 23] Generated Node #2: [2, 81, 23] from Operation: 92-69=23 Current State: 29:[2, 81, 23], Operations: ['92-69=23'] Exploring Operation: 81-23=58, Resulting Numbers: [2, 58] Generated Node #3: [2, 58] from Operation: 81-23=58 Current State: 29:[2, 58], Operations: ['92-69=23', '81-23=58'] Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[92, 2, 69, 81], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [2, 69, 11] Generated Node #0,0: 29:[2, 69, 11] Operation: 92-81=11 Exploring Operation: 92-69=23, Resulting Numbers: [2, 81, 23] Generated Node #0,1: 29:[2, 81, 23] Operation: 92-69=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[2, 69, 11], Operations: ['92-81=11'] Exploring Operation: 69-2=67, Resulting Numbers: [11, 67] Generated Node #0,0,0: 29:[11, 67] Operation: 69-2=67 Exploring Operation: 2*11=22, Resulting Numbers: [69, 22] Generated Node #0,0,1: 29:[69, 22] Operation: 2*11=22 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 29:[69, 22], Operations: ['92-81=11', '2*11=22'] Exploring Operation: 69-22=47, Resulting Numbers: [47] 47,29 unequal: No Solution Exploring Operation: 69+22=91, Resulting Numbers: [91] 91,29 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: 29:[11, 67], Operations: ['92-81=11', '69-2=67'] Exploring Operation: 11+67=78, Resulting Numbers: [78] 78,29 unequal: No Solution Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[2, 81, 23], Operations: ['92-69=23'] Exploring Operation: 2+23=25, Resulting Numbers: [81, 25] Generated Node #0,1,0: 29:[81, 25] Operation: 2+23=25 Exploring Operation: 81-2=79, Resulting Numbers: [23, 79] Generated Node #0,1,1: 29:[23, 79] Operation: 81-2=79 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 29:[81, 25], Operations: ['92-69=23', '2+23=25'] Exploring Operation: 81-25=56, Resulting Numbers: [56] 56,29 unequal: No Solution Exploring Operation: 81+25=106, Resulting Numbers: [106] 106,29 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: 29:[23, 79], Operations: ['92-69=23', '81-2=79'] Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,29 unequal: No Solution Exploring Operation: 23+79=102, Resulting Numbers: [102] 102,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 23, 49, 6, 17 ]
85
[ "23-17=6", "6*6=36", "49+36=85" ]
Current State: 85:[23, 49, 6, 17], Operations: [] Exploring Operation: 23-17=6, Resulting Numbers: [49, 6, 6] Generated Node #2: [49, 6, 6] from Operation: 23-17=6 Current State: 85:[49, 6, 6], Operations: ['23-17=6'] Exploring Operation: 6*6=36, Resulting Numbers: [49, 36] Generated Node #3: [49, 36] from Operation: 6*6=36 Current State: 85:[49, 36], Operations: ['23-17=6', '6*6=36'] Exploring Operation: 49+36=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[23, 49, 6, 17], Operations: [] Exploring Operation: 49-23=26, Resulting Numbers: [6, 17, 26] Generated Node #0,0: 85:[6, 17, 26] Operation: 49-23=26 Exploring Operation: 23+49=72, Resulting Numbers: [6, 17, 72] Generated Node #0,1: 85:[6, 17, 72] Operation: 23+49=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[6, 17, 26], Operations: ['49-23=26'] Exploring Operation: 26-6=20, Resulting Numbers: [17, 20] Generated Node #0,0,0: 85:[17, 20] Operation: 26-6=20 Exploring Operation: 26-17=9, Resulting Numbers: [6, 9] Generated Node #0,0,1: 85:[6, 9] Operation: 26-17=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[17, 20], Operations: ['49-23=26', '26-6=20'] Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,85 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: 85:[6, 9], Operations: ['49-23=26', '26-17=9'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,85 unequal: No Solution Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,85 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: 85:[6, 17, 72], Operations: ['23+49=72'] Exploring Operation: 17+72=89, Resulting Numbers: [6, 89] Generated Node #0,1,0: 85:[6, 89] Operation: 17+72=89 Exploring Operation: 72/6=12, Resulting Numbers: [17, 12] Generated Node #0,1,1: 85:[17, 12] Operation: 72/6=12 Moving to Node #0,1,0 Current State: 85:[6, 89], Operations: ['23+49=72', '17+72=89'] Exploring Operation: 89-6=83, Resulting Numbers: [83] 83,85 unequal: No Solution Exploring Operation: 6+89=95, Resulting Numbers: [95] 95,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[17, 12], Operations: ['23+49=72', '72/6=12'] Exploring Operation: 17+12=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,85 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
[ 71, 69, 63, 52 ]
89
[ "71-69=2", "52/2=26", "63+26=89" ]
Current State: 89:[71, 69, 63, 52], Operations: [] Exploring Operation: 71-69=2, Resulting Numbers: [63, 52, 2] Generated Node #2: [63, 52, 2] from Operation: 71-69=2 Current State: 89:[63, 52, 2], Operations: ['71-69=2'] Exploring Operation: 52/2=26, Resulting Numbers: [63, 26] Generated Node #3: [63, 26] from Operation: 52/2=26 Current State: 89:[63, 26], Operations: ['71-69=2', '52/2=26'] Exploring Operation: 63+26=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[71, 69, 63, 52], Operations: [] Exploring Operation: 71+52=123, Resulting Numbers: [69, 63, 123] Generated Node #0,0: 89:[69, 63, 123] Operation: 71+52=123 Exploring Operation: 69+52=121, Resulting Numbers: [71, 63, 121] Generated Node #0,1: 89:[71, 63, 121] Operation: 69+52=121 Exploring Operation: 63+52=115, Resulting Numbers: [71, 69, 115] Generated Node #0,2: 89:[71, 69, 115] Operation: 63+52=115 Moving to Node #0,2 Current State: 89:[71, 69, 115], Operations: ['63+52=115'] Exploring Operation: 115-71=44, Resulting Numbers: [69, 44] Generated Node #0,2,0: 89:[69, 44] Operation: 115-71=44 Exploring Operation: 71+69=140, Resulting Numbers: [115, 140] Generated Node #0,2,1: 89:[115, 140] Operation: 71+69=140 Exploring Operation: 115-69=46, Resulting Numbers: [71, 46] Generated Node #0,2,2: 89:[71, 46] Operation: 115-69=46 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[71, 46], Operations: ['63+52=115', '115-69=46'] Exploring Operation: 71*46=3266, Resulting Numbers: [3266] 3266,89 unequal: No Solution Exploring Operation: 71+46=117, Resulting Numbers: [117] 117,89 unequal: No Solution Exploring Operation: 71-46=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 #0,2,0 Current State: 89:[69, 44], Operations: ['63+52=115', '115-71=44'] Exploring Operation: 69-44=25, Resulting Numbers: [25] 25,89 unequal: No Solution Exploring Operation: 69+44=113, Resulting Numbers: [113] 113,89 unequal: No Solution Exploring Operation: 69*44=3036, Resulting Numbers: [3036] 3036,89 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:[115, 140], Operations: ['63+52=115', '71+69=140'] Exploring Operation: 140-115=25, Resulting Numbers: [25] 25,89 unequal: No Solution Exploring Operation: 115*140=16100, Resulting Numbers: [16100] 16100,89 unequal: No Solution Exploring Operation: 115+140=255, Resulting Numbers: [255] 255,89 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: 89:[71, 63, 121], Operations: ['69+52=121'] Exploring Operation: 121-71=50, Resulting Numbers: [63, 50] Generated Node #0,1,0: 89:[63, 50] Operation: 121-71=50 Exploring Operation: 71+63=134, Resulting Numbers: [121, 134] Generated Node #0,1,1: 89:[121, 134] Operation: 71+63=134 Exploring Operation: 121-63=58, Resulting Numbers: [71, 58] Generated Node #0,1,2: 89:[71, 58] Operation: 121-63=58 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 89:[71, 58], Operations: ['69+52=121', '121-63=58'] Exploring Operation: 71*58=4118, Resulting Numbers: [4118] 4118,89 unequal: No Solution Exploring Operation: 71+58=129, Resulting Numbers: [129] 129,89 unequal: No Solution Exploring Operation: 71-58=13, Resulting Numbers: [13] 13,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[63, 50], Operations: ['69+52=121', '121-71=50'] Exploring Operation: 63*50=3150, Resulting Numbers: [3150] 3150,89 unequal: No Solution Exploring Operation: 63+50=113, Resulting Numbers: [113] 113,89 unequal: No Solution Exploring Operation: 63-50=13, Resulting Numbers: [13] 13,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[121, 134], Operations: ['69+52=121', '71+63=134'] Exploring Operation: 121+134=255, Resulting Numbers: [255] 255,89 unequal: No Solution Exploring Operation: 134-121=13, Resulting Numbers: [13] 13,89 unequal: No Solution Exploring Operation: 121*134=16214, Resulting Numbers: [16214] 16214,89 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: 89:[69, 63, 123], Operations: ['71+52=123'] Exploring Operation: 123-69=54, Resulting Numbers: [63, 54] Generated Node #0,0,0: 89:[63, 54] Operation: 123-69=54 Exploring Operation: 69+63=132, Resulting Numbers: [123, 132] Generated Node #0,0,1: 89:[123, 132] Operation: 69+63=132 Exploring Operation: 123-63=60, Resulting Numbers: [69, 60] Generated Node #0,0,2: 89:[69, 60] Operation: 123-63=60 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 89:[69, 60], Operations: ['71+52=123', '123-63=60'] Exploring Operation: 69+60=129, Resulting Numbers: [129] 129,89 unequal: No Solution Exploring Operation: 69*60=4140, Resulting Numbers: [4140] 4140,89 unequal: No Solution Exploring Operation: 69-60=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 #0,0,0 Current State: 89:[63, 54], Operations: ['71+52=123', '123-69=54'] Exploring Operation: 63+54=117, Resulting Numbers: [117] 117,89 unequal: No Solution Exploring Operation: 63*54=3402, Resulting Numbers: [3402] 3402,89 unequal: No Solution Exploring Operation: 63-54=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 #0,0,1 Current State: 89:[123, 132], Operations: ['71+52=123', '69+63=132'] Exploring Operation: 123+132=255, Resulting Numbers: [255] 255,89 unequal: No Solution Exploring Operation: 123*132=16236, Resulting Numbers: [16236] 16236,89 unequal: No Solution Exploring Operation: 132-123=9, Resulting Numbers: [9] 9,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 17, 7, 8, 7 ]
62
[ "17-7=10", "7*10=70", "70-8=62" ]
Current State: 62:[17, 7, 8, 7], Operations: [] Exploring Operation: 17-7=10, Resulting Numbers: [8, 10] Generated Node #2: [8, 10] from Operation: 17-7=10 Current State: 62:[8, 10], Operations: ['17-7=10'] Exploring Operation: 7*10=70, Resulting Numbers: [8, 70] Generated Node #3: [8, 70] from Operation: 7*10=70 Current State: 62:[8, 70], Operations: ['17-7=10', '7*10=70'] Exploring Operation: 70-8=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[17, 7, 8, 7], Operations: [] Exploring Operation: 17-8=9, Resulting Numbers: [7, 7, 9] Generated Node #0,0: 62:[7, 7, 9] Operation: 17-8=9 Exploring Operation: 17+8=25, Resulting Numbers: [7, 7, 25] Generated Node #0,1: 62:[7, 7, 25] Operation: 17+8=25 Exploring Operation: 17+7=24, Resulting Numbers: [8, 7, 24] Generated Node #0,2: 62:[8, 7, 24] Operation: 17+7=24 Exploring Operation: 17+7=24, Resulting Numbers: [7, 8, 24] Generated Node #0,3: 62:[7, 8, 24] Operation: 17+7=24 Moving to Node #0,1 Current State: 62:[7, 7, 25], Operations: ['17+8=25'] Exploring Operation: 7+25=32, Resulting Numbers: [7, 32] Generated Node #0,1,0: 62:[7, 32] Operation: 7+25=32 Exploring Operation: 7/7=1, Resulting Numbers: [25, 1] Generated Node #0,1,1: 62:[25, 1] Operation: 7/7=1 Exploring Operation: 7+25=32, Resulting Numbers: [7, 32] Generated Node #0,1,2: 62:[7, 32] Operation: 7+25=32 Exploring Operation: 7-7=0, Resulting Numbers: [25, 0] Generated Node #0,1,3: 62:[25, 0] Operation: 7-7=0 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[7, 32], Operations: ['17+8=25', '7+25=32'] Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,62 unequal: No Solution Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 62:[7, 32], Operations: ['17+8=25', '7+25=32'] Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,62 unequal: No Solution Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 62:[25, 1], Operations: ['17+8=25', '7/7=1'] Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,62 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 62:[25, 0], Operations: ['17+8=25', '7-7=0'] Exploring Operation: 25+0=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 25*0=0, Resulting Numbers: [0] 0,62 unequal: No Solution Exploring Operation: 25-0=25, Resulting Numbers: [25] 25,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 62:[7, 7, 9], Operations: ['17-8=9'] Exploring Operation: 7*9=63, Resulting Numbers: [7, 63] Generated Node #0,0,0: 62:[7, 63] Operation: 7*9=63 Exploring Operation: 9-7=2, Resulting Numbers: [7, 2] Generated Node #0,0,1: 62:[7, 2] Operation: 9-7=2 Exploring Operation: 9-7=2, Resulting Numbers: [7, 2] Generated Node #0,0,2: 62:[7, 2] Operation: 9-7=2 Exploring Operation: 7*9=63, Resulting Numbers: [7, 63] Generated Node #0,0,3: 62:[7, 63] Operation: 7*9=63 Moving to Node #0,3 Current State: 62:[7, 8, 24], Operations: ['17+7=24'] Exploring Operation: 7+24=31, Resulting Numbers: [8, 31] Generated Node #0,3,0: 62:[8, 31] Operation: 7+24=31 Exploring Operation: 24/8=3, Resulting Numbers: [7, 3] Generated Node #0,3,1: 62:[7, 3] Operation: 24/8=3 Exploring Operation: 8-7=1, Resulting Numbers: [24, 1] Generated Node #0,3,2: 62:[24, 1] Operation: 8-7=1 Exploring Operation: 8+24=32, Resulting Numbers: [7, 32] Generated Node #0,3,3: 62:[7, 32] Operation: 8+24=32 Moving to Node #0,2 Current State: 62:[8, 7, 24], Operations: ['17+7=24'] Exploring Operation: 8-7=1, Resulting Numbers: [24, 1] Generated Node #0,2,0: 62:[24, 1] Operation: 8-7=1 Exploring Operation: 7+24=31, Resulting Numbers: [8, 31] Generated Node #0,2,1: 62:[8, 31] Operation: 7+24=31 Exploring Operation: 24/8=3, Resulting Numbers: [7, 3] Generated Node #0,2,2: 62:[7, 3] Operation: 24/8=3 Exploring Operation: 8+24=32, Resulting Numbers: [7, 32] Generated Node #0,2,3: 62:[7, 32] Operation: 8+24=32 Moving to Node #0,0,1 Current State: 62:[7, 2], Operations: ['17-8=9', '9-7=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,62 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[7, 2], Operations: ['17-8=9', '9-7=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,62 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,62 unequal: No Solution Moving to Node #0,0,0 Current State: 62:[7, 63], Operations: ['17-8=9', '7*9=63'] Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,62 unequal: No Solution Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,62 unequal: No Solution Exploring Operation: 7*63=441, Resulting Numbers: [441] 441,62 unequal: No Solution Exploring Operation: 7+63=70, Resulting Numbers: [70] 70,62 unequal: No Solution Moving to Node #0,3,3 Current State: 62:[7, 32], Operations: ['17+7=24', '8+24=32'] Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,62 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,62 unequal: No Solution Moving to Node #0,3,1 Current State: 62:[7, 3], Operations: ['17+7=24', '24/8=3'] Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,62 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,62 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[7, 3], Operations: ['17+7=24', '24/8=3'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,62 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,62 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[8, 31], Operations: ['17+7=24', '7+24=31'] Exploring Operation: 8+31=39, Resulting Numbers: [39] 39,62 unequal: No Solution Exploring Operation: 8*31=248, Resulting Numbers: [248] 248,62 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,62 unequal: No Solution Moving to Node #0,3,0 Current State: 62:[8, 31], Operations: ['17+7=24', '7+24=31'] Exploring Operation: 8*31=248, Resulting Numbers: [248] 248,62 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 8+31=39, Resulting Numbers: [39] 39,62 unequal: No Solution Moving to Node #0,2,3 Current State: 62:[7, 32], Operations: ['17+7=24', '8+24=32'] Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,62 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,62 unequal: No Solution Moving to Node #0,0,3 Current State: 62:[7, 63], Operations: ['17-8=9', '7*9=63'] Exploring Operation: 7+63=70, Resulting Numbers: [70] 70,62 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,62 unequal: No Solution Exploring Operation: 7*63=441, Resulting Numbers: [441] 441,62 unequal: No Solution Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[24, 1], Operations: ['17+7=24', '8-7=1'] Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,62 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 24*1=24, Resulting Numbers: [24] 24,62 unequal: No Solution Moving to Node #0,3,2 Current State: 62:[24, 1], Operations: ['17+7=24', '8-7=1'] Exploring Operation: 24*1=24, Resulting Numbers: [24] 24,62 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,62 unequal: No Solution Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,62 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 59, 4, 21, 24 ]
16
[ "59+21=80", "4*24=96", "96-80=16" ]
Current State: 16:[59, 4, 21, 24], Operations: [] Exploring Operation: 59+21=80, Resulting Numbers: [4, 24, 80] Generated Node #2: [4, 24, 80] from Operation: 59+21=80 Current State: 16:[4, 24, 80], Operations: ['59+21=80'] Exploring Operation: 4*24=96, Resulting Numbers: [80, 96] Generated Node #3: [80, 96] from Operation: 4*24=96 Current State: 16:[80, 96], Operations: ['59+21=80', '4*24=96'] Exploring Operation: 96-80=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[59, 4, 21, 24], Operations: [] Exploring Operation: 59-21=38, Resulting Numbers: [4, 24, 38] Generated Node #0,0: 16:[4, 24, 38] Operation: 59-21=38 Exploring Operation: 24-21=3, Resulting Numbers: [59, 4, 3] Generated Node #0,1: 16:[59, 4, 3] Operation: 24-21=3 Exploring Operation: 59-24=35, Resulting Numbers: [4, 21, 35] Generated Node #0,2: 16:[4, 21, 35] Operation: 59-24=35 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[4, 21, 35], Operations: ['59-24=35'] Exploring Operation: 21-4=17, Resulting Numbers: [35, 17] Generated Node #0,2,0: 16:[35, 17] Operation: 21-4=17 Exploring Operation: 35-4=31, Resulting Numbers: [21, 31] Generated Node #0,2,1: 16:[21, 31] Operation: 35-4=31 Exploring Operation: 35-21=14, Resulting Numbers: [4, 14] Generated Node #0,2,2: 16:[4, 14] Operation: 35-21=14 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 16:[4, 14], Operations: ['59-24=35', '35-21=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,16 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,16 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 #0,2,0 Current State: 16:[35, 17], Operations: ['59-24=35', '21-4=17'] Exploring Operation: 35*17=595, Resulting Numbers: [595] 595,16 unequal: No Solution Exploring Operation: 35+17=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,16 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 #0,2,1 Current State: 16:[21, 31], Operations: ['59-24=35', '35-4=31'] Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,16 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,16 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, 24, 38], Operations: ['59-21=38'] Exploring Operation: 24-4=20, Resulting Numbers: [38, 20] Generated Node #0,0,0: 16:[38, 20] Operation: 24-4=20 Exploring Operation: 24/4=6, Resulting Numbers: [38, 6] Generated Node #0,0,1: 16:[38, 6] Operation: 24/4=6 Exploring Operation: 38-24=14, Resulting Numbers: [4, 14] Generated Node #0,0,2: 16:[4, 14] Operation: 38-24=14 Moving to Node #0,0,2 Current State: 16:[4, 14], Operations: ['59-21=38', '38-24=14'] Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,16 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,16 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[38, 6], Operations: ['59-21=38', '24/4=6'] Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,16 unequal: No Solution Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,16 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[38, 20], Operations: ['59-21=38', '24-4=20'] Exploring Operation: 38-20=18, Resulting Numbers: [18] 18,16 unequal: No Solution Exploring Operation: 38*20=760, Resulting Numbers: [760] 760,16 unequal: No Solution Exploring Operation: 38+20=58, Resulting Numbers: [58] 58,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[59, 4, 3], Operations: ['24-21=3'] Exploring Operation: 59-4=55, Resulting Numbers: [3, 55] Generated Node #0,1,0: 16:[3, 55] Operation: 59-4=55 Exploring Operation: 59-3=56, Resulting Numbers: [4, 56] Generated Node #0,1,1: 16:[4, 56] Operation: 59-3=56 Exploring Operation: 4+3=7, Resulting Numbers: [59, 7] Generated Node #0,1,2: 16:[59, 7] Operation: 4+3=7 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[3, 55], Operations: ['24-21=3', '59-4=55'] Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 3+55=58, Resulting Numbers: [58] 58,16 unequal: No Solution Exploring Operation: 3*55=165, Resulting Numbers: [165] 165,16 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, 56], Operations: ['24-21=3', '59-3=56'] Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,16 unequal: No Solution Exploring Operation: 4+56=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,16 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 #0,1,2 Current State: 16:[59, 7], Operations: ['24-21=3', '4+3=7'] Exploring Operation: 59-7=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 59+7=66, Resulting Numbers: [66] 66,16 unequal: No Solution Exploring Operation: 59*7=413, Resulting Numbers: [413] 413,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 49, 9, 85, 42 ]
22
[ "49-42=7", "9*7=63", "85-63=22" ]
Current State: 22:[49, 9, 85, 42], Operations: [] Exploring Operation: 49-42=7, Resulting Numbers: [9, 85, 7] Generated Node #2: [9, 85, 7] from Operation: 49-42=7 Current State: 22:[9, 85, 7], Operations: ['49-42=7'] Exploring Operation: 9*7=63, Resulting Numbers: [85, 63] Generated Node #3: [85, 63] from Operation: 9*7=63 Current State: 22:[85, 63], Operations: ['49-42=7', '9*7=63'] Exploring Operation: 85-63=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[49, 9, 85, 42], Operations: [] Exploring Operation: 85-9=76, Resulting Numbers: [49, 42, 76] Generated Node #0,0: 22:[49, 42, 76] Operation: 85-9=76 Exploring Operation: 85-49=36, Resulting Numbers: [9, 42, 36] Generated Node #0,1: 22:[9, 42, 36] Operation: 85-49=36 Exploring Operation: 49-9=40, Resulting Numbers: [85, 42, 40] Generated Node #0,2: 22:[85, 42, 40] Operation: 49-9=40 Exploring Operation: 85-42=43, Resulting Numbers: [49, 9, 43] Generated Node #0,3: 22:[49, 9, 43] Operation: 85-42=43 Exploring Operation: 49-42=7, Resulting Numbers: [9, 85, 7] Generated Node #0,4: 22:[9, 85, 7] Operation: 49-42=7 Moving to Node #0,1 Current State: 22:[9, 42, 36], Operations: ['85-49=36'] Exploring Operation: 42-36=6, Resulting Numbers: [9, 6] Generated Node #0,1,0: 22:[9, 6] Operation: 42-36=6 Exploring Operation: 42-9=33, Resulting Numbers: [36, 33] Generated Node #0,1,1: 22:[36, 33] Operation: 42-9=33 Exploring Operation: 9+42=51, Resulting Numbers: [36, 51] Generated Node #0,1,2: 22:[36, 51] Operation: 9+42=51 Exploring Operation: 36/9=4, Resulting Numbers: [42, 4] Generated Node #0,1,3: 22:[42, 4] Operation: 36/9=4 Exploring Operation: 36-9=27, Resulting Numbers: [42, 27] Generated Node #0,1,4: 22:[42, 27] Operation: 36-9=27 Moving to Node #0,3 Current State: 22:[49, 9, 43], Operations: ['85-42=43'] Exploring Operation: 49-9=40, Resulting Numbers: [43, 40] Generated Node #0,3,0: 22:[43, 40] Operation: 49-9=40 Exploring Operation: 49+9=58, Resulting Numbers: [43, 58] Generated Node #0,3,1: 22:[43, 58] Operation: 49+9=58 Exploring Operation: 43-9=34, Resulting Numbers: [49, 34] Generated Node #0,3,2: 22:[49, 34] Operation: 43-9=34 Exploring Operation: 9+43=52, Resulting Numbers: [49, 52] Generated Node #0,3,3: 22:[49, 52] Operation: 9+43=52 Exploring Operation: 49-43=6, Resulting Numbers: [9, 6] Generated Node #0,3,4: 22:[9, 6] Operation: 49-43=6 Moving to Node #0,4 Current State: 22:[9, 85, 7], Operations: ['49-42=7'] Exploring Operation: 85-7=78, Resulting Numbers: [9, 78] Generated Node #0,4,0: 22:[9, 78] Operation: 85-7=78 Exploring Operation: 85+7=92, Resulting Numbers: [9, 92] Generated Node #0,4,1: 22:[9, 92] Operation: 85+7=92 Exploring Operation: 9-7=2, Resulting Numbers: [85, 2] Generated Node #0,4,2: 22:[85, 2] Operation: 9-7=2 Exploring Operation: 85-9=76, Resulting Numbers: [7, 76] Generated Node #0,4,3: 22:[7, 76] Operation: 85-9=76 Exploring Operation: 9+7=16, Resulting Numbers: [85, 16] Generated Node #0,4,4: 22:[85, 16] Operation: 9+7=16 Moving to Node #0,0 Current State: 22:[49, 42, 76], Operations: ['85-9=76'] Exploring Operation: 76-42=34, Resulting Numbers: [49, 34] Generated Node #0,0,0: 22:[49, 34] Operation: 76-42=34 Exploring Operation: 49+42=91, Resulting Numbers: [76, 91] Generated Node #0,0,1: 22:[76, 91] Operation: 49+42=91 Exploring Operation: 76-49=27, Resulting Numbers: [42, 27] Generated Node #0,0,2: 22:[42, 27] Operation: 76-49=27 Exploring Operation: 49+76=125, Resulting Numbers: [42, 125] Generated Node #0,0,3: 22:[42, 125] Operation: 49+76=125 Exploring Operation: 49-42=7, Resulting Numbers: [76, 7] Generated Node #0,0,4: 22:[76, 7] Operation: 49-42=7 Moving to Node #0,2 Current State: 22:[85, 42, 40], Operations: ['49-9=40'] Exploring Operation: 85-42=43, Resulting Numbers: [40, 43] Generated Node #0,2,0: 22:[40, 43] Operation: 85-42=43 Exploring Operation: 85-40=45, Resulting Numbers: [42, 45] Generated Node #0,2,1: 22:[42, 45] Operation: 85-40=45 Exploring Operation: 85+42=127, Resulting Numbers: [40, 127] Generated Node #0,2,2: 22:[40, 127] Operation: 85+42=127 Exploring Operation: 85+40=125, Resulting Numbers: [42, 125] Generated Node #0,2,3: 22:[42, 125] Operation: 85+40=125 Exploring Operation: 42-40=2, Resulting Numbers: [85, 2] Generated Node #0,2,4: 22:[85, 2] Operation: 42-40=2 Moving to Node #0,1,0 Current State: 22:[9, 6], Operations: ['85-49=36', '42-36=6'] Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,22 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,22 unequal: No Solution Moving to Node #0,3,4 Current State: 22:[9, 6], Operations: ['85-42=43', '49-43=6'] Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,22 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,22 unequal: No Solution Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,22 unequal: No Solution Moving to Node #0,1,3 Current State: 22:[42, 4], Operations: ['85-49=36', '36/9=4'] Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,22 unequal: No Solution Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,22 unequal: No Solution Exploring Operation: 42*4=168, Resulting Numbers: [168] 168,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[36, 33], Operations: ['85-49=36', '42-9=33'] Exploring Operation: 36-33=3, Resulting Numbers: [3] 3,22 unequal: No Solution Exploring Operation: 36*33=1188, Resulting Numbers: [1188] 1188,22 unequal: No Solution Exploring Operation: 36+33=69, Resulting Numbers: [69] 69,22 unequal: No Solution Moving to Node #0,1,4 Current State: 22:[42, 27], Operations: ['85-49=36', '36-9=27'] Exploring Operation: 42+27=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 42*27=1134, Resulting Numbers: [1134] 1134,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[42, 27], Operations: ['85-9=76', '76-49=27'] Exploring Operation: 42*27=1134, Resulting Numbers: [1134] 1134,22 unequal: No Solution Exploring Operation: 42+27=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,22 unequal: No Solution Moving to Node #0,3,0 Current State: 22:[43, 40], Operations: ['85-42=43', '49-9=40'] Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,22 unequal: No Solution Exploring Operation: 43*40=1720, Resulting Numbers: [1720] 1720,22 unequal: No Solution Exploring Operation: 43+40=83, Resulting Numbers: [83] 83,22 unequal: No Solution Moving to Node #0,2,0 Current State: 22:[40, 43], Operations: ['49-9=40', '85-42=43'] Exploring Operation: 40*43=1720, Resulting Numbers: [1720] 1720,22 unequal: No Solution Exploring Operation: 40+43=83, Resulting Numbers: [83] 83,22 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,22 unequal: No Solution Moving to Node #0,0,0 Current State: 22:[49, 34], Operations: ['85-9=76', '76-42=34'] Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 49+34=83, Resulting Numbers: [83] 83,22 unequal: No Solution Exploring Operation: 49*34=1666, Resulting Numbers: [1666] 1666,22 unequal: No Solution Moving to Node #0,3,2 Current State: 22:[49, 34], Operations: ['85-42=43', '43-9=34'] Exploring Operation: 49+34=83, Resulting Numbers: [83] 83,22 unequal: No Solution Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 49*34=1666, Resulting Numbers: [1666] 1666,22 unequal: No Solution Moving to Node #0,2,1 Current State: 22:[42, 45], Operations: ['49-9=40', '85-40=45'] Exploring Operation: 45-42=3, Resulting Numbers: [3] 3,22 unequal: No Solution Exploring Operation: 42+45=87, Resulting Numbers: [87] 87,22 unequal: No Solution Exploring Operation: 42*45=1890, Resulting Numbers: [1890] 1890,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[36, 51], Operations: ['85-49=36', '9+42=51'] Exploring Operation: 36*51=1836, Resulting Numbers: [1836] 1836,22 unequal: No Solution Exploring Operation: 51-36=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 36+51=87, Resulting Numbers: [87] 87,22 unequal: No Solution Moving to Node #0,3,3 Current State: 22:[49, 52], Operations: ['85-42=43', '9+43=52'] Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,22 unequal: No Solution Exploring Operation: 49*52=2548, Resulting Numbers: [2548] 2548,22 unequal: No Solution Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,22 unequal: No Solution Moving to Node #0,3,1 Current State: 22:[43, 58], Operations: ['85-42=43', '49+9=58'] Exploring Operation: 58-43=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 43+58=101, Resulting Numbers: [101] 101,22 unequal: No Solution Exploring Operation: 43*58=2494, Resulting Numbers: [2494] 2494,22 unequal: No Solution Moving to Node #0,4,3 Current State: 22:[7, 76], Operations: ['49-42=7', '85-9=76'] Exploring Operation: 7*76=532, Resulting Numbers: [532] 532,22 unequal: No Solution Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 7+76=83, Resulting Numbers: [83] 83,22 unequal: No Solution Moving to Node #0,0,4 Current State: 22:[76, 7], Operations: ['85-9=76', '49-42=7'] Exploring Operation: 76+7=83, Resulting Numbers: [83] 83,22 unequal: No Solution Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 76*7=532, Resulting Numbers: [532] 532,22 unequal: No Solution Moving to Node #0,4,0 Current State: 22:[9, 78], Operations: ['49-42=7', '85-7=78'] Exploring Operation: 78-9=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 9+78=87, Resulting Numbers: [87] 87,22 unequal: No Solution Exploring Operation: 9*78=702, Resulting Numbers: [702] 702,22 unequal: No Solution Moving to Node #0,2,4 Current State: 22:[85, 2], Operations: ['49-9=40', '42-40=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,22 unequal: No Solution Exploring Operation: 85*2=170, Resulting Numbers: [170] 170,22 unequal: No Solution Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,22 unequal: No Solution Moving to Node #0,4,2 Current State: 22:[85, 2], Operations: ['49-42=7', '9-7=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,22 unequal: No Solution Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,22 unequal: No Solution Exploring Operation: 85*2=170, Resulting Numbers: [170] 170,22 unequal: No Solution Moving to Node #0,4,4 Current State: 22:[85, 16], Operations: ['49-42=7', '9+7=16'] Exploring Operation: 85*16=1360, Resulting Numbers: [1360] 1360,22 unequal: No Solution Exploring Operation: 85+16=101, Resulting Numbers: [101] 101,22 unequal: No Solution Exploring Operation: 85-16=69, Resulting Numbers: [69] 69,22 unequal: No Solution Moving to Node #0,4,1 Current State: 22:[9, 92], Operations: ['49-42=7', '85+7=92'] Exploring Operation: 9*92=828, Resulting Numbers: [828] 828,22 unequal: No Solution Exploring Operation: 9+92=101, Resulting Numbers: [101] 101,22 unequal: No Solution Exploring Operation: 92-9=83, Resulting Numbers: [83] 83,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[40, 127], Operations: ['49-9=40', '85+42=127'] Exploring Operation: 127-40=87, Resulting Numbers: [87] 87,22 unequal: No Solution Exploring Operation: 40*127=5080, Resulting Numbers: [5080] 5080,22 unequal: No Solution Exploring Operation: 40+127=167, Resulting Numbers: [167] 167,22 unequal: No Solution Moving to Node #0,2,3 Current State: 22:[42, 125], Operations: ['49-9=40', '85+40=125'] Exploring Operation: 42*125=5250, Resulting Numbers: [5250] 5250,22 unequal: No Solution Exploring Operation: 125-42=83, Resulting Numbers: [83] 83,22 unequal: No Solution Exploring Operation: 42+125=167, Resulting Numbers: [167] 167,22 unequal: No Solution Moving to Node #0,0,3 Current State: 22:[42, 125], Operations: ['85-9=76', '49+76=125'] Exploring Operation: 42*125=5250, Resulting Numbers: [5250] 5250,22 unequal: No Solution Exploring Operation: 125-42=83, Resulting Numbers: [83] 83,22 unequal: No Solution Exploring Operation: 42+125=167, Resulting Numbers: [167] 167,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[76, 91], Operations: ['85-9=76', '49+42=91'] Exploring Operation: 91-76=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 76+91=167, Resulting Numbers: [167] 167,22 unequal: No Solution Exploring Operation: 76*91=6916, Resulting Numbers: [6916] 6916,22 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 36, 82, 83, 75 ]
39
[ "75-36=39", "83-82=1", "39*1=39" ]
Current State: 39:[36, 82, 83, 75], Operations: [] Exploring Operation: 75-36=39, Resulting Numbers: [82, 83, 39] Generated Node #2: [82, 83, 39] from Operation: 75-36=39 Current State: 39:[82, 83, 39], Operations: ['75-36=39'] Exploring Operation: 83-82=1, Resulting Numbers: [39, 1] Generated Node #3: [39, 1] from Operation: 83-82=1 Current State: 39:[39, 1], Operations: ['75-36=39', '83-82=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[36, 82, 83, 75], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [36, 75, 1] Generated Node #0,0: 39:[36, 75, 1] Operation: 83-82=1 Exploring Operation: 82-75=7, Resulting Numbers: [36, 83, 7] Generated Node #0,1: 39:[36, 83, 7] Operation: 82-75=7 Moving to Node #0,0 Current State: 39:[36, 75, 1], Operations: ['83-82=1'] Exploring Operation: 36+1=37, Resulting Numbers: [75, 37] Generated Node #0,0,0: 39:[75, 37] Operation: 36+1=37 Exploring Operation: 75-36=39, Resulting Numbers: [1, 39] Generated Node #0,0,1: 39:[1, 39] Operation: 75-36=39 Moving to Node #0,1 Current State: 39:[36, 83, 7], Operations: ['82-75=7'] Exploring Operation: 83-36=47, Resulting Numbers: [7, 47] Generated Node #0,1,0: 39:[7, 47] Operation: 83-36=47 Exploring Operation: 83-7=76, Resulting Numbers: [36, 76] Generated Node #0,1,1: 39:[36, 76] Operation: 83-7=76 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[7, 47], Operations: ['82-75=7', '83-36=47'] Exploring Operation: 7+47=54, Resulting Numbers: [54] 54,39 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,39 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 #0,1,1 Current State: 39:[36, 76], Operations: ['82-75=7', '83-7=76'] Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,39 unequal: No Solution Exploring Operation: 36+76=112, Resulting Numbers: [112] 112,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 39:[1, 39], Operations: ['83-82=1', '75-36=39'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[36, 82, 83, 75], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [36, 75, 1] Generated Node #0,0: 39:[36, 75, 1] Operation: 83-82=1 Moving to Node #0,0 Current State: 39:[36, 75, 1], Operations: ['83-82=1'] Exploring Operation: 75-36=39, Resulting Numbers: [1, 39] Generated Node #0,0,1: 39:[1, 39] Operation: 75-36=39 Moving to Node #0,0,1 Current State: 39:[1, 39], Operations: ['83-82=1', '75-36=39'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 23, 64, 93, 2 ]
17
[ "23*2=46", "93-64=29", "46-29=17" ]
Current State: 17:[23, 64, 93, 2], Operations: [] Exploring Operation: 23*2=46, Resulting Numbers: [64, 93, 46] Generated Node #2: [64, 93, 46] from Operation: 23*2=46 Current State: 17:[64, 93, 46], Operations: ['23*2=46'] Exploring Operation: 93-64=29, Resulting Numbers: [46, 29] Generated Node #3: [46, 29] from Operation: 93-64=29 Current State: 17:[46, 29], Operations: ['23*2=46', '93-64=29'] Exploring Operation: 46-29=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[23, 64, 93, 2], Operations: [] Exploring Operation: 64/2=32, Resulting Numbers: [23, 93, 32] Generated Node #0,0: 17:[23, 93, 32] Operation: 64/2=32 Exploring Operation: 93-64=29, Resulting Numbers: [23, 2, 29] Generated Node #0,1: 17:[23, 2, 29] Operation: 93-64=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[23, 2, 29], Operations: ['93-64=29'] Exploring Operation: 23-2=21, Resulting Numbers: [29, 21] Generated Node #0,1,0: 17:[29, 21] Operation: 23-2=21 Exploring Operation: 29-2=27, Resulting Numbers: [23, 27] Generated Node #0,1,1: 17:[23, 27] Operation: 29-2=27 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 17:[29, 21], Operations: ['93-64=29', '23-2=21'] Exploring Operation: 29+21=50, Resulting Numbers: [50] 50,17 unequal: No Solution Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 17:[23, 27], Operations: ['93-64=29', '29-2=27'] Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 23+27=50, Resulting Numbers: [50] 50,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[23, 93, 32], Operations: ['64/2=32'] Exploring Operation: 93-32=61, Resulting Numbers: [23, 61] Generated Node #0,0,0: 17:[23, 61] Operation: 93-32=61 Exploring Operation: 93-23=70, Resulting Numbers: [32, 70] Generated Node #0,0,1: 17:[32, 70] Operation: 93-23=70 Moving to Node #0,0,0 Current State: 17:[23, 61], Operations: ['64/2=32', '93-32=61'] Exploring Operation: 23+61=84, Resulting Numbers: [84] 84,17 unequal: No Solution Exploring Operation: 61-23=38, Resulting Numbers: [38] 38,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[32, 70], Operations: ['64/2=32', '93-23=70'] Exploring Operation: 70-32=38, Resulting Numbers: [38] 38,17 unequal: No Solution Exploring Operation: 32+70=102, Resulting Numbers: [102] 102,17 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
[ 78, 50, 48, 88 ]
93
[ "78*88=6864", "6864/48=143", "143-50=93" ]
Current State: 93:[78, 50, 48, 88], Operations: [] Exploring Operation: 78*88=6864, Resulting Numbers: [50, 48, 6864] Generated Node #2: [50, 48, 6864] from Operation: 78*88=6864 Current State: 93:[50, 48, 6864], Operations: ['78*88=6864'] Exploring Operation: 6864/48=143, Resulting Numbers: [50, 143] Generated Node #3: [50, 143] from Operation: 6864/48=143 Current State: 93:[50, 143], Operations: ['78*88=6864', '6864/48=143'] Exploring Operation: 143-50=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[78, 50, 48, 88], Operations: [] Exploring Operation: 78-48=30, Resulting Numbers: [50, 88, 30] Generated Node #0,0: 93:[50, 88, 30] Operation: 78-48=30 Exploring Operation: 78-50=28, Resulting Numbers: [48, 88, 28] Generated Node #0,1: 93:[48, 88, 28] Operation: 78-50=28 Exploring Operation: 50-48=2, Resulting Numbers: [78, 88, 2] Generated Node #0,2: 93:[78, 88, 2] Operation: 50-48=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[78, 88, 2], Operations: ['50-48=2'] Exploring Operation: 78/2=39, Resulting Numbers: [88, 39] Generated Node #0,2,0: 93:[88, 39] Operation: 78/2=39 Exploring Operation: 88-78=10, Resulting Numbers: [2, 10] Generated Node #0,2,1: 93:[2, 10] Operation: 88-78=10 Exploring Operation: 78+2=80, Resulting Numbers: [88, 80] Generated Node #0,2,2: 93:[88, 80] Operation: 78+2=80 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 93:[2, 10], Operations: ['50-48=2', '88-78=10'] Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,93 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,93 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,93 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: 93:[88, 39], Operations: ['50-48=2', '78/2=39'] Exploring Operation: 88-39=49, Resulting Numbers: [49] 49,93 unequal: No Solution Exploring Operation: 88*39=3432, Resulting Numbers: [3432] 3432,93 unequal: No Solution Exploring Operation: 88+39=127, Resulting Numbers: [127] 127,93 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: 93:[88, 80], Operations: ['50-48=2', '78+2=80'] Exploring Operation: 88-80=8, Resulting Numbers: [8] 8,93 unequal: No Solution Exploring Operation: 88*80=7040, Resulting Numbers: [7040] 7040,93 unequal: No Solution Exploring Operation: 88+80=168, Resulting Numbers: [168] 168,93 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: 93:[50, 88, 30], Operations: ['78-48=30'] Exploring Operation: 88-50=38, Resulting Numbers: [30, 38] Generated Node #0,0,0: 93:[30, 38] Operation: 88-50=38 Exploring Operation: 50-30=20, Resulting Numbers: [88, 20] Generated Node #0,0,1: 93:[88, 20] Operation: 50-30=20 Exploring Operation: 50+30=80, Resulting Numbers: [88, 80] Generated Node #0,0,2: 93:[88, 80] Operation: 50+30=80 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 93:[30, 38], Operations: ['78-48=30', '88-50=38'] Exploring Operation: 30*38=1140, Resulting Numbers: [1140] 1140,93 unequal: No Solution Exploring Operation: 30+38=68, Resulting Numbers: [68] 68,93 unequal: No Solution Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,93 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: 93:[88, 20], Operations: ['78-48=30', '50-30=20'] Exploring Operation: 88-20=68, Resulting Numbers: [68] 68,93 unequal: No Solution Exploring Operation: 88*20=1760, Resulting Numbers: [1760] 1760,93 unequal: No Solution Exploring Operation: 88+20=108, Resulting Numbers: [108] 108,93 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: 93:[88, 80], Operations: ['78-48=30', '50+30=80'] Exploring Operation: 88*80=7040, Resulting Numbers: [7040] 7040,93 unequal: No Solution Exploring Operation: 88+80=168, Resulting Numbers: [168] 168,93 unequal: No Solution Exploring Operation: 88-80=8, Resulting Numbers: [8] 8,93 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: 93:[48, 88, 28], Operations: ['78-50=28'] Exploring Operation: 48-28=20, Resulting Numbers: [88, 20] Generated Node #0,1,0: 93:[88, 20] Operation: 48-28=20 Exploring Operation: 48+28=76, Resulting Numbers: [88, 76] Generated Node #0,1,1: 93:[88, 76] Operation: 48+28=76 Exploring Operation: 88-48=40, Resulting Numbers: [28, 40] Generated Node #0,1,2: 93:[28, 40] Operation: 88-48=40 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 93:[28, 40], Operations: ['78-50=28', '88-48=40'] Exploring Operation: 28+40=68, Resulting Numbers: [68] 68,93 unequal: No Solution Exploring Operation: 28*40=1120, Resulting Numbers: [1120] 1120,93 unequal: No Solution Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,93 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: 93:[88, 20], Operations: ['78-50=28', '48-28=20'] Exploring Operation: 88+20=108, Resulting Numbers: [108] 108,93 unequal: No Solution Exploring Operation: 88-20=68, Resulting Numbers: [68] 68,93 unequal: No Solution Exploring Operation: 88*20=1760, Resulting Numbers: [1760] 1760,93 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: 93:[88, 76], Operations: ['78-50=28', '48+28=76'] Exploring Operation: 88+76=164, Resulting Numbers: [164] 164,93 unequal: No Solution Exploring Operation: 88*76=6688, Resulting Numbers: [6688] 6688,93 unequal: No Solution Exploring Operation: 88-76=12, Resulting Numbers: [12] 12,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 64, 7, 3, 91 ]
80
[ "64-7=57", "3*57=171", "171-91=80" ]
Current State: 80:[64, 7, 3, 91], Operations: [] Exploring Operation: 64-7=57, Resulting Numbers: [3, 91, 57] Generated Node #2: [3, 91, 57] from Operation: 64-7=57 Current State: 80:[3, 91, 57], Operations: ['64-7=57'] Exploring Operation: 3*57=171, Resulting Numbers: [91, 171] Generated Node #3: [91, 171] from Operation: 3*57=171 Current State: 80:[91, 171], Operations: ['64-7=57', '3*57=171'] Exploring Operation: 171-91=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[64, 7, 3, 91], Operations: [] Exploring Operation: 91/7=13, Resulting Numbers: [64, 3, 13] Generated Node #0,0: 80:[64, 3, 13] Operation: 91/7=13 Exploring Operation: 91-64=27, Resulting Numbers: [7, 3, 27] Generated Node #0,1: 80:[7, 3, 27] Operation: 91-64=27 Moving to Node #0,1 Current State: 80:[7, 3, 27], Operations: ['91-64=27'] Exploring Operation: 27-7=20, Resulting Numbers: [3, 20] Generated Node #0,1,0: 80:[3, 20] Operation: 27-7=20 Exploring Operation: 3*27=81, Resulting Numbers: [7, 81] Generated Node #0,1,1: 80:[7, 81] Operation: 3*27=81 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 80:[3, 20], Operations: ['91-64=27', '27-7=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,80 unequal: No Solution Exploring Operation: 3+20=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 #0,1,1 Current State: 80:[7, 81], Operations: ['91-64=27', '3*27=81'] Exploring Operation: 81-7=74, Resulting Numbers: [74] 74,80 unequal: No Solution Exploring Operation: 7+81=88, Resulting Numbers: [88] 88,80 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: 80:[64, 3, 13], Operations: ['91/7=13'] Exploring Operation: 64-13=51, Resulting Numbers: [3, 51] Generated Node #0,0,0: 80:[3, 51] Operation: 64-13=51 Exploring Operation: 64+13=77, Resulting Numbers: [3, 77] Generated Node #0,0,1: 80:[3, 77] Operation: 64+13=77 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[3, 77], Operations: ['91/7=13', '64+13=77'] Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,80 unequal: No Solution Exploring Operation: 3+77=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[64, 7, 3, 91], Operations: [] Exploring Operation: 91/7=13, Resulting Numbers: [64, 3, 13] Generated Node #0,0: 80:[64, 3, 13] Operation: 91/7=13 Moving to Node #0,0 Current State: 80:[64, 3, 13], Operations: ['91/7=13'] Exploring Operation: 64+13=77, Resulting Numbers: [3, 77] Generated Node #0,0,1: 80:[3, 77] Operation: 64+13=77 Moving to Node #0,0,1 Current State: 80:[3, 77], Operations: ['91/7=13', '64+13=77'] Exploring Operation: 3+77=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 30, 43, 29, 67 ]
35
[ "30+43=73", "67-29=38", "73-38=35" ]
Current State: 35:[30, 43, 29, 67], Operations: [] Exploring Operation: 30+43=73, Resulting Numbers: [29, 67, 73] Generated Node #2: [29, 67, 73] from Operation: 30+43=73 Current State: 35:[29, 67, 73], Operations: ['30+43=73'] Exploring Operation: 67-29=38, Resulting Numbers: [73, 38] Generated Node #3: [73, 38] from Operation: 67-29=38 Current State: 35:[73, 38], Operations: ['30+43=73', '67-29=38'] Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[30, 43, 29, 67], Operations: [] Exploring Operation: 67-30=37, Resulting Numbers: [43, 29, 37] Generated Node #0,0: 35:[43, 29, 37] Operation: 67-30=37 Exploring Operation: 67-29=38, Resulting Numbers: [30, 43, 38] Generated Node #0,1: 35:[30, 43, 38] Operation: 67-29=38 Exploring Operation: 67-43=24, Resulting Numbers: [30, 29, 24] Generated Node #0,2: 35:[30, 29, 24] Operation: 67-43=24 Moving to Node #0,0 Current State: 35:[43, 29, 37], Operations: ['67-30=37'] Exploring Operation: 37-29=8, Resulting Numbers: [43, 8] Generated Node #0,0,0: 35:[43, 8] Operation: 37-29=8 Exploring Operation: 43-29=14, Resulting Numbers: [37, 14] Generated Node #0,0,1: 35:[37, 14] Operation: 43-29=14 Exploring Operation: 43-37=6, Resulting Numbers: [29, 6] Generated Node #0,0,2: 35:[29, 6] Operation: 43-37=6 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 35:[29, 6], Operations: ['67-30=37', '43-37=6'] Exploring Operation: 29*6=174, Resulting Numbers: [174] 174,35 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,35 unequal: No Solution Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[30, 43, 29, 67], Operations: [] Exploring Operation: 67-30=37, Resulting Numbers: [43, 29, 37] Generated Node #0,0: 35:[43, 29, 37] Operation: 67-30=37 Moving to Node #0,0 Current State: 35:[43, 29, 37], Operations: ['67-30=37'] Exploring Operation: 43-37=6, Resulting Numbers: [29, 6] Generated Node #0,0,2: 35:[29, 6] Operation: 43-37=6 Moving to Node #0,0,2 Current State: 35:[29, 6], Operations: ['67-30=37', '43-37=6'] Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 40, 60, 27, 20 ]
57
[ "40*27=1080", "60+1080=1140", "1140/20=57" ]
Current State: 57:[40, 60, 27, 20], Operations: [] Exploring Operation: 40*27=1080, Resulting Numbers: [60, 20, 1080] Generated Node #2: [60, 20, 1080] from Operation: 40*27=1080 Current State: 57:[60, 20, 1080], Operations: ['40*27=1080'] Exploring Operation: 60+1080=1140, Resulting Numbers: [20, 1140] Generated Node #3: [20, 1140] from Operation: 60+1080=1140 Current State: 57:[20, 1140], Operations: ['40*27=1080', '60+1080=1140'] Exploring Operation: 1140/20=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[40, 60, 27, 20], Operations: [] Exploring Operation: 40-27=13, Resulting Numbers: [60, 20, 13] Generated Node #0,0: 57:[60, 20, 13] Operation: 40-27=13 Exploring Operation: 60-40=20, Resulting Numbers: [27, 20, 20] Generated Node #0,1: 57:[27, 20, 20] Operation: 60-40=20 Moving to Node #0,0 Current State: 57:[60, 20, 13], Operations: ['40-27=13'] Exploring Operation: 20-13=7, Resulting Numbers: [60, 7] Generated Node #0,0,0: 57:[60, 7] Operation: 20-13=7 Exploring Operation: 60/20=3, Resulting Numbers: [13, 3] Generated Node #0,0,1: 57:[13, 3] Operation: 60/20=3 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 57:[13, 3], Operations: ['40-27=13', '60/20=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,57 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[60, 7], Operations: ['40-27=13', '20-13=7'] Exploring Operation: 60-7=53, Resulting Numbers: [53] 53,57 unequal: No Solution Exploring Operation: 60+7=67, Resulting Numbers: [67] 67,57 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: 57:[27, 20, 20], Operations: ['60-40=20'] Exploring Operation: 27-20=7, Resulting Numbers: [20, 7] Generated Node #0,1,0: 57:[20, 7] Operation: 27-20=7 Exploring Operation: 27-20=7, Resulting Numbers: [20, 7] Generated Node #0,1,1: 57:[20, 7] Operation: 27-20=7 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[20, 7], Operations: ['60-40=20', '27-20=7'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 57:[20, 7], Operations: ['60-40=20', '27-20=7'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,57 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
[ 88, 78, 85, 52 ]
43
[ "88-78=10", "85-52=33", "10+33=43" ]
Current State: 43:[88, 78, 85, 52], Operations: [] Exploring Operation: 88-78=10, Resulting Numbers: [85, 52, 10] Generated Node #2: [85, 52, 10] from Operation: 88-78=10 Current State: 43:[85, 52, 10], Operations: ['88-78=10'] Exploring Operation: 85-52=33, Resulting Numbers: [10, 33] Generated Node #3: [10, 33] from Operation: 85-52=33 Current State: 43:[10, 33], Operations: ['88-78=10', '85-52=33'] Exploring Operation: 10+33=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[88, 78, 85, 52], Operations: [] Exploring Operation: 88-78=10, Resulting Numbers: [85, 52, 10] Generated Node #0,0: 43:[85, 52, 10] Operation: 88-78=10 Exploring Operation: 88-85=3, Resulting Numbers: [78, 52, 3] Generated Node #0,1: 43:[78, 52, 3] Operation: 88-85=3 Exploring Operation: 85-78=7, Resulting Numbers: [88, 52, 7] Generated Node #0,2: 43:[88, 52, 7] Operation: 85-78=7 Exploring Operation: 85-52=33, Resulting Numbers: [88, 78, 33] Generated Node #0,3: 43:[88, 78, 33] Operation: 85-52=33 Exploring Operation: 88-52=36, Resulting Numbers: [78, 85, 36] Generated Node #0,4: 43:[78, 85, 36] Operation: 88-52=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[85, 52, 10], Operations: ['88-78=10'] Exploring Operation: 85+10=95, Resulting Numbers: [52, 95] Generated Node #0,0,0: 43:[52, 95] Operation: 85+10=95 Exploring Operation: 52-10=42, Resulting Numbers: [85, 42] Generated Node #0,0,1: 43:[85, 42] Operation: 52-10=42 Exploring Operation: 85-52=33, Resulting Numbers: [10, 33] Generated Node #0,0,2: 43:[10, 33] Operation: 85-52=33 Exploring Operation: 85-10=75, Resulting Numbers: [52, 75] Generated Node #0,0,3: 43:[52, 75] Operation: 85-10=75 Exploring Operation: 52+10=62, Resulting Numbers: [85, 62] Generated Node #0,0,4: 43:[85, 62] Operation: 52+10=62 Moving to Node #0,0,3 Current State: 43:[52, 75], Operations: ['88-78=10', '85-10=75'] Exploring Operation: 52*75=3900, Resulting Numbers: [3900] 3900,43 unequal: No Solution Exploring Operation: 75-52=23, Resulting Numbers: [23] 23,43 unequal: No Solution Exploring Operation: 52+75=127, Resulting Numbers: [127] 127,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[10, 33], Operations: ['88-78=10', '85-52=33'] Exploring Operation: 10*33=330, Resulting Numbers: [330] 330,43 unequal: No Solution Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,43 unequal: No Solution Exploring Operation: 10+33=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[88, 78, 85, 52], Operations: [] Exploring Operation: 88-78=10, Resulting Numbers: [85, 52, 10] Generated Node #0,0: 43:[85, 52, 10] Operation: 88-78=10 Moving to Node #0,0 Current State: 43:[85, 52, 10], Operations: ['88-78=10'] Exploring Operation: 85-52=33, Resulting Numbers: [10, 33] Generated Node #0,0,2: 43:[10, 33] Operation: 85-52=33 Moving to Node #0,0,2 Current State: 43:[10, 33], Operations: ['88-78=10', '85-52=33'] Exploring Operation: 10+33=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 16, 67, 3, 71 ]
54
[ "67-16=51", "51/3=17", "71-17=54" ]
Current State: 54:[16, 67, 3, 71], Operations: [] Exploring Operation: 67-16=51, Resulting Numbers: [3, 71, 51] Generated Node #2: [3, 71, 51] from Operation: 67-16=51 Current State: 54:[3, 71, 51], Operations: ['67-16=51'] Exploring Operation: 51/3=17, Resulting Numbers: [71, 17] Generated Node #3: [71, 17] from Operation: 51/3=17 Current State: 54:[71, 17], Operations: ['67-16=51', '51/3=17'] Exploring Operation: 71-17=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[16, 67, 3, 71], Operations: [] Exploring Operation: 67-3=64, Resulting Numbers: [16, 71, 64] Generated Node #0,0: 54:[16, 71, 64] Operation: 67-3=64 Exploring Operation: 71-16=55, Resulting Numbers: [67, 3, 55] Generated Node #0,1: 54:[67, 3, 55] Operation: 71-16=55 Exploring Operation: 71-67=4, Resulting Numbers: [16, 3, 4] Generated Node #0,2: 54:[16, 3, 4] Operation: 71-67=4 Exploring Operation: 71-3=68, Resulting Numbers: [16, 67, 68] Generated Node #0,3: 54:[16, 67, 68] Operation: 71-3=68 Exploring Operation: 67-16=51, Resulting Numbers: [3, 71, 51] Generated Node #0,4: 54:[3, 71, 51] Operation: 67-16=51 Moving to Node #0,2 Current State: 54:[16, 3, 4], Operations: ['71-67=4'] Exploring Operation: 16-4=12, Resulting Numbers: [3, 12] Generated Node #0,2,0: 54:[3, 12] Operation: 16-4=12 Exploring Operation: 16+3=19, Resulting Numbers: [4, 19] Generated Node #0,2,1: 54:[4, 19] Operation: 16+3=19 Exploring Operation: 16+4=20, Resulting Numbers: [3, 20] Generated Node #0,2,2: 54:[3, 20] Operation: 16+4=20 Exploring Operation: 16/4=4, Resulting Numbers: [3, 4] Generated Node #0,2,3: 54:[3, 4] Operation: 16/4=4 Exploring Operation: 3+4=7, Resulting Numbers: [16, 7] Generated Node #0,2,4: 54:[16, 7] Operation: 3+4=7 Moving to Node #0,1 Current State: 54:[67, 3, 55], Operations: ['71-16=55'] Exploring Operation: 55-3=52, Resulting Numbers: [67, 52] Generated Node #0,1,0: 54:[67, 52] Operation: 55-3=52 Exploring Operation: 3+55=58, Resulting Numbers: [67, 58] Generated Node #0,1,1: 54:[67, 58] Operation: 3+55=58 Exploring Operation: 67+3=70, Resulting Numbers: [55, 70] Generated Node #0,1,2: 54:[55, 70] Operation: 67+3=70 Exploring Operation: 67-3=64, Resulting Numbers: [55, 64] Generated Node #0,1,3: 54:[55, 64] Operation: 67-3=64 Exploring Operation: 67-55=12, Resulting Numbers: [3, 12] Generated Node #0,1,4: 54:[3, 12] Operation: 67-55=12 Moving to Node #0,4 Current State: 54:[3, 71, 51], Operations: ['67-16=51'] Exploring Operation: 71-51=20, Resulting Numbers: [3, 20] Generated Node #0,4,0: 54:[3, 20] Operation: 71-51=20 Exploring Operation: 51/3=17, Resulting Numbers: [71, 17] Generated Node #0,4,1: 54:[71, 17] Operation: 51/3=17 Exploring Operation: 3+51=54, Resulting Numbers: [71, 54] Generated Node #0,4,2: 54:[71, 54] Operation: 3+51=54 Exploring Operation: 71-3=68, Resulting Numbers: [51, 68] Generated Node #0,4,3: 54:[51, 68] Operation: 71-3=68 Exploring Operation: 3+71=74, Resulting Numbers: [51, 74] Generated Node #0,4,4: 54:[51, 74] Operation: 3+71=74 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 54:[3, 20], Operations: ['67-16=51', '71-51=20'] Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,54 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,54 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 #0,4,2 Current State: 54:[71, 54], Operations: ['67-16=51', '3+51=54'] Exploring Operation: 71+54=125, Resulting Numbers: [125] 125,54 unequal: No Solution Exploring Operation: 71-54=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 71*54=3834, Resulting Numbers: [3834] 3834,54 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 #0,4,3 Current State: 54:[51, 68], Operations: ['67-16=51', '71-3=68'] Exploring Operation: 51*68=3468, Resulting Numbers: [3468] 3468,54 unequal: No Solution Exploring Operation: 68-51=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 51+68=119, Resulting Numbers: [119] 119,54 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 #0,4,1 Current State: 54:[71, 17], Operations: ['67-16=51', '51/3=17'] Exploring Operation: 71+17=88, Resulting Numbers: [88] 88,54 unequal: No Solution Exploring Operation: 71-17=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[16, 67, 3, 71], Operations: [] Exploring Operation: 67-16=51, Resulting Numbers: [3, 71, 51] Generated Node #0,4: 54:[3, 71, 51] Operation: 67-16=51 Moving to Node #0,4 Current State: 54:[3, 71, 51], Operations: ['67-16=51'] Exploring Operation: 51/3=17, Resulting Numbers: [71, 17] Generated Node #0,4,1: 54:[71, 17] Operation: 51/3=17 Moving to Node #0,4,1 Current State: 54:[71, 17], Operations: ['67-16=51', '51/3=17'] Exploring Operation: 71-17=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
mult_heuristic
[ 23, 96, 45, 53 ]
88
[ "53-45=8", "23*8=184", "184-96=88" ]
Current State: 88:[23, 96, 45, 53], Operations: [] Exploring Operation: 53-45=8, Resulting Numbers: [23, 96, 8] Generated Node #2: [23, 96, 8] from Operation: 53-45=8 Current State: 88:[23, 96, 8], Operations: ['53-45=8'] Exploring Operation: 23*8=184, Resulting Numbers: [96, 184] Generated Node #3: [96, 184] from Operation: 23*8=184 Current State: 88:[96, 184], Operations: ['53-45=8', '23*8=184'] Exploring Operation: 184-96=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[23, 96, 45, 53], Operations: [] Exploring Operation: 96-45=51, Resulting Numbers: [23, 53, 51] Generated Node #0,0: 88:[23, 53, 51] Operation: 96-45=51 Exploring Operation: 96-53=43, Resulting Numbers: [23, 45, 43] Generated Node #0,1: 88:[23, 45, 43] Operation: 96-53=43 Exploring Operation: 53-45=8, Resulting Numbers: [23, 96, 8] Generated Node #0,2: 88:[23, 96, 8] Operation: 53-45=8 Exploring Operation: 45-23=22, Resulting Numbers: [96, 53, 22] Generated Node #0,3: 88:[96, 53, 22] Operation: 45-23=22 Exploring Operation: 53-23=30, Resulting Numbers: [96, 45, 30] Generated Node #0,4: 88:[96, 45, 30] Operation: 53-23=30 Moving to Node #0,1 Current State: 88:[23, 45, 43], Operations: ['96-53=43'] Exploring Operation: 23+45=68, Resulting Numbers: [43, 68] Generated Node #0,1,0: 88:[43, 68] Operation: 23+45=68 Exploring Operation: 45-23=22, Resulting Numbers: [43, 22] Generated Node #0,1,1: 88:[43, 22] Operation: 45-23=22 Exploring Operation: 43-23=20, Resulting Numbers: [45, 20] Generated Node #0,1,2: 88:[45, 20] Operation: 43-23=20 Exploring Operation: 45+43=88, Resulting Numbers: [23, 88] Generated Node #0,1,3: 88:[23, 88] Operation: 45+43=88 Exploring Operation: 45-43=2, Resulting Numbers: [23, 2] Generated Node #0,1,4: 88:[23, 2] Operation: 45-43=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 88:[43, 22], Operations: ['96-53=43', '45-23=22'] Exploring Operation: 43-22=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 43+22=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 43*22=946, Resulting Numbers: [946] 946,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 88:[23, 88], Operations: ['96-53=43', '45+43=88'] Exploring Operation: 23+88=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 23*88=2024, Resulting Numbers: [2024] 2024,88 unequal: No Solution Exploring Operation: 88-23=65, Resulting Numbers: [65] 65,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 88:[23, 2], Operations: ['96-53=43', '45-43=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 88:[45, 20], Operations: ['96-53=43', '43-23=20'] Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 45+20=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 45*20=900, Resulting Numbers: [900] 900,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[43, 68], Operations: ['96-53=43', '23+45=68'] Exploring Operation: 43+68=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 43*68=2924, Resulting Numbers: [2924] 2924,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 88:[23, 96, 8], Operations: ['53-45=8'] Exploring Operation: 96-8=88, Resulting Numbers: [23, 88] Generated Node #0,2,0: 88:[23, 88] Operation: 96-8=88 Exploring Operation: 96-23=73, Resulting Numbers: [8, 73] Generated Node #0,2,1: 88:[8, 73] Operation: 96-23=73 Exploring Operation: 23-8=15, Resulting Numbers: [96, 15] Generated Node #0,2,2: 88:[96, 15] Operation: 23-8=15 Exploring Operation: 96/8=12, Resulting Numbers: [23, 12] Generated Node #0,2,3: 88:[23, 12] Operation: 96/8=12 Exploring Operation: 23+8=31, Resulting Numbers: [96, 31] Generated Node #0,2,4: 88:[96, 31] Operation: 23+8=31 Moving to Node #0,0 Current State: 88:[23, 53, 51], Operations: ['96-45=51'] Exploring Operation: 51-23=28, Resulting Numbers: [53, 28] Generated Node #0,0,0: 88:[53, 28] Operation: 51-23=28 Exploring Operation: 23+53=76, Resulting Numbers: [51, 76] Generated Node #0,0,1: 88:[51, 76] Operation: 23+53=76 Exploring Operation: 53-23=30, Resulting Numbers: [51, 30] Generated Node #0,0,2: 88:[51, 30] Operation: 53-23=30 Exploring Operation: 53+51=104, Resulting Numbers: [23, 104] Generated Node #0,0,3: 88:[23, 104] Operation: 53+51=104 Exploring Operation: 53-51=2, Resulting Numbers: [23, 2] Generated Node #0,0,4: 88:[23, 2] Operation: 53-51=2 Moving to Node #0,3 Current State: 88:[96, 53, 22], Operations: ['45-23=22'] Exploring Operation: 53+22=75, Resulting Numbers: [96, 75] Generated Node #0,3,0: 88:[96, 75] Operation: 53+22=75 Exploring Operation: 96-53=43, Resulting Numbers: [22, 43] Generated Node #0,3,1: 88:[22, 43] Operation: 96-53=43 Exploring Operation: 96+22=118, Resulting Numbers: [53, 118] Generated Node #0,3,2: 88:[53, 118] Operation: 96+22=118 Exploring Operation: 53-22=31, Resulting Numbers: [96, 31] Generated Node #0,3,3: 88:[96, 31] Operation: 53-22=31 Exploring Operation: 96-22=74, Resulting Numbers: [53, 74] Generated Node #0,3,4: 88:[53, 74] Operation: 96-22=74 Moving to Node #0,4 Current State: 88:[96, 45, 30], Operations: ['53-23=30'] Exploring Operation: 45+30=75, Resulting Numbers: [96, 75] Generated Node #0,4,0: 88:[96, 75] Operation: 45+30=75 Exploring Operation: 96-45=51, Resulting Numbers: [30, 51] Generated Node #0,4,1: 88:[30, 51] Operation: 96-45=51 Exploring Operation: 45-30=15, Resulting Numbers: [96, 15] Generated Node #0,4,2: 88:[96, 15] Operation: 45-30=15 Exploring Operation: 96-30=66, Resulting Numbers: [45, 66] Generated Node #0,4,3: 88:[45, 66] Operation: 96-30=66 Exploring Operation: 96+30=126, Resulting Numbers: [45, 126] Generated Node #0,4,4: 88:[45, 126] Operation: 96+30=126 Moving to Node #0,2,0 Current State: 88:[23, 88], Operations: ['53-45=8', '96-8=88'] Exploring Operation: 88-23=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 23*88=2024, Resulting Numbers: [2024] 2024,88 unequal: No Solution Exploring Operation: 23+88=111, Resulting Numbers: [111] 111,88 unequal: No Solution Moving to Node #0,0,4 Current State: 88:[23, 2], Operations: ['96-45=51', '53-51=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,88 unequal: No Solution Moving to Node #0,3,1 Current State: 88:[22, 43], Operations: ['45-23=22', '96-53=43'] Exploring Operation: 22+43=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 43-22=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 22*43=946, Resulting Numbers: [946] 946,88 unequal: No Solution Moving to Node #0,2,3 Current State: 88:[23, 12], Operations: ['53-45=8', '96/8=12'] Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,88 unequal: No Solution Exploring Operation: 23*12=276, Resulting Numbers: [276] 276,88 unequal: No Solution Exploring Operation: 23+12=35, Resulting Numbers: [35] 35,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[96, 15], Operations: ['53-45=8', '23-8=15'] Exploring Operation: 96-15=81, Resulting Numbers: [81] 81,88 unequal: No Solution Exploring Operation: 96*15=1440, Resulting Numbers: [1440] 1440,88 unequal: No Solution Exploring Operation: 96+15=111, Resulting Numbers: [111] 111,88 unequal: No Solution Moving to Node #0,4,2 Current State: 88:[96, 15], Operations: ['53-23=30', '45-30=15'] Exploring Operation: 96*15=1440, Resulting Numbers: [1440] 1440,88 unequal: No Solution Exploring Operation: 96+15=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 96-15=81, Resulting Numbers: [81] 81,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[53, 28], Operations: ['96-45=51', '51-23=28'] Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,88 unequal: No Solution Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[8, 73], Operations: ['53-45=8', '96-23=73'] Exploring Operation: 8+73=81, Resulting Numbers: [81] 81,88 unequal: No Solution Exploring Operation: 8*73=584, Resulting Numbers: [584] 584,88 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,88 unequal: No Solution Moving to Node #0,4,1 Current State: 88:[30, 51], Operations: ['53-23=30', '96-45=51'] Exploring Operation: 30+51=81, Resulting Numbers: [81] 81,88 unequal: No Solution Exploring Operation: 51-30=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 30*51=1530, Resulting Numbers: [1530] 1530,88 unequal: No Solution Moving to Node #0,0,2 Current State: 88:[51, 30], Operations: ['96-45=51', '53-23=30'] Exploring Operation: 51*30=1530, Resulting Numbers: [1530] 1530,88 unequal: No Solution Exploring Operation: 51+30=81, Resulting Numbers: [81] 81,88 unequal: No Solution Exploring Operation: 51-30=21, Resulting Numbers: [21] 21,88 unequal: No Solution Moving to Node #0,3,3 Current State: 88:[96, 31], Operations: ['45-23=22', '53-22=31'] Exploring Operation: 96+31=127, Resulting Numbers: [127] 127,88 unequal: No Solution Exploring Operation: 96*31=2976, Resulting Numbers: [2976] 2976,88 unequal: No Solution Exploring Operation: 96-31=65, Resulting Numbers: [65] 65,88 unequal: No Solution Moving to Node #0,2,4 Current State: 88:[96, 31], Operations: ['53-45=8', '23+8=31'] Exploring Operation: 96+31=127, Resulting Numbers: [127] 127,88 unequal: No Solution Exploring Operation: 96*31=2976, Resulting Numbers: [2976] 2976,88 unequal: No Solution Exploring Operation: 96-31=65, Resulting Numbers: [65] 65,88 unequal: No Solution Moving to Node #0,0,3 Current State: 88:[23, 104], Operations: ['96-45=51', '53+51=104'] Exploring Operation: 23*104=2392, Resulting Numbers: [2392] 2392,88 unequal: No Solution Exploring Operation: 23+104=127, Resulting Numbers: [127] 127,88 unequal: No Solution Exploring Operation: 104-23=81, Resulting Numbers: [81] 81,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[51, 76], Operations: ['96-45=51', '23+53=76'] Exploring Operation: 76-51=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 51+76=127, Resulting Numbers: [127] 127,88 unequal: No Solution Exploring Operation: 51*76=3876, Resulting Numbers: [3876] 3876,88 unequal: No Solution Moving to Node #0,4,0 Current State: 88:[96, 75], Operations: ['53-23=30', '45+30=75'] Exploring Operation: 96-75=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 96+75=171, Resulting Numbers: [171] 171,88 unequal: No Solution Exploring Operation: 96*75=7200, Resulting Numbers: [7200] 7200,88 unequal: No Solution Moving to Node #0,3,0 Current State: 88:[96, 75], Operations: ['45-23=22', '53+22=75'] Exploring Operation: 96+75=171, Resulting Numbers: [171] 171,88 unequal: No Solution Exploring Operation: 96*75=7200, Resulting Numbers: [7200] 7200,88 unequal: No Solution Exploring Operation: 96-75=21, Resulting Numbers: [21] 21,88 unequal: No Solution Moving to Node #0,4,3 Current State: 88:[45, 66], Operations: ['53-23=30', '96-30=66'] Exploring Operation: 45+66=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 45*66=2970, Resulting Numbers: [2970] 2970,88 unequal: No Solution Exploring Operation: 66-45=21, Resulting Numbers: [21] 21,88 unequal: No Solution Moving to Node #0,3,4 Current State: 88:[53, 74], Operations: ['45-23=22', '96-22=74'] Exploring Operation: 74-53=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 53*74=3922, Resulting Numbers: [3922] 3922,88 unequal: No Solution Exploring Operation: 53+74=127, Resulting Numbers: [127] 127,88 unequal: No Solution Moving to Node #0,4,4 Current State: 88:[45, 126], Operations: ['53-23=30', '96+30=126'] Exploring Operation: 45*126=5670, Resulting Numbers: [5670] 5670,88 unequal: No Solution Exploring Operation: 45+126=171, Resulting Numbers: [171] 171,88 unequal: No Solution Exploring Operation: 126-45=81, Resulting Numbers: [81] 81,88 unequal: No Solution Moving to Node #0,3,2 Current State: 88:[53, 118], Operations: ['45-23=22', '96+22=118'] Exploring Operation: 53*118=6254, Resulting Numbers: [6254] 6254,88 unequal: No Solution Exploring Operation: 53+118=171, Resulting Numbers: [171] 171,88 unequal: No Solution Exploring Operation: 118-53=65, Resulting Numbers: [65] 65,88 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 32, 99, 20, 80 ]
49
[ "20*80=1600", "1600/32=50", "99-50=49" ]
Current State: 49:[32, 99, 20, 80], Operations: [] Exploring Operation: 20*80=1600, Resulting Numbers: [32, 99, 1600] Generated Node #2: [32, 99, 1600] from Operation: 20*80=1600 Current State: 49:[32, 99, 1600], Operations: ['20*80=1600'] Exploring Operation: 1600/32=50, Resulting Numbers: [99, 50] Generated Node #3: [99, 50] from Operation: 1600/32=50 Current State: 49:[99, 50], Operations: ['20*80=1600', '1600/32=50'] Exploring Operation: 99-50=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[32, 99, 20, 80], Operations: [] Exploring Operation: 99-32=67, Resulting Numbers: [20, 80, 67] Generated Node #0,0: 49:[20, 80, 67] Operation: 99-32=67 Exploring Operation: 80-32=48, Resulting Numbers: [99, 20, 48] Generated Node #0,1: 49:[99, 20, 48] Operation: 80-32=48 Exploring Operation: 99-80=19, Resulting Numbers: [32, 20, 19] Generated Node #0,2: 49:[32, 20, 19] Operation: 99-80=19 Moving to Node #0,2 Current State: 49:[32, 20, 19], Operations: ['99-80=19'] Exploring Operation: 32+20=52, Resulting Numbers: [19, 52] Generated Node #0,2,0: 49:[19, 52] Operation: 32+20=52 Exploring Operation: 32+19=51, Resulting Numbers: [20, 51] Generated Node #0,2,1: 49:[20, 51] Operation: 32+19=51 Exploring Operation: 32-20=12, Resulting Numbers: [19, 12] Generated Node #0,2,2: 49:[19, 12] Operation: 32-20=12 Moving to Node #0,0 Current State: 49:[20, 80, 67], Operations: ['99-32=67'] Exploring Operation: 80-67=13, Resulting Numbers: [20, 13] Generated Node #0,0,0: 49:[20, 13] Operation: 80-67=13 Exploring Operation: 80-20=60, Resulting Numbers: [67, 60] Generated Node #0,0,1: 49:[67, 60] Operation: 80-20=60 Exploring Operation: 80/20=4, Resulting Numbers: [67, 4] Generated Node #0,0,2: 49:[67, 4] Operation: 80/20=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 49:[20, 13], Operations: ['99-32=67', '80-67=13'] Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,49 unequal: No Solution Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,49 unequal: No Solution Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,49 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 #0,0,2 Current State: 49:[67, 4], Operations: ['99-32=67', '80/20=4'] Exploring Operation: 67*4=268, Resulting Numbers: [268] 268,49 unequal: No Solution Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 67+4=71, Resulting Numbers: [71] 71,49 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:[67, 60], Operations: ['99-32=67', '80-20=60'] Exploring Operation: 67+60=127, Resulting Numbers: [127] 127,49 unequal: No Solution Exploring Operation: 67*60=4020, Resulting Numbers: [4020] 4020,49 unequal: No Solution Exploring Operation: 67-60=7, Resulting Numbers: [7] 7,49 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: 49:[99, 20, 48], Operations: ['80-32=48'] Exploring Operation: 99-20=79, Resulting Numbers: [48, 79] Generated Node #0,1,0: 49:[48, 79] Operation: 99-20=79 Exploring Operation: 20+48=68, Resulting Numbers: [99, 68] Generated Node #0,1,1: 49:[99, 68] Operation: 20+48=68 Exploring Operation: 99-48=51, Resulting Numbers: [20, 51] Generated Node #0,1,2: 49:[20, 51] Operation: 99-48=51 Moving to Node #0,2,0 Current State: 49:[19, 52], Operations: ['99-80=19', '32+20=52'] Exploring Operation: 19+52=71, Resulting Numbers: [71] 71,49 unequal: No Solution Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,49 unequal: No Solution Exploring Operation: 19*52=988, Resulting Numbers: [988] 988,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[20, 51], Operations: ['99-80=19', '32+19=51'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 20+51=71, Resulting Numbers: [71] 71,49 unequal: No Solution Exploring Operation: 20*51=1020, Resulting Numbers: [1020] 1020,49 unequal: No Solution Moving to Node #0,1,2 Current State: 49:[20, 51], Operations: ['80-32=48', '99-48=51'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 20*51=1020, Resulting Numbers: [1020] 1020,49 unequal: No Solution Exploring Operation: 20+51=71, Resulting Numbers: [71] 71,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[19, 12], Operations: ['99-80=19', '32-20=12'] Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,49 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,49 unequal: No Solution Moving to Node #0,1,0 Current State: 49:[48, 79], Operations: ['80-32=48', '99-20=79'] Exploring Operation: 48+79=127, Resulting Numbers: [127] 127,49 unequal: No Solution Exploring Operation: 79-48=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 48*79=3792, Resulting Numbers: [3792] 3792,49 unequal: No Solution Moving to Node #0,1,1 Current State: 49:[99, 68], Operations: ['80-32=48', '20+48=68'] Exploring Operation: 99+68=167, Resulting Numbers: [167] 167,49 unequal: No Solution Exploring Operation: 99-68=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 99*68=6732, Resulting Numbers: [6732] 6732,49 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 61, 40, 42, 75 ]
16
[ "61+40=101", "42+75=117", "117-101=16" ]
Current State: 16:[61, 40, 42, 75], Operations: [] Exploring Operation: 61+40=101, Resulting Numbers: [42, 75, 101] Generated Node #2: [42, 75, 101] from Operation: 61+40=101 Current State: 16:[42, 75, 101], Operations: ['61+40=101'] Exploring Operation: 42+75=117, Resulting Numbers: [101, 117] Generated Node #3: [101, 117] from Operation: 42+75=117 Current State: 16:[101, 117], Operations: ['61+40=101', '42+75=117'] Exploring Operation: 117-101=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[61, 40, 42, 75], Operations: [] Exploring Operation: 61-42=19, Resulting Numbers: [40, 75, 19] Generated Node #0,0: 16:[40, 75, 19] Operation: 61-42=19 Exploring Operation: 75-61=14, Resulting Numbers: [40, 42, 14] Generated Node #0,1: 16:[40, 42, 14] Operation: 75-61=14 Exploring Operation: 75-42=33, Resulting Numbers: [61, 40, 33] Generated Node #0,2: 16:[61, 40, 33] Operation: 75-42=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[40, 42, 14], Operations: ['75-61=14'] Exploring Operation: 42/14=3, Resulting Numbers: [40, 3] Generated Node #0,1,0: 16:[40, 3] Operation: 42/14=3 Exploring Operation: 40-14=26, Resulting Numbers: [42, 26] Generated Node #0,1,1: 16:[42, 26] Operation: 40-14=26 Exploring Operation: 42-40=2, Resulting Numbers: [14, 2] Generated Node #0,1,2: 16:[14, 2] Operation: 42-40=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 16:[14, 2], Operations: ['75-61=14', '42-40=2'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,16 unequal: No Solution Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[61, 40, 42, 75], Operations: [] Exploring Operation: 75-61=14, Resulting Numbers: [40, 42, 14] Generated Node #0,1: 16:[40, 42, 14] Operation: 75-61=14 Moving to Node #0,1 Current State: 16:[40, 42, 14], Operations: ['75-61=14'] Exploring Operation: 42-40=2, Resulting Numbers: [14, 2] Generated Node #0,1,2: 16:[14, 2] Operation: 42-40=2 Moving to Node #0,1,2 Current State: 16:[14, 2], Operations: ['75-61=14', '42-40=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 23, 27, 12, 6 ]
19
[ "23*12=276", "276/6=46", "46-27=19" ]
Current State: 19:[23, 27, 12, 6], Operations: [] Exploring Operation: 23*12=276, Resulting Numbers: [27, 6, 276] Generated Node #2: [27, 6, 276] from Operation: 23*12=276 Current State: 19:[27, 6, 276], Operations: ['23*12=276'] Exploring Operation: 276/6=46, Resulting Numbers: [27, 46] Generated Node #3: [27, 46] from Operation: 276/6=46 Current State: 19:[27, 46], Operations: ['23*12=276', '276/6=46'] Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[23, 27, 12, 6], Operations: [] Exploring Operation: 27-12=15, Resulting Numbers: [23, 6, 15] Generated Node #0,0: 19:[23, 6, 15] Operation: 27-12=15 Exploring Operation: 12+6=18, Resulting Numbers: [23, 27, 18] Generated Node #0,1: 19:[23, 27, 18] Operation: 12+6=18 Exploring Operation: 27-6=21, Resulting Numbers: [23, 12, 21] Generated Node #0,2: 19:[23, 12, 21] Operation: 27-6=21 Exploring Operation: 23-6=17, Resulting Numbers: [27, 12, 17] Generated Node #0,3: 19:[27, 12, 17] Operation: 23-6=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[23, 27, 18], Operations: ['12+6=18'] Exploring Operation: 27-23=4, Resulting Numbers: [18, 4] Generated Node #0,1,0: 19:[18, 4] Operation: 27-23=4 Exploring Operation: 27-18=9, Resulting Numbers: [23, 9] Generated Node #0,1,1: 19:[23, 9] Operation: 27-18=9 Exploring Operation: 23-18=5, Resulting Numbers: [27, 5] Generated Node #0,1,2: 19:[27, 5] Operation: 23-18=5 Exploring Operation: 23+18=41, Resulting Numbers: [27, 41] Generated Node #0,1,3: 19:[27, 41] Operation: 23+18=41 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 19:[23, 9], Operations: ['12+6=18', '27-18=9'] Exploring Operation: 23+9=32, Resulting Numbers: [32] 32,19 unequal: No Solution Exploring Operation: 23*9=207, Resulting Numbers: [207] 207,19 unequal: No Solution Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 19:[18, 4], Operations: ['12+6=18', '27-23=4'] Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 19:[27, 5], Operations: ['12+6=18', '23-18=5'] Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,19 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 19:[27, 41], Operations: ['12+6=18', '23+18=41'] Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,19 unequal: No Solution Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,19 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[23, 12, 21], Operations: ['27-6=21'] Exploring Operation: 23+12=35, Resulting Numbers: [21, 35] Generated Node #0,2,0: 19:[21, 35] Operation: 23+12=35 Exploring Operation: 12+21=33, Resulting Numbers: [23, 33] Generated Node #0,2,1: 19:[23, 33] Operation: 12+21=33 Exploring Operation: 23-12=11, Resulting Numbers: [21, 11] Generated Node #0,2,2: 19:[21, 11] Operation: 23-12=11 Exploring Operation: 21-12=9, Resulting Numbers: [23, 9] Generated Node #0,2,3: 19:[23, 9] Operation: 21-12=9 Moving to Node #0,2,2 Current State: 19:[21, 11], Operations: ['27-6=21', '23-12=11'] Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 21*11=231, Resulting Numbers: [231] 231,19 unequal: No Solution Exploring Operation: 21+11=32, Resulting Numbers: [32] 32,19 unequal: No Solution Moving to Node #0,2,3 Current State: 19:[23, 9], Operations: ['27-6=21', '21-12=9'] Exploring Operation: 23+9=32, Resulting Numbers: [32] 32,19 unequal: No Solution Exploring Operation: 23*9=207, Resulting Numbers: [207] 207,19 unequal: No Solution Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,19 unequal: No Solution Moving to Node #0,2,1 Current State: 19:[23, 33], Operations: ['27-6=21', '12+21=33'] Exploring Operation: 23+33=56, Resulting Numbers: [56] 56,19 unequal: No Solution Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 23*33=759, Resulting Numbers: [759] 759,19 unequal: No Solution Moving to Node #0,2,0 Current State: 19:[21, 35], Operations: ['27-6=21', '23+12=35'] Exploring Operation: 21*35=735, Resulting Numbers: [735] 735,19 unequal: No Solution Exploring Operation: 21+35=56, Resulting Numbers: [56] 56,19 unequal: No Solution Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 19:[27, 12, 17], Operations: ['23-6=17'] Exploring Operation: 27-17=10, Resulting Numbers: [12, 10] Generated Node #0,3,0: 19:[12, 10] Operation: 27-17=10 Exploring Operation: 12+17=29, Resulting Numbers: [27, 29] Generated Node #0,3,1: 19:[27, 29] Operation: 12+17=29 Exploring Operation: 27+12=39, Resulting Numbers: [17, 39] Generated Node #0,3,2: 19:[17, 39] Operation: 27+12=39 Exploring Operation: 27-12=15, Resulting Numbers: [17, 15] Generated Node #0,3,3: 19:[17, 15] Operation: 27-12=15 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 19:[17, 15], Operations: ['23-6=17', '27-12=15'] Exploring Operation: 17*15=255, Resulting Numbers: [255] 255,19 unequal: No Solution Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,19 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 19:[12, 10], Operations: ['23-6=17', '27-17=10'] Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 12*10=120, Resulting Numbers: [120] 120,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 19:[27, 29], Operations: ['23-6=17', '12+17=29'] Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,19 unequal: No Solution Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,19 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 19:[17, 39], Operations: ['23-6=17', '27+12=39'] Exploring Operation: 17+39=56, Resulting Numbers: [56] 56,19 unequal: No Solution Exploring Operation: 39-17=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 17*39=663, Resulting Numbers: [663] 663,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[23, 6, 15], Operations: ['27-12=15'] Exploring Operation: 15-6=9, Resulting Numbers: [23, 9] Generated Node #0,0,0: 19:[23, 9] Operation: 15-6=9 Exploring Operation: 23-6=17, Resulting Numbers: [15, 17] Generated Node #0,0,1: 19:[15, 17] Operation: 23-6=17 Exploring Operation: 23+6=29, Resulting Numbers: [15, 29] Generated Node #0,0,2: 19:[15, 29] Operation: 23+6=29 Exploring Operation: 6+15=21, Resulting Numbers: [23, 21] Generated Node #0,0,3: 19:[23, 21] Operation: 6+15=21 Moving to Node #0,0,1 Current State: 19:[15, 17], Operations: ['27-12=15', '23-6=17'] Exploring Operation: 15*17=255, Resulting Numbers: [255] 255,19 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,19 unequal: No Solution Moving to Node #0,0,3 Current State: 19:[23, 21], Operations: ['27-12=15', '6+15=21'] Exploring Operation: 23*21=483, Resulting Numbers: [483] 483,19 unequal: No Solution Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,19 unequal: No Solution Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,19 unequal: No Solution Moving to Node #0,0,2 Current State: 19:[15, 29], Operations: ['27-12=15', '23+6=29'] Exploring Operation: 15+29=44, Resulting Numbers: [44] 44,19 unequal: No Solution Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,19 unequal: No Solution Exploring Operation: 15*29=435, Resulting Numbers: [435] 435,19 unequal: No Solution Moving to Node #0,0,0 Current State: 19:[23, 9], Operations: ['27-12=15', '15-6=9'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,19 unequal: No Solution Exploring Operation: 23+9=32, Resulting Numbers: [32] 32,19 unequal: No Solution Exploring Operation: 23*9=207, Resulting Numbers: [207] 207,19 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
[ 56, 53, 19, 56 ]
19
[ "56-56=0", "53*0=0", "19+0=19" ]
Current State: 19:[56, 53, 19, 56], Operations: [] Exploring Operation: 56-56=0, Resulting Numbers: [53, 19, 0] Generated Node #2: [53, 19, 0] from Operation: 56-56=0 Current State: 19:[53, 19, 0], Operations: ['56-56=0'] Exploring Operation: 53*0=0, Resulting Numbers: [19, 0] Generated Node #3: [19, 0] from Operation: 53*0=0 Current State: 19:[19, 0], Operations: ['56-56=0', '53*0=0'] Exploring Operation: 19+0=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[56, 53, 19, 56], Operations: [] Exploring Operation: 56/56=1, Resulting Numbers: [53, 19, 1] Generated Node #0,0: 19:[53, 19, 1] Operation: 56/56=1 Exploring Operation: 56-53=3, Resulting Numbers: [19, 56, 3] Generated Node #0,1: 19:[19, 56, 3] Operation: 56-53=3 Exploring Operation: 56-56=0, Resulting Numbers: [53, 19, 0] Generated Node #0,2: 19:[53, 19, 0] Operation: 56-56=0 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[53, 19, 1], Operations: ['56/56=1'] Exploring Operation: 53*1=53, Resulting Numbers: [19, 53] Generated Node #0,0,0: 19:[19, 53] Operation: 53*1=53 Exploring Operation: 53-19=34, Resulting Numbers: [1, 34] Generated Node #0,0,1: 19:[1, 34] Operation: 53-19=34 Exploring Operation: 53-1=52, Resulting Numbers: [19, 52] Generated Node #0,0,2: 19:[19, 52] Operation: 53-1=52 Moving to Node #0,0,1 Current State: 19:[1, 34], Operations: ['56/56=1', '53-19=34'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 1*34=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,19 unequal: No Solution Moving to Node #0,0,2 Current State: 19:[19, 52], Operations: ['56/56=1', '53-1=52'] Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,19 unequal: No Solution Exploring Operation: 19*52=988, Resulting Numbers: [988] 988,19 unequal: No Solution Exploring Operation: 19+52=71, Resulting Numbers: [71] 71,19 unequal: No Solution Moving to Node #0,0,0 Current State: 19:[19, 53], Operations: ['56/56=1', '53*1=53'] Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 19*53=1007, Resulting Numbers: [1007] 1007,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[19, 56, 3], Operations: ['56-53=3'] Exploring Operation: 19+3=22, Resulting Numbers: [56, 22] Generated Node #0,1,0: 19:[56, 22] Operation: 19+3=22 Exploring Operation: 56-3=53, Resulting Numbers: [19, 53] Generated Node #0,1,1: 19:[19, 53] Operation: 56-3=53 Exploring Operation: 56-19=37, Resulting Numbers: [3, 37] Generated Node #0,1,2: 19:[3, 37] Operation: 56-19=37 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 19:[19, 53], Operations: ['56-53=3', '56-3=53'] Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 19*53=1007, Resulting Numbers: [1007] 1007,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 19:[3, 37], Operations: ['56-53=3', '56-19=37'] Exploring Operation: 3*37=111, Resulting Numbers: [111] 111,19 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 19:[56, 22], Operations: ['56-53=3', '19+3=22'] Exploring Operation: 56*22=1232, Resulting Numbers: [1232] 1232,19 unequal: No Solution Exploring Operation: 56+22=78, Resulting Numbers: [78] 78,19 unequal: No Solution Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[53, 19, 0], Operations: ['56-56=0'] Exploring Operation: 53*0=0, Resulting Numbers: [19, 0] Generated Node #0,2,0: 19:[19, 0] Operation: 53*0=0 Exploring Operation: 53-19=34, Resulting Numbers: [0, 34] Generated Node #0,2,1: 19:[0, 34] Operation: 53-19=34 Exploring Operation: 53+0=53, Resulting Numbers: [19, 53] Generated Node #0,2,2: 19:[19, 53] Operation: 53+0=53 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 19:[19, 0], Operations: ['56-56=0', '53*0=0'] Exploring Operation: 19+0=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[56, 53, 19, 56], Operations: [] Exploring Operation: 56-56=0, Resulting Numbers: [53, 19, 0] Generated Node #0,2: 19:[53, 19, 0] Operation: 56-56=0 Moving to Node #0,2 Current State: 19:[53, 19, 0], Operations: ['56-56=0'] Exploring Operation: 53*0=0, Resulting Numbers: [19, 0] Generated Node #0,2,0: 19:[19, 0] Operation: 53*0=0 Moving to Node #0,2,0 Current State: 19:[19, 0], Operations: ['56-56=0', '53*0=0'] Exploring Operation: 19+0=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_3
mult_heuristic
[ 29, 28, 90, 5 ]
39
[ "29+28=57", "90/5=18", "57-18=39" ]
Current State: 39:[29, 28, 90, 5], Operations: [] Exploring Operation: 29+28=57, Resulting Numbers: [90, 5, 57] Generated Node #2: [90, 5, 57] from Operation: 29+28=57 Current State: 39:[90, 5, 57], Operations: ['29+28=57'] Exploring Operation: 90/5=18, Resulting Numbers: [57, 18] Generated Node #3: [57, 18] from Operation: 90/5=18 Current State: 39:[57, 18], Operations: ['29+28=57', '90/5=18'] Exploring Operation: 57-18=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[29, 28, 90, 5], Operations: [] Exploring Operation: 90-28=62, Resulting Numbers: [29, 5, 62] Generated Node #0,0: 39:[29, 5, 62] Operation: 90-28=62 Exploring Operation: 29-28=1, Resulting Numbers: [90, 5, 1] Generated Node #0,1: 39:[90, 5, 1] Operation: 29-28=1 Exploring Operation: 90/5=18, Resulting Numbers: [29, 28, 18] Generated Node #0,2: 39:[29, 28, 18] Operation: 90/5=18 Exploring Operation: 90-29=61, Resulting Numbers: [28, 5, 61] Generated Node #0,3: 39:[28, 5, 61] Operation: 90-29=61 Moving to Node #0,2 Current State: 39:[29, 28, 18], Operations: ['90/5=18'] Exploring Operation: 29-28=1, Resulting Numbers: [18, 1] Generated Node #0,2,0: 39:[18, 1] Operation: 29-28=1 Exploring Operation: 28-18=10, Resulting Numbers: [29, 10] Generated Node #0,2,1: 39:[29, 10] Operation: 28-18=10 Exploring Operation: 28+18=46, Resulting Numbers: [29, 46] Generated Node #0,2,2: 39:[29, 46] Operation: 28+18=46 Exploring Operation: 29-18=11, Resulting Numbers: [28, 11] Generated Node #0,2,3: 39:[28, 11] Operation: 29-18=11 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[18, 1], Operations: ['90/5=18', '29-28=1'] Exploring Operation: 18*1=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 18+1=19, Resulting Numbers: [19] 19,39 unequal: No Solution Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 39:[29, 10], Operations: ['90/5=18', '28-18=10'] Exploring Operation: 29*10=290, Resulting Numbers: [290] 290,39 unequal: No Solution Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[29, 28, 90, 5], Operations: [] Exploring Operation: 90/5=18, Resulting Numbers: [29, 28, 18] Generated Node #0,2: 39:[29, 28, 18] Operation: 90/5=18 Moving to Node #0,2 Current State: 39:[29, 28, 18], Operations: ['90/5=18'] Exploring Operation: 28-18=10, Resulting Numbers: [29, 10] Generated Node #0,2,1: 39:[29, 10] Operation: 28-18=10 Moving to Node #0,2,1 Current State: 39:[29, 10], Operations: ['90/5=18', '28-18=10'] Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 14, 95, 37, 14 ]
57
[ "14/14=1", "95-37=58", "58-1=57" ]
Current State: 57:[14, 95, 37, 14], Operations: [] Exploring Operation: 14/14=1, Resulting Numbers: [95, 37, 1] Generated Node #2: [95, 37, 1] from Operation: 14/14=1 Current State: 57:[95, 37, 1], Operations: ['14/14=1'] Exploring Operation: 95-37=58, Resulting Numbers: [1, 58] Generated Node #3: [1, 58] from Operation: 95-37=58 Current State: 57:[1, 58], Operations: ['14/14=1', '95-37=58'] Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[14, 95, 37, 14], Operations: [] Exploring Operation: 95-14=81, Resulting Numbers: [37, 14, 81] Generated Node #0,0: 57:[37, 14, 81] Operation: 95-14=81 Exploring Operation: 37-14=23, Resulting Numbers: [95, 14, 23] Generated Node #0,1: 57:[95, 14, 23] Operation: 37-14=23 Exploring Operation: 95-37=58, Resulting Numbers: [14, 14, 58] Generated Node #0,2: 57:[14, 14, 58] Operation: 95-37=58 Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[14, 14, 58], Operations: ['95-37=58'] Exploring Operation: 14-14=0, Resulting Numbers: [58, 0] Generated Node #0,2,0: 57:[58, 0] Operation: 14-14=0 Exploring Operation: 14/14=1, Resulting Numbers: [58, 1] Generated Node #0,2,1: 57:[58, 1] Operation: 14/14=1 Exploring Operation: 14+14=28, Resulting Numbers: [58, 28] Generated Node #0,2,2: 57:[58, 28] Operation: 14+14=28 Moving to Node #0,2,1 Current State: 57:[58, 1], Operations: ['95-37=58', '14/14=1'] Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,57 unequal: No Solution Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[14, 95, 37, 14], Operations: [] Exploring Operation: 95-37=58, Resulting Numbers: [14, 14, 58] Generated Node #0,2: 57:[14, 14, 58] Operation: 95-37=58 Moving to Node #0,2 Current State: 57:[14, 14, 58], Operations: ['95-37=58'] Exploring Operation: 14/14=1, Resulting Numbers: [58, 1] Generated Node #0,2,1: 57:[58, 1] Operation: 14/14=1 Moving to Node #0,2,1 Current State: 57:[58, 1], Operations: ['95-37=58', '14/14=1'] Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 76, 73, 38, 29 ]
22
[ "76/38=2", "73-29=44", "44/2=22" ]
Current State: 22:[76, 73, 38, 29], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [73, 29, 2] Generated Node #2: [73, 29, 2] from Operation: 76/38=2 Current State: 22:[73, 29, 2], Operations: ['76/38=2'] Exploring Operation: 73-29=44, Resulting Numbers: [2, 44] Generated Node #3: [2, 44] from Operation: 73-29=44 Current State: 22:[2, 44], Operations: ['76/38=2', '73-29=44'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[76, 73, 38, 29], Operations: [] Exploring Operation: 76-73=3, Resulting Numbers: [38, 29, 3] Generated Node #0,0: 22:[38, 29, 3] Operation: 76-73=3 Exploring Operation: 76/38=2, Resulting Numbers: [73, 29, 2] Generated Node #0,1: 22:[73, 29, 2] Operation: 76/38=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[38, 29, 3], Operations: ['76-73=3'] Exploring Operation: 38-3=35, Resulting Numbers: [29, 35] Generated Node #0,0,0: 22:[29, 35] Operation: 38-3=35 Exploring Operation: 38-29=9, Resulting Numbers: [3, 9] Generated Node #0,0,1: 22:[3, 9] Operation: 38-29=9 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 22:[3, 9], Operations: ['76-73=3', '38-29=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,22 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,22 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:[29, 35], Operations: ['76-73=3', '38-3=35'] Exploring Operation: 29+35=64, Resulting Numbers: [64] 64,22 unequal: No Solution Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,22 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 #0,1 Current State: 22:[73, 29, 2], Operations: ['76/38=2'] Exploring Operation: 73-29=44, Resulting Numbers: [2, 44] Generated Node #0,1,0: 22:[2, 44] Operation: 73-29=44 Exploring Operation: 73-2=71, Resulting Numbers: [29, 71] Generated Node #0,1,1: 22:[29, 71] Operation: 73-2=71 Moving to Node #0,1,0 Current State: 22:[2, 44], Operations: ['76/38=2', '73-29=44'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[76, 73, 38, 29], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [73, 29, 2] Generated Node #0,1: 22:[73, 29, 2] Operation: 76/38=2 Moving to Node #0,1 Current State: 22:[73, 29, 2], Operations: ['76/38=2'] Exploring Operation: 73-29=44, Resulting Numbers: [2, 44] Generated Node #0,1,0: 22:[2, 44] Operation: 73-29=44 Moving to Node #0,1,0 Current State: 22:[2, 44], Operations: ['76/38=2', '73-29=44'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 45, 9, 6, 47 ]
27
[ "47-45=2", "9*6=54", "54/2=27" ]
Current State: 27:[45, 9, 6, 47], Operations: [] Exploring Operation: 47-45=2, Resulting Numbers: [9, 6, 2] Generated Node #2: [9, 6, 2] from Operation: 47-45=2 Current State: 27:[9, 6, 2], Operations: ['47-45=2'] Exploring Operation: 9*6=54, Resulting Numbers: [2, 54] Generated Node #3: [2, 54] from Operation: 9*6=54 Current State: 27:[2, 54], Operations: ['47-45=2', '9*6=54'] Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[45, 9, 6, 47], Operations: [] Exploring Operation: 47-45=2, Resulting Numbers: [9, 6, 2] Generated Node #0,0: 27:[9, 6, 2] Operation: 47-45=2 Moving to Node #0,0 Current State: 27:[9, 6, 2], Operations: ['47-45=2'] Exploring Operation: 6/2=3, Resulting Numbers: [9, 3] Generated Node #0,0,0: 27:[9, 3] Operation: 6/2=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[9, 3], Operations: ['47-45=2', '6/2=3'] Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[45, 9, 6, 47], Operations: [] Exploring Operation: 47-45=2, Resulting Numbers: [9, 6, 2] Generated Node #0,0: 27:[9, 6, 2] Operation: 47-45=2 Moving to Node #0,0 Current State: 27:[9, 6, 2], Operations: ['47-45=2'] Exploring Operation: 6/2=3, Resulting Numbers: [9, 3] Generated Node #0,0,0: 27:[9, 3] Operation: 6/2=3 Moving to Node #0,0,0 Current State: 27:[9, 3], Operations: ['47-45=2', '6/2=3'] Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 30, 88, 18, 59 ]
99
[ "88-30=58", "59-18=41", "58+41=99" ]
Current State: 99:[30, 88, 18, 59], Operations: [] Exploring Operation: 88-30=58, Resulting Numbers: [18, 59, 58] Generated Node #2: [18, 59, 58] from Operation: 88-30=58 Current State: 99:[18, 59, 58], Operations: ['88-30=58'] Exploring Operation: 59-18=41, Resulting Numbers: [58, 41] Generated Node #3: [58, 41] from Operation: 59-18=41 Current State: 99:[58, 41], Operations: ['88-30=58', '59-18=41'] Exploring Operation: 58+41=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[30, 88, 18, 59], Operations: [] Exploring Operation: 88-59=29, Resulting Numbers: [30, 18, 29] Generated Node #0,0: 99:[30, 18, 29] Operation: 88-59=29 Exploring Operation: 59-18=41, Resulting Numbers: [30, 88, 41] Generated Node #0,1: 99:[30, 88, 41] Operation: 59-18=41 Exploring Operation: 59-30=29, Resulting Numbers: [88, 18, 29] Generated Node #0,2: 99:[88, 18, 29] Operation: 59-30=29 Moving to Node #0,0 Current State: 99:[30, 18, 29], Operations: ['88-59=29'] Exploring Operation: 30-18=12, Resulting Numbers: [29, 12] Generated Node #0,0,0: 99:[29, 12] Operation: 30-18=12 Exploring Operation: 29-18=11, Resulting Numbers: [30, 11] Generated Node #0,0,1: 99:[30, 11] Operation: 29-18=11 Exploring Operation: 30-29=1, Resulting Numbers: [18, 1] Generated Node #0,0,2: 99:[18, 1] Operation: 30-29=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[30, 11], Operations: ['88-59=29', '29-18=11'] Exploring Operation: 30+11=41, Resulting Numbers: [41] 41,99 unequal: No Solution Exploring Operation: 30*11=330, Resulting Numbers: [330] 330,99 unequal: No Solution Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[29, 12], Operations: ['88-59=29', '30-18=12'] Exploring Operation: 29+12=41, Resulting Numbers: [41] 41,99 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 29*12=348, Resulting Numbers: [348] 348,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 99:[18, 1], Operations: ['88-59=29', '30-29=1'] Exploring Operation: 18*1=18, Resulting Numbers: [18] 18,99 unequal: No Solution Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 99:[30, 88, 41], Operations: ['59-18=41'] Exploring Operation: 30+88=118, Resulting Numbers: [41, 118] Generated Node #0,1,0: 99:[41, 118] Operation: 30+88=118 Exploring Operation: 88-41=47, Resulting Numbers: [30, 47] Generated Node #0,1,1: 99:[30, 47] Operation: 88-41=47 Exploring Operation: 41-30=11, Resulting Numbers: [88, 11] Generated Node #0,1,2: 99:[88, 11] Operation: 41-30=11 Moving to Node #0,2 Current State: 99:[88, 18, 29], Operations: ['59-30=29'] Exploring Operation: 29-18=11, Resulting Numbers: [88, 11] Generated Node #0,2,0: 99:[88, 11] Operation: 29-18=11 Exploring Operation: 88+29=117, Resulting Numbers: [18, 117] Generated Node #0,2,1: 99:[18, 117] Operation: 88+29=117 Exploring Operation: 88+18=106, Resulting Numbers: [29, 106] Generated Node #0,2,2: 99:[29, 106] Operation: 88+18=106 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 99:[88, 11], Operations: ['59-30=29', '29-18=11'] Exploring Operation: 88/11=8, Resulting Numbers: [8] 8,99 unequal: No Solution Exploring Operation: 88-11=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 88+11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[30, 88, 18, 59], Operations: [] Exploring Operation: 59-30=29, Resulting Numbers: [88, 18, 29] Generated Node #0,2: 99:[88, 18, 29] Operation: 59-30=29 Moving to Node #0,2 Current State: 99:[88, 18, 29], Operations: ['59-30=29'] Exploring Operation: 29-18=11, Resulting Numbers: [88, 11] Generated Node #0,2,0: 99:[88, 11] Operation: 29-18=11 Moving to Node #0,2,0 Current State: 99:[88, 11], Operations: ['59-30=29', '29-18=11'] Exploring Operation: 88+11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_3
mult_heuristic
[ 39, 6, 33, 14 ]
75
[ "33-14=19", "6*19=114", "114-39=75" ]
Current State: 75:[39, 6, 33, 14], Operations: [] Exploring Operation: 33-14=19, Resulting Numbers: [39, 6, 19] Generated Node #2: [39, 6, 19] from Operation: 33-14=19 Current State: 75:[39, 6, 19], Operations: ['33-14=19'] Exploring Operation: 6*19=114, Resulting Numbers: [39, 114] Generated Node #3: [39, 114] from Operation: 6*19=114 Current State: 75:[39, 114], Operations: ['33-14=19', '6*19=114'] Exploring Operation: 114-39=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[39, 6, 33, 14], Operations: [] Exploring Operation: 33-6=27, Resulting Numbers: [39, 14, 27] Generated Node #0,0: 75:[39, 14, 27] Operation: 33-6=27 Exploring Operation: 39-33=6, Resulting Numbers: [6, 14, 6] Generated Node #0,1: 75:[6, 14, 6] Operation: 39-33=6 Exploring Operation: 39-14=25, Resulting Numbers: [6, 33, 25] Generated Node #0,2: 75:[6, 33, 25] Operation: 39-14=25 Exploring Operation: 39-6=33, Resulting Numbers: [33, 14, 33] Generated Node #0,3: 75:[33, 14, 33] Operation: 39-6=33 Exploring Operation: 39+33=72, Resulting Numbers: [6, 14, 72] Generated Node #0,4: 75:[6, 14, 72] Operation: 39+33=72 Moving to Node #0,1 Current State: 75:[6, 14, 6], Operations: ['39-33=6'] Exploring Operation: 6+6=12, Resulting Numbers: [14, 12] Generated Node #0,1,0: 75:[14, 12] Operation: 6+6=12 Exploring Operation: 14-6=8, Resulting Numbers: [6, 8] Generated Node #0,1,1: 75:[6, 8] Operation: 14-6=8 Exploring Operation: 14-6=8, Resulting Numbers: [6, 8] Generated Node #0,1,2: 75:[6, 8] Operation: 14-6=8 Exploring Operation: 6-6=0, Resulting Numbers: [14, 0] Generated Node #0,1,3: 75:[14, 0] Operation: 6-6=0 Exploring Operation: 6/6=1, Resulting Numbers: [14, 1] Generated Node #0,1,4: 75:[14, 1] Operation: 6/6=1 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 75:[14, 1], Operations: ['39-33=6', '6/6=1'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 75:[14, 12], Operations: ['39-33=6', '6+6=12'] Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,75 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 75:[6, 8], Operations: ['39-33=6', '14-6=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,75 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 75:[6, 8], Operations: ['39-33=6', '14-6=8'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 75:[14, 0], Operations: ['39-33=6', '6-6=0'] Exploring Operation: 14*0=0, Resulting Numbers: [0] 0,75 unequal: No Solution Exploring Operation: 14-0=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 14+0=14, Resulting Numbers: [14] 14,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 75:[6, 14, 72], Operations: ['39+33=72'] Exploring Operation: 72/6=12, Resulting Numbers: [14, 12] Generated Node #0,4,0: 75:[14, 12] Operation: 72/6=12 Exploring Operation: 6+72=78, Resulting Numbers: [14, 78] Generated Node #0,4,1: 75:[14, 78] Operation: 6+72=78 Exploring Operation: 14-6=8, Resulting Numbers: [72, 8] Generated Node #0,4,2: 75:[72, 8] Operation: 14-6=8 Exploring Operation: 6+14=20, Resulting Numbers: [72, 20] Generated Node #0,4,3: 75:[72, 20] Operation: 6+14=20 Exploring Operation: 72-6=66, Resulting Numbers: [14, 66] Generated Node #0,4,4: 75:[14, 66] Operation: 72-6=66 Moving to Node #0,2 Current State: 75:[6, 33, 25], Operations: ['39-14=25'] Exploring Operation: 25-6=19, Resulting Numbers: [33, 19] Generated Node #0,2,0: 75:[33, 19] Operation: 25-6=19 Exploring Operation: 33-25=8, Resulting Numbers: [6, 8] Generated Node #0,2,1: 75:[6, 8] Operation: 33-25=8 Exploring Operation: 33-6=27, Resulting Numbers: [25, 27] Generated Node #0,2,2: 75:[25, 27] Operation: 33-6=27 Exploring Operation: 6+25=31, Resulting Numbers: [33, 31] Generated Node #0,2,3: 75:[33, 31] Operation: 6+25=31 Exploring Operation: 6+33=39, Resulting Numbers: [25, 39] Generated Node #0,2,4: 75:[25, 39] Operation: 6+33=39 Moving to Node #0,0 Current State: 75:[39, 14, 27], Operations: ['33-6=27'] Exploring Operation: 39+27=66, Resulting Numbers: [14, 66] Generated Node #0,0,0: 75:[14, 66] Operation: 39+27=66 Exploring Operation: 39-14=25, Resulting Numbers: [27, 25] Generated Node #0,0,1: 75:[27, 25] Operation: 39-14=25 Exploring Operation: 39-27=12, Resulting Numbers: [14, 12] Generated Node #0,0,2: 75:[14, 12] Operation: 39-27=12 Exploring Operation: 39+14=53, Resulting Numbers: [27, 53] Generated Node #0,0,3: 75:[27, 53] Operation: 39+14=53 Exploring Operation: 27-14=13, Resulting Numbers: [39, 13] Generated Node #0,0,4: 75:[39, 13] Operation: 27-14=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 75:[27, 25], Operations: ['33-6=27', '39-14=25'] Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 27+25=52, Resulting Numbers: [52] 52,75 unequal: No Solution Exploring Operation: 27*25=675, Resulting Numbers: [675] 675,75 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 #0,0,2 Current State: 75:[14, 12], Operations: ['33-6=27', '39-27=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,75 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,75 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,75 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 #0,0,0 Current State: 75:[14, 66], Operations: ['33-6=27', '39+27=66'] Exploring Operation: 14+66=80, Resulting Numbers: [80] 80,75 unequal: No Solution Exploring Operation: 66-14=52, Resulting Numbers: [52] 52,75 unequal: No Solution Exploring Operation: 14*66=924, Resulting Numbers: [924] 924,75 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 #0,0,4 Current State: 75:[39, 13], Operations: ['33-6=27', '27-14=13'] Exploring Operation: 39*13=507, Resulting Numbers: [507] 507,75 unequal: No Solution Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,75 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,75 unequal: No Solution Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,75 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 #0,0,3 Current State: 75:[27, 53], Operations: ['33-6=27', '39+14=53'] Exploring Operation: 27+53=80, Resulting Numbers: [80] 80,75 unequal: No Solution Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,75 unequal: No Solution Exploring Operation: 27*53=1431, Resulting Numbers: [1431] 1431,75 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: 75:[33, 14, 33], Operations: ['39-6=33'] Exploring Operation: 33/33=1, Resulting Numbers: [14, 1] Generated Node #0,3,0: 75:[14, 1] Operation: 33/33=1 Exploring Operation: 33+33=66, Resulting Numbers: [14, 66] Generated Node #0,3,1: 75:[14, 66] Operation: 33+33=66 Exploring Operation: 33-14=19, Resulting Numbers: [33, 19] Generated Node #0,3,2: 75:[33, 19] Operation: 33-14=19 Exploring Operation: 33-14=19, Resulting Numbers: [33, 19] Generated Node #0,3,3: 75:[33, 19] Operation: 33-14=19 Exploring Operation: 33-33=0, Resulting Numbers: [14, 0] Generated Node #0,3,4: 75:[14, 0] Operation: 33-33=0 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 75:[14, 1], Operations: ['39-6=33', '33/33=1'] Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,75 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 #0,3,4 Current State: 75:[14, 0], Operations: ['39-6=33', '33-33=0'] Exploring Operation: 14+0=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 14*0=0, Resulting Numbers: [0] 0,75 unequal: No Solution Exploring Operation: 14-0=14, Resulting Numbers: [14] 14,75 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 #0,3,1 Current State: 75:[14, 66], Operations: ['39-6=33', '33+33=66'] Exploring Operation: 14+66=80, Resulting Numbers: [80] 80,75 unequal: No Solution Exploring Operation: 14*66=924, Resulting Numbers: [924] 924,75 unequal: No Solution Exploring Operation: 66-14=52, Resulting Numbers: [52] 52,75 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 #0,3,2 Current State: 75:[33, 19], Operations: ['39-6=33', '33-14=19'] Exploring Operation: 33*19=627, Resulting Numbers: [627] 627,75 unequal: No Solution Exploring Operation: 33-19=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 33+19=52, Resulting Numbers: [52] 52,75 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 #0,3,3 Current State: 75:[33, 19], Operations: ['39-6=33', '33-14=19'] Exploring Operation: 33-19=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 33+19=52, Resulting Numbers: [52] 52,75 unequal: No Solution Exploring Operation: 33*19=627, Resulting Numbers: [627] 627,75 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: 75:[25, 27], Operations: ['39-14=25', '33-6=27'] Exploring Operation: 25+27=52, Resulting Numbers: [52] 52,75 unequal: No Solution Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 25*27=675, Resulting Numbers: [675] 675,75 unequal: No Solution Moving to Node #0,4,0 Current State: 75:[14, 12], Operations: ['39+33=72', '72/6=12'] Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,75 unequal: No Solution Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,75 unequal: No Solution Moving to Node #0,2,1 Current State: 75:[6, 8], Operations: ['39-14=25', '33-25=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,75 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,75 unequal: No Solution Moving to Node #0,4,1 Current State: 75:[14, 78], Operations: ['39+33=72', '6+72=78'] Exploring Operation: 14*78=1092, Resulting Numbers: [1092] 1092,75 unequal: No Solution Exploring Operation: 14+78=92, Resulting Numbers: [92] 92,75 unequal: No Solution Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,75 unequal: No Solution Moving to Node #0,4,2 Current State: 75:[72, 8], Operations: ['39+33=72', '14-6=8'] Exploring Operation: 72*8=576, Resulting Numbers: [576] 576,75 unequal: No Solution Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,75 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,75 unequal: No Solution Moving to Node #0,4,3 Current State: 75:[72, 20], Operations: ['39+33=72', '6+14=20'] Exploring Operation: 72*20=1440, Resulting Numbers: [1440] 1440,75 unequal: No Solution Exploring Operation: 72+20=92, Resulting Numbers: [92] 92,75 unequal: No Solution Exploring Operation: 72-20=52, Resulting Numbers: [52] 52,75 unequal: No Solution Moving to Node #0,4,4 Current State: 75:[14, 66], Operations: ['39+33=72', '72-6=66'] Exploring Operation: 14*66=924, Resulting Numbers: [924] 924,75 unequal: No Solution Exploring Operation: 14+66=80, Resulting Numbers: [80] 80,75 unequal: No Solution Exploring Operation: 66-14=52, Resulting Numbers: [52] 52,75 unequal: No Solution Moving to Node #0,2,0 Current State: 75:[33, 19], Operations: ['39-14=25', '25-6=19'] Exploring Operation: 33-19=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 33*19=627, Resulting Numbers: [627] 627,75 unequal: No Solution Exploring Operation: 33+19=52, Resulting Numbers: [52] 52,75 unequal: No Solution Moving to Node #0,2,4 Current State: 75:[25, 39], Operations: ['39-14=25', '6+33=39'] Exploring Operation: 25*39=975, Resulting Numbers: [975] 975,75 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 25+39=64, Resulting Numbers: [64] 64,75 unequal: No Solution Moving to Node #0,2,3 Current State: 75:[33, 31], Operations: ['39-14=25', '6+25=31'] Exploring Operation: 33*31=1023, Resulting Numbers: [1023] 1023,75 unequal: No Solution Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,75 unequal: No Solution Exploring Operation: 33-31=2, Resulting Numbers: [2] 2,75 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 57, 73, 37, 64 ]
41
[ "73-57=16", "64/16=4", "37+4=41" ]
Current State: 41:[57, 73, 37, 64], Operations: [] Exploring Operation: 73-57=16, Resulting Numbers: [37, 64, 16] Generated Node #2: [37, 64, 16] from Operation: 73-57=16 Current State: 41:[37, 64, 16], Operations: ['73-57=16'] Exploring Operation: 64/16=4, Resulting Numbers: [37, 4] Generated Node #3: [37, 4] from Operation: 64/16=4 Current State: 41:[37, 4], Operations: ['73-57=16', '64/16=4'] Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[57, 73, 37, 64], Operations: [] Exploring Operation: 73-37=36, Resulting Numbers: [57, 64, 36] Generated Node #0,0: 41:[57, 64, 36] Operation: 73-37=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[57, 64, 36], Operations: ['73-37=36'] Exploring Operation: 64-36=28, Resulting Numbers: [57, 28] Generated Node #0,0,0: 41:[57, 28] Operation: 64-36=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[57, 28], Operations: ['73-37=36', '64-36=28'] Exploring Operation: 57-28=29, Resulting Numbers: [29] 29,41 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
[ 1, 55, 22, 32 ]
79
[ "55*32=1760", "1760/22=80", "80-1=79" ]
Current State: 79:[1, 55, 22, 32], Operations: [] Exploring Operation: 55*32=1760, Resulting Numbers: [1, 22, 1760] Generated Node #2: [1, 22, 1760] from Operation: 55*32=1760 Current State: 79:[1, 22, 1760], Operations: ['55*32=1760'] Exploring Operation: 1760/22=80, Resulting Numbers: [1, 80] Generated Node #3: [1, 80] from Operation: 1760/22=80 Current State: 79:[1, 80], Operations: ['55*32=1760', '1760/22=80'] Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[1, 55, 22, 32], Operations: [] Exploring Operation: 1+55=56, Resulting Numbers: [22, 32, 56] Generated Node #0,0: 79:[22, 32, 56] Operation: 1+55=56 Exploring Operation: 1+22=23, Resulting Numbers: [55, 32, 23] Generated Node #0,1: 79:[55, 32, 23] Operation: 1+22=23 Exploring Operation: 1+32=33, Resulting Numbers: [55, 22, 33] Generated Node #0,2: 79:[55, 22, 33] Operation: 1+32=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[22, 32, 56], Operations: ['1+55=56'] Exploring Operation: 32+56=88, Resulting Numbers: [22, 88] Generated Node #0,0,0: 79:[22, 88] Operation: 32+56=88 Exploring Operation: 22+56=78, Resulting Numbers: [32, 78] Generated Node #0,0,1: 79:[32, 78] Operation: 22+56=78 Exploring Operation: 22+32=54, Resulting Numbers: [56, 54] Generated Node #0,0,2: 79:[56, 54] Operation: 22+32=54 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 79:[32, 78], Operations: ['1+55=56', '22+56=78'] Exploring Operation: 32*78=2496, Resulting Numbers: [2496] 2496,79 unequal: No Solution Exploring Operation: 32+78=110, Resulting Numbers: [110] 110,79 unequal: No Solution Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 79:[56, 54], Operations: ['1+55=56', '22+32=54'] Exploring Operation: 56-54=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 56*54=3024, Resulting Numbers: [3024] 3024,79 unequal: No Solution Exploring Operation: 56+54=110, Resulting Numbers: [110] 110,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[22, 88], Operations: ['1+55=56', '32+56=88'] Exploring Operation: 88/22=4, Resulting Numbers: [4] 4,79 unequal: No Solution Exploring Operation: 88-22=66, Resulting Numbers: [66] 66,79 unequal: No Solution Exploring Operation: 22+88=110, Resulting Numbers: [110] 110,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[55, 32, 23], Operations: ['1+22=23'] Exploring Operation: 55+23=78, Resulting Numbers: [32, 78] Generated Node #0,1,0: 79:[32, 78] Operation: 55+23=78 Exploring Operation: 32+23=55, Resulting Numbers: [55, 55] Generated Node #0,1,1: 79:[55, 55] Operation: 32+23=55 Exploring Operation: 55+32=87, Resulting Numbers: [23, 87] Generated Node #0,1,2: 79:[23, 87] Operation: 55+32=87 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 79:[32, 78], Operations: ['1+22=23', '55+23=78'] Exploring Operation: 32+78=110, Resulting Numbers: [110] 110,79 unequal: No Solution Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,79 unequal: No Solution Exploring Operation: 32*78=2496, Resulting Numbers: [2496] 2496,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 79:[55, 55], Operations: ['1+22=23', '32+23=55'] Exploring Operation: 55-55=0, Resulting Numbers: [0] 0,79 unequal: No Solution Exploring Operation: 55+55=110, Resulting Numbers: [110] 110,79 unequal: No Solution Exploring Operation: 55/55=1, Resulting Numbers: [1] 1,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 79:[23, 87], Operations: ['1+22=23', '55+32=87'] Exploring Operation: 23+87=110, Resulting Numbers: [110] 110,79 unequal: No Solution Exploring Operation: 87-23=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 23*87=2001, Resulting Numbers: [2001] 2001,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[55, 22, 33], Operations: ['1+32=33'] Exploring Operation: 22+33=55, Resulting Numbers: [55, 55] Generated Node #0,2,0: 79:[55, 55] Operation: 22+33=55 Exploring Operation: 55+22=77, Resulting Numbers: [33, 77] Generated Node #0,2,1: 79:[33, 77] Operation: 55+22=77 Exploring Operation: 55+33=88, Resulting Numbers: [22, 88] Generated Node #0,2,2: 79:[22, 88] Operation: 55+33=88 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 79:[55, 55], Operations: ['1+32=33', '22+33=55'] Exploring Operation: 55/55=1, Resulting Numbers: [1] 1,79 unequal: No Solution Exploring Operation: 55+55=110, Resulting Numbers: [110] 110,79 unequal: No Solution Exploring Operation: 55-55=0, Resulting Numbers: [0] 0,79 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:[33, 77], Operations: ['1+32=33', '55+22=77'] Exploring Operation: 33*77=2541, Resulting Numbers: [2541] 2541,79 unequal: No Solution Exploring Operation: 77-33=44, Resulting Numbers: [44] 44,79 unequal: No Solution Exploring Operation: 33+77=110, Resulting Numbers: [110] 110,79 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 #0,2,2 Current State: 79:[22, 88], Operations: ['1+32=33', '55+33=88'] Exploring Operation: 88-22=66, Resulting Numbers: [66] 66,79 unequal: No Solution Exploring Operation: 22+88=110, Resulting Numbers: [110] 110,79 unequal: No Solution Exploring Operation: 88/22=4, Resulting Numbers: [4] 4,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 61, 90, 56, 75 ]
94
[ "75-61=14", "56/14=4", "90+4=94" ]
Current State: 94:[61, 90, 56, 75], Operations: [] Exploring Operation: 75-61=14, Resulting Numbers: [90, 56, 14] Generated Node #2: [90, 56, 14] from Operation: 75-61=14 Current State: 94:[90, 56, 14], Operations: ['75-61=14'] Exploring Operation: 56/14=4, Resulting Numbers: [90, 4] Generated Node #3: [90, 4] from Operation: 56/14=4 Current State: 94:[90, 4], Operations: ['75-61=14', '56/14=4'] Exploring Operation: 90+4=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[61, 90, 56, 75], Operations: [] Exploring Operation: 61-56=5, Resulting Numbers: [90, 75, 5] Generated Node #0,0: 94:[90, 75, 5] Operation: 61-56=5 Exploring Operation: 75-61=14, Resulting Numbers: [90, 56, 14] Generated Node #0,1: 94:[90, 56, 14] Operation: 75-61=14 Exploring Operation: 75-56=19, Resulting Numbers: [61, 90, 19] Generated Node #0,2: 94:[61, 90, 19] Operation: 75-56=19 Moving to Node #0,1 Current State: 94:[90, 56, 14], Operations: ['75-61=14'] Exploring Operation: 90+14=104, Resulting Numbers: [56, 104] Generated Node #0,1,0: 94:[56, 104] Operation: 90+14=104 Exploring Operation: 56/14=4, Resulting Numbers: [90, 4] Generated Node #0,1,1: 94:[90, 4] Operation: 56/14=4 Exploring Operation: 56-14=42, Resulting Numbers: [90, 42] Generated Node #0,1,2: 94:[90, 42] Operation: 56-14=42 Moving to Node #0,0 Current State: 94:[90, 75, 5], Operations: ['61-56=5'] Exploring Operation: 75+5=80, Resulting Numbers: [90, 80] Generated Node #0,0,0: 94:[90, 80] Operation: 75+5=80 Exploring Operation: 90-75=15, Resulting Numbers: [5, 15] Generated Node #0,0,1: 94:[5, 15] Operation: 90-75=15 Exploring Operation: 75/5=15, Resulting Numbers: [90, 15] Generated Node #0,0,2: 94:[90, 15] Operation: 75/5=15 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 94:[5, 15], Operations: ['61-56=5', '90-75=15'] Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,94 unequal: No Solution Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 94:[90, 15], Operations: ['61-56=5', '75/5=15'] Exploring Operation: 90-15=75, Resulting Numbers: [75] 75,94 unequal: No Solution Exploring Operation: 90+15=105, Resulting Numbers: [105] 105,94 unequal: No Solution Exploring Operation: 90/15=6, Resulting Numbers: [6] 6,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[90, 80], Operations: ['61-56=5', '75+5=80'] Exploring Operation: 90+80=170, Resulting Numbers: [170] 170,94 unequal: No Solution Exploring Operation: 90*80=7200, Resulting Numbers: [7200] 7200,94 unequal: No Solution Exploring Operation: 90-80=10, Resulting Numbers: [10] 10,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 94:[61, 90, 19], Operations: ['75-56=19'] Exploring Operation: 61+19=80, Resulting Numbers: [90, 80] Generated Node #0,2,0: 94:[90, 80] Operation: 61+19=80 Exploring Operation: 61-19=42, Resulting Numbers: [90, 42] Generated Node #0,2,1: 94:[90, 42] Operation: 61-19=42 Exploring Operation: 90+19=109, Resulting Numbers: [61, 109] Generated Node #0,2,2: 94:[61, 109] Operation: 90+19=109 Moving to Node #0,1,1 Current State: 94:[90, 4], Operations: ['75-61=14', '56/14=4'] Exploring Operation: 90+4=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[61, 90, 56, 75], Operations: [] Exploring Operation: 75-61=14, Resulting Numbers: [90, 56, 14] Generated Node #0,1: 94:[90, 56, 14] Operation: 75-61=14 Moving to Node #0,1 Current State: 94:[90, 56, 14], Operations: ['75-61=14'] Exploring Operation: 56/14=4, Resulting Numbers: [90, 4] Generated Node #0,1,1: 94:[90, 4] Operation: 56/14=4 Moving to Node #0,1,1 Current State: 94:[90, 4], Operations: ['75-61=14', '56/14=4'] Exploring Operation: 90+4=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.977431
hs_3
sum_heuristic
[ 29, 86, 43, 28 ]
42
[ "86-29=57", "43-28=15", "57-15=42" ]
Current State: 42:[29, 86, 43, 28], Operations: [] Exploring Operation: 86-29=57, Resulting Numbers: [43, 28, 57] Generated Node #2: [43, 28, 57] from Operation: 86-29=57 Current State: 42:[43, 28, 57], Operations: ['86-29=57'] Exploring Operation: 43-28=15, Resulting Numbers: [57, 15] Generated Node #3: [57, 15] from Operation: 43-28=15 Current State: 42:[57, 15], Operations: ['86-29=57', '43-28=15'] Exploring Operation: 57-15=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[29, 86, 43, 28], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [29, 28, 2] Generated Node #0,0: 42:[29, 28, 2] Operation: 86/43=2 Moving to Node #0,0 Current State: 42:[29, 28, 2], Operations: ['86/43=2'] Exploring Operation: 29-28=1, Resulting Numbers: [2, 1] Generated Node #0,0,0: 42:[2, 1] Operation: 29-28=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[2, 1], Operations: ['86/43=2', '29-28=1'] Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,42 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
[ 79, 74, 22, 91 ]
64
[ "79*74=5846", "5846-22=5824", "5824/91=64" ]
Current State: 64:[79, 74, 22, 91], Operations: [] Exploring Operation: 79*74=5846, Resulting Numbers: [22, 91, 5846] Generated Node #2: [22, 91, 5846] from Operation: 79*74=5846 Current State: 64:[22, 91, 5846], Operations: ['79*74=5846'] Exploring Operation: 5846-22=5824, Resulting Numbers: [91, 5824] Generated Node #3: [91, 5824] from Operation: 5846-22=5824 Current State: 64:[91, 5824], Operations: ['79*74=5846', '5846-22=5824'] Exploring Operation: 5824/91=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[79, 74, 22, 91], Operations: [] Exploring Operation: 91-79=12, Resulting Numbers: [74, 22, 12] Generated Node #0,0: 64:[74, 22, 12] Operation: 91-79=12 Exploring Operation: 79-74=5, Resulting Numbers: [22, 91, 5] Generated Node #0,1: 64:[22, 91, 5] Operation: 79-74=5 Exploring Operation: 91-74=17, Resulting Numbers: [79, 22, 17] Generated Node #0,2: 64:[79, 22, 17] Operation: 91-74=17 Exploring Operation: 91-22=69, Resulting Numbers: [79, 74, 69] Generated Node #0,3: 64:[79, 74, 69] Operation: 91-22=69 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[74, 22, 12], Operations: ['91-79=12'] Exploring Operation: 74-22=52, Resulting Numbers: [12, 52] Generated Node #0,0,0: 64:[12, 52] Operation: 74-22=52 Exploring Operation: 22-12=10, Resulting Numbers: [74, 10] Generated Node #0,0,1: 64:[74, 10] Operation: 22-12=10 Exploring Operation: 74-12=62, Resulting Numbers: [22, 62] Generated Node #0,0,2: 64:[22, 62] Operation: 74-12=62 Exploring Operation: 22+12=34, Resulting Numbers: [74, 34] Generated Node #0,0,3: 64:[74, 34] Operation: 22+12=34 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 64:[22, 62], Operations: ['91-79=12', '74-12=62'] Exploring Operation: 22+62=84, Resulting Numbers: [84] 84,64 unequal: No Solution Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,64 unequal: No Solution Exploring Operation: 22*62=1364, Resulting Numbers: [1364] 1364,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 64:[74, 10], Operations: ['91-79=12', '22-12=10'] Exploring Operation: 74+10=84, Resulting Numbers: [84] 84,64 unequal: No Solution Exploring Operation: 74*10=740, Resulting Numbers: [740] 740,64 unequal: No Solution Exploring Operation: 74-10=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[79, 74, 22, 91], Operations: [] Exploring Operation: 91-79=12, Resulting Numbers: [74, 22, 12] Generated Node #0,0: 64:[74, 22, 12] Operation: 91-79=12 Moving to Node #0,0 Current State: 64:[74, 22, 12], Operations: ['91-79=12'] Exploring Operation: 22-12=10, Resulting Numbers: [74, 10] Generated Node #0,0,1: 64:[74, 10] Operation: 22-12=10 Moving to Node #0,0,1 Current State: 64:[74, 10], Operations: ['91-79=12', '22-12=10'] Exploring Operation: 74-10=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 96, 16, 66, 15 ]
57
[ "96/16=6", "66-15=51", "6+51=57" ]
Current State: 57:[96, 16, 66, 15], Operations: [] Exploring Operation: 96/16=6, Resulting Numbers: [66, 15, 6] Generated Node #2: [66, 15, 6] from Operation: 96/16=6 Current State: 57:[66, 15, 6], Operations: ['96/16=6'] Exploring Operation: 66-15=51, Resulting Numbers: [6, 51] Generated Node #3: [6, 51] from Operation: 66-15=51 Current State: 57:[6, 51], Operations: ['96/16=6', '66-15=51'] Exploring Operation: 6+51=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[96, 16, 66, 15], Operations: [] Exploring Operation: 96/16=6, Resulting Numbers: [66, 15, 6] Generated Node #0,0: 57:[66, 15, 6] Operation: 96/16=6 Moving to Node #0,0 Current State: 57:[66, 15, 6], Operations: ['96/16=6'] Exploring Operation: 66-6=60, Resulting Numbers: [15, 60] Generated Node #0,0,0: 57:[15, 60] Operation: 66-6=60 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[15, 60], Operations: ['96/16=6', '66-6=60'] Exploring Operation: 60/15=4, Resulting Numbers: [4] 4,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 50, 77, 27, 97 ]
98
[ "77-50=27", "27/27=1", "97+1=98" ]
Current State: 98:[50, 77, 27, 97], Operations: [] Exploring Operation: 77-50=27, Resulting Numbers: [27, 97, 27] Generated Node #2: [27, 97, 27] from Operation: 77-50=27 Current State: 98:[27, 97, 27], Operations: ['77-50=27'] Exploring Operation: 27/27=1, Resulting Numbers: [97, 1] Generated Node #3: [97, 1] from Operation: 27/27=1 Current State: 98:[97, 1], Operations: ['77-50=27', '27/27=1'] Exploring Operation: 97+1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[50, 77, 27, 97], Operations: [] Exploring Operation: 77-27=50, Resulting Numbers: [50, 97, 50] Generated Node #0,0: 98:[50, 97, 50] Operation: 77-27=50 Exploring Operation: 77-50=27, Resulting Numbers: [27, 97, 27] Generated Node #0,1: 98:[27, 97, 27] Operation: 77-50=27 Exploring Operation: 77+27=104, Resulting Numbers: [50, 97, 104] Generated Node #0,2: 98:[50, 97, 104] Operation: 77+27=104 Exploring Operation: 97-77=20, Resulting Numbers: [50, 27, 20] Generated Node #0,3: 98:[50, 27, 20] Operation: 97-77=20 Moving to Node #0,0 Current State: 98:[50, 97, 50], Operations: ['77-27=50'] Exploring Operation: 97-50=47, Resulting Numbers: [50, 47] Generated Node #0,0,0: 98:[50, 47] Operation: 97-50=47 Exploring Operation: 50-50=0, Resulting Numbers: [97, 0] Generated Node #0,0,1: 98:[97, 0] Operation: 50-50=0 Exploring Operation: 50/50=1, Resulting Numbers: [97, 1] Generated Node #0,0,2: 98:[97, 1] Operation: 50/50=1 Exploring Operation: 50+50=100, Resulting Numbers: [97, 100] Generated Node #0,0,3: 98:[97, 100] Operation: 50+50=100 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 98:[97, 1], Operations: ['77-27=50', '50/50=1'] Exploring Operation: 97/1=97, Resulting Numbers: [97] 97,98 unequal: No Solution Exploring Operation: 97+1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[50, 77, 27, 97], Operations: [] Exploring Operation: 77-27=50, Resulting Numbers: [50, 97, 50] Generated Node #0,0: 98:[50, 97, 50] Operation: 77-27=50 Moving to Node #0,0 Current State: 98:[50, 97, 50], Operations: ['77-27=50'] Exploring Operation: 50/50=1, Resulting Numbers: [97, 1] Generated Node #0,0,2: 98:[97, 1] Operation: 50/50=1 Moving to Node #0,0,2 Current State: 98:[97, 1], Operations: ['77-27=50', '50/50=1'] Exploring Operation: 97+1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 22, 47, 59, 11 ]
71
[ "22*59=1298", "1298/11=118", "118-47=71" ]
Current State: 71:[22, 47, 59, 11], Operations: [] Exploring Operation: 22*59=1298, Resulting Numbers: [47, 11, 1298] Generated Node #2: [47, 11, 1298] from Operation: 22*59=1298 Current State: 71:[47, 11, 1298], Operations: ['22*59=1298'] Exploring Operation: 1298/11=118, Resulting Numbers: [47, 118] Generated Node #3: [47, 118] from Operation: 1298/11=118 Current State: 71:[47, 118], Operations: ['22*59=1298', '1298/11=118'] Exploring Operation: 118-47=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[22, 47, 59, 11], Operations: [] Exploring Operation: 22+47=69, Resulting Numbers: [59, 11, 69] Generated Node #0,0: 71:[59, 11, 69] Operation: 22+47=69 Exploring Operation: 59+11=70, Resulting Numbers: [22, 47, 70] Generated Node #0,1: 71:[22, 47, 70] Operation: 59+11=70 Exploring Operation: 47+11=58, Resulting Numbers: [22, 59, 58] Generated Node #0,2: 71:[22, 59, 58] Operation: 47+11=58 Exploring Operation: 22+11=33, Resulting Numbers: [47, 59, 33] Generated Node #0,3: 71:[47, 59, 33] Operation: 22+11=33 Moving to Node #0,0 Current State: 71:[59, 11, 69], Operations: ['22+47=69'] Exploring Operation: 59-11=48, Resulting Numbers: [69, 48] Generated Node #0,0,0: 71:[69, 48] Operation: 59-11=48 Exploring Operation: 11+69=80, Resulting Numbers: [59, 80] Generated Node #0,0,1: 71:[59, 80] Operation: 11+69=80 Exploring Operation: 69-11=58, Resulting Numbers: [59, 58] Generated Node #0,0,2: 71:[59, 58] Operation: 69-11=58 Exploring Operation: 59+11=70, Resulting Numbers: [69, 70] Generated Node #0,0,3: 71:[69, 70] Operation: 59+11=70 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 71:[69, 70], Operations: ['22+47=69', '59+11=70'] Exploring Operation: 69*70=4830, Resulting Numbers: [4830] 4830,71 unequal: No Solution Exploring Operation: 70-69=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 69+70=139, Resulting Numbers: [139] 139,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 71:[59, 80], Operations: ['22+47=69', '11+69=80'] Exploring Operation: 59+80=139, Resulting Numbers: [139] 139,71 unequal: No Solution Exploring Operation: 80-59=21, Resulting Numbers: [21] 21,71 unequal: No Solution Exploring Operation: 59*80=4720, Resulting Numbers: [4720] 4720,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[69, 48], Operations: ['22+47=69', '59-11=48'] Exploring Operation: 69-48=21, Resulting Numbers: [21] 21,71 unequal: No Solution Exploring Operation: 69+48=117, Resulting Numbers: [117] 117,71 unequal: No Solution Exploring Operation: 69*48=3312, Resulting Numbers: [3312] 3312,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 71:[59, 58], Operations: ['22+47=69', '69-11=58'] Exploring Operation: 59+58=117, Resulting Numbers: [117] 117,71 unequal: No Solution Exploring Operation: 59-58=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 59*58=3422, Resulting Numbers: [3422] 3422,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 71:[22, 59, 58], Operations: ['47+11=58'] Exploring Operation: 58-22=36, Resulting Numbers: [59, 36] Generated Node #0,2,0: 71:[59, 36] Operation: 58-22=36 Exploring Operation: 59-22=37, Resulting Numbers: [58, 37] Generated Node #0,2,1: 71:[58, 37] Operation: 59-22=37 Exploring Operation: 22+59=81, Resulting Numbers: [58, 81] Generated Node #0,2,2: 71:[58, 81] Operation: 22+59=81 Exploring Operation: 22+58=80, Resulting Numbers: [59, 80] Generated Node #0,2,3: 71:[59, 80] Operation: 22+58=80 Moving to Node #0,1 Current State: 71:[22, 47, 70], Operations: ['59+11=70'] Exploring Operation: 22+70=92, Resulting Numbers: [47, 92] Generated Node #0,1,0: 71:[47, 92] Operation: 22+70=92 Exploring Operation: 47-22=25, Resulting Numbers: [70, 25] Generated Node #0,1,1: 71:[70, 25] Operation: 47-22=25 Exploring Operation: 22+47=69, Resulting Numbers: [70, 69] Generated Node #0,1,2: 71:[70, 69] Operation: 22+47=69 Exploring Operation: 70-22=48, Resulting Numbers: [47, 48] Generated Node #0,1,3: 71:[47, 48] Operation: 70-22=48 Moving to Node #0,3 Current State: 71:[47, 59, 33], Operations: ['22+11=33'] Exploring Operation: 59-33=26, Resulting Numbers: [47, 26] Generated Node #0,3,0: 71:[47, 26] Operation: 59-33=26 Exploring Operation: 59+33=92, Resulting Numbers: [47, 92] Generated Node #0,3,1: 71:[47, 92] Operation: 59+33=92 Exploring Operation: 47-33=14, Resulting Numbers: [59, 14] Generated Node #0,3,2: 71:[59, 14] Operation: 47-33=14 Exploring Operation: 47+33=80, Resulting Numbers: [59, 80] Generated Node #0,3,3: 71:[59, 80] Operation: 47+33=80 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 71:[59, 80], Operations: ['22+11=33', '47+33=80'] Exploring Operation: 59+80=139, Resulting Numbers: [139] 139,71 unequal: No Solution Exploring Operation: 80-59=21, Resulting Numbers: [21] 21,71 unequal: No Solution Exploring Operation: 59*80=4720, Resulting Numbers: [4720] 4720,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 71:[47, 92], Operations: ['22+11=33', '59+33=92'] Exploring Operation: 47*92=4324, Resulting Numbers: [4324] 4324,71 unequal: No Solution Exploring Operation: 92-47=45, Resulting Numbers: [45] 45,71 unequal: No Solution Exploring Operation: 47+92=139, Resulting Numbers: [139] 139,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 71:[47, 26], Operations: ['22+11=33', '59-33=26'] Exploring Operation: 47-26=21, Resulting Numbers: [21] 21,71 unequal: No Solution Exploring Operation: 47*26=1222, Resulting Numbers: [1222] 1222,71 unequal: No Solution Exploring Operation: 47+26=73, Resulting Numbers: [73] 73,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 71:[59, 14], Operations: ['22+11=33', '47-33=14'] Exploring Operation: 59+14=73, Resulting Numbers: [73] 73,71 unequal: No Solution Exploring Operation: 59-14=45, Resulting Numbers: [45] 45,71 unequal: No Solution Exploring Operation: 59*14=826, Resulting Numbers: [826] 826,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 71:[70, 69], Operations: ['59+11=70', '22+47=69'] Exploring Operation: 70-69=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 70*69=4830, Resulting Numbers: [4830] 4830,71 unequal: No Solution Exploring Operation: 70+69=139, Resulting Numbers: [139] 139,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[59, 80], Operations: ['47+11=58', '22+58=80'] Exploring Operation: 59+80=139, Resulting Numbers: [139] 139,71 unequal: No Solution Exploring Operation: 80-59=21, Resulting Numbers: [21] 21,71 unequal: No Solution Exploring Operation: 59*80=4720, Resulting Numbers: [4720] 4720,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[58, 81], Operations: ['47+11=58', '22+59=81'] Exploring Operation: 58*81=4698, Resulting Numbers: [4698] 4698,71 unequal: No Solution Exploring Operation: 81-58=23, Resulting Numbers: [23] 23,71 unequal: No Solution Exploring Operation: 58+81=139, Resulting Numbers: [139] 139,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[47, 92], Operations: ['59+11=70', '22+70=92'] Exploring Operation: 47*92=4324, Resulting Numbers: [4324] 4324,71 unequal: No Solution Exploring Operation: 47+92=139, Resulting Numbers: [139] 139,71 unequal: No Solution Exploring Operation: 92-47=45, Resulting Numbers: [45] 45,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[59, 36], Operations: ['47+11=58', '58-22=36'] Exploring Operation: 59-36=23, Resulting Numbers: [23] 23,71 unequal: No Solution Exploring Operation: 59+36=95, Resulting Numbers: [95] 95,71 unequal: No Solution Exploring Operation: 59*36=2124, Resulting Numbers: [2124] 2124,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[70, 25], Operations: ['59+11=70', '47-22=25'] Exploring Operation: 70+25=95, Resulting Numbers: [95] 95,71 unequal: No Solution Exploring Operation: 70-25=45, Resulting Numbers: [45] 45,71 unequal: No Solution Exploring Operation: 70*25=1750, Resulting Numbers: [1750] 1750,71 unequal: No Solution Moving to Node #0,1,3 Current State: 71:[47, 48], Operations: ['59+11=70', '70-22=48'] Exploring Operation: 48-47=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 47*48=2256, Resulting Numbers: [2256] 2256,71 unequal: No Solution Exploring Operation: 47+48=95, Resulting Numbers: [95] 95,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[58, 37], Operations: ['47+11=58', '59-22=37'] Exploring Operation: 58-37=21, Resulting Numbers: [21] 21,71 unequal: No Solution Exploring Operation: 58+37=95, Resulting Numbers: [95] 95,71 unequal: No Solution Exploring Operation: 58*37=2146, Resulting Numbers: [2146] 2146,71 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 91, 53, 45, 32 ]
39
[ "91-53=38", "45+32=77", "77-38=39" ]
Current State: 39:[91, 53, 45, 32], Operations: [] Exploring Operation: 91-53=38, Resulting Numbers: [45, 32, 38] Generated Node #2: [45, 32, 38] from Operation: 91-53=38 Current State: 39:[45, 32, 38], Operations: ['91-53=38'] Exploring Operation: 45+32=77, Resulting Numbers: [38, 77] Generated Node #3: [38, 77] from Operation: 45+32=77 Current State: 39:[38, 77], Operations: ['91-53=38', '45+32=77'] Exploring Operation: 77-38=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[91, 53, 45, 32], Operations: [] Exploring Operation: 91-53=38, Resulting Numbers: [45, 32, 38] Generated Node #0,0: 39:[45, 32, 38] Operation: 91-53=38 Exploring Operation: 91-45=46, Resulting Numbers: [53, 32, 46] Generated Node #0,1: 39:[53, 32, 46] Operation: 91-45=46 Exploring Operation: 91-32=59, Resulting Numbers: [53, 45, 59] Generated Node #0,2: 39:[53, 45, 59] Operation: 91-32=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[45, 32, 38], Operations: ['91-53=38'] Exploring Operation: 38-32=6, Resulting Numbers: [45, 6] Generated Node #0,0,0: 39:[45, 6] Operation: 38-32=6 Exploring Operation: 45-32=13, Resulting Numbers: [38, 13] Generated Node #0,0,1: 39:[38, 13] Operation: 45-32=13 Exploring Operation: 45-38=7, Resulting Numbers: [32, 7] Generated Node #0,0,2: 39:[32, 7] Operation: 45-38=7 Moving to Node #0,0,1 Current State: 39:[38, 13], Operations: ['91-53=38', '45-32=13'] Exploring Operation: 38*13=494, Resulting Numbers: [494] 494,39 unequal: No Solution Exploring Operation: 38-13=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 38+13=51, Resulting Numbers: [51] 51,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[45, 6], Operations: ['91-53=38', '38-32=6'] Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,39 unequal: No Solution Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,39 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[91, 53, 45, 32], Operations: [] Exploring Operation: 91-53=38, Resulting Numbers: [45, 32, 38] Generated Node #0,0: 39:[45, 32, 38] Operation: 91-53=38 Moving to Node #0,0 Current State: 39:[45, 32, 38], Operations: ['91-53=38'] Exploring Operation: 38-32=6, Resulting Numbers: [45, 6] Generated Node #0,0,0: 39:[45, 6] Operation: 38-32=6 Moving to Node #0,0,0 Current State: 39:[45, 6], Operations: ['91-53=38', '38-32=6'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 42, 33, 44, 71 ]
19
[ "44-42=2", "71-33=38", "38/2=19" ]
Current State: 19:[42, 33, 44, 71], Operations: [] Exploring Operation: 44-42=2, Resulting Numbers: [33, 71, 2] Generated Node #2: [33, 71, 2] from Operation: 44-42=2 Current State: 19:[33, 71, 2], Operations: ['44-42=2'] Exploring Operation: 71-33=38, Resulting Numbers: [2, 38] Generated Node #3: [2, 38] from Operation: 71-33=38 Current State: 19:[2, 38], Operations: ['44-42=2', '71-33=38'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[42, 33, 44, 71], Operations: [] Exploring Operation: 71-44=27, Resulting Numbers: [42, 33, 27] Generated Node #0,0: 19:[42, 33, 27] Operation: 71-44=27 Exploring Operation: 71-42=29, Resulting Numbers: [33, 44, 29] Generated Node #0,1: 19:[33, 44, 29] Operation: 71-42=29 Moving to Node #0,0 Current State: 19:[42, 33, 27], Operations: ['71-44=27'] Exploring Operation: 42-33=9, Resulting Numbers: [27, 9] Generated Node #0,0,0: 19:[27, 9] Operation: 42-33=9 Exploring Operation: 42-27=15, Resulting Numbers: [33, 15] Generated Node #0,0,1: 19:[33, 15] Operation: 42-27=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[27, 9], Operations: ['71-44=27', '42-33=9'] Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,19 unequal: No Solution Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 19:[33, 15], Operations: ['71-44=27', '42-27=15'] Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,19 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,19 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: 19:[33, 44, 29], Operations: ['71-42=29'] Exploring Operation: 44-33=11, Resulting Numbers: [29, 11] Generated Node #0,1,0: 19:[29, 11] Operation: 44-33=11 Exploring Operation: 44-29=15, Resulting Numbers: [33, 15] Generated Node #0,1,1: 19:[33, 15] Operation: 44-29=15 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 19:[29, 11], Operations: ['71-42=29', '44-33=11'] Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,19 unequal: No Solution Exploring Operation: 29+11=40, Resulting Numbers: [40] 40,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 19:[33, 15], Operations: ['71-42=29', '44-29=15'] Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,19 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,19 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
[ 47, 86, 4, 62 ]
53
[ "86-62=24", "24/4=6", "47+6=53" ]
Current State: 53:[47, 86, 4, 62], Operations: [] Exploring Operation: 86-62=24, Resulting Numbers: [47, 4, 24] Generated Node #2: [47, 4, 24] from Operation: 86-62=24 Current State: 53:[47, 4, 24], Operations: ['86-62=24'] Exploring Operation: 24/4=6, Resulting Numbers: [47, 6] Generated Node #3: [47, 6] from Operation: 24/4=6 Current State: 53:[47, 6], Operations: ['86-62=24', '24/4=6'] Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[47, 86, 4, 62], Operations: [] Exploring Operation: 47-4=43, Resulting Numbers: [86, 62, 43] Generated Node #0,0: 53:[86, 62, 43] Operation: 47-4=43 Exploring Operation: 62-4=58, Resulting Numbers: [47, 86, 58] Generated Node #0,1: 53:[47, 86, 58] Operation: 62-4=58 Exploring Operation: 86-4=82, Resulting Numbers: [47, 62, 82] Generated Node #0,2: 53:[47, 62, 82] Operation: 86-4=82 Exploring Operation: 47+4=51, Resulting Numbers: [86, 62, 51] Generated Node #0,3: 53:[86, 62, 51] Operation: 47+4=51 Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[47, 86, 58], Operations: ['62-4=58'] Exploring Operation: 58-47=11, Resulting Numbers: [86, 11] Generated Node #0,1,0: 53:[86, 11] Operation: 58-47=11 Exploring Operation: 47+86=133, Resulting Numbers: [58, 133] Generated Node #0,1,1: 53:[58, 133] Operation: 47+86=133 Exploring Operation: 86-58=28, Resulting Numbers: [47, 28] Generated Node #0,1,2: 53:[47, 28] Operation: 86-58=28 Exploring Operation: 86-47=39, Resulting Numbers: [58, 39] Generated Node #0,1,3: 53:[58, 39] Operation: 86-47=39 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 53:[58, 39], Operations: ['62-4=58', '86-47=39'] Exploring Operation: 58*39=2262, Resulting Numbers: [2262] 2262,53 unequal: No Solution Exploring Operation: 58-39=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 58+39=97, Resulting Numbers: [97] 97,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 53:[47, 28], Operations: ['62-4=58', '86-58=28'] Exploring Operation: 47-28=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 47+28=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 47*28=1316, Resulting Numbers: [1316] 1316,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[86, 11], Operations: ['62-4=58', '58-47=11'] Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 86*11=946, Resulting Numbers: [946] 946,53 unequal: No Solution Exploring Operation: 86+11=97, Resulting Numbers: [97] 97,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[58, 133], Operations: ['62-4=58', '47+86=133'] Exploring Operation: 133-58=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 58+133=191, Resulting Numbers: [191] 191,53 unequal: No Solution Exploring Operation: 58*133=7714, Resulting Numbers: [7714] 7714,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 53:[47, 62, 82], Operations: ['86-4=82'] Exploring Operation: 62-47=15, Resulting Numbers: [82, 15] Generated Node #0,2,0: 53:[82, 15] Operation: 62-47=15 Exploring Operation: 82-47=35, Resulting Numbers: [62, 35] Generated Node #0,2,1: 53:[62, 35] Operation: 82-47=35 Exploring Operation: 82-62=20, Resulting Numbers: [47, 20] Generated Node #0,2,2: 53:[47, 20] Operation: 82-62=20 Exploring Operation: 47+62=109, Resulting Numbers: [82, 109] Generated Node #0,2,3: 53:[82, 109] Operation: 47+62=109 Moving to Node #0,2,1 Current State: 53:[62, 35], Operations: ['86-4=82', '82-47=35'] Exploring Operation: 62-35=27, Resulting Numbers: [27] 27,53 unequal: No Solution Exploring Operation: 62*35=2170, Resulting Numbers: [2170] 2170,53 unequal: No Solution Exploring Operation: 62+35=97, Resulting Numbers: [97] 97,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[47, 20], Operations: ['86-4=82', '82-62=20'] Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,53 unequal: No Solution Exploring Operation: 47*20=940, Resulting Numbers: [940] 940,53 unequal: No Solution Exploring Operation: 47+20=67, Resulting Numbers: [67] 67,53 unequal: No Solution Moving to Node #0,2,0 Current State: 53:[82, 15], Operations: ['86-4=82', '62-47=15'] Exploring Operation: 82-15=67, Resulting Numbers: [67] 67,53 unequal: No Solution Exploring Operation: 82+15=97, Resulting Numbers: [97] 97,53 unequal: No Solution Exploring Operation: 82*15=1230, Resulting Numbers: [1230] 1230,53 unequal: No Solution Moving to Node #0,2,3 Current State: 53:[82, 109], Operations: ['86-4=82', '47+62=109'] Exploring Operation: 82+109=191, Resulting Numbers: [191] 191,53 unequal: No Solution Exploring Operation: 82*109=8938, Resulting Numbers: [8938] 8938,53 unequal: No Solution Exploring Operation: 109-82=27, Resulting Numbers: [27] 27,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 53:[86, 62, 51], Operations: ['47+4=51'] Exploring Operation: 86-62=24, Resulting Numbers: [51, 24] Generated Node #0,3,0: 53:[51, 24] Operation: 86-62=24 Exploring Operation: 86+51=137, Resulting Numbers: [62, 137] Generated Node #0,3,1: 53:[62, 137] Operation: 86+51=137 Exploring Operation: 62-51=11, Resulting Numbers: [86, 11] Generated Node #0,3,2: 53:[86, 11] Operation: 62-51=11 Exploring Operation: 86-51=35, Resulting Numbers: [62, 35] Generated Node #0,3,3: 53:[62, 35] Operation: 86-51=35 Moving to Node #0,3,3 Current State: 53:[62, 35], Operations: ['47+4=51', '86-51=35'] Exploring Operation: 62+35=97, Resulting Numbers: [97] 97,53 unequal: No Solution Exploring Operation: 62-35=27, Resulting Numbers: [27] 27,53 unequal: No Solution Exploring Operation: 62*35=2170, Resulting Numbers: [2170] 2170,53 unequal: No Solution Moving to Node #0,3,0 Current State: 53:[51, 24], Operations: ['47+4=51', '86-62=24'] Exploring Operation: 51-24=27, Resulting Numbers: [27] 27,53 unequal: No Solution Exploring Operation: 51+24=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 51*24=1224, Resulting Numbers: [1224] 1224,53 unequal: No Solution Moving to Node #0,3,2 Current State: 53:[86, 11], Operations: ['47+4=51', '62-51=11'] Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 86*11=946, Resulting Numbers: [946] 946,53 unequal: No Solution Exploring Operation: 86+11=97, Resulting Numbers: [97] 97,53 unequal: No Solution Moving to Node #0,3,1 Current State: 53:[62, 137], Operations: ['47+4=51', '86+51=137'] Exploring Operation: 62*137=8494, Resulting Numbers: [8494] 8494,53 unequal: No Solution Exploring Operation: 62+137=199, Resulting Numbers: [199] 199,53 unequal: No Solution Exploring Operation: 137-62=75, Resulting Numbers: [75] 75,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[86, 62, 43], Operations: ['47-4=43'] Exploring Operation: 86-43=43, Resulting Numbers: [62, 43] Generated Node #0,0,0: 53:[62, 43] Operation: 86-43=43 Exploring Operation: 86-62=24, Resulting Numbers: [43, 24] Generated Node #0,0,1: 53:[43, 24] Operation: 86-62=24 Exploring Operation: 62-43=19, Resulting Numbers: [86, 19] Generated Node #0,0,2: 53:[86, 19] Operation: 62-43=19 Exploring Operation: 86/43=2, Resulting Numbers: [62, 2] Generated Node #0,0,3: 53:[62, 2] Operation: 86/43=2 Moving to Node #0,0,0 Current State: 53:[62, 43], Operations: ['47-4=43', '86-43=43'] Exploring Operation: 62*43=2666, Resulting Numbers: [2666] 2666,53 unequal: No Solution Exploring Operation: 62+43=105, Resulting Numbers: [105] 105,53 unequal: No Solution Exploring Operation: 62-43=19, Resulting Numbers: [19] 19,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[43, 24], Operations: ['47-4=43', '86-62=24'] Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,53 unequal: No Solution Exploring Operation: 43*24=1032, Resulting Numbers: [1032] 1032,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[62, 2], Operations: ['47-4=43', '86/43=2'] Exploring Operation: 62*2=124, Resulting Numbers: [124] 124,53 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,53 unequal: No Solution Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,53 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[86, 19], Operations: ['47-4=43', '62-43=19'] Exploring Operation: 86*19=1634, Resulting Numbers: [1634] 1634,53 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,53 unequal: No Solution Exploring Operation: 86+19=105, Resulting Numbers: [105] 105,53 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
[ 99, 45, 8, 84 ]
38
[ "99-45=54", "8+84=92", "92-54=38" ]
Current State: 38:[99, 45, 8, 84], Operations: [] Exploring Operation: 99-45=54, Resulting Numbers: [8, 84, 54] Generated Node #2: [8, 84, 54] from Operation: 99-45=54 Current State: 38:[8, 84, 54], Operations: ['99-45=54'] Exploring Operation: 8+84=92, Resulting Numbers: [54, 92] Generated Node #3: [54, 92] from Operation: 8+84=92 Current State: 38:[54, 92], Operations: ['99-45=54', '8+84=92'] Exploring Operation: 92-54=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[99, 45, 8, 84], Operations: [] Exploring Operation: 99-45=54, Resulting Numbers: [8, 84, 54] Generated Node #0,0: 38:[8, 84, 54] Operation: 99-45=54 Exploring Operation: 99-84=15, Resulting Numbers: [45, 8, 15] Generated Node #0,1: 38:[45, 8, 15] Operation: 99-84=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[45, 8, 15], Operations: ['99-84=15'] Exploring Operation: 45/15=3, Resulting Numbers: [8, 3] Generated Node #0,1,0: 38:[8, 3] Operation: 45/15=3 Exploring Operation: 45-8=37, Resulting Numbers: [15, 37] Generated Node #0,1,1: 38:[15, 37] Operation: 45-8=37 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 38:[15, 37], Operations: ['99-84=15', '45-8=37'] Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,38 unequal: No Solution Exploring Operation: 15+37=52, Resulting Numbers: [52] 52,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 38:[8, 3], Operations: ['99-84=15', '45/15=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[8, 84, 54], Operations: ['99-45=54'] Exploring Operation: 84-8=76, Resulting Numbers: [54, 76] Generated Node #0,0,0: 38:[54, 76] Operation: 84-8=76 Exploring Operation: 84-54=30, Resulting Numbers: [8, 30] Generated Node #0,0,1: 38:[8, 30] Operation: 84-54=30 Moving to Node #0,0,1 Current State: 38:[8, 30], Operations: ['99-45=54', '84-54=30'] Exploring Operation: 8+30=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[99, 45, 8, 84], Operations: [] Exploring Operation: 99-45=54, Resulting Numbers: [8, 84, 54] Generated Node #0,0: 38:[8, 84, 54] Operation: 99-45=54 Moving to Node #0,0 Current State: 38:[8, 84, 54], Operations: ['99-45=54'] Exploring Operation: 84-54=30, Resulting Numbers: [8, 30] Generated Node #0,0,1: 38:[8, 30] Operation: 84-54=30 Moving to Node #0,0,1 Current State: 38:[8, 30], Operations: ['99-45=54', '84-54=30'] Exploring Operation: 8+30=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 51, 14, 4, 3 ]
25
[ "51-14=37", "4*3=12", "37-12=25" ]
Current State: 25:[51, 14, 4, 3], Operations: [] Exploring Operation: 51-14=37, Resulting Numbers: [4, 3, 37] Generated Node #2: [4, 3, 37] from Operation: 51-14=37 Current State: 25:[4, 3, 37], Operations: ['51-14=37'] Exploring Operation: 4*3=12, Resulting Numbers: [37, 12] Generated Node #3: [37, 12] from Operation: 4*3=12 Current State: 25:[37, 12], Operations: ['51-14=37', '4*3=12'] Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[51, 14, 4, 3], Operations: [] Exploring Operation: 51/3=17, Resulting Numbers: [14, 4, 17] Generated Node #0,0: 25:[14, 4, 17] Operation: 51/3=17 Exploring Operation: 51-14=37, Resulting Numbers: [4, 3, 37] Generated Node #0,1: 25:[4, 3, 37] Operation: 51-14=37 Exploring Operation: 51-4=47, Resulting Numbers: [14, 3, 47] Generated Node #0,2: 25:[14, 3, 47] Operation: 51-4=47 Exploring Operation: 51-3=48, Resulting Numbers: [14, 4, 48] Generated Node #0,3: 25:[14, 4, 48] Operation: 51-3=48 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[4, 3, 37], Operations: ['51-14=37'] Exploring Operation: 37-4=33, Resulting Numbers: [3, 33] Generated Node #0,1,0: 25:[3, 33] Operation: 37-4=33 Exploring Operation: 37-3=34, Resulting Numbers: [4, 34] Generated Node #0,1,1: 25:[4, 34] Operation: 37-3=34 Exploring Operation: 4+3=7, Resulting Numbers: [37, 7] Generated Node #0,1,2: 25:[37, 7] Operation: 4+3=7 Exploring Operation: 4-3=1, Resulting Numbers: [37, 1] Generated Node #0,1,3: 25:[37, 1] Operation: 4-3=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[3, 33], Operations: ['51-14=37', '37-4=33'] Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,25 unequal: No Solution Exploring Operation: 3+33=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,25 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: 25:[4, 34], Operations: ['51-14=37', '37-3=34'] Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,25 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,25 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,25 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: 25:[37, 7], Operations: ['51-14=37', '4+3=7'] Exploring Operation: 37*7=259, Resulting Numbers: [259] 259,25 unequal: No Solution Exploring Operation: 37-7=30, Resulting Numbers: [30] 30,25 unequal: No Solution Exploring Operation: 37+7=44, Resulting Numbers: [44] 44,25 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: 25:[37, 1], Operations: ['51-14=37', '4-3=1'] Exploring Operation: 37*1=37, Resulting Numbers: [37] 37,25 unequal: No Solution Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,25 unequal: No Solution Exploring Operation: 37+1=38, Resulting Numbers: [38] 38,25 unequal: No Solution Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,25 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: 25:[14, 4, 17], Operations: ['51/3=17'] Exploring Operation: 14-4=10, Resulting Numbers: [17, 10] Generated Node #0,0,0: 25:[17, 10] Operation: 14-4=10 Exploring Operation: 4+17=21, Resulting Numbers: [14, 21] Generated Node #0,0,1: 25:[14, 21] Operation: 4+17=21 Exploring Operation: 14+17=31, Resulting Numbers: [4, 31] Generated Node #0,0,2: 25:[4, 31] Operation: 14+17=31 Exploring Operation: 17-14=3, Resulting Numbers: [4, 3] Generated Node #0,0,3: 25:[4, 3] Operation: 17-14=3 Moving to Node #0,0,3 Current State: 25:[4, 3], Operations: ['51/3=17', '17-14=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,25 unequal: No Solution Moving to Node #0,0,2 Current State: 25:[4, 31], Operations: ['51/3=17', '14+17=31'] Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,25 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,25 unequal: No Solution Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[14, 21], Operations: ['51/3=17', '4+17=21'] Exploring Operation: 14*21=294, Resulting Numbers: [294] 294,25 unequal: No Solution Exploring Operation: 14+21=35, Resulting Numbers: [35] 35,25 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,25 unequal: No Solution Moving to Node #0,0,0 Current State: 25:[17, 10], Operations: ['51/3=17', '14-4=10'] Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,25 unequal: No Solution Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,25 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,25 unequal: No Solution No 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: 25:[14, 3, 47], Operations: ['51-4=47'] Exploring Operation: 47-14=33, Resulting Numbers: [3, 33] Generated Node #0,2,0: 25:[3, 33] Operation: 47-14=33 Exploring Operation: 14-3=11, Resulting Numbers: [47, 11] Generated Node #0,2,1: 25:[47, 11] Operation: 14-3=11 Exploring Operation: 14+3=17, Resulting Numbers: [47, 17] Generated Node #0,2,2: 25:[47, 17] Operation: 14+3=17 Exploring Operation: 47-3=44, Resulting Numbers: [14, 44] Generated Node #0,2,3: 25:[14, 44] Operation: 47-3=44 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 25:[3, 33], Operations: ['51-4=47', '47-14=33'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,25 unequal: No Solution Exploring Operation: 3+33=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,25 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: 25:[47, 11], Operations: ['51-4=47', '14-3=11'] Exploring Operation: 47+11=58, Resulting Numbers: [58] 58,25 unequal: No Solution Exploring Operation: 47-11=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 47*11=517, Resulting Numbers: [517] 517,25 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: 25:[14, 44], Operations: ['51-4=47', '47-3=44'] Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,25 unequal: No Solution Exploring Operation: 14*44=616, Resulting Numbers: [616] 616,25 unequal: No Solution Exploring Operation: 14+44=58, Resulting Numbers: [58] 58,25 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: 25:[47, 17], Operations: ['51-4=47', '14+3=17'] Exploring Operation: 47+17=64, Resulting Numbers: [64] 64,25 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,25 unequal: No Solution Exploring Operation: 47*17=799, Resulting Numbers: [799] 799,25 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: 25:[14, 4, 48], Operations: ['51-3=48'] Exploring Operation: 48-4=44, Resulting Numbers: [14, 44] Generated Node #0,3,0: 25:[14, 44] Operation: 48-4=44 Exploring Operation: 48-14=34, Resulting Numbers: [4, 34] Generated Node #0,3,1: 25:[4, 34] Operation: 48-14=34 Exploring Operation: 48/4=12, Resulting Numbers: [14, 12] Generated Node #0,3,2: 25:[14, 12] Operation: 48/4=12 Exploring Operation: 14-4=10, Resulting Numbers: [48, 10] Generated Node #0,3,3: 25:[48, 10] Operation: 14-4=10 Moving to Node #0,3,1 Current State: 25:[4, 34], Operations: ['51-3=48', '48-14=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,25 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,25 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,25 unequal: No Solution Moving to Node #0,3,2 Current State: 25:[14, 12], Operations: ['51-3=48', '48/4=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,25 unequal: No Solution Moving to Node #0,3,3 Current State: 25:[48, 10], Operations: ['51-3=48', '14-4=10'] Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,25 unequal: No Solution Exploring Operation: 48*10=480, Resulting Numbers: [480] 480,25 unequal: No Solution Exploring Operation: 48+10=58, Resulting Numbers: [58] 58,25 unequal: No Solution Moving to Node #0,3,0 Current State: 25:[14, 44], Operations: ['51-3=48', '48-4=44'] Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,25 unequal: No Solution Exploring Operation: 14+44=58, Resulting Numbers: [58] 58,25 unequal: No Solution Exploring Operation: 14*44=616, Resulting Numbers: [616] 616,25 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
[ 58, 4, 22, 70 ]
70
[ "70-58=12", "4*12=48", "22+48=70" ]
Current State: 70:[58, 4, 22, 70], Operations: [] Exploring Operation: 70-58=12, Resulting Numbers: [4, 22, 12] Generated Node #2: [4, 22, 12] from Operation: 70-58=12 Current State: 70:[4, 22, 12], Operations: ['70-58=12'] Exploring Operation: 4*12=48, Resulting Numbers: [22, 48] Generated Node #3: [22, 48] from Operation: 4*12=48 Current State: 70:[22, 48], Operations: ['70-58=12', '4*12=48'] Exploring Operation: 22+48=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[58, 4, 22, 70], Operations: [] Exploring Operation: 58-22=36, Resulting Numbers: [4, 70, 36] Generated Node #0,0: 70:[4, 70, 36] Operation: 58-22=36 Exploring Operation: 70-58=12, Resulting Numbers: [4, 22, 12] Generated Node #0,1: 70:[4, 22, 12] Operation: 70-58=12 Exploring Operation: 58+22=80, Resulting Numbers: [4, 70, 80] Generated Node #0,2: 70:[4, 70, 80] Operation: 58+22=80 Moving to Node #0,0 Current State: 70:[4, 70, 36], Operations: ['58-22=36'] Exploring Operation: 70-36=34, Resulting Numbers: [4, 34] Generated Node #0,0,0: 70:[4, 34] Operation: 70-36=34 Exploring Operation: 36/4=9, Resulting Numbers: [70, 9] Generated Node #0,0,1: 70:[70, 9] Operation: 36/4=9 Exploring Operation: 36-4=32, Resulting Numbers: [70, 32] Generated Node #0,0,2: 70:[70, 32] Operation: 36-4=32 Moving to Node #0,1 Current State: 70:[4, 22, 12], Operations: ['70-58=12'] Exploring Operation: 22-4=18, Resulting Numbers: [12, 18] Generated Node #0,1,0: 70:[12, 18] Operation: 22-4=18 Exploring Operation: 22+12=34, Resulting Numbers: [4, 34] Generated Node #0,1,1: 70:[4, 34] Operation: 22+12=34 Exploring Operation: 22-12=10, Resulting Numbers: [4, 10] Generated Node #0,1,2: 70:[4, 10] Operation: 22-12=10 Moving to Node #0,2 Current State: 70:[4, 70, 80], Operations: ['58+22=80'] Exploring Operation: 80-4=76, Resulting Numbers: [70, 76] Generated Node #0,2,0: 70:[70, 76] Operation: 80-4=76 Exploring Operation: 80/4=20, Resulting Numbers: [70, 20] Generated Node #0,2,1: 70:[70, 20] Operation: 80/4=20 Exploring Operation: 80-70=10, Resulting Numbers: [4, 10] Generated Node #0,2,2: 70:[4, 10] Operation: 80-70=10 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 70:[4, 10], Operations: ['58+22=80', '80-70=10'] Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,70 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 70:[70, 76], Operations: ['58+22=80', '80-4=76'] Exploring Operation: 76-70=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 70+76=146, Resulting Numbers: [146] 146,70 unequal: No Solution Exploring Operation: 70*76=5320, Resulting Numbers: [5320] 5320,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 70:[70, 20], Operations: ['58+22=80', '80/4=20'] Exploring Operation: 70+20=90, Resulting Numbers: [90] 90,70 unequal: No Solution Exploring Operation: 70*20=1400, Resulting Numbers: [1400] 1400,70 unequal: No Solution Exploring Operation: 70-20=50, Resulting Numbers: [50] 50,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 70:[70, 9], Operations: ['58-22=36', '36/4=9'] Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,70 unequal: No Solution Exploring Operation: 70*9=630, Resulting Numbers: [630] 630,70 unequal: No Solution Exploring Operation: 70+9=79, Resulting Numbers: [79] 79,70 unequal: No Solution Moving to Node #0,1,2 Current State: 70:[4, 10], Operations: ['70-58=12', '22-12=10'] Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,70 unequal: No Solution Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,70 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[4, 34], Operations: ['70-58=12', '22+12=34'] Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,70 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,70 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[4, 34], Operations: ['58-22=36', '70-36=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,70 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,70 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[70, 32], Operations: ['58-22=36', '36-4=32'] Exploring Operation: 70*32=2240, Resulting Numbers: [2240] 2240,70 unequal: No Solution Exploring Operation: 70-32=38, Resulting Numbers: [38] 38,70 unequal: No Solution Exploring Operation: 70+32=102, Resulting Numbers: [102] 102,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[12, 18], Operations: ['70-58=12', '22-4=18'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,70 unequal: No Solution Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,70 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 34, 21, 9, 12 ]
58
[ "34+21=55", "12-9=3", "55+3=58" ]
Current State: 58:[34, 21, 9, 12], Operations: [] Exploring Operation: 34+21=55, Resulting Numbers: [9, 12, 55] Generated Node #2: [9, 12, 55] from Operation: 34+21=55 Current State: 58:[9, 12, 55], Operations: ['34+21=55'] Exploring Operation: 12-9=3, Resulting Numbers: [55, 3] Generated Node #3: [55, 3] from Operation: 12-9=3 Current State: 58:[55, 3], Operations: ['34+21=55', '12-9=3'] Exploring Operation: 55+3=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[34, 21, 9, 12], Operations: [] Exploring Operation: 34+21=55, Resulting Numbers: [9, 12, 55] Generated Node #0,0: 58:[9, 12, 55] Operation: 34+21=55 Exploring Operation: 21+12=33, Resulting Numbers: [34, 9, 33] Generated Node #0,1: 58:[34, 9, 33] Operation: 21+12=33 Exploring Operation: 12-9=3, Resulting Numbers: [34, 21, 3] Generated Node #0,2: 58:[34, 21, 3] Operation: 12-9=3 Exploring Operation: 21-12=9, Resulting Numbers: [34, 9, 9] Generated Node #0,3: 58:[34, 9, 9] Operation: 21-12=9 Exploring Operation: 21+9=30, Resulting Numbers: [34, 12, 30] Generated Node #0,4: 58:[34, 12, 30] Operation: 21+9=30 Moving to Node #0,2 Current State: 58:[34, 21, 3], Operations: ['12-9=3'] Exploring Operation: 34+21=55, Resulting Numbers: [3, 55] Generated Node #0,2,0: 58:[3, 55] Operation: 34+21=55 Exploring Operation: 21+3=24, Resulting Numbers: [34, 24] Generated Node #0,2,1: 58:[34, 24] Operation: 21+3=24 Exploring Operation: 21/3=7, Resulting Numbers: [34, 7] Generated Node #0,2,2: 58:[34, 7] Operation: 21/3=7 Exploring Operation: 34-3=31, Resulting Numbers: [21, 31] Generated Node #0,2,3: 58:[21, 31] Operation: 34-3=31 Exploring Operation: 21*3=63, Resulting Numbers: [34, 63] Generated Node #0,2,4: 58:[34, 63] Operation: 21*3=63 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 58:[3, 55], Operations: ['12-9=3', '34+21=55'] Exploring Operation: 3+55=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[34, 21, 9, 12], Operations: [] Exploring Operation: 12-9=3, Resulting Numbers: [34, 21, 3] Generated Node #0,2: 58:[34, 21, 3] Operation: 12-9=3 Moving to Node #0,2 Current State: 58:[34, 21, 3], Operations: ['12-9=3'] Exploring Operation: 34+21=55, Resulting Numbers: [3, 55] Generated Node #0,2,0: 58:[3, 55] Operation: 34+21=55 Moving to Node #0,2,0 Current State: 58:[3, 55], Operations: ['12-9=3', '34+21=55'] Exploring Operation: 3+55=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 88, 53, 55, 82 ]
62
[ "88-53=35", "82-55=27", "35+27=62" ]
Current State: 62:[88, 53, 55, 82], Operations: [] Exploring Operation: 88-53=35, Resulting Numbers: [55, 82, 35] Generated Node #2: [55, 82, 35] from Operation: 88-53=35 Current State: 62:[55, 82, 35], Operations: ['88-53=35'] Exploring Operation: 82-55=27, Resulting Numbers: [35, 27] Generated Node #3: [35, 27] from Operation: 82-55=27 Current State: 62:[35, 27], Operations: ['88-53=35', '82-55=27'] Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[88, 53, 55, 82], Operations: [] Exploring Operation: 88-53=35, Resulting Numbers: [55, 82, 35] Generated Node #0,0: 62:[55, 82, 35] Operation: 88-53=35 Exploring Operation: 88-82=6, Resulting Numbers: [53, 55, 6] Generated Node #0,1: 62:[53, 55, 6] Operation: 88-82=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[53, 55, 6], Operations: ['88-82=6'] Exploring Operation: 53+6=59, Resulting Numbers: [55, 59] Generated Node #0,1,0: 62:[55, 59] Operation: 53+6=59 Exploring Operation: 55-53=2, Resulting Numbers: [6, 2] Generated Node #0,1,1: 62:[6, 2] Operation: 55-53=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 62:[6, 2], Operations: ['88-82=6', '55-53=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,62 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,62 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: 62:[55, 59], Operations: ['88-82=6', '53+6=59'] Exploring Operation: 59-55=4, Resulting Numbers: [4] 4,62 unequal: No Solution Exploring Operation: 55+59=114, Resulting Numbers: [114] 114,62 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: 62:[55, 82, 35], Operations: ['88-53=35'] Exploring Operation: 82-35=47, Resulting Numbers: [55, 47] Generated Node #0,0,0: 62:[55, 47] Operation: 82-35=47 Exploring Operation: 82-55=27, Resulting Numbers: [35, 27] Generated Node #0,0,1: 62:[35, 27] Operation: 82-55=27 Moving to Node #0,0,1 Current State: 62:[35, 27], Operations: ['88-53=35', '82-55=27'] Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,62 unequal: No Solution Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[88, 53, 55, 82], Operations: [] Exploring Operation: 88-53=35, Resulting Numbers: [55, 82, 35] Generated Node #0,0: 62:[55, 82, 35] Operation: 88-53=35 Moving to Node #0,0 Current State: 62:[55, 82, 35], Operations: ['88-53=35'] Exploring Operation: 82-55=27, Resulting Numbers: [35, 27] Generated Node #0,0,1: 62:[35, 27] Operation: 82-55=27 Moving to Node #0,0,1 Current State: 62:[35, 27], Operations: ['88-53=35', '82-55=27'] Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 12, 2, 69, 66 ]
42
[ "12+2=14", "69-66=3", "14*3=42" ]
Current State: 42:[12, 2, 69, 66], Operations: [] Exploring Operation: 12+2=14, Resulting Numbers: [69, 66, 14] Generated Node #2: [69, 66, 14] from Operation: 12+2=14 Current State: 42:[69, 66, 14], Operations: ['12+2=14'] Exploring Operation: 69-66=3, Resulting Numbers: [14, 3] Generated Node #3: [14, 3] from Operation: 69-66=3 Current State: 42:[14, 3], Operations: ['12+2=14', '69-66=3'] Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[12, 2, 69, 66], Operations: [] Exploring Operation: 69-12=57, Resulting Numbers: [2, 66, 57] Generated Node #0,0: 42:[2, 66, 57] Operation: 69-12=57 Exploring Operation: 66/2=33, Resulting Numbers: [12, 69, 33] Generated Node #0,1: 42:[12, 69, 33] Operation: 66/2=33 Exploring Operation: 66-12=54, Resulting Numbers: [2, 69, 54] Generated Node #0,2: 42:[2, 69, 54] Operation: 66-12=54 Exploring Operation: 69-66=3, Resulting Numbers: [12, 2, 3] Generated Node #0,3: 42:[12, 2, 3] Operation: 69-66=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 42:[12, 2, 3], Operations: ['69-66=3'] Exploring Operation: 12/2=6, Resulting Numbers: [3, 6] Generated Node #0,3,0: 42:[3, 6] Operation: 12/2=6 Exploring Operation: 12+2=14, Resulting Numbers: [3, 14] Generated Node #0,3,1: 42:[3, 14] Operation: 12+2=14 Exploring Operation: 12/3=4, Resulting Numbers: [2, 4] Generated Node #0,3,2: 42:[2, 4] Operation: 12/3=4 Exploring Operation: 12+3=15, Resulting Numbers: [2, 15] Generated Node #0,3,3: 42:[2, 15] Operation: 12+3=15 Moving to Node #0,3,0 Current State: 42:[3, 6], Operations: ['69-66=3', '12/2=6'] Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,42 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,42 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,42 unequal: No Solution Moving to Node #0,3,1 Current State: 42:[3, 14], Operations: ['69-66=3', '12+2=14'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,42 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[12, 2, 69, 66], Operations: [] Exploring Operation: 69-66=3, Resulting Numbers: [12, 2, 3] Generated Node #0,3: 42:[12, 2, 3] Operation: 69-66=3 Moving to Node #0,3 Current State: 42:[12, 2, 3], Operations: ['69-66=3'] Exploring Operation: 12+2=14, Resulting Numbers: [3, 14] Generated Node #0,3,1: 42:[3, 14] Operation: 12+2=14 Moving to Node #0,3,1 Current State: 42:[3, 14], Operations: ['69-66=3', '12+2=14'] Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 47, 17, 90, 81 ]
73
[ "47+17=64", "90-81=9", "64+9=73" ]
Current State: 73:[47, 17, 90, 81], Operations: [] Exploring Operation: 47+17=64, Resulting Numbers: [90, 81, 64] Generated Node #2: [90, 81, 64] from Operation: 47+17=64 Current State: 73:[90, 81, 64], Operations: ['47+17=64'] Exploring Operation: 90-81=9, Resulting Numbers: [64, 9] Generated Node #3: [64, 9] from Operation: 90-81=9 Current State: 73:[64, 9], Operations: ['47+17=64', '90-81=9'] Exploring Operation: 64+9=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[47, 17, 90, 81], Operations: [] Exploring Operation: 90-17=73, Resulting Numbers: [47, 81, 73] Generated Node #0,0: 73:[47, 81, 73] Operation: 90-17=73 Exploring Operation: 47-17=30, Resulting Numbers: [90, 81, 30] Generated Node #0,1: 73:[90, 81, 30] Operation: 47-17=30 Exploring Operation: 81-17=64, Resulting Numbers: [47, 90, 64] Generated Node #0,2: 73:[47, 90, 64] Operation: 81-17=64 Exploring Operation: 47+17=64, Resulting Numbers: [90, 81, 64] Generated Node #0,3: 73:[90, 81, 64] Operation: 47+17=64 Moving to Node #0,0 Current State: 73:[47, 81, 73], Operations: ['90-17=73'] Exploring Operation: 73-47=26, Resulting Numbers: [81, 26] Generated Node #0,0,0: 73:[81, 26] Operation: 73-47=26 Exploring Operation: 81-47=34, Resulting Numbers: [73, 34] Generated Node #0,0,1: 73:[73, 34] Operation: 81-47=34 Exploring Operation: 47+81=128, Resulting Numbers: [73, 128] Generated Node #0,0,2: 73:[73, 128] Operation: 47+81=128 Exploring Operation: 47+73=120, Resulting Numbers: [81, 120] Generated Node #0,0,3: 73:[81, 120] Operation: 47+73=120 Moving to Node #0,3 Current State: 73:[90, 81, 64], Operations: ['47+17=64'] Exploring Operation: 90+64=154, Resulting Numbers: [81, 154] Generated Node #0,3,0: 73:[81, 154] Operation: 90+64=154 Exploring Operation: 90-81=9, Resulting Numbers: [64, 9] Generated Node #0,3,1: 73:[64, 9] Operation: 90-81=9 Exploring Operation: 90-64=26, Resulting Numbers: [81, 26] Generated Node #0,3,2: 73:[81, 26] Operation: 90-64=26 Exploring Operation: 81-64=17, Resulting Numbers: [90, 17] Generated Node #0,3,3: 73:[90, 17] Operation: 81-64=17 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 73:[81, 26], Operations: ['47+17=64', '90-64=26'] Exploring Operation: 81+26=107, Resulting Numbers: [107] 107,73 unequal: No Solution Exploring Operation: 81-26=55, Resulting Numbers: [55] 55,73 unequal: No Solution Exploring Operation: 81*26=2106, Resulting Numbers: [2106] 2106,73 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:[64, 9], Operations: ['47+17=64', '90-81=9'] Exploring Operation: 64+9=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[47, 17, 90, 81], Operations: [] Exploring Operation: 47+17=64, Resulting Numbers: [90, 81, 64] Generated Node #0,3: 73:[90, 81, 64] Operation: 47+17=64 Moving to Node #0,3 Current State: 73:[90, 81, 64], Operations: ['47+17=64'] Exploring Operation: 90-81=9, Resulting Numbers: [64, 9] Generated Node #0,3,1: 73:[64, 9] Operation: 90-81=9 Moving to Node #0,3,1 Current State: 73:[64, 9], Operations: ['47+17=64', '90-81=9'] Exploring Operation: 64+9=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 14, 10, 25, 65 ]
64
[ "14+10=24", "65-25=40", "24+40=64" ]
Current State: 64:[14, 10, 25, 65], Operations: [] Exploring Operation: 14+10=24, Resulting Numbers: [25, 65, 24] Generated Node #2: [25, 65, 24] from Operation: 14+10=24 Current State: 64:[25, 65, 24], Operations: ['14+10=24'] Exploring Operation: 65-25=40, Resulting Numbers: [24, 40] Generated Node #3: [24, 40] from Operation: 65-25=40 Current State: 64:[24, 40], Operations: ['14+10=24', '65-25=40'] Exploring Operation: 24+40=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[14, 10, 25, 65], Operations: [] Exploring Operation: 25-14=11, Resulting Numbers: [10, 65, 11] Generated Node #0,0: 64:[10, 65, 11] Operation: 25-14=11 Exploring Operation: 25-10=15, Resulting Numbers: [14, 65, 15] Generated Node #0,1: 64:[14, 65, 15] Operation: 25-10=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[14, 65, 15], Operations: ['25-10=15'] Exploring Operation: 14+15=29, Resulting Numbers: [65, 29] Generated Node #0,1,0: 64:[65, 29] Operation: 14+15=29 Exploring Operation: 15-14=1, Resulting Numbers: [65, 1] Generated Node #0,1,1: 64:[65, 1] Operation: 15-14=1 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 64:[65, 1], Operations: ['25-10=15', '15-14=1'] Exploring Operation: 65*1=65, Resulting Numbers: [65] 65,64 unequal: No Solution Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[14, 10, 25, 65], Operations: [] Exploring Operation: 25-10=15, Resulting Numbers: [14, 65, 15] Generated Node #0,1: 64:[14, 65, 15] Operation: 25-10=15 Moving to Node #0,1 Current State: 64:[14, 65, 15], Operations: ['25-10=15'] Exploring Operation: 15-14=1, Resulting Numbers: [65, 1] Generated Node #0,1,1: 64:[65, 1] Operation: 15-14=1 Moving to Node #0,1,1 Current State: 64:[65, 1], Operations: ['25-10=15', '15-14=1'] Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 64, 49, 16, 94 ]
63
[ "64-49=15", "94-16=78", "78-15=63" ]
Current State: 63:[64, 49, 16, 94], Operations: [] Exploring Operation: 64-49=15, Resulting Numbers: [16, 94, 15] Generated Node #2: [16, 94, 15] from Operation: 64-49=15 Current State: 63:[16, 94, 15], Operations: ['64-49=15'] Exploring Operation: 94-16=78, Resulting Numbers: [15, 78] Generated Node #3: [15, 78] from Operation: 94-16=78 Current State: 63:[15, 78], Operations: ['64-49=15', '94-16=78'] Exploring Operation: 78-15=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[64, 49, 16, 94], Operations: [] Exploring Operation: 94-49=45, Resulting Numbers: [64, 16, 45] Generated Node #0,0: 63:[64, 16, 45] Operation: 94-49=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[64, 16, 45], Operations: ['94-49=45'] Exploring Operation: 16+45=61, Resulting Numbers: [64, 61] Generated Node #0,0,0: 63:[64, 61] Operation: 16+45=61 Moving to Node #0,0,0 Current State: 63:[64, 61], Operations: ['94-49=45', '16+45=61'] Exploring Operation: 64-61=3, Resulting Numbers: [3] 3,63 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
[ 30, 30, 24, 90 ]
96
[ "30+90=120", "120/30=4", "24*4=96" ]
Current State: 96:[30, 30, 24, 90], Operations: [] Exploring Operation: 30+90=120, Resulting Numbers: [24, 120] Generated Node #2: [24, 120] from Operation: 30+90=120 Current State: 96:[24, 120], Operations: ['30+90=120'] Exploring Operation: 120/30=4, Resulting Numbers: [24, 4] Generated Node #3: [24, 4] from Operation: 120/30=4 Current State: 96:[24, 4], Operations: ['30+90=120', '120/30=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[30, 30, 24, 90], Operations: [] Exploring Operation: 90/30=3, Resulting Numbers: [30, 24, 3] Generated Node #0,0: 96:[30, 24, 3] Operation: 90/30=3 Exploring Operation: 30/30=1, Resulting Numbers: [24, 90, 1] Generated Node #0,1: 96:[24, 90, 1] Operation: 30/30=1 Exploring Operation: 90/30=3, Resulting Numbers: [30, 24, 3] Generated Node #0,2: 96:[30, 24, 3] Operation: 90/30=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[30, 24, 3], Operations: ['90/30=3'] Exploring Operation: 30+3=33, Resulting Numbers: [24, 33] Generated Node #0,0,0: 96:[24, 33] Operation: 30+3=33 Exploring Operation: 30/3=10, Resulting Numbers: [24, 10] Generated Node #0,0,1: 96:[24, 10] Operation: 30/3=10 Exploring Operation: 30-24=6, Resulting Numbers: [3, 6] Generated Node #0,0,2: 96:[3, 6] Operation: 30-24=6 Moving to Node #0,0,2 Current State: 96:[3, 6], Operations: ['90/30=3', '30-24=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,96 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[24, 33], Operations: ['90/30=3', '30+3=33'] Exploring Operation: 24+33=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,96 unequal: No Solution Exploring Operation: 24*33=792, Resulting Numbers: [792] 792,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[24, 10], Operations: ['90/30=3', '30/3=10'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,96 unequal: No Solution Exploring Operation: 24*10=240, Resulting Numbers: [240] 240,96 unequal: No Solution Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,96 unequal: No Solution No 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: 96:[30, 24, 3], Operations: ['90/30=3'] Exploring Operation: 30-24=6, Resulting Numbers: [3, 6] Generated Node #0,2,0: 96:[3, 6] Operation: 30-24=6 Exploring Operation: 30/3=10, Resulting Numbers: [24, 10] Generated Node #0,2,1: 96:[24, 10] Operation: 30/3=10 Exploring Operation: 30+3=33, Resulting Numbers: [24, 33] Generated Node #0,2,2: 96:[24, 33] Operation: 30+3=33 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 96:[3, 6], Operations: ['90/30=3', '30-24=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,96 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: 96:[24, 33], Operations: ['90/30=3', '30+3=33'] Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,96 unequal: No Solution Exploring Operation: 24+33=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 24*33=792, Resulting Numbers: [792] 792,96 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: 96:[24, 10], Operations: ['90/30=3', '30/3=10'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,96 unequal: No Solution Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,96 unequal: No Solution Exploring Operation: 24*10=240, Resulting Numbers: [240] 240,96 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: 96:[24, 90, 1], Operations: ['30/30=1'] Exploring Operation: 24/1=24, Resulting Numbers: [90, 24] Generated Node #0,1,0: 96:[90, 24] Operation: 24/1=24 Exploring Operation: 90+1=91, Resulting Numbers: [24, 91] Generated Node #0,1,1: 96:[24, 91] Operation: 90+1=91 Exploring Operation: 24*1=24, Resulting Numbers: [90, 24] Generated Node #0,1,2: 96:[90, 24] Operation: 24*1=24 Moving to Node #0,1,1 Current State: 96:[24, 91], Operations: ['30/30=1', '90+1=91'] Exploring Operation: 91-24=67, Resulting Numbers: [67] 67,96 unequal: No Solution Exploring Operation: 24+91=115, Resulting Numbers: [115] 115,96 unequal: No Solution Exploring Operation: 24*91=2184, Resulting Numbers: [2184] 2184,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[90, 24], Operations: ['30/30=1', '24/1=24'] Exploring Operation: 90-24=66, Resulting Numbers: [66] 66,96 unequal: No Solution Exploring Operation: 90*24=2160, Resulting Numbers: [2160] 2160,96 unequal: No Solution Exploring Operation: 90+24=114, Resulting Numbers: [114] 114,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[90, 24], Operations: ['30/30=1', '24*1=24'] Exploring Operation: 90-24=66, Resulting Numbers: [66] 66,96 unequal: No Solution Exploring Operation: 90*24=2160, Resulting Numbers: [2160] 2160,96 unequal: No Solution Exploring Operation: 90+24=114, Resulting Numbers: [114] 114,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 20, 84, 1, 2 ]
21
[ "20+1=21", "84/2=42", "42-21=21" ]
Current State: 21:[20, 84, 1, 2], Operations: [] Exploring Operation: 20+1=21, Resulting Numbers: [84, 2, 21] Generated Node #2: [84, 2, 21] from Operation: 20+1=21 Current State: 21:[84, 2, 21], Operations: ['20+1=21'] Exploring Operation: 84/2=42, Resulting Numbers: [21, 42] Generated Node #3: [21, 42] from Operation: 84/2=42 Current State: 21:[21, 42], Operations: ['20+1=21', '84/2=42'] Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[20, 84, 1, 2], Operations: [] Exploring Operation: 84-1=83, Resulting Numbers: [20, 2, 83] Generated Node #0,0: 21:[20, 2, 83] Operation: 84-1=83 Exploring Operation: 20+1=21, Resulting Numbers: [84, 2, 21] Generated Node #0,1: 21:[84, 2, 21] Operation: 20+1=21 Exploring Operation: 84-20=64, Resulting Numbers: [1, 2, 64] Generated Node #0,2: 21:[1, 2, 64] Operation: 84-20=64 Exploring Operation: 84/2=42, Resulting Numbers: [20, 1, 42] Generated Node #0,3: 21:[20, 1, 42] Operation: 84/2=42 Start Sub Search at level 1: Moving to Node #0,3 Current State: 21:[20, 1, 42], Operations: ['84/2=42'] Exploring Operation: 42-1=41, Resulting Numbers: [20, 41] Generated Node #0,3,0: 21:[20, 41] Operation: 42-1=41 Exploring Operation: 42-20=22, Resulting Numbers: [1, 22] Generated Node #0,3,1: 21:[1, 22] Operation: 42-20=22 Exploring Operation: 20+1=21, Resulting Numbers: [42, 21] Generated Node #0,3,2: 21:[42, 21] Operation: 20+1=21 Exploring Operation: 20*1=20, Resulting Numbers: [42, 20] Generated Node #0,3,3: 21:[42, 20] Operation: 20*1=20 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 21:[1, 22], Operations: ['84/2=42', '42-20=22'] Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,21 unequal: No Solution Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,21 unequal: No Solution Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,21 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[20, 84, 1, 2], Operations: [] Exploring Operation: 84/2=42, Resulting Numbers: [20, 1, 42] Generated Node #0,3: 21:[20, 1, 42] Operation: 84/2=42 Moving to Node #0,3 Current State: 21:[20, 1, 42], Operations: ['84/2=42'] Exploring Operation: 42-20=22, Resulting Numbers: [1, 22] Generated Node #0,3,1: 21:[1, 22] Operation: 42-20=22 Moving to Node #0,3,1 Current State: 21:[1, 22], Operations: ['84/2=42', '42-20=22'] Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 9, 84, 6, 15 ]
79
[ "9-6=3", "15/3=5", "84-5=79" ]
Current State: 79:[9, 84, 6, 15], Operations: [] Exploring Operation: 9-6=3, Resulting Numbers: [84, 15, 3] Generated Node #2: [84, 15, 3] from Operation: 9-6=3 Current State: 79:[84, 15, 3], Operations: ['9-6=3'] Exploring Operation: 15/3=5, Resulting Numbers: [84, 5] Generated Node #3: [84, 5] from Operation: 15/3=5 Current State: 79:[84, 5], Operations: ['9-6=3', '15/3=5'] Exploring Operation: 84-5=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[9, 84, 6, 15], Operations: [] Exploring Operation: 9+15=24, Resulting Numbers: [84, 6, 24] Generated Node #0,0: 79:[84, 6, 24] Operation: 9+15=24 Exploring Operation: 9*6=54, Resulting Numbers: [84, 15, 54] Generated Node #0,1: 79:[84, 15, 54] Operation: 9*6=54 Exploring Operation: 6*15=90, Resulting Numbers: [9, 84, 90] Generated Node #0,2: 79:[9, 84, 90] Operation: 6*15=90 Exploring Operation: 9+6=15, Resulting Numbers: [84, 15, 15] Generated Node #0,3: 79:[84, 15, 15] Operation: 9+6=15 Moving to Node #0,2 Current State: 79:[9, 84, 90], Operations: ['6*15=90'] Exploring Operation: 90-9=81, Resulting Numbers: [84, 81] Generated Node #0,2,0: 79:[84, 81] Operation: 90-9=81 Exploring Operation: 9+84=93, Resulting Numbers: [90, 93] Generated Node #0,2,1: 79:[90, 93] Operation: 9+84=93 Exploring Operation: 9+90=99, Resulting Numbers: [84, 99] Generated Node #0,2,2: 79:[84, 99] Operation: 9+90=99 Exploring Operation: 84-9=75, Resulting Numbers: [90, 75] Generated Node #0,2,3: 79:[90, 75] Operation: 84-9=75 Moving to Node #0,1 Current State: 79:[84, 15, 54], Operations: ['9*6=54'] Exploring Operation: 84-15=69, Resulting Numbers: [54, 69] Generated Node #0,1,0: 79:[54, 69] Operation: 84-15=69 Exploring Operation: 54-15=39, Resulting Numbers: [84, 39] Generated Node #0,1,1: 79:[84, 39] Operation: 54-15=39 Exploring Operation: 84+15=99, Resulting Numbers: [54, 99] Generated Node #0,1,2: 79:[54, 99] Operation: 84+15=99 Exploring Operation: 15+54=69, Resulting Numbers: [84, 69] Generated Node #0,1,3: 79:[84, 69] Operation: 15+54=69 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 79:[84, 69], Operations: ['9*6=54', '15+54=69'] Exploring Operation: 84+69=153, Resulting Numbers: [153] 153,79 unequal: No Solution Exploring Operation: 84-69=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 84*69=5796, Resulting Numbers: [5796] 5796,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[54, 69], Operations: ['9*6=54', '84-15=69'] Exploring Operation: 69-54=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 54+69=123, Resulting Numbers: [123] 123,79 unequal: No Solution Exploring Operation: 54*69=3726, Resulting Numbers: [3726] 3726,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[84, 39], Operations: ['9*6=54', '54-15=39'] Exploring Operation: 84-39=45, Resulting Numbers: [45] 45,79 unequal: No Solution Exploring Operation: 84*39=3276, Resulting Numbers: [3276] 3276,79 unequal: No Solution Exploring Operation: 84+39=123, Resulting Numbers: [123] 123,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[54, 99], Operations: ['9*6=54', '84+15=99'] Exploring Operation: 99-54=45, Resulting Numbers: [45] 45,79 unequal: No Solution Exploring Operation: 54+99=153, Resulting Numbers: [153] 153,79 unequal: No Solution Exploring Operation: 54*99=5346, Resulting Numbers: [5346] 5346,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 79:[84, 15, 15], Operations: ['9+6=15'] Exploring Operation: 84-15=69, Resulting Numbers: [15, 69] Generated Node #0,3,0: 79:[15, 69] Operation: 84-15=69 Exploring Operation: 15/15=1, Resulting Numbers: [84, 1] Generated Node #0,3,1: 79:[84, 1] Operation: 15/15=1 Exploring Operation: 15+15=30, Resulting Numbers: [84, 30] Generated Node #0,3,2: 79:[84, 30] Operation: 15+15=30 Exploring Operation: 84-15=69, Resulting Numbers: [15, 69] Generated Node #0,3,3: 79:[15, 69] Operation: 84-15=69 Moving to Node #0,0 Current State: 79:[84, 6, 24], Operations: ['9+15=24'] Exploring Operation: 6+24=30, Resulting Numbers: [84, 30] Generated Node #0,0,0: 79:[84, 30] Operation: 6+24=30 Exploring Operation: 84+6=90, Resulting Numbers: [24, 90] Generated Node #0,0,1: 79:[24, 90] Operation: 84+6=90 Exploring Operation: 84-6=78, Resulting Numbers: [24, 78] Generated Node #0,0,2: 79:[24, 78] Operation: 84-6=78 Exploring Operation: 24-6=18, Resulting Numbers: [84, 18] Generated Node #0,0,3: 79:[84, 18] Operation: 24-6=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[84, 30], Operations: ['9+15=24', '6+24=30'] Exploring Operation: 84+30=114, Resulting Numbers: [114] 114,79 unequal: No Solution Exploring Operation: 84*30=2520, Resulting Numbers: [2520] 2520,79 unequal: No Solution Exploring Operation: 84-30=54, Resulting Numbers: [54] 54,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 79:[24, 78], Operations: ['9+15=24', '84-6=78'] Exploring Operation: 24*78=1872, Resulting Numbers: [1872] 1872,79 unequal: No Solution Exploring Operation: 78-24=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 24+78=102, Resulting Numbers: [102] 102,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[24, 90], Operations: ['9+15=24', '84+6=90'] Exploring Operation: 90-24=66, Resulting Numbers: [66] 66,79 unequal: No Solution Exploring Operation: 24*90=2160, Resulting Numbers: [2160] 2160,79 unequal: No Solution Exploring Operation: 24+90=114, Resulting Numbers: [114] 114,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 79:[84, 18], Operations: ['9+15=24', '24-6=18'] Exploring Operation: 84+18=102, Resulting Numbers: [102] 102,79 unequal: No Solution Exploring Operation: 84*18=1512, Resulting Numbers: [1512] 1512,79 unequal: No Solution Exploring Operation: 84-18=66, Resulting Numbers: [66] 66,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 79:[84, 81], Operations: ['6*15=90', '90-9=81'] Exploring Operation: 84-81=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 84+81=165, Resulting Numbers: [165] 165,79 unequal: No Solution Exploring Operation: 84*81=6804, Resulting Numbers: [6804] 6804,79 unequal: No Solution Moving to Node #0,2,3 Current State: 79:[90, 75], Operations: ['6*15=90', '84-9=75'] Exploring Operation: 90+75=165, Resulting Numbers: [165] 165,79 unequal: No Solution Exploring Operation: 90-75=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 90*75=6750, Resulting Numbers: [6750] 6750,79 unequal: No Solution Moving to Node #0,2,1 Current State: 79:[90, 93], Operations: ['6*15=90', '9+84=93'] Exploring Operation: 93-90=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 90+93=183, Resulting Numbers: [183] 183,79 unequal: No Solution Exploring Operation: 90*93=8370, Resulting Numbers: [8370] 8370,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[84, 99], Operations: ['6*15=90', '9+90=99'] Exploring Operation: 99-84=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 84+99=183, Resulting Numbers: [183] 183,79 unequal: No Solution Exploring Operation: 84*99=8316, Resulting Numbers: [8316] 8316,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[84, 30], Operations: ['9+6=15', '15+15=30'] Exploring Operation: 84+30=114, Resulting Numbers: [114] 114,79 unequal: No Solution Exploring Operation: 84-30=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 84*30=2520, Resulting Numbers: [2520] 2520,79 unequal: No Solution Moving to Node #0,3,0 Current State: 79:[15, 69], Operations: ['9+6=15', '84-15=69'] Exploring Operation: 15*69=1035, Resulting Numbers: [1035] 1035,79 unequal: No Solution Exploring Operation: 15+69=84, Resulting Numbers: [84] 84,79 unequal: No Solution Exploring Operation: 69-15=54, Resulting Numbers: [54] 54,79 unequal: No Solution Moving to Node #0,3,3 Current State: 79:[15, 69], Operations: ['9+6=15', '84-15=69'] Exploring Operation: 15*69=1035, Resulting Numbers: [1035] 1035,79 unequal: No Solution Exploring Operation: 15+69=84, Resulting Numbers: [84] 84,79 unequal: No Solution Exploring Operation: 69-15=54, Resulting Numbers: [54] 54,79 unequal: No Solution Moving to Node #0,3,1 Current State: 79:[84, 1], Operations: ['9+6=15', '15/15=1'] Exploring Operation: 84-1=83, Resulting Numbers: [83] 83,79 unequal: No Solution Exploring Operation: 84*1=84, Resulting Numbers: [84] 84,79 unequal: No Solution Exploring Operation: 84/1=84, Resulting Numbers: [84] 84,79 unequal: No Solution Exploring Operation: 84+1=85, Resulting Numbers: [85] 85,79 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 11, 12, 46, 20 ]
43
[ "11+12=23", "46+20=66", "66-23=43" ]
Current State: 43:[11, 12, 46, 20], Operations: [] Exploring Operation: 11+12=23, Resulting Numbers: [46, 20, 23] Generated Node #2: [46, 20, 23] from Operation: 11+12=23 Current State: 43:[46, 20, 23], Operations: ['11+12=23'] Exploring Operation: 46+20=66, Resulting Numbers: [23, 66] Generated Node #3: [23, 66] from Operation: 46+20=66 Current State: 43:[23, 66], Operations: ['11+12=23', '46+20=66'] Exploring Operation: 66-23=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[11, 12, 46, 20], Operations: [] Exploring Operation: 11+20=31, Resulting Numbers: [12, 46, 31] Generated Node #0,0: 43:[12, 46, 31] Operation: 11+20=31 Exploring Operation: 11+12=23, Resulting Numbers: [46, 20, 23] Generated Node #0,1: 43:[46, 20, 23] Operation: 11+12=23 Moving to Node #0,0 Current State: 43:[12, 46, 31], Operations: ['11+20=31'] Exploring Operation: 46-12=34, Resulting Numbers: [31, 34] Generated Node #0,0,0: 43:[31, 34] Operation: 46-12=34 Exploring Operation: 12+31=43, Resulting Numbers: [46, 43] Generated Node #0,0,1: 43:[46, 43] Operation: 12+31=43 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 43:[46, 43], Operations: ['11+20=31', '12+31=43'] Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[31, 34], Operations: ['11+20=31', '46-12=34'] Exploring Operation: 31+34=65, Resulting Numbers: [65] 65,43 unequal: No Solution Exploring Operation: 34-31=3, Resulting Numbers: [3] 3,43 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: 43:[46, 20, 23], Operations: ['11+12=23'] Exploring Operation: 20+23=43, Resulting Numbers: [46, 43] Generated Node #0,1,0: 43:[46, 43] Operation: 20+23=43 Exploring Operation: 46-20=26, Resulting Numbers: [23, 26] Generated Node #0,1,1: 43:[23, 26] Operation: 46-20=26 Moving to Node #0,1,0 Current State: 43:[46, 43], Operations: ['11+12=23', '20+23=43'] Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,43 unequal: No Solution Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[23, 26], Operations: ['11+12=23', '46-20=26'] Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,43 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 68, 83, 82, 2 ]
29
[ "68*2=136", "83+82=165", "165-136=29" ]
Current State: 29:[68, 83, 82, 2], Operations: [] Exploring Operation: 68*2=136, Resulting Numbers: [83, 82, 136] Generated Node #2: [83, 82, 136] from Operation: 68*2=136 Current State: 29:[83, 82, 136], Operations: ['68*2=136'] Exploring Operation: 83+82=165, Resulting Numbers: [136, 165] Generated Node #3: [136, 165] from Operation: 83+82=165 Current State: 29:[136, 165], Operations: ['68*2=136', '83+82=165'] Exploring Operation: 165-136=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[68, 83, 82, 2], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [68, 2, 1] Generated Node #0,0: 29:[68, 2, 1] Operation: 83-82=1 Exploring Operation: 83-68=15, Resulting Numbers: [82, 2, 15] Generated Node #0,1: 29:[82, 2, 15] Operation: 83-68=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[68, 2, 1], Operations: ['83-82=1'] Exploring Operation: 68-2=66, Resulting Numbers: [1, 66] Generated Node #0,0,0: 29:[1, 66] Operation: 68-2=66 Exploring Operation: 68/2=34, Resulting Numbers: [1, 34] Generated Node #0,0,1: 29:[1, 34] Operation: 68/2=34 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 29:[1, 34], Operations: ['83-82=1', '68/2=34'] Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,29 unequal: No Solution Exploring Operation: 1*34=34, Resulting Numbers: [34] 34,29 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: 29:[1, 66], Operations: ['83-82=1', '68-2=66'] Exploring Operation: 1*66=66, Resulting Numbers: [66] 66,29 unequal: No Solution Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[82, 2, 15], Operations: ['83-68=15'] Exploring Operation: 2*15=30, Resulting Numbers: [82, 30] Generated Node #0,1,0: 29:[82, 30] Operation: 2*15=30 Exploring Operation: 82/2=41, Resulting Numbers: [15, 41] Generated Node #0,1,1: 29:[15, 41] Operation: 82/2=41 Moving to Node #0,1,1 Current State: 29:[15, 41], Operations: ['83-68=15', '82/2=41'] Exploring Operation: 15+41=56, Resulting Numbers: [56] 56,29 unequal: No Solution Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[82, 30], Operations: ['83-68=15', '2*15=30'] Exploring Operation: 82-30=52, Resulting Numbers: [52] 52,29 unequal: No Solution Exploring Operation: 82+30=112, Resulting Numbers: [112] 112,29 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
[ 2, 95, 92, 4 ]
36
[ "92/4=23", "95-23=72", "72/2=36" ]
Current State: 36:[2, 95, 92, 4], Operations: [] Exploring Operation: 92/4=23, Resulting Numbers: [2, 95, 23] Generated Node #2: [2, 95, 23] from Operation: 92/4=23 Current State: 36:[2, 95, 23], Operations: ['92/4=23'] Exploring Operation: 95-23=72, Resulting Numbers: [2, 72] Generated Node #3: [2, 72] from Operation: 95-23=72 Current State: 36:[2, 72], Operations: ['92/4=23', '95-23=72'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[2, 95, 92, 4], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [2, 4, 3] Generated Node #0,0: 36:[2, 4, 3] Operation: 95-92=3 Moving to Node #0,0 Current State: 36:[2, 4, 3], Operations: ['95-92=3'] Exploring Operation: 2+4=6, Resulting Numbers: [3, 6] Generated Node #0,0,0: 36:[3, 6] Operation: 2+4=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[3, 6], Operations: ['95-92=3', '2+4=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,36 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
[ 50, 12, 55, 34 ]
51
[ "50-12=38", "55+34=89", "89-38=51" ]
Current State: 51:[50, 12, 55, 34], Operations: [] Exploring Operation: 50-12=38, Resulting Numbers: [55, 34, 38] Generated Node #2: [55, 34, 38] from Operation: 50-12=38 Current State: 51:[55, 34, 38], Operations: ['50-12=38'] Exploring Operation: 55+34=89, Resulting Numbers: [38, 89] Generated Node #3: [38, 89] from Operation: 55+34=89 Current State: 51:[38, 89], Operations: ['50-12=38', '55+34=89'] Exploring Operation: 89-38=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[50, 12, 55, 34], Operations: [] Exploring Operation: 34-12=22, Resulting Numbers: [50, 55, 22] Generated Node #0,0: 51:[50, 55, 22] Operation: 34-12=22 Exploring Operation: 50-34=16, Resulting Numbers: [12, 55, 16] Generated Node #0,1: 51:[12, 55, 16] Operation: 50-34=16 Exploring Operation: 12+34=46, Resulting Numbers: [50, 55, 46] Generated Node #0,2: 51:[50, 55, 46] Operation: 12+34=46 Moving to Node #0,0 Current State: 51:[50, 55, 22], Operations: ['34-12=22'] Exploring Operation: 55-22=33, Resulting Numbers: [50, 33] Generated Node #0,0,0: 51:[50, 33] Operation: 55-22=33 Exploring Operation: 50-22=28, Resulting Numbers: [55, 28] Generated Node #0,0,1: 51:[55, 28] Operation: 50-22=28 Exploring Operation: 55-50=5, Resulting Numbers: [22, 5] Generated Node #0,0,2: 51:[22, 5] Operation: 55-50=5 Moving to Node #0,1 Current State: 51:[12, 55, 16], Operations: ['50-34=16'] Exploring Operation: 16-12=4, Resulting Numbers: [55, 4] Generated Node #0,1,0: 51:[55, 4] Operation: 16-12=4 Exploring Operation: 12+16=28, Resulting Numbers: [55, 28] Generated Node #0,1,1: 51:[55, 28] Operation: 12+16=28 Exploring Operation: 55-12=43, Resulting Numbers: [16, 43] Generated Node #0,1,2: 51:[16, 43] Operation: 55-12=43 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 51:[55, 4], Operations: ['50-34=16', '16-12=4'] Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[50, 12, 55, 34], Operations: [] Exploring Operation: 50-34=16, Resulting Numbers: [12, 55, 16] Generated Node #0,1: 51:[12, 55, 16] Operation: 50-34=16 Moving to Node #0,1 Current State: 51:[12, 55, 16], Operations: ['50-34=16'] Exploring Operation: 16-12=4, Resulting Numbers: [55, 4] Generated Node #0,1,0: 51:[55, 4] Operation: 16-12=4 Moving to Node #0,1,0 Current State: 51:[55, 4], Operations: ['50-34=16', '16-12=4'] Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 14, 29, 20, 8 ]
86
[ "29-20=9", "8*9=72", "14+72=86" ]
Current State: 86:[14, 29, 20, 8], Operations: [] Exploring Operation: 29-20=9, Resulting Numbers: [14, 8, 9] Generated Node #2: [14, 8, 9] from Operation: 29-20=9 Current State: 86:[14, 8, 9], Operations: ['29-20=9'] Exploring Operation: 8*9=72, Resulting Numbers: [14, 72] Generated Node #3: [14, 72] from Operation: 8*9=72 Current State: 86:[14, 72], Operations: ['29-20=9', '8*9=72'] Exploring Operation: 14+72=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[14, 29, 20, 8], Operations: [] Exploring Operation: 20-14=6, Resulting Numbers: [29, 8, 6] Generated Node #0,0: 86:[29, 8, 6] Operation: 20-14=6 Exploring Operation: 14+29=43, Resulting Numbers: [20, 8, 43] Generated Node #0,1: 86:[20, 8, 43] Operation: 14+29=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[29, 8, 6], Operations: ['20-14=6'] Exploring Operation: 29+6=35, Resulting Numbers: [8, 35] Generated Node #0,0,0: 86:[8, 35] Operation: 29+6=35 Exploring Operation: 29+8=37, Resulting Numbers: [6, 37] Generated Node #0,0,1: 86:[6, 37] Operation: 29+8=37 Moving to Node #0,0,1 Current State: 86:[6, 37], Operations: ['20-14=6', '29+8=37'] Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[8, 35], Operations: ['20-14=6', '29+6=35'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,86 unequal: No Solution Exploring Operation: 8+35=43, Resulting Numbers: [43] 43,86 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 Current State: 86:[20, 8, 43], Operations: ['14+29=43'] Exploring Operation: 20+8=28, Resulting Numbers: [43, 28] Generated Node #0,1,0: 86:[43, 28] Operation: 20+8=28 Exploring Operation: 20-8=12, Resulting Numbers: [43, 12] Generated Node #0,1,1: 86:[43, 12] Operation: 20-8=12 Moving to Node #0,1,1 Current State: 86:[43, 12], Operations: ['14+29=43', '20-8=12'] Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,86 unequal: No Solution Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[43, 28], Operations: ['14+29=43', '20+8=28'] Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,86 unequal: No Solution Exploring Operation: 43+28=71, Resulting Numbers: [71] 71,86 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
[ 14, 80, 23, 34 ]
16
[ "80-34=46", "46/23=2", "14+2=16" ]
Current State: 16:[14, 80, 23, 34], Operations: [] Exploring Operation: 80-34=46, Resulting Numbers: [14, 23, 46] Generated Node #2: [14, 23, 46] from Operation: 80-34=46 Current State: 16:[14, 23, 46], Operations: ['80-34=46'] Exploring Operation: 46/23=2, Resulting Numbers: [14, 2] Generated Node #3: [14, 2] from Operation: 46/23=2 Current State: 16:[14, 2], Operations: ['80-34=46', '46/23=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[14, 80, 23, 34], Operations: [] Exploring Operation: 80-23=57, Resulting Numbers: [14, 34, 57] Generated Node #0,0: 16:[14, 34, 57] Operation: 80-23=57 Exploring Operation: 80-14=66, Resulting Numbers: [23, 34, 66] Generated Node #0,1: 16:[23, 34, 66] Operation: 80-14=66 Exploring Operation: 80-34=46, Resulting Numbers: [14, 23, 46] Generated Node #0,2: 16:[14, 23, 46] Operation: 80-34=46 Exploring Operation: 34-23=11, Resulting Numbers: [14, 80, 11] Generated Node #0,3: 16:[14, 80, 11] Operation: 34-23=11 Exploring Operation: 34-14=20, Resulting Numbers: [80, 23, 20] Generated Node #0,4: 16:[80, 23, 20] Operation: 34-14=20 Moving to Node #0,2 Current State: 16:[14, 23, 46], Operations: ['80-34=46'] Exploring Operation: 46/23=2, Resulting Numbers: [14, 2] Generated Node #0,2,0: 16:[14, 2] Operation: 46/23=2 Exploring Operation: 46-14=32, Resulting Numbers: [23, 32] Generated Node #0,2,1: 16:[23, 32] Operation: 46-14=32 Exploring Operation: 14+23=37, Resulting Numbers: [46, 37] Generated Node #0,2,2: 16:[46, 37] Operation: 14+23=37 Exploring Operation: 46-23=23, Resulting Numbers: [14, 23] Generated Node #0,2,3: 16:[14, 23] Operation: 46-23=23 Exploring Operation: 23-14=9, Resulting Numbers: [46, 9] Generated Node #0,2,4: 16:[46, 9] Operation: 23-14=9 Moving to Node #0,0 Current State: 16:[14, 34, 57], Operations: ['80-23=57'] Exploring Operation: 14+57=71, Resulting Numbers: [34, 71] Generated Node #0,0,0: 16:[34, 71] Operation: 14+57=71 Exploring Operation: 34-14=20, Resulting Numbers: [57, 20] Generated Node #0,0,1: 16:[57, 20] Operation: 34-14=20 Exploring Operation: 57-34=23, Resulting Numbers: [14, 23] Generated Node #0,0,2: 16:[14, 23] Operation: 57-34=23 Exploring Operation: 14+34=48, Resulting Numbers: [57, 48] Generated Node #0,0,3: 16:[57, 48] Operation: 14+34=48 Exploring Operation: 57-14=43, Resulting Numbers: [34, 43] Generated Node #0,0,4: 16:[34, 43] Operation: 57-14=43 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[14, 23], Operations: ['80-23=57', '57-34=23'] Exploring Operation: 14*23=322, Resulting Numbers: [322] 322,16 unequal: No Solution Exploring Operation: 14+23=37, Resulting Numbers: [37] 37,16 unequal: No Solution Exploring Operation: 23-14=9, Resulting Numbers: [9] 9,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[57, 20], Operations: ['80-23=57', '34-14=20'] Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,16 unequal: No Solution Exploring Operation: 57+20=77, Resulting Numbers: [77] 77,16 unequal: No Solution Exploring Operation: 57*20=1140, Resulting Numbers: [1140] 1140,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 16:[34, 43], Operations: ['80-23=57', '57-14=43'] Exploring Operation: 43-34=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 34+43=77, Resulting Numbers: [77] 77,16 unequal: No Solution Exploring Operation: 34*43=1462, Resulting Numbers: [1462] 1462,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[34, 71], Operations: ['80-23=57', '14+57=71'] Exploring Operation: 34*71=2414, Resulting Numbers: [2414] 2414,16 unequal: No Solution Exploring Operation: 71-34=37, Resulting Numbers: [37] 37,16 unequal: No Solution Exploring Operation: 34+71=105, Resulting Numbers: [105] 105,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 16:[57, 48], Operations: ['80-23=57', '14+34=48'] Exploring Operation: 57*48=2736, Resulting Numbers: [2736] 2736,16 unequal: No Solution Exploring Operation: 57+48=105, Resulting Numbers: [105] 105,16 unequal: No Solution Exploring Operation: 57-48=9, Resulting Numbers: [9] 9,16 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: 16:[14, 80, 11], Operations: ['34-23=11'] Exploring Operation: 80-11=69, Resulting Numbers: [14, 69] Generated Node #0,3,0: 16:[14, 69] Operation: 80-11=69 Exploring Operation: 80+11=91, Resulting Numbers: [14, 91] Generated Node #0,3,1: 16:[14, 91] Operation: 80+11=91 Exploring Operation: 14+11=25, Resulting Numbers: [80, 25] Generated Node #0,3,2: 16:[80, 25] Operation: 14+11=25 Exploring Operation: 80-14=66, Resulting Numbers: [11, 66] Generated Node #0,3,3: 16:[11, 66] Operation: 80-14=66 Exploring Operation: 14-11=3, Resulting Numbers: [80, 3] Generated Node #0,3,4: 16:[80, 3] Operation: 14-11=3 Moving to Node #0,1 Current State: 16:[23, 34, 66], Operations: ['80-14=66'] Exploring Operation: 66-34=32, Resulting Numbers: [23, 32] Generated Node #0,1,0: 16:[23, 32] Operation: 66-34=32 Exploring Operation: 23+34=57, Resulting Numbers: [66, 57] Generated Node #0,1,1: 16:[66, 57] Operation: 23+34=57 Exploring Operation: 66-23=43, Resulting Numbers: [34, 43] Generated Node #0,1,2: 16:[34, 43] Operation: 66-23=43 Exploring Operation: 34-23=11, Resulting Numbers: [66, 11] Generated Node #0,1,3: 16:[66, 11] Operation: 34-23=11 Exploring Operation: 23+66=89, Resulting Numbers: [34, 89] Generated Node #0,1,4: 16:[34, 89] Operation: 23+66=89 Moving to Node #0,4 Current State: 16:[80, 23, 20], Operations: ['34-14=20'] Exploring Operation: 23-20=3, Resulting Numbers: [80, 3] Generated Node #0,4,0: 16:[80, 3] Operation: 23-20=3 Exploring Operation: 80-20=60, Resulting Numbers: [23, 60] Generated Node #0,4,1: 16:[23, 60] Operation: 80-20=60 Exploring Operation: 80-23=57, Resulting Numbers: [20, 57] Generated Node #0,4,2: 16:[20, 57] Operation: 80-23=57 Exploring Operation: 80/20=4, Resulting Numbers: [23, 4] Generated Node #0,4,3: 16:[23, 4] Operation: 80/20=4 Exploring Operation: 80+23=103, Resulting Numbers: [20, 103] Generated Node #0,4,4: 16:[20, 103] Operation: 80+23=103 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 16:[23, 4], Operations: ['34-14=20', '80/20=4'] Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,16 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 16:[20, 57], Operations: ['34-14=20', '80-23=57'] Exploring Operation: 20+57=77, Resulting Numbers: [77] 77,16 unequal: No Solution Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,16 unequal: No Solution Exploring Operation: 20*57=1140, Resulting Numbers: [1140] 1140,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 16:[23, 60], Operations: ['34-14=20', '80-20=60'] Exploring Operation: 23*60=1380, Resulting Numbers: [1380] 1380,16 unequal: No Solution Exploring Operation: 23+60=83, Resulting Numbers: [83] 83,16 unequal: No Solution Exploring Operation: 60-23=37, Resulting Numbers: [37] 37,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 16:[80, 3], Operations: ['34-14=20', '23-20=3'] Exploring Operation: 80*3=240, Resulting Numbers: [240] 240,16 unequal: No Solution Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,16 unequal: No Solution Exploring Operation: 80+3=83, Resulting Numbers: [83] 83,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 16:[20, 103], Operations: ['34-14=20', '80+23=103'] Exploring Operation: 20*103=2060, Resulting Numbers: [2060] 2060,16 unequal: No Solution Exploring Operation: 103-20=83, Resulting Numbers: [83] 83,16 unequal: No Solution Exploring Operation: 20+103=123, Resulting Numbers: [123] 123,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 16:[14, 2], Operations: ['80-34=46', '46/23=2'] Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,16 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,16 unequal: No Solution Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[14, 80, 23, 34], Operations: [] Exploring Operation: 80-34=46, Resulting Numbers: [14, 23, 46] Generated Node #0,2: 16:[14, 23, 46] Operation: 80-34=46 Moving to Node #0,2 Current State: 16:[14, 23, 46], Operations: ['80-34=46'] Exploring Operation: 46/23=2, Resulting Numbers: [14, 2] Generated Node #0,2,0: 16:[14, 2] Operation: 46/23=2 Moving to Node #0,2,0 Current State: 16:[14, 2], Operations: ['80-34=46', '46/23=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
0.94184
hs_5
mult_heuristic
[ 6, 67, 60, 97 ]
98
[ "67-6=61", "97-60=37", "61+37=98" ]
Current State: 98:[6, 67, 60, 97], Operations: [] Exploring Operation: 67-6=61, Resulting Numbers: [60, 97, 61] Generated Node #2: [60, 97, 61] from Operation: 67-6=61 Current State: 98:[60, 97, 61], Operations: ['67-6=61'] Exploring Operation: 97-60=37, Resulting Numbers: [61, 37] Generated Node #3: [61, 37] from Operation: 97-60=37 Current State: 98:[61, 37], Operations: ['67-6=61', '97-60=37'] Exploring Operation: 61+37=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[6, 67, 60, 97], Operations: [] Exploring Operation: 67-6=61, Resulting Numbers: [60, 97, 61] Generated Node #0,0: 98:[60, 97, 61] Operation: 67-6=61 Exploring Operation: 60/6=10, Resulting Numbers: [67, 97, 10] Generated Node #0,1: 98:[67, 97, 10] Operation: 60/6=10 Exploring Operation: 67-60=7, Resulting Numbers: [6, 97, 7] Generated Node #0,2: 98:[6, 97, 7] Operation: 67-60=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[6, 97, 7], Operations: ['67-60=7'] Exploring Operation: 6+97=103, Resulting Numbers: [7, 103] Generated Node #0,2,0: 98:[7, 103] Operation: 6+97=103 Exploring Operation: 6+7=13, Resulting Numbers: [97, 13] Generated Node #0,2,1: 98:[97, 13] Operation: 6+7=13 Exploring Operation: 7-6=1, Resulting Numbers: [97, 1] Generated Node #0,2,2: 98:[97, 1] Operation: 7-6=1 Moving to Node #0,2,1 Current State: 98:[97, 13], Operations: ['67-60=7', '6+7=13'] Exploring Operation: 97+13=110, Resulting Numbers: [110] 110,98 unequal: No Solution Exploring Operation: 97-13=84, Resulting Numbers: [84] 84,98 unequal: No Solution Exploring Operation: 97*13=1261, Resulting Numbers: [1261] 1261,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[97, 1], Operations: ['67-60=7', '7-6=1'] Exploring Operation: 97+1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[6, 67, 60, 97], Operations: [] Exploring Operation: 67-60=7, Resulting Numbers: [6, 97, 7] Generated Node #0,2: 98:[6, 97, 7] Operation: 67-60=7 Moving to Node #0,2 Current State: 98:[6, 97, 7], Operations: ['67-60=7'] Exploring Operation: 7-6=1, Resulting Numbers: [97, 1] Generated Node #0,2,2: 98:[97, 1] Operation: 7-6=1 Moving to Node #0,2,2 Current State: 98:[97, 1], Operations: ['67-60=7', '7-6=1'] Exploring Operation: 97+1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 6, 59, 76, 3 ]
35
[ "6*3=18", "76-59=17", "18+17=35" ]
Current State: 35:[6, 59, 76, 3], Operations: [] Exploring Operation: 6*3=18, Resulting Numbers: [59, 76, 18] Generated Node #2: [59, 76, 18] from Operation: 6*3=18 Current State: 35:[59, 76, 18], Operations: ['6*3=18'] Exploring Operation: 76-59=17, Resulting Numbers: [18, 17] Generated Node #3: [18, 17] from Operation: 76-59=17 Current State: 35:[18, 17], Operations: ['6*3=18', '76-59=17'] Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[6, 59, 76, 3], Operations: [] Exploring Operation: 76-59=17, Resulting Numbers: [6, 3, 17] Generated Node #0,0: 35:[6, 3, 17] Operation: 76-59=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[6, 3, 17], Operations: ['76-59=17'] Exploring Operation: 17-6=11, Resulting Numbers: [3, 11] Generated Node #0,0,0: 35:[3, 11] Operation: 17-6=11 Moving to Node #0,0,0 Current State: 35:[3, 11], Operations: ['76-59=17', '17-6=11'] Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,35 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
[ 71, 99, 49, 67 ]
37
[ "71-67=4", "99+49=148", "148/4=37" ]
Current State: 37:[71, 99, 49, 67], Operations: [] Exploring Operation: 71-67=4, Resulting Numbers: [99, 49, 4] Generated Node #2: [99, 49, 4] from Operation: 71-67=4 Current State: 37:[99, 49, 4], Operations: ['71-67=4'] Exploring Operation: 99+49=148, Resulting Numbers: [4, 148] Generated Node #3: [4, 148] from Operation: 99+49=148 Current State: 37:[4, 148], Operations: ['71-67=4', '99+49=148'] Exploring Operation: 148/4=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[71, 99, 49, 67], Operations: [] Exploring Operation: 99-71=28, Resulting Numbers: [49, 67, 28] Generated Node #0,0: 37:[49, 67, 28] Operation: 99-71=28 Exploring Operation: 99-67=32, Resulting Numbers: [71, 49, 32] Generated Node #0,1: 37:[71, 49, 32] Operation: 99-67=32 Moving to Node #0,0 Current State: 37:[49, 67, 28], Operations: ['99-71=28'] Exploring Operation: 67-49=18, Resulting Numbers: [28, 18] Generated Node #0,0,0: 37:[28, 18] Operation: 67-49=18 Exploring Operation: 67-28=39, Resulting Numbers: [49, 39] Generated Node #0,0,1: 37:[49, 39] Operation: 67-28=39 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[49, 39], Operations: ['99-71=28', '67-28=39'] Exploring Operation: 49+39=88, Resulting Numbers: [88] 88,37 unequal: No Solution Exploring Operation: 49-39=10, Resulting Numbers: [10] 10,37 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:[28, 18], Operations: ['99-71=28', '67-49=18'] Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,37 unequal: No Solution Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,37 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:[71, 49, 32], Operations: ['99-67=32'] Exploring Operation: 71-49=22, Resulting Numbers: [32, 22] Generated Node #0,1,0: 37:[32, 22] Operation: 71-49=22 Exploring Operation: 71-32=39, Resulting Numbers: [49, 39] Generated Node #0,1,1: 37:[49, 39] Operation: 71-32=39 Moving to Node #0,1,1 Current State: 37:[49, 39], Operations: ['99-67=32', '71-32=39'] Exploring Operation: 49+39=88, Resulting Numbers: [88] 88,37 unequal: No Solution Exploring Operation: 49-39=10, Resulting Numbers: [10] 10,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[32, 22], Operations: ['99-67=32', '71-49=22'] Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 32+22=54, Resulting Numbers: [54] 54,37 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 1, 63, 5, 41 ]
88
[ "5-1=4", "63-41=22", "4*22=88" ]
Current State: 88:[1, 63, 5, 41], Operations: [] Exploring Operation: 5-1=4, Resulting Numbers: [63, 41, 4] Generated Node #2: [63, 41, 4] from Operation: 5-1=4 Current State: 88:[63, 41, 4], Operations: ['5-1=4'] Exploring Operation: 63-41=22, Resulting Numbers: [4, 22] Generated Node #3: [4, 22] from Operation: 63-41=22 Current State: 88:[4, 22], Operations: ['5-1=4', '63-41=22'] Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[1, 63, 5, 41], Operations: [] Exploring Operation: 63-41=22, Resulting Numbers: [1, 5, 22] Generated Node #0,0: 88:[1, 5, 22] Operation: 63-41=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[1, 5, 22], Operations: ['63-41=22'] Exploring Operation: 5-1=4, Resulting Numbers: [22, 4] Generated Node #0,0,0: 88:[22, 4] Operation: 5-1=4 Moving to Node #0,0,0 Current State: 88:[22, 4], Operations: ['63-41=22', '5-1=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[1, 63, 5, 41], Operations: [] Exploring Operation: 63-41=22, Resulting Numbers: [1, 5, 22] Generated Node #0,0: 88:[1, 5, 22] Operation: 63-41=22 Moving to Node #0,0 Current State: 88:[1, 5, 22], Operations: ['63-41=22'] Exploring Operation: 5-1=4, Resulting Numbers: [22, 4] Generated Node #0,0,0: 88:[22, 4] Operation: 5-1=4 Moving to Node #0,0,0 Current State: 88:[22, 4], Operations: ['63-41=22', '5-1=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 99, 16, 89, 86 ]
86
[ "99-16=83", "89-86=3", "83+3=86" ]
Current State: 86:[99, 16, 89, 86], Operations: [] Exploring Operation: 99-16=83, Resulting Numbers: [89, 86, 83] Generated Node #2: [89, 86, 83] from Operation: 99-16=83 Current State: 86:[89, 86, 83], Operations: ['99-16=83'] Exploring Operation: 89-86=3, Resulting Numbers: [83, 3] Generated Node #3: [83, 3] from Operation: 89-86=3 Current State: 86:[83, 3], Operations: ['99-16=83', '89-86=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[99, 16, 89, 86], Operations: [] Exploring Operation: 89-16=73, Resulting Numbers: [99, 86, 73] Generated Node #0,0: 86:[99, 86, 73] Operation: 89-16=73 Exploring Operation: 99-89=10, Resulting Numbers: [16, 86, 10] Generated Node #0,1: 86:[16, 86, 10] Operation: 99-89=10 Exploring Operation: 99-16=83, Resulting Numbers: [89, 86, 83] Generated Node #0,2: 86:[89, 86, 83] Operation: 99-16=83 Exploring Operation: 99-86=13, Resulting Numbers: [16, 89, 13] Generated Node #0,3: 86:[16, 89, 13] Operation: 99-86=13 Moving to Node #0,2 Current State: 86:[89, 86, 83], Operations: ['99-16=83'] Exploring Operation: 89+83=172, Resulting Numbers: [86, 172] Generated Node #0,2,0: 86:[86, 172] Operation: 89+83=172 Exploring Operation: 89-86=3, Resulting Numbers: [83, 3] Generated Node #0,2,1: 86:[83, 3] Operation: 89-86=3 Exploring Operation: 89-83=6, Resulting Numbers: [86, 6] Generated Node #0,2,2: 86:[86, 6] Operation: 89-83=6 Exploring Operation: 86-83=3, Resulting Numbers: [89, 3] Generated Node #0,2,3: 86:[89, 3] Operation: 86-83=3 Moving to Node #0,1 Current State: 86:[16, 86, 10], Operations: ['99-89=10'] Exploring Operation: 16+10=26, Resulting Numbers: [86, 26] Generated Node #0,1,0: 86:[86, 26] Operation: 16+10=26 Exploring Operation: 16-10=6, Resulting Numbers: [86, 6] Generated Node #0,1,1: 86:[86, 6] Operation: 16-10=6 Exploring Operation: 16+86=102, Resulting Numbers: [10, 102] Generated Node #0,1,2: 86:[10, 102] Operation: 16+86=102 Exploring Operation: 86-16=70, Resulting Numbers: [10, 70] Generated Node #0,1,3: 86:[10, 70] Operation: 86-16=70 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[86, 6], Operations: ['99-89=10', '16-10=6'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,86 unequal: No Solution Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,86 unequal: No Solution Exploring Operation: 86*6=516, Resulting Numbers: [516] 516,86 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:[86, 26], Operations: ['99-89=10', '16+10=26'] Exploring Operation: 86-26=60, Resulting Numbers: [60] 60,86 unequal: No Solution Exploring Operation: 86+26=112, Resulting Numbers: [112] 112,86 unequal: No Solution Exploring Operation: 86*26=2236, Resulting Numbers: [2236] 2236,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[10, 102], Operations: ['99-89=10', '16+86=102'] Exploring Operation: 10*102=1020, Resulting Numbers: [1020] 1020,86 unequal: No Solution Exploring Operation: 10+102=112, Resulting Numbers: [112] 112,86 unequal: No Solution Exploring Operation: 102-10=92, Resulting Numbers: [92] 92,86 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:[10, 70], Operations: ['99-89=10', '86-16=70'] Exploring Operation: 10+70=80, Resulting Numbers: [80] 80,86 unequal: No Solution Exploring Operation: 70/10=7, Resulting Numbers: [7] 7,86 unequal: No Solution Exploring Operation: 10*70=700, Resulting Numbers: [700] 700,86 unequal: No Solution Exploring Operation: 70-10=60, Resulting Numbers: [60] 60,86 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:[99, 86, 73], Operations: ['89-16=73'] Exploring Operation: 86-73=13, Resulting Numbers: [99, 13] Generated Node #0,0,0: 86:[99, 13] Operation: 86-73=13 Exploring Operation: 99+73=172, Resulting Numbers: [86, 172] Generated Node #0,0,1: 86:[86, 172] Operation: 99+73=172 Exploring Operation: 99-73=26, Resulting Numbers: [86, 26] Generated Node #0,0,2: 86:[86, 26] Operation: 99-73=26 Exploring Operation: 99-86=13, Resulting Numbers: [73, 13] Generated Node #0,0,3: 86:[73, 13] Operation: 99-86=13 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 86:[86, 26], Operations: ['89-16=73', '99-73=26'] Exploring Operation: 86+26=112, Resulting Numbers: [112] 112,86 unequal: No Solution Exploring Operation: 86*26=2236, Resulting Numbers: [2236] 2236,86 unequal: No Solution Exploring Operation: 86-26=60, Resulting Numbers: [60] 60,86 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 #0,0,0 Current State: 86:[99, 13], Operations: ['89-16=73', '86-73=13'] Exploring Operation: 99-13=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[99, 16, 89, 86], Operations: [] Exploring Operation: 89-16=73, Resulting Numbers: [99, 86, 73] Generated Node #0,0: 86:[99, 86, 73] Operation: 89-16=73 Moving to Node #0,0 Current State: 86:[99, 86, 73], Operations: ['89-16=73'] Exploring Operation: 86-73=13, Resulting Numbers: [99, 13] Generated Node #0,0,0: 86:[99, 13] Operation: 86-73=13 Moving to Node #0,0,0 Current State: 86:[99, 13], Operations: ['89-16=73', '86-73=13'] Exploring Operation: 99-13=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_4
mult_heuristic
[ 64, 62, 75, 9 ]
53
[ "75-62=13", "9*13=117", "117-64=53" ]
Current State: 53:[64, 62, 75, 9], Operations: [] Exploring Operation: 75-62=13, Resulting Numbers: [64, 9, 13] Generated Node #2: [64, 9, 13] from Operation: 75-62=13 Current State: 53:[64, 9, 13], Operations: ['75-62=13'] Exploring Operation: 9*13=117, Resulting Numbers: [64, 117] Generated Node #3: [64, 117] from Operation: 9*13=117 Current State: 53:[64, 117], Operations: ['75-62=13', '9*13=117'] Exploring Operation: 117-64=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[64, 62, 75, 9], Operations: [] Exploring Operation: 64-9=55, Resulting Numbers: [62, 75, 55] Generated Node #0,0: 53:[62, 75, 55] Operation: 64-9=55 Exploring Operation: 62-9=53, Resulting Numbers: [64, 75, 53] Generated Node #0,1: 53:[64, 75, 53] Operation: 62-9=53 Moving to Node #0,0 Current State: 53:[62, 75, 55], Operations: ['64-9=55'] Exploring Operation: 75-55=20, Resulting Numbers: [62, 20] Generated Node #0,0,0: 53:[62, 20] Operation: 75-55=20 Exploring Operation: 75-62=13, Resulting Numbers: [55, 13] Generated Node #0,0,1: 53:[55, 13] Operation: 75-62=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[62, 20], Operations: ['64-9=55', '75-55=20'] Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,53 unequal: No Solution Exploring Operation: 62+20=82, Resulting Numbers: [82] 82,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[55, 13], Operations: ['64-9=55', '75-62=13'] Exploring Operation: 55+13=68, Resulting Numbers: [68] 68,53 unequal: No Solution Exploring Operation: 55-13=42, Resulting Numbers: [42] 42,53 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: 53:[64, 75, 53], Operations: ['62-9=53'] Exploring Operation: 75-64=11, Resulting Numbers: [53, 11] Generated Node #0,1,0: 53:[53, 11] Operation: 75-64=11 Exploring Operation: 75-53=22, Resulting Numbers: [64, 22] Generated Node #0,1,1: 53:[64, 22] Operation: 75-53=22 Moving to Node #0,1,0 Current State: 53:[53, 11], Operations: ['62-9=53', '75-64=11'] Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,53 unequal: No Solution Exploring Operation: 53+11=64, Resulting Numbers: [64] 64,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[64, 22], Operations: ['62-9=53', '75-53=22'] Exploring Operation: 64+22=86, Resulting Numbers: [86] 86,53 unequal: No Solution Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,53 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 2, 44, 65, 35 ]
54
[ "2+44=46", "65+35=100", "100-46=54" ]
Current State: 54:[2, 44, 65, 35], Operations: [] Exploring Operation: 2+44=46, Resulting Numbers: [65, 35, 46] Generated Node #2: [65, 35, 46] from Operation: 2+44=46 Current State: 54:[65, 35, 46], Operations: ['2+44=46'] Exploring Operation: 65+35=100, Resulting Numbers: [46, 100] Generated Node #3: [46, 100] from Operation: 65+35=100 Current State: 54:[46, 100], Operations: ['2+44=46', '65+35=100'] Exploring Operation: 100-46=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[2, 44, 65, 35], Operations: [] Exploring Operation: 44-35=9, Resulting Numbers: [2, 65, 9] Generated Node #0,0: 54:[2, 65, 9] Operation: 44-35=9 Exploring Operation: 65-44=21, Resulting Numbers: [2, 35, 21] Generated Node #0,1: 54:[2, 35, 21] Operation: 65-44=21 Moving to Node #0,0 Current State: 54:[2, 65, 9], Operations: ['44-35=9'] Exploring Operation: 65-9=56, Resulting Numbers: [2, 56] Generated Node #0,0,0: 54:[2, 56] Operation: 65-9=56 Exploring Operation: 65-2=63, Resulting Numbers: [9, 63] Generated Node #0,0,1: 54:[9, 63] Operation: 65-2=63 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[2, 56], Operations: ['44-35=9', '65-9=56'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[2, 44, 65, 35], Operations: [] Exploring Operation: 44-35=9, Resulting Numbers: [2, 65, 9] Generated Node #0,0: 54:[2, 65, 9] Operation: 44-35=9 Moving to Node #0,0 Current State: 54:[2, 65, 9], Operations: ['44-35=9'] Exploring Operation: 65-9=56, Resulting Numbers: [2, 56] Generated Node #0,0,0: 54:[2, 56] Operation: 65-9=56 Moving to Node #0,0,0 Current State: 54:[2, 56], Operations: ['44-35=9', '65-9=56'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 40, 4, 54, 7 ]
91
[ "40+4=44", "54-7=47", "44+47=91" ]
Current State: 91:[40, 4, 54, 7], Operations: [] Exploring Operation: 40+4=44, Resulting Numbers: [54, 7, 44] Generated Node #2: [54, 7, 44] from Operation: 40+4=44 Current State: 91:[54, 7, 44], Operations: ['40+4=44'] Exploring Operation: 54-7=47, Resulting Numbers: [44, 47] Generated Node #3: [44, 47] from Operation: 54-7=47 Current State: 91:[44, 47], Operations: ['40+4=44', '54-7=47'] Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[40, 4, 54, 7], Operations: [] Exploring Operation: 40+54=94, Resulting Numbers: [4, 7, 94] Generated Node #0,0: 91:[4, 7, 94] Operation: 40+54=94 Exploring Operation: 54-40=14, Resulting Numbers: [4, 7, 14] Generated Node #0,1: 91:[4, 7, 14] Operation: 54-40=14 Exploring Operation: 40/4=10, Resulting Numbers: [54, 7, 10] Generated Node #0,2: 91:[54, 7, 10] Operation: 40/4=10 Moving to Node #0,1 Current State: 91:[4, 7, 14], Operations: ['54-40=14'] Exploring Operation: 4+7=11, Resulting Numbers: [14, 11] Generated Node #0,1,0: 91:[14, 11] Operation: 4+7=11 Exploring Operation: 14-4=10, Resulting Numbers: [7, 10] Generated Node #0,1,1: 91:[7, 10] Operation: 14-4=10 Exploring Operation: 14-7=7, Resulting Numbers: [4, 7] Generated Node #0,1,2: 91:[4, 7] Operation: 14-7=7 Moving to Node #0,0 Current State: 91:[4, 7, 94], Operations: ['40+54=94'] Exploring Operation: 4+7=11, Resulting Numbers: [94, 11] Generated Node #0,0,0: 91:[94, 11] Operation: 4+7=11 Exploring Operation: 7-4=3, Resulting Numbers: [94, 3] Generated Node #0,0,1: 91:[94, 3] Operation: 7-4=3 Exploring Operation: 94-4=90, Resulting Numbers: [7, 90] Generated Node #0,0,2: 91:[7, 90] Operation: 94-4=90 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 91:[7, 90], Operations: ['40+54=94', '94-4=90'] Exploring Operation: 7+90=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,91 unequal: No Solution Exploring Operation: 7*90=630, Resulting Numbers: [630] 630,91 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 #0,0,0 Current State: 91:[94, 11], Operations: ['40+54=94', '4+7=11'] Exploring Operation: 94*11=1034, Resulting Numbers: [1034] 1034,91 unequal: No Solution Exploring Operation: 94+11=105, Resulting Numbers: [105] 105,91 unequal: No Solution Exploring Operation: 94-11=83, Resulting Numbers: [83] 83,91 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 #0,0,1 Current State: 91:[94, 3], Operations: ['40+54=94', '7-4=3'] Exploring Operation: 94*3=282, Resulting Numbers: [282] 282,91 unequal: No Solution Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[40, 4, 54, 7], Operations: [] Exploring Operation: 40+54=94, Resulting Numbers: [4, 7, 94] Generated Node #0,0: 91:[4, 7, 94] Operation: 40+54=94 Moving to Node #0,0 Current State: 91:[4, 7, 94], Operations: ['40+54=94'] Exploring Operation: 7-4=3, Resulting Numbers: [94, 3] Generated Node #0,0,1: 91:[94, 3] Operation: 7-4=3 Moving to Node #0,0,1 Current State: 91:[94, 3], Operations: ['40+54=94', '7-4=3'] Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_3
mult_heuristic
[ 48, 44, 46, 71 ]
98
[ "48-46=2", "71*2=142", "142-44=98" ]
Current State: 98:[48, 44, 46, 71], Operations: [] Exploring Operation: 48-46=2, Resulting Numbers: [44, 71, 2] Generated Node #2: [44, 71, 2] from Operation: 48-46=2 Current State: 98:[44, 71, 2], Operations: ['48-46=2'] Exploring Operation: 71*2=142, Resulting Numbers: [44, 142] Generated Node #3: [44, 142] from Operation: 71*2=142 Current State: 98:[44, 142], Operations: ['48-46=2', '71*2=142'] Exploring Operation: 142-44=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[48, 44, 46, 71], Operations: [] Exploring Operation: 71-48=23, Resulting Numbers: [44, 46, 23] Generated Node #0,0: 98:[44, 46, 23] Operation: 71-48=23 Exploring Operation: 71-44=27, Resulting Numbers: [48, 46, 27] Generated Node #0,1: 98:[48, 46, 27] Operation: 71-44=27 Exploring Operation: 71-46=25, Resulting Numbers: [48, 44, 25] Generated Node #0,2: 98:[48, 44, 25] Operation: 71-46=25 Moving to Node #0,0 Current State: 98:[44, 46, 23], Operations: ['71-48=23'] Exploring Operation: 46-44=2, Resulting Numbers: [23, 2] Generated Node #0,0,0: 98:[23, 2] Operation: 46-44=2 Exploring Operation: 44-23=21, Resulting Numbers: [46, 21] Generated Node #0,0,1: 98:[46, 21] Operation: 44-23=21 Exploring Operation: 46/23=2, Resulting Numbers: [44, 2] Generated Node #0,0,2: 98:[44, 2] Operation: 46/23=2 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 98:[44, 2], Operations: ['71-48=23', '46/23=2'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,98 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,98 unequal: No Solution No 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: 98:[23, 2], Operations: ['71-48=23', '46-44=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,98 unequal: No Solution Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,98 unequal: No Solution No 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: 98:[46, 21], Operations: ['71-48=23', '44-23=21'] Exploring Operation: 46+21=67, Resulting Numbers: [67] 67,98 unequal: No Solution Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,98 unequal: No Solution Exploring Operation: 46*21=966, Resulting Numbers: [966] 966,98 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: 98:[48, 46, 27], Operations: ['71-44=27'] Exploring Operation: 48-27=21, Resulting Numbers: [46, 21] Generated Node #0,1,0: 98:[46, 21] Operation: 48-27=21 Exploring Operation: 46-27=19, Resulting Numbers: [48, 19] Generated Node #0,1,1: 98:[48, 19] Operation: 46-27=19 Exploring Operation: 48-46=2, Resulting Numbers: [27, 2] Generated Node #0,1,2: 98:[27, 2] Operation: 48-46=2 Moving to Node #0,2 Current State: 98:[48, 44, 25], Operations: ['71-46=25'] Exploring Operation: 48-25=23, Resulting Numbers: [44, 23] Generated Node #0,2,0: 98:[44, 23] Operation: 48-25=23 Exploring Operation: 48-44=4, Resulting Numbers: [25, 4] Generated Node #0,2,1: 98:[25, 4] Operation: 48-44=4 Exploring Operation: 44-25=19, Resulting Numbers: [48, 19] Generated Node #0,2,2: 98:[48, 19] Operation: 44-25=19 Moving to Node #0,1,1 Current State: 98:[48, 19], Operations: ['71-44=27', '46-27=19'] Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,98 unequal: No Solution Exploring Operation: 48+19=67, Resulting Numbers: [67] 67,98 unequal: No Solution Exploring Operation: 48*19=912, Resulting Numbers: [912] 912,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[48, 19], Operations: ['71-46=25', '44-25=19'] Exploring Operation: 48+19=67, Resulting Numbers: [67] 67,98 unequal: No Solution Exploring Operation: 48*19=912, Resulting Numbers: [912] 912,98 unequal: No Solution Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[46, 21], Operations: ['71-44=27', '48-27=21'] Exploring Operation: 46*21=966, Resulting Numbers: [966] 966,98 unequal: No Solution Exploring Operation: 46+21=67, Resulting Numbers: [67] 67,98 unequal: No Solution Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[27, 2], Operations: ['71-44=27', '48-46=2'] Exploring Operation: 27+2=29, Resulting Numbers: [29] 29,98 unequal: No Solution Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,98 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[25, 4], Operations: ['71-46=25', '48-44=4'] Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,98 unequal: No Solution Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,98 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,98 unequal: No Solution Moving to Node #0,2,0 Current State: 98:[44, 23], Operations: ['71-46=25', '48-25=23'] Exploring Operation: 44+23=67, Resulting Numbers: [67] 67,98 unequal: No Solution Exploring Operation: 44*23=1012, Resulting Numbers: [1012] 1012,98 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,98 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 42, 38, 6, 2 ]
55
[ "42-6=36", "38/2=19", "36+19=55" ]
Current State: 55:[42, 38, 6, 2], Operations: [] Exploring Operation: 42-6=36, Resulting Numbers: [38, 2, 36] Generated Node #2: [38, 2, 36] from Operation: 42-6=36 Current State: 55:[38, 2, 36], Operations: ['42-6=36'] Exploring Operation: 38/2=19, Resulting Numbers: [36, 19] Generated Node #3: [36, 19] from Operation: 38/2=19 Current State: 55:[36, 19], Operations: ['42-6=36', '38/2=19'] Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[42, 38, 6, 2], Operations: [] Exploring Operation: 38/2=19, Resulting Numbers: [42, 6, 19] Generated Node #0,0: 55:[42, 6, 19] Operation: 38/2=19 Exploring Operation: 42-38=4, Resulting Numbers: [6, 2, 4] Generated Node #0,1: 55:[6, 2, 4] Operation: 42-38=4 Exploring Operation: 42+6=48, Resulting Numbers: [38, 2, 48] Generated Node #0,2: 55:[38, 2, 48] Operation: 42+6=48 Exploring Operation: 42/6=7, Resulting Numbers: [38, 2, 7] Generated Node #0,3: 55:[38, 2, 7] Operation: 42/6=7 Moving to Node #0,1 Current State: 55:[6, 2, 4], Operations: ['42-38=4'] Exploring Operation: 6*2=12, Resulting Numbers: [4, 12] Generated Node #0,1,0: 55:[4, 12] Operation: 6*2=12 Exploring Operation: 6-2=4, Resulting Numbers: [4, 4] Generated Node #0,1,1: 55:[4, 4] Operation: 6-2=4 Exploring Operation: 6/2=3, Resulting Numbers: [4, 3] Generated Node #0,1,2: 55:[4, 3] Operation: 6/2=3 Exploring Operation: 2+4=6, Resulting Numbers: [6, 6] Generated Node #0,1,3: 55:[6, 6] Operation: 2+4=6 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[4, 12], Operations: ['42-38=4', '6*2=12'] Exploring Operation: 4*12=48, Resulting Numbers: [48] 48,55 unequal: No Solution Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 4+12=16, Resulting Numbers: [16] 16,55 unequal: No Solution No 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: 55:[4, 4], Operations: ['42-38=4', '6-2=4'] Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,55 unequal: No Solution Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,55 unequal: No Solution No 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: 55:[6, 6], Operations: ['42-38=4', '2+4=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,55 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,55 unequal: No Solution No 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: 55:[4, 3], Operations: ['42-38=4', '6/2=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,55 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: 55:[38, 2, 7], Operations: ['42/6=7'] Exploring Operation: 38+2=40, Resulting Numbers: [7, 40] Generated Node #0,3,0: 55:[7, 40] Operation: 38+2=40 Exploring Operation: 38/2=19, Resulting Numbers: [7, 19] Generated Node #0,3,1: 55:[7, 19] Operation: 38/2=19 Exploring Operation: 7-2=5, Resulting Numbers: [38, 5] Generated Node #0,3,2: 55:[38, 5] Operation: 7-2=5 Exploring Operation: 38+7=45, Resulting Numbers: [2, 45] Generated Node #0,3,3: 55:[2, 45] Operation: 38+7=45 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 55:[7, 19], Operations: ['42/6=7', '38/2=19'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,55 unequal: No Solution Exploring Operation: 7*19=133, Resulting Numbers: [133] 133,55 unequal: No Solution No 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: 55:[2, 45], Operations: ['42/6=7', '38+7=45'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,55 unequal: No Solution Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,55 unequal: No Solution Exploring Operation: 2+45=47, Resulting Numbers: [47] 47,55 unequal: No Solution No 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: 55:[7, 40], Operations: ['42/6=7', '38+2=40'] Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,55 unequal: No Solution Exploring Operation: 7*40=280, Resulting Numbers: [280] 280,55 unequal: No Solution Exploring Operation: 7+40=47, Resulting Numbers: [47] 47,55 unequal: No Solution No 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: 55:[38, 5], Operations: ['42/6=7', '7-2=5'] Exploring Operation: 38*5=190, Resulting Numbers: [190] 190,55 unequal: No Solution Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,55 unequal: No Solution Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,55 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: 55:[42, 6, 19], Operations: ['38/2=19'] Exploring Operation: 42+19=61, Resulting Numbers: [6, 61] Generated Node #0,0,0: 55:[6, 61] Operation: 42+19=61 Exploring Operation: 42/6=7, Resulting Numbers: [19, 7] Generated Node #0,0,1: 55:[19, 7] Operation: 42/6=7 Exploring Operation: 42+6=48, Resulting Numbers: [19, 48] Generated Node #0,0,2: 55:[19, 48] Operation: 42+6=48 Exploring Operation: 42-19=23, Resulting Numbers: [6, 23] Generated Node #0,0,3: 55:[6, 23] Operation: 42-19=23 Moving to Node #0,2 Current State: 55:[38, 2, 48], Operations: ['42+6=48'] Exploring Operation: 38+2=40, Resulting Numbers: [48, 40] Generated Node #0,2,0: 55:[48, 40] Operation: 38+2=40 Exploring Operation: 48-38=10, Resulting Numbers: [2, 10] Generated Node #0,2,1: 55:[2, 10] Operation: 48-38=10 Exploring Operation: 38/2=19, Resulting Numbers: [48, 19] Generated Node #0,2,2: 55:[48, 19] Operation: 38/2=19 Exploring Operation: 2+48=50, Resulting Numbers: [38, 50] Generated Node #0,2,3: 55:[38, 50] Operation: 2+48=50 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 55:[2, 10], Operations: ['42+6=48', '48-38=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,55 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,55 unequal: No Solution No 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: 55:[48, 19], Operations: ['42+6=48', '38/2=19'] Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,55 unequal: No Solution Exploring Operation: 48*19=912, Resulting Numbers: [912] 912,55 unequal: No Solution Exploring Operation: 48+19=67, Resulting Numbers: [67] 67,55 unequal: No Solution No 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: 55:[48, 40], Operations: ['42+6=48', '38+2=40'] Exploring Operation: 48*40=1920, Resulting Numbers: [1920] 1920,55 unequal: No Solution Exploring Operation: 48+40=88, Resulting Numbers: [88] 88,55 unequal: No Solution Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,55 unequal: No Solution No 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: 55:[38, 50], Operations: ['42+6=48', '2+48=50'] Exploring Operation: 38*50=1900, Resulting Numbers: [1900] 1900,55 unequal: No Solution Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 38+50=88, Resulting Numbers: [88] 88,55 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: 55:[6, 61], Operations: ['38/2=19', '42+19=61'] Exploring Operation: 6+61=67, Resulting Numbers: [67] 67,55 unequal: No Solution Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[42, 38, 6, 2], Operations: [] Exploring Operation: 38/2=19, Resulting Numbers: [42, 6, 19] Generated Node #0,0: 55:[42, 6, 19] Operation: 38/2=19 Moving to Node #0,0 Current State: 55:[42, 6, 19], Operations: ['38/2=19'] Exploring Operation: 42+19=61, Resulting Numbers: [6, 61] Generated Node #0,0,0: 55:[6, 61] Operation: 42+19=61 Moving to Node #0,0,0 Current State: 55:[6, 61], Operations: ['38/2=19', '42+19=61'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
0.942708
hs_4
sum_heuristic
[ 11, 84, 17, 8 ]
24
[ "11+17=28", "84*8=672", "672/28=24" ]
Current State: 24:[11, 84, 17, 8], Operations: [] Exploring Operation: 11+17=28, Resulting Numbers: [84, 8, 28] Generated Node #2: [84, 8, 28] from Operation: 11+17=28 Current State: 24:[84, 8, 28], Operations: ['11+17=28'] Exploring Operation: 84*8=672, Resulting Numbers: [28, 672] Generated Node #3: [28, 672] from Operation: 84*8=672 Current State: 24:[28, 672], Operations: ['11+17=28', '84*8=672'] Exploring Operation: 672/28=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[11, 84, 17, 8], Operations: [] Exploring Operation: 84-11=73, Resulting Numbers: [17, 8, 73] Generated Node #0,0: 24:[17, 8, 73] Operation: 84-11=73 Exploring Operation: 84-17=67, Resulting Numbers: [11, 8, 67] Generated Node #0,1: 24:[11, 8, 67] Operation: 84-17=67 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[11, 8, 67], Operations: ['84-17=67'] Exploring Operation: 67-11=56, Resulting Numbers: [8, 56] Generated Node #0,1,0: 24:[8, 56] Operation: 67-11=56 Exploring Operation: 67-8=59, Resulting Numbers: [11, 59] Generated Node #0,1,1: 24:[11, 59] Operation: 67-8=59 Moving to Node #0,1,0 Current State: 24:[8, 56], Operations: ['84-17=67', '67-11=56'] Exploring Operation: 56/8=7, Resulting Numbers: [7] 7,24 unequal: No Solution Exploring Operation: 56-8=48, Resulting Numbers: [48] 48,24 unequal: No Solution Moving to Node #0,1,1 Current State: 24:[11, 59], Operations: ['84-17=67', '67-8=59'] Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,24 unequal: No Solution Exploring Operation: 11+59=70, Resulting Numbers: [70] 70,24 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 Current State: 24:[17, 8, 73], Operations: ['84-11=73'] Exploring Operation: 73-17=56, Resulting Numbers: [8, 56] Generated Node #0,0,0: 24:[8, 56] Operation: 73-17=56 Exploring Operation: 73-8=65, Resulting Numbers: [17, 65] Generated Node #0,0,1: 24:[17, 65] Operation: 73-8=65 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[8, 56], Operations: ['84-11=73', '73-17=56'] Exploring Operation: 56/8=7, Resulting Numbers: [7] 7,24 unequal: No Solution Exploring Operation: 56-8=48, Resulting Numbers: [48] 48,24 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: 24:[17, 65], Operations: ['84-11=73', '73-8=65'] Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,24 unequal: No Solution Exploring Operation: 17+65=82, Resulting Numbers: [82] 82,24 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
[ 46, 21, 54, 74 ]
87
[ "46+21=67", "74-54=20", "67+20=87" ]
Current State: 87:[46, 21, 54, 74], Operations: [] Exploring Operation: 46+21=67, Resulting Numbers: [54, 74, 67] Generated Node #2: [54, 74, 67] from Operation: 46+21=67 Current State: 87:[54, 74, 67], Operations: ['46+21=67'] Exploring Operation: 74-54=20, Resulting Numbers: [67, 20] Generated Node #3: [67, 20] from Operation: 74-54=20 Current State: 87:[67, 20], Operations: ['46+21=67', '74-54=20'] Exploring Operation: 67+20=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[46, 21, 54, 74], Operations: [] Exploring Operation: 46+54=100, Resulting Numbers: [21, 74, 100] Generated Node #0,0: 87:[21, 74, 100] Operation: 46+54=100 Exploring Operation: 54-46=8, Resulting Numbers: [21, 74, 8] Generated Node #0,1: 87:[21, 74, 8] Operation: 54-46=8 Exploring Operation: 74-46=28, Resulting Numbers: [21, 54, 28] Generated Node #0,2: 87:[21, 54, 28] Operation: 74-46=28 Moving to Node #0,1 Current State: 87:[21, 74, 8], Operations: ['54-46=8'] Exploring Operation: 21+8=29, Resulting Numbers: [74, 29] Generated Node #0,1,0: 87:[74, 29] Operation: 21+8=29 Exploring Operation: 21+74=95, Resulting Numbers: [8, 95] Generated Node #0,1,1: 87:[8, 95] Operation: 21+74=95 Exploring Operation: 74+8=82, Resulting Numbers: [21, 82] Generated Node #0,1,2: 87:[21, 82] Operation: 74+8=82 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 87:[74, 29], Operations: ['54-46=8', '21+8=29'] Exploring Operation: 74+29=103, Resulting Numbers: [103] 103,87 unequal: No Solution Exploring Operation: 74*29=2146, Resulting Numbers: [2146] 2146,87 unequal: No Solution Exploring Operation: 74-29=45, Resulting Numbers: [45] 45,87 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 #0,1,1 Current State: 87:[8, 95], Operations: ['54-46=8', '21+74=95'] Exploring Operation: 8+95=103, Resulting Numbers: [103] 103,87 unequal: No Solution Exploring Operation: 8*95=760, Resulting Numbers: [760] 760,87 unequal: No Solution Exploring Operation: 95-8=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[46, 21, 54, 74], Operations: [] Exploring Operation: 54-46=8, Resulting Numbers: [21, 74, 8] Generated Node #0,1: 87:[21, 74, 8] Operation: 54-46=8 Moving to Node #0,1 Current State: 87:[21, 74, 8], Operations: ['54-46=8'] Exploring Operation: 21+74=95, Resulting Numbers: [8, 95] Generated Node #0,1,1: 87:[8, 95] Operation: 21+74=95 Moving to Node #0,1,1 Current State: 87:[8, 95], Operations: ['54-46=8', '21+74=95'] Exploring Operation: 95-8=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 88, 54, 21, 90 ]
48
[ "90-88=2", "54/2=27", "21+27=48" ]
Current State: 48:[88, 54, 21, 90], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [54, 21, 2] Generated Node #2: [54, 21, 2] from Operation: 90-88=2 Current State: 48:[54, 21, 2], Operations: ['90-88=2'] Exploring Operation: 54/2=27, Resulting Numbers: [21, 27] Generated Node #3: [21, 27] from Operation: 54/2=27 Current State: 48:[21, 27], Operations: ['90-88=2', '54/2=27'] Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[88, 54, 21, 90], Operations: [] Exploring Operation: 90-21=69, Resulting Numbers: [88, 54, 69] Generated Node #0,0: 48:[88, 54, 69] Operation: 90-21=69 Exploring Operation: 90-88=2, Resulting Numbers: [54, 21, 2] Generated Node #0,1: 48:[54, 21, 2] Operation: 90-88=2 Exploring Operation: 88-54=34, Resulting Numbers: [21, 90, 34] Generated Node #0,2: 48:[21, 90, 34] Operation: 88-54=34 Exploring Operation: 90-54=36, Resulting Numbers: [88, 21, 36] Generated Node #0,3: 48:[88, 21, 36] Operation: 90-54=36 Exploring Operation: 88-21=67, Resulting Numbers: [54, 90, 67] Generated Node #0,4: 48:[54, 90, 67] Operation: 88-21=67 Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[54, 21, 2], Operations: ['90-88=2'] Exploring Operation: 54-21=33, Resulting Numbers: [2, 33] Generated Node #0,1,0: 48:[2, 33] Operation: 54-21=33 Exploring Operation: 21-2=19, Resulting Numbers: [54, 19] Generated Node #0,1,1: 48:[54, 19] Operation: 21-2=19 Exploring Operation: 21+2=23, Resulting Numbers: [54, 23] Generated Node #0,1,2: 48:[54, 23] Operation: 21+2=23 Exploring Operation: 54/2=27, Resulting Numbers: [21, 27] Generated Node #0,1,3: 48:[21, 27] Operation: 54/2=27 Exploring Operation: 54-2=52, Resulting Numbers: [21, 52] Generated Node #0,1,4: 48:[21, 52] Operation: 54-2=52 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 48:[21, 27], Operations: ['90-88=2', '54/2=27'] Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,48 unequal: No Solution Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[88, 54, 21, 90], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [54, 21, 2] Generated Node #0,1: 48:[54, 21, 2] Operation: 90-88=2 Moving to Node #0,1 Current State: 48:[54, 21, 2], Operations: ['90-88=2'] Exploring Operation: 54/2=27, Resulting Numbers: [21, 27] Generated Node #0,1,3: 48:[21, 27] Operation: 54/2=27 Moving to Node #0,1,3 Current State: 48:[21, 27], Operations: ['90-88=2', '54/2=27'] Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 87, 14, 92, 15 ]
61
[ "92-87=5", "15*5=75", "75-14=61" ]
Current State: 61:[87, 14, 92, 15], Operations: [] Exploring Operation: 92-87=5, Resulting Numbers: [14, 15, 5] Generated Node #2: [14, 15, 5] from Operation: 92-87=5 Current State: 61:[14, 15, 5], Operations: ['92-87=5'] Exploring Operation: 15*5=75, Resulting Numbers: [14, 75] Generated Node #3: [14, 75] from Operation: 15*5=75 Current State: 61:[14, 75], Operations: ['92-87=5', '15*5=75'] Exploring Operation: 75-14=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[87, 14, 92, 15], Operations: [] Exploring Operation: 14+15=29, Resulting Numbers: [87, 92, 29] Generated Node #0,0: 61:[87, 92, 29] Operation: 14+15=29 Exploring Operation: 87-14=73, Resulting Numbers: [92, 15, 73] Generated Node #0,1: 61:[92, 15, 73] Operation: 87-14=73 Exploring Operation: 87-15=72, Resulting Numbers: [14, 92, 72] Generated Node #0,2: 61:[14, 92, 72] Operation: 87-15=72 Exploring Operation: 92-14=78, Resulting Numbers: [87, 15, 78] Generated Node #0,3: 61:[87, 15, 78] Operation: 92-14=78 Moving to Node #0,0 Current State: 61:[87, 92, 29], Operations: ['14+15=29'] Exploring Operation: 87+29=116, Resulting Numbers: [92, 116] Generated Node #0,0,0: 61:[92, 116] Operation: 87+29=116 Exploring Operation: 92+29=121, Resulting Numbers: [87, 121] Generated Node #0,0,1: 61:[87, 121] Operation: 92+29=121 Exploring Operation: 92-29=63, Resulting Numbers: [87, 63] Generated Node #0,0,2: 61:[87, 63] Operation: 92-29=63 Exploring Operation: 87-29=58, Resulting Numbers: [92, 58] Generated Node #0,0,3: 61:[92, 58] Operation: 87-29=58 Moving to Node #0,2 Current State: 61:[14, 92, 72], Operations: ['87-15=72'] Exploring Operation: 72-14=58, Resulting Numbers: [92, 58] Generated Node #0,2,0: 61:[92, 58] Operation: 72-14=58 Exploring Operation: 14+72=86, Resulting Numbers: [92, 86] Generated Node #0,2,1: 61:[92, 86] Operation: 14+72=86 Exploring Operation: 92-14=78, Resulting Numbers: [72, 78] Generated Node #0,2,2: 61:[72, 78] Operation: 92-14=78 Exploring Operation: 14+92=106, Resulting Numbers: [72, 106] Generated Node #0,2,3: 61:[72, 106] Operation: 14+92=106 Moving to Node #0,1 Current State: 61:[92, 15, 73], Operations: ['87-14=73'] Exploring Operation: 92+15=107, Resulting Numbers: [73, 107] Generated Node #0,1,0: 61:[73, 107] Operation: 92+15=107 Exploring Operation: 92-15=77, Resulting Numbers: [73, 77] Generated Node #0,1,1: 61:[73, 77] Operation: 92-15=77 Exploring Operation: 73-15=58, Resulting Numbers: [92, 58] Generated Node #0,1,2: 61:[92, 58] Operation: 73-15=58 Exploring Operation: 15+73=88, Resulting Numbers: [92, 88] Generated Node #0,1,3: 61:[92, 88] Operation: 15+73=88 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[73, 77], Operations: ['87-14=73', '92-15=77'] Exploring Operation: 73+77=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 77-73=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 73*77=5621, Resulting Numbers: [5621] 5621,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 61:[92, 58], Operations: ['87-14=73', '73-15=58'] Exploring Operation: 92+58=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 92*58=5336, Resulting Numbers: [5336] 5336,61 unequal: No Solution Exploring Operation: 92-58=34, Resulting Numbers: [34] 34,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 61:[73, 107], Operations: ['87-14=73', '92+15=107'] Exploring Operation: 73*107=7811, Resulting Numbers: [7811] 7811,61 unequal: No Solution Exploring Operation: 73+107=180, Resulting Numbers: [180] 180,61 unequal: No Solution Exploring Operation: 107-73=34, Resulting Numbers: [34] 34,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 61:[92, 88], Operations: ['87-14=73', '15+73=88'] Exploring Operation: 92*88=8096, Resulting Numbers: [8096] 8096,61 unequal: No Solution Exploring Operation: 92+88=180, Resulting Numbers: [180] 180,61 unequal: No Solution Exploring Operation: 92-88=4, Resulting Numbers: [4] 4,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 61:[87, 15, 78], Operations: ['92-14=78'] Exploring Operation: 87+15=102, Resulting Numbers: [78, 102] Generated Node #0,3,0: 61:[78, 102] Operation: 87+15=102 Exploring Operation: 15+78=93, Resulting Numbers: [87, 93] Generated Node #0,3,1: 61:[87, 93] Operation: 15+78=93 Exploring Operation: 87-15=72, Resulting Numbers: [78, 72] Generated Node #0,3,2: 61:[78, 72] Operation: 87-15=72 Exploring Operation: 78-15=63, Resulting Numbers: [87, 63] Generated Node #0,3,3: 61:[87, 63] Operation: 78-15=63 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 61:[78, 72], Operations: ['92-14=78', '87-15=72'] Exploring Operation: 78-72=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 78*72=5616, Resulting Numbers: [5616] 5616,61 unequal: No Solution Exploring Operation: 78+72=150, Resulting Numbers: [150] 150,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 61:[87, 63], Operations: ['92-14=78', '78-15=63'] Exploring Operation: 87-63=24, Resulting Numbers: [24] 24,61 unequal: No Solution Exploring Operation: 87*63=5481, Resulting Numbers: [5481] 5481,61 unequal: No Solution Exploring Operation: 87+63=150, Resulting Numbers: [150] 150,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 61:[78, 102], Operations: ['92-14=78', '87+15=102'] Exploring Operation: 78*102=7956, Resulting Numbers: [7956] 7956,61 unequal: No Solution Exploring Operation: 78+102=180, Resulting Numbers: [180] 180,61 unequal: No Solution Exploring Operation: 102-78=24, Resulting Numbers: [24] 24,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 61:[87, 93], Operations: ['92-14=78', '15+78=93'] Exploring Operation: 93-87=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 87*93=8091, Resulting Numbers: [8091] 8091,61 unequal: No Solution Exploring Operation: 87+93=180, Resulting Numbers: [180] 180,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 61:[87, 63], Operations: ['14+15=29', '92-29=63'] Exploring Operation: 87*63=5481, Resulting Numbers: [5481] 5481,61 unequal: No Solution Exploring Operation: 87+63=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 87-63=24, Resulting Numbers: [24] 24,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[72, 78], Operations: ['87-15=72', '92-14=78'] Exploring Operation: 72+78=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 72*78=5616, Resulting Numbers: [5616] 5616,61 unequal: No Solution Exploring Operation: 78-72=6, Resulting Numbers: [6] 6,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[92, 58], Operations: ['87-15=72', '72-14=58'] Exploring Operation: 92-58=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 92*58=5336, Resulting Numbers: [5336] 5336,61 unequal: No Solution Exploring Operation: 92+58=150, Resulting Numbers: [150] 150,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[92, 58], Operations: ['14+15=29', '87-29=58'] Exploring Operation: 92+58=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 92-58=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 92*58=5336, Resulting Numbers: [5336] 5336,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[92, 86], Operations: ['87-15=72', '14+72=86'] Exploring Operation: 92+86=178, Resulting Numbers: [178] 178,61 unequal: No Solution Exploring Operation: 92*86=7912, Resulting Numbers: [7912] 7912,61 unequal: No Solution Exploring Operation: 92-86=6, Resulting Numbers: [6] 6,61 unequal: No Solution Moving to Node #0,2,3 Current State: 61:[72, 106], Operations: ['87-15=72', '14+92=106'] Exploring Operation: 72*106=7632, Resulting Numbers: [7632] 7632,61 unequal: No Solution Exploring Operation: 106-72=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 72+106=178, Resulting Numbers: [178] 178,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[92, 116], Operations: ['14+15=29', '87+29=116'] Exploring Operation: 92+116=208, Resulting Numbers: [208] 208,61 unequal: No Solution Exploring Operation: 92*116=10672, Resulting Numbers: [10672] 10672,61 unequal: No Solution Exploring Operation: 116-92=24, Resulting Numbers: [24] 24,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[87, 121], Operations: ['14+15=29', '92+29=121'] Exploring Operation: 87*121=10527, Resulting Numbers: [10527] 10527,61 unequal: No Solution Exploring Operation: 121-87=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 87+121=208, Resulting Numbers: [208] 208,61 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 23, 11, 8, 13 ]
38
[ "13-11=2", "23*2=46", "46-8=38" ]
Current State: 38:[23, 11, 8, 13], Operations: [] Exploring Operation: 13-11=2, Resulting Numbers: [23, 8, 2] Generated Node #2: [23, 8, 2] from Operation: 13-11=2 Current State: 38:[23, 8, 2], Operations: ['13-11=2'] Exploring Operation: 23*2=46, Resulting Numbers: [8, 46] Generated Node #3: [8, 46] from Operation: 23*2=46 Current State: 38:[8, 46], Operations: ['13-11=2', '23*2=46'] Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[23, 11, 8, 13], Operations: [] Exploring Operation: 11+8=19, Resulting Numbers: [23, 13, 19] Generated Node #0,0: 38:[23, 13, 19] Operation: 11+8=19 Exploring Operation: 8+13=21, Resulting Numbers: [23, 11, 21] Generated Node #0,1: 38:[23, 11, 21] Operation: 8+13=21 Exploring Operation: 11+13=24, Resulting Numbers: [23, 8, 24] Generated Node #0,2: 38:[23, 8, 24] Operation: 11+13=24 Exploring Operation: 13-11=2, Resulting Numbers: [23, 8, 2] Generated Node #0,3: 38:[23, 8, 2] Operation: 13-11=2 Exploring Operation: 11-8=3, Resulting Numbers: [23, 13, 3] Generated Node #0,4: 38:[23, 13, 3] Operation: 11-8=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[23, 13, 19], Operations: ['11+8=19'] Exploring Operation: 23-13=10, Resulting Numbers: [19, 10] Generated Node #0,0,0: 38:[19, 10] Operation: 23-13=10 Exploring Operation: 23+19=42, Resulting Numbers: [13, 42] Generated Node #0,0,1: 38:[13, 42] Operation: 23+19=42 Exploring Operation: 23-19=4, Resulting Numbers: [13, 4] Generated Node #0,0,2: 38:[13, 4] Operation: 23-19=4 Exploring Operation: 23+13=36, Resulting Numbers: [19, 36] Generated Node #0,0,3: 38:[19, 36] Operation: 23+13=36 Exploring Operation: 19-13=6, Resulting Numbers: [23, 6] Generated Node #0,0,4: 38:[23, 6] Operation: 19-13=6 Moving to Node #0,0,3 Current State: 38:[19, 36], Operations: ['11+8=19', '23+13=36'] Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,38 unequal: No Solution Exploring Operation: 19*36=684, Resulting Numbers: [684] 684,38 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[13, 4], Operations: ['11+8=19', '23-19=4'] Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,38 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,38 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[19, 10], Operations: ['11+8=19', '23-13=10'] Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,38 unequal: No Solution Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,38 unequal: No Solution Moving to Node #0,0,4 Current State: 38:[23, 6], Operations: ['11+8=19', '19-13=6'] Exploring Operation: 23*6=138, Resulting Numbers: [138] 138,38 unequal: No Solution Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[13, 42], Operations: ['11+8=19', '23+19=42'] Exploring Operation: 13*42=546, Resulting Numbers: [546] 546,38 unequal: No Solution Exploring Operation: 42-13=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 13+42=55, Resulting Numbers: [55] 55,38 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 #0,3 Current State: 38:[23, 8, 2], Operations: ['13-11=2'] Exploring Operation: 8*2=16, Resulting Numbers: [23, 16] Generated Node #0,3,0: 38:[23, 16] Operation: 8*2=16 Exploring Operation: 23-2=21, Resulting Numbers: [8, 21] Generated Node #0,3,1: 38:[8, 21] Operation: 23-2=21 Exploring Operation: 23+8=31, Resulting Numbers: [2, 31] Generated Node #0,3,2: 38:[2, 31] Operation: 23+8=31 Exploring Operation: 23-8=15, Resulting Numbers: [2, 15] Generated Node #0,3,3: 38:[2, 15] Operation: 23-8=15 Exploring Operation: 8/2=4, Resulting Numbers: [23, 4] Generated Node #0,3,4: 38:[23, 4] Operation: 8/2=4 Moving to Node #0,3,3 Current State: 38:[2, 15], Operations: ['13-11=2', '23-8=15'] Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,38 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,38 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,38 unequal: No Solution Moving to Node #0,3,4 Current State: 38:[23, 4], Operations: ['13-11=2', '8/2=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,38 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,38 unequal: No Solution Moving to Node #0,3,0 Current State: 38:[23, 16], Operations: ['13-11=2', '8*2=16'] Exploring Operation: 23*16=368, Resulting Numbers: [368] 368,38 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 23+16=39, Resulting Numbers: [39] 39,38 unequal: No Solution Moving to Node #0,3,2 Current State: 38:[2, 31], Operations: ['13-11=2', '23+8=31'] Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,38 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,38 unequal: No Solution Moving to Node #0,3,1 Current State: 38:[8, 21], Operations: ['13-11=2', '23-2=21'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,38 unequal: No Solution Exploring Operation: 8*21=168, Resulting Numbers: [168] 168,38 unequal: No Solution Exploring Operation: 8+21=29, Resulting Numbers: [29] 29,38 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 #0,4 Current State: 38:[23, 13, 3], Operations: ['11-8=3'] Exploring Operation: 23-13=10, Resulting Numbers: [3, 10] Generated Node #0,4,0: 38:[3, 10] Operation: 23-13=10 Exploring Operation: 23-3=20, Resulting Numbers: [13, 20] Generated Node #0,4,1: 38:[13, 20] Operation: 23-3=20 Exploring Operation: 13+3=16, Resulting Numbers: [23, 16] Generated Node #0,4,2: 38:[23, 16] Operation: 13+3=16 Exploring Operation: 23+13=36, Resulting Numbers: [3, 36] Generated Node #0,4,3: 38:[3, 36] Operation: 23+13=36 Exploring Operation: 13*3=39, Resulting Numbers: [23, 39] Generated Node #0,4,4: 38:[23, 39] Operation: 13*3=39 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 38:[3, 36], Operations: ['11-8=3', '23+13=36'] Exploring Operation: 3*36=108, Resulting Numbers: [108] 108,38 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,38 unequal: No Solution Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 38:[23, 39], Operations: ['11-8=3', '13*3=39'] Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 23+39=62, Resulting Numbers: [62] 62,38 unequal: No Solution Exploring Operation: 23*39=897, Resulting Numbers: [897] 897,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 38:[13, 20], Operations: ['11-8=3', '23-3=20'] Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 13*20=260, Resulting Numbers: [260] 260,38 unequal: No Solution Exploring Operation: 13+20=33, Resulting Numbers: [33] 33,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 38:[23, 16], Operations: ['11-8=3', '13+3=16'] Exploring Operation: 23*16=368, Resulting Numbers: [368] 368,38 unequal: No Solution Exploring Operation: 23+16=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 38:[3, 10], Operations: ['11-8=3', '23-13=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,38 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,38 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[23, 11, 21], Operations: ['8+13=21'] Exploring Operation: 11+21=32, Resulting Numbers: [23, 32] Generated Node #0,1,0: 38:[23, 32] Operation: 11+21=32 Exploring Operation: 23-11=12, Resulting Numbers: [21, 12] Generated Node #0,1,1: 38:[21, 12] Operation: 23-11=12 Exploring Operation: 23+11=34, Resulting Numbers: [21, 34] Generated Node #0,1,2: 38:[21, 34] Operation: 23+11=34 Exploring Operation: 23-21=2, Resulting Numbers: [11, 2] Generated Node #0,1,3: 38:[11, 2] Operation: 23-21=2 Exploring Operation: 21-11=10, Resulting Numbers: [23, 10] Generated Node #0,1,4: 38:[23, 10] Operation: 21-11=10 Moving to Node #0,1,2 Current State: 38:[21, 34], Operations: ['8+13=21', '23+11=34'] Exploring Operation: 21*34=714, Resulting Numbers: [714] 714,38 unequal: No Solution Exploring Operation: 21+34=55, Resulting Numbers: [55] 55,38 unequal: No Solution Exploring Operation: 34-21=13, Resulting Numbers: [13] 13,38 unequal: No Solution Moving to Node #0,1,3 Current State: 38:[11, 2], Operations: ['8+13=21', '23-21=2'] Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,38 unequal: No Solution Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,38 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[21, 12], Operations: ['8+13=21', '23-11=12'] Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,38 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,38 unequal: No Solution Exploring Operation: 21*12=252, Resulting Numbers: [252] 252,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[23, 32], Operations: ['8+13=21', '11+21=32'] Exploring Operation: 32-23=9, Resulting Numbers: [9] 9,38 unequal: No Solution Exploring Operation: 23*32=736, Resulting Numbers: [736] 736,38 unequal: No Solution Exploring Operation: 23+32=55, Resulting Numbers: [55] 55,38 unequal: No Solution Moving to Node #0,1,4 Current State: 38:[23, 10], Operations: ['8+13=21', '21-11=10'] Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,38 unequal: No Solution Exploring Operation: 23*10=230, Resulting Numbers: [230] 230,38 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,38 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 #0,2 Current State: 38:[23, 8, 24], Operations: ['11+13=24'] Exploring Operation: 24-23=1, Resulting Numbers: [8, 1] Generated Node #0,2,0: 38:[8, 1] Operation: 24-23=1 Exploring Operation: 24/8=3, Resulting Numbers: [23, 3] Generated Node #0,2,1: 38:[23, 3] Operation: 24/8=3 Exploring Operation: 24-8=16, Resulting Numbers: [23, 16] Generated Node #0,2,2: 38:[23, 16] Operation: 24-8=16 Exploring Operation: 8+24=32, Resulting Numbers: [23, 32] Generated Node #0,2,3: 38:[23, 32] Operation: 8+24=32 Exploring Operation: 23-8=15, Resulting Numbers: [24, 15] Generated Node #0,2,4: 38:[24, 15] Operation: 23-8=15 Moving to Node #0,2,1 Current State: 38:[23, 3], Operations: ['11+13=24', '24/8=3'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,38 unequal: No Solution Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,38 unequal: No Solution Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[23, 16], Operations: ['11+13=24', '24-8=16'] Exploring Operation: 23+16=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 23*16=368, Resulting Numbers: [368] 368,38 unequal: No Solution Moving to Node #0,2,0 Current State: 38:[8, 1], Operations: ['11+13=24', '24-23=1'] Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 8+1=9, Resulting Numbers: [9] 9,38 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,38 unequal: No Solution Moving to Node #0,2,4 Current State: 38:[24, 15], Operations: ['11+13=24', '23-8=15'] Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 24*15=360, Resulting Numbers: [360] 360,38 unequal: No Solution Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,38 unequal: No Solution Moving to Node #0,2,3 Current State: 38:[23, 32], Operations: ['11+13=24', '8+24=32'] Exploring Operation: 23+32=55, Resulting Numbers: [55] 55,38 unequal: No Solution Exploring Operation: 32-23=9, Resulting Numbers: [9] 9,38 unequal: No Solution Exploring Operation: 23*32=736, Resulting Numbers: [736] 736,38 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
[ 69, 70, 40, 80 ]
39
[ "70-69=1", "80-40=40", "40-1=39" ]
Current State: 39:[69, 70, 40, 80], Operations: [] Exploring Operation: 70-69=1, Resulting Numbers: [40, 80, 1] Generated Node #2: [40, 80, 1] from Operation: 70-69=1 Current State: 39:[40, 80, 1], Operations: ['70-69=1'] Exploring Operation: 80-40=40, Resulting Numbers: [1, 40] Generated Node #3: [1, 40] from Operation: 80-40=40 Current State: 39:[1, 40], Operations: ['70-69=1', '80-40=40'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[69, 70, 40, 80], Operations: [] Exploring Operation: 80-70=10, Resulting Numbers: [69, 40, 10] Generated Node #0,0: 39:[69, 40, 10] Operation: 80-70=10 Exploring Operation: 80-69=11, Resulting Numbers: [70, 40, 11] Generated Node #0,1: 39:[70, 40, 11] Operation: 80-69=11 Moving to Node #0,0 Current State: 39:[69, 40, 10], Operations: ['80-70=10'] Exploring Operation: 69-10=59, Resulting Numbers: [40, 59] Generated Node #0,0,0: 39:[40, 59] Operation: 69-10=59 Exploring Operation: 69-40=29, Resulting Numbers: [10, 29] Generated Node #0,0,1: 39:[10, 29] Operation: 69-40=29 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 39:[10, 29], Operations: ['80-70=10', '69-40=29'] Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,39 unequal: No Solution Exploring Operation: 10+29=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[69, 70, 40, 80], Operations: [] Exploring Operation: 80-70=10, Resulting Numbers: [69, 40, 10] Generated Node #0,0: 39:[69, 40, 10] Operation: 80-70=10 Moving to Node #0,0 Current State: 39:[69, 40, 10], Operations: ['80-70=10'] Exploring Operation: 69-40=29, Resulting Numbers: [10, 29] Generated Node #0,0,1: 39:[10, 29] Operation: 69-40=29 Moving to Node #0,0,1 Current State: 39:[10, 29], Operations: ['80-70=10', '69-40=29'] Exploring Operation: 10+29=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 6, 3, 76, 8 ]
54
[ "6*76=456", "456/8=57", "57-3=54" ]
Current State: 54:[6, 3, 76, 8], Operations: [] Exploring Operation: 6*76=456, Resulting Numbers: [3, 8, 456] Generated Node #2: [3, 8, 456] from Operation: 6*76=456 Current State: 54:[3, 8, 456], Operations: ['6*76=456'] Exploring Operation: 456/8=57, Resulting Numbers: [3, 57] Generated Node #3: [3, 57] from Operation: 456/8=57 Current State: 54:[3, 57], Operations: ['6*76=456', '456/8=57'] Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[6, 3, 76, 8], Operations: [] Exploring Operation: 76-8=68, Resulting Numbers: [6, 3, 68] Generated Node #0,0: 54:[6, 3, 68] Operation: 76-8=68 Exploring Operation: 76-6=70, Resulting Numbers: [3, 8, 70] Generated Node #0,1: 54:[3, 8, 70] Operation: 76-6=70 Moving to Node #0,0 Current State: 54:[6, 3, 68], Operations: ['76-8=68'] Exploring Operation: 68-6=62, Resulting Numbers: [3, 62] Generated Node #0,0,0: 54:[3, 62] Operation: 68-6=62 Exploring Operation: 68-3=65, Resulting Numbers: [6, 65] Generated Node #0,0,1: 54:[6, 65] Operation: 68-3=65 Moving to Node #0,1 Current State: 54:[3, 8, 70], Operations: ['76-6=70'] Exploring Operation: 70-3=67, Resulting Numbers: [8, 67] Generated Node #0,1,0: 54:[8, 67] Operation: 70-3=67 Exploring Operation: 70-8=62, Resulting Numbers: [3, 62] Generated Node #0,1,1: 54:[3, 62] Operation: 70-8=62 Moving to Node #0,0,0 Current State: 54:[3, 62], Operations: ['76-8=68', '68-6=62'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,54 unequal: No Solution Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[3, 62], Operations: ['76-6=70', '70-8=62'] Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,54 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[6, 65], Operations: ['76-8=68', '68-3=65'] Exploring Operation: 6+65=71, Resulting Numbers: [71] 71,54 unequal: No Solution Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[8, 67], Operations: ['76-6=70', '70-3=67'] Exploring Operation: 67-8=59, Resulting Numbers: [59] 59,54 unequal: No Solution Exploring Operation: 8+67=75, Resulting Numbers: [75] 75,54 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 50, 51, 99, 78 ]
81
[ "51+99=150", "150/50=3", "78+3=81" ]
Current State: 81:[50, 51, 99, 78], Operations: [] Exploring Operation: 51+99=150, Resulting Numbers: [50, 78, 150] Generated Node #2: [50, 78, 150] from Operation: 51+99=150 Current State: 81:[50, 78, 150], Operations: ['51+99=150'] Exploring Operation: 150/50=3, Resulting Numbers: [78, 3] Generated Node #3: [78, 3] from Operation: 150/50=3 Current State: 81:[78, 3], Operations: ['51+99=150', '150/50=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[50, 51, 99, 78], Operations: [] Exploring Operation: 50+51=101, Resulting Numbers: [99, 78, 101] Generated Node #0,0: 81:[99, 78, 101] Operation: 50+51=101 Exploring Operation: 51-50=1, Resulting Numbers: [99, 78, 1] Generated Node #0,1: 81:[99, 78, 1] Operation: 51-50=1 Exploring Operation: 78-51=27, Resulting Numbers: [50, 99, 27] Generated Node #0,2: 81:[50, 99, 27] Operation: 78-51=27 Moving to Node #0,1 Current State: 81:[99, 78, 1], Operations: ['51-50=1'] Exploring Operation: 99-1=98, Resulting Numbers: [78, 98] Generated Node #0,1,0: 81:[78, 98] Operation: 99-1=98 Exploring Operation: 99-78=21, Resulting Numbers: [1, 21] Generated Node #0,1,1: 81:[1, 21] Operation: 99-78=21 Exploring Operation: 78+1=79, Resulting Numbers: [99, 79] Generated Node #0,1,2: 81:[99, 79] Operation: 78+1=79 Moving to Node #0,0 Current State: 81:[99, 78, 101], Operations: ['50+51=101'] Exploring Operation: 99-78=21, Resulting Numbers: [101, 21] Generated Node #0,0,0: 81:[101, 21] Operation: 99-78=21 Exploring Operation: 101-99=2, Resulting Numbers: [78, 2] Generated Node #0,0,1: 81:[78, 2] Operation: 101-99=2 Exploring Operation: 101-78=23, Resulting Numbers: [99, 23] Generated Node #0,0,2: 81:[99, 23] Operation: 101-78=23 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[78, 2], Operations: ['50+51=101', '101-99=2'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,81 unequal: No Solution Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,81 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 #0,0,2 Current State: 81:[99, 23], Operations: ['50+51=101', '101-78=23'] Exploring Operation: 99*23=2277, Resulting Numbers: [2277] 2277,81 unequal: No Solution Exploring Operation: 99+23=122, Resulting Numbers: [122] 122,81 unequal: No Solution Exploring Operation: 99-23=76, Resulting Numbers: [76] 76,81 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 #0,0,0 Current State: 81:[101, 21], Operations: ['50+51=101', '99-78=21'] Exploring Operation: 101*21=2121, Resulting Numbers: [2121] 2121,81 unequal: No Solution Exploring Operation: 101-21=80, Resulting Numbers: [80] 80,81 unequal: No Solution Exploring Operation: 101+21=122, Resulting Numbers: [122] 122,81 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: 81:[50, 99, 27], Operations: ['78-51=27'] Exploring Operation: 50+27=77, Resulting Numbers: [99, 77] Generated Node #0,2,0: 81:[99, 77] Operation: 50+27=77 Exploring Operation: 99-50=49, Resulting Numbers: [27, 49] Generated Node #0,2,1: 81:[27, 49] Operation: 99-50=49 Exploring Operation: 50-27=23, Resulting Numbers: [99, 23] Generated Node #0,2,2: 81:[99, 23] Operation: 50-27=23 Moving to Node #0,1,1 Current State: 81:[1, 21], Operations: ['51-50=1', '99-78=21'] Exploring Operation: 1*21=21, Resulting Numbers: [21] 21,81 unequal: No Solution Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,81 unequal: No Solution Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,81 unequal: No Solution Moving to Node #0,1,2 Current State: 81:[99, 79], Operations: ['51-50=1', '78+1=79'] Exploring Operation: 99-79=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 99+79=178, Resulting Numbers: [178] 178,81 unequal: No Solution Exploring Operation: 99*79=7821, Resulting Numbers: [7821] 7821,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[78, 98], Operations: ['51-50=1', '99-1=98'] Exploring Operation: 98-78=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 78+98=176, Resulting Numbers: [176] 176,81 unequal: No Solution Exploring Operation: 78*98=7644, Resulting Numbers: [7644] 7644,81 unequal: No Solution Moving to Node #0,2,2 Current State: 81:[99, 23], Operations: ['78-51=27', '50-27=23'] Exploring Operation: 99+23=122, Resulting Numbers: [122] 122,81 unequal: No Solution Exploring Operation: 99*23=2277, Resulting Numbers: [2277] 2277,81 unequal: No Solution Exploring Operation: 99-23=76, Resulting Numbers: [76] 76,81 unequal: No Solution Moving to Node #0,2,0 Current State: 81:[99, 77], Operations: ['78-51=27', '50+27=77'] Exploring Operation: 99+77=176, Resulting Numbers: [176] 176,81 unequal: No Solution Exploring Operation: 99-77=22, Resulting Numbers: [22] 22,81 unequal: No Solution Exploring Operation: 99*77=7623, Resulting Numbers: [7623] 7623,81 unequal: No Solution Moving to Node #0,2,1 Current State: 81:[27, 49], Operations: ['78-51=27', '99-50=49'] Exploring Operation: 27+49=76, Resulting Numbers: [76] 76,81 unequal: No Solution Exploring Operation: 49-27=22, Resulting Numbers: [22] 22,81 unequal: No Solution Exploring Operation: 27*49=1323, Resulting Numbers: [1323] 1323,81 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 40, 91, 26, 6 ]
31
[ "91-40=51", "26-6=20", "51-20=31" ]
Current State: 31:[40, 91, 26, 6], Operations: [] Exploring Operation: 91-40=51, Resulting Numbers: [26, 6, 51] Generated Node #2: [26, 6, 51] from Operation: 91-40=51 Current State: 31:[26, 6, 51], Operations: ['91-40=51'] Exploring Operation: 26-6=20, Resulting Numbers: [51, 20] Generated Node #3: [51, 20] from Operation: 26-6=20 Current State: 31:[51, 20], Operations: ['91-40=51', '26-6=20'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[40, 91, 26, 6], Operations: [] Exploring Operation: 40-6=34, Resulting Numbers: [91, 26, 34] Generated Node #0,0: 31:[91, 26, 34] Operation: 40-6=34 Exploring Operation: 91-40=51, Resulting Numbers: [26, 6, 51] Generated Node #0,1: 31:[26, 6, 51] Operation: 91-40=51 Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[26, 6, 51], Operations: ['91-40=51'] Exploring Operation: 26+6=32, Resulting Numbers: [51, 32] Generated Node #0,1,0: 31:[51, 32] Operation: 26+6=32 Exploring Operation: 51-6=45, Resulting Numbers: [26, 45] Generated Node #0,1,1: 31:[26, 45] Operation: 51-6=45 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 31:[26, 45], Operations: ['91-40=51', '51-6=45'] Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,31 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,31 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 #0,1,0 Current State: 31:[51, 32], Operations: ['91-40=51', '26+6=32'] Exploring Operation: 51-32=19, Resulting Numbers: [19] 19,31 unequal: No Solution Exploring Operation: 51+32=83, Resulting Numbers: [83] 83,31 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[91, 26, 34], Operations: ['40-6=34'] Exploring Operation: 91-34=57, Resulting Numbers: [26, 57] Generated Node #0,0,0: 31:[26, 57] Operation: 91-34=57 Exploring Operation: 91-26=65, Resulting Numbers: [34, 65] Generated Node #0,0,1: 31:[34, 65] Operation: 91-26=65 Moving to Node #0,0,0 Current State: 31:[26, 57], Operations: ['40-6=34', '91-34=57'] Exploring Operation: 26+57=83, Resulting Numbers: [83] 83,31 unequal: No Solution Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[40, 91, 26, 6], Operations: [] Exploring Operation: 40-6=34, Resulting Numbers: [91, 26, 34] Generated Node #0,0: 31:[91, 26, 34] Operation: 40-6=34 Moving to Node #0,0 Current State: 31:[91, 26, 34], Operations: ['40-6=34'] Exploring Operation: 91-34=57, Resulting Numbers: [26, 57] Generated Node #0,0,0: 31:[26, 57] Operation: 91-34=57 Moving to Node #0,0,0 Current State: 31:[26, 57], Operations: ['40-6=34', '91-34=57'] Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 98, 16, 94, 9 ]
61
[ "98*9=882", "94+882=976", "976/16=61" ]
Current State: 61:[98, 16, 94, 9], Operations: [] Exploring Operation: 98*9=882, Resulting Numbers: [16, 94, 882] Generated Node #2: [16, 94, 882] from Operation: 98*9=882 Current State: 61:[16, 94, 882], Operations: ['98*9=882'] Exploring Operation: 94+882=976, Resulting Numbers: [16, 976] Generated Node #3: [16, 976] from Operation: 94+882=976 Current State: 61:[16, 976], Operations: ['98*9=882', '94+882=976'] Exploring Operation: 976/16=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[98, 16, 94, 9], Operations: [] Exploring Operation: 98-9=89, Resulting Numbers: [16, 94, 89] Generated Node #0,0: 61:[16, 94, 89] Operation: 98-9=89 Exploring Operation: 94-16=78, Resulting Numbers: [98, 9, 78] Generated Node #0,1: 61:[98, 9, 78] Operation: 94-16=78 Exploring Operation: 98-16=82, Resulting Numbers: [94, 9, 82] Generated Node #0,2: 61:[94, 9, 82] Operation: 98-16=82 Moving to Node #0,0 Current State: 61:[16, 94, 89], Operations: ['98-9=89'] Exploring Operation: 94-16=78, Resulting Numbers: [89, 78] Generated Node #0,0,0: 61:[89, 78] Operation: 94-16=78 Exploring Operation: 16+94=110, Resulting Numbers: [89, 110] Generated Node #0,0,1: 61:[89, 110] Operation: 16+94=110 Exploring Operation: 89-16=73, Resulting Numbers: [94, 73] Generated Node #0,0,2: 61:[94, 73] Operation: 89-16=73 Moving to Node #0,1 Current State: 61:[98, 9, 78], Operations: ['94-16=78'] Exploring Operation: 98+9=107, Resulting Numbers: [78, 107] Generated Node #0,1,0: 61:[78, 107] Operation: 98+9=107 Exploring Operation: 98-9=89, Resulting Numbers: [78, 89] Generated Node #0,1,1: 61:[78, 89] Operation: 98-9=89 Exploring Operation: 78-9=69, Resulting Numbers: [98, 69] Generated Node #0,1,2: 61:[98, 69] Operation: 78-9=69 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[78, 89], Operations: ['94-16=78', '98-9=89'] Exploring Operation: 78*89=6942, Resulting Numbers: [6942] 6942,61 unequal: No Solution Exploring Operation: 89-78=11, Resulting Numbers: [11] 11,61 unequal: No Solution Exploring Operation: 78+89=167, Resulting Numbers: [167] 167,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 61:[98, 69], Operations: ['94-16=78', '78-9=69'] Exploring Operation: 98-69=29, Resulting Numbers: [29] 29,61 unequal: No Solution Exploring Operation: 98*69=6762, Resulting Numbers: [6762] 6762,61 unequal: No Solution Exploring Operation: 98+69=167, Resulting Numbers: [167] 167,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 61:[78, 107], Operations: ['94-16=78', '98+9=107'] Exploring Operation: 107-78=29, Resulting Numbers: [29] 29,61 unequal: No Solution Exploring Operation: 78+107=185, Resulting Numbers: [185] 185,61 unequal: No Solution Exploring Operation: 78*107=8346, Resulting Numbers: [8346] 8346,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 61:[94, 9, 82], Operations: ['98-16=82'] Exploring Operation: 94+9=103, Resulting Numbers: [82, 103] Generated Node #0,2,0: 61:[82, 103] Operation: 94+9=103 Exploring Operation: 94-9=85, Resulting Numbers: [82, 85] Generated Node #0,2,1: 61:[82, 85] Operation: 94-9=85 Exploring Operation: 82-9=73, Resulting Numbers: [94, 73] Generated Node #0,2,2: 61:[94, 73] Operation: 82-9=73 Moving to Node #0,0,0 Current State: 61:[89, 78], Operations: ['98-9=89', '94-16=78'] Exploring Operation: 89+78=167, Resulting Numbers: [167] 167,61 unequal: No Solution Exploring Operation: 89-78=11, Resulting Numbers: [11] 11,61 unequal: No Solution Exploring Operation: 89*78=6942, Resulting Numbers: [6942] 6942,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[94, 73], Operations: ['98-9=89', '89-16=73'] Exploring Operation: 94*73=6862, Resulting Numbers: [6862] 6862,61 unequal: No Solution Exploring Operation: 94-73=21, Resulting Numbers: [21] 21,61 unequal: No Solution Exploring Operation: 94+73=167, Resulting Numbers: [167] 167,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[94, 73], Operations: ['98-16=82', '82-9=73'] Exploring Operation: 94-73=21, Resulting Numbers: [21] 21,61 unequal: No Solution Exploring Operation: 94*73=6862, Resulting Numbers: [6862] 6862,61 unequal: No Solution Exploring Operation: 94+73=167, Resulting Numbers: [167] 167,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[82, 85], Operations: ['98-16=82', '94-9=85'] Exploring Operation: 82+85=167, Resulting Numbers: [167] 167,61 unequal: No Solution Exploring Operation: 85-82=3, Resulting Numbers: [3] 3,61 unequal: No Solution Exploring Operation: 82*85=6970, Resulting Numbers: [6970] 6970,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[82, 103], Operations: ['98-16=82', '94+9=103'] Exploring Operation: 82*103=8446, Resulting Numbers: [8446] 8446,61 unequal: No Solution Exploring Operation: 103-82=21, Resulting Numbers: [21] 21,61 unequal: No Solution Exploring Operation: 82+103=185, Resulting Numbers: [185] 185,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[89, 110], Operations: ['98-9=89', '16+94=110'] Exploring Operation: 110-89=21, Resulting Numbers: [21] 21,61 unequal: No Solution Exploring Operation: 89+110=199, Resulting Numbers: [199] 199,61 unequal: No Solution Exploring Operation: 89*110=9790, Resulting Numbers: [9790] 9790,61 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 35, 51, 19, 7 ]
42
[ "51-35=16", "19+7=26", "16+26=42" ]
Current State: 42:[35, 51, 19, 7], Operations: [] Exploring Operation: 51-35=16, Resulting Numbers: [19, 7, 16] Generated Node #2: [19, 7, 16] from Operation: 51-35=16 Current State: 42:[19, 7, 16], Operations: ['51-35=16'] Exploring Operation: 19+7=26, Resulting Numbers: [16, 26] Generated Node #3: [16, 26] from Operation: 19+7=26 Current State: 42:[16, 26], Operations: ['51-35=16', '19+7=26'] Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[35, 51, 19, 7], Operations: [] Exploring Operation: 51-35=16, Resulting Numbers: [19, 7, 16] Generated Node #0,0: 42:[19, 7, 16] Operation: 51-35=16 Moving to Node #0,0 Current State: 42:[19, 7, 16], Operations: ['51-35=16'] Exploring Operation: 19-16=3, Resulting Numbers: [7, 3] Generated Node #0,0,0: 42:[7, 3] Operation: 19-16=3 Moving to Node #0,0,0 Current State: 42:[7, 3], Operations: ['51-35=16', '19-16=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,42 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 80, 71, 87, 13 ]
91
[ "80-71=9", "87+13=100", "100-9=91" ]
Current State: 91:[80, 71, 87, 13], Operations: [] Exploring Operation: 80-71=9, Resulting Numbers: [87, 13, 9] Generated Node #2: [87, 13, 9] from Operation: 80-71=9 Current State: 91:[87, 13, 9], Operations: ['80-71=9'] Exploring Operation: 87+13=100, Resulting Numbers: [9, 100] Generated Node #3: [9, 100] from Operation: 87+13=100 Current State: 91:[9, 100], Operations: ['80-71=9', '87+13=100'] Exploring Operation: 100-9=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[80, 71, 87, 13], Operations: [] Exploring Operation: 80-71=9, Resulting Numbers: [87, 13, 9] Generated Node #0,0: 91:[87, 13, 9] Operation: 80-71=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[87, 13, 9], Operations: ['80-71=9'] Exploring Operation: 87+9=96, Resulting Numbers: [13, 96] Generated Node #0,0,0: 91:[13, 96] Operation: 87+9=96 Moving to Node #0,0,0 Current State: 91:[13, 96], Operations: ['80-71=9', '87+9=96'] Exploring Operation: 96-13=83, Resulting Numbers: [83] 83,91 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
[ 59, 62, 9, 11 ]
42
[ "62-59=3", "11*3=33", "9+33=42" ]
Current State: 42:[59, 62, 9, 11], Operations: [] Exploring Operation: 62-59=3, Resulting Numbers: [9, 11, 3] Generated Node #2: [9, 11, 3] from Operation: 62-59=3 Current State: 42:[9, 11, 3], Operations: ['62-59=3'] Exploring Operation: 11*3=33, Resulting Numbers: [9, 33] Generated Node #3: [9, 33] from Operation: 11*3=33 Current State: 42:[9, 33], Operations: ['62-59=3', '11*3=33'] Exploring Operation: 9+33=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[59, 62, 9, 11], Operations: [] Exploring Operation: 59-11=48, Resulting Numbers: [62, 9, 48] Generated Node #0,0: 42:[62, 9, 48] Operation: 59-11=48 Exploring Operation: 62-59=3, Resulting Numbers: [9, 11, 3] Generated Node #0,1: 42:[9, 11, 3] Operation: 62-59=3 Exploring Operation: 62-11=51, Resulting Numbers: [59, 9, 51] Generated Node #0,2: 42:[59, 9, 51] Operation: 62-11=51 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[9, 11, 3], Operations: ['62-59=3'] Exploring Operation: 11-9=2, Resulting Numbers: [3, 2] Generated Node #0,1,0: 42:[3, 2] Operation: 11-9=2 Exploring Operation: 9+11=20, Resulting Numbers: [3, 20] Generated Node #0,1,1: 42:[3, 20] Operation: 9+11=20 Exploring Operation: 11+3=14, Resulting Numbers: [9, 14] Generated Node #0,1,2: 42:[9, 14] Operation: 11+3=14 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 42:[3, 2], Operations: ['62-59=3', '11-9=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,42 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,42 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: 42:[3, 20], Operations: ['62-59=3', '9+11=20'] Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,42 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,42 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: 42:[9, 14], Operations: ['62-59=3', '11+3=14'] Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,42 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,42 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: 42:[62, 9, 48], Operations: ['59-11=48'] Exploring Operation: 48-9=39, Resulting Numbers: [62, 39] Generated Node #0,0,0: 42:[62, 39] Operation: 48-9=39 Exploring Operation: 62-48=14, Resulting Numbers: [9, 14] Generated Node #0,0,1: 42:[9, 14] Operation: 62-48=14 Exploring Operation: 62-9=53, Resulting Numbers: [48, 53] Generated Node #0,0,2: 42:[48, 53] Operation: 62-9=53 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 42:[9, 14], Operations: ['59-11=48', '62-48=14'] Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,42 unequal: No Solution Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,42 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: 42:[48, 53], Operations: ['59-11=48', '62-9=53'] Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 48*53=2544, Resulting Numbers: [2544] 2544,42 unequal: No Solution Exploring Operation: 48+53=101, Resulting Numbers: [101] 101,42 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: 42:[62, 39], Operations: ['59-11=48', '48-9=39'] Exploring Operation: 62+39=101, Resulting Numbers: [101] 101,42 unequal: No Solution Exploring Operation: 62*39=2418, Resulting Numbers: [2418] 2418,42 unequal: No Solution Exploring Operation: 62-39=23, Resulting Numbers: [23] 23,42 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: 42:[59, 9, 51], Operations: ['62-11=51'] Exploring Operation: 59-51=8, Resulting Numbers: [9, 8] Generated Node #0,2,0: 42:[9, 8] Operation: 59-51=8 Exploring Operation: 59-9=50, Resulting Numbers: [51, 50] Generated Node #0,2,1: 42:[51, 50] Operation: 59-9=50 Exploring Operation: 51-9=42, Resulting Numbers: [59, 42] Generated Node #0,2,2: 42:[59, 42] Operation: 51-9=42 Moving to Node #0,2,0 Current State: 42:[9, 8], Operations: ['62-11=51', '59-51=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,42 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,42 unequal: No Solution Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,42 unequal: No Solution Moving to Node #0,2,1 Current State: 42:[51, 50], Operations: ['62-11=51', '59-9=50'] Exploring Operation: 51*50=2550, Resulting Numbers: [2550] 2550,42 unequal: No Solution Exploring Operation: 51-50=1, Resulting Numbers: [1] 1,42 unequal: No Solution Exploring Operation: 51+50=101, Resulting Numbers: [101] 101,42 unequal: No Solution Moving to Node #0,2,2 Current State: 42:[59, 42], Operations: ['62-11=51', '51-9=42'] Exploring Operation: 59+42=101, Resulting Numbers: [101] 101,42 unequal: No Solution Exploring Operation: 59*42=2478, Resulting Numbers: [2478] 2478,42 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,42 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
[ 50, 78, 2, 58 ]
90
[ "78-58=20", "2*20=40", "50+40=90" ]
Current State: 90:[50, 78, 2, 58], Operations: [] Exploring Operation: 78-58=20, Resulting Numbers: [50, 2, 20] Generated Node #2: [50, 2, 20] from Operation: 78-58=20 Current State: 90:[50, 2, 20], Operations: ['78-58=20'] Exploring Operation: 2*20=40, Resulting Numbers: [50, 40] Generated Node #3: [50, 40] from Operation: 2*20=40 Current State: 90:[50, 40], Operations: ['78-58=20', '2*20=40'] Exploring Operation: 50+40=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[50, 78, 2, 58], Operations: [] Exploring Operation: 78-58=20, Resulting Numbers: [50, 2, 20] Generated Node #0,0: 90:[50, 2, 20] Operation: 78-58=20 Exploring Operation: 58-50=8, Resulting Numbers: [78, 2, 8] Generated Node #0,1: 90:[78, 2, 8] Operation: 58-50=8 Moving to Node #0,0 Current State: 90:[50, 2, 20], Operations: ['78-58=20'] Exploring Operation: 50-2=48, Resulting Numbers: [20, 48] Generated Node #0,0,0: 90:[20, 48] Operation: 50-2=48 Exploring Operation: 50-20=30, Resulting Numbers: [2, 30] Generated Node #0,0,1: 90:[2, 30] Operation: 50-20=30 Moving to Node #0,1 Current State: 90:[78, 2, 8], Operations: ['58-50=8'] Exploring Operation: 78+8=86, Resulting Numbers: [2, 86] Generated Node #0,1,0: 90:[2, 86] Operation: 78+8=86 Exploring Operation: 78/2=39, Resulting Numbers: [8, 39] Generated Node #0,1,1: 90:[8, 39] Operation: 78/2=39 Moving to Node #0,0,1 Current State: 90:[2, 30], Operations: ['78-58=20', '50-20=30'] Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,90 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[2, 86], Operations: ['58-50=8', '78+8=86'] Exploring Operation: 2+86=88, Resulting Numbers: [88] 88,90 unequal: No Solution Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[20, 48], Operations: ['78-58=20', '50-2=48'] Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,90 unequal: No Solution Exploring Operation: 20+48=68, Resulting Numbers: [68] 68,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[8, 39], Operations: ['58-50=8', '78/2=39'] Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 8+39=47, Resulting Numbers: [47] 47,90 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 10, 3, 81, 60 ]
93
[ "10+81=91", "91-60=31", "3*31=93" ]
Current State: 93:[10, 3, 81, 60], Operations: [] Exploring Operation: 10+81=91, Resulting Numbers: [3, 60, 91] Generated Node #2: [3, 60, 91] from Operation: 10+81=91 Current State: 93:[3, 60, 91], Operations: ['10+81=91'] Exploring Operation: 91-60=31, Resulting Numbers: [3, 31] Generated Node #3: [3, 31] from Operation: 91-60=31 Current State: 93:[3, 31], Operations: ['10+81=91', '91-60=31'] Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[10, 3, 81, 60], Operations: [] Exploring Operation: 60/10=6, Resulting Numbers: [3, 81, 6] Generated Node #0,0: 93:[3, 81, 6] Operation: 60/10=6 Moving to Node #0,0 Current State: 93:[3, 81, 6], Operations: ['60/10=6'] Exploring Operation: 81+6=87, Resulting Numbers: [3, 87] Generated Node #0,0,0: 93:[3, 87] Operation: 81+6=87 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[3, 87], Operations: ['60/10=6', '81+6=87'] Exploring Operation: 87/3=29, Resulting Numbers: [29] 29,93 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
[ 74, 35, 58, 29 ]
37
[ "74-35=39", "58/29=2", "39-2=37" ]
Current State: 37:[74, 35, 58, 29], Operations: [] Exploring Operation: 74-35=39, Resulting Numbers: [58, 29, 39] Generated Node #2: [58, 29, 39] from Operation: 74-35=39 Current State: 37:[58, 29, 39], Operations: ['74-35=39'] Exploring Operation: 58/29=2, Resulting Numbers: [39, 2] Generated Node #3: [39, 2] from Operation: 58/29=2 Current State: 37:[39, 2], Operations: ['74-35=39', '58/29=2'] Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[74, 35, 58, 29], Operations: [] Exploring Operation: 74-35=39, Resulting Numbers: [58, 29, 39] Generated Node #0,0: 37:[58, 29, 39] Operation: 74-35=39 Exploring Operation: 74-58=16, Resulting Numbers: [35, 29, 16] Generated Node #0,1: 37:[35, 29, 16] Operation: 74-58=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[58, 29, 39], Operations: ['74-35=39'] Exploring Operation: 58-39=19, Resulting Numbers: [29, 19] Generated Node #0,0,0: 37:[29, 19] Operation: 58-39=19 Exploring Operation: 58-29=29, Resulting Numbers: [39, 29] Generated Node #0,0,1: 37:[39, 29] Operation: 58-29=29 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 37:[39, 29], Operations: ['74-35=39', '58-29=29'] Exploring Operation: 39+29=68, Resulting Numbers: [68] 68,37 unequal: No Solution Exploring Operation: 39-29=10, Resulting Numbers: [10] 10,37 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: 37:[29, 19], Operations: ['74-35=39', '58-39=19'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 29+19=48, Resulting Numbers: [48] 48,37 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: 37:[35, 29, 16], Operations: ['74-58=16'] Exploring Operation: 35+16=51, Resulting Numbers: [29, 51] Generated Node #0,1,0: 37:[29, 51] Operation: 35+16=51 Exploring Operation: 29+16=45, Resulting Numbers: [35, 45] Generated Node #0,1,1: 37:[35, 45] Operation: 29+16=45 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 37:[35, 45], Operations: ['74-58=16', '29+16=45'] Exploring Operation: 45-35=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 35+45=80, Resulting Numbers: [80] 80,37 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: 37:[29, 51], Operations: ['74-58=16', '35+16=51'] Exploring Operation: 29+51=80, Resulting Numbers: [80] 80,37 unequal: No Solution Exploring Operation: 51-29=22, Resulting Numbers: [22] 22,37 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
[ 26, 86, 31, 81 ]
25
[ "31-26=5", "86-81=5", "5*5=25" ]
Current State: 25:[26, 86, 31, 81], Operations: [] Exploring Operation: 31-26=5, Resulting Numbers: [86, 81, 5] Generated Node #2: [86, 81, 5] from Operation: 31-26=5 Current State: 25:[86, 81, 5], Operations: ['31-26=5'] Exploring Operation: 86-81=5, Resulting Numbers: [5, 5] Generated Node #3: [5, 5] from Operation: 86-81=5 Current State: 25:[5, 5], Operations: ['31-26=5', '86-81=5'] Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[26, 86, 31, 81], Operations: [] Exploring Operation: 86-31=55, Resulting Numbers: [26, 81, 55] Generated Node #0,0: 25:[26, 81, 55] Operation: 86-31=55 Exploring Operation: 86-81=5, Resulting Numbers: [26, 31, 5] Generated Node #0,1: 25:[26, 31, 5] Operation: 86-81=5 Exploring Operation: 81-31=50, Resulting Numbers: [26, 86, 50] Generated Node #0,2: 25:[26, 86, 50] Operation: 81-31=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[26, 31, 5], Operations: ['86-81=5'] Exploring Operation: 31-26=5, Resulting Numbers: [5, 5] Generated Node #0,1,0: 25:[5, 5] Operation: 31-26=5 Exploring Operation: 31-5=26, Resulting Numbers: [26, 26] Generated Node #0,1,1: 25:[26, 26] Operation: 31-5=26 Exploring Operation: 26-5=21, Resulting Numbers: [31, 21] Generated Node #0,1,2: 25:[31, 21] Operation: 26-5=21 Moving to Node #0,1,0 Current State: 25:[5, 5], Operations: ['86-81=5', '31-26=5'] Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[26, 86, 31, 81], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [26, 31, 5] Generated Node #0,1: 25:[26, 31, 5] Operation: 86-81=5 Moving to Node #0,1 Current State: 25:[26, 31, 5], Operations: ['86-81=5'] Exploring Operation: 31-26=5, Resulting Numbers: [5, 5] Generated Node #0,1,0: 25:[5, 5] Operation: 31-26=5 Moving to Node #0,1,0 Current State: 25:[5, 5], Operations: ['86-81=5', '31-26=5'] Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 2, 47, 30, 26 ]
25
[ "2*26=52", "47+30=77", "77-52=25" ]
Current State: 25:[2, 47, 30, 26], Operations: [] Exploring Operation: 2*26=52, Resulting Numbers: [47, 30, 52] Generated Node #2: [47, 30, 52] from Operation: 2*26=52 Current State: 25:[47, 30, 52], Operations: ['2*26=52'] Exploring Operation: 47+30=77, Resulting Numbers: [52, 77] Generated Node #3: [52, 77] from Operation: 47+30=77 Current State: 25:[52, 77], Operations: ['2*26=52', '47+30=77'] Exploring Operation: 77-52=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[2, 47, 30, 26], Operations: [] Exploring Operation: 47-26=21, Resulting Numbers: [2, 30, 21] Generated Node #0,0: 25:[2, 30, 21] Operation: 47-26=21 Exploring Operation: 30-2=28, Resulting Numbers: [47, 26, 28] Generated Node #0,1: 25:[47, 26, 28] Operation: 30-2=28 Exploring Operation: 30-26=4, Resulting Numbers: [2, 47, 4] Generated Node #0,2: 25:[2, 47, 4] Operation: 30-26=4 Exploring Operation: 47-2=45, Resulting Numbers: [30, 26, 45] Generated Node #0,3: 25:[30, 26, 45] Operation: 47-2=45 Exploring Operation: 47-30=17, Resulting Numbers: [2, 26, 17] Generated Node #0,4: 25:[2, 26, 17] Operation: 47-30=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[2, 30, 21], Operations: ['47-26=21'] Exploring Operation: 30-21=9, Resulting Numbers: [2, 9] Generated Node #0,0,0: 25:[2, 9] Operation: 30-21=9 Exploring Operation: 30-2=28, Resulting Numbers: [21, 28] Generated Node #0,0,1: 25:[21, 28] Operation: 30-2=28 Exploring Operation: 21-2=19, Resulting Numbers: [30, 19] Generated Node #0,0,2: 25:[30, 19] Operation: 21-2=19 Exploring Operation: 2+30=32, Resulting Numbers: [21, 32] Generated Node #0,0,3: 25:[21, 32] Operation: 2+30=32 Exploring Operation: 2+21=23, Resulting Numbers: [30, 23] Generated Node #0,0,4: 25:[30, 23] Operation: 2+21=23 Moving to Node #0,0,0 Current State: 25:[2, 9], Operations: ['47-26=21', '30-21=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,25 unequal: No Solution Moving to Node #0,0,4 Current State: 25:[30, 23], Operations: ['47-26=21', '2+21=23'] Exploring Operation: 30-23=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 30*23=690, Resulting Numbers: [690] 690,25 unequal: No Solution Exploring Operation: 30+23=53, Resulting Numbers: [53] 53,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[21, 28], Operations: ['47-26=21', '30-2=28'] Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,25 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,25 unequal: No Solution Moving to Node #0,0,2 Current State: 25:[30, 19], Operations: ['47-26=21', '21-2=19'] Exploring Operation: 30-19=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 30+19=49, Resulting Numbers: [49] 49,25 unequal: No Solution Exploring Operation: 30*19=570, Resulting Numbers: [570] 570,25 unequal: No Solution Moving to Node #0,0,3 Current State: 25:[21, 32], Operations: ['47-26=21', '2+30=32'] Exploring Operation: 21+32=53, Resulting Numbers: [53] 53,25 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 21*32=672, Resulting Numbers: [672] 672,25 unequal: No Solution No 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: 25:[2, 26, 17], Operations: ['47-30=17'] Exploring Operation: 2+26=28, Resulting Numbers: [17, 28] Generated Node #0,4,0: 25:[17, 28] Operation: 2+26=28 Exploring Operation: 2+17=19, Resulting Numbers: [26, 19] Generated Node #0,4,1: 25:[26, 19] Operation: 2+17=19 Exploring Operation: 26-2=24, Resulting Numbers: [17, 24] Generated Node #0,4,2: 25:[17, 24] Operation: 26-2=24 Exploring Operation: 26-17=9, Resulting Numbers: [2, 9] Generated Node #0,4,3: 25:[2, 9] Operation: 26-17=9 Exploring Operation: 2*17=34, Resulting Numbers: [26, 34] Generated Node #0,4,4: 25:[26, 34] Operation: 2*17=34 Moving to Node #0,4,1 Current State: 25:[26, 19], Operations: ['47-30=17', '2+17=19'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,25 unequal: No Solution Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,25 unequal: No Solution Moving to Node #0,4,3 Current State: 25:[2, 9], Operations: ['47-30=17', '26-17=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,25 unequal: No Solution Moving to Node #0,4,2 Current State: 25:[17, 24], Operations: ['47-30=17', '26-2=24'] Exploring Operation: 17+24=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 24-17=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 17*24=408, Resulting Numbers: [408] 408,25 unequal: No Solution Moving to Node #0,4,4 Current State: 25:[26, 34], Operations: ['47-30=17', '2*17=34'] Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,25 unequal: No Solution Exploring Operation: 26+34=60, Resulting Numbers: [60] 60,25 unequal: No Solution Exploring Operation: 26*34=884, Resulting Numbers: [884] 884,25 unequal: No Solution Moving to Node #0,4,0 Current State: 25:[17, 28], Operations: ['47-30=17', '2+26=28'] Exploring Operation: 17*28=476, Resulting Numbers: [476] 476,25 unequal: No Solution Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 17+28=45, Resulting Numbers: [45] 45,25 unequal: No Solution No 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: 25:[47, 26, 28], Operations: ['30-2=28'] Exploring Operation: 47-28=19, Resulting Numbers: [26, 19] Generated Node #0,1,0: 25:[26, 19] Operation: 47-28=19 Exploring Operation: 47+26=73, Resulting Numbers: [28, 73] Generated Node #0,1,1: 25:[28, 73] Operation: 47+26=73 Exploring Operation: 47+28=75, Resulting Numbers: [26, 75] Generated Node #0,1,2: 25:[26, 75] Operation: 47+28=75 Exploring Operation: 47-26=21, Resulting Numbers: [28, 21] Generated Node #0,1,3: 25:[28, 21] Operation: 47-26=21 Exploring Operation: 28-26=2, Resulting Numbers: [47, 2] Generated Node #0,1,4: 25:[47, 2] Operation: 28-26=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[26, 19], Operations: ['30-2=28', '47-28=19'] Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,25 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,25 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: 25:[28, 21], Operations: ['30-2=28', '47-26=21'] Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 28+21=49, Resulting Numbers: [49] 49,25 unequal: No Solution Exploring Operation: 28*21=588, Resulting Numbers: [588] 588,25 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: 25:[47, 2], Operations: ['30-2=28', '28-26=2'] Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,25 unequal: No Solution Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,25 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,25 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: 25:[28, 73], Operations: ['30-2=28', '47+26=73'] Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,25 unequal: No Solution Exploring Operation: 28*73=2044, Resulting Numbers: [2044] 2044,25 unequal: No Solution Exploring Operation: 28+73=101, Resulting Numbers: [101] 101,25 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: 25:[26, 75], Operations: ['30-2=28', '47+28=75'] Exploring Operation: 26+75=101, Resulting Numbers: [101] 101,25 unequal: No Solution Exploring Operation: 75-26=49, Resulting Numbers: [49] 49,25 unequal: No Solution Exploring Operation: 26*75=1950, Resulting Numbers: [1950] 1950,25 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: 25:[2, 47, 4], Operations: ['30-26=4'] Exploring Operation: 2*4=8, Resulting Numbers: [47, 8] Generated Node #0,2,0: 25:[47, 8] Operation: 2*4=8 Exploring Operation: 2+4=6, Resulting Numbers: [47, 6] Generated Node #0,2,1: 25:[47, 6] Operation: 2+4=6 Exploring Operation: 47-4=43, Resulting Numbers: [2, 43] Generated Node #0,2,2: 25:[2, 43] Operation: 47-4=43 Exploring Operation: 2+47=49, Resulting Numbers: [4, 49] Generated Node #0,2,3: 25:[4, 49] Operation: 2+47=49 Exploring Operation: 47-2=45, Resulting Numbers: [4, 45] Generated Node #0,2,4: 25:[4, 45] Operation: 47-2=45 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 25:[2, 43], Operations: ['30-26=4', '47-4=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,25 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,25 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: 25:[4, 45], Operations: ['30-26=4', '47-2=45'] Exploring Operation: 4+45=49, Resulting Numbers: [49] 49,25 unequal: No Solution Exploring Operation: 4*45=180, Resulting Numbers: [180] 180,25 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,25 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: 25:[47, 6], Operations: ['30-26=4', '2+4=6'] Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,25 unequal: No Solution Exploring Operation: 47*6=282, Resulting Numbers: [282] 282,25 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,25 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: 25:[47, 8], Operations: ['30-26=4', '2*4=8'] Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,25 unequal: No Solution Exploring Operation: 47+8=55, Resulting Numbers: [55] 55,25 unequal: No Solution Exploring Operation: 47*8=376, Resulting Numbers: [376] 376,25 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: 25:[4, 49], Operations: ['30-26=4', '2+47=49'] Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,25 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,25 unequal: No Solution Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,25 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: 25:[30, 26, 45], Operations: ['47-2=45'] Exploring Operation: 45-26=19, Resulting Numbers: [30, 19] Generated Node #0,3,0: 25:[30, 19] Operation: 45-26=19 Exploring Operation: 30+26=56, Resulting Numbers: [45, 56] Generated Node #0,3,1: 25:[45, 56] Operation: 30+26=56 Exploring Operation: 30-26=4, Resulting Numbers: [45, 4] Generated Node #0,3,2: 25:[45, 4] Operation: 30-26=4 Exploring Operation: 30+45=75, Resulting Numbers: [26, 75] Generated Node #0,3,3: 25:[26, 75] Operation: 30+45=75 Exploring Operation: 45-30=15, Resulting Numbers: [26, 15] Generated Node #0,3,4: 25:[26, 15] Operation: 45-30=15 Moving to Node #0,3,0 Current State: 25:[30, 19], Operations: ['47-2=45', '45-26=19'] Exploring Operation: 30*19=570, Resulting Numbers: [570] 570,25 unequal: No Solution Exploring Operation: 30+19=49, Resulting Numbers: [49] 49,25 unequal: No Solution Exploring Operation: 30-19=11, Resulting Numbers: [11] 11,25 unequal: No Solution Moving to Node #0,3,4 Current State: 25:[26, 15], Operations: ['47-2=45', '45-30=15'] Exploring Operation: 26*15=390, Resulting Numbers: [390] 390,25 unequal: No Solution Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,25 unequal: No Solution Moving to Node #0,3,2 Current State: 25:[45, 4], Operations: ['47-2=45', '30-26=4'] Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,25 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,25 unequal: No Solution Moving to Node #0,3,1 Current State: 25:[45, 56], Operations: ['47-2=45', '30+26=56'] Exploring Operation: 45*56=2520, Resulting Numbers: [2520] 2520,25 unequal: No Solution Exploring Operation: 45+56=101, Resulting Numbers: [101] 101,25 unequal: No Solution Exploring Operation: 56-45=11, Resulting Numbers: [11] 11,25 unequal: No Solution Moving to Node #0,3,3 Current State: 25:[26, 75], Operations: ['47-2=45', '30+45=75'] Exploring Operation: 26*75=1950, Resulting Numbers: [1950] 1950,25 unequal: No Solution Exploring Operation: 26+75=101, Resulting Numbers: [101] 101,25 unequal: No Solution Exploring Operation: 75-26=49, Resulting Numbers: [49] 49,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 4, 41, 42, 48 ]
52
[ "4+48=52", "42-41=1", "52*1=52" ]
Current State: 52:[4, 41, 42, 48], Operations: [] Exploring Operation: 4+48=52, Resulting Numbers: [41, 42, 52] Generated Node #2: [41, 42, 52] from Operation: 4+48=52 Current State: 52:[41, 42, 52], Operations: ['4+48=52'] Exploring Operation: 42-41=1, Resulting Numbers: [52, 1] Generated Node #3: [52, 1] from Operation: 42-41=1 Current State: 52:[52, 1], Operations: ['4+48=52', '42-41=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[4, 41, 42, 48], Operations: [] Exploring Operation: 4+41=45, Resulting Numbers: [42, 48, 45] Generated Node #0,0: 52:[42, 48, 45] Operation: 4+41=45 Exploring Operation: 48-42=6, Resulting Numbers: [4, 41, 6] Generated Node #0,1: 52:[4, 41, 6] Operation: 48-42=6 Exploring Operation: 42-41=1, Resulting Numbers: [4, 48, 1] Generated Node #0,2: 52:[4, 48, 1] Operation: 42-41=1 Exploring Operation: 48-41=7, Resulting Numbers: [4, 42, 7] Generated Node #0,3: 52:[4, 42, 7] Operation: 48-41=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[4, 48, 1], Operations: ['42-41=1'] Exploring Operation: 48/4=12, Resulting Numbers: [1, 12] Generated Node #0,2,0: 52:[1, 12] Operation: 48/4=12 Exploring Operation: 4+48=52, Resulting Numbers: [1, 52] Generated Node #0,2,1: 52:[1, 52] Operation: 4+48=52 Exploring Operation: 48+1=49, Resulting Numbers: [4, 49] Generated Node #0,2,2: 52:[4, 49] Operation: 48+1=49 Exploring Operation: 4*1=4, Resulting Numbers: [48, 4] Generated Node #0,2,3: 52:[48, 4] Operation: 4*1=4 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 52:[1, 52], Operations: ['42-41=1', '4+48=52'] Exploring Operation: 1+52=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 1*52=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[4, 41, 42, 48], Operations: [] Exploring Operation: 42-41=1, Resulting Numbers: [4, 48, 1] Generated Node #0,2: 52:[4, 48, 1] Operation: 42-41=1 Moving to Node #0,2 Current State: 52:[4, 48, 1], Operations: ['42-41=1'] Exploring Operation: 4+48=52, Resulting Numbers: [1, 52] Generated Node #0,2,1: 52:[1, 52] Operation: 4+48=52 Moving to Node #0,2,1 Current State: 52:[1, 52], Operations: ['42-41=1', '4+48=52'] Exploring Operation: 1*52=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 69, 12, 80, 83 ]
11
[ "83-80=3", "69/3=23", "23-12=11" ]
Current State: 11:[69, 12, 80, 83], Operations: [] Exploring Operation: 83-80=3, Resulting Numbers: [69, 12, 3] Generated Node #2: [69, 12, 3] from Operation: 83-80=3 Current State: 11:[69, 12, 3], Operations: ['83-80=3'] Exploring Operation: 69/3=23, Resulting Numbers: [12, 23] Generated Node #3: [12, 23] from Operation: 69/3=23 Current State: 11:[12, 23], Operations: ['83-80=3', '69/3=23'] Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[69, 12, 80, 83], Operations: [] Exploring Operation: 83-80=3, Resulting Numbers: [69, 12, 3] Generated Node #0,0: 11:[69, 12, 3] Operation: 83-80=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[69, 12, 3], Operations: ['83-80=3'] Exploring Operation: 69/3=23, Resulting Numbers: [12, 23] Generated Node #0,0,0: 11:[12, 23] Operation: 69/3=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[12, 23], Operations: ['83-80=3', '69/3=23'] Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[69, 12, 80, 83], Operations: [] Exploring Operation: 83-80=3, Resulting Numbers: [69, 12, 3] Generated Node #0,0: 11:[69, 12, 3] Operation: 83-80=3 Moving to Node #0,0 Current State: 11:[69, 12, 3], Operations: ['83-80=3'] Exploring Operation: 69/3=23, Resulting Numbers: [12, 23] Generated Node #0,0,0: 11:[12, 23] Operation: 69/3=23 Moving to Node #0,0,0 Current State: 11:[12, 23], Operations: ['83-80=3', '69/3=23'] Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic