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, 4, 7, 37 ]
71
[ "20+7=27", "4*27=108", "108-37=71" ]
Current State: 71:[20, 4, 7, 37], Operations: [] Exploring Operation: 20+7=27, Resulting Numbers: [4, 37, 27] Generated Node #2: [4, 37, 27] from Operation: 20+7=27 Current State: 71:[4, 37, 27], Operations: ['20+7=27'] Exploring Operation: 4*27=108, Resulting Numbers: [37, 108] Generated Node #3: [37, 108] from Operation: 4*27=108 Current State: 71:[37, 108], Operations: ['20+7=27', '4*27=108'] Exploring Operation: 108-37=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[20, 4, 7, 37], Operations: [] Exploring Operation: 20*4=80, Resulting Numbers: [7, 37, 80] Generated Node #0,0: 71:[7, 37, 80] Operation: 20*4=80 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[7, 37, 80], Operations: ['20*4=80'] Exploring Operation: 7+37=44, Resulting Numbers: [80, 44] Generated Node #0,0,0: 71:[80, 44] Operation: 7+37=44 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[80, 44], Operations: ['20*4=80', '7+37=44'] Exploring Operation: 80-44=36, Resulting Numbers: [36] 36,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 78, 73, 2, 56 ]
90
[ "78/2=39", "73+56=129", "129-39=90" ]
Current State: 90:[78, 73, 2, 56], Operations: [] Exploring Operation: 78/2=39, Resulting Numbers: [73, 56, 39] Generated Node #2: [73, 56, 39] from Operation: 78/2=39 Current State: 90:[73, 56, 39], Operations: ['78/2=39'] Exploring Operation: 73+56=129, Resulting Numbers: [39, 129] Generated Node #3: [39, 129] from Operation: 73+56=129 Current State: 90:[39, 129], Operations: ['78/2=39', '73+56=129'] Exploring Operation: 129-39=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[78, 73, 2, 56], Operations: [] Exploring Operation: 56/2=28, Resulting Numbers: [78, 73, 28] Generated Node #0,0: 90:[78, 73, 28] Operation: 56/2=28 Exploring Operation: 78-56=22, Resulting Numbers: [73, 2, 22] Generated Node #0,1: 90:[73, 2, 22] Operation: 78-56=22 Exploring Operation: 78-73=5, Resulting Numbers: [2, 56, 5] Generated Node #0,2: 90:[2, 56, 5] Operation: 78-73=5 Exploring Operation: 73-56=17, Resulting Numbers: [78, 2, 17] Generated Node #0,3: 90:[78, 2, 17] Operation: 73-56=17 Moving to Node #0,2 Current State: 90:[2, 56, 5], Operations: ['78-73=5'] Exploring Operation: 56/2=28, Resulting Numbers: [5, 28] Generated Node #0,2,0: 90:[5, 28] Operation: 56/2=28 Exploring Operation: 56-2=54, Resulting Numbers: [5, 54] Generated Node #0,2,1: 90:[5, 54] Operation: 56-2=54 Exploring Operation: 2*5=10, Resulting Numbers: [56, 10] Generated Node #0,2,2: 90:[56, 10] Operation: 2*5=10 Exploring Operation: 56-5=51, Resulting Numbers: [2, 51] Generated Node #0,2,3: 90:[2, 51] Operation: 56-5=51 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 90:[5, 28], Operations: ['78-73=5', '56/2=28'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,90 unequal: No Solution Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 5*28=140, Resulting Numbers: [140] 140,90 unequal: No Solution No 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: 90:[2, 51], Operations: ['78-73=5', '56-5=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,90 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,90 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,90 unequal: No Solution No 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: 90:[5, 54], Operations: ['78-73=5', '56-2=54'] Exploring Operation: 5+54=59, Resulting Numbers: [59] 59,90 unequal: No Solution Exploring Operation: 5*54=270, Resulting Numbers: [270] 270,90 unequal: No Solution Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,90 unequal: No Solution No 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: 90:[56, 10], Operations: ['78-73=5', '2*5=10'] Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,90 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,90 unequal: No Solution Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,90 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: 90:[78, 2, 17], Operations: ['73-56=17'] Exploring Operation: 78+2=80, Resulting Numbers: [17, 80] Generated Node #0,3,0: 90:[17, 80] Operation: 78+2=80 Exploring Operation: 17-2=15, Resulting Numbers: [78, 15] Generated Node #0,3,1: 90:[78, 15] Operation: 17-2=15 Exploring Operation: 78/2=39, Resulting Numbers: [17, 39] Generated Node #0,3,2: 90:[17, 39] Operation: 78/2=39 Exploring Operation: 78+17=95, Resulting Numbers: [2, 95] Generated Node #0,3,3: 90:[2, 95] Operation: 78+17=95 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 90:[2, 95], Operations: ['73-56=17', '78+17=95'] Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,90 unequal: No Solution Exploring Operation: 2+95=97, Resulting Numbers: [97] 97,90 unequal: No Solution Exploring Operation: 2*95=190, Resulting Numbers: [190] 190,90 unequal: No Solution No 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: 90:[17, 39], Operations: ['73-56=17', '78/2=39'] Exploring Operation: 17+39=56, Resulting Numbers: [56] 56,90 unequal: No Solution Exploring Operation: 17*39=663, Resulting Numbers: [663] 663,90 unequal: No Solution Exploring Operation: 39-17=22, Resulting Numbers: [22] 22,90 unequal: No Solution No 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: 90:[17, 80], Operations: ['73-56=17', '78+2=80'] Exploring Operation: 17+80=97, Resulting Numbers: [97] 97,90 unequal: No Solution Exploring Operation: 80-17=63, Resulting Numbers: [63] 63,90 unequal: No Solution Exploring Operation: 17*80=1360, Resulting Numbers: [1360] 1360,90 unequal: No Solution No 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: 90:[78, 15], Operations: ['73-56=17', '17-2=15'] Exploring Operation: 78+15=93, Resulting Numbers: [93] 93,90 unequal: No Solution Exploring Operation: 78*15=1170, Resulting Numbers: [1170] 1170,90 unequal: No Solution Exploring Operation: 78-15=63, Resulting Numbers: [63] 63,90 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: 90:[73, 2, 22], Operations: ['78-56=22'] Exploring Operation: 73+22=95, Resulting Numbers: [2, 95] Generated Node #0,1,0: 90:[2, 95] Operation: 73+22=95 Exploring Operation: 2*22=44, Resulting Numbers: [73, 44] Generated Node #0,1,1: 90:[73, 44] Operation: 2*22=44 Exploring Operation: 73-22=51, Resulting Numbers: [2, 51] Generated Node #0,1,2: 90:[2, 51] Operation: 73-22=51 Exploring Operation: 22/2=11, Resulting Numbers: [73, 11] Generated Node #0,1,3: 90:[73, 11] Operation: 22/2=11 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[2, 95], Operations: ['78-56=22', '73+22=95'] Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,90 unequal: No Solution Exploring Operation: 2+95=97, Resulting Numbers: [97] 97,90 unequal: No Solution Exploring Operation: 2*95=190, Resulting Numbers: [190] 190,90 unequal: No Solution No 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: 90:[2, 51], Operations: ['78-56=22', '73-22=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,90 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,90 unequal: No Solution No 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: 90:[73, 44], Operations: ['78-56=22', '2*22=44'] Exploring Operation: 73*44=3212, Resulting Numbers: [3212] 3212,90 unequal: No Solution Exploring Operation: 73+44=117, Resulting Numbers: [117] 117,90 unequal: No Solution Exploring Operation: 73-44=29, Resulting Numbers: [29] 29,90 unequal: No Solution No 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: 90:[73, 11], Operations: ['78-56=22', '22/2=11'] Exploring Operation: 73*11=803, Resulting Numbers: [803] 803,90 unequal: No Solution Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,90 unequal: No Solution Exploring Operation: 73+11=84, Resulting Numbers: [84] 84,90 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: 90:[78, 73, 28], Operations: ['56/2=28'] Exploring Operation: 73+28=101, Resulting Numbers: [78, 101] Generated Node #0,0,0: 90:[78, 101] Operation: 73+28=101 Exploring Operation: 73-28=45, Resulting Numbers: [78, 45] Generated Node #0,0,1: 90:[78, 45] Operation: 73-28=45 Exploring Operation: 78-28=50, Resulting Numbers: [73, 50] Generated Node #0,0,2: 90:[73, 50] Operation: 78-28=50 Exploring Operation: 78-73=5, Resulting Numbers: [28, 5] Generated Node #0,0,3: 90:[28, 5] Operation: 78-73=5 Moving to Node #0,0,3 Current State: 90:[28, 5], Operations: ['56/2=28', '78-73=5'] Exploring Operation: 28*5=140, Resulting Numbers: [140] 140,90 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,90 unequal: No Solution Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[78, 45], Operations: ['56/2=28', '73-28=45'] Exploring Operation: 78*45=3510, Resulting Numbers: [3510] 3510,90 unequal: No Solution Exploring Operation: 78+45=123, Resulting Numbers: [123] 123,90 unequal: No Solution Exploring Operation: 78-45=33, Resulting Numbers: [33] 33,90 unequal: No Solution Moving to Node #0,0,2 Current State: 90:[73, 50], Operations: ['56/2=28', '78-28=50'] Exploring Operation: 73+50=123, Resulting Numbers: [123] 123,90 unequal: No Solution Exploring Operation: 73*50=3650, Resulting Numbers: [3650] 3650,90 unequal: No Solution Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[78, 101], Operations: ['56/2=28', '73+28=101'] Exploring Operation: 78+101=179, Resulting Numbers: [179] 179,90 unequal: No Solution Exploring Operation: 101-78=23, Resulting Numbers: [23] 23,90 unequal: No Solution Exploring Operation: 78*101=7878, Resulting Numbers: [7878] 7878,90 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 61, 16, 52, 99 ]
92
[ "61-16=45", "99-52=47", "45+47=92" ]
Current State: 92:[61, 16, 52, 99], Operations: [] Exploring Operation: 61-16=45, Resulting Numbers: [52, 99, 45] Generated Node #2: [52, 99, 45] from Operation: 61-16=45 Current State: 92:[52, 99, 45], Operations: ['61-16=45'] Exploring Operation: 99-52=47, Resulting Numbers: [45, 47] Generated Node #3: [45, 47] from Operation: 99-52=47 Current State: 92:[45, 47], Operations: ['61-16=45', '99-52=47'] Exploring Operation: 45+47=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[61, 16, 52, 99], Operations: [] Exploring Operation: 61-52=9, Resulting Numbers: [16, 99, 9] Generated Node #0,0: 92:[16, 99, 9] Operation: 61-52=9 Exploring Operation: 61-16=45, Resulting Numbers: [52, 99, 45] Generated Node #0,1: 92:[52, 99, 45] Operation: 61-16=45 Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[52, 99, 45], Operations: ['61-16=45'] Exploring Operation: 52-45=7, Resulting Numbers: [99, 7] Generated Node #0,1,0: 92:[99, 7] Operation: 52-45=7 Exploring Operation: 99-52=47, Resulting Numbers: [45, 47] Generated Node #0,1,1: 92:[45, 47] Operation: 99-52=47 Moving to Node #0,1,1 Current State: 92:[45, 47], Operations: ['61-16=45', '99-52=47'] Exploring Operation: 45+47=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[61, 16, 52, 99], Operations: [] Exploring Operation: 61-16=45, Resulting Numbers: [52, 99, 45] Generated Node #0,1: 92:[52, 99, 45] Operation: 61-16=45 Moving to Node #0,1 Current State: 92:[52, 99, 45], Operations: ['61-16=45'] Exploring Operation: 99-52=47, Resulting Numbers: [45, 47] Generated Node #0,1,1: 92:[45, 47] Operation: 99-52=47 Moving to Node #0,1,1 Current State: 92:[45, 47], Operations: ['61-16=45', '99-52=47'] Exploring Operation: 45+47=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 2, 46, 22, 90 ]
23
[ "90/2=45", "46+22=68", "68-45=23" ]
Current State: 23:[2, 46, 22, 90], Operations: [] Exploring Operation: 90/2=45, Resulting Numbers: [46, 22, 45] Generated Node #2: [46, 22, 45] from Operation: 90/2=45 Current State: 23:[46, 22, 45], Operations: ['90/2=45'] Exploring Operation: 46+22=68, Resulting Numbers: [45, 68] Generated Node #3: [45, 68] from Operation: 46+22=68 Current State: 23:[45, 68], Operations: ['90/2=45', '46+22=68'] Exploring Operation: 68-45=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[2, 46, 22, 90], Operations: [] Exploring Operation: 90-46=44, Resulting Numbers: [2, 22, 44] Generated Node #0,0: 23:[2, 22, 44] Operation: 90-46=44 Exploring Operation: 46/2=23, Resulting Numbers: [22, 90, 23] Generated Node #0,1: 23:[22, 90, 23] Operation: 46/2=23 Exploring Operation: 46-2=44, Resulting Numbers: [22, 90, 44] Generated Node #0,2: 23:[22, 90, 44] Operation: 46-2=44 Exploring Operation: 90/2=45, Resulting Numbers: [46, 22, 45] Generated Node #0,3: 23:[46, 22, 45] Operation: 90/2=45 Exploring Operation: 90-2=88, Resulting Numbers: [46, 22, 88] Generated Node #0,4: 23:[46, 22, 88] Operation: 90-2=88 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[2, 22, 44], Operations: ['90-46=44'] Exploring Operation: 2+22=24, Resulting Numbers: [44, 24] Generated Node #0,0,0: 23:[44, 24] Operation: 2+22=24 Exploring Operation: 44-2=42, Resulting Numbers: [22, 42] Generated Node #0,0,1: 23:[22, 42] Operation: 44-2=42 Exploring Operation: 44-22=22, Resulting Numbers: [2, 22] Generated Node #0,0,2: 23:[2, 22] Operation: 44-22=22 Exploring Operation: 22-2=20, Resulting Numbers: [44, 20] Generated Node #0,0,3: 23:[44, 20] Operation: 22-2=20 Exploring Operation: 44/2=22, Resulting Numbers: [22, 22] Generated Node #0,0,4: 23:[22, 22] Operation: 44/2=22 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 23:[22, 22], Operations: ['90-46=44', '44/2=22'] Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 22*22=484, Resulting Numbers: [484] 484,23 unequal: No Solution Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,23 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,23 unequal: No Solution No 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: 23:[22, 42], Operations: ['90-46=44', '44-2=42'] Exploring Operation: 22+42=64, Resulting Numbers: [64] 64,23 unequal: No Solution Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 22*42=924, Resulting Numbers: [924] 924,23 unequal: No Solution No 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: 23:[44, 24], Operations: ['90-46=44', '2+22=24'] Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 44+24=68, Resulting Numbers: [68] 68,23 unequal: No Solution Exploring Operation: 44*24=1056, Resulting Numbers: [1056] 1056,23 unequal: No Solution No 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: 23:[2, 22], Operations: ['90-46=44', '44-22=22'] Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,23 unequal: No Solution No 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: 23:[44, 20], Operations: ['90-46=44', '22-2=20'] Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,23 unequal: No Solution Exploring Operation: 44*20=880, Resulting Numbers: [880] 880,23 unequal: No Solution Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,23 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: 23:[46, 22, 45], Operations: ['90/2=45'] Exploring Operation: 46+22=68, Resulting Numbers: [45, 68] Generated Node #0,3,0: 23:[45, 68] Operation: 46+22=68 Exploring Operation: 22+45=67, Resulting Numbers: [46, 67] Generated Node #0,3,1: 23:[46, 67] Operation: 22+45=67 Exploring Operation: 46-22=24, Resulting Numbers: [45, 24] Generated Node #0,3,2: 23:[45, 24] Operation: 46-22=24 Exploring Operation: 46-45=1, Resulting Numbers: [22, 1] Generated Node #0,3,3: 23:[22, 1] Operation: 46-45=1 Exploring Operation: 45-22=23, Resulting Numbers: [46, 23] Generated Node #0,3,4: 23:[46, 23] Operation: 45-22=23 Moving to Node #0,3,2 Current State: 23:[45, 24], Operations: ['90/2=45', '46-22=24'] Exploring Operation: 45+24=69, Resulting Numbers: [69] 69,23 unequal: No Solution Exploring Operation: 45*24=1080, Resulting Numbers: [1080] 1080,23 unequal: No Solution Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,23 unequal: No Solution Moving to Node #0,3,4 Current State: 23:[46, 23], Operations: ['90/2=45', '45-22=23'] Exploring Operation: 46*23=1058, Resulting Numbers: [1058] 1058,23 unequal: No Solution Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[2, 46, 22, 90], Operations: [] Exploring Operation: 90/2=45, Resulting Numbers: [46, 22, 45] Generated Node #0,3: 23:[46, 22, 45] Operation: 90/2=45 Moving to Node #0,3 Current State: 23:[46, 22, 45], Operations: ['90/2=45'] Exploring Operation: 45-22=23, Resulting Numbers: [46, 23] Generated Node #0,3,4: 23:[46, 23] Operation: 45-22=23 Moving to Node #0,3,4 Current State: 23:[46, 23], Operations: ['90/2=45', '45-22=23'] Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 25, 46, 19, 56 ]
58
[ "46-25=21", "56-19=37", "21+37=58" ]
Current State: 58:[25, 46, 19, 56], Operations: [] Exploring Operation: 46-25=21, Resulting Numbers: [19, 56, 21] Generated Node #2: [19, 56, 21] from Operation: 46-25=21 Current State: 58:[19, 56, 21], Operations: ['46-25=21'] Exploring Operation: 56-19=37, Resulting Numbers: [21, 37] Generated Node #3: [21, 37] from Operation: 56-19=37 Current State: 58:[21, 37], Operations: ['46-25=21', '56-19=37'] Exploring Operation: 21+37=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[25, 46, 19, 56], Operations: [] Exploring Operation: 56-46=10, Resulting Numbers: [25, 19, 10] Generated Node #0,0: 58:[25, 19, 10] Operation: 56-46=10 Exploring Operation: 25-19=6, Resulting Numbers: [46, 56, 6] Generated Node #0,1: 58:[46, 56, 6] Operation: 25-19=6 Exploring Operation: 46-25=21, Resulting Numbers: [19, 56, 21] Generated Node #0,2: 58:[19, 56, 21] Operation: 46-25=21 Exploring Operation: 46-19=27, Resulting Numbers: [25, 56, 27] Generated Node #0,3: 58:[25, 56, 27] Operation: 46-19=27 Exploring Operation: 46+19=65, Resulting Numbers: [25, 56, 65] Generated Node #0,4: 58:[25, 56, 65] Operation: 46+19=65 Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[25, 56, 27], Operations: ['46-19=27'] Exploring Operation: 27-25=2, Resulting Numbers: [56, 2] Generated Node #0,3,0: 58:[56, 2] Operation: 27-25=2 Exploring Operation: 25+27=52, Resulting Numbers: [56, 52] Generated Node #0,3,1: 58:[56, 52] Operation: 25+27=52 Exploring Operation: 25+56=81, Resulting Numbers: [27, 81] Generated Node #0,3,2: 58:[27, 81] Operation: 25+56=81 Exploring Operation: 56-25=31, Resulting Numbers: [27, 31] Generated Node #0,3,3: 58:[27, 31] Operation: 56-25=31 Exploring Operation: 56-27=29, Resulting Numbers: [25, 29] Generated Node #0,3,4: 58:[25, 29] Operation: 56-27=29 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 58:[56, 2], Operations: ['46-19=27', '27-25=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,58 unequal: No Solution Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[25, 46, 19, 56], Operations: [] Exploring Operation: 46-19=27, Resulting Numbers: [25, 56, 27] Generated Node #0,3: 58:[25, 56, 27] Operation: 46-19=27 Moving to Node #0,3 Current State: 58:[25, 56, 27], Operations: ['46-19=27'] Exploring Operation: 27-25=2, Resulting Numbers: [56, 2] Generated Node #0,3,0: 58:[56, 2] Operation: 27-25=2 Moving to Node #0,3,0 Current State: 58:[56, 2], Operations: ['46-19=27', '27-25=2'] Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 36, 55, 15, 35 ]
72
[ "55+15=70", "36*70=2520", "2520/35=72" ]
Current State: 72:[36, 55, 15, 35], Operations: [] Exploring Operation: 55+15=70, Resulting Numbers: [36, 35, 70] Generated Node #2: [36, 35, 70] from Operation: 55+15=70 Current State: 72:[36, 35, 70], Operations: ['55+15=70'] Exploring Operation: 36*70=2520, Resulting Numbers: [35, 2520] Generated Node #3: [35, 2520] from Operation: 36*70=2520 Current State: 72:[35, 2520], Operations: ['55+15=70', '36*70=2520'] Exploring Operation: 2520/35=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[36, 55, 15, 35], Operations: [] Exploring Operation: 55-35=20, Resulting Numbers: [36, 15, 20] Generated Node #0,0: 72:[36, 15, 20] Operation: 55-35=20 Exploring Operation: 55+15=70, Resulting Numbers: [36, 35, 70] Generated Node #0,1: 72:[36, 35, 70] Operation: 55+15=70 Exploring Operation: 55-36=19, Resulting Numbers: [15, 35, 19] Generated Node #0,2: 72:[15, 35, 19] Operation: 55-36=19 Exploring Operation: 55-15=40, Resulting Numbers: [36, 35, 40] Generated Node #0,3: 72:[36, 35, 40] Operation: 55-15=40 Moving to Node #0,1 Current State: 72:[36, 35, 70], Operations: ['55+15=70'] Exploring Operation: 36+35=71, Resulting Numbers: [70, 71] Generated Node #0,1,0: 72:[70, 71] Operation: 36+35=71 Exploring Operation: 70-35=35, Resulting Numbers: [36, 35] Generated Node #0,1,1: 72:[36, 35] Operation: 70-35=35 Exploring Operation: 70/35=2, Resulting Numbers: [36, 2] Generated Node #0,1,2: 72:[36, 2] Operation: 70/35=2 Exploring Operation: 36-35=1, Resulting Numbers: [70, 1] Generated Node #0,1,3: 72:[70, 1] Operation: 36-35=1 Moving to Node #0,2 Current State: 72:[15, 35, 19], Operations: ['55-36=19'] Exploring Operation: 35-19=16, Resulting Numbers: [15, 16] Generated Node #0,2,0: 72:[15, 16] Operation: 35-19=16 Exploring Operation: 35-15=20, Resulting Numbers: [19, 20] Generated Node #0,2,1: 72:[19, 20] Operation: 35-15=20 Exploring Operation: 19-15=4, Resulting Numbers: [35, 4] Generated Node #0,2,2: 72:[35, 4] Operation: 19-15=4 Exploring Operation: 15+19=34, Resulting Numbers: [35, 34] Generated Node #0,2,3: 72:[35, 34] Operation: 15+19=34 Moving to Node #0,0 Current State: 72:[36, 15, 20], Operations: ['55-35=20'] Exploring Operation: 20-15=5, Resulting Numbers: [36, 5] Generated Node #0,0,0: 72:[36, 5] Operation: 20-15=5 Exploring Operation: 36-20=16, Resulting Numbers: [15, 16] Generated Node #0,0,1: 72:[15, 16] Operation: 36-20=16 Exploring Operation: 36-15=21, Resulting Numbers: [20, 21] Generated Node #0,0,2: 72:[20, 21] Operation: 36-15=21 Exploring Operation: 15+20=35, Resulting Numbers: [36, 35] Generated Node #0,0,3: 72:[36, 35] Operation: 15+20=35 Moving to Node #0,3 Current State: 72:[36, 35, 40], Operations: ['55-15=40'] Exploring Operation: 40-36=4, Resulting Numbers: [35, 4] Generated Node #0,3,0: 72:[35, 4] Operation: 40-36=4 Exploring Operation: 36+35=71, Resulting Numbers: [40, 71] Generated Node #0,3,1: 72:[40, 71] Operation: 36+35=71 Exploring Operation: 40-35=5, Resulting Numbers: [36, 5] Generated Node #0,3,2: 72:[36, 5] Operation: 40-35=5 Exploring Operation: 35+40=75, Resulting Numbers: [36, 75] Generated Node #0,3,3: 72:[36, 75] Operation: 35+40=75 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 72:[35, 4], Operations: ['55-15=40', '40-36=4'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,72 unequal: No Solution Exploring Operation: 35*4=140, Resulting Numbers: [140] 140,72 unequal: No Solution Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 72:[36, 5], Operations: ['55-15=40', '40-35=5'] Exploring Operation: 36*5=180, Resulting Numbers: [180] 180,72 unequal: No Solution Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,72 unequal: No Solution Exploring Operation: 36+5=41, Resulting Numbers: [41] 41,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 72:[36, 75], Operations: ['55-15=40', '35+40=75'] Exploring Operation: 36*75=2700, Resulting Numbers: [2700] 2700,72 unequal: No Solution Exploring Operation: 75-36=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 36+75=111, Resulting Numbers: [111] 111,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 72:[40, 71], Operations: ['55-15=40', '36+35=71'] Exploring Operation: 40*71=2840, Resulting Numbers: [2840] 2840,72 unequal: No Solution Exploring Operation: 40+71=111, Resulting Numbers: [111] 111,72 unequal: No Solution Exploring Operation: 71-40=31, Resulting Numbers: [31] 31,72 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: 72:[36, 2], Operations: ['55+15=70', '70/35=2'] Exploring Operation: 36*2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[36, 55, 15, 35], Operations: [] Exploring Operation: 55+15=70, Resulting Numbers: [36, 35, 70] Generated Node #0,1: 72:[36, 35, 70] Operation: 55+15=70 Moving to Node #0,1 Current State: 72:[36, 35, 70], Operations: ['55+15=70'] Exploring Operation: 70/35=2, Resulting Numbers: [36, 2] Generated Node #0,1,2: 72:[36, 2] Operation: 70/35=2 Moving to Node #0,1,2 Current State: 72:[36, 2], Operations: ['55+15=70', '70/35=2'] Exploring Operation: 36*2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.967882
hs_4
mult_heuristic
[ 52, 91, 47, 35 ]
61
[ "52+91=143", "47+35=82", "143-82=61" ]
Current State: 61:[52, 91, 47, 35], Operations: [] Exploring Operation: 52+91=143, Resulting Numbers: [47, 35, 143] Generated Node #2: [47, 35, 143] from Operation: 52+91=143 Current State: 61:[47, 35, 143], Operations: ['52+91=143'] Exploring Operation: 47+35=82, Resulting Numbers: [143, 82] Generated Node #3: [143, 82] from Operation: 47+35=82 Current State: 61:[143, 82], Operations: ['52+91=143', '47+35=82'] Exploring Operation: 143-82=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[52, 91, 47, 35], Operations: [] Exploring Operation: 91-35=56, Resulting Numbers: [52, 47, 56] Generated Node #0,0: 61:[52, 47, 56] Operation: 91-35=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[52, 47, 56], Operations: ['91-35=56'] Exploring Operation: 52+47=99, Resulting Numbers: [56, 99] Generated Node #0,0,0: 61:[56, 99] Operation: 52+47=99 Moving to Node #0,0,0 Current State: 61:[56, 99], Operations: ['91-35=56', '52+47=99'] Exploring Operation: 99-56=43, Resulting Numbers: [43] 43,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 12, 83, 32, 18 ]
45
[ "12+83=95", "32+18=50", "95-50=45" ]
Current State: 45:[12, 83, 32, 18], Operations: [] Exploring Operation: 12+83=95, Resulting Numbers: [32, 18, 95] Generated Node #2: [32, 18, 95] from Operation: 12+83=95 Current State: 45:[32, 18, 95], Operations: ['12+83=95'] Exploring Operation: 32+18=50, Resulting Numbers: [95, 50] Generated Node #3: [95, 50] from Operation: 32+18=50 Current State: 45:[95, 50], Operations: ['12+83=95', '32+18=50'] Exploring Operation: 95-50=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[12, 83, 32, 18], Operations: [] Exploring Operation: 83-32=51, Resulting Numbers: [12, 18, 51] Generated Node #0,0: 45:[12, 18, 51] Operation: 83-32=51 Moving to Node #0,0 Current State: 45:[12, 18, 51], Operations: ['83-32=51'] Exploring Operation: 18-12=6, Resulting Numbers: [51, 6] Generated Node #0,0,0: 45:[51, 6] Operation: 18-12=6 Moving to Node #0,0,0 Current State: 45:[51, 6], Operations: ['83-32=51', '18-12=6'] Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[12, 83, 32, 18], Operations: [] Exploring Operation: 83-32=51, Resulting Numbers: [12, 18, 51] Generated Node #0,0: 45:[12, 18, 51] Operation: 83-32=51 Moving to Node #0,0 Current State: 45:[12, 18, 51], Operations: ['83-32=51'] Exploring Operation: 18-12=6, Resulting Numbers: [51, 6] Generated Node #0,0,0: 45:[51, 6] Operation: 18-12=6 Moving to Node #0,0,0 Current State: 45:[51, 6], Operations: ['83-32=51', '18-12=6'] Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 12, 54, 95, 2 ]
62
[ "12+54=66", "66/2=33", "95-33=62" ]
Current State: 62:[12, 54, 95, 2], Operations: [] Exploring Operation: 12+54=66, Resulting Numbers: [95, 2, 66] Generated Node #2: [95, 2, 66] from Operation: 12+54=66 Current State: 62:[95, 2, 66], Operations: ['12+54=66'] Exploring Operation: 66/2=33, Resulting Numbers: [95, 33] Generated Node #3: [95, 33] from Operation: 66/2=33 Current State: 62:[95, 33], Operations: ['12+54=66', '66/2=33'] Exploring Operation: 95-33=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[12, 54, 95, 2], Operations: [] Exploring Operation: 95-12=83, Resulting Numbers: [54, 2, 83] Generated Node #0,0: 62:[54, 2, 83] Operation: 95-12=83 Exploring Operation: 95-54=41, Resulting Numbers: [12, 2, 41] Generated Node #0,1: 62:[12, 2, 41] Operation: 95-54=41 Moving to Node #0,1 Current State: 62:[12, 2, 41], Operations: ['95-54=41'] Exploring Operation: 41-12=29, Resulting Numbers: [2, 29] Generated Node #0,1,0: 62:[2, 29] Operation: 41-12=29 Exploring Operation: 12+41=53, Resulting Numbers: [2, 53] Generated Node #0,1,1: 62:[2, 53] Operation: 12+41=53 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[2, 29], Operations: ['95-54=41', '41-12=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,62 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,62 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:[2, 53], Operations: ['95-54=41', '12+41=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,62 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,62 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:[54, 2, 83], Operations: ['95-12=83'] Exploring Operation: 83-54=29, Resulting Numbers: [2, 29] Generated Node #0,0,0: 62:[2, 29] Operation: 83-54=29 Exploring Operation: 54/2=27, Resulting Numbers: [83, 27] Generated Node #0,0,1: 62:[83, 27] Operation: 54/2=27 Moving to Node #0,0,0 Current State: 62:[2, 29], Operations: ['95-12=83', '83-54=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,62 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,62 unequal: No Solution Moving to Node #0,0,1 Current State: 62:[83, 27], Operations: ['95-12=83', '54/2=27'] Exploring Operation: 83-27=56, Resulting Numbers: [56] 56,62 unequal: No Solution Exploring Operation: 83+27=110, Resulting Numbers: [110] 110,62 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 33, 19, 24, 28 ]
81
[ "33-24=9", "28-19=9", "9*9=81" ]
Current State: 81:[33, 19, 24, 28], Operations: [] Exploring Operation: 33-24=9, Resulting Numbers: [19, 28, 9] Generated Node #2: [19, 28, 9] from Operation: 33-24=9 Current State: 81:[19, 28, 9], Operations: ['33-24=9'] Exploring Operation: 28-19=9, Resulting Numbers: [9, 9] Generated Node #3: [9, 9] from Operation: 28-19=9 Current State: 81:[9, 9], Operations: ['33-24=9', '28-19=9'] Exploring Operation: 9*9=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[33, 19, 24, 28], Operations: [] Exploring Operation: 33-24=9, Resulting Numbers: [19, 28, 9] Generated Node #0,0: 81:[19, 28, 9] Operation: 33-24=9 Exploring Operation: 33-19=14, Resulting Numbers: [24, 28, 14] Generated Node #0,1: 81:[24, 28, 14] Operation: 33-19=14 Exploring Operation: 24-19=5, Resulting Numbers: [33, 28, 5] Generated Node #0,2: 81:[33, 28, 5] Operation: 24-19=5 Exploring Operation: 33-28=5, Resulting Numbers: [19, 24, 5] Generated Node #0,3: 81:[19, 24, 5] Operation: 33-28=5 Exploring Operation: 28-19=9, Resulting Numbers: [33, 24, 9] Generated Node #0,4: 81:[33, 24, 9] Operation: 28-19=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[19, 28, 9], Operations: ['33-24=9'] Exploring Operation: 19-9=10, Resulting Numbers: [28, 10] Generated Node #0,0,0: 81:[28, 10] Operation: 19-9=10 Exploring Operation: 28-9=19, Resulting Numbers: [19, 19] Generated Node #0,0,1: 81:[19, 19] Operation: 28-9=19 Exploring Operation: 28+9=37, Resulting Numbers: [19, 37] Generated Node #0,0,2: 81:[19, 37] Operation: 28+9=37 Exploring Operation: 28-19=9, Resulting Numbers: [9, 9] Generated Node #0,0,3: 81:[9, 9] Operation: 28-19=9 Exploring Operation: 19+9=28, Resulting Numbers: [28, 28] Generated Node #0,0,4: 81:[28, 28] Operation: 19+9=28 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 81:[9, 9], Operations: ['33-24=9', '28-19=9'] Exploring Operation: 9*9=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[33, 19, 24, 28], Operations: [] Exploring Operation: 33-24=9, Resulting Numbers: [19, 28, 9] Generated Node #0,0: 81:[19, 28, 9] Operation: 33-24=9 Moving to Node #0,0 Current State: 81:[19, 28, 9], Operations: ['33-24=9'] Exploring Operation: 28-19=9, Resulting Numbers: [9, 9] Generated Node #0,0,3: 81:[9, 9] Operation: 28-19=9 Moving to Node #0,0,3 Current State: 81:[9, 9], Operations: ['33-24=9', '28-19=9'] Exploring Operation: 9*9=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 61, 11, 23, 25 ]
39
[ "25-23=2", "11*2=22", "61-22=39" ]
Current State: 39:[61, 11, 23, 25], Operations: [] Exploring Operation: 25-23=2, Resulting Numbers: [61, 11, 2] Generated Node #2: [61, 11, 2] from Operation: 25-23=2 Current State: 39:[61, 11, 2], Operations: ['25-23=2'] Exploring Operation: 11*2=22, Resulting Numbers: [61, 22] Generated Node #3: [61, 22] from Operation: 11*2=22 Current State: 39:[61, 22], Operations: ['25-23=2', '11*2=22'] Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[61, 11, 23, 25], Operations: [] Exploring Operation: 61-11=50, Resulting Numbers: [23, 25, 50] Generated Node #0,0: 39:[23, 25, 50] Operation: 61-11=50 Exploring Operation: 61-25=36, Resulting Numbers: [11, 23, 36] Generated Node #0,1: 39:[11, 23, 36] Operation: 61-25=36 Exploring Operation: 61-23=38, Resulting Numbers: [11, 25, 38] Generated Node #0,2: 39:[11, 25, 38] Operation: 61-23=38 Exploring Operation: 25-23=2, Resulting Numbers: [61, 11, 2] Generated Node #0,3: 39:[61, 11, 2] Operation: 25-23=2 Moving to Node #0,1 Current State: 39:[11, 23, 36], Operations: ['61-25=36'] Exploring Operation: 23-11=12, Resulting Numbers: [36, 12] Generated Node #0,1,0: 39:[36, 12] Operation: 23-11=12 Exploring Operation: 11+36=47, Resulting Numbers: [23, 47] Generated Node #0,1,1: 39:[23, 47] Operation: 11+36=47 Exploring Operation: 36-23=13, Resulting Numbers: [11, 13] Generated Node #0,1,2: 39:[11, 13] Operation: 36-23=13 Exploring Operation: 11+23=34, Resulting Numbers: [36, 34] Generated Node #0,1,3: 39:[36, 34] Operation: 11+23=34 Moving to Node #0,2 Current State: 39:[11, 25, 38], Operations: ['61-23=38'] Exploring Operation: 38-25=13, Resulting Numbers: [11, 13] Generated Node #0,2,0: 39:[11, 13] Operation: 38-25=13 Exploring Operation: 25-11=14, Resulting Numbers: [38, 14] Generated Node #0,2,1: 39:[38, 14] Operation: 25-11=14 Exploring Operation: 11+25=36, Resulting Numbers: [38, 36] Generated Node #0,2,2: 39:[38, 36] Operation: 11+25=36 Exploring Operation: 11+38=49, Resulting Numbers: [25, 49] Generated Node #0,2,3: 39:[25, 49] Operation: 11+38=49 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[11, 13], Operations: ['61-23=38', '38-25=13'] Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,39 unequal: No Solution Exploring Operation: 11*13=143, Resulting Numbers: [143] 143,39 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:[38, 14], Operations: ['61-23=38', '25-11=14'] Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,39 unequal: No Solution Exploring Operation: 38*14=532, Resulting Numbers: [532] 532,39 unequal: No Solution Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,39 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:[38, 36], Operations: ['61-23=38', '11+25=36'] Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 38*36=1368, Resulting Numbers: [1368] 1368,39 unequal: No Solution Exploring Operation: 38+36=74, Resulting Numbers: [74] 74,39 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 #0,2,3 Current State: 39:[25, 49], Operations: ['61-23=38', '11+38=49'] Exploring Operation: 25+49=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 25*49=1225, Resulting Numbers: [1225] 1225,39 unequal: No Solution Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,39 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: 39:[61, 11, 2], Operations: ['25-23=2'] Exploring Operation: 61-11=50, Resulting Numbers: [2, 50] Generated Node #0,3,0: 39:[2, 50] Operation: 61-11=50 Exploring Operation: 61+2=63, Resulting Numbers: [11, 63] Generated Node #0,3,1: 39:[11, 63] Operation: 61+2=63 Exploring Operation: 11+2=13, Resulting Numbers: [61, 13] Generated Node #0,3,2: 39:[61, 13] Operation: 11+2=13 Exploring Operation: 61-2=59, Resulting Numbers: [11, 59] Generated Node #0,3,3: 39:[11, 59] Operation: 61-2=59 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 39:[2, 50], Operations: ['25-23=2', '61-11=50'] Exploring Operation: 2*50=100, Resulting Numbers: [100] 100,39 unequal: No Solution Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,39 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 39:[61, 13], Operations: ['25-23=2', '11+2=13'] Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,39 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 39:[11, 59], Operations: ['25-23=2', '61-2=59'] Exploring Operation: 11+59=70, Resulting Numbers: [70] 70,39 unequal: No Solution Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,39 unequal: No Solution Exploring Operation: 11*59=649, Resulting Numbers: [649] 649,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 39:[11, 63], Operations: ['25-23=2', '61+2=63'] Exploring Operation: 11+63=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 63-11=52, Resulting Numbers: [52] 52,39 unequal: No Solution Exploring Operation: 11*63=693, Resulting Numbers: [693] 693,39 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: 39:[23, 25, 50], Operations: ['61-11=50'] Exploring Operation: 25-23=2, Resulting Numbers: [50, 2] Generated Node #0,0,0: 39:[50, 2] Operation: 25-23=2 Exploring Operation: 50-25=25, Resulting Numbers: [23, 25] Generated Node #0,0,1: 39:[23, 25] Operation: 50-25=25 Exploring Operation: 50/25=2, Resulting Numbers: [23, 2] Generated Node #0,0,2: 39:[23, 2] Operation: 50/25=2 Exploring Operation: 23+25=48, Resulting Numbers: [50, 48] Generated Node #0,0,3: 39:[50, 48] Operation: 23+25=48 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 39:[23, 2], Operations: ['61-11=50', '50/25=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,39 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 #0,0,0 Current State: 39:[50, 2], Operations: ['61-11=50', '25-23=2'] Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,39 unequal: No Solution Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,39 unequal: No Solution Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,39 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 #0,0,3 Current State: 39:[50, 48], Operations: ['61-11=50', '23+25=48'] Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,39 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,39 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 #0,0,1 Current State: 39:[23, 25], Operations: ['61-11=50', '50-25=25'] Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,39 unequal: No Solution Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 23*25=575, Resulting Numbers: [575] 575,39 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: 39:[11, 13], Operations: ['61-25=36', '36-23=13'] Exploring Operation: 11*13=143, Resulting Numbers: [143] 143,39 unequal: No Solution Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,39 unequal: No Solution Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[36, 12], Operations: ['61-25=36', '23-11=12'] Exploring Operation: 36+12=48, Resulting Numbers: [48] 48,39 unequal: No Solution Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,39 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 36*12=432, Resulting Numbers: [432] 432,39 unequal: No Solution Moving to Node #0,1,3 Current State: 39:[36, 34], Operations: ['61-25=36', '11+23=34'] Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 36*34=1224, Resulting Numbers: [1224] 1224,39 unequal: No Solution Exploring Operation: 36+34=70, Resulting Numbers: [70] 70,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[23, 47], Operations: ['61-25=36', '11+36=47'] Exploring Operation: 23*47=1081, Resulting Numbers: [1081] 1081,39 unequal: No Solution Exploring Operation: 23+47=70, Resulting Numbers: [70] 70,39 unequal: No Solution Exploring Operation: 47-23=24, Resulting Numbers: [24] 24,39 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 9, 40, 74, 22 ]
72
[ "40-22=18", "18/9=2", "74-2=72" ]
Current State: 72:[9, 40, 74, 22], Operations: [] Exploring Operation: 40-22=18, Resulting Numbers: [9, 74, 18] Generated Node #2: [9, 74, 18] from Operation: 40-22=18 Current State: 72:[9, 74, 18], Operations: ['40-22=18'] Exploring Operation: 18/9=2, Resulting Numbers: [74, 2] Generated Node #3: [74, 2] from Operation: 18/9=2 Current State: 72:[74, 2], Operations: ['40-22=18', '18/9=2'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[9, 40, 74, 22], Operations: [] Exploring Operation: 74-40=34, Resulting Numbers: [9, 22, 34] Generated Node #0,0: 72:[9, 22, 34] Operation: 74-40=34 Exploring Operation: 40-22=18, Resulting Numbers: [9, 74, 18] Generated Node #0,1: 72:[9, 74, 18] Operation: 40-22=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[9, 74, 18], Operations: ['40-22=18'] Exploring Operation: 18-9=9, Resulting Numbers: [74, 9] Generated Node #0,1,0: 72:[74, 9] Operation: 18-9=9 Exploring Operation: 18/9=2, Resulting Numbers: [74, 2] Generated Node #0,1,1: 72:[74, 2] Operation: 18/9=2 Moving to Node #0,1,0 Current State: 72:[74, 9], Operations: ['40-22=18', '18-9=9'] Exploring Operation: 74-9=65, Resulting Numbers: [65] 65,72 unequal: No Solution Exploring Operation: 74+9=83, Resulting Numbers: [83] 83,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[74, 2], Operations: ['40-22=18', '18/9=2'] Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[9, 40, 74, 22], Operations: [] Exploring Operation: 40-22=18, Resulting Numbers: [9, 74, 18] Generated Node #0,1: 72:[9, 74, 18] Operation: 40-22=18 Moving to Node #0,1 Current State: 72:[9, 74, 18], Operations: ['40-22=18'] Exploring Operation: 18/9=2, Resulting Numbers: [74, 2] Generated Node #0,1,1: 72:[74, 2] Operation: 18/9=2 Moving to Node #0,1,1 Current State: 72:[74, 2], Operations: ['40-22=18', '18/9=2'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 22, 83, 87, 40 ]
14
[ "83-22=61", "87-40=47", "61-47=14" ]
Current State: 14:[22, 83, 87, 40], Operations: [] Exploring Operation: 83-22=61, Resulting Numbers: [87, 40, 61] Generated Node #2: [87, 40, 61] from Operation: 83-22=61 Current State: 14:[87, 40, 61], Operations: ['83-22=61'] Exploring Operation: 87-40=47, Resulting Numbers: [61, 47] Generated Node #3: [61, 47] from Operation: 87-40=47 Current State: 14:[61, 47], Operations: ['83-22=61', '87-40=47'] Exploring Operation: 61-47=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[22, 83, 87, 40], Operations: [] Exploring Operation: 87-40=47, Resulting Numbers: [22, 83, 47] Generated Node #0,0: 14:[22, 83, 47] Operation: 87-40=47 Exploring Operation: 87-22=65, Resulting Numbers: [83, 40, 65] Generated Node #0,1: 14:[83, 40, 65] Operation: 87-22=65 Exploring Operation: 83-40=43, Resulting Numbers: [22, 87, 43] Generated Node #0,2: 14:[22, 87, 43] Operation: 83-40=43 Exploring Operation: 83-22=61, Resulting Numbers: [87, 40, 61] Generated Node #0,3: 14:[87, 40, 61] Operation: 83-22=61 Exploring Operation: 87-83=4, Resulting Numbers: [22, 40, 4] Generated Node #0,4: 14:[22, 40, 4] Operation: 87-83=4 Moving to Node #0,4 Current State: 14:[22, 40, 4], Operations: ['87-83=4'] Exploring Operation: 22-4=18, Resulting Numbers: [40, 18] Generated Node #0,4,0: 14:[40, 18] Operation: 22-4=18 Exploring Operation: 40-4=36, Resulting Numbers: [22, 36] Generated Node #0,4,1: 14:[22, 36] Operation: 40-4=36 Exploring Operation: 40/4=10, Resulting Numbers: [22, 10] Generated Node #0,4,2: 14:[22, 10] Operation: 40/4=10 Exploring Operation: 22+4=26, Resulting Numbers: [40, 26] Generated Node #0,4,3: 14:[40, 26] Operation: 22+4=26 Exploring Operation: 40-22=18, Resulting Numbers: [4, 18] Generated Node #0,4,4: 14:[4, 18] Operation: 40-22=18 Moving to Node #0,2 Current State: 14:[22, 87, 43], Operations: ['83-40=43'] Exploring Operation: 87-22=65, Resulting Numbers: [43, 65] Generated Node #0,2,0: 14:[43, 65] Operation: 87-22=65 Exploring Operation: 43-22=21, Resulting Numbers: [87, 21] Generated Node #0,2,1: 14:[87, 21] Operation: 43-22=21 Exploring Operation: 87-43=44, Resulting Numbers: [22, 44] Generated Node #0,2,2: 14:[22, 44] Operation: 87-43=44 Exploring Operation: 22+43=65, Resulting Numbers: [87, 65] Generated Node #0,2,3: 14:[87, 65] Operation: 22+43=65 Exploring Operation: 22+87=109, Resulting Numbers: [43, 109] Generated Node #0,2,4: 14:[43, 109] Operation: 22+87=109 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 14:[22, 44], Operations: ['83-40=43', '87-43=44'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,14 unequal: No Solution Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 22*44=968, Resulting Numbers: [968] 968,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 14:[43, 65], Operations: ['83-40=43', '87-22=65'] Exploring Operation: 43*65=2795, Resulting Numbers: [2795] 2795,14 unequal: No Solution Exploring Operation: 65-43=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 43+65=108, Resulting Numbers: [108] 108,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 14:[87, 21], Operations: ['83-40=43', '43-22=21'] Exploring Operation: 87-21=66, Resulting Numbers: [66] 66,14 unequal: No Solution Exploring Operation: 87*21=1827, Resulting Numbers: [1827] 1827,14 unequal: No Solution Exploring Operation: 87+21=108, Resulting Numbers: [108] 108,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 14:[87, 65], Operations: ['83-40=43', '22+43=65'] Exploring Operation: 87+65=152, Resulting Numbers: [152] 152,14 unequal: No Solution Exploring Operation: 87-65=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 87*65=5655, Resulting Numbers: [5655] 5655,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 14:[43, 109], Operations: ['83-40=43', '22+87=109'] Exploring Operation: 109-43=66, Resulting Numbers: [66] 66,14 unequal: No Solution Exploring Operation: 43*109=4687, Resulting Numbers: [4687] 4687,14 unequal: No Solution Exploring Operation: 43+109=152, Resulting Numbers: [152] 152,14 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: 14:[22, 83, 47], Operations: ['87-40=47'] Exploring Operation: 83-47=36, Resulting Numbers: [22, 36] Generated Node #0,0,0: 14:[22, 36] Operation: 83-47=36 Exploring Operation: 47-22=25, Resulting Numbers: [83, 25] Generated Node #0,0,1: 14:[83, 25] Operation: 47-22=25 Exploring Operation: 83-22=61, Resulting Numbers: [47, 61] Generated Node #0,0,2: 14:[47, 61] Operation: 83-22=61 Exploring Operation: 22+83=105, Resulting Numbers: [47, 105] Generated Node #0,0,3: 14:[47, 105] Operation: 22+83=105 Exploring Operation: 22+47=69, Resulting Numbers: [83, 69] Generated Node #0,0,4: 14:[83, 69] Operation: 22+47=69 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[22, 36], Operations: ['87-40=47', '83-47=36'] Exploring Operation: 22+36=58, Resulting Numbers: [58] 58,14 unequal: No Solution Exploring Operation: 22*36=792, Resulting Numbers: [792] 792,14 unequal: No Solution Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[22, 83, 87, 40], Operations: [] Exploring Operation: 87-40=47, Resulting Numbers: [22, 83, 47] Generated Node #0,0: 14:[22, 83, 47] Operation: 87-40=47 Moving to Node #0,0 Current State: 14:[22, 83, 47], Operations: ['87-40=47'] Exploring Operation: 83-47=36, Resulting Numbers: [22, 36] Generated Node #0,0,0: 14:[22, 36] Operation: 83-47=36 Moving to Node #0,0,0 Current State: 14:[22, 36], Operations: ['87-40=47', '83-47=36'] Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic
[ 56, 53, 25, 71 ]
73
[ "53-25=28", "56/28=2", "71+2=73" ]
Current State: 73:[56, 53, 25, 71], Operations: [] Exploring Operation: 53-25=28, Resulting Numbers: [56, 71, 28] Generated Node #2: [56, 71, 28] from Operation: 53-25=28 Current State: 73:[56, 71, 28], Operations: ['53-25=28'] Exploring Operation: 56/28=2, Resulting Numbers: [71, 2] Generated Node #3: [71, 2] from Operation: 56/28=2 Current State: 73:[71, 2], Operations: ['53-25=28', '56/28=2'] Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[56, 53, 25, 71], Operations: [] Exploring Operation: 53+25=78, Resulting Numbers: [56, 71, 78] Generated Node #0,0: 73:[56, 71, 78] Operation: 53+25=78 Exploring Operation: 25+71=96, Resulting Numbers: [56, 53, 96] Generated Node #0,1: 73:[56, 53, 96] Operation: 25+71=96 Exploring Operation: 53-25=28, Resulting Numbers: [56, 71, 28] Generated Node #0,2: 73:[56, 71, 28] Operation: 53-25=28 Exploring Operation: 56-25=31, Resulting Numbers: [53, 71, 31] Generated Node #0,3: 73:[53, 71, 31] Operation: 56-25=31 Exploring Operation: 56+25=81, Resulting Numbers: [53, 71, 81] Generated Node #0,4: 73:[53, 71, 81] Operation: 56+25=81 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[56, 71, 78], Operations: ['53+25=78'] Exploring Operation: 78-71=7, Resulting Numbers: [56, 7] Generated Node #0,0,0: 73:[56, 7] Operation: 78-71=7 Exploring Operation: 71-56=15, Resulting Numbers: [78, 15] Generated Node #0,0,1: 73:[78, 15] Operation: 71-56=15 Exploring Operation: 78-56=22, Resulting Numbers: [71, 22] Generated Node #0,0,2: 73:[71, 22] Operation: 78-56=22 Exploring Operation: 56+78=134, Resulting Numbers: [71, 134] Generated Node #0,0,3: 73:[71, 134] Operation: 56+78=134 Exploring Operation: 56+71=127, Resulting Numbers: [78, 127] Generated Node #0,0,4: 73:[78, 127] Operation: 56+71=127 Moving to Node #0,0,2 Current State: 73:[71, 22], Operations: ['53+25=78', '78-56=22'] Exploring Operation: 71-22=49, Resulting Numbers: [49] 49,73 unequal: No Solution Exploring Operation: 71*22=1562, Resulting Numbers: [1562] 1562,73 unequal: No Solution Exploring Operation: 71+22=93, Resulting Numbers: [93] 93,73 unequal: No Solution Moving to Node #0,0,4 Current State: 73:[78, 127], Operations: ['53+25=78', '56+71=127'] Exploring Operation: 78+127=205, Resulting Numbers: [205] 205,73 unequal: No Solution Exploring Operation: 78*127=9906, Resulting Numbers: [9906] 9906,73 unequal: No Solution Exploring Operation: 127-78=49, Resulting Numbers: [49] 49,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[78, 15], Operations: ['53+25=78', '71-56=15'] Exploring Operation: 78-15=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 78+15=93, Resulting Numbers: [93] 93,73 unequal: No Solution Exploring Operation: 78*15=1170, Resulting Numbers: [1170] 1170,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[71, 134], Operations: ['53+25=78', '56+78=134'] Exploring Operation: 134-71=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 71*134=9514, Resulting Numbers: [9514] 9514,73 unequal: No Solution Exploring Operation: 71+134=205, Resulting Numbers: [205] 205,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[56, 7], Operations: ['53+25=78', '78-71=7'] Exploring Operation: 56*7=392, Resulting Numbers: [392] 392,73 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,73 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 56+7=63, Resulting Numbers: [63] 63,73 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 #0,4 Current State: 73:[53, 71, 81], Operations: ['56+25=81'] Exploring Operation: 81-53=28, Resulting Numbers: [71, 28] Generated Node #0,4,0: 73:[71, 28] Operation: 81-53=28 Exploring Operation: 71-53=18, Resulting Numbers: [81, 18] Generated Node #0,4,1: 73:[81, 18] Operation: 71-53=18 Exploring Operation: 81-71=10, Resulting Numbers: [53, 10] Generated Node #0,4,2: 73:[53, 10] Operation: 81-71=10 Exploring Operation: 53+71=124, Resulting Numbers: [81, 124] Generated Node #0,4,3: 73:[81, 124] Operation: 53+71=124 Exploring Operation: 53+81=134, Resulting Numbers: [71, 134] Generated Node #0,4,4: 73:[71, 134] Operation: 53+81=134 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 73:[71, 28], Operations: ['56+25=81', '81-53=28'] Exploring Operation: 71+28=99, Resulting Numbers: [99] 99,73 unequal: No Solution Exploring Operation: 71*28=1988, Resulting Numbers: [1988] 1988,73 unequal: No Solution Exploring Operation: 71-28=43, Resulting Numbers: [43] 43,73 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 #0,4,3 Current State: 73:[81, 124], Operations: ['56+25=81', '53+71=124'] Exploring Operation: 81*124=10044, Resulting Numbers: [10044] 10044,73 unequal: No Solution Exploring Operation: 124-81=43, Resulting Numbers: [43] 43,73 unequal: No Solution Exploring Operation: 81+124=205, Resulting Numbers: [205] 205,73 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 #0,4,1 Current State: 73:[81, 18], Operations: ['56+25=81', '71-53=18'] Exploring Operation: 81+18=99, Resulting Numbers: [99] 99,73 unequal: No Solution Exploring Operation: 81-18=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 81*18=1458, Resulting Numbers: [1458] 1458,73 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 #0,4,4 Current State: 73:[71, 134], Operations: ['56+25=81', '53+81=134'] Exploring Operation: 134-71=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 71*134=9514, Resulting Numbers: [9514] 9514,73 unequal: No Solution Exploring Operation: 71+134=205, Resulting Numbers: [205] 205,73 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 #0,4,2 Current State: 73:[53, 10], Operations: ['56+25=81', '81-71=10'] Exploring Operation: 53-10=43, Resulting Numbers: [43] 43,73 unequal: No Solution Exploring Operation: 53+10=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 53*10=530, Resulting Numbers: [530] 530,73 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:[56, 53, 96], Operations: ['25+71=96'] Exploring Operation: 53+96=149, Resulting Numbers: [56, 149] Generated Node #0,1,0: 73:[56, 149] Operation: 53+96=149 Exploring Operation: 56+53=109, Resulting Numbers: [96, 109] Generated Node #0,1,1: 73:[96, 109] Operation: 56+53=109 Exploring Operation: 96-53=43, Resulting Numbers: [56, 43] Generated Node #0,1,2: 73:[56, 43] Operation: 96-53=43 Exploring Operation: 96-56=40, Resulting Numbers: [53, 40] Generated Node #0,1,3: 73:[53, 40] Operation: 96-56=40 Exploring Operation: 56-53=3, Resulting Numbers: [96, 3] Generated Node #0,1,4: 73:[96, 3] Operation: 56-53=3 Moving to Node #0,1,2 Current State: 73:[56, 43], Operations: ['25+71=96', '96-53=43'] Exploring Operation: 56+43=99, Resulting Numbers: [99] 99,73 unequal: No Solution Exploring Operation: 56*43=2408, Resulting Numbers: [2408] 2408,73 unequal: No Solution Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,73 unequal: No Solution Moving to Node #0,1,3 Current State: 73:[53, 40], Operations: ['25+71=96', '96-56=40'] Exploring Operation: 53+40=93, Resulting Numbers: [93] 93,73 unequal: No Solution Exploring Operation: 53-40=13, Resulting Numbers: [13] 13,73 unequal: No Solution Exploring Operation: 53*40=2120, Resulting Numbers: [2120] 2120,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[96, 109], Operations: ['25+71=96', '56+53=109'] Exploring Operation: 96+109=205, Resulting Numbers: [205] 205,73 unequal: No Solution Exploring Operation: 109-96=13, Resulting Numbers: [13] 13,73 unequal: No Solution Exploring Operation: 96*109=10464, Resulting Numbers: [10464] 10464,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[56, 149], Operations: ['25+71=96', '53+96=149'] Exploring Operation: 149-56=93, Resulting Numbers: [93] 93,73 unequal: No Solution Exploring Operation: 56*149=8344, Resulting Numbers: [8344] 8344,73 unequal: No Solution Exploring Operation: 56+149=205, Resulting Numbers: [205] 205,73 unequal: No Solution Moving to Node #0,1,4 Current State: 73:[96, 3], Operations: ['25+71=96', '56-53=3'] Exploring Operation: 96+3=99, Resulting Numbers: [99] 99,73 unequal: No Solution Exploring Operation: 96/3=32, Resulting Numbers: [32] 32,73 unequal: No Solution Exploring Operation: 96*3=288, Resulting Numbers: [288] 288,73 unequal: No Solution Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,73 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 #0,2 Current State: 73:[56, 71, 28], Operations: ['53-25=28'] Exploring Operation: 56/28=2, Resulting Numbers: [71, 2] Generated Node #0,2,0: 73:[71, 2] Operation: 56/28=2 Exploring Operation: 71+28=99, Resulting Numbers: [56, 99] Generated Node #0,2,1: 73:[56, 99] Operation: 71+28=99 Exploring Operation: 71-28=43, Resulting Numbers: [56, 43] Generated Node #0,2,2: 73:[56, 43] Operation: 71-28=43 Exploring Operation: 56+28=84, Resulting Numbers: [71, 84] Generated Node #0,2,3: 73:[71, 84] Operation: 56+28=84 Exploring Operation: 56-28=28, Resulting Numbers: [71, 28] Generated Node #0,2,4: 73:[71, 28] Operation: 56-28=28 Moving to Node #0,2,3 Current State: 73:[71, 84], Operations: ['53-25=28', '56+28=84'] Exploring Operation: 84-71=13, Resulting Numbers: [13] 13,73 unequal: No Solution Exploring Operation: 71*84=5964, Resulting Numbers: [5964] 5964,73 unequal: No Solution Exploring Operation: 71+84=155, Resulting Numbers: [155] 155,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[56, 99], Operations: ['53-25=28', '71+28=99'] Exploring Operation: 56*99=5544, Resulting Numbers: [5544] 5544,73 unequal: No Solution Exploring Operation: 56+99=155, Resulting Numbers: [155] 155,73 unequal: No Solution Exploring Operation: 99-56=43, Resulting Numbers: [43] 43,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[56, 43], Operations: ['53-25=28', '71-28=43'] Exploring Operation: 56+43=99, Resulting Numbers: [99] 99,73 unequal: No Solution Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,73 unequal: No Solution Exploring Operation: 56*43=2408, Resulting Numbers: [2408] 2408,73 unequal: No Solution Moving to Node #0,2,4 Current State: 73:[71, 28], Operations: ['53-25=28', '56-28=28'] Exploring Operation: 71+28=99, Resulting Numbers: [99] 99,73 unequal: No Solution Exploring Operation: 71*28=1988, Resulting Numbers: [1988] 1988,73 unequal: No Solution Exploring Operation: 71-28=43, Resulting Numbers: [43] 43,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[71, 2], Operations: ['53-25=28', '56/28=2'] Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[56, 53, 25, 71], Operations: [] Exploring Operation: 53-25=28, Resulting Numbers: [56, 71, 28] Generated Node #0,2: 73:[56, 71, 28] Operation: 53-25=28 Moving to Node #0,2 Current State: 73:[56, 71, 28], Operations: ['53-25=28'] Exploring Operation: 56/28=2, Resulting Numbers: [71, 2] Generated Node #0,2,0: 73:[71, 2] Operation: 56/28=2 Moving to Node #0,2,0 Current State: 73:[71, 2], Operations: ['53-25=28', '56/28=2'] Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.922743
hs_5
sum_heuristic
[ 29, 85, 28, 89 ]
91
[ "85-29=56", "56/28=2", "89+2=91" ]
Current State: 91:[29, 85, 28, 89], Operations: [] Exploring Operation: 85-29=56, Resulting Numbers: [28, 89, 56] Generated Node #2: [28, 89, 56] from Operation: 85-29=56 Current State: 91:[28, 89, 56], Operations: ['85-29=56'] Exploring Operation: 56/28=2, Resulting Numbers: [89, 2] Generated Node #3: [89, 2] from Operation: 56/28=2 Current State: 91:[89, 2], Operations: ['85-29=56', '56/28=2'] Exploring Operation: 89+2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[29, 85, 28, 89], Operations: [] Exploring Operation: 29-28=1, Resulting Numbers: [85, 89, 1] Generated Node #0,0: 91:[85, 89, 1] Operation: 29-28=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[85, 89, 1], Operations: ['29-28=1'] Exploring Operation: 85+1=86, Resulting Numbers: [89, 86] Generated Node #0,0,0: 91:[89, 86] Operation: 85+1=86 Moving to Node #0,0,0 Current State: 91:[89, 86], Operations: ['29-28=1', '85+1=86'] Exploring Operation: 89-86=3, Resulting Numbers: [3] 3,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 27, 47, 9, 19 ]
54
[ "47-9=38", "27*38=1026", "1026/19=54" ]
Current State: 54:[27, 47, 9, 19], Operations: [] Exploring Operation: 47-9=38, Resulting Numbers: [27, 19, 38] Generated Node #2: [27, 19, 38] from Operation: 47-9=38 Current State: 54:[27, 19, 38], Operations: ['47-9=38'] Exploring Operation: 27*38=1026, Resulting Numbers: [19, 1026] Generated Node #3: [19, 1026] from Operation: 27*38=1026 Current State: 54:[19, 1026], Operations: ['47-9=38', '27*38=1026'] Exploring Operation: 1026/19=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[27, 47, 9, 19], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [9, 19, 20] Generated Node #0,0: 54:[9, 19, 20] Operation: 47-27=20 Exploring Operation: 47-19=28, Resulting Numbers: [27, 9, 28] Generated Node #0,1: 54:[27, 9, 28] Operation: 47-19=28 Moving to Node #0,1 Current State: 54:[27, 9, 28], Operations: ['47-19=28'] Exploring Operation: 27/9=3, Resulting Numbers: [28, 3] Generated Node #0,1,0: 54:[28, 3] Operation: 27/9=3 Exploring Operation: 27-9=18, Resulting Numbers: [28, 18] Generated Node #0,1,1: 54:[28, 18] Operation: 27-9=18 Moving to Node #0,0 Current State: 54:[9, 19, 20], Operations: ['47-27=20'] Exploring Operation: 9+19=28, Resulting Numbers: [20, 28] Generated Node #0,0,0: 54:[20, 28] Operation: 9+19=28 Exploring Operation: 20-19=1, Resulting Numbers: [9, 1] Generated Node #0,0,1: 54:[9, 1] Operation: 20-19=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[9, 1], Operations: ['47-27=20', '20-19=1'] Exploring Operation: 9*1=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 9/1=9, Resulting Numbers: [9] 9,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[20, 28], Operations: ['47-27=20', '9+19=28'] Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,54 unequal: No Solution Exploring Operation: 20+28=48, Resulting Numbers: [48] 48,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 54:[28, 3], Operations: ['47-19=28', '27/9=3'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,54 unequal: No Solution Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[28, 18], Operations: ['47-19=28', '27-9=18'] Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,54 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 37, 58, 55, 48 ]
82
[ "58-37=21", "55+48=103", "103-21=82" ]
Current State: 82:[37, 58, 55, 48], Operations: [] Exploring Operation: 58-37=21, Resulting Numbers: [55, 48, 21] Generated Node #2: [55, 48, 21] from Operation: 58-37=21 Current State: 82:[55, 48, 21], Operations: ['58-37=21'] Exploring Operation: 55+48=103, Resulting Numbers: [21, 103] Generated Node #3: [21, 103] from Operation: 55+48=103 Current State: 82:[21, 103], Operations: ['58-37=21', '55+48=103'] Exploring Operation: 103-21=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[37, 58, 55, 48], Operations: [] Exploring Operation: 58-48=10, Resulting Numbers: [37, 55, 10] Generated Node #0,0: 82:[37, 55, 10] Operation: 58-48=10 Exploring Operation: 58-55=3, Resulting Numbers: [37, 48, 3] Generated Node #0,1: 82:[37, 48, 3] Operation: 58-55=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[37, 48, 3], Operations: ['58-55=3'] Exploring Operation: 37+3=40, Resulting Numbers: [48, 40] Generated Node #0,1,0: 82:[48, 40] Operation: 37+3=40 Exploring Operation: 37+48=85, Resulting Numbers: [3, 85] Generated Node #0,1,1: 82:[3, 85] Operation: 37+48=85 Moving to Node #0,1,1 Current State: 82:[3, 85], Operations: ['58-55=3', '37+48=85'] Exploring Operation: 3+85=88, Resulting Numbers: [88] 88,82 unequal: No Solution Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[37, 58, 55, 48], Operations: [] Exploring Operation: 58-55=3, Resulting Numbers: [37, 48, 3] Generated Node #0,1: 82:[37, 48, 3] Operation: 58-55=3 Moving to Node #0,1 Current State: 82:[37, 48, 3], Operations: ['58-55=3'] Exploring Operation: 37+48=85, Resulting Numbers: [3, 85] Generated Node #0,1,1: 82:[3, 85] Operation: 37+48=85 Moving to Node #0,1,1 Current State: 82:[3, 85], Operations: ['58-55=3', '37+48=85'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 43, 18, 36, 72 ]
86
[ "72-36=36", "43*36=1548", "1548/18=86" ]
Current State: 86:[43, 18, 36, 72], Operations: [] Exploring Operation: 72-36=36, Resulting Numbers: [43, 18, 36] Generated Node #2: [43, 18, 36] from Operation: 72-36=36 Current State: 86:[43, 18, 36], Operations: ['72-36=36'] Exploring Operation: 43*36=1548, Resulting Numbers: [18, 1548] Generated Node #3: [18, 1548] from Operation: 43*36=1548 Current State: 86:[18, 1548], Operations: ['72-36=36', '43*36=1548'] Exploring Operation: 1548/18=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[43, 18, 36, 72], Operations: [] Exploring Operation: 72/18=4, Resulting Numbers: [43, 36, 4] Generated Node #0,0: 86:[43, 36, 4] Operation: 72/18=4 Exploring Operation: 18+72=90, Resulting Numbers: [43, 36, 90] Generated Node #0,1: 86:[43, 36, 90] Operation: 18+72=90 Moving to Node #0,0 Current State: 86:[43, 36, 4], Operations: ['72/18=4'] Exploring Operation: 43-36=7, Resulting Numbers: [4, 7] Generated Node #0,0,0: 86:[4, 7] Operation: 43-36=7 Exploring Operation: 36+4=40, Resulting Numbers: [43, 40] Generated Node #0,0,1: 86:[43, 40] Operation: 36+4=40 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 86:[43, 40], Operations: ['72/18=4', '36+4=40'] Exploring Operation: 43+40=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[4, 7], Operations: ['72/18=4', '43-36=7'] Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 86:[43, 36, 90], Operations: ['18+72=90'] Exploring Operation: 43-36=7, Resulting Numbers: [90, 7] Generated Node #0,1,0: 86:[90, 7] Operation: 43-36=7 Exploring Operation: 43+36=79, Resulting Numbers: [90, 79] Generated Node #0,1,1: 86:[90, 79] Operation: 43+36=79 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[90, 7], Operations: ['18+72=90', '43-36=7'] Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 90+7=97, Resulting Numbers: [97] 97,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[90, 79], Operations: ['18+72=90', '43+36=79'] Exploring Operation: 90-79=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 90+79=169, Resulting Numbers: [169] 169,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 6, 39, 27, 48 ]
59
[ "39+27=66", "66/6=11", "48+11=59" ]
Current State: 59:[6, 39, 27, 48], Operations: [] Exploring Operation: 39+27=66, Resulting Numbers: [6, 48, 66] Generated Node #2: [6, 48, 66] from Operation: 39+27=66 Current State: 59:[6, 48, 66], Operations: ['39+27=66'] Exploring Operation: 66/6=11, Resulting Numbers: [48, 11] Generated Node #3: [48, 11] from Operation: 66/6=11 Current State: 59:[48, 11], Operations: ['39+27=66', '66/6=11'] Exploring Operation: 48+11=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[6, 39, 27, 48], Operations: [] Exploring Operation: 27-6=21, Resulting Numbers: [39, 48, 21] Generated Node #0,0: 59:[39, 48, 21] Operation: 27-6=21 Exploring Operation: 6+39=45, Resulting Numbers: [27, 48, 45] Generated Node #0,1: 59:[27, 48, 45] Operation: 6+39=45 Exploring Operation: 39-6=33, Resulting Numbers: [27, 48, 33] Generated Node #0,2: 59:[27, 48, 33] Operation: 39-6=33 Exploring Operation: 6+27=33, Resulting Numbers: [39, 48, 33] Generated Node #0,3: 59:[39, 48, 33] Operation: 6+27=33 Exploring Operation: 6+48=54, Resulting Numbers: [39, 27, 54] Generated Node #0,4: 59:[39, 27, 54] Operation: 6+48=54 Moving to Node #0,1 Current State: 59:[27, 48, 45], Operations: ['6+39=45'] Exploring Operation: 45-27=18, Resulting Numbers: [48, 18] Generated Node #0,1,0: 59:[48, 18] Operation: 45-27=18 Exploring Operation: 48-27=21, Resulting Numbers: [45, 21] Generated Node #0,1,1: 59:[45, 21] Operation: 48-27=21 Exploring Operation: 27+48=75, Resulting Numbers: [45, 75] Generated Node #0,1,2: 59:[45, 75] Operation: 27+48=75 Exploring Operation: 27+45=72, Resulting Numbers: [48, 72] Generated Node #0,1,3: 59:[48, 72] Operation: 27+45=72 Exploring Operation: 48+45=93, Resulting Numbers: [27, 93] Generated Node #0,1,4: 59:[27, 93] Operation: 48+45=93 Moving to Node #0,4 Current State: 59:[39, 27, 54], Operations: ['6+48=54'] Exploring Operation: 39+54=93, Resulting Numbers: [27, 93] Generated Node #0,4,0: 59:[27, 93] Operation: 39+54=93 Exploring Operation: 27+54=81, Resulting Numbers: [39, 81] Generated Node #0,4,1: 59:[39, 81] Operation: 27+54=81 Exploring Operation: 54-27=27, Resulting Numbers: [39, 27] Generated Node #0,4,2: 59:[39, 27] Operation: 54-27=27 Exploring Operation: 39-27=12, Resulting Numbers: [54, 12] Generated Node #0,4,3: 59:[54, 12] Operation: 39-27=12 Exploring Operation: 39+27=66, Resulting Numbers: [54, 66] Generated Node #0,4,4: 59:[54, 66] Operation: 39+27=66 Moving to Node #0,3 Current State: 59:[39, 48, 33], Operations: ['6+27=33'] Exploring Operation: 48+33=81, Resulting Numbers: [39, 81] Generated Node #0,3,0: 59:[39, 81] Operation: 48+33=81 Exploring Operation: 39+48=87, Resulting Numbers: [33, 87] Generated Node #0,3,1: 59:[33, 87] Operation: 39+48=87 Exploring Operation: 39+33=72, Resulting Numbers: [48, 72] Generated Node #0,3,2: 59:[48, 72] Operation: 39+33=72 Exploring Operation: 39-33=6, Resulting Numbers: [48, 6] Generated Node #0,3,3: 59:[48, 6] Operation: 39-33=6 Exploring Operation: 48-33=15, Resulting Numbers: [39, 15] Generated Node #0,3,4: 59:[39, 15] Operation: 48-33=15 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 59:[48, 72], Operations: ['6+27=33', '39+33=72'] Exploring Operation: 48+72=120, Resulting Numbers: [120] 120,59 unequal: No Solution Exploring Operation: 72-48=24, Resulting Numbers: [24] 24,59 unequal: No Solution Exploring Operation: 48*72=3456, Resulting Numbers: [3456] 3456,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 59:[39, 81], Operations: ['6+27=33', '48+33=81'] Exploring Operation: 39*81=3159, Resulting Numbers: [3159] 3159,59 unequal: No Solution Exploring Operation: 81-39=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 39+81=120, Resulting Numbers: [120] 120,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 59:[33, 87], Operations: ['6+27=33', '39+48=87'] Exploring Operation: 33*87=2871, Resulting Numbers: [2871] 2871,59 unequal: No Solution Exploring Operation: 33+87=120, Resulting Numbers: [120] 120,59 unequal: No Solution Exploring Operation: 87-33=54, Resulting Numbers: [54] 54,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 59:[48, 6], Operations: ['6+27=33', '39-33=6'] Exploring Operation: 48*6=288, Resulting Numbers: [288] 288,59 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 59:[39, 15], Operations: ['6+27=33', '48-33=15'] Exploring Operation: 39+15=54, Resulting Numbers: [54] 54,59 unequal: No Solution Exploring Operation: 39*15=585, Resulting Numbers: [585] 585,59 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 59:[39, 48, 21], Operations: ['27-6=21'] Exploring Operation: 39-21=18, Resulting Numbers: [48, 18] Generated Node #0,0,0: 59:[48, 18] Operation: 39-21=18 Exploring Operation: 39+21=60, Resulting Numbers: [48, 60] Generated Node #0,0,1: 59:[48, 60] Operation: 39+21=60 Exploring Operation: 48+21=69, Resulting Numbers: [39, 69] Generated Node #0,0,2: 59:[39, 69] Operation: 48+21=69 Exploring Operation: 39+48=87, Resulting Numbers: [21, 87] Generated Node #0,0,3: 59:[21, 87] Operation: 39+48=87 Exploring Operation: 48-21=27, Resulting Numbers: [39, 27] Generated Node #0,0,4: 59:[39, 27] Operation: 48-21=27 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[48, 60], Operations: ['27-6=21', '39+21=60'] Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,59 unequal: No Solution Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 59:[39, 69], Operations: ['27-6=21', '48+21=69'] Exploring Operation: 69-39=30, Resulting Numbers: [30] 30,59 unequal: No Solution Exploring Operation: 39*69=2691, Resulting Numbers: [2691] 2691,59 unequal: No Solution Exploring Operation: 39+69=108, Resulting Numbers: [108] 108,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[48, 18], Operations: ['27-6=21', '39-21=18'] Exploring Operation: 48+18=66, Resulting Numbers: [66] 66,59 unequal: No Solution Exploring Operation: 48*18=864, Resulting Numbers: [864] 864,59 unequal: No Solution Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 59:[39, 27], Operations: ['27-6=21', '48-21=27'] Exploring Operation: 39*27=1053, Resulting Numbers: [1053] 1053,59 unequal: No Solution Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,59 unequal: No Solution Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 59:[21, 87], Operations: ['27-6=21', '39+48=87'] Exploring Operation: 87-21=66, Resulting Numbers: [66] 66,59 unequal: No Solution Exploring Operation: 21+87=108, Resulting Numbers: [108] 108,59 unequal: No Solution Exploring Operation: 21*87=1827, Resulting Numbers: [1827] 1827,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 59:[27, 48, 33], Operations: ['39-6=33'] Exploring Operation: 27+48=75, Resulting Numbers: [33, 75] Generated Node #0,2,0: 59:[33, 75] Operation: 27+48=75 Exploring Operation: 48+33=81, Resulting Numbers: [27, 81] Generated Node #0,2,1: 59:[27, 81] Operation: 48+33=81 Exploring Operation: 33-27=6, Resulting Numbers: [48, 6] Generated Node #0,2,2: 59:[48, 6] Operation: 33-27=6 Exploring Operation: 27+33=60, Resulting Numbers: [48, 60] Generated Node #0,2,3: 59:[48, 60] Operation: 27+33=60 Exploring Operation: 48-27=21, Resulting Numbers: [33, 21] Generated Node #0,2,4: 59:[33, 21] Operation: 48-27=21 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 59:[48, 60], Operations: ['39-6=33', '27+33=60'] Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,59 unequal: No Solution Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[33, 75], Operations: ['39-6=33', '27+48=75'] Exploring Operation: 33+75=108, Resulting Numbers: [108] 108,59 unequal: No Solution Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 33*75=2475, Resulting Numbers: [2475] 2475,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[27, 81], Operations: ['39-6=33', '48+33=81'] Exploring Operation: 27*81=2187, Resulting Numbers: [2187] 2187,59 unequal: No Solution Exploring Operation: 81/27=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 81-27=54, Resulting Numbers: [54] 54,59 unequal: No Solution Exploring Operation: 27+81=108, Resulting Numbers: [108] 108,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[48, 6], Operations: ['39-6=33', '33-27=6'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 48*6=288, Resulting Numbers: [288] 288,59 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 59:[33, 21], Operations: ['39-6=33', '48-27=21'] Exploring Operation: 33*21=693, Resulting Numbers: [693] 693,59 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,4 Current State: 59:[54, 66], Operations: ['6+48=54', '39+27=66'] Exploring Operation: 54*66=3564, Resulting Numbers: [3564] 3564,59 unequal: No Solution Exploring Operation: 66-54=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 54+66=120, Resulting Numbers: [120] 120,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[48, 72], Operations: ['6+39=45', '27+45=72'] Exploring Operation: 72-48=24, Resulting Numbers: [24] 24,59 unequal: No Solution Exploring Operation: 48*72=3456, Resulting Numbers: [3456] 3456,59 unequal: No Solution Exploring Operation: 48+72=120, Resulting Numbers: [120] 120,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[45, 75], Operations: ['6+39=45', '27+48=75'] Exploring Operation: 45+75=120, Resulting Numbers: [120] 120,59 unequal: No Solution Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,59 unequal: No Solution Exploring Operation: 45*75=3375, Resulting Numbers: [3375] 3375,59 unequal: No Solution Moving to Node #0,4,1 Current State: 59:[39, 81], Operations: ['6+48=54', '27+54=81'] Exploring Operation: 39+81=120, Resulting Numbers: [120] 120,59 unequal: No Solution Exploring Operation: 39*81=3159, Resulting Numbers: [3159] 3159,59 unequal: No Solution Exploring Operation: 81-39=42, Resulting Numbers: [42] 42,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[48, 18], Operations: ['6+39=45', '45-27=18'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,59 unequal: No Solution Exploring Operation: 48*18=864, Resulting Numbers: [864] 864,59 unequal: No Solution Exploring Operation: 48+18=66, Resulting Numbers: [66] 66,59 unequal: No Solution Moving to Node #0,4,3 Current State: 59:[54, 12], Operations: ['6+48=54', '39-27=12'] Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,59 unequal: No Solution Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[45, 21], Operations: ['6+39=45', '48-27=21'] Exploring Operation: 45+21=66, Resulting Numbers: [66] 66,59 unequal: No Solution Exploring Operation: 45*21=945, Resulting Numbers: [945] 945,59 unequal: No Solution Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,59 unequal: No Solution Moving to Node #0,4,2 Current State: 59:[39, 27], Operations: ['6+48=54', '54-27=27'] Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,59 unequal: No Solution Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 39*27=1053, Resulting Numbers: [1053] 1053,59 unequal: No Solution Moving to Node #0,1,4 Current State: 59:[27, 93], Operations: ['6+39=45', '48+45=93'] Exploring Operation: 93-27=66, Resulting Numbers: [66] 66,59 unequal: No Solution Exploring Operation: 27*93=2511, Resulting Numbers: [2511] 2511,59 unequal: No Solution Exploring Operation: 27+93=120, Resulting Numbers: [120] 120,59 unequal: No Solution Moving to Node #0,4,0 Current State: 59:[27, 93], Operations: ['6+48=54', '39+54=93'] Exploring Operation: 93-27=66, Resulting Numbers: [66] 66,59 unequal: No Solution Exploring Operation: 27+93=120, Resulting Numbers: [120] 120,59 unequal: No Solution Exploring Operation: 27*93=2511, Resulting Numbers: [2511] 2511,59 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 12, 15, 99, 54 ]
47
[ "99-15=84", "84/12=7", "54-7=47" ]
Current State: 47:[12, 15, 99, 54], Operations: [] Exploring Operation: 99-15=84, Resulting Numbers: [12, 54, 84] Generated Node #2: [12, 54, 84] from Operation: 99-15=84 Current State: 47:[12, 54, 84], Operations: ['99-15=84'] Exploring Operation: 84/12=7, Resulting Numbers: [54, 7] Generated Node #3: [54, 7] from Operation: 84/12=7 Current State: 47:[54, 7], Operations: ['99-15=84', '84/12=7'] Exploring Operation: 54-7=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[12, 15, 99, 54], Operations: [] Exploring Operation: 99-54=45, Resulting Numbers: [12, 15, 45] Generated Node #0,0: 47:[12, 15, 45] Operation: 99-54=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[12, 15, 45], Operations: ['99-54=45'] Exploring Operation: 12+15=27, Resulting Numbers: [45, 27] Generated Node #0,0,0: 47:[45, 27] Operation: 12+15=27 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[45, 27], Operations: ['99-54=45', '12+15=27'] Exploring Operation: 45+27=72, Resulting Numbers: [72] 72,47 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
[ 41, 70, 63, 6 ]
29
[ "41+70=111", "63+111=174", "174/6=29" ]
Current State: 29:[41, 70, 63, 6], Operations: [] Exploring Operation: 41+70=111, Resulting Numbers: [63, 6, 111] Generated Node #2: [63, 6, 111] from Operation: 41+70=111 Current State: 29:[63, 6, 111], Operations: ['41+70=111'] Exploring Operation: 63+111=174, Resulting Numbers: [6, 174] Generated Node #3: [6, 174] from Operation: 63+111=174 Current State: 29:[6, 174], Operations: ['41+70=111', '63+111=174'] Exploring Operation: 174/6=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[41, 70, 63, 6], Operations: [] Exploring Operation: 70-41=29, Resulting Numbers: [63, 6, 29] Generated Node #0,0: 29:[63, 6, 29] Operation: 70-41=29 Exploring Operation: 63-41=22, Resulting Numbers: [70, 6, 22] Generated Node #0,1: 29:[70, 6, 22] Operation: 63-41=22 Exploring Operation: 70-63=7, Resulting Numbers: [41, 6, 7] Generated Node #0,2: 29:[41, 6, 7] Operation: 70-63=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[63, 6, 29], Operations: ['70-41=29'] Exploring Operation: 63-29=34, Resulting Numbers: [6, 34] Generated Node #0,0,0: 29:[6, 34] Operation: 63-29=34 Exploring Operation: 63-6=57, Resulting Numbers: [29, 57] Generated Node #0,0,1: 29:[29, 57] Operation: 63-6=57 Exploring Operation: 63+6=69, Resulting Numbers: [29, 69] Generated Node #0,0,2: 29:[29, 69] Operation: 63+6=69 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[6, 34], Operations: ['70-41=29', '63-29=34'] Exploring Operation: 6*34=204, Resulting Numbers: [204] 204,29 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 6+34=40, Resulting Numbers: [40] 40,29 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 #0,0,1 Current State: 29:[29, 57], Operations: ['70-41=29', '63-6=57'] Exploring Operation: 29+57=86, Resulting Numbers: [86] 86,29 unequal: No Solution Exploring Operation: 57-29=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 29*57=1653, Resulting Numbers: [1653] 1653,29 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 #0,0,2 Current State: 29:[29, 69], Operations: ['70-41=29', '63+6=69'] Exploring Operation: 29+69=98, Resulting Numbers: [98] 98,29 unequal: No Solution Exploring Operation: 29*69=2001, Resulting Numbers: [2001] 2001,29 unequal: No Solution Exploring Operation: 69-29=40, Resulting Numbers: [40] 40,29 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 #0,2 Current State: 29:[41, 6, 7], Operations: ['70-63=7'] Exploring Operation: 41-6=35, Resulting Numbers: [7, 35] Generated Node #0,2,0: 29:[7, 35] Operation: 41-6=35 Exploring Operation: 41-7=34, Resulting Numbers: [6, 34] Generated Node #0,2,1: 29:[6, 34] Operation: 41-7=34 Exploring Operation: 6*7=42, Resulting Numbers: [41, 42] Generated Node #0,2,2: 29:[41, 42] Operation: 6*7=42 Moving to Node #0,2,2 Current State: 29:[41, 42], Operations: ['70-63=7', '6*7=42'] Exploring Operation: 41+42=83, Resulting Numbers: [83] 83,29 unequal: No Solution Exploring Operation: 42-41=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 41*42=1722, Resulting Numbers: [1722] 1722,29 unequal: No Solution Moving to Node #0,2,0 Current State: 29:[7, 35], Operations: ['70-63=7', '41-6=35'] Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,29 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[6, 34], Operations: ['70-63=7', '41-7=34'] Exploring Operation: 6+34=40, Resulting Numbers: [40] 40,29 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 6*34=204, Resulting Numbers: [204] 204,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[70, 6, 22], Operations: ['63-41=22'] Exploring Operation: 70-22=48, Resulting Numbers: [6, 48] Generated Node #0,1,0: 29:[6, 48] Operation: 70-22=48 Exploring Operation: 6+22=28, Resulting Numbers: [70, 28] Generated Node #0,1,1: 29:[70, 28] Operation: 6+22=28 Exploring Operation: 70-6=64, Resulting Numbers: [22, 64] Generated Node #0,1,2: 29:[22, 64] Operation: 70-6=64 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 29:[6, 48], Operations: ['63-41=22', '70-22=48'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,29 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,29 unequal: No Solution Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,29 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:[70, 28], Operations: ['63-41=22', '6+22=28'] Exploring Operation: 70-28=42, Resulting Numbers: [42] 42,29 unequal: No Solution Exploring Operation: 70*28=1960, Resulting Numbers: [1960] 1960,29 unequal: No Solution Exploring Operation: 70+28=98, Resulting Numbers: [98] 98,29 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 #0,1,2 Current State: 29:[22, 64], Operations: ['63-41=22', '70-6=64'] Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,29 unequal: No Solution Exploring Operation: 22+64=86, Resulting Numbers: [86] 86,29 unequal: No Solution Exploring Operation: 22*64=1408, Resulting Numbers: [1408] 1408,29 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_3
mult_heuristic
[ 35, 13, 42, 2 ]
92
[ "35+13=48", "42+2=44", "48+44=92" ]
Current State: 92:[35, 13, 42, 2], Operations: [] Exploring Operation: 35+13=48, Resulting Numbers: [42, 2, 48] Generated Node #2: [42, 2, 48] from Operation: 35+13=48 Current State: 92:[42, 2, 48], Operations: ['35+13=48'] Exploring Operation: 42+2=44, Resulting Numbers: [48, 44] Generated Node #3: [48, 44] from Operation: 42+2=44 Current State: 92:[48, 44], Operations: ['35+13=48', '42+2=44'] Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[35, 13, 42, 2], Operations: [] Exploring Operation: 35+13=48, Resulting Numbers: [42, 2, 48] Generated Node #0,0: 92:[42, 2, 48] Operation: 35+13=48 Exploring Operation: 35-13=22, Resulting Numbers: [42, 2, 22] Generated Node #0,1: 92:[42, 2, 22] Operation: 35-13=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[42, 2, 22], Operations: ['35-13=22'] Exploring Operation: 42/2=21, Resulting Numbers: [22, 21] Generated Node #0,1,0: 92:[22, 21] Operation: 42/2=21 Exploring Operation: 42+2=44, Resulting Numbers: [22, 44] Generated Node #0,1,1: 92:[22, 44] Operation: 42+2=44 Moving to Node #0,1,0 Current State: 92:[22, 21], Operations: ['35-13=22', '42/2=21'] Exploring Operation: 22+21=43, Resulting Numbers: [43] 43,92 unequal: No Solution Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[22, 44], Operations: ['35-13=22', '42+2=44'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,92 unequal: No Solution Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[42, 2, 48], Operations: ['35+13=48'] Exploring Operation: 42+48=90, Resulting Numbers: [2, 90] Generated Node #0,0,0: 92:[2, 90] Operation: 42+48=90 Exploring Operation: 48-42=6, Resulting Numbers: [2, 6] Generated Node #0,0,1: 92:[2, 6] Operation: 48-42=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[2, 90], Operations: ['35+13=48', '42+48=90'] Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,92 unequal: No Solution Exploring Operation: 2+90=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[35, 13, 42, 2], Operations: [] Exploring Operation: 35+13=48, Resulting Numbers: [42, 2, 48] Generated Node #0,0: 92:[42, 2, 48] Operation: 35+13=48 Moving to Node #0,0 Current State: 92:[42, 2, 48], Operations: ['35+13=48'] Exploring Operation: 42+48=90, Resulting Numbers: [2, 90] Generated Node #0,0,0: 92:[2, 90] Operation: 42+48=90 Moving to Node #0,0,0 Current State: 92:[2, 90], Operations: ['35+13=48', '42+48=90'] Exploring Operation: 2+90=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 85, 80, 5, 46 ]
85
[ "80-46=34", "5*34=170", "170-85=85" ]
Current State: 85:[85, 80, 5, 46], Operations: [] Exploring Operation: 80-46=34, Resulting Numbers: [85, 5, 34] Generated Node #2: [85, 5, 34] from Operation: 80-46=34 Current State: 85:[85, 5, 34], Operations: ['80-46=34'] Exploring Operation: 5*34=170, Resulting Numbers: [85, 170] Generated Node #3: [85, 170] from Operation: 5*34=170 Current State: 85:[85, 170], Operations: ['80-46=34', '5*34=170'] Exploring Operation: 170-85=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[85, 80, 5, 46], Operations: [] Exploring Operation: 85-46=39, Resulting Numbers: [80, 5, 39] Generated Node #0,0: 85:[80, 5, 39] Operation: 85-46=39 Exploring Operation: 80-46=34, Resulting Numbers: [85, 5, 34] Generated Node #0,1: 85:[85, 5, 34] Operation: 80-46=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[85, 5, 34], Operations: ['80-46=34'] Exploring Operation: 85/5=17, Resulting Numbers: [34, 17] Generated Node #0,1,0: 85:[34, 17] Operation: 85/5=17 Exploring Operation: 34-5=29, Resulting Numbers: [85, 29] Generated Node #0,1,1: 85:[85, 29] Operation: 34-5=29 Moving to Node #0,1,1 Current State: 85:[85, 29], Operations: ['80-46=34', '34-5=29'] Exploring Operation: 85-29=56, Resulting Numbers: [56] 56,85 unequal: No Solution Exploring Operation: 85+29=114, Resulting Numbers: [114] 114,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[34, 17], Operations: ['80-46=34', '85/5=17'] Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[80, 5, 39], Operations: ['85-46=39'] Exploring Operation: 39-5=34, Resulting Numbers: [80, 34] Generated Node #0,0,0: 85:[80, 34] Operation: 39-5=34 Exploring Operation: 80+5=85, Resulting Numbers: [39, 85] Generated Node #0,0,1: 85:[39, 85] Operation: 80+5=85 Moving to Node #0,0,0 Current State: 85:[80, 34], Operations: ['85-46=39', '39-5=34'] Exploring Operation: 80-34=46, Resulting Numbers: [46] 46,85 unequal: No Solution Exploring Operation: 80+34=114, Resulting Numbers: [114] 114,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[39, 85], Operations: ['85-46=39', '80+5=85'] Exploring Operation: 85-39=46, Resulting Numbers: [46] 46,85 unequal: No Solution Exploring Operation: 39+85=124, Resulting Numbers: [124] 124,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 31, 46, 34, 36 ]
58
[ "34-31=3", "36/3=12", "46+12=58" ]
Current State: 58:[31, 46, 34, 36], Operations: [] Exploring Operation: 34-31=3, Resulting Numbers: [46, 36, 3] Generated Node #2: [46, 36, 3] from Operation: 34-31=3 Current State: 58:[46, 36, 3], Operations: ['34-31=3'] Exploring Operation: 36/3=12, Resulting Numbers: [46, 12] Generated Node #3: [46, 12] from Operation: 36/3=12 Current State: 58:[46, 12], Operations: ['34-31=3', '36/3=12'] Exploring Operation: 46+12=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[31, 46, 34, 36], Operations: [] Exploring Operation: 36-34=2, Resulting Numbers: [31, 46, 2] Generated Node #0,0: 58:[31, 46, 2] Operation: 36-34=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[31, 46, 2], Operations: ['36-34=2'] Exploring Operation: 46/2=23, Resulting Numbers: [31, 23] Generated Node #0,0,0: 58:[31, 23] Operation: 46/2=23 Moving to Node #0,0,0 Current State: 58:[31, 23], Operations: ['36-34=2', '46/2=23'] Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,58 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
[ 6, 32, 18, 87 ]
61
[ "18/6=3", "87/3=29", "32+29=61" ]
Current State: 61:[6, 32, 18, 87], Operations: [] Exploring Operation: 18/6=3, Resulting Numbers: [32, 87, 3] Generated Node #2: [32, 87, 3] from Operation: 18/6=3 Current State: 61:[32, 87, 3], Operations: ['18/6=3'] Exploring Operation: 87/3=29, Resulting Numbers: [32, 29] Generated Node #3: [32, 29] from Operation: 87/3=29 Current State: 61:[32, 29], Operations: ['18/6=3', '87/3=29'] Exploring Operation: 32+29=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[6, 32, 18, 87], Operations: [] Exploring Operation: 87-6=81, Resulting Numbers: [32, 18, 81] Generated Node #0,0: 61:[32, 18, 81] Operation: 87-6=81 Exploring Operation: 32+18=50, Resulting Numbers: [6, 87, 50] Generated Node #0,1: 61:[6, 87, 50] Operation: 32+18=50 Exploring Operation: 87-18=69, Resulting Numbers: [6, 32, 69] Generated Node #0,2: 61:[6, 32, 69] Operation: 87-18=69 Exploring Operation: 6+18=24, Resulting Numbers: [32, 87, 24] Generated Node #0,3: 61:[32, 87, 24] Operation: 6+18=24 Exploring Operation: 6+32=38, Resulting Numbers: [18, 87, 38] Generated Node #0,4: 61:[18, 87, 38] Operation: 6+32=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[32, 18, 81], Operations: ['87-6=81'] Exploring Operation: 32+18=50, Resulting Numbers: [81, 50] Generated Node #0,0,0: 61:[81, 50] Operation: 32+18=50 Exploring Operation: 18+81=99, Resulting Numbers: [32, 99] Generated Node #0,0,1: 61:[32, 99] Operation: 18+81=99 Exploring Operation: 32-18=14, Resulting Numbers: [81, 14] Generated Node #0,0,2: 61:[81, 14] Operation: 32-18=14 Exploring Operation: 81-18=63, Resulting Numbers: [32, 63] Generated Node #0,0,3: 61:[32, 63] Operation: 81-18=63 Exploring Operation: 81-32=49, Resulting Numbers: [18, 49] Generated Node #0,0,4: 61:[18, 49] Operation: 81-32=49 Moving to Node #0,0,0 Current State: 61:[81, 50], Operations: ['87-6=81', '32+18=50'] Exploring Operation: 81-50=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 81*50=4050, Resulting Numbers: [4050] 4050,61 unequal: No Solution Exploring Operation: 81+50=131, Resulting Numbers: [131] 131,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[32, 63], Operations: ['87-6=81', '81-18=63'] Exploring Operation: 32+63=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 32*63=2016, Resulting Numbers: [2016] 2016,61 unequal: No Solution Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,61 unequal: No Solution Moving to Node #0,0,4 Current State: 61:[18, 49], Operations: ['87-6=81', '81-32=49'] Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 18+49=67, Resulting Numbers: [67] 67,61 unequal: No Solution Exploring Operation: 18*49=882, Resulting Numbers: [882] 882,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[32, 99], Operations: ['87-6=81', '18+81=99'] Exploring Operation: 32+99=131, Resulting Numbers: [131] 131,61 unequal: No Solution Exploring Operation: 32*99=3168, Resulting Numbers: [3168] 3168,61 unequal: No Solution Exploring Operation: 99-32=67, Resulting Numbers: [67] 67,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[81, 14], Operations: ['87-6=81', '32-18=14'] Exploring Operation: 81-14=67, Resulting Numbers: [67] 67,61 unequal: No Solution Exploring Operation: 81+14=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 81*14=1134, Resulting Numbers: [1134] 1134,61 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 Current State: 61:[6, 87, 50], Operations: ['32+18=50'] Exploring Operation: 6+87=93, Resulting Numbers: [50, 93] Generated Node #0,1,0: 61:[50, 93] Operation: 6+87=93 Exploring Operation: 50-6=44, Resulting Numbers: [87, 44] Generated Node #0,1,1: 61:[87, 44] Operation: 50-6=44 Exploring Operation: 87-50=37, Resulting Numbers: [6, 37] Generated Node #0,1,2: 61:[6, 37] Operation: 87-50=37 Exploring Operation: 87-6=81, Resulting Numbers: [50, 81] Generated Node #0,1,3: 61:[50, 81] Operation: 87-6=81 Exploring Operation: 6+50=56, Resulting Numbers: [87, 56] Generated Node #0,1,4: 61:[87, 56] Operation: 6+50=56 Moving to Node #0,1,3 Current State: 61:[50, 81], Operations: ['32+18=50', '87-6=81'] Exploring Operation: 81-50=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 50*81=4050, Resulting Numbers: [4050] 4050,61 unequal: No Solution Exploring Operation: 50+81=131, Resulting Numbers: [131] 131,61 unequal: No Solution Moving to Node #0,1,4 Current State: 61:[87, 56], Operations: ['32+18=50', '6+50=56'] Exploring Operation: 87*56=4872, Resulting Numbers: [4872] 4872,61 unequal: No Solution Exploring Operation: 87+56=143, Resulting Numbers: [143] 143,61 unequal: No Solution Exploring Operation: 87-56=31, Resulting Numbers: [31] 31,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[50, 93], Operations: ['32+18=50', '6+87=93'] Exploring Operation: 93-50=43, Resulting Numbers: [43] 43,61 unequal: No Solution Exploring Operation: 50+93=143, Resulting Numbers: [143] 143,61 unequal: No Solution Exploring Operation: 50*93=4650, Resulting Numbers: [4650] 4650,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[87, 44], Operations: ['32+18=50', '50-6=44'] Exploring Operation: 87+44=131, Resulting Numbers: [131] 131,61 unequal: No Solution Exploring Operation: 87*44=3828, Resulting Numbers: [3828] 3828,61 unequal: No Solution Exploring Operation: 87-44=43, Resulting Numbers: [43] 43,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[6, 37], Operations: ['32+18=50', '87-50=37'] Exploring Operation: 6*37=222, Resulting Numbers: [222] 222,61 unequal: No Solution Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,61 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[6, 32, 69], Operations: ['87-18=69'] Exploring Operation: 69-32=37, Resulting Numbers: [6, 37] Generated Node #0,2,0: 61:[6, 37] Operation: 69-32=37 Exploring Operation: 6+32=38, Resulting Numbers: [69, 38] Generated Node #0,2,1: 61:[69, 38] Operation: 6+32=38 Exploring Operation: 6+69=75, Resulting Numbers: [32, 75] Generated Node #0,2,2: 61:[32, 75] Operation: 6+69=75 Exploring Operation: 32-6=26, Resulting Numbers: [69, 26] Generated Node #0,2,3: 61:[69, 26] Operation: 32-6=26 Exploring Operation: 69-6=63, Resulting Numbers: [32, 63] Generated Node #0,2,4: 61:[32, 63] Operation: 69-6=63 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 61:[69, 38], Operations: ['87-18=69', '6+32=38'] Exploring Operation: 69+38=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 69*38=2622, Resulting Numbers: [2622] 2622,61 unequal: No Solution No 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: 61:[32, 63], Operations: ['87-18=69', '69-6=63'] Exploring Operation: 32+63=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 32*63=2016, Resulting Numbers: [2016] 2016,61 unequal: No Solution Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,61 unequal: No Solution No 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: 61:[32, 75], Operations: ['87-18=69', '6+69=75'] Exploring Operation: 32+75=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 32*75=2400, Resulting Numbers: [2400] 2400,61 unequal: No Solution Exploring Operation: 75-32=43, Resulting Numbers: [43] 43,61 unequal: No Solution No 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: 61:[69, 26], Operations: ['87-18=69', '32-6=26'] Exploring Operation: 69-26=43, Resulting Numbers: [43] 43,61 unequal: No Solution Exploring Operation: 69*26=1794, Resulting Numbers: [1794] 1794,61 unequal: No Solution Exploring Operation: 69+26=95, Resulting Numbers: [95] 95,61 unequal: No Solution No 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: 61:[6, 37], Operations: ['87-18=69', '69-32=37'] Exploring Operation: 6*37=222, Resulting Numbers: [222] 222,61 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,61 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: 61:[32, 87, 24], Operations: ['6+18=24'] Exploring Operation: 87+24=111, Resulting Numbers: [32, 111] Generated Node #0,3,0: 61:[32, 111] Operation: 87+24=111 Exploring Operation: 32+24=56, Resulting Numbers: [87, 56] Generated Node #0,3,1: 61:[87, 56] Operation: 32+24=56 Exploring Operation: 32-24=8, Resulting Numbers: [87, 8] Generated Node #0,3,2: 61:[87, 8] Operation: 32-24=8 Exploring Operation: 87-24=63, Resulting Numbers: [32, 63] Generated Node #0,3,3: 61:[32, 63] Operation: 87-24=63 Exploring Operation: 87-32=55, Resulting Numbers: [24, 55] Generated Node #0,3,4: 61:[24, 55] Operation: 87-32=55 Moving to Node #0,3,1 Current State: 61:[87, 56], Operations: ['6+18=24', '32+24=56'] Exploring Operation: 87+56=143, Resulting Numbers: [143] 143,61 unequal: No Solution Exploring Operation: 87*56=4872, Resulting Numbers: [4872] 4872,61 unequal: No Solution Exploring Operation: 87-56=31, Resulting Numbers: [31] 31,61 unequal: No Solution Moving to Node #0,3,3 Current State: 61:[32, 63], Operations: ['6+18=24', '87-24=63'] Exploring Operation: 32+63=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 32*63=2016, Resulting Numbers: [2016] 2016,61 unequal: No Solution Moving to Node #0,3,4 Current State: 61:[24, 55], Operations: ['6+18=24', '87-32=55'] Exploring Operation: 24*55=1320, Resulting Numbers: [1320] 1320,61 unequal: No Solution Exploring Operation: 55-24=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 24+55=79, Resulting Numbers: [79] 79,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[32, 111], Operations: ['6+18=24', '87+24=111'] Exploring Operation: 111-32=79, Resulting Numbers: [79] 79,61 unequal: No Solution Exploring Operation: 32*111=3552, Resulting Numbers: [3552] 3552,61 unequal: No Solution Exploring Operation: 32+111=143, Resulting Numbers: [143] 143,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[87, 8], Operations: ['6+18=24', '32-24=8'] Exploring Operation: 87+8=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 87-8=79, Resulting Numbers: [79] 79,61 unequal: No Solution Exploring Operation: 87*8=696, Resulting Numbers: [696] 696,61 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 #0,4 Current State: 61:[18, 87, 38], Operations: ['6+32=38'] Exploring Operation: 18+38=56, Resulting Numbers: [87, 56] Generated Node #0,4,0: 61:[87, 56] Operation: 18+38=56 Exploring Operation: 18+87=105, Resulting Numbers: [38, 105] Generated Node #0,4,1: 61:[38, 105] Operation: 18+87=105 Exploring Operation: 38-18=20, Resulting Numbers: [87, 20] Generated Node #0,4,2: 61:[87, 20] Operation: 38-18=20 Exploring Operation: 87-18=69, Resulting Numbers: [38, 69] Generated Node #0,4,3: 61:[38, 69] Operation: 87-18=69 Exploring Operation: 87-38=49, Resulting Numbers: [18, 49] Generated Node #0,4,4: 61:[18, 49] Operation: 87-38=49 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 61:[87, 56], Operations: ['6+32=38', '18+38=56'] Exploring Operation: 87+56=143, Resulting Numbers: [143] 143,61 unequal: No Solution Exploring Operation: 87-56=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 87*56=4872, Resulting Numbers: [4872] 4872,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 61:[38, 69], Operations: ['6+32=38', '87-18=69'] Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 38+69=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 38*69=2622, Resulting Numbers: [2622] 2622,61 unequal: No Solution No 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: 61:[18, 49], Operations: ['6+32=38', '87-38=49'] Exploring Operation: 18+49=67, Resulting Numbers: [67] 67,61 unequal: No Solution Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 18*49=882, Resulting Numbers: [882] 882,61 unequal: No Solution No 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: 61:[38, 105], Operations: ['6+32=38', '18+87=105'] Exploring Operation: 105-38=67, Resulting Numbers: [67] 67,61 unequal: No Solution Exploring Operation: 38*105=3990, Resulting Numbers: [3990] 3990,61 unequal: No Solution Exploring Operation: 38+105=143, Resulting Numbers: [143] 143,61 unequal: No Solution No 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: 61:[87, 20], Operations: ['6+32=38', '38-18=20'] Exploring Operation: 87*20=1740, Resulting Numbers: [1740] 1740,61 unequal: No Solution Exploring Operation: 87+20=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 87-20=67, Resulting Numbers: [67] 67,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 78, 95, 1, 83 ]
65
[ "95-78=17", "83-1=82", "82-17=65" ]
Current State: 65:[78, 95, 1, 83], Operations: [] Exploring Operation: 95-78=17, Resulting Numbers: [1, 83, 17] Generated Node #2: [1, 83, 17] from Operation: 95-78=17 Current State: 65:[1, 83, 17], Operations: ['95-78=17'] Exploring Operation: 83-1=82, Resulting Numbers: [17, 82] Generated Node #3: [17, 82] from Operation: 83-1=82 Current State: 65:[17, 82], Operations: ['95-78=17', '83-1=82'] Exploring Operation: 82-17=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[78, 95, 1, 83], Operations: [] Exploring Operation: 78-1=77, Resulting Numbers: [95, 83, 77] Generated Node #0,0: 65:[95, 83, 77] Operation: 78-1=77 Exploring Operation: 83-78=5, Resulting Numbers: [95, 1, 5] Generated Node #0,1: 65:[95, 1, 5] Operation: 83-78=5 Exploring Operation: 95-83=12, Resulting Numbers: [78, 1, 12] Generated Node #0,2: 65:[78, 1, 12] Operation: 95-83=12 Exploring Operation: 95-78=17, Resulting Numbers: [1, 83, 17] Generated Node #0,3: 65:[1, 83, 17] Operation: 95-78=17 Moving to Node #0,2 Current State: 65:[78, 1, 12], Operations: ['95-83=12'] Exploring Operation: 78-12=66, Resulting Numbers: [1, 66] Generated Node #0,2,0: 65:[1, 66] Operation: 78-12=66 Exploring Operation: 1+12=13, Resulting Numbers: [78, 13] Generated Node #0,2,1: 65:[78, 13] Operation: 1+12=13 Exploring Operation: 78-1=77, Resulting Numbers: [12, 77] Generated Node #0,2,2: 65:[12, 77] Operation: 78-1=77 Exploring Operation: 78*1=78, Resulting Numbers: [12, 78] Generated Node #0,2,3: 65:[12, 78] Operation: 78*1=78 Moving to Node #0,3 Current State: 65:[1, 83, 17], Operations: ['95-78=17'] Exploring Operation: 83-1=82, Resulting Numbers: [17, 82] Generated Node #0,3,0: 65:[17, 82] Operation: 83-1=82 Exploring Operation: 1*83=83, Resulting Numbers: [17, 83] Generated Node #0,3,1: 65:[17, 83] Operation: 1*83=83 Exploring Operation: 83-17=66, Resulting Numbers: [1, 66] Generated Node #0,3,2: 65:[1, 66] Operation: 83-17=66 Exploring Operation: 17-1=16, Resulting Numbers: [83, 16] Generated Node #0,3,3: 65:[83, 16] Operation: 17-1=16 Moving to Node #0,1 Current State: 65:[95, 1, 5], Operations: ['83-78=5'] Exploring Operation: 95*1=95, Resulting Numbers: [5, 95] Generated Node #0,1,0: 65:[5, 95] Operation: 95*1=95 Exploring Operation: 95-5=90, Resulting Numbers: [1, 90] Generated Node #0,1,1: 65:[1, 90] Operation: 95-5=90 Exploring Operation: 95/5=19, Resulting Numbers: [1, 19] Generated Node #0,1,2: 65:[1, 19] Operation: 95/5=19 Exploring Operation: 95-1=94, Resulting Numbers: [5, 94] Generated Node #0,1,3: 65:[5, 94] Operation: 95-1=94 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[1, 19], Operations: ['83-78=5', '95/5=19'] Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,65 unequal: No Solution Exploring Operation: 1+19=20, Resulting Numbers: [20] 20,65 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,65 unequal: No Solution Exploring Operation: 1*19=19, Resulting Numbers: [19] 19,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[1, 90], Operations: ['83-78=5', '95-5=90'] Exploring Operation: 1+90=91, Resulting Numbers: [91] 91,65 unequal: No Solution Exploring Operation: 90-1=89, Resulting Numbers: [89] 89,65 unequal: No Solution Exploring Operation: 90/1=90, Resulting Numbers: [90] 90,65 unequal: No Solution Exploring Operation: 1*90=90, Resulting Numbers: [90] 90,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 65:[5, 94], Operations: ['83-78=5', '95-1=94'] Exploring Operation: 5+94=99, Resulting Numbers: [99] 99,65 unequal: No Solution Exploring Operation: 5*94=470, Resulting Numbers: [470] 470,65 unequal: No Solution Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[5, 95], Operations: ['83-78=5', '95*1=95'] Exploring Operation: 5+95=100, Resulting Numbers: [100] 100,65 unequal: No Solution Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,65 unequal: No Solution Exploring Operation: 95-5=90, Resulting Numbers: [90] 90,65 unequal: No Solution Exploring Operation: 5*95=475, Resulting Numbers: [475] 475,65 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: 65:[95, 83, 77], Operations: ['78-1=77'] Exploring Operation: 95+83=178, Resulting Numbers: [77, 178] Generated Node #0,0,0: 65:[77, 178] Operation: 95+83=178 Exploring Operation: 95-77=18, Resulting Numbers: [83, 18] Generated Node #0,0,1: 65:[83, 18] Operation: 95-77=18 Exploring Operation: 83-77=6, Resulting Numbers: [95, 6] Generated Node #0,0,2: 65:[95, 6] Operation: 83-77=6 Exploring Operation: 95-83=12, Resulting Numbers: [77, 12] Generated Node #0,0,3: 65:[77, 12] Operation: 95-83=12 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 65:[77, 12], Operations: ['78-1=77', '95-83=12'] Exploring Operation: 77-12=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[78, 95, 1, 83], Operations: [] Exploring Operation: 78-1=77, Resulting Numbers: [95, 83, 77] Generated Node #0,0: 65:[95, 83, 77] Operation: 78-1=77 Moving to Node #0,0 Current State: 65:[95, 83, 77], Operations: ['78-1=77'] Exploring Operation: 95-83=12, Resulting Numbers: [77, 12] Generated Node #0,0,3: 65:[77, 12] Operation: 95-83=12 Moving to Node #0,0,3 Current State: 65:[77, 12], Operations: ['78-1=77', '95-83=12'] Exploring Operation: 77-12=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_4
sum_heuristic
[ 35, 44, 92, 81 ]
99
[ "44-35=9", "92-81=11", "9*11=99" ]
Current State: 99:[35, 44, 92, 81], Operations: [] Exploring Operation: 44-35=9, Resulting Numbers: [92, 81, 9] Generated Node #2: [92, 81, 9] from Operation: 44-35=9 Current State: 99:[92, 81, 9], Operations: ['44-35=9'] Exploring Operation: 92-81=11, Resulting Numbers: [9, 11] Generated Node #3: [9, 11] from Operation: 92-81=11 Current State: 99:[9, 11], Operations: ['44-35=9', '92-81=11'] Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[35, 44, 92, 81], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [35, 44, 11] Generated Node #0,0: 99:[35, 44, 11] Operation: 92-81=11 Exploring Operation: 81-44=37, Resulting Numbers: [35, 92, 37] Generated Node #0,1: 99:[35, 92, 37] Operation: 81-44=37 Moving to Node #0,0 Current State: 99:[35, 44, 11], Operations: ['92-81=11'] Exploring Operation: 44-35=9, Resulting Numbers: [11, 9] Generated Node #0,0,0: 99:[11, 9] Operation: 44-35=9 Exploring Operation: 44-11=33, Resulting Numbers: [35, 33] Generated Node #0,0,1: 99:[35, 33] Operation: 44-11=33 Moving to Node #0,1 Current State: 99:[35, 92, 37], Operations: ['81-44=37'] Exploring Operation: 37-35=2, Resulting Numbers: [92, 2] Generated Node #0,1,0: 99:[92, 2] Operation: 37-35=2 Exploring Operation: 92-37=55, Resulting Numbers: [35, 55] Generated Node #0,1,1: 99:[35, 55] Operation: 92-37=55 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[92, 2], Operations: ['81-44=37', '37-35=2'] Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,99 unequal: No Solution Exploring Operation: 92+2=94, Resulting Numbers: [94] 94,99 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 #0,1,1 Current State: 99:[35, 55], Operations: ['81-44=37', '92-37=55'] Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,99 unequal: No Solution Exploring Operation: 35+55=90, Resulting Numbers: [90] 90,99 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: 99:[11, 9], Operations: ['92-81=11', '44-35=9'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,99 unequal: No Solution Exploring Operation: 11*9=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[35, 44, 92, 81], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [35, 44, 11] Generated Node #0,0: 99:[35, 44, 11] Operation: 92-81=11 Moving to Node #0,0 Current State: 99:[35, 44, 11], Operations: ['92-81=11'] Exploring Operation: 44-35=9, Resulting Numbers: [11, 9] Generated Node #0,0,0: 99:[11, 9] Operation: 44-35=9 Moving to Node #0,0,0 Current State: 99:[11, 9], Operations: ['92-81=11', '44-35=9'] Exploring Operation: 11*9=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 83, 90, 81, 6 ]
30
[ "83-81=2", "90/6=15", "2*15=30" ]
Current State: 30:[83, 90, 81, 6], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [90, 6, 2] Generated Node #2: [90, 6, 2] from Operation: 83-81=2 Current State: 30:[90, 6, 2], Operations: ['83-81=2'] Exploring Operation: 90/6=15, Resulting Numbers: [2, 15] Generated Node #3: [2, 15] from Operation: 90/6=15 Current State: 30:[2, 15], Operations: ['83-81=2', '90/6=15'] Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[83, 90, 81, 6], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [90, 6, 2] Generated Node #0,0: 30:[90, 6, 2] Operation: 83-81=2 Exploring Operation: 90-83=7, Resulting Numbers: [81, 6, 7] Generated Node #0,1: 30:[81, 6, 7] Operation: 90-83=7 Exploring Operation: 90-81=9, Resulting Numbers: [83, 6, 9] Generated Node #0,2: 30:[83, 6, 9] Operation: 90-81=9 Exploring Operation: 90/6=15, Resulting Numbers: [83, 81, 15] Generated Node #0,3: 30:[83, 81, 15] Operation: 90/6=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[81, 6, 7], Operations: ['90-83=7'] Exploring Operation: 6+7=13, Resulting Numbers: [81, 13] Generated Node #0,1,0: 30:[81, 13] Operation: 6+7=13 Exploring Operation: 7-6=1, Resulting Numbers: [81, 1] Generated Node #0,1,1: 30:[81, 1] Operation: 7-6=1 Exploring Operation: 81-7=74, Resulting Numbers: [6, 74] Generated Node #0,1,2: 30:[6, 74] Operation: 81-7=74 Exploring Operation: 81-6=75, Resulting Numbers: [7, 75] Generated Node #0,1,3: 30:[7, 75] Operation: 81-6=75 Moving to Node #0,1,2 Current State: 30:[6, 74], Operations: ['90-83=7', '81-7=74'] Exploring Operation: 6+74=80, Resulting Numbers: [80] 80,30 unequal: No Solution Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,30 unequal: No Solution Exploring Operation: 6*74=444, Resulting Numbers: [444] 444,30 unequal: No Solution Moving to Node #0,1,3 Current State: 30:[7, 75], Operations: ['90-83=7', '81-6=75'] Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,30 unequal: No Solution Exploring Operation: 7*75=525, Resulting Numbers: [525] 525,30 unequal: No Solution Exploring Operation: 7+75=82, Resulting Numbers: [82] 82,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[81, 1], Operations: ['90-83=7', '7-6=1'] Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,30 unequal: No Solution Exploring Operation: 81+1=82, Resulting Numbers: [82] 82,30 unequal: No Solution Exploring Operation: 81/1=81, Resulting Numbers: [81] 81,30 unequal: No Solution Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[81, 13], Operations: ['90-83=7', '6+7=13'] Exploring Operation: 81+13=94, Resulting Numbers: [94] 94,30 unequal: No Solution Exploring Operation: 81*13=1053, Resulting Numbers: [1053] 1053,30 unequal: No Solution Exploring Operation: 81-13=68, Resulting Numbers: [68] 68,30 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:[83, 6, 9], Operations: ['90-81=9'] Exploring Operation: 6+9=15, Resulting Numbers: [83, 15] Generated Node #0,2,0: 30:[83, 15] Operation: 6+9=15 Exploring Operation: 83-9=74, Resulting Numbers: [6, 74] Generated Node #0,2,1: 30:[6, 74] Operation: 83-9=74 Exploring Operation: 9-6=3, Resulting Numbers: [83, 3] Generated Node #0,2,2: 30:[83, 3] Operation: 9-6=3 Exploring Operation: 83-6=77, Resulting Numbers: [9, 77] Generated Node #0,2,3: 30:[9, 77] Operation: 83-6=77 Moving to Node #0,2,1 Current State: 30:[6, 74], Operations: ['90-81=9', '83-9=74'] Exploring Operation: 6+74=80, Resulting Numbers: [80] 80,30 unequal: No Solution Exploring Operation: 6*74=444, Resulting Numbers: [444] 444,30 unequal: No Solution Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,30 unequal: No Solution Moving to Node #0,2,3 Current State: 30:[9, 77], Operations: ['90-81=9', '83-6=77'] Exploring Operation: 9*77=693, Resulting Numbers: [693] 693,30 unequal: No Solution Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,30 unequal: No Solution Exploring Operation: 9+77=86, Resulting Numbers: [86] 86,30 unequal: No Solution Moving to Node #0,2,2 Current State: 30:[83, 3], Operations: ['90-81=9', '9-6=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,30 unequal: No Solution Exploring Operation: 83-3=80, Resulting Numbers: [80] 80,30 unequal: No Solution Exploring Operation: 83*3=249, Resulting Numbers: [249] 249,30 unequal: No Solution Moving to Node #0,2,0 Current State: 30:[83, 15], Operations: ['90-81=9', '6+9=15'] Exploring Operation: 83-15=68, Resulting Numbers: [68] 68,30 unequal: No Solution Exploring Operation: 83*15=1245, Resulting Numbers: [1245] 1245,30 unequal: No Solution Exploring Operation: 83+15=98, Resulting Numbers: [98] 98,30 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 #0,0 Current State: 30:[90, 6, 2], Operations: ['83-81=2'] Exploring Operation: 90-2=88, Resulting Numbers: [6, 88] Generated Node #0,0,0: 30:[6, 88] Operation: 90-2=88 Exploring Operation: 90/2=45, Resulting Numbers: [6, 45] Generated Node #0,0,1: 30:[6, 45] Operation: 90/2=45 Exploring Operation: 90-6=84, Resulting Numbers: [2, 84] Generated Node #0,0,2: 30:[2, 84] Operation: 90-6=84 Exploring Operation: 90/6=15, Resulting Numbers: [2, 15] Generated Node #0,0,3: 30:[2, 15] Operation: 90/6=15 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 30:[2, 15], Operations: ['83-81=2', '90/6=15'] Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[83, 90, 81, 6], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [90, 6, 2] Generated Node #0,0: 30:[90, 6, 2] Operation: 83-81=2 Moving to Node #0,0 Current State: 30:[90, 6, 2], Operations: ['83-81=2'] Exploring Operation: 90/6=15, Resulting Numbers: [2, 15] Generated Node #0,0,3: 30:[2, 15] Operation: 90/6=15 Moving to Node #0,0,3 Current State: 30:[2, 15], Operations: ['83-81=2', '90/6=15'] Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.959201
hs_4
mult_heuristic
[ 58, 64, 9, 1 ]
65
[ "64-1=63", "63/9=7", "58+7=65" ]
Current State: 65:[58, 64, 9, 1], Operations: [] Exploring Operation: 64-1=63, Resulting Numbers: [58, 9, 63] Generated Node #2: [58, 9, 63] from Operation: 64-1=63 Current State: 65:[58, 9, 63], Operations: ['64-1=63'] Exploring Operation: 63/9=7, Resulting Numbers: [58, 7] Generated Node #3: [58, 7] from Operation: 63/9=7 Current State: 65:[58, 7], Operations: ['64-1=63', '63/9=7'] Exploring Operation: 58+7=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[58, 64, 9, 1], Operations: [] Exploring Operation: 58+9=67, Resulting Numbers: [64, 1, 67] Generated Node #0,0: 65:[64, 1, 67] Operation: 58+9=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[64, 1, 67], Operations: ['58+9=67'] Exploring Operation: 64+1=65, Resulting Numbers: [67, 65] Generated Node #0,0,0: 65:[67, 65] Operation: 64+1=65 Moving to Node #0,0,0 Current State: 65:[67, 65], Operations: ['58+9=67', '64+1=65'] Exploring Operation: 67-65=2, Resulting Numbers: [2] 2,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 62, 20, 8, 32 ]
67
[ "20*8=160", "160/32=5", "62+5=67" ]
Current State: 67:[62, 20, 8, 32], Operations: [] Exploring Operation: 20*8=160, Resulting Numbers: [62, 32, 160] Generated Node #2: [62, 32, 160] from Operation: 20*8=160 Current State: 67:[62, 32, 160], Operations: ['20*8=160'] Exploring Operation: 160/32=5, Resulting Numbers: [62, 5] Generated Node #3: [62, 5] from Operation: 160/32=5 Current State: 67:[62, 5], Operations: ['20*8=160', '160/32=5'] Exploring Operation: 62+5=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[62, 20, 8, 32], Operations: [] Exploring Operation: 62+8=70, Resulting Numbers: [20, 32, 70] Generated Node #0,0: 67:[20, 32, 70] Operation: 62+8=70 Exploring Operation: 20+32=52, Resulting Numbers: [62, 8, 52] Generated Node #0,1: 67:[62, 8, 52] Operation: 20+32=52 Exploring Operation: 62-8=54, Resulting Numbers: [20, 32, 54] Generated Node #0,2: 67:[20, 32, 54] Operation: 62-8=54 Exploring Operation: 20+8=28, Resulting Numbers: [62, 32, 28] Generated Node #0,3: 67:[62, 32, 28] Operation: 20+8=28 Exploring Operation: 8+32=40, Resulting Numbers: [62, 20, 40] Generated Node #0,4: 67:[62, 20, 40] Operation: 8+32=40 Moving to Node #0,1 Current State: 67:[62, 8, 52], Operations: ['20+32=52'] Exploring Operation: 52-8=44, Resulting Numbers: [62, 44] Generated Node #0,1,0: 67:[62, 44] Operation: 52-8=44 Exploring Operation: 62+8=70, Resulting Numbers: [52, 70] Generated Node #0,1,1: 67:[52, 70] Operation: 62+8=70 Exploring Operation: 8+52=60, Resulting Numbers: [62, 60] Generated Node #0,1,2: 67:[62, 60] Operation: 8+52=60 Exploring Operation: 62-8=54, Resulting Numbers: [52, 54] Generated Node #0,1,3: 67:[52, 54] Operation: 62-8=54 Exploring Operation: 62+52=114, Resulting Numbers: [8, 114] Generated Node #0,1,4: 67:[8, 114] Operation: 62+52=114 Moving to Node #0,4 Current State: 67:[62, 20, 40], Operations: ['8+32=40'] Exploring Operation: 40/20=2, Resulting Numbers: [62, 2] Generated Node #0,4,0: 67:[62, 2] Operation: 40/20=2 Exploring Operation: 40-20=20, Resulting Numbers: [62, 20] Generated Node #0,4,1: 67:[62, 20] Operation: 40-20=20 Exploring Operation: 62-20=42, Resulting Numbers: [40, 42] Generated Node #0,4,2: 67:[40, 42] Operation: 62-20=42 Exploring Operation: 62+20=82, Resulting Numbers: [40, 82] Generated Node #0,4,3: 67:[40, 82] Operation: 62+20=82 Exploring Operation: 20+40=60, Resulting Numbers: [62, 60] Generated Node #0,4,4: 67:[62, 60] Operation: 20+40=60 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 67:[62, 60], Operations: ['8+32=40', '20+40=60'] Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 62+60=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 62*60=3720, Resulting Numbers: [3720] 3720,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 67:[40, 82], Operations: ['8+32=40', '62+20=82'] Exploring Operation: 40*82=3280, Resulting Numbers: [3280] 3280,67 unequal: No Solution Exploring Operation: 82-40=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 40+82=122, Resulting Numbers: [122] 122,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 67:[62, 20], Operations: ['8+32=40', '40-20=20'] Exploring Operation: 62*20=1240, Resulting Numbers: [1240] 1240,67 unequal: No Solution Exploring Operation: 62+20=82, Resulting Numbers: [82] 82,67 unequal: No Solution Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 67:[40, 42], Operations: ['8+32=40', '62-20=42'] Exploring Operation: 40*42=1680, Resulting Numbers: [1680] 1680,67 unequal: No Solution Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 40+42=82, Resulting Numbers: [82] 82,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 67:[62, 2], Operations: ['8+32=40', '40/20=2'] Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,67 unequal: No Solution Exploring Operation: 62*2=124, Resulting Numbers: [124] 124,67 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,67 unequal: No Solution Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,67 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: 67:[62, 32, 28], Operations: ['20+8=28'] Exploring Operation: 32-28=4, Resulting Numbers: [62, 4] Generated Node #0,3,0: 67:[62, 4] Operation: 32-28=4 Exploring Operation: 32+28=60, Resulting Numbers: [62, 60] Generated Node #0,3,1: 67:[62, 60] Operation: 32+28=60 Exploring Operation: 62-28=34, Resulting Numbers: [32, 34] Generated Node #0,3,2: 67:[32, 34] Operation: 62-28=34 Exploring Operation: 62+28=90, Resulting Numbers: [32, 90] Generated Node #0,3,3: 67:[32, 90] Operation: 62+28=90 Exploring Operation: 62+32=94, Resulting Numbers: [28, 94] Generated Node #0,3,4: 67:[28, 94] Operation: 62+32=94 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 67:[62, 60], Operations: ['20+8=28', '32+28=60'] Exploring Operation: 62*60=3720, Resulting Numbers: [3720] 3720,67 unequal: No Solution Exploring Operation: 62+60=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 67:[32, 90], Operations: ['20+8=28', '62+28=90'] Exploring Operation: 32*90=2880, Resulting Numbers: [2880] 2880,67 unequal: No Solution Exploring Operation: 32+90=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 90-32=58, Resulting Numbers: [58] 58,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 67:[28, 94], Operations: ['20+8=28', '62+32=94'] Exploring Operation: 28+94=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 94-28=66, Resulting Numbers: [66] 66,67 unequal: No Solution Exploring Operation: 28*94=2632, Resulting Numbers: [2632] 2632,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 67:[62, 4], Operations: ['20+8=28', '32-28=4'] Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,67 unequal: No Solution Exploring Operation: 62+4=66, Resulting Numbers: [66] 66,67 unequal: No Solution Exploring Operation: 62*4=248, Resulting Numbers: [248] 248,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 67:[32, 34], Operations: ['20+8=28', '62-28=34'] Exploring Operation: 32+34=66, Resulting Numbers: [66] 66,67 unequal: No Solution Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 32*34=1088, Resulting Numbers: [1088] 1088,67 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: 67:[20, 32, 70], Operations: ['62+8=70'] Exploring Operation: 70-20=50, Resulting Numbers: [32, 50] Generated Node #0,0,0: 67:[32, 50] Operation: 70-20=50 Exploring Operation: 20+32=52, Resulting Numbers: [70, 52] Generated Node #0,0,1: 67:[70, 52] Operation: 20+32=52 Exploring Operation: 20+70=90, Resulting Numbers: [32, 90] Generated Node #0,0,2: 67:[32, 90] Operation: 20+70=90 Exploring Operation: 70-32=38, Resulting Numbers: [20, 38] Generated Node #0,0,3: 67:[20, 38] Operation: 70-32=38 Exploring Operation: 32-20=12, Resulting Numbers: [70, 12] Generated Node #0,0,4: 67:[70, 12] Operation: 32-20=12 Moving to Node #0,2 Current State: 67:[20, 32, 54], Operations: ['62-8=54'] Exploring Operation: 54-20=34, Resulting Numbers: [32, 34] Generated Node #0,2,0: 67:[32, 34] Operation: 54-20=34 Exploring Operation: 32-20=12, Resulting Numbers: [54, 12] Generated Node #0,2,1: 67:[54, 12] Operation: 32-20=12 Exploring Operation: 32+54=86, Resulting Numbers: [20, 86] Generated Node #0,2,2: 67:[20, 86] Operation: 32+54=86 Exploring Operation: 20+54=74, Resulting Numbers: [32, 74] Generated Node #0,2,3: 67:[32, 74] Operation: 20+54=74 Exploring Operation: 20+32=52, Resulting Numbers: [54, 52] Generated Node #0,2,4: 67:[54, 52] Operation: 20+32=52 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 67:[54, 52], Operations: ['62-8=54', '20+32=52'] Exploring Operation: 54+52=106, Resulting Numbers: [106] 106,67 unequal: No Solution Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 54*52=2808, Resulting Numbers: [2808] 2808,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 67:[32, 74], Operations: ['62-8=54', '20+54=74'] Exploring Operation: 74-32=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 32*74=2368, Resulting Numbers: [2368] 2368,67 unequal: No Solution Exploring Operation: 32+74=106, Resulting Numbers: [106] 106,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 67:[20, 86], Operations: ['62-8=54', '32+54=86'] Exploring Operation: 86-20=66, Resulting Numbers: [66] 66,67 unequal: No Solution Exploring Operation: 20+86=106, Resulting Numbers: [106] 106,67 unequal: No Solution Exploring Operation: 20*86=1720, Resulting Numbers: [1720] 1720,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[32, 34], Operations: ['62-8=54', '54-20=34'] Exploring Operation: 32+34=66, Resulting Numbers: [66] 66,67 unequal: No Solution Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 32*34=1088, Resulting Numbers: [1088] 1088,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[54, 12], Operations: ['62-8=54', '32-20=12'] Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,67 unequal: No Solution Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,67 unequal: No Solution Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,67 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: 67:[62, 60], Operations: ['20+32=52', '8+52=60'] Exploring Operation: 62+60=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 62*60=3720, Resulting Numbers: [3720] 3720,67 unequal: No Solution Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[70, 52], Operations: ['62+8=70', '20+32=52'] Exploring Operation: 70+52=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 70*52=3640, Resulting Numbers: [3640] 3640,67 unequal: No Solution Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[52, 70], Operations: ['20+32=52', '62+8=70'] Exploring Operation: 52+70=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,67 unequal: No Solution Exploring Operation: 52*70=3640, Resulting Numbers: [3640] 3640,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[62, 44], Operations: ['20+32=52', '52-8=44'] Exploring Operation: 62-44=18, Resulting Numbers: [18] 18,67 unequal: No Solution Exploring Operation: 62*44=2728, Resulting Numbers: [2728] 2728,67 unequal: No Solution Exploring Operation: 62+44=106, Resulting Numbers: [106] 106,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[52, 54], Operations: ['20+32=52', '62-8=54'] Exploring Operation: 52*54=2808, Resulting Numbers: [2808] 2808,67 unequal: No Solution Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 52+54=106, Resulting Numbers: [106] 106,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[32, 50], Operations: ['62+8=70', '70-20=50'] Exploring Operation: 32*50=1600, Resulting Numbers: [1600] 1600,67 unequal: No Solution Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,67 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[32, 90], Operations: ['62+8=70', '20+70=90'] Exploring Operation: 32*90=2880, Resulting Numbers: [2880] 2880,67 unequal: No Solution Exploring Operation: 90-32=58, Resulting Numbers: [58] 58,67 unequal: No Solution Exploring Operation: 32+90=122, Resulting Numbers: [122] 122,67 unequal: No Solution Moving to Node #0,0,4 Current State: 67:[70, 12], Operations: ['62+8=70', '32-20=12'] Exploring Operation: 70-12=58, Resulting Numbers: [58] 58,67 unequal: No Solution Exploring Operation: 70*12=840, Resulting Numbers: [840] 840,67 unequal: No Solution Exploring Operation: 70+12=82, Resulting Numbers: [82] 82,67 unequal: No Solution Moving to Node #0,0,3 Current State: 67:[20, 38], Operations: ['62+8=70', '70-32=38'] Exploring Operation: 20+38=58, Resulting Numbers: [58] 58,67 unequal: No Solution Exploring Operation: 20*38=760, Resulting Numbers: [760] 760,67 unequal: No Solution Exploring Operation: 38-20=18, Resulting Numbers: [18] 18,67 unequal: No Solution Moving to Node #0,1,4 Current State: 67:[8, 114], Operations: ['20+32=52', '62+52=114'] Exploring Operation: 8*114=912, Resulting Numbers: [912] 912,67 unequal: No Solution Exploring Operation: 8+114=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 114-8=106, Resulting Numbers: [106] 106,67 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 24, 9, 3, 43 ]
22
[ "43-24=19", "9/3=3", "19+3=22" ]
Current State: 22:[24, 9, 3, 43], Operations: [] Exploring Operation: 43-24=19, Resulting Numbers: [9, 3, 19] Generated Node #2: [9, 3, 19] from Operation: 43-24=19 Current State: 22:[9, 3, 19], Operations: ['43-24=19'] Exploring Operation: 9/3=3, Resulting Numbers: [19, 3] Generated Node #3: [19, 3] from Operation: 9/3=3 Current State: 22:[19, 3], Operations: ['43-24=19', '9/3=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[24, 9, 3, 43], Operations: [] Exploring Operation: 43-24=19, Resulting Numbers: [9, 3, 19] Generated Node #0,0: 22:[9, 3, 19] Operation: 43-24=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[9, 3, 19], Operations: ['43-24=19'] Exploring Operation: 19-9=10, Resulting Numbers: [3, 10] Generated Node #0,0,0: 22:[3, 10] Operation: 19-9=10 Moving to Node #0,0,0 Current State: 22:[3, 10], Operations: ['43-24=19', '19-9=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 30, 96, 2, 19 ]
37
[ "30-19=11", "96/2=48", "48-11=37" ]
Current State: 37:[30, 96, 2, 19], Operations: [] Exploring Operation: 30-19=11, Resulting Numbers: [96, 2, 11] Generated Node #2: [96, 2, 11] from Operation: 30-19=11 Current State: 37:[96, 2, 11], Operations: ['30-19=11'] Exploring Operation: 96/2=48, Resulting Numbers: [11, 48] Generated Node #3: [11, 48] from Operation: 96/2=48 Current State: 37:[11, 48], Operations: ['30-19=11', '96/2=48'] Exploring Operation: 48-11=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[30, 96, 2, 19], Operations: [] Exploring Operation: 96/2=48, Resulting Numbers: [30, 19, 48] Generated Node #0,0: 37:[30, 19, 48] Operation: 96/2=48 Exploring Operation: 2*19=38, Resulting Numbers: [30, 96, 38] Generated Node #0,1: 37:[30, 96, 38] Operation: 2*19=38 Moving to Node #0,0 Current State: 37:[30, 19, 48], Operations: ['96/2=48'] Exploring Operation: 30+19=49, Resulting Numbers: [48, 49] Generated Node #0,0,0: 37:[48, 49] Operation: 30+19=49 Exploring Operation: 48-19=29, Resulting Numbers: [30, 29] Generated Node #0,0,1: 37:[30, 29] Operation: 48-19=29 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[30, 29], Operations: ['96/2=48', '48-19=29'] Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 30+29=59, Resulting Numbers: [59] 59,37 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:[48, 49], Operations: ['96/2=48', '30+19=49'] Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 48+49=97, Resulting Numbers: [97] 97,37 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:[30, 96, 38], Operations: ['2*19=38'] Exploring Operation: 96-30=66, Resulting Numbers: [38, 66] Generated Node #0,1,0: 37:[38, 66] Operation: 96-30=66 Exploring Operation: 96-38=58, Resulting Numbers: [30, 58] Generated Node #0,1,1: 37:[30, 58] Operation: 96-38=58 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 37:[30, 58], Operations: ['2*19=38', '96-38=58'] Exploring Operation: 30+58=88, Resulting Numbers: [88] 88,37 unequal: No Solution Exploring Operation: 58-30=28, Resulting Numbers: [28] 28,37 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 #0,1,0 Current State: 37:[38, 66], Operations: ['2*19=38', '96-30=66'] Exploring Operation: 38+66=104, Resulting Numbers: [104] 104,37 unequal: No Solution Exploring Operation: 66-38=28, Resulting Numbers: [28] 28,37 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
[ 30, 4, 49, 81 ]
58
[ "30-4=26", "81-49=32", "26+32=58" ]
Current State: 58:[30, 4, 49, 81], Operations: [] Exploring Operation: 30-4=26, Resulting Numbers: [49, 81, 26] Generated Node #2: [49, 81, 26] from Operation: 30-4=26 Current State: 58:[49, 81, 26], Operations: ['30-4=26'] Exploring Operation: 81-49=32, Resulting Numbers: [26, 32] Generated Node #3: [26, 32] from Operation: 81-49=32 Current State: 58:[26, 32], Operations: ['30-4=26', '81-49=32'] Exploring Operation: 26+32=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[30, 4, 49, 81], Operations: [] Exploring Operation: 81-49=32, Resulting Numbers: [30, 4, 32] Generated Node #0,0: 58:[30, 4, 32] Operation: 81-49=32 Moving to Node #0,0 Current State: 58:[30, 4, 32], Operations: ['81-49=32'] Exploring Operation: 32-30=2, Resulting Numbers: [4, 2] Generated Node #0,0,0: 58:[4, 2] Operation: 32-30=2 Moving to Node #0,0,0 Current State: 58:[4, 2], Operations: ['81-49=32', '32-30=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,58 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 73, 18, 22, 14 ]
71
[ "22+14=36", "36/18=2", "73-2=71" ]
Current State: 71:[73, 18, 22, 14], Operations: [] Exploring Operation: 22+14=36, Resulting Numbers: [73, 18, 36] Generated Node #2: [73, 18, 36] from Operation: 22+14=36 Current State: 71:[73, 18, 36], Operations: ['22+14=36'] Exploring Operation: 36/18=2, Resulting Numbers: [73, 2] Generated Node #3: [73, 2] from Operation: 36/18=2 Current State: 71:[73, 2], Operations: ['22+14=36', '36/18=2'] Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[73, 18, 22, 14], Operations: [] Exploring Operation: 18+22=40, Resulting Numbers: [73, 14, 40] Generated Node #0,0: 71:[73, 14, 40] Operation: 18+22=40 Exploring Operation: 22+14=36, Resulting Numbers: [73, 18, 36] Generated Node #0,1: 71:[73, 18, 36] Operation: 22+14=36 Exploring Operation: 18+14=32, Resulting Numbers: [73, 22, 32] Generated Node #0,2: 71:[73, 22, 32] Operation: 18+14=32 Moving to Node #0,0 Current State: 71:[73, 14, 40], Operations: ['18+22=40'] Exploring Operation: 73-14=59, Resulting Numbers: [40, 59] Generated Node #0,0,0: 71:[40, 59] Operation: 73-14=59 Exploring Operation: 73+14=87, Resulting Numbers: [40, 87] Generated Node #0,0,1: 71:[40, 87] Operation: 73+14=87 Exploring Operation: 14+40=54, Resulting Numbers: [73, 54] Generated Node #0,0,2: 71:[73, 54] Operation: 14+40=54 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 71:[73, 54], Operations: ['18+22=40', '14+40=54'] Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,71 unequal: No Solution Exploring Operation: 73+54=127, Resulting Numbers: [127] 127,71 unequal: No Solution Exploring Operation: 73*54=3942, Resulting Numbers: [3942] 3942,71 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:[40, 59], Operations: ['18+22=40', '73-14=59'] Exploring Operation: 40+59=99, Resulting Numbers: [99] 99,71 unequal: No Solution Exploring Operation: 40*59=2360, Resulting Numbers: [2360] 2360,71 unequal: No Solution Exploring Operation: 59-40=19, Resulting Numbers: [19] 19,71 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:[40, 87], Operations: ['18+22=40', '73+14=87'] Exploring Operation: 40*87=3480, Resulting Numbers: [3480] 3480,71 unequal: No Solution Exploring Operation: 40+87=127, Resulting Numbers: [127] 127,71 unequal: No Solution Exploring Operation: 87-40=47, Resulting Numbers: [47] 47,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 71:[73, 18, 36], Operations: ['22+14=36'] Exploring Operation: 18+36=54, Resulting Numbers: [73, 54] Generated Node #0,1,0: 71:[73, 54] Operation: 18+36=54 Exploring Operation: 73-18=55, Resulting Numbers: [36, 55] Generated Node #0,1,1: 71:[36, 55] Operation: 73-18=55 Exploring Operation: 73+18=91, Resulting Numbers: [36, 91] Generated Node #0,1,2: 71:[36, 91] Operation: 73+18=91 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 71:[73, 54], Operations: ['22+14=36', '18+36=54'] Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,71 unequal: No Solution Exploring Operation: 73+54=127, Resulting Numbers: [127] 127,71 unequal: No Solution Exploring Operation: 73*54=3942, Resulting Numbers: [3942] 3942,71 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 #0,1,1 Current State: 71:[36, 55], Operations: ['22+14=36', '73-18=55'] Exploring Operation: 36+55=91, Resulting Numbers: [91] 91,71 unequal: No Solution Exploring Operation: 36*55=1980, Resulting Numbers: [1980] 1980,71 unequal: No Solution Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,71 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 #0,1,2 Current State: 71:[36, 91], Operations: ['22+14=36', '73+18=91'] Exploring Operation: 36*91=3276, Resulting Numbers: [3276] 3276,71 unequal: No Solution Exploring Operation: 36+91=127, Resulting Numbers: [127] 127,71 unequal: No Solution Exploring Operation: 91-36=55, Resulting Numbers: [55] 55,71 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:[73, 22, 32], Operations: ['18+14=32'] Exploring Operation: 73+22=95, Resulting Numbers: [32, 95] Generated Node #0,2,0: 71:[32, 95] Operation: 73+22=95 Exploring Operation: 22+32=54, Resulting Numbers: [73, 54] Generated Node #0,2,1: 71:[73, 54] Operation: 22+32=54 Exploring Operation: 73-22=51, Resulting Numbers: [32, 51] Generated Node #0,2,2: 71:[32, 51] Operation: 73-22=51 Moving to Node #0,2,1 Current State: 71:[73, 54], Operations: ['18+14=32', '22+32=54'] Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,71 unequal: No Solution Exploring Operation: 73+54=127, Resulting Numbers: [127] 127,71 unequal: No Solution Exploring Operation: 73*54=3942, Resulting Numbers: [3942] 3942,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[32, 51], Operations: ['18+14=32', '73-22=51'] Exploring Operation: 51-32=19, Resulting Numbers: [19] 19,71 unequal: No Solution Exploring Operation: 32*51=1632, Resulting Numbers: [1632] 1632,71 unequal: No Solution Exploring Operation: 32+51=83, Resulting Numbers: [83] 83,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[32, 95], Operations: ['18+14=32', '73+22=95'] Exploring Operation: 32+95=127, Resulting Numbers: [127] 127,71 unequal: No Solution Exploring Operation: 95-32=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 32*95=3040, Resulting Numbers: [3040] 3040,71 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 76, 52, 2, 41 ]
23
[ "76+52=128", "128/2=64", "64-41=23" ]
Current State: 23:[76, 52, 2, 41], Operations: [] Exploring Operation: 76+52=128, Resulting Numbers: [2, 41, 128] Generated Node #2: [2, 41, 128] from Operation: 76+52=128 Current State: 23:[2, 41, 128], Operations: ['76+52=128'] Exploring Operation: 128/2=64, Resulting Numbers: [41, 64] Generated Node #3: [41, 64] from Operation: 128/2=64 Current State: 23:[41, 64], Operations: ['76+52=128', '128/2=64'] Exploring Operation: 64-41=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[76, 52, 2, 41], Operations: [] Exploring Operation: 76/2=38, Resulting Numbers: [52, 41, 38] Generated Node #0,0: 23:[52, 41, 38] Operation: 76/2=38 Exploring Operation: 76-52=24, Resulting Numbers: [2, 41, 24] Generated Node #0,1: 23:[2, 41, 24] Operation: 76-52=24 Exploring Operation: 52-41=11, Resulting Numbers: [76, 2, 11] Generated Node #0,2: 23:[76, 2, 11] Operation: 52-41=11 Exploring Operation: 76-41=35, Resulting Numbers: [52, 2, 35] Generated Node #0,3: 23:[52, 2, 35] Operation: 76-41=35 Exploring Operation: 52/2=26, Resulting Numbers: [76, 41, 26] Generated Node #0,4: 23:[76, 41, 26] Operation: 52/2=26 Moving to Node #0,1 Current State: 23:[2, 41, 24], Operations: ['76-52=24'] Exploring Operation: 2+24=26, Resulting Numbers: [41, 26] Generated Node #0,1,0: 23:[41, 26] Operation: 2+24=26 Exploring Operation: 41-24=17, Resulting Numbers: [2, 17] Generated Node #0,1,1: 23:[2, 17] Operation: 41-24=17 Exploring Operation: 2+41=43, Resulting Numbers: [24, 43] Generated Node #0,1,2: 23:[24, 43] Operation: 2+41=43 Exploring Operation: 41-2=39, Resulting Numbers: [24, 39] Generated Node #0,1,3: 23:[24, 39] Operation: 41-2=39 Exploring Operation: 24-2=22, Resulting Numbers: [41, 22] Generated Node #0,1,4: 23:[41, 22] Operation: 24-2=22 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 23:[24, 39], Operations: ['76-52=24', '41-2=39'] Exploring Operation: 24*39=936, Resulting Numbers: [936] 936,23 unequal: No Solution Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 24+39=63, Resulting Numbers: [63] 63,23 unequal: No Solution No 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: 23:[41, 22], Operations: ['76-52=24', '24-2=22'] Exploring Operation: 41+22=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 41*22=902, Resulting Numbers: [902] 902,23 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,23 unequal: No Solution No 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: 23:[41, 26], Operations: ['76-52=24', '2+24=26'] Exploring Operation: 41+26=67, Resulting Numbers: [67] 67,23 unequal: No Solution Exploring Operation: 41-26=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 41*26=1066, Resulting Numbers: [1066] 1066,23 unequal: No Solution No 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: 23:[24, 43], Operations: ['76-52=24', '2+41=43'] Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,23 unequal: No Solution Exploring Operation: 24*43=1032, Resulting Numbers: [1032] 1032,23 unequal: No Solution No 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: 23:[2, 17], Operations: ['76-52=24', '41-24=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,23 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: 23:[52, 2, 35], Operations: ['76-41=35'] Exploring Operation: 52-2=50, Resulting Numbers: [35, 50] Generated Node #0,3,0: 23:[35, 50] Operation: 52-2=50 Exploring Operation: 52/2=26, Resulting Numbers: [35, 26] Generated Node #0,3,1: 23:[35, 26] Operation: 52/2=26 Exploring Operation: 35-2=33, Resulting Numbers: [52, 33] Generated Node #0,3,2: 23:[52, 33] Operation: 35-2=33 Exploring Operation: 52-35=17, Resulting Numbers: [2, 17] Generated Node #0,3,3: 23:[2, 17] Operation: 52-35=17 Exploring Operation: 52+2=54, Resulting Numbers: [35, 54] Generated Node #0,3,4: 23:[35, 54] Operation: 52+2=54 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 23:[35, 26], Operations: ['76-41=35', '52/2=26'] Exploring Operation: 35*26=910, Resulting Numbers: [910] 910,23 unequal: No Solution Exploring Operation: 35+26=61, Resulting Numbers: [61] 61,23 unequal: No Solution Exploring Operation: 35-26=9, Resulting Numbers: [9] 9,23 unequal: No Solution No 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: 23:[2, 17], Operations: ['76-41=35', '52-35=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,23 unequal: No Solution No 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: 23:[35, 50], Operations: ['76-41=35', '52-2=50'] Exploring Operation: 35+50=85, Resulting Numbers: [85] 85,23 unequal: No Solution Exploring Operation: 35*50=1750, Resulting Numbers: [1750] 1750,23 unequal: No Solution Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,23 unequal: No Solution No 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: 23:[52, 33], Operations: ['76-41=35', '35-2=33'] Exploring Operation: 52+33=85, Resulting Numbers: [85] 85,23 unequal: No Solution Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 52*33=1716, Resulting Numbers: [1716] 1716,23 unequal: No Solution No 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: 23:[35, 54], Operations: ['76-41=35', '52+2=54'] Exploring Operation: 54-35=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 35+54=89, Resulting Numbers: [89] 89,23 unequal: No Solution Exploring Operation: 35*54=1890, Resulting Numbers: [1890] 1890,23 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: 23:[52, 41, 38], Operations: ['76/2=38'] Exploring Operation: 52+38=90, Resulting Numbers: [41, 90] Generated Node #0,0,0: 23:[41, 90] Operation: 52+38=90 Exploring Operation: 52-41=11, Resulting Numbers: [38, 11] Generated Node #0,0,1: 23:[38, 11] Operation: 52-41=11 Exploring Operation: 52+41=93, Resulting Numbers: [38, 93] Generated Node #0,0,2: 23:[38, 93] Operation: 52+41=93 Exploring Operation: 41-38=3, Resulting Numbers: [52, 3] Generated Node #0,0,3: 23:[52, 3] Operation: 41-38=3 Exploring Operation: 52-38=14, Resulting Numbers: [41, 14] Generated Node #0,0,4: 23:[41, 14] Operation: 52-38=14 Moving to Node #0,4 Current State: 23:[76, 41, 26], Operations: ['52/2=26'] Exploring Operation: 76+26=102, Resulting Numbers: [41, 102] Generated Node #0,4,0: 23:[41, 102] Operation: 76+26=102 Exploring Operation: 41-26=15, Resulting Numbers: [76, 15] Generated Node #0,4,1: 23:[76, 15] Operation: 41-26=15 Exploring Operation: 76-26=50, Resulting Numbers: [41, 50] Generated Node #0,4,2: 23:[41, 50] Operation: 76-26=50 Exploring Operation: 76+41=117, Resulting Numbers: [26, 117] Generated Node #0,4,3: 23:[26, 117] Operation: 76+41=117 Exploring Operation: 76-41=35, Resulting Numbers: [26, 35] Generated Node #0,4,4: 23:[26, 35] Operation: 76-41=35 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 23:[26, 35], Operations: ['52/2=26', '76-41=35'] Exploring Operation: 26+35=61, Resulting Numbers: [61] 61,23 unequal: No Solution Exploring Operation: 35-26=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 26*35=910, Resulting Numbers: [910] 910,23 unequal: No Solution No 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: 23:[41, 50], Operations: ['52/2=26', '76-26=50'] Exploring Operation: 41*50=2050, Resulting Numbers: [2050] 2050,23 unequal: No Solution Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 41+50=91, Resulting Numbers: [91] 91,23 unequal: No Solution No 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: 23:[76, 15], Operations: ['52/2=26', '41-26=15'] Exploring Operation: 76*15=1140, Resulting Numbers: [1140] 1140,23 unequal: No Solution Exploring Operation: 76-15=61, Resulting Numbers: [61] 61,23 unequal: No Solution Exploring Operation: 76+15=91, Resulting Numbers: [91] 91,23 unequal: No Solution No 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: 23:[41, 102], Operations: ['52/2=26', '76+26=102'] Exploring Operation: 102-41=61, Resulting Numbers: [61] 61,23 unequal: No Solution Exploring Operation: 41+102=143, Resulting Numbers: [143] 143,23 unequal: No Solution Exploring Operation: 41*102=4182, Resulting Numbers: [4182] 4182,23 unequal: No Solution No 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: 23:[26, 117], Operations: ['52/2=26', '76+41=117'] Exploring Operation: 117-26=91, Resulting Numbers: [91] 91,23 unequal: No Solution Exploring Operation: 26*117=3042, Resulting Numbers: [3042] 3042,23 unequal: No Solution Exploring Operation: 26+117=143, Resulting Numbers: [143] 143,23 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: 23:[76, 2, 11], Operations: ['52-41=11'] Exploring Operation: 2+11=13, Resulting Numbers: [76, 13] Generated Node #0,2,0: 23:[76, 13] Operation: 2+11=13 Exploring Operation: 2*11=22, Resulting Numbers: [76, 22] Generated Node #0,2,1: 23:[76, 22] Operation: 2*11=22 Exploring Operation: 76-2=74, Resulting Numbers: [11, 74] Generated Node #0,2,2: 23:[11, 74] Operation: 76-2=74 Exploring Operation: 76/2=38, Resulting Numbers: [11, 38] Generated Node #0,2,3: 23:[11, 38] Operation: 76/2=38 Exploring Operation: 76-11=65, Resulting Numbers: [2, 65] Generated Node #0,2,4: 23:[2, 65] Operation: 76-11=65 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 23:[11, 38], Operations: ['52-41=11', '76/2=38'] Exploring Operation: 38-11=27, Resulting Numbers: [27] 27,23 unequal: No Solution Exploring Operation: 11+38=49, Resulting Numbers: [49] 49,23 unequal: No Solution Exploring Operation: 11*38=418, Resulting Numbers: [418] 418,23 unequal: No Solution No 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: 23:[76, 22], Operations: ['52-41=11', '2*11=22'] Exploring Operation: 76+22=98, Resulting Numbers: [98] 98,23 unequal: No Solution Exploring Operation: 76-22=54, Resulting Numbers: [54] 54,23 unequal: No Solution Exploring Operation: 76*22=1672, Resulting Numbers: [1672] 1672,23 unequal: No Solution No 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: 23:[76, 13], Operations: ['52-41=11', '2+11=13'] Exploring Operation: 76+13=89, Resulting Numbers: [89] 89,23 unequal: No Solution Exploring Operation: 76*13=988, Resulting Numbers: [988] 988,23 unequal: No Solution Exploring Operation: 76-13=63, Resulting Numbers: [63] 63,23 unequal: No Solution No 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: 23:[11, 74], Operations: ['52-41=11', '76-2=74'] Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 11*74=814, Resulting Numbers: [814] 814,23 unequal: No Solution Exploring Operation: 11+74=85, Resulting Numbers: [85] 85,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 23:[2, 65], Operations: ['52-41=11', '76-11=65'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 2+65=67, Resulting Numbers: [67] 67,23 unequal: No Solution Exploring Operation: 2*65=130, Resulting Numbers: [130] 130,23 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: 23:[38, 11], Operations: ['76/2=38', '52-41=11'] Exploring Operation: 38-11=27, Resulting Numbers: [27] 27,23 unequal: No Solution Exploring Operation: 38+11=49, Resulting Numbers: [49] 49,23 unequal: No Solution Exploring Operation: 38*11=418, Resulting Numbers: [418] 418,23 unequal: No Solution Moving to Node #0,0,4 Current State: 23:[41, 14], Operations: ['76/2=38', '52-38=14'] Exploring Operation: 41*14=574, Resulting Numbers: [574] 574,23 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,23 unequal: No Solution Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[52, 3], Operations: ['76/2=38', '41-38=3'] Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,23 unequal: No Solution Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,23 unequal: No Solution Exploring Operation: 52*3=156, Resulting Numbers: [156] 156,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[41, 90], Operations: ['76/2=38', '52+38=90'] Exploring Operation: 41+90=131, Resulting Numbers: [131] 131,23 unequal: No Solution Exploring Operation: 41*90=3690, Resulting Numbers: [3690] 3690,23 unequal: No Solution Exploring Operation: 90-41=49, Resulting Numbers: [49] 49,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[38, 93], Operations: ['76/2=38', '52+41=93'] Exploring Operation: 38+93=131, Resulting Numbers: [131] 131,23 unequal: No Solution Exploring Operation: 93-38=55, Resulting Numbers: [55] 55,23 unequal: No Solution Exploring Operation: 38*93=3534, Resulting Numbers: [3534] 3534,23 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 68, 83, 52, 86 ]
48
[ "68-52=16", "86-83=3", "16*3=48" ]
Current State: 48:[68, 83, 52, 86], Operations: [] Exploring Operation: 68-52=16, Resulting Numbers: [83, 86, 16] Generated Node #2: [83, 86, 16] from Operation: 68-52=16 Current State: 48:[83, 86, 16], Operations: ['68-52=16'] Exploring Operation: 86-83=3, Resulting Numbers: [16, 3] Generated Node #3: [16, 3] from Operation: 86-83=3 Current State: 48:[16, 3], Operations: ['68-52=16', '86-83=3'] Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[68, 83, 52, 86], Operations: [] Exploring Operation: 86-68=18, Resulting Numbers: [83, 52, 18] Generated Node #0,0: 48:[83, 52, 18] Operation: 86-68=18 Exploring Operation: 86-83=3, Resulting Numbers: [68, 52, 3] Generated Node #0,1: 48:[68, 52, 3] Operation: 86-83=3 Moving to Node #0,1 Current State: 48:[68, 52, 3], Operations: ['86-83=3'] Exploring Operation: 68-3=65, Resulting Numbers: [52, 65] Generated Node #0,1,0: 48:[52, 65] Operation: 68-3=65 Exploring Operation: 68-52=16, Resulting Numbers: [3, 16] Generated Node #0,1,1: 48:[3, 16] Operation: 68-52=16 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 48:[3, 16], Operations: ['86-83=3', '68-52=16'] Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[68, 83, 52, 86], Operations: [] Exploring Operation: 86-83=3, Resulting Numbers: [68, 52, 3] Generated Node #0,1: 48:[68, 52, 3] Operation: 86-83=3 Moving to Node #0,1 Current State: 48:[68, 52, 3], Operations: ['86-83=3'] Exploring Operation: 68-52=16, Resulting Numbers: [3, 16] Generated Node #0,1,1: 48:[3, 16] Operation: 68-52=16 Moving to Node #0,1,1 Current State: 48:[3, 16], Operations: ['86-83=3', '68-52=16'] Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 79, 50, 42, 3 ]
85
[ "79+50=129", "129/3=43", "42+43=85" ]
Current State: 85:[79, 50, 42, 3], Operations: [] Exploring Operation: 79+50=129, Resulting Numbers: [42, 3, 129] Generated Node #2: [42, 3, 129] from Operation: 79+50=129 Current State: 85:[42, 3, 129], Operations: ['79+50=129'] Exploring Operation: 129/3=43, Resulting Numbers: [42, 43] Generated Node #3: [42, 43] from Operation: 129/3=43 Current State: 85:[42, 43], Operations: ['79+50=129', '129/3=43'] Exploring Operation: 42+43=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[79, 50, 42, 3], Operations: [] Exploring Operation: 50-42=8, Resulting Numbers: [79, 3, 8] Generated Node #0,0: 85:[79, 3, 8] Operation: 50-42=8 Exploring Operation: 50+42=92, Resulting Numbers: [79, 3, 92] Generated Node #0,1: 85:[79, 3, 92] Operation: 50+42=92 Exploring Operation: 79-50=29, Resulting Numbers: [42, 3, 29] Generated Node #0,2: 85:[42, 3, 29] Operation: 79-50=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[79, 3, 8], Operations: ['50-42=8'] Exploring Operation: 79+8=87, Resulting Numbers: [3, 87] Generated Node #0,0,0: 85:[3, 87] Operation: 79+8=87 Exploring Operation: 79+3=82, Resulting Numbers: [8, 82] Generated Node #0,0,1: 85:[8, 82] Operation: 79+3=82 Exploring Operation: 8-3=5, Resulting Numbers: [79, 5] Generated Node #0,0,2: 85:[79, 5] Operation: 8-3=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[3, 87], Operations: ['50-42=8', '79+8=87'] Exploring Operation: 87/3=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 87-3=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 3+87=90, Resulting Numbers: [90] 90,85 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:[8, 82], Operations: ['50-42=8', '79+3=82'] Exploring Operation: 82-8=74, Resulting Numbers: [74] 74,85 unequal: No Solution Exploring Operation: 8*82=656, Resulting Numbers: [656] 656,85 unequal: No Solution Exploring Operation: 8+82=90, Resulting Numbers: [90] 90,85 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 #0,0,2 Current State: 85:[79, 5], Operations: ['50-42=8', '8-3=5'] Exploring Operation: 79-5=74, Resulting Numbers: [74] 74,85 unequal: No Solution Exploring Operation: 79*5=395, Resulting Numbers: [395] 395,85 unequal: No Solution Exploring Operation: 79+5=84, Resulting Numbers: [84] 84,85 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:[79, 3, 92], Operations: ['50+42=92'] Exploring Operation: 92-79=13, Resulting Numbers: [3, 13] Generated Node #0,1,0: 85:[3, 13] Operation: 92-79=13 Exploring Operation: 79+3=82, Resulting Numbers: [92, 82] Generated Node #0,1,1: 85:[92, 82] Operation: 79+3=82 Exploring Operation: 92-3=89, Resulting Numbers: [79, 89] Generated Node #0,1,2: 85:[79, 89] Operation: 92-3=89 Moving to Node #0,1,0 Current State: 85:[3, 13], Operations: ['50+42=92', '92-79=13'] Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,85 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[92, 82], Operations: ['50+42=92', '79+3=82'] Exploring Operation: 92-82=10, Resulting Numbers: [10] 10,85 unequal: No Solution Exploring Operation: 92+82=174, Resulting Numbers: [174] 174,85 unequal: No Solution Exploring Operation: 92*82=7544, Resulting Numbers: [7544] 7544,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[79, 89], Operations: ['50+42=92', '92-3=89'] Exploring Operation: 79+89=168, Resulting Numbers: [168] 168,85 unequal: No Solution Exploring Operation: 89-79=10, Resulting Numbers: [10] 10,85 unequal: No Solution Exploring Operation: 79*89=7031, Resulting Numbers: [7031] 7031,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 85:[42, 3, 29], Operations: ['79-50=29'] Exploring Operation: 42+29=71, Resulting Numbers: [3, 71] Generated Node #0,2,0: 85:[3, 71] Operation: 42+29=71 Exploring Operation: 42/3=14, Resulting Numbers: [29, 14] Generated Node #0,2,1: 85:[29, 14] Operation: 42/3=14 Exploring Operation: 42-29=13, Resulting Numbers: [3, 13] Generated Node #0,2,2: 85:[3, 13] Operation: 42-29=13 Moving to Node #0,2,2 Current State: 85:[3, 13], Operations: ['79-50=29', '42-29=13'] Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,85 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[29, 14], Operations: ['79-50=29', '42/3=14'] Exploring Operation: 29*14=406, Resulting Numbers: [406] 406,85 unequal: No Solution Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 29+14=43, Resulting Numbers: [43] 43,85 unequal: No Solution Moving to Node #0,2,0 Current State: 85:[3, 71], Operations: ['79-50=29', '42+29=71'] Exploring Operation: 3*71=213, Resulting Numbers: [213] 213,85 unequal: No Solution Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,85 unequal: No Solution Exploring Operation: 3+71=74, Resulting Numbers: [74] 74,85 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
[ 4, 83, 96, 77 ]
18
[ "96/4=24", "83-77=6", "24-6=18" ]
Current State: 18:[4, 83, 96, 77], Operations: [] Exploring Operation: 96/4=24, Resulting Numbers: [83, 77, 24] Generated Node #2: [83, 77, 24] from Operation: 96/4=24 Current State: 18:[83, 77, 24], Operations: ['96/4=24'] Exploring Operation: 83-77=6, Resulting Numbers: [24, 6] Generated Node #3: [24, 6] from Operation: 83-77=6 Current State: 18:[24, 6], Operations: ['96/4=24', '83-77=6'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[4, 83, 96, 77], Operations: [] Exploring Operation: 96-77=19, Resulting Numbers: [4, 83, 19] Generated Node #0,0: 18:[4, 83, 19] Operation: 96-77=19 Exploring Operation: 96-83=13, Resulting Numbers: [4, 77, 13] Generated Node #0,1: 18:[4, 77, 13] Operation: 96-83=13 Moving to Node #0,1 Current State: 18:[4, 77, 13], Operations: ['96-83=13'] Exploring Operation: 77-13=64, Resulting Numbers: [4, 64] Generated Node #0,1,0: 18:[4, 64] Operation: 77-13=64 Exploring Operation: 77-4=73, Resulting Numbers: [13, 73] Generated Node #0,1,1: 18:[13, 73] Operation: 77-4=73 Moving to Node #0,0 Current State: 18:[4, 83, 19], Operations: ['96-77=19'] Exploring Operation: 83-19=64, Resulting Numbers: [4, 64] Generated Node #0,0,0: 18:[4, 64] Operation: 83-19=64 Exploring Operation: 83-4=79, Resulting Numbers: [19, 79] Generated Node #0,0,1: 18:[19, 79] Operation: 83-4=79 Moving to Node #0,1,0 Current State: 18:[4, 64], Operations: ['96-83=13', '77-13=64'] Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,18 unequal: No Solution Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[4, 64], Operations: ['96-77=19', '83-19=64'] Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[13, 73], Operations: ['96-83=13', '77-4=73'] Exploring Operation: 73-13=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 13+73=86, Resulting Numbers: [86] 86,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[19, 79], Operations: ['96-77=19', '83-4=79'] Exploring Operation: 19+79=98, Resulting Numbers: [98] 98,18 unequal: No Solution Exploring Operation: 79-19=60, Resulting Numbers: [60] 60,18 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 49, 89, 8, 40 ]
45
[ "89-49=40", "40/8=5", "40+5=45" ]
Current State: 45:[49, 89, 8, 40], Operations: [] Exploring Operation: 89-49=40, Resulting Numbers: [8, 40, 40] Generated Node #2: [8, 40, 40] from Operation: 89-49=40 Current State: 45:[8, 40, 40], Operations: ['89-49=40'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,45 equal: Goal Reached Exploring Operation: 40+5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[49, 89, 8, 40], Operations: [] Exploring Operation: 89-40=49, Resulting Numbers: [49, 8, 49] Generated Node #0,0: 45:[49, 8, 49] Operation: 89-40=49 Exploring Operation: 89-49=40, Resulting Numbers: [8, 40, 40] Generated Node #0,1: 45:[8, 40, 40] Operation: 89-49=40 Moving to Node #0,0 Current State: 45:[49, 8, 49], Operations: ['89-40=49'] Exploring Operation: 49/49=1, Resulting Numbers: [8, 1] Generated Node #0,0,0: 45:[8, 1] Operation: 49/49=1 Exploring Operation: 49-49=0, Resulting Numbers: [8, 0] Generated Node #0,0,1: 45:[8, 0] Operation: 49-49=0 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[8, 1], Operations: ['89-40=49', '49/49=1'] Exploring Operation: 8+1=9, Resulting Numbers: [9] 9,45 unequal: No Solution Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[8, 0], Operations: ['89-40=49', '49-49=0'] Exploring Operation: 8+0=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 8-0=8, Resulting Numbers: [8] 8,45 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: 45:[8, 40, 40], Operations: ['89-49=40'] Exploring Operation: 40/40=1, Resulting Numbers: [8, 1] Generated Node #0,1,0: 45:[8, 1] Operation: 40/40=1 Exploring Operation: 40-40=0, Resulting Numbers: [8, 0] Generated Node #0,1,1: 45:[8, 0] Operation: 40-40=0 Moving to Node #0,1,0 Current State: 45:[8, 1], Operations: ['89-49=40', '40/40=1'] Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 8+1=9, Resulting Numbers: [9] 9,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[8, 0], Operations: ['89-49=40', '40-40=0'] Exploring Operation: 8-0=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 8+0=8, Resulting Numbers: [8] 8,45 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 13, 9, 30, 51 ]
59
[ "13+9=22", "30+51=81", "81-22=59" ]
Current State: 59:[13, 9, 30, 51], Operations: [] Exploring Operation: 13+9=22, Resulting Numbers: [30, 51, 22] Generated Node #2: [30, 51, 22] from Operation: 13+9=22 Current State: 59:[30, 51, 22], Operations: ['13+9=22'] Exploring Operation: 30+51=81, Resulting Numbers: [22, 81] Generated Node #3: [22, 81] from Operation: 30+51=81 Current State: 59:[22, 81], Operations: ['13+9=22', '30+51=81'] Exploring Operation: 81-22=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[13, 9, 30, 51], Operations: [] Exploring Operation: 9+51=60, Resulting Numbers: [13, 30, 60] Generated Node #0,0: 59:[13, 30, 60] Operation: 9+51=60 Exploring Operation: 13+30=43, Resulting Numbers: [9, 51, 43] Generated Node #0,1: 59:[9, 51, 43] Operation: 13+30=43 Exploring Operation: 13+9=22, Resulting Numbers: [30, 51, 22] Generated Node #0,2: 59:[30, 51, 22] Operation: 13+9=22 Exploring Operation: 9+30=39, Resulting Numbers: [13, 51, 39] Generated Node #0,3: 59:[13, 51, 39] Operation: 9+30=39 Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[9, 51, 43], Operations: ['13+30=43'] Exploring Operation: 51-9=42, Resulting Numbers: [43, 42] Generated Node #0,1,0: 59:[43, 42] Operation: 51-9=42 Exploring Operation: 9+43=52, Resulting Numbers: [51, 52] Generated Node #0,1,1: 59:[51, 52] Operation: 9+43=52 Exploring Operation: 43-9=34, Resulting Numbers: [51, 34] Generated Node #0,1,2: 59:[51, 34] Operation: 43-9=34 Exploring Operation: 9+51=60, Resulting Numbers: [43, 60] Generated Node #0,1,3: 59:[43, 60] Operation: 9+51=60 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 59:[51, 52], Operations: ['13+30=43', '9+43=52'] Exploring Operation: 51*52=2652, Resulting Numbers: [2652] 2652,59 unequal: No Solution Exploring Operation: 51+52=103, Resulting Numbers: [103] 103,59 unequal: No Solution Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 59:[43, 60], Operations: ['13+30=43', '9+51=60'] Exploring Operation: 43*60=2580, Resulting Numbers: [2580] 2580,59 unequal: No Solution Exploring Operation: 60-43=17, Resulting Numbers: [17] 17,59 unequal: No Solution Exploring Operation: 43+60=103, Resulting Numbers: [103] 103,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 59:[43, 42], Operations: ['13+30=43', '51-9=42'] Exploring Operation: 43-42=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 43+42=85, Resulting Numbers: [85] 85,59 unequal: No Solution Exploring Operation: 43*42=1806, Resulting Numbers: [1806] 1806,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 59:[51, 34], Operations: ['13+30=43', '43-9=34'] Exploring Operation: 51*34=1734, Resulting Numbers: [1734] 1734,59 unequal: No Solution Exploring Operation: 51-34=17, Resulting Numbers: [17] 17,59 unequal: No Solution Exploring Operation: 51+34=85, Resulting Numbers: [85] 85,59 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: 59:[30, 51, 22], Operations: ['13+9=22'] Exploring Operation: 30-22=8, Resulting Numbers: [51, 8] Generated Node #0,2,0: 59:[51, 8] Operation: 30-22=8 Exploring Operation: 30+22=52, Resulting Numbers: [51, 52] Generated Node #0,2,1: 59:[51, 52] Operation: 30+22=52 Exploring Operation: 30+51=81, Resulting Numbers: [22, 81] Generated Node #0,2,2: 59:[22, 81] Operation: 30+51=81 Exploring Operation: 51+22=73, Resulting Numbers: [30, 73] Generated Node #0,2,3: 59:[30, 73] Operation: 51+22=73 Moving to Node #0,2,1 Current State: 59:[51, 52], Operations: ['13+9=22', '30+22=52'] Exploring Operation: 51+52=103, Resulting Numbers: [103] 103,59 unequal: No Solution Exploring Operation: 51*52=2652, Resulting Numbers: [2652] 2652,59 unequal: No Solution Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[30, 73], Operations: ['13+9=22', '51+22=73'] Exploring Operation: 30*73=2190, Resulting Numbers: [2190] 2190,59 unequal: No Solution Exploring Operation: 73-30=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 30+73=103, Resulting Numbers: [103] 103,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[22, 81], Operations: ['13+9=22', '30+51=81'] Exploring Operation: 22+81=103, Resulting Numbers: [103] 103,59 unequal: No Solution Exploring Operation: 22*81=1782, Resulting Numbers: [1782] 1782,59 unequal: No Solution Exploring Operation: 81-22=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[13, 9, 30, 51], Operations: [] Exploring Operation: 13+9=22, Resulting Numbers: [30, 51, 22] Generated Node #0,2: 59:[30, 51, 22] Operation: 13+9=22 Moving to Node #0,2 Current State: 59:[30, 51, 22], Operations: ['13+9=22'] Exploring Operation: 30+51=81, Resulting Numbers: [22, 81] Generated Node #0,2,2: 59:[22, 81] Operation: 30+51=81 Moving to Node #0,2,2 Current State: 59:[22, 81], Operations: ['13+9=22', '30+51=81'] Exploring Operation: 81-22=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_4
mult_heuristic
[ 53, 18, 24, 7 ]
61
[ "53*7=371", "18*24=432", "432-371=61" ]
Current State: 61:[53, 18, 24, 7], Operations: [] Exploring Operation: 53*7=371, Resulting Numbers: [18, 24, 371] Generated Node #2: [18, 24, 371] from Operation: 53*7=371 Current State: 61:[18, 24, 371], Operations: ['53*7=371'] Exploring Operation: 18*24=432, Resulting Numbers: [371, 432] Generated Node #3: [371, 432] from Operation: 18*24=432 Current State: 61:[371, 432], Operations: ['53*7=371', '18*24=432'] Exploring Operation: 432-371=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[53, 18, 24, 7], Operations: [] Exploring Operation: 53+7=60, Resulting Numbers: [18, 24, 60] Generated Node #0,0: 61:[18, 24, 60] Operation: 53+7=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[18, 24, 60], Operations: ['53+7=60'] Exploring Operation: 18+24=42, Resulting Numbers: [60, 42] Generated Node #0,0,0: 61:[60, 42] Operation: 18+24=42 Moving to Node #0,0,0 Current State: 61:[60, 42], Operations: ['53+7=60', '18+24=42'] Exploring Operation: 60+42=102, Resulting Numbers: [102] 102,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 18, 80, 44, 81 ]
26
[ "44-18=26", "81-80=1", "26*1=26" ]
Current State: 26:[18, 80, 44, 81], Operations: [] Exploring Operation: 44-18=26, Resulting Numbers: [80, 81, 26] Generated Node #2: [80, 81, 26] from Operation: 44-18=26 Current State: 26:[80, 81, 26], Operations: ['44-18=26'] Exploring Operation: 81-80=1, Resulting Numbers: [26, 1] Generated Node #3: [26, 1] from Operation: 81-80=1 Current State: 26:[26, 1], Operations: ['44-18=26', '81-80=1'] Exploring Operation: 26*1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[18, 80, 44, 81], Operations: [] Exploring Operation: 81-44=37, Resulting Numbers: [18, 80, 37] Generated Node #0,0: 26:[18, 80, 37] Operation: 81-44=37 Exploring Operation: 44-18=26, Resulting Numbers: [80, 81, 26] Generated Node #0,1: 26:[80, 81, 26] Operation: 44-18=26 Exploring Operation: 80-44=36, Resulting Numbers: [18, 81, 36] Generated Node #0,2: 26:[18, 81, 36] Operation: 80-44=36 Exploring Operation: 80-18=62, Resulting Numbers: [44, 81, 62] Generated Node #0,3: 26:[44, 81, 62] Operation: 80-18=62 Exploring Operation: 81-80=1, Resulting Numbers: [18, 44, 1] Generated Node #0,4: 26:[18, 44, 1] Operation: 81-80=1 Moving to Node #0,4 Current State: 26:[18, 44, 1], Operations: ['81-80=1'] Exploring Operation: 18/1=18, Resulting Numbers: [44, 18] Generated Node #0,4,0: 26:[44, 18] Operation: 18/1=18 Exploring Operation: 18-1=17, Resulting Numbers: [44, 17] Generated Node #0,4,1: 26:[44, 17] Operation: 18-1=17 Exploring Operation: 44-1=43, Resulting Numbers: [18, 43] Generated Node #0,4,2: 26:[18, 43] Operation: 44-1=43 Exploring Operation: 18*1=18, Resulting Numbers: [44, 18] Generated Node #0,4,3: 26:[44, 18] Operation: 18*1=18 Exploring Operation: 44-18=26, Resulting Numbers: [1, 26] Generated Node #0,4,4: 26:[1, 26] Operation: 44-18=26 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 26:[1, 26], Operations: ['81-80=1', '44-18=26'] Exploring Operation: 1*26=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[18, 80, 44, 81], Operations: [] Exploring Operation: 81-80=1, Resulting Numbers: [18, 44, 1] Generated Node #0,4: 26:[18, 44, 1] Operation: 81-80=1 Moving to Node #0,4 Current State: 26:[18, 44, 1], Operations: ['81-80=1'] Exploring Operation: 44-18=26, Resulting Numbers: [1, 26] Generated Node #0,4,4: 26:[1, 26] Operation: 44-18=26 Moving to Node #0,4,4 Current State: 26:[1, 26], Operations: ['81-80=1', '44-18=26'] Exploring Operation: 1*26=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 48, 40, 33, 55 ]
33
[ "48*55=2640", "2640/40=66", "66-33=33" ]
Current State: 33:[48, 40, 33, 55], Operations: [] Exploring Operation: 48*55=2640, Resulting Numbers: [40, 33, 2640] Generated Node #2: [40, 33, 2640] from Operation: 48*55=2640 Current State: 33:[40, 33, 2640], Operations: ['48*55=2640'] Exploring Operation: 2640/40=66, Resulting Numbers: [33, 66] Generated Node #3: [33, 66] from Operation: 2640/40=66 Current State: 33:[33, 66], Operations: ['48*55=2640', '2640/40=66'] Exploring Operation: 66-33=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[48, 40, 33, 55], Operations: [] Exploring Operation: 55-48=7, Resulting Numbers: [40, 33, 7] Generated Node #0,0: 33:[40, 33, 7] Operation: 55-48=7 Exploring Operation: 55-40=15, Resulting Numbers: [48, 33, 15] Generated Node #0,1: 33:[48, 33, 15] Operation: 55-40=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[40, 33, 7], Operations: ['55-48=7'] Exploring Operation: 40-7=33, Resulting Numbers: [33, 33] Generated Node #0,0,0: 33:[33, 33] Operation: 40-7=33 Exploring Operation: 40-33=7, Resulting Numbers: [7, 7] Generated Node #0,0,1: 33:[7, 7] Operation: 40-33=7 Moving to Node #0,0,0 Current State: 33:[33, 33], Operations: ['55-48=7', '40-7=33'] Exploring Operation: 33-33=0, Resulting Numbers: [0] 0,33 unequal: No Solution Exploring Operation: 33/33=1, Resulting Numbers: [1] 1,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[7, 7], Operations: ['55-48=7', '40-33=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[48, 33, 15], Operations: ['55-40=15'] Exploring Operation: 48-15=33, Resulting Numbers: [33, 33] Generated Node #0,1,0: 33:[33, 33] Operation: 48-15=33 Exploring Operation: 48-33=15, Resulting Numbers: [15, 15] Generated Node #0,1,1: 33:[15, 15] Operation: 48-33=15 Moving to Node #0,1,0 Current State: 33:[33, 33], Operations: ['55-40=15', '48-15=33'] Exploring Operation: 33/33=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 33-33=0, Resulting Numbers: [0] 0,33 unequal: No Solution Moving to Node #0,1,1 Current State: 33:[15, 15], Operations: ['55-40=15', '48-33=15'] Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,33 unequal: No Solution Exploring Operation: 15/15=1, Resulting Numbers: [1] 1,33 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
[ 9, 38, 96, 17 ]
95
[ "9*17=153", "96-38=58", "153-58=95" ]
Current State: 95:[9, 38, 96, 17], Operations: [] Exploring Operation: 9*17=153, Resulting Numbers: [38, 96, 153] Generated Node #2: [38, 96, 153] from Operation: 9*17=153 Current State: 95:[38, 96, 153], Operations: ['9*17=153'] Exploring Operation: 96-38=58, Resulting Numbers: [153, 58] Generated Node #3: [153, 58] from Operation: 96-38=58 Current State: 95:[153, 58], Operations: ['9*17=153', '96-38=58'] Exploring Operation: 153-58=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[9, 38, 96, 17], Operations: [] Exploring Operation: 38-9=29, Resulting Numbers: [96, 17, 29] Generated Node #0,0: 95:[96, 17, 29] Operation: 38-9=29 Exploring Operation: 38-17=21, Resulting Numbers: [9, 96, 21] Generated Node #0,1: 95:[9, 96, 21] Operation: 38-17=21 Moving to Node #0,1 Current State: 95:[9, 96, 21], Operations: ['38-17=21'] Exploring Operation: 96-9=87, Resulting Numbers: [21, 87] Generated Node #0,1,0: 95:[21, 87] Operation: 96-9=87 Exploring Operation: 21-9=12, Resulting Numbers: [96, 12] Generated Node #0,1,1: 95:[96, 12] Operation: 21-9=12 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 95:[96, 12], Operations: ['38-17=21', '21-9=12'] Exploring Operation: 96/12=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 96-12=84, Resulting Numbers: [84] 84,95 unequal: No Solution No 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: 95:[21, 87], Operations: ['38-17=21', '96-9=87'] Exploring Operation: 21+87=108, Resulting Numbers: [108] 108,95 unequal: No Solution Exploring Operation: 87-21=66, Resulting Numbers: [66] 66,95 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: 95:[96, 17, 29], Operations: ['38-9=29'] Exploring Operation: 96-17=79, Resulting Numbers: [29, 79] Generated Node #0,0,0: 95:[29, 79] Operation: 96-17=79 Exploring Operation: 29-17=12, Resulting Numbers: [96, 12] Generated Node #0,0,1: 95:[96, 12] Operation: 29-17=12 Moving to Node #0,0,1 Current State: 95:[96, 12], Operations: ['38-9=29', '29-17=12'] Exploring Operation: 96-12=84, Resulting Numbers: [84] 84,95 unequal: No Solution Exploring Operation: 96/12=8, Resulting Numbers: [8] 8,95 unequal: No Solution Moving to Node #0,0,0 Current State: 95:[29, 79], Operations: ['38-9=29', '96-17=79'] Exploring Operation: 29+79=108, Resulting Numbers: [108] 108,95 unequal: No Solution Exploring Operation: 79-29=50, Resulting Numbers: [50] 50,95 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 95, 30, 72, 96 ]
89
[ "95-30=65", "96-72=24", "65+24=89" ]
Current State: 89:[95, 30, 72, 96], Operations: [] Exploring Operation: 95-30=65, Resulting Numbers: [72, 96, 65] Generated Node #2: [72, 96, 65] from Operation: 95-30=65 Current State: 89:[72, 96, 65], Operations: ['95-30=65'] Exploring Operation: 96-72=24, Resulting Numbers: [65, 24] Generated Node #3: [65, 24] from Operation: 96-72=24 Current State: 89:[65, 24], Operations: ['95-30=65', '96-72=24'] Exploring Operation: 65+24=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[95, 30, 72, 96], Operations: [] Exploring Operation: 95+30=125, Resulting Numbers: [72, 96, 125] Generated Node #0,0: 89:[72, 96, 125] Operation: 95+30=125 Exploring Operation: 96-30=66, Resulting Numbers: [95, 72, 66] Generated Node #0,1: 89:[95, 72, 66] Operation: 96-30=66 Exploring Operation: 95-30=65, Resulting Numbers: [72, 96, 65] Generated Node #0,2: 89:[72, 96, 65] Operation: 95-30=65 Exploring Operation: 30+72=102, Resulting Numbers: [95, 96, 102] Generated Node #0,3: 89:[95, 96, 102] Operation: 30+72=102 Start Sub Search at level 1: Moving to Node #0,3 Current State: 89:[95, 96, 102], Operations: ['30+72=102'] Exploring Operation: 102-96=6, Resulting Numbers: [95, 6] Generated Node #0,3,0: 89:[95, 6] Operation: 102-96=6 Exploring Operation: 95+96=191, Resulting Numbers: [102, 191] Generated Node #0,3,1: 89:[102, 191] Operation: 95+96=191 Exploring Operation: 96-95=1, Resulting Numbers: [102, 1] Generated Node #0,3,2: 89:[102, 1] Operation: 96-95=1 Exploring Operation: 102-95=7, Resulting Numbers: [96, 7] Generated Node #0,3,3: 89:[96, 7] Operation: 102-95=7 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 89:[95, 6], Operations: ['30+72=102', '102-96=6'] Exploring Operation: 95*6=570, Resulting Numbers: [570] 570,89 unequal: No Solution Exploring Operation: 95+6=101, Resulting Numbers: [101] 101,89 unequal: No Solution Exploring Operation: 95-6=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[95, 30, 72, 96], Operations: [] Exploring Operation: 30+72=102, Resulting Numbers: [95, 96, 102] Generated Node #0,3: 89:[95, 96, 102] Operation: 30+72=102 Moving to Node #0,3 Current State: 89:[95, 96, 102], Operations: ['30+72=102'] Exploring Operation: 102-96=6, Resulting Numbers: [95, 6] Generated Node #0,3,0: 89:[95, 6] Operation: 102-96=6 Moving to Node #0,3,0 Current State: 89:[95, 6], Operations: ['30+72=102', '102-96=6'] Exploring Operation: 95-6=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 62, 7, 51, 64 ]
69
[ "62+64=126", "126/7=18", "51+18=69" ]
Current State: 69:[62, 7, 51, 64], Operations: [] Exploring Operation: 62+64=126, Resulting Numbers: [7, 51, 126] Generated Node #2: [7, 51, 126] from Operation: 62+64=126 Current State: 69:[7, 51, 126], Operations: ['62+64=126'] Exploring Operation: 126/7=18, Resulting Numbers: [51, 18] Generated Node #3: [51, 18] from Operation: 126/7=18 Current State: 69:[51, 18], Operations: ['62+64=126', '126/7=18'] Exploring Operation: 51+18=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[62, 7, 51, 64], Operations: [] Exploring Operation: 62+7=69, Resulting Numbers: [51, 64, 69] Generated Node #0,0: 69:[51, 64, 69] Operation: 62+7=69 Exploring Operation: 64-51=13, Resulting Numbers: [62, 7, 13] Generated Node #0,1: 69:[62, 7, 13] Operation: 64-51=13 Exploring Operation: 62-51=11, Resulting Numbers: [7, 64, 11] Generated Node #0,2: 69:[7, 64, 11] Operation: 62-51=11 Moving to Node #0,2 Current State: 69:[7, 64, 11], Operations: ['62-51=11'] Exploring Operation: 7+64=71, Resulting Numbers: [11, 71] Generated Node #0,2,0: 69:[11, 71] Operation: 7+64=71 Exploring Operation: 7+11=18, Resulting Numbers: [64, 18] Generated Node #0,2,1: 69:[64, 18] Operation: 7+11=18 Exploring Operation: 11-7=4, Resulting Numbers: [64, 4] Generated Node #0,2,2: 69:[64, 4] Operation: 11-7=4 Moving to Node #0,1 Current State: 69:[62, 7, 13], Operations: ['64-51=13'] Exploring Operation: 62+7=69, Resulting Numbers: [13, 69] Generated Node #0,1,0: 69:[13, 69] Operation: 62+7=69 Exploring Operation: 7+13=20, Resulting Numbers: [62, 20] Generated Node #0,1,1: 69:[62, 20] Operation: 7+13=20 Exploring Operation: 62+13=75, Resulting Numbers: [7, 75] Generated Node #0,1,2: 69:[7, 75] Operation: 62+13=75 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[13, 69], Operations: ['64-51=13', '62+7=69'] Exploring Operation: 69-13=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 13*69=897, Resulting Numbers: [897] 897,69 unequal: No Solution Exploring Operation: 13+69=82, Resulting Numbers: [82] 82,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[62, 20], Operations: ['64-51=13', '7+13=20'] Exploring Operation: 62+20=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 62*20=1240, Resulting Numbers: [1240] 1240,69 unequal: No Solution Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[7, 75], Operations: ['64-51=13', '62+13=75'] Exploring Operation: 7*75=525, Resulting Numbers: [525] 525,69 unequal: No Solution Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 7+75=82, Resulting Numbers: [82] 82,69 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: 69:[51, 64, 69], Operations: ['62+7=69'] Exploring Operation: 64-51=13, Resulting Numbers: [69, 13] Generated Node #0,0,0: 69:[69, 13] Operation: 64-51=13 Exploring Operation: 69-64=5, Resulting Numbers: [51, 5] Generated Node #0,0,1: 69:[51, 5] Operation: 69-64=5 Exploring Operation: 69-51=18, Resulting Numbers: [64, 18] Generated Node #0,0,2: 69:[64, 18] Operation: 69-51=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[69, 13], Operations: ['62+7=69', '64-51=13'] Exploring Operation: 69-13=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 69*13=897, Resulting Numbers: [897] 897,69 unequal: No Solution Exploring Operation: 69+13=82, Resulting Numbers: [82] 82,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[64, 18], Operations: ['62+7=69', '69-51=18'] Exploring Operation: 64-18=46, Resulting Numbers: [46] 46,69 unequal: No Solution Exploring Operation: 64+18=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 64*18=1152, Resulting Numbers: [1152] 1152,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[51, 5], Operations: ['62+7=69', '69-64=5'] Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,69 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,69 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: 69:[64, 4], Operations: ['62-51=11', '11-7=4'] Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,69 unequal: No Solution Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[11, 71], Operations: ['62-51=11', '7+64=71'] Exploring Operation: 11+71=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 11*71=781, Resulting Numbers: [781] 781,69 unequal: No Solution Exploring Operation: 71-11=60, Resulting Numbers: [60] 60,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[64, 18], Operations: ['62-51=11', '7+11=18'] Exploring Operation: 64+18=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 64*18=1152, Resulting Numbers: [1152] 1152,69 unequal: No Solution Exploring Operation: 64-18=46, Resulting Numbers: [46] 46,69 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 33, 30, 10, 77 ]
90
[ "33-30=3", "10+77=87", "3+87=90" ]
Current State: 90:[33, 30, 10, 77], Operations: [] Exploring Operation: 33-30=3, Resulting Numbers: [10, 77, 3] Generated Node #2: [10, 77, 3] from Operation: 33-30=3 Current State: 90:[10, 77, 3], Operations: ['33-30=3'] Exploring Operation: 10+77=87, Resulting Numbers: [3, 87] Generated Node #3: [3, 87] from Operation: 10+77=87 Current State: 90:[3, 87], Operations: ['33-30=3', '10+77=87'] Exploring Operation: 3+87=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[33, 30, 10, 77], Operations: [] Exploring Operation: 77-33=44, Resulting Numbers: [30, 10, 44] Generated Node #0,0: 90:[30, 10, 44] Operation: 77-33=44 Exploring Operation: 77-30=47, Resulting Numbers: [33, 10, 47] Generated Node #0,1: 90:[33, 10, 47] Operation: 77-30=47 Moving to Node #0,0 Current State: 90:[30, 10, 44], Operations: ['77-33=44'] Exploring Operation: 44-30=14, Resulting Numbers: [10, 14] Generated Node #0,0,0: 90:[10, 14] Operation: 44-30=14 Exploring Operation: 30/10=3, Resulting Numbers: [44, 3] Generated Node #0,0,1: 90:[44, 3] Operation: 30/10=3 Moving to Node #0,1 Current State: 90:[33, 10, 47], Operations: ['77-30=47'] Exploring Operation: 47-33=14, Resulting Numbers: [10, 14] Generated Node #0,1,0: 90:[10, 14] Operation: 47-33=14 Exploring Operation: 33+10=43, Resulting Numbers: [47, 43] Generated Node #0,1,1: 90:[47, 43] Operation: 33+10=43 Moving to Node #0,0,0 Current State: 90:[10, 14], Operations: ['77-33=44', '44-30=14'] Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,90 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[10, 14], Operations: ['77-30=47', '47-33=14'] Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[44, 3], Operations: ['77-33=44', '30/10=3'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,90 unequal: No Solution Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[47, 43], Operations: ['77-30=47', '33+10=43'] Exploring Operation: 47-43=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 47+43=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[33, 30, 10, 77], Operations: [] Exploring Operation: 77-30=47, Resulting Numbers: [33, 10, 47] Generated Node #0,1: 90:[33, 10, 47] Operation: 77-30=47 Moving to Node #0,1 Current State: 90:[33, 10, 47], Operations: ['77-30=47'] Exploring Operation: 33+10=43, Resulting Numbers: [47, 43] Generated Node #0,1,1: 90:[47, 43] Operation: 33+10=43 Moving to Node #0,1,1 Current State: 90:[47, 43], Operations: ['77-30=47', '33+10=43'] Exploring Operation: 47+43=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
0.984375
hs_2
sum_heuristic
[ 10, 33, 78, 33 ]
22
[ "33-10=23", "78-33=45", "45-23=22" ]
Current State: 22:[10, 33, 78, 33], Operations: [] Exploring Operation: 33-10=23, Resulting Numbers: [78, 23] Generated Node #2: [78, 23] from Operation: 33-10=23 Current State: 22:[78, 23], Operations: ['33-10=23'] Exploring Operation: 78-33=45, Resulting Numbers: [23, 45] Generated Node #3: [23, 45] from Operation: 78-33=45 Current State: 22:[23, 45], Operations: ['33-10=23', '78-33=45'] Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[10, 33, 78, 33], Operations: [] Exploring Operation: 33-10=23, Resulting Numbers: [78, 33, 23] Generated Node #0,0: 22:[78, 33, 23] Operation: 33-10=23 Exploring Operation: 33-33=0, Resulting Numbers: [10, 78, 0] Generated Node #0,1: 22:[10, 78, 0] Operation: 33-33=0 Exploring Operation: 78-33=45, Resulting Numbers: [10, 33, 45] Generated Node #0,2: 22:[10, 33, 45] Operation: 78-33=45 Exploring Operation: 78-33=45, Resulting Numbers: [10, 33, 45] Generated Node #0,3: 22:[10, 33, 45] Operation: 78-33=45 Exploring Operation: 33/33=1, Resulting Numbers: [10, 78, 1] Generated Node #0,4: 22:[10, 78, 1] Operation: 33/33=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[10, 33, 45], Operations: ['78-33=45'] Exploring Operation: 33-10=23, Resulting Numbers: [45, 23] Generated Node #0,2,0: 22:[45, 23] Operation: 33-10=23 Exploring Operation: 10+45=55, Resulting Numbers: [33, 55] Generated Node #0,2,1: 22:[33, 55] Operation: 10+45=55 Exploring Operation: 45-33=12, Resulting Numbers: [10, 12] Generated Node #0,2,2: 22:[10, 12] Operation: 45-33=12 Exploring Operation: 45-10=35, Resulting Numbers: [33, 35] Generated Node #0,2,3: 22:[33, 35] Operation: 45-10=35 Exploring Operation: 10+33=43, Resulting Numbers: [45, 43] Generated Node #0,2,4: 22:[45, 43] Operation: 10+33=43 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 22:[10, 12], Operations: ['78-33=45', '45-33=12'] Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[10, 33, 78, 33], Operations: [] Exploring Operation: 78-33=45, Resulting Numbers: [10, 33, 45] Generated Node #0,2: 22:[10, 33, 45] Operation: 78-33=45 Moving to Node #0,2 Current State: 22:[10, 33, 45], Operations: ['78-33=45'] Exploring Operation: 45-33=12, Resulting Numbers: [10, 12] Generated Node #0,2,2: 22:[10, 12] Operation: 45-33=12 Moving to Node #0,2,2 Current State: 22:[10, 12], Operations: ['78-33=45', '45-33=12'] Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 17, 89, 71, 15 ]
20
[ "17+89=106", "71+15=86", "106-86=20" ]
Current State: 20:[17, 89, 71, 15], Operations: [] Exploring Operation: 17+89=106, Resulting Numbers: [71, 15, 106] Generated Node #2: [71, 15, 106] from Operation: 17+89=106 Current State: 20:[71, 15, 106], Operations: ['17+89=106'] Exploring Operation: 71+15=86, Resulting Numbers: [106, 86] Generated Node #3: [106, 86] from Operation: 71+15=86 Current State: 20:[106, 86], Operations: ['17+89=106', '71+15=86'] Exploring Operation: 106-86=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[17, 89, 71, 15], Operations: [] Exploring Operation: 89-17=72, Resulting Numbers: [71, 15, 72] Generated Node #0,0: 20:[71, 15, 72] Operation: 89-17=72 Exploring Operation: 71-17=54, Resulting Numbers: [89, 15, 54] Generated Node #0,1: 20:[89, 15, 54] Operation: 71-17=54 Exploring Operation: 89-15=74, Resulting Numbers: [17, 71, 74] Generated Node #0,2: 20:[17, 71, 74] Operation: 89-15=74 Exploring Operation: 89-71=18, Resulting Numbers: [17, 15, 18] Generated Node #0,3: 20:[17, 15, 18] Operation: 89-71=18 Moving to Node #0,3 Current State: 20:[17, 15, 18], Operations: ['89-71=18'] Exploring Operation: 18-17=1, Resulting Numbers: [15, 1] Generated Node #0,3,0: 20:[15, 1] Operation: 18-17=1 Exploring Operation: 17-15=2, Resulting Numbers: [18, 2] Generated Node #0,3,1: 20:[18, 2] Operation: 17-15=2 Exploring Operation: 17+15=32, Resulting Numbers: [18, 32] Generated Node #0,3,2: 20:[18, 32] Operation: 17+15=32 Exploring Operation: 18-15=3, Resulting Numbers: [17, 3] Generated Node #0,3,3: 20:[17, 3] Operation: 18-15=3 Moving to Node #0,1 Current State: 20:[89, 15, 54], Operations: ['71-17=54'] Exploring Operation: 89+15=104, Resulting Numbers: [54, 104] Generated Node #0,1,0: 20:[54, 104] Operation: 89+15=104 Exploring Operation: 89-54=35, Resulting Numbers: [15, 35] Generated Node #0,1,1: 20:[15, 35] Operation: 89-54=35 Exploring Operation: 89-15=74, Resulting Numbers: [54, 74] Generated Node #0,1,2: 20:[54, 74] Operation: 89-15=74 Exploring Operation: 54-15=39, Resulting Numbers: [89, 39] Generated Node #0,1,3: 20:[89, 39] Operation: 54-15=39 Moving to Node #0,0 Current State: 20:[71, 15, 72], Operations: ['89-17=72'] Exploring Operation: 71-15=56, Resulting Numbers: [72, 56] Generated Node #0,0,0: 20:[72, 56] Operation: 71-15=56 Exploring Operation: 72-15=57, Resulting Numbers: [71, 57] Generated Node #0,0,1: 20:[71, 57] Operation: 72-15=57 Exploring Operation: 71+15=86, Resulting Numbers: [72, 86] Generated Node #0,0,2: 20:[72, 86] Operation: 71+15=86 Exploring Operation: 72-71=1, Resulting Numbers: [15, 1] Generated Node #0,0,3: 20:[15, 1] Operation: 72-71=1 Moving to Node #0,2 Current State: 20:[17, 71, 74], Operations: ['89-15=74'] Exploring Operation: 74-17=57, Resulting Numbers: [71, 57] Generated Node #0,2,0: 20:[71, 57] Operation: 74-17=57 Exploring Operation: 17+71=88, Resulting Numbers: [74, 88] Generated Node #0,2,1: 20:[74, 88] Operation: 17+71=88 Exploring Operation: 71-17=54, Resulting Numbers: [74, 54] Generated Node #0,2,2: 20:[74, 54] Operation: 71-17=54 Exploring Operation: 74-71=3, Resulting Numbers: [17, 3] Generated Node #0,2,3: 20:[17, 3] Operation: 74-71=3 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 20:[17, 3], Operations: ['89-15=74', '74-71=3'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,20 unequal: No Solution Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,20 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[17, 89, 71, 15], Operations: [] Exploring Operation: 89-15=74, Resulting Numbers: [17, 71, 74] Generated Node #0,2: 20:[17, 71, 74] Operation: 89-15=74 Moving to Node #0,2 Current State: 20:[17, 71, 74], Operations: ['89-15=74'] Exploring Operation: 74-71=3, Resulting Numbers: [17, 3] Generated Node #0,2,3: 20:[17, 3] Operation: 74-71=3 Moving to Node #0,2,3 Current State: 20:[17, 3], Operations: ['89-15=74', '74-71=3'] Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_4
sum_heuristic
[ 14, 4, 84, 16 ]
88
[ "84/14=6", "16+6=22", "4*22=88" ]
Current State: 88:[14, 4, 84, 16], Operations: [] Exploring Operation: 84/14=6, Resulting Numbers: [4, 16, 6] Generated Node #2: [4, 16, 6] from Operation: 84/14=6 Current State: 88:[4, 16, 6], Operations: ['84/14=6'] Exploring Operation: 16+6=22, Resulting Numbers: [4, 22] Generated Node #3: [4, 22] from Operation: 16+6=22 Current State: 88:[4, 22], Operations: ['84/14=6', '16+6=22'] Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[14, 4, 84, 16], Operations: [] Exploring Operation: 84/14=6, Resulting Numbers: [4, 16, 6] Generated Node #0,0: 88:[4, 16, 6] Operation: 84/14=6 Exploring Operation: 16-14=2, Resulting Numbers: [4, 84, 2] Generated Node #0,1: 88:[4, 84, 2] Operation: 16-14=2 Exploring Operation: 16/4=4, Resulting Numbers: [14, 84, 4] Generated Node #0,2: 88:[14, 84, 4] Operation: 16/4=4 Moving to Node #0,1 Current State: 88:[4, 84, 2], Operations: ['16-14=2'] Exploring Operation: 84/4=21, Resulting Numbers: [2, 21] Generated Node #0,1,0: 88:[2, 21] Operation: 84/4=21 Exploring Operation: 84+2=86, Resulting Numbers: [4, 86] Generated Node #0,1,1: 88:[4, 86] Operation: 84+2=86 Exploring Operation: 4+84=88, Resulting Numbers: [2, 88] Generated Node #0,1,2: 88:[2, 88] Operation: 4+84=88 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 88:[2, 88], Operations: ['16-14=2', '4+84=88'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,88 unequal: No Solution Exploring Operation: 2+88=90, Resulting Numbers: [90] 90,88 unequal: No Solution Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[2, 21], Operations: ['16-14=2', '84/4=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,88 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,88 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,88 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 #0,1,1 Current State: 88:[4, 86], Operations: ['16-14=2', '84+2=86'] Exploring Operation: 4*86=344, Resulting Numbers: [344] 344,88 unequal: No Solution Exploring Operation: 4+86=90, Resulting Numbers: [90] 90,88 unequal: No Solution Exploring Operation: 86-4=82, Resulting Numbers: [82] 82,88 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: 88:[4, 16, 6], Operations: ['84/14=6'] Exploring Operation: 16-6=10, Resulting Numbers: [4, 10] Generated Node #0,0,0: 88:[4, 10] Operation: 16-6=10 Exploring Operation: 16/4=4, Resulting Numbers: [6, 4] Generated Node #0,0,1: 88:[6, 4] Operation: 16/4=4 Exploring Operation: 16+6=22, Resulting Numbers: [4, 22] Generated Node #0,0,2: 88:[4, 22] Operation: 16+6=22 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 88:[4, 22], Operations: ['84/14=6', '16+6=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,88 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[14, 4, 84, 16], Operations: [] Exploring Operation: 84/14=6, Resulting Numbers: [4, 16, 6] Generated Node #0,0: 88:[4, 16, 6] Operation: 84/14=6 Moving to Node #0,0 Current State: 88:[4, 16, 6], Operations: ['84/14=6'] Exploring Operation: 16+6=22, Resulting Numbers: [4, 22] Generated Node #0,0,2: 88:[4, 22] Operation: 16+6=22 Moving to Node #0,0,2 Current State: 88:[4, 22], Operations: ['84/14=6', '16+6=22'] Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 3, 51, 8, 96 ]
33
[ "51-8=43", "3*43=129", "129-96=33" ]
Current State: 33:[3, 51, 8, 96], Operations: [] Exploring Operation: 51-8=43, Resulting Numbers: [3, 96, 43] Generated Node #2: [3, 96, 43] from Operation: 51-8=43 Current State: 33:[3, 96, 43], Operations: ['51-8=43'] Exploring Operation: 3*43=129, Resulting Numbers: [96, 129] Generated Node #3: [96, 129] from Operation: 3*43=129 Current State: 33:[96, 129], Operations: ['51-8=43', '3*43=129'] Exploring Operation: 129-96=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[3, 51, 8, 96], Operations: [] Exploring Operation: 96-51=45, Resulting Numbers: [3, 8, 45] Generated Node #0,0: 33:[3, 8, 45] Operation: 96-51=45 Moving to Node #0,0 Current State: 33:[3, 8, 45], Operations: ['96-51=45'] Exploring Operation: 45-8=37, Resulting Numbers: [3, 37] Generated Node #0,0,0: 33:[3, 37] Operation: 45-8=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[3, 37], Operations: ['96-51=45', '45-8=37'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 62, 57, 21, 91 ]
75
[ "62-57=5", "91-21=70", "5+70=75" ]
Current State: 75:[62, 57, 21, 91], Operations: [] Exploring Operation: 62-57=5, Resulting Numbers: [21, 91, 5] Generated Node #2: [21, 91, 5] from Operation: 62-57=5 Current State: 75:[21, 91, 5], Operations: ['62-57=5'] Exploring Operation: 91-21=70, Resulting Numbers: [5, 70] Generated Node #3: [5, 70] from Operation: 91-21=70 Current State: 75:[5, 70], Operations: ['62-57=5', '91-21=70'] Exploring Operation: 5+70=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[62, 57, 21, 91], Operations: [] Exploring Operation: 91-62=29, Resulting Numbers: [57, 21, 29] Generated Node #0,0: 75:[57, 21, 29] Operation: 91-62=29 Exploring Operation: 62-57=5, Resulting Numbers: [21, 91, 5] Generated Node #0,1: 75:[21, 91, 5] Operation: 62-57=5 Exploring Operation: 91-57=34, Resulting Numbers: [62, 21, 34] Generated Node #0,2: 75:[62, 21, 34] Operation: 91-57=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[21, 91, 5], Operations: ['62-57=5'] Exploring Operation: 21+5=26, Resulting Numbers: [91, 26] Generated Node #0,1,0: 75:[91, 26] Operation: 21+5=26 Exploring Operation: 91-5=86, Resulting Numbers: [21, 86] Generated Node #0,1,1: 75:[21, 86] Operation: 91-5=86 Exploring Operation: 91-21=70, Resulting Numbers: [5, 70] Generated Node #0,1,2: 75:[5, 70] Operation: 91-21=70 Moving to Node #0,1,2 Current State: 75:[5, 70], Operations: ['62-57=5', '91-21=70'] Exploring Operation: 5+70=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[62, 57, 21, 91], Operations: [] Exploring Operation: 62-57=5, Resulting Numbers: [21, 91, 5] Generated Node #0,1: 75:[21, 91, 5] Operation: 62-57=5 Moving to Node #0,1 Current State: 75:[21, 91, 5], Operations: ['62-57=5'] Exploring Operation: 91-21=70, Resulting Numbers: [5, 70] Generated Node #0,1,2: 75:[5, 70] Operation: 91-21=70 Moving to Node #0,1,2 Current State: 75:[5, 70], Operations: ['62-57=5', '91-21=70'] Exploring Operation: 5+70=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 80, 66, 46, 40 ]
18
[ "80/40=2", "66-46=20", "20-2=18" ]
Current State: 18:[80, 66, 46, 40], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [66, 46, 2] Generated Node #2: [66, 46, 2] from Operation: 80/40=2 Current State: 18:[66, 46, 2], Operations: ['80/40=2'] Exploring Operation: 66-46=20, Resulting Numbers: [2, 20] Generated Node #3: [2, 20] from Operation: 66-46=20 Current State: 18:[2, 20], Operations: ['80/40=2', '66-46=20'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[80, 66, 46, 40], Operations: [] Exploring Operation: 80-66=14, Resulting Numbers: [46, 40, 14] Generated Node #0,0: 18:[46, 40, 14] Operation: 80-66=14 Exploring Operation: 80-46=34, Resulting Numbers: [66, 40, 34] Generated Node #0,1: 18:[66, 40, 34] Operation: 80-46=34 Exploring Operation: 80/40=2, Resulting Numbers: [66, 46, 2] Generated Node #0,2: 18:[66, 46, 2] Operation: 80/40=2 Moving to Node #0,0 Current State: 18:[46, 40, 14], Operations: ['80-66=14'] Exploring Operation: 46-14=32, Resulting Numbers: [40, 32] Generated Node #0,0,0: 18:[40, 32] Operation: 46-14=32 Exploring Operation: 46-40=6, Resulting Numbers: [14, 6] Generated Node #0,0,1: 18:[14, 6] Operation: 46-40=6 Exploring Operation: 40-14=26, Resulting Numbers: [46, 26] Generated Node #0,0,2: 18:[46, 26] Operation: 40-14=26 Moving to Node #0,2 Current State: 18:[66, 46, 2], Operations: ['80/40=2'] Exploring Operation: 46/2=23, Resulting Numbers: [66, 23] Generated Node #0,2,0: 18:[66, 23] Operation: 46/2=23 Exploring Operation: 66/2=33, Resulting Numbers: [46, 33] Generated Node #0,2,1: 18:[46, 33] Operation: 66/2=33 Exploring Operation: 66-46=20, Resulting Numbers: [2, 20] Generated Node #0,2,2: 18:[2, 20] Operation: 66-46=20 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[2, 20], Operations: ['80/40=2', '66-46=20'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[80, 66, 46, 40], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [66, 46, 2] Generated Node #0,2: 18:[66, 46, 2] Operation: 80/40=2 Moving to Node #0,2 Current State: 18:[66, 46, 2], Operations: ['80/40=2'] Exploring Operation: 66-46=20, Resulting Numbers: [2, 20] Generated Node #0,2,2: 18:[2, 20] Operation: 66-46=20 Moving to Node #0,2,2 Current State: 18:[2, 20], Operations: ['80/40=2', '66-46=20'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 48, 36, 74, 87 ]
71
[ "48+36=84", "87-74=13", "84-13=71" ]
Current State: 71:[48, 36, 74, 87], Operations: [] Exploring Operation: 48+36=84, Resulting Numbers: [74, 87, 84] Generated Node #2: [74, 87, 84] from Operation: 48+36=84 Current State: 71:[74, 87, 84], Operations: ['48+36=84'] Exploring Operation: 87-74=13, Resulting Numbers: [84, 13] Generated Node #3: [84, 13] from Operation: 87-74=13 Current State: 71:[84, 13], Operations: ['48+36=84', '87-74=13'] Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[48, 36, 74, 87], Operations: [] Exploring Operation: 48+36=84, Resulting Numbers: [74, 87, 84] Generated Node #0,0: 71:[74, 87, 84] Operation: 48+36=84 Exploring Operation: 87-48=39, Resulting Numbers: [36, 74, 39] Generated Node #0,1: 71:[36, 74, 39] Operation: 87-48=39 Exploring Operation: 87-36=51, Resulting Numbers: [48, 74, 51] Generated Node #0,2: 71:[48, 74, 51] Operation: 87-36=51 Exploring Operation: 74-36=38, Resulting Numbers: [48, 87, 38] Generated Node #0,3: 71:[48, 87, 38] Operation: 74-36=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[74, 87, 84], Operations: ['48+36=84'] Exploring Operation: 87-74=13, Resulting Numbers: [84, 13] Generated Node #0,0,0: 71:[84, 13] Operation: 87-74=13 Exploring Operation: 74+87=161, Resulting Numbers: [84, 161] Generated Node #0,0,1: 71:[84, 161] Operation: 74+87=161 Exploring Operation: 84-74=10, Resulting Numbers: [87, 10] Generated Node #0,0,2: 71:[87, 10] Operation: 84-74=10 Exploring Operation: 87-84=3, Resulting Numbers: [74, 3] Generated Node #0,0,3: 71:[74, 3] Operation: 87-84=3 Moving to Node #0,0,0 Current State: 71:[84, 13], Operations: ['48+36=84', '87-74=13'] Exploring Operation: 84+13=97, Resulting Numbers: [97] 97,71 unequal: No Solution Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[48, 36, 74, 87], Operations: [] Exploring Operation: 48+36=84, Resulting Numbers: [74, 87, 84] Generated Node #0,0: 71:[74, 87, 84] Operation: 48+36=84 Moving to Node #0,0 Current State: 71:[74, 87, 84], Operations: ['48+36=84'] Exploring Operation: 87-74=13, Resulting Numbers: [84, 13] Generated Node #0,0,0: 71:[84, 13] Operation: 87-74=13 Moving to Node #0,0,0 Current State: 71:[84, 13], Operations: ['48+36=84', '87-74=13'] Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 43, 26, 22, 12 ]
39
[ "26+22=48", "48/12=4", "43-4=39" ]
Current State: 39:[43, 26, 22, 12], Operations: [] Exploring Operation: 26+22=48, Resulting Numbers: [43, 12, 48] Generated Node #2: [43, 12, 48] from Operation: 26+22=48 Current State: 39:[43, 12, 48], Operations: ['26+22=48'] Exploring Operation: 48/12=4, Resulting Numbers: [43, 4] Generated Node #3: [43, 4] from Operation: 48/12=4 Current State: 39:[43, 4], Operations: ['26+22=48', '48/12=4'] Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[43, 26, 22, 12], Operations: [] Exploring Operation: 26-22=4, Resulting Numbers: [43, 12, 4] Generated Node #0,0: 39:[43, 12, 4] Operation: 26-22=4 Exploring Operation: 26+22=48, Resulting Numbers: [43, 12, 48] Generated Node #0,1: 39:[43, 12, 48] Operation: 26+22=48 Exploring Operation: 43-26=17, Resulting Numbers: [22, 12, 17] Generated Node #0,2: 39:[22, 12, 17] Operation: 43-26=17 Exploring Operation: 26+12=38, Resulting Numbers: [43, 22, 38] Generated Node #0,3: 39:[43, 22, 38] Operation: 26+12=38 Exploring Operation: 26-12=14, Resulting Numbers: [43, 22, 14] Generated Node #0,4: 39:[43, 22, 14] Operation: 26-12=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[43, 12, 4], Operations: ['26-22=4'] Exploring Operation: 12/4=3, Resulting Numbers: [43, 3] Generated Node #0,0,0: 39:[43, 3] Operation: 12/4=3 Exploring Operation: 43-4=39, Resulting Numbers: [12, 39] Generated Node #0,0,1: 39:[12, 39] Operation: 43-4=39 Exploring Operation: 43+4=47, Resulting Numbers: [12, 47] Generated Node #0,0,2: 39:[12, 47] Operation: 43+4=47 Exploring Operation: 43-12=31, Resulting Numbers: [4, 31] Generated Node #0,0,3: 39:[4, 31] Operation: 43-12=31 Exploring Operation: 12+4=16, Resulting Numbers: [43, 16] Generated Node #0,0,4: 39:[43, 16] Operation: 12+4=16 Moving to Node #0,0,1 Current State: 39:[12, 39], Operations: ['26-22=4', '43-4=39'] Exploring Operation: 39-12=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 12*39=468, Resulting Numbers: [468] 468,39 unequal: No Solution Exploring Operation: 12+39=51, Resulting Numbers: [51] 51,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[43, 3], Operations: ['26-22=4', '12/4=3'] Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 43*3=129, Resulting Numbers: [129] 129,39 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,39 unequal: No Solution Moving to Node #0,0,4 Current State: 39:[43, 16], Operations: ['26-22=4', '12+4=16'] Exploring Operation: 43*16=688, Resulting Numbers: [688] 688,39 unequal: No Solution Exploring Operation: 43-16=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 43+16=59, Resulting Numbers: [59] 59,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[12, 47], Operations: ['26-22=4', '43+4=47'] Exploring Operation: 12*47=564, Resulting Numbers: [564] 564,39 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 12+47=59, Resulting Numbers: [59] 59,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[4, 31], Operations: ['26-22=4', '43-12=31'] Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,39 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[43, 12, 48], Operations: ['26+22=48'] Exploring Operation: 43-12=31, Resulting Numbers: [48, 31] Generated Node #0,1,0: 39:[48, 31] Operation: 43-12=31 Exploring Operation: 48-43=5, Resulting Numbers: [12, 5] Generated Node #0,1,1: 39:[12, 5] Operation: 48-43=5 Exploring Operation: 48-12=36, Resulting Numbers: [43, 36] Generated Node #0,1,2: 39:[43, 36] Operation: 48-12=36 Exploring Operation: 48/12=4, Resulting Numbers: [43, 4] Generated Node #0,1,3: 39:[43, 4] Operation: 48/12=4 Exploring Operation: 43+12=55, Resulting Numbers: [48, 55] Generated Node #0,1,4: 39:[48, 55] Operation: 43+12=55 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 39:[12, 5], Operations: ['26+22=48', '48-43=5'] Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,39 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,39 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 39:[43, 4], Operations: ['26+22=48', '48/12=4'] Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[43, 26, 22, 12], Operations: [] Exploring Operation: 26+22=48, Resulting Numbers: [43, 12, 48] Generated Node #0,1: 39:[43, 12, 48] Operation: 26+22=48 Moving to Node #0,1 Current State: 39:[43, 12, 48], Operations: ['26+22=48'] Exploring Operation: 48/12=4, Resulting Numbers: [43, 4] Generated Node #0,1,3: 39:[43, 4] Operation: 48/12=4 Moving to Node #0,1,3 Current State: 39:[43, 4], Operations: ['26+22=48', '48/12=4'] Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_5
mult_heuristic
[ 27, 2, 7, 44 ]
66
[ "27+2=29", "44-7=37", "29+37=66" ]
Current State: 66:[27, 2, 7, 44], Operations: [] Exploring Operation: 27+2=29, Resulting Numbers: [7, 44, 29] Generated Node #2: [7, 44, 29] from Operation: 27+2=29 Current State: 66:[7, 44, 29], Operations: ['27+2=29'] Exploring Operation: 44-7=37, Resulting Numbers: [29, 37] Generated Node #3: [29, 37] from Operation: 44-7=37 Current State: 66:[29, 37], Operations: ['27+2=29', '44-7=37'] Exploring Operation: 29+37=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[27, 2, 7, 44], Operations: [] Exploring Operation: 44-27=17, Resulting Numbers: [2, 7, 17] Generated Node #0,0: 66:[2, 7, 17] Operation: 44-27=17 Exploring Operation: 44/2=22, Resulting Numbers: [27, 7, 22] Generated Node #0,1: 66:[27, 7, 22] Operation: 44/2=22 Exploring Operation: 44-7=37, Resulting Numbers: [27, 2, 37] Generated Node #0,2: 66:[27, 2, 37] Operation: 44-7=37 Exploring Operation: 27+44=71, Resulting Numbers: [2, 7, 71] Generated Node #0,3: 66:[2, 7, 71] Operation: 27+44=71 Moving to Node #0,0 Current State: 66:[2, 7, 17], Operations: ['44-27=17'] Exploring Operation: 17-7=10, Resulting Numbers: [2, 10] Generated Node #0,0,0: 66:[2, 10] Operation: 17-7=10 Exploring Operation: 7+17=24, Resulting Numbers: [2, 24] Generated Node #0,0,1: 66:[2, 24] Operation: 7+17=24 Exploring Operation: 2*17=34, Resulting Numbers: [7, 34] Generated Node #0,0,2: 66:[7, 34] Operation: 2*17=34 Exploring Operation: 2+17=19, Resulting Numbers: [7, 19] Generated Node #0,0,3: 66:[7, 19] Operation: 2+17=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 66:[2, 10], Operations: ['44-27=17', '17-7=10'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,66 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,66 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 66:[2, 24], Operations: ['44-27=17', '7+17=24'] Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,66 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 66:[7, 34], Operations: ['44-27=17', '2*17=34'] Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,66 unequal: No Solution Exploring Operation: 7*34=238, Resulting Numbers: [238] 238,66 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 66:[7, 19], Operations: ['44-27=17', '2+17=19'] Exploring Operation: 7*19=133, Resulting Numbers: [133] 133,66 unequal: No Solution Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,66 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,66 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: 66:[2, 7, 71], Operations: ['27+44=71'] Exploring Operation: 2+7=9, Resulting Numbers: [71, 9] Generated Node #0,3,0: 66:[71, 9] Operation: 2+7=9 Exploring Operation: 7-2=5, Resulting Numbers: [71, 5] Generated Node #0,3,1: 66:[71, 5] Operation: 7-2=5 Exploring Operation: 71-2=69, Resulting Numbers: [7, 69] Generated Node #0,3,2: 66:[7, 69] Operation: 71-2=69 Exploring Operation: 71-7=64, Resulting Numbers: [2, 64] Generated Node #0,3,3: 66:[2, 64] Operation: 71-7=64 Moving to Node #0,1 Current State: 66:[27, 7, 22], Operations: ['44/2=22'] Exploring Operation: 27-7=20, Resulting Numbers: [22, 20] Generated Node #0,1,0: 66:[22, 20] Operation: 27-7=20 Exploring Operation: 27-22=5, Resulting Numbers: [7, 5] Generated Node #0,1,1: 66:[7, 5] Operation: 27-22=5 Exploring Operation: 7+22=29, Resulting Numbers: [27, 29] Generated Node #0,1,2: 66:[27, 29] Operation: 7+22=29 Exploring Operation: 27+7=34, Resulting Numbers: [22, 34] Generated Node #0,1,3: 66:[22, 34] Operation: 27+7=34 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 66:[22, 34], Operations: ['44/2=22', '27+7=34'] Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 22*34=748, Resulting Numbers: [748] 748,66 unequal: No Solution Exploring Operation: 22+34=56, Resulting Numbers: [56] 56,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 66:[22, 20], Operations: ['44/2=22', '27-7=20'] Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,66 unequal: No Solution Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,66 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 66:[7, 5], Operations: ['44/2=22', '27-22=5'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,66 unequal: No Solution Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,66 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 66:[27, 29], Operations: ['44/2=22', '7+22=29'] Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,66 unequal: No Solution Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,66 unequal: No Solution Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,66 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: 66:[27, 2, 37], Operations: ['44-7=37'] Exploring Operation: 37-2=35, Resulting Numbers: [27, 35] Generated Node #0,2,0: 66:[27, 35] Operation: 37-2=35 Exploring Operation: 27-2=25, Resulting Numbers: [37, 25] Generated Node #0,2,1: 66:[37, 25] Operation: 27-2=25 Exploring Operation: 37-27=10, Resulting Numbers: [2, 10] Generated Node #0,2,2: 66:[2, 10] Operation: 37-27=10 Exploring Operation: 27+37=64, Resulting Numbers: [2, 64] Generated Node #0,2,3: 66:[2, 64] Operation: 27+37=64 Moving to Node #0,2,2 Current State: 66:[2, 10], Operations: ['44-7=37', '37-27=10'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,66 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,66 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,66 unequal: No Solution Moving to Node #0,2,3 Current State: 66:[2, 64], Operations: ['44-7=37', '27+37=64'] Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[27, 2, 7, 44], Operations: [] Exploring Operation: 44-7=37, Resulting Numbers: [27, 2, 37] Generated Node #0,2: 66:[27, 2, 37] Operation: 44-7=37 Moving to Node #0,2 Current State: 66:[27, 2, 37], Operations: ['44-7=37'] Exploring Operation: 27+37=64, Resulting Numbers: [2, 64] Generated Node #0,2,3: 66:[2, 64] Operation: 27+37=64 Moving to Node #0,2,3 Current State: 66:[2, 64], Operations: ['44-7=37', '27+37=64'] Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
0.952257
hs_4
mult_heuristic
[ 25, 18, 83, 85 ]
24
[ "25-18=7", "83+85=168", "168/7=24" ]
Current State: 24:[25, 18, 83, 85], Operations: [] Exploring Operation: 25-18=7, Resulting Numbers: [83, 85, 7] Generated Node #2: [83, 85, 7] from Operation: 25-18=7 Current State: 24:[83, 85, 7], Operations: ['25-18=7'] Exploring Operation: 83+85=168, Resulting Numbers: [7, 168] Generated Node #3: [7, 168] from Operation: 83+85=168 Current State: 24:[7, 168], Operations: ['25-18=7', '83+85=168'] Exploring Operation: 168/7=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[25, 18, 83, 85], Operations: [] Exploring Operation: 85-25=60, Resulting Numbers: [18, 83, 60] Generated Node #0,0: 24:[18, 83, 60] Operation: 85-25=60 Exploring Operation: 83-25=58, Resulting Numbers: [18, 85, 58] Generated Node #0,1: 24:[18, 85, 58] Operation: 83-25=58 Exploring Operation: 85-83=2, Resulting Numbers: [25, 18, 2] Generated Node #0,2: 24:[25, 18, 2] Operation: 85-83=2 Exploring Operation: 83-18=65, Resulting Numbers: [25, 85, 65] Generated Node #0,3: 24:[25, 85, 65] Operation: 83-18=65 Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[25, 18, 2], Operations: ['85-83=2'] Exploring Operation: 18/2=9, Resulting Numbers: [25, 9] Generated Node #0,2,0: 24:[25, 9] Operation: 18/2=9 Exploring Operation: 18+2=20, Resulting Numbers: [25, 20] Generated Node #0,2,1: 24:[25, 20] Operation: 18+2=20 Exploring Operation: 25-18=7, Resulting Numbers: [2, 7] Generated Node #0,2,2: 24:[2, 7] Operation: 25-18=7 Exploring Operation: 18-2=16, Resulting Numbers: [25, 16] Generated Node #0,2,3: 24:[25, 16] Operation: 18-2=16 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 24:[2, 7], Operations: ['85-83=2', '25-18=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,24 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,24 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 #0,2,0 Current State: 24:[25, 9], Operations: ['85-83=2', '18/2=9'] Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,24 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,24 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 #0,2,1 Current State: 24:[25, 20], Operations: ['85-83=2', '18+2=20'] Exploring Operation: 25*20=500, Resulting Numbers: [500] 500,24 unequal: No Solution Exploring Operation: 25+20=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,24 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 #0,2,3 Current State: 24:[25, 16], Operations: ['85-83=2', '18-2=16'] Exploring Operation: 25*16=400, Resulting Numbers: [400] 400,24 unequal: No Solution Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,24 unequal: No Solution Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,24 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[18, 83, 60], Operations: ['85-25=60'] Exploring Operation: 83-18=65, Resulting Numbers: [60, 65] Generated Node #0,0,0: 24:[60, 65] Operation: 83-18=65 Exploring Operation: 83-60=23, Resulting Numbers: [18, 23] Generated Node #0,0,1: 24:[18, 23] Operation: 83-60=23 Exploring Operation: 60-18=42, Resulting Numbers: [83, 42] Generated Node #0,0,2: 24:[83, 42] Operation: 60-18=42 Exploring Operation: 18+83=101, Resulting Numbers: [60, 101] Generated Node #0,0,3: 24:[60, 101] Operation: 18+83=101 Moving to Node #0,0,1 Current State: 24:[18, 23], Operations: ['85-25=60', '83-60=23'] Exploring Operation: 18*23=414, Resulting Numbers: [414] 414,24 unequal: No Solution Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 18+23=41, Resulting Numbers: [41] 41,24 unequal: No Solution Moving to Node #0,0,2 Current State: 24:[83, 42], Operations: ['85-25=60', '60-18=42'] Exploring Operation: 83-42=41, Resulting Numbers: [41] 41,24 unequal: No Solution Exploring Operation: 83+42=125, Resulting Numbers: [125] 125,24 unequal: No Solution Exploring Operation: 83*42=3486, Resulting Numbers: [3486] 3486,24 unequal: No Solution Moving to Node #0,0,0 Current State: 24:[60, 65], Operations: ['85-25=60', '83-18=65'] Exploring Operation: 60+65=125, Resulting Numbers: [125] 125,24 unequal: No Solution Exploring Operation: 65-60=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 60*65=3900, Resulting Numbers: [3900] 3900,24 unequal: No Solution Moving to Node #0,0,3 Current State: 24:[60, 101], Operations: ['85-25=60', '18+83=101'] Exploring Operation: 60+101=161, Resulting Numbers: [161] 161,24 unequal: No Solution Exploring Operation: 60*101=6060, Resulting Numbers: [6060] 6060,24 unequal: No Solution Exploring Operation: 101-60=41, Resulting Numbers: [41] 41,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[18, 85, 58], Operations: ['83-25=58'] Exploring Operation: 85-58=27, Resulting Numbers: [18, 27] Generated Node #0,1,0: 24:[18, 27] Operation: 85-58=27 Exploring Operation: 18+85=103, Resulting Numbers: [58, 103] Generated Node #0,1,1: 24:[58, 103] Operation: 18+85=103 Exploring Operation: 58-18=40, Resulting Numbers: [85, 40] Generated Node #0,1,2: 24:[85, 40] Operation: 58-18=40 Exploring Operation: 85-18=67, Resulting Numbers: [58, 67] Generated Node #0,1,3: 24:[58, 67] Operation: 85-18=67 Moving to Node #0,1,0 Current State: 24:[18, 27], Operations: ['83-25=58', '85-58=27'] Exploring Operation: 18*27=486, Resulting Numbers: [486] 486,24 unequal: No Solution Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,24 unequal: No Solution Moving to Node #0,1,3 Current State: 24:[58, 67], Operations: ['83-25=58', '85-18=67'] Exploring Operation: 67-58=9, Resulting Numbers: [9] 9,24 unequal: No Solution Exploring Operation: 58*67=3886, Resulting Numbers: [3886] 3886,24 unequal: No Solution Exploring Operation: 58+67=125, Resulting Numbers: [125] 125,24 unequal: No Solution Moving to Node #0,1,2 Current State: 24:[85, 40], Operations: ['83-25=58', '58-18=40'] Exploring Operation: 85-40=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 85+40=125, Resulting Numbers: [125] 125,24 unequal: No Solution Exploring Operation: 85*40=3400, Resulting Numbers: [3400] 3400,24 unequal: No Solution Moving to Node #0,1,1 Current State: 24:[58, 103], Operations: ['83-25=58', '18+85=103'] Exploring Operation: 58*103=5974, Resulting Numbers: [5974] 5974,24 unequal: No Solution Exploring Operation: 58+103=161, Resulting Numbers: [161] 161,24 unequal: No Solution Exploring Operation: 103-58=45, Resulting Numbers: [45] 45,24 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 #0,3 Current State: 24:[25, 85, 65], Operations: ['83-18=65'] Exploring Operation: 85-25=60, Resulting Numbers: [65, 60] Generated Node #0,3,0: 24:[65, 60] Operation: 85-25=60 Exploring Operation: 65-25=40, Resulting Numbers: [85, 40] Generated Node #0,3,1: 24:[85, 40] Operation: 65-25=40 Exploring Operation: 25+85=110, Resulting Numbers: [65, 110] Generated Node #0,3,2: 24:[65, 110] Operation: 25+85=110 Exploring Operation: 85-65=20, Resulting Numbers: [25, 20] Generated Node #0,3,3: 24:[25, 20] Operation: 85-65=20 Moving to Node #0,3,3 Current State: 24:[25, 20], Operations: ['83-18=65', '85-65=20'] Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 25*20=500, Resulting Numbers: [500] 500,24 unequal: No Solution Exploring Operation: 25+20=45, Resulting Numbers: [45] 45,24 unequal: No Solution Moving to Node #0,3,1 Current State: 24:[85, 40], Operations: ['83-18=65', '65-25=40'] Exploring Operation: 85+40=125, Resulting Numbers: [125] 125,24 unequal: No Solution Exploring Operation: 85-40=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 85*40=3400, Resulting Numbers: [3400] 3400,24 unequal: No Solution Moving to Node #0,3,0 Current State: 24:[65, 60], Operations: ['83-18=65', '85-25=60'] Exploring Operation: 65+60=125, Resulting Numbers: [125] 125,24 unequal: No Solution Exploring Operation: 65-60=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 65*60=3900, Resulting Numbers: [3900] 3900,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[65, 110], Operations: ['83-18=65', '25+85=110'] Exploring Operation: 110-65=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 65*110=7150, Resulting Numbers: [7150] 7150,24 unequal: No Solution Exploring Operation: 65+110=175, Resulting Numbers: [175] 175,24 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
[ 2, 1, 72, 97 ]
61
[ "2*1=2", "72/2=36", "97-36=61" ]
Current State: 61:[2, 1, 72, 97], Operations: [] Exploring Operation: 2*1=2, Resulting Numbers: [72, 97, 2] Generated Node #2: [72, 97, 2] from Operation: 2*1=2 Current State: 61:[72, 97, 2], Operations: ['2*1=2'] Exploring Operation: 72/2=36, Resulting Numbers: [97, 36] Generated Node #3: [97, 36] from Operation: 72/2=36 Current State: 61:[97, 36], Operations: ['2*1=2', '72/2=36'] Exploring Operation: 97-36=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[2, 1, 72, 97], Operations: [] Exploring Operation: 72-2=70, Resulting Numbers: [1, 97, 70] Generated Node #0,0: 61:[1, 97, 70] Operation: 72-2=70 Exploring Operation: 2+1=3, Resulting Numbers: [72, 97, 3] Generated Node #0,1: 61:[72, 97, 3] Operation: 2+1=3 Exploring Operation: 97-2=95, Resulting Numbers: [1, 72, 95] Generated Node #0,2: 61:[1, 72, 95] Operation: 97-2=95 Exploring Operation: 72-1=71, Resulting Numbers: [2, 97, 71] Generated Node #0,3: 61:[2, 97, 71] Operation: 72-1=71 Exploring Operation: 97-1=96, Resulting Numbers: [2, 72, 96] Generated Node #0,4: 61:[2, 72, 96] Operation: 97-1=96 Moving to Node #0,0 Current State: 61:[1, 97, 70], Operations: ['72-2=70'] Exploring Operation: 1*97=97, Resulting Numbers: [70, 97] Generated Node #0,0,0: 61:[70, 97] Operation: 1*97=97 Exploring Operation: 97/1=97, Resulting Numbers: [70, 97] Generated Node #0,0,1: 61:[70, 97] Operation: 97/1=97 Exploring Operation: 1*70=70, Resulting Numbers: [97, 70] Generated Node #0,0,2: 61:[97, 70] Operation: 1*70=70 Exploring Operation: 97-1=96, Resulting Numbers: [70, 96] Generated Node #0,0,3: 61:[70, 96] Operation: 97-1=96 Exploring Operation: 70-1=69, Resulting Numbers: [97, 69] Generated Node #0,0,4: 61:[97, 69] Operation: 70-1=69 Moving to Node #0,2 Current State: 61:[1, 72, 95], Operations: ['97-2=95'] Exploring Operation: 72-1=71, Resulting Numbers: [95, 71] Generated Node #0,2,0: 61:[95, 71] Operation: 72-1=71 Exploring Operation: 95-1=94, Resulting Numbers: [72, 94] Generated Node #0,2,1: 61:[72, 94] Operation: 95-1=94 Exploring Operation: 1*95=95, Resulting Numbers: [72, 95] Generated Node #0,2,2: 61:[72, 95] Operation: 1*95=95 Exploring Operation: 1*72=72, Resulting Numbers: [95, 72] Generated Node #0,2,3: 61:[95, 72] Operation: 1*72=72 Exploring Operation: 72/1=72, Resulting Numbers: [95, 72] Generated Node #0,2,4: 61:[95, 72] Operation: 72/1=72 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[95, 71], Operations: ['97-2=95', '72-1=71'] Exploring Operation: 95*71=6745, Resulting Numbers: [6745] 6745,61 unequal: No Solution Exploring Operation: 95+71=166, Resulting Numbers: [166] 166,61 unequal: No Solution Exploring Operation: 95-71=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 #0,2,1 Current State: 61:[72, 94], Operations: ['97-2=95', '95-1=94'] Exploring Operation: 72*94=6768, Resulting Numbers: [6768] 6768,61 unequal: No Solution Exploring Operation: 72+94=166, Resulting Numbers: [166] 166,61 unequal: No Solution Exploring Operation: 94-72=22, Resulting Numbers: [22] 22,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 61:[72, 95], Operations: ['97-2=95', '1*95=95'] Exploring Operation: 95-72=23, Resulting Numbers: [23] 23,61 unequal: No Solution Exploring Operation: 72*95=6840, Resulting Numbers: [6840] 6840,61 unequal: No Solution Exploring Operation: 72+95=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 #0,2,3 Current State: 61:[95, 72], Operations: ['97-2=95', '1*72=72'] Exploring Operation: 95-72=23, Resulting Numbers: [23] 23,61 unequal: No Solution Exploring Operation: 95*72=6840, Resulting Numbers: [6840] 6840,61 unequal: No Solution Exploring Operation: 95+72=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 #0,2,4 Current State: 61:[95, 72], Operations: ['97-2=95', '72/1=72'] Exploring Operation: 95*72=6840, Resulting Numbers: [6840] 6840,61 unequal: No Solution Exploring Operation: 95+72=167, Resulting Numbers: [167] 167,61 unequal: No Solution Exploring Operation: 95-72=23, Resulting Numbers: [23] 23,61 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: 61:[2, 72, 96], Operations: ['97-1=96'] Exploring Operation: 2+72=74, Resulting Numbers: [96, 74] Generated Node #0,4,0: 61:[96, 74] Operation: 2+72=74 Exploring Operation: 2+96=98, Resulting Numbers: [72, 98] Generated Node #0,4,1: 61:[72, 98] Operation: 2+96=98 Exploring Operation: 96-2=94, Resulting Numbers: [72, 94] Generated Node #0,4,2: 61:[72, 94] Operation: 96-2=94 Exploring Operation: 72-2=70, Resulting Numbers: [96, 70] Generated Node #0,4,3: 61:[96, 70] Operation: 72-2=70 Exploring Operation: 96/2=48, Resulting Numbers: [72, 48] Generated Node #0,4,4: 61:[72, 48] Operation: 96/2=48 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 61:[72, 48], Operations: ['97-1=96', '96/2=48'] Exploring Operation: 72-48=24, Resulting Numbers: [24] 24,61 unequal: No Solution Exploring Operation: 72*48=3456, Resulting Numbers: [3456] 3456,61 unequal: No Solution Exploring Operation: 72+48=120, Resulting Numbers: [120] 120,61 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 #0,4,2 Current State: 61:[72, 94], Operations: ['97-1=96', '96-2=94'] Exploring Operation: 72*94=6768, Resulting Numbers: [6768] 6768,61 unequal: No Solution Exploring Operation: 72+94=166, Resulting Numbers: [166] 166,61 unequal: No Solution Exploring Operation: 94-72=22, Resulting Numbers: [22] 22,61 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 #0,4,3 Current State: 61:[96, 70], Operations: ['97-1=96', '72-2=70'] Exploring Operation: 96-70=26, Resulting Numbers: [26] 26,61 unequal: No Solution Exploring Operation: 96*70=6720, Resulting Numbers: [6720] 6720,61 unequal: No Solution Exploring Operation: 96+70=166, Resulting Numbers: [166] 166,61 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 #0,4,0 Current State: 61:[96, 74], Operations: ['97-1=96', '2+72=74'] Exploring Operation: 96*74=7104, Resulting Numbers: [7104] 7104,61 unequal: No Solution Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,61 unequal: No Solution Exploring Operation: 96+74=170, Resulting Numbers: [170] 170,61 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 #0,4,1 Current State: 61:[72, 98], Operations: ['97-1=96', '2+96=98'] Exploring Operation: 98-72=26, Resulting Numbers: [26] 26,61 unequal: No Solution Exploring Operation: 72+98=170, Resulting Numbers: [170] 170,61 unequal: No Solution Exploring Operation: 72*98=7056, Resulting Numbers: [7056] 7056,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 61:[72, 97, 3], Operations: ['2+1=3'] Exploring Operation: 97+3=100, Resulting Numbers: [72, 100] Generated Node #0,1,0: 61:[72, 100] Operation: 97+3=100 Exploring Operation: 72+3=75, Resulting Numbers: [97, 75] Generated Node #0,1,1: 61:[97, 75] Operation: 72+3=75 Exploring Operation: 72-3=69, Resulting Numbers: [97, 69] Generated Node #0,1,2: 61:[97, 69] Operation: 72-3=69 Exploring Operation: 97-3=94, Resulting Numbers: [72, 94] Generated Node #0,1,3: 61:[72, 94] Operation: 97-3=94 Exploring Operation: 72/3=24, Resulting Numbers: [97, 24] Generated Node #0,1,4: 61:[97, 24] Operation: 72/3=24 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 61:[97, 69], Operations: ['2+1=3', '72-3=69'] Exploring Operation: 97*69=6693, Resulting Numbers: [6693] 6693,61 unequal: No Solution Exploring Operation: 97+69=166, Resulting Numbers: [166] 166,61 unequal: No Solution Exploring Operation: 97-69=28, Resulting Numbers: [28] 28,61 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:[72, 94], Operations: ['2+1=3', '97-3=94'] Exploring Operation: 72+94=166, Resulting Numbers: [166] 166,61 unequal: No Solution Exploring Operation: 72*94=6768, Resulting Numbers: [6768] 6768,61 unequal: No Solution Exploring Operation: 94-72=22, Resulting Numbers: [22] 22,61 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:[72, 100], Operations: ['2+1=3', '97+3=100'] Exploring Operation: 100-72=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 72*100=7200, Resulting Numbers: [7200] 7200,61 unequal: No Solution Exploring Operation: 72+100=172, Resulting Numbers: [172] 172,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[97, 75], Operations: ['2+1=3', '72+3=75'] Exploring Operation: 97*75=7275, Resulting Numbers: [7275] 7275,61 unequal: No Solution Exploring Operation: 97+75=172, Resulting Numbers: [172] 172,61 unequal: No Solution Exploring Operation: 97-75=22, Resulting Numbers: [22] 22,61 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 #0,1,4 Current State: 61:[97, 24], Operations: ['2+1=3', '72/3=24'] Exploring Operation: 97-24=73, Resulting Numbers: [73] 73,61 unequal: No Solution Exploring Operation: 97*24=2328, Resulting Numbers: [2328] 2328,61 unequal: No Solution Exploring Operation: 97+24=121, Resulting Numbers: [121] 121,61 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:[2, 97, 71], Operations: ['72-1=71'] Exploring Operation: 97-71=26, Resulting Numbers: [2, 26] Generated Node #0,3,0: 61:[2, 26] Operation: 97-71=26 Exploring Operation: 2+71=73, Resulting Numbers: [97, 73] Generated Node #0,3,1: 61:[97, 73] Operation: 2+71=73 Exploring Operation: 71-2=69, Resulting Numbers: [97, 69] Generated Node #0,3,2: 61:[97, 69] Operation: 71-2=69 Exploring Operation: 97-2=95, Resulting Numbers: [71, 95] Generated Node #0,3,3: 61:[71, 95] Operation: 97-2=95 Exploring Operation: 2+97=99, Resulting Numbers: [71, 99] Generated Node #0,3,4: 61:[71, 99] Operation: 2+97=99 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 61:[97, 69], Operations: ['72-1=71', '71-2=69'] Exploring Operation: 97+69=166, Resulting Numbers: [166] 166,61 unequal: No Solution Exploring Operation: 97-69=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 97*69=6693, Resulting Numbers: [6693] 6693,61 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:[71, 95], Operations: ['72-1=71', '97-2=95'] Exploring Operation: 71+95=166, Resulting Numbers: [166] 166,61 unequal: No Solution Exploring Operation: 95-71=24, Resulting Numbers: [24] 24,61 unequal: No Solution Exploring Operation: 71*95=6745, Resulting Numbers: [6745] 6745,61 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:[97, 73], Operations: ['72-1=71', '2+71=73'] Exploring Operation: 97-73=24, Resulting Numbers: [24] 24,61 unequal: No Solution Exploring Operation: 97*73=7081, Resulting Numbers: [7081] 7081,61 unequal: No Solution Exploring Operation: 97+73=170, Resulting Numbers: [170] 170,61 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 #0,3,4 Current State: 61:[71, 99], Operations: ['72-1=71', '2+97=99'] Exploring Operation: 99-71=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 71+99=170, Resulting Numbers: [170] 170,61 unequal: No Solution Exploring Operation: 71*99=7029, Resulting Numbers: [7029] 7029,61 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:[2, 26], Operations: ['72-1=71', '97-71=26'] Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,61 unequal: No Solution Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 61:[70, 96], Operations: ['72-2=70', '97-1=96'] Exploring Operation: 96-70=26, Resulting Numbers: [26] 26,61 unequal: No Solution Exploring Operation: 70*96=6720, Resulting Numbers: [6720] 6720,61 unequal: No Solution Exploring Operation: 70+96=166, Resulting Numbers: [166] 166,61 unequal: No Solution Moving to Node #0,0,4 Current State: 61:[97, 69], Operations: ['72-2=70', '70-1=69'] Exploring Operation: 97+69=166, Resulting Numbers: [166] 166,61 unequal: No Solution Exploring Operation: 97-69=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 97*69=6693, Resulting Numbers: [6693] 6693,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[70, 97], Operations: ['72-2=70', '1*97=97'] Exploring Operation: 70+97=167, Resulting Numbers: [167] 167,61 unequal: No Solution Exploring Operation: 97-70=27, Resulting Numbers: [27] 27,61 unequal: No Solution Exploring Operation: 70*97=6790, Resulting Numbers: [6790] 6790,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[70, 97], Operations: ['72-2=70', '97/1=97'] Exploring Operation: 70*97=6790, Resulting Numbers: [6790] 6790,61 unequal: No Solution Exploring Operation: 70+97=167, Resulting Numbers: [167] 167,61 unequal: No Solution Exploring Operation: 97-70=27, Resulting Numbers: [27] 27,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[97, 70], Operations: ['72-2=70', '1*70=70'] Exploring Operation: 97-70=27, Resulting Numbers: [27] 27,61 unequal: No Solution Exploring Operation: 97+70=167, Resulting Numbers: [167] 167,61 unequal: No Solution Exploring Operation: 97*70=6790, Resulting Numbers: [6790] 6790,61 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 95, 96, 30, 6 ]
84
[ "96-30=66", "66/6=11", "95-11=84" ]
Current State: 84:[95, 96, 30, 6], Operations: [] Exploring Operation: 96-30=66, Resulting Numbers: [95, 6, 66] Generated Node #2: [95, 6, 66] from Operation: 96-30=66 Current State: 84:[95, 6, 66], Operations: ['96-30=66'] Exploring Operation: 66/6=11, Resulting Numbers: [95, 11] Generated Node #3: [95, 11] from Operation: 66/6=11 Current State: 84:[95, 11], Operations: ['96-30=66', '66/6=11'] Exploring Operation: 95-11=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[95, 96, 30, 6], Operations: [] Exploring Operation: 96-6=90, Resulting Numbers: [95, 30, 90] Generated Node #0,0: 84:[95, 30, 90] Operation: 96-6=90 Exploring Operation: 96-95=1, Resulting Numbers: [30, 6, 1] Generated Node #0,1: 84:[30, 6, 1] Operation: 96-95=1 Exploring Operation: 95-6=89, Resulting Numbers: [96, 30, 89] Generated Node #0,2: 84:[96, 30, 89] Operation: 95-6=89 Exploring Operation: 96/6=16, Resulting Numbers: [95, 30, 16] Generated Node #0,3: 84:[95, 30, 16] Operation: 96/6=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[30, 6, 1], Operations: ['96-95=1'] Exploring Operation: 30/6=5, Resulting Numbers: [1, 5] Generated Node #0,1,0: 84:[1, 5] Operation: 30/6=5 Exploring Operation: 30*1=30, Resulting Numbers: [6, 30] Generated Node #0,1,1: 84:[6, 30] Operation: 30*1=30 Exploring Operation: 30/1=30, Resulting Numbers: [6, 30] Generated Node #0,1,2: 84:[6, 30] Operation: 30/1=30 Exploring Operation: 30-1=29, Resulting Numbers: [6, 29] Generated Node #0,1,3: 84:[6, 29] Operation: 30-1=29 Moving to Node #0,1,3 Current State: 84:[6, 29], Operations: ['96-95=1', '30-1=29'] Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,84 unequal: No Solution Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[6, 30], Operations: ['96-95=1', '30*1=30'] Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,84 unequal: No Solution Exploring Operation: 6+30=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 6*30=180, Resulting Numbers: [180] 180,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[1, 5], Operations: ['96-95=1', '30/6=5'] Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[6, 30], Operations: ['96-95=1', '30/1=30'] Exploring Operation: 6+30=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,84 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 6*30=180, Resulting Numbers: [180] 180,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 84:[95, 30, 16], Operations: ['96/6=16'] Exploring Operation: 95-16=79, Resulting Numbers: [30, 79] Generated Node #0,3,0: 84:[30, 79] Operation: 95-16=79 Exploring Operation: 30+16=46, Resulting Numbers: [95, 46] Generated Node #0,3,1: 84:[95, 46] Operation: 30+16=46 Exploring Operation: 30-16=14, Resulting Numbers: [95, 14] Generated Node #0,3,2: 84:[95, 14] Operation: 30-16=14 Exploring Operation: 95-30=65, Resulting Numbers: [16, 65] Generated Node #0,3,3: 84:[16, 65] Operation: 95-30=65 Moving to Node #0,3,0 Current State: 84:[30, 79], Operations: ['96/6=16', '95-16=79'] Exploring Operation: 30*79=2370, Resulting Numbers: [2370] 2370,84 unequal: No Solution Exploring Operation: 79-30=49, Resulting Numbers: [49] 49,84 unequal: No Solution Exploring Operation: 30+79=109, Resulting Numbers: [109] 109,84 unequal: No Solution Moving to Node #0,3,2 Current State: 84:[95, 14], Operations: ['96/6=16', '30-16=14'] Exploring Operation: 95-14=81, Resulting Numbers: [81] 81,84 unequal: No Solution Exploring Operation: 95+14=109, Resulting Numbers: [109] 109,84 unequal: No Solution Exploring Operation: 95*14=1330, Resulting Numbers: [1330] 1330,84 unequal: No Solution Moving to Node #0,3,1 Current State: 84:[95, 46], Operations: ['96/6=16', '30+16=46'] Exploring Operation: 95*46=4370, Resulting Numbers: [4370] 4370,84 unequal: No Solution Exploring Operation: 95-46=49, Resulting Numbers: [49] 49,84 unequal: No Solution Exploring Operation: 95+46=141, Resulting Numbers: [141] 141,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[16, 65], Operations: ['96/6=16', '95-30=65'] Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,84 unequal: No Solution Exploring Operation: 16*65=1040, Resulting Numbers: [1040] 1040,84 unequal: No Solution Exploring Operation: 16+65=81, Resulting Numbers: [81] 81,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[95, 30, 90], Operations: ['96-6=90'] Exploring Operation: 95-90=5, Resulting Numbers: [30, 5] Generated Node #0,0,0: 84:[30, 5] Operation: 95-90=5 Exploring Operation: 95-30=65, Resulting Numbers: [90, 65] Generated Node #0,0,1: 84:[90, 65] Operation: 95-30=65 Exploring Operation: 90-30=60, Resulting Numbers: [95, 60] Generated Node #0,0,2: 84:[95, 60] Operation: 90-30=60 Exploring Operation: 90/30=3, Resulting Numbers: [95, 3] Generated Node #0,0,3: 84:[95, 3] Operation: 90/30=3 Moving to Node #0,0,0 Current State: 84:[30, 5], Operations: ['96-6=90', '95-90=5'] Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 30*5=150, Resulting Numbers: [150] 150,84 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[95, 3], Operations: ['96-6=90', '90/30=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,84 unequal: No Solution Exploring Operation: 95*3=285, Resulting Numbers: [285] 285,84 unequal: No Solution Exploring Operation: 95-3=92, Resulting Numbers: [92] 92,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[90, 65], Operations: ['96-6=90', '95-30=65'] Exploring Operation: 90+65=155, Resulting Numbers: [155] 155,84 unequal: No Solution Exploring Operation: 90-65=25, Resulting Numbers: [25] 25,84 unequal: No Solution Exploring Operation: 90*65=5850, Resulting Numbers: [5850] 5850,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[95, 60], Operations: ['96-6=90', '90-30=60'] Exploring Operation: 95*60=5700, Resulting Numbers: [5700] 5700,84 unequal: No Solution Exploring Operation: 95-60=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 95+60=155, Resulting Numbers: [155] 155,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 84:[96, 30, 89], Operations: ['95-6=89'] Exploring Operation: 96-30=66, Resulting Numbers: [89, 66] Generated Node #0,2,0: 84:[89, 66] Operation: 96-30=66 Exploring Operation: 96-89=7, Resulting Numbers: [30, 7] Generated Node #0,2,1: 84:[30, 7] Operation: 96-89=7 Exploring Operation: 96+30=126, Resulting Numbers: [89, 126] Generated Node #0,2,2: 84:[89, 126] Operation: 96+30=126 Exploring Operation: 89-30=59, Resulting Numbers: [96, 59] Generated Node #0,2,3: 84:[96, 59] Operation: 89-30=59 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 84:[30, 7], Operations: ['95-6=89', '96-89=7'] Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,84 unequal: No Solution Exploring Operation: 30*7=210, Resulting Numbers: [210] 210,84 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,84 unequal: No Solution No 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: 84:[89, 66], Operations: ['95-6=89', '96-30=66'] Exploring Operation: 89+66=155, Resulting Numbers: [155] 155,84 unequal: No Solution Exploring Operation: 89-66=23, Resulting Numbers: [23] 23,84 unequal: No Solution Exploring Operation: 89*66=5874, Resulting Numbers: [5874] 5874,84 unequal: No Solution No 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: 84:[96, 59], Operations: ['95-6=89', '89-30=59'] Exploring Operation: 96*59=5664, Resulting Numbers: [5664] 5664,84 unequal: No Solution Exploring Operation: 96-59=37, Resulting Numbers: [37] 37,84 unequal: No Solution Exploring Operation: 96+59=155, Resulting Numbers: [155] 155,84 unequal: No Solution No 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: 84:[89, 126], Operations: ['95-6=89', '96+30=126'] Exploring Operation: 126-89=37, Resulting Numbers: [37] 37,84 unequal: No Solution Exploring Operation: 89*126=11214, Resulting Numbers: [11214] 11214,84 unequal: No Solution Exploring Operation: 89+126=215, Resulting Numbers: [215] 215,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 33, 23, 25, 56 ]
14
[ "33*23=759", "25+759=784", "784/56=14" ]
Current State: 14:[33, 23, 25, 56], Operations: [] Exploring Operation: 33*23=759, Resulting Numbers: [25, 56, 759] Generated Node #2: [25, 56, 759] from Operation: 33*23=759 Current State: 14:[25, 56, 759], Operations: ['33*23=759'] Exploring Operation: 25+759=784, Resulting Numbers: [56, 784] Generated Node #3: [56, 784] from Operation: 25+759=784 Current State: 14:[56, 784], Operations: ['33*23=759', '25+759=784'] Exploring Operation: 784/56=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[33, 23, 25, 56], Operations: [] Exploring Operation: 56-25=31, Resulting Numbers: [33, 23, 31] Generated Node #0,0: 14:[33, 23, 31] Operation: 56-25=31 Exploring Operation: 56-33=23, Resulting Numbers: [23, 25, 23] Generated Node #0,1: 14:[23, 25, 23] Operation: 56-33=23 Moving to Node #0,1 Current State: 14:[23, 25, 23], Operations: ['56-33=23'] Exploring Operation: 25-23=2, Resulting Numbers: [23, 2] Generated Node #0,1,0: 14:[23, 2] Operation: 25-23=2 Exploring Operation: 25-23=2, Resulting Numbers: [23, 2] Generated Node #0,1,1: 14:[23, 2] Operation: 25-23=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[23, 2], Operations: ['56-33=23', '25-23=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,14 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 14:[23, 2], Operations: ['56-33=23', '25-23=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,14 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,14 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: 14:[33, 23, 31], Operations: ['56-25=31'] Exploring Operation: 33-31=2, Resulting Numbers: [23, 2] Generated Node #0,0,0: 14:[23, 2] Operation: 33-31=2 Exploring Operation: 33-23=10, Resulting Numbers: [31, 10] Generated Node #0,0,1: 14:[31, 10] Operation: 33-23=10 Moving to Node #0,0,0 Current State: 14:[23, 2], Operations: ['56-25=31', '33-31=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,14 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[31, 10], Operations: ['56-25=31', '33-23=10'] Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,14 unequal: No Solution Exploring Operation: 31+10=41, Resulting Numbers: [41] 41,14 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 4, 41, 1, 72 ]
22
[ "72/4=18", "41-1=40", "40-18=22" ]
Current State: 22:[4, 41, 1, 72], Operations: [] Exploring Operation: 72/4=18, Resulting Numbers: [41, 1, 18] Generated Node #2: [41, 1, 18] from Operation: 72/4=18 Current State: 22:[41, 1, 18], Operations: ['72/4=18'] Exploring Operation: 41-1=40, Resulting Numbers: [18, 40] Generated Node #3: [18, 40] from Operation: 41-1=40 Current State: 22:[18, 40], Operations: ['72/4=18', '41-1=40'] Exploring Operation: 40-18=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[4, 41, 1, 72], Operations: [] Exploring Operation: 72-41=31, Resulting Numbers: [4, 1, 31] Generated Node #0,0: 22:[4, 1, 31] Operation: 72-41=31 Exploring Operation: 72/4=18, Resulting Numbers: [41, 1, 18] Generated Node #0,1: 22:[41, 1, 18] Operation: 72/4=18 Moving to Node #0,0 Current State: 22:[4, 1, 31], Operations: ['72-41=31'] Exploring Operation: 31-4=27, Resulting Numbers: [1, 27] Generated Node #0,0,0: 22:[1, 27] Operation: 31-4=27 Exploring Operation: 4-1=3, Resulting Numbers: [31, 3] Generated Node #0,0,1: 22:[31, 3] Operation: 4-1=3 Moving to Node #0,1 Current State: 22:[41, 1, 18], Operations: ['72/4=18'] Exploring Operation: 41-18=23, Resulting Numbers: [1, 23] Generated Node #0,1,0: 22:[1, 23] Operation: 41-18=23 Exploring Operation: 41-1=40, Resulting Numbers: [18, 40] Generated Node #0,1,1: 22:[18, 40] Operation: 41-1=40 Moving to Node #0,1,0 Current State: 22:[1, 23], Operations: ['72/4=18', '41-18=23'] Exploring Operation: 1*23=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[4, 41, 1, 72], Operations: [] Exploring Operation: 72/4=18, Resulting Numbers: [41, 1, 18] Generated Node #0,1: 22:[41, 1, 18] Operation: 72/4=18 Moving to Node #0,1 Current State: 22:[41, 1, 18], Operations: ['72/4=18'] Exploring Operation: 41-18=23, Resulting Numbers: [1, 23] Generated Node #0,1,0: 22:[1, 23] Operation: 41-18=23 Moving to Node #0,1,0 Current State: 22:[1, 23], Operations: ['72/4=18', '41-18=23'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.989583
hs_2
mult_heuristic
[ 84, 51, 82, 24 ]
54
[ "84-82=2", "51-24=27", "2*27=54" ]
Current State: 54:[84, 51, 82, 24], Operations: [] Exploring Operation: 84-82=2, Resulting Numbers: [51, 24, 2] Generated Node #2: [51, 24, 2] from Operation: 84-82=2 Current State: 54:[51, 24, 2], Operations: ['84-82=2'] Exploring Operation: 51-24=27, Resulting Numbers: [2, 27] Generated Node #3: [2, 27] from Operation: 51-24=27 Current State: 54:[2, 27], Operations: ['84-82=2', '51-24=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[84, 51, 82, 24], Operations: [] Exploring Operation: 84-82=2, Resulting Numbers: [51, 24, 2] Generated Node #0,0: 54:[51, 24, 2] Operation: 84-82=2 Exploring Operation: 84-51=33, Resulting Numbers: [82, 24, 33] Generated Node #0,1: 54:[82, 24, 33] Operation: 84-51=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[51, 24, 2], Operations: ['84-82=2'] Exploring Operation: 51+2=53, Resulting Numbers: [24, 53] Generated Node #0,0,0: 54:[24, 53] Operation: 51+2=53 Exploring Operation: 51-24=27, Resulting Numbers: [2, 27] Generated Node #0,0,1: 54:[2, 27] Operation: 51-24=27 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 54:[2, 27], Operations: ['84-82=2', '51-24=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[84, 51, 82, 24], Operations: [] Exploring Operation: 84-82=2, Resulting Numbers: [51, 24, 2] Generated Node #0,0: 54:[51, 24, 2] Operation: 84-82=2 Moving to Node #0,0 Current State: 54:[51, 24, 2], Operations: ['84-82=2'] Exploring Operation: 51-24=27, Resulting Numbers: [2, 27] Generated Node #0,0,1: 54:[2, 27] Operation: 51-24=27 Moving to Node #0,0,1 Current State: 54:[2, 27], Operations: ['84-82=2', '51-24=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 31, 97, 79, 72 ]
59
[ "97-31=66", "79-72=7", "66-7=59" ]
Current State: 59:[31, 97, 79, 72], Operations: [] Exploring Operation: 97-31=66, Resulting Numbers: [79, 72, 66] Generated Node #2: [79, 72, 66] from Operation: 97-31=66 Current State: 59:[79, 72, 66], Operations: ['97-31=66'] Exploring Operation: 79-72=7, Resulting Numbers: [66, 7] Generated Node #3: [66, 7] from Operation: 79-72=7 Current State: 59:[66, 7], Operations: ['97-31=66', '79-72=7'] Exploring Operation: 66-7=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[31, 97, 79, 72], Operations: [] Exploring Operation: 79-31=48, Resulting Numbers: [97, 72, 48] Generated Node #0,0: 59:[97, 72, 48] Operation: 79-31=48 Exploring Operation: 97-72=25, Resulting Numbers: [31, 79, 25] Generated Node #0,1: 59:[31, 79, 25] Operation: 97-72=25 Exploring Operation: 72-31=41, Resulting Numbers: [97, 79, 41] Generated Node #0,2: 59:[97, 79, 41] Operation: 72-31=41 Exploring Operation: 97-79=18, Resulting Numbers: [31, 72, 18] Generated Node #0,3: 59:[31, 72, 18] Operation: 97-79=18 Exploring Operation: 97-31=66, Resulting Numbers: [79, 72, 66] Generated Node #0,4: 59:[79, 72, 66] Operation: 97-31=66 Moving to Node #0,4 Current State: 59:[79, 72, 66], Operations: ['97-31=66'] Exploring Operation: 79+66=145, Resulting Numbers: [72, 145] Generated Node #0,4,0: 59:[72, 145] Operation: 79+66=145 Exploring Operation: 79+72=151, Resulting Numbers: [66, 151] Generated Node #0,4,1: 59:[66, 151] Operation: 79+72=151 Exploring Operation: 79-72=7, Resulting Numbers: [66, 7] Generated Node #0,4,2: 59:[66, 7] Operation: 79-72=7 Exploring Operation: 79-66=13, Resulting Numbers: [72, 13] Generated Node #0,4,3: 59:[72, 13] Operation: 79-66=13 Exploring Operation: 72-66=6, Resulting Numbers: [79, 6] Generated Node #0,4,4: 59:[79, 6] Operation: 72-66=6 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 59:[66, 7], Operations: ['97-31=66', '79-72=7'] Exploring Operation: 66+7=73, Resulting Numbers: [73] 73,59 unequal: No Solution Exploring Operation: 66*7=462, Resulting Numbers: [462] 462,59 unequal: No Solution Exploring Operation: 66-7=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[31, 97, 79, 72], Operations: [] Exploring Operation: 97-31=66, Resulting Numbers: [79, 72, 66] Generated Node #0,4: 59:[79, 72, 66] Operation: 97-31=66 Moving to Node #0,4 Current State: 59:[79, 72, 66], Operations: ['97-31=66'] Exploring Operation: 79-72=7, Resulting Numbers: [66, 7] Generated Node #0,4,2: 59:[66, 7] Operation: 79-72=7 Moving to Node #0,4,2 Current State: 59:[66, 7], Operations: ['97-31=66', '79-72=7'] Exploring Operation: 66-7=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 60, 44, 58, 54 ]
76
[ "60-58=2", "44/2=22", "54+22=76" ]
Current State: 76:[60, 44, 58, 54], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [44, 54, 2] Generated Node #2: [44, 54, 2] from Operation: 60-58=2 Current State: 76:[44, 54, 2], Operations: ['60-58=2'] Exploring Operation: 44/2=22, Resulting Numbers: [54, 22] Generated Node #3: [54, 22] from Operation: 44/2=22 Current State: 76:[54, 22], Operations: ['60-58=2', '44/2=22'] Exploring Operation: 54+22=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[60, 44, 58, 54], Operations: [] Exploring Operation: 60-54=6, Resulting Numbers: [44, 58, 6] Generated Node #0,0: 76:[44, 58, 6] Operation: 60-54=6 Exploring Operation: 60-58=2, Resulting Numbers: [44, 54, 2] Generated Node #0,1: 76:[44, 54, 2] Operation: 60-58=2 Exploring Operation: 58-54=4, Resulting Numbers: [60, 44, 4] Generated Node #0,2: 76:[60, 44, 4] Operation: 58-54=4 Moving to Node #0,1 Current State: 76:[44, 54, 2], Operations: ['60-58=2'] Exploring Operation: 54/2=27, Resulting Numbers: [44, 27] Generated Node #0,1,0: 76:[44, 27] Operation: 54/2=27 Exploring Operation: 44/2=22, Resulting Numbers: [54, 22] Generated Node #0,1,1: 76:[54, 22] Operation: 44/2=22 Exploring Operation: 54-44=10, Resulting Numbers: [2, 10] Generated Node #0,1,2: 76:[2, 10] Operation: 54-44=10 Moving to Node #0,2 Current State: 76:[60, 44, 4], Operations: ['58-54=4'] Exploring Operation: 60-44=16, Resulting Numbers: [4, 16] Generated Node #0,2,0: 76:[4, 16] Operation: 60-44=16 Exploring Operation: 60/4=15, Resulting Numbers: [44, 15] Generated Node #0,2,1: 76:[44, 15] Operation: 60/4=15 Exploring Operation: 60+4=64, Resulting Numbers: [44, 64] Generated Node #0,2,2: 76:[44, 64] Operation: 60+4=64 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 76:[4, 16], Operations: ['58-54=4', '60-44=16'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 76:[44, 15], Operations: ['58-54=4', '60/4=15'] Exploring Operation: 44-15=29, Resulting Numbers: [29] 29,76 unequal: No Solution Exploring Operation: 44+15=59, Resulting Numbers: [59] 59,76 unequal: No Solution Exploring Operation: 44*15=660, Resulting Numbers: [660] 660,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 76:[44, 64], Operations: ['58-54=4', '60+4=64'] Exploring Operation: 44*64=2816, Resulting Numbers: [2816] 2816,76 unequal: No Solution Exploring Operation: 64-44=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 44+64=108, Resulting Numbers: [108] 108,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 76:[44, 58, 6], Operations: ['60-54=6'] Exploring Operation: 58-44=14, Resulting Numbers: [6, 14] Generated Node #0,0,0: 76:[6, 14] Operation: 58-44=14 Exploring Operation: 58+6=64, Resulting Numbers: [44, 64] Generated Node #0,0,1: 76:[44, 64] Operation: 58+6=64 Exploring Operation: 44-6=38, Resulting Numbers: [58, 38] Generated Node #0,0,2: 76:[58, 38] Operation: 44-6=38 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[6, 14], Operations: ['60-54=6', '58-44=14'] Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 76:[44, 64], Operations: ['60-54=6', '58+6=64'] Exploring Operation: 64-44=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 44*64=2816, Resulting Numbers: [2816] 2816,76 unequal: No Solution Exploring Operation: 44+64=108, Resulting Numbers: [108] 108,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 76:[58, 38], Operations: ['60-54=6', '44-6=38'] Exploring Operation: 58-38=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 58+38=96, Resulting Numbers: [96] 96,76 unequal: No Solution Exploring Operation: 58*38=2204, Resulting Numbers: [2204] 2204,76 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: 76:[2, 10], Operations: ['60-58=2', '54-44=10'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,76 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[44, 27], Operations: ['60-58=2', '54/2=27'] Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,76 unequal: No Solution Exploring Operation: 44*27=1188, Resulting Numbers: [1188] 1188,76 unequal: No Solution Exploring Operation: 44+27=71, Resulting Numbers: [71] 71,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[54, 22], Operations: ['60-58=2', '44/2=22'] Exploring Operation: 54*22=1188, Resulting Numbers: [1188] 1188,76 unequal: No Solution Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 54+22=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[60, 44, 58, 54], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [44, 54, 2] Generated Node #0,1: 76:[44, 54, 2] Operation: 60-58=2 Moving to Node #0,1 Current State: 76:[44, 54, 2], Operations: ['60-58=2'] Exploring Operation: 44/2=22, Resulting Numbers: [54, 22] Generated Node #0,1,1: 76:[54, 22] Operation: 44/2=22 Moving to Node #0,1,1 Current State: 76:[54, 22], Operations: ['60-58=2', '44/2=22'] Exploring Operation: 54+22=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
0.962674
hs_3
mult_heuristic
[ 88, 33, 84, 36 ]
73
[ "88+33=121", "84-36=48", "121-48=73" ]
Current State: 73:[88, 33, 84, 36], Operations: [] Exploring Operation: 88+33=121, Resulting Numbers: [84, 36, 121] Generated Node #2: [84, 36, 121] from Operation: 88+33=121 Current State: 73:[84, 36, 121], Operations: ['88+33=121'] Exploring Operation: 84-36=48, Resulting Numbers: [121, 48] Generated Node #3: [121, 48] from Operation: 84-36=48 Current State: 73:[121, 48], Operations: ['88+33=121', '84-36=48'] Exploring Operation: 121-48=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[88, 33, 84, 36], Operations: [] Exploring Operation: 33+36=69, Resulting Numbers: [88, 84, 69] Generated Node #0,0: 73:[88, 84, 69] Operation: 33+36=69 Exploring Operation: 88-33=55, Resulting Numbers: [84, 36, 55] Generated Node #0,1: 73:[84, 36, 55] Operation: 88-33=55 Exploring Operation: 88-36=52, Resulting Numbers: [33, 84, 52] Generated Node #0,2: 73:[33, 84, 52] Operation: 88-36=52 Moving to Node #0,0 Current State: 73:[88, 84, 69], Operations: ['33+36=69'] Exploring Operation: 88-84=4, Resulting Numbers: [69, 4] Generated Node #0,0,0: 73:[69, 4] Operation: 88-84=4 Exploring Operation: 84-69=15, Resulting Numbers: [88, 15] Generated Node #0,0,1: 73:[88, 15] Operation: 84-69=15 Exploring Operation: 88-69=19, Resulting Numbers: [84, 19] Generated Node #0,0,2: 73:[84, 19] Operation: 88-69=19 Moving to Node #0,1 Current State: 73:[84, 36, 55], Operations: ['88-33=55'] Exploring Operation: 84-36=48, Resulting Numbers: [55, 48] Generated Node #0,1,0: 73:[55, 48] Operation: 84-36=48 Exploring Operation: 84+36=120, Resulting Numbers: [55, 120] Generated Node #0,1,1: 73:[55, 120] Operation: 84+36=120 Exploring Operation: 36+55=91, Resulting Numbers: [84, 91] Generated Node #0,1,2: 73:[84, 91] Operation: 36+55=91 Moving to Node #0,2 Current State: 73:[33, 84, 52], Operations: ['88-36=52'] Exploring Operation: 33+84=117, Resulting Numbers: [52, 117] Generated Node #0,2,0: 73:[52, 117] Operation: 33+84=117 Exploring Operation: 84-33=51, Resulting Numbers: [52, 51] Generated Node #0,2,1: 73:[52, 51] Operation: 84-33=51 Exploring Operation: 33+52=85, Resulting Numbers: [84, 85] Generated Node #0,2,2: 73:[84, 85] Operation: 33+52=85 Moving to Node #0,2,2 Current State: 73:[84, 85], Operations: ['88-36=52', '33+52=85'] Exploring Operation: 84*85=7140, Resulting Numbers: [7140] 7140,73 unequal: No Solution Exploring Operation: 85-84=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 84+85=169, Resulting Numbers: [169] 169,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[84, 91], Operations: ['88-33=55', '36+55=91'] Exploring Operation: 84+91=175, Resulting Numbers: [175] 175,73 unequal: No Solution Exploring Operation: 84*91=7644, Resulting Numbers: [7644] 7644,73 unequal: No Solution Exploring Operation: 91-84=7, Resulting Numbers: [7] 7,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[55, 48], Operations: ['88-33=55', '84-36=48'] Exploring Operation: 55*48=2640, Resulting Numbers: [2640] 2640,73 unequal: No Solution Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,73 unequal: No Solution Exploring Operation: 55+48=103, Resulting Numbers: [103] 103,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[52, 51], Operations: ['88-36=52', '84-33=51'] Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 52+51=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 52*51=2652, Resulting Numbers: [2652] 2652,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[55, 120], Operations: ['88-33=55', '84+36=120'] Exploring Operation: 120-55=65, Resulting Numbers: [65] 65,73 unequal: No Solution Exploring Operation: 55+120=175, Resulting Numbers: [175] 175,73 unequal: No Solution Exploring Operation: 55*120=6600, Resulting Numbers: [6600] 6600,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[84, 19], Operations: ['33+36=69', '88-69=19'] Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,73 unequal: No Solution Exploring Operation: 84+19=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 84*19=1596, Resulting Numbers: [1596] 1596,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[52, 117], Operations: ['88-36=52', '33+84=117'] Exploring Operation: 52*117=6084, Resulting Numbers: [6084] 6084,73 unequal: No Solution Exploring Operation: 52+117=169, Resulting Numbers: [169] 169,73 unequal: No Solution Exploring Operation: 117-52=65, Resulting Numbers: [65] 65,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[69, 4], Operations: ['33+36=69', '88-84=4'] Exploring Operation: 69*4=276, Resulting Numbers: [276] 276,73 unequal: No Solution Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,73 unequal: No Solution Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[88, 33, 84, 36], Operations: [] Exploring Operation: 33+36=69, Resulting Numbers: [88, 84, 69] Generated Node #0,0: 73:[88, 84, 69] Operation: 33+36=69 Moving to Node #0,0 Current State: 73:[88, 84, 69], Operations: ['33+36=69'] Exploring Operation: 88-84=4, Resulting Numbers: [69, 4] Generated Node #0,0,0: 73:[69, 4] Operation: 88-84=4 Moving to Node #0,0,0 Current State: 73:[69, 4], Operations: ['33+36=69', '88-84=4'] Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
0.965278
hs_3
sum_heuristic
[ 12, 5, 97, 7 ]
24
[ "97-12=85", "85/5=17", "7+17=24" ]
Current State: 24:[12, 5, 97, 7], Operations: [] Exploring Operation: 97-12=85, Resulting Numbers: [5, 7, 85] Generated Node #2: [5, 7, 85] from Operation: 97-12=85 Current State: 24:[5, 7, 85], Operations: ['97-12=85'] Exploring Operation: 85/5=17, Resulting Numbers: [7, 17] Generated Node #3: [7, 17] from Operation: 85/5=17 Current State: 24:[7, 17], Operations: ['97-12=85', '85/5=17'] Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[12, 5, 97, 7], Operations: [] Exploring Operation: 97-12=85, Resulting Numbers: [5, 7, 85] Generated Node #0,0: 24:[5, 7, 85] Operation: 97-12=85 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[5, 7, 85], Operations: ['97-12=85'] Exploring Operation: 85/5=17, Resulting Numbers: [7, 17] Generated Node #0,0,0: 24:[7, 17] Operation: 85/5=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[7, 17], Operations: ['97-12=85', '85/5=17'] Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[12, 5, 97, 7], Operations: [] Exploring Operation: 97-12=85, Resulting Numbers: [5, 7, 85] Generated Node #0,0: 24:[5, 7, 85] Operation: 97-12=85 Moving to Node #0,0 Current State: 24:[5, 7, 85], Operations: ['97-12=85'] Exploring Operation: 85/5=17, Resulting Numbers: [7, 17] Generated Node #0,0,0: 24:[7, 17] Operation: 85/5=17 Moving to Node #0,0,0 Current State: 24:[7, 17], Operations: ['97-12=85', '85/5=17'] Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 99, 27, 18, 18 ]
15
[ "99-18=81", "81/27=3", "18-3=15" ]
Current State: 15:[99, 27, 18, 18], Operations: [] Exploring Operation: 99-18=81, Resulting Numbers: [27, 81] Generated Node #2: [27, 81] from Operation: 99-18=81 Current State: 15:[27, 81], Operations: ['99-18=81'] Exploring Operation: 81/27=3, Resulting Numbers: [3] 3,15 equal: Goal Reached Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[99, 27, 18, 18], Operations: [] Exploring Operation: 27-18=9, Resulting Numbers: [99, 18, 9] Generated Node #0,0: 15:[99, 18, 9] Operation: 27-18=9 Exploring Operation: 99-27=72, Resulting Numbers: [18, 18, 72] Generated Node #0,1: 15:[18, 18, 72] Operation: 99-27=72 Exploring Operation: 99-18=81, Resulting Numbers: [27, 18, 81] Generated Node #0,2: 15:[27, 18, 81] Operation: 99-18=81 Exploring Operation: 27-18=9, Resulting Numbers: [99, 18, 9] Generated Node #0,3: 15:[99, 18, 9] Operation: 27-18=9 Exploring Operation: 99-18=81, Resulting Numbers: [27, 18, 81] Generated Node #0,4: 15:[27, 18, 81] Operation: 99-18=81 Moving to Node #0,1 Current State: 15:[18, 18, 72], Operations: ['99-27=72'] Exploring Operation: 18/18=1, Resulting Numbers: [72, 1] Generated Node #0,1,0: 15:[72, 1] Operation: 18/18=1 Exploring Operation: 72-18=54, Resulting Numbers: [18, 54] Generated Node #0,1,1: 15:[18, 54] Operation: 72-18=54 Exploring Operation: 72/18=4, Resulting Numbers: [18, 4] Generated Node #0,1,2: 15:[18, 4] Operation: 72/18=4 Exploring Operation: 72-18=54, Resulting Numbers: [18, 54] Generated Node #0,1,3: 15:[18, 54] Operation: 72-18=54 Exploring Operation: 72/18=4, Resulting Numbers: [18, 4] Generated Node #0,1,4: 15:[18, 4] Operation: 72/18=4 Moving to Node #0,4 Current State: 15:[27, 18, 81], Operations: ['99-18=81'] Exploring Operation: 27+18=45, Resulting Numbers: [81, 45] Generated Node #0,4,0: 15:[81, 45] Operation: 27+18=45 Exploring Operation: 27-18=9, Resulting Numbers: [81, 9] Generated Node #0,4,1: 15:[81, 9] Operation: 27-18=9 Exploring Operation: 81/27=3, Resulting Numbers: [18, 3] Generated Node #0,4,2: 15:[18, 3] Operation: 81/27=3 Exploring Operation: 81-27=54, Resulting Numbers: [18, 54] Generated Node #0,4,3: 15:[18, 54] Operation: 81-27=54 Exploring Operation: 81-18=63, Resulting Numbers: [27, 63] Generated Node #0,4,4: 15:[27, 63] Operation: 81-18=63 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 15:[18, 3], Operations: ['99-18=81', '81/27=3'] Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,15 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[99, 27, 18, 18], Operations: [] Exploring Operation: 99-18=81, Resulting Numbers: [27, 18, 81] Generated Node #0,4: 15:[27, 18, 81] Operation: 99-18=81 Moving to Node #0,4 Current State: 15:[27, 18, 81], Operations: ['99-18=81'] Exploring Operation: 81/27=3, Resulting Numbers: [18, 3] Generated Node #0,4,2: 15:[18, 3] Operation: 81/27=3 Moving to Node #0,4,2 Current State: 15:[18, 3], Operations: ['99-18=81', '81/27=3'] Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 61, 47, 61, 18 ]
57
[ "61-47=14", "61-18=43", "14+43=57" ]
Current State: 57:[61, 47, 61, 18], Operations: [] Exploring Operation: 61-47=14, Resulting Numbers: [18, 14] Generated Node #2: [18, 14] from Operation: 61-47=14 Current State: 57:[18, 14], Operations: ['61-47=14'] Exploring Operation: 61-18=43, Resulting Numbers: [14, 43] Generated Node #3: [14, 43] from Operation: 61-18=43 Current State: 57:[14, 43], Operations: ['61-47=14', '61-18=43'] Exploring Operation: 14+43=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[61, 47, 61, 18], Operations: [] Exploring Operation: 61-47=14, Resulting Numbers: [61, 18, 14] Generated Node #0,0: 57:[61, 18, 14] Operation: 61-47=14 Exploring Operation: 61-47=14, Resulting Numbers: [61, 18, 14] Generated Node #0,1: 57:[61, 18, 14] Operation: 61-47=14 Moving to Node #0,0 Current State: 57:[61, 18, 14], Operations: ['61-47=14'] Exploring Operation: 18-14=4, Resulting Numbers: [61, 4] Generated Node #0,0,0: 57:[61, 4] Operation: 18-14=4 Exploring Operation: 61-14=47, Resulting Numbers: [18, 47] Generated Node #0,0,1: 57:[18, 47] Operation: 61-14=47 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[61, 4], Operations: ['61-47=14', '18-14=4'] Exploring Operation: 61+4=65, Resulting Numbers: [65] 65,57 unequal: No Solution Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[61, 47, 61, 18], Operations: [] Exploring Operation: 61-47=14, Resulting Numbers: [61, 18, 14] Generated Node #0,0: 57:[61, 18, 14] Operation: 61-47=14 Moving to Node #0,0 Current State: 57:[61, 18, 14], Operations: ['61-47=14'] Exploring Operation: 18-14=4, Resulting Numbers: [61, 4] Generated Node #0,0,0: 57:[61, 4] Operation: 18-14=4 Moving to Node #0,0,0 Current State: 57:[61, 4], Operations: ['61-47=14', '18-14=4'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 92, 93, 85, 62 ]
97
[ "85-62=23", "92/23=4", "93+4=97" ]
Current State: 97:[92, 93, 85, 62], Operations: [] Exploring Operation: 85-62=23, Resulting Numbers: [92, 93, 23] Generated Node #2: [92, 93, 23] from Operation: 85-62=23 Current State: 97:[92, 93, 23], Operations: ['85-62=23'] Exploring Operation: 92/23=4, Resulting Numbers: [93, 4] Generated Node #3: [93, 4] from Operation: 92/23=4 Current State: 97:[93, 4], Operations: ['85-62=23', '92/23=4'] Exploring Operation: 93+4=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[92, 93, 85, 62], Operations: [] Exploring Operation: 93+62=155, Resulting Numbers: [92, 85, 155] Generated Node #0,0: 97:[92, 85, 155] Operation: 93+62=155 Exploring Operation: 92-62=30, Resulting Numbers: [93, 85, 30] Generated Node #0,1: 97:[93, 85, 30] Operation: 92-62=30 Exploring Operation: 93-62=31, Resulting Numbers: [92, 85, 31] Generated Node #0,2: 97:[92, 85, 31] Operation: 93-62=31 Exploring Operation: 85+62=147, Resulting Numbers: [92, 93, 147] Generated Node #0,3: 97:[92, 93, 147] Operation: 85+62=147 Exploring Operation: 92+62=154, Resulting Numbers: [93, 85, 154] Generated Node #0,4: 97:[93, 85, 154] Operation: 92+62=154 Start Sub Search at level 1: Moving to Node #0,3 Current State: 97:[92, 93, 147], Operations: ['85+62=147'] Exploring Operation: 92+147=239, Resulting Numbers: [93, 239] Generated Node #0,3,0: 97:[93, 239] Operation: 92+147=239 Exploring Operation: 147-92=55, Resulting Numbers: [93, 55] Generated Node #0,3,1: 97:[93, 55] Operation: 147-92=55 Exploring Operation: 147-93=54, Resulting Numbers: [92, 54] Generated Node #0,3,2: 97:[92, 54] Operation: 147-93=54 Exploring Operation: 92+93=185, Resulting Numbers: [147, 185] Generated Node #0,3,3: 97:[147, 185] Operation: 92+93=185 Exploring Operation: 93-92=1, Resulting Numbers: [147, 1] Generated Node #0,3,4: 97:[147, 1] Operation: 93-92=1 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 97:[93, 55], Operations: ['85+62=147', '147-92=55'] Exploring Operation: 93-55=38, Resulting Numbers: [38] 38,97 unequal: No Solution Exploring Operation: 93*55=5115, Resulting Numbers: [5115] 5115,97 unequal: No Solution Exploring Operation: 93+55=148, Resulting Numbers: [148] 148,97 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 #0,3,2 Current State: 97:[92, 54], Operations: ['85+62=147', '147-93=54'] Exploring Operation: 92*54=4968, Resulting Numbers: [4968] 4968,97 unequal: No Solution Exploring Operation: 92+54=146, Resulting Numbers: [146] 146,97 unequal: No Solution Exploring Operation: 92-54=38, Resulting Numbers: [38] 38,97 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 #0,3,3 Current State: 97:[147, 185], Operations: ['85+62=147', '92+93=185'] Exploring Operation: 147*185=27195, Resulting Numbers: [27195] 27195,97 unequal: No Solution Exploring Operation: 147+185=332, Resulting Numbers: [332] 332,97 unequal: No Solution Exploring Operation: 185-147=38, Resulting Numbers: [38] 38,97 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 #0,3,0 Current State: 97:[93, 239], Operations: ['85+62=147', '92+147=239'] Exploring Operation: 239-93=146, Resulting Numbers: [146] 146,97 unequal: No Solution Exploring Operation: 93*239=22227, Resulting Numbers: [22227] 22227,97 unequal: No Solution Exploring Operation: 93+239=332, Resulting Numbers: [332] 332,97 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 #0,3,4 Current State: 97:[147, 1], Operations: ['85+62=147', '93-92=1'] Exploring Operation: 147+1=148, Resulting Numbers: [148] 148,97 unequal: No Solution Exploring Operation: 147*1=147, Resulting Numbers: [147] 147,97 unequal: No Solution Exploring Operation: 147/1=147, Resulting Numbers: [147] 147,97 unequal: No Solution Exploring Operation: 147-1=146, Resulting Numbers: [146] 146,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 97:[93, 85, 154], Operations: ['92+62=154'] Exploring Operation: 154-85=69, Resulting Numbers: [93, 69] Generated Node #0,4,0: 97:[93, 69] Operation: 154-85=69 Exploring Operation: 93+85=178, Resulting Numbers: [154, 178] Generated Node #0,4,1: 97:[154, 178] Operation: 93+85=178 Exploring Operation: 93-85=8, Resulting Numbers: [154, 8] Generated Node #0,4,2: 97:[154, 8] Operation: 93-85=8 Exploring Operation: 85+154=239, Resulting Numbers: [93, 239] Generated Node #0,4,3: 97:[93, 239] Operation: 85+154=239 Exploring Operation: 154-93=61, Resulting Numbers: [85, 61] Generated Node #0,4,4: 97:[85, 61] Operation: 154-93=61 Moving to Node #0,4,0 Current State: 97:[93, 69], Operations: ['92+62=154', '154-85=69'] Exploring Operation: 93+69=162, Resulting Numbers: [162] 162,97 unequal: No Solution Exploring Operation: 93-69=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 93*69=6417, Resulting Numbers: [6417] 6417,97 unequal: No Solution Moving to Node #0,4,4 Current State: 97:[85, 61], Operations: ['92+62=154', '154-93=61'] Exploring Operation: 85+61=146, Resulting Numbers: [146] 146,97 unequal: No Solution Exploring Operation: 85-61=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 85*61=5185, Resulting Numbers: [5185] 5185,97 unequal: No Solution Moving to Node #0,4,1 Current State: 97:[154, 178], Operations: ['92+62=154', '93+85=178'] Exploring Operation: 178-154=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 154*178=27412, Resulting Numbers: [27412] 27412,97 unequal: No Solution Exploring Operation: 154+178=332, Resulting Numbers: [332] 332,97 unequal: No Solution Moving to Node #0,4,2 Current State: 97:[154, 8], Operations: ['92+62=154', '93-85=8'] Exploring Operation: 154*8=1232, Resulting Numbers: [1232] 1232,97 unequal: No Solution Exploring Operation: 154+8=162, Resulting Numbers: [162] 162,97 unequal: No Solution Exploring Operation: 154-8=146, Resulting Numbers: [146] 146,97 unequal: No Solution Moving to Node #0,4,3 Current State: 97:[93, 239], Operations: ['92+62=154', '85+154=239'] Exploring Operation: 93*239=22227, Resulting Numbers: [22227] 22227,97 unequal: No Solution Exploring Operation: 239-93=146, Resulting Numbers: [146] 146,97 unequal: No Solution Exploring Operation: 93+239=332, Resulting Numbers: [332] 332,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[92, 85, 155], Operations: ['93+62=155'] Exploring Operation: 92-85=7, Resulting Numbers: [155, 7] Generated Node #0,0,0: 97:[155, 7] Operation: 92-85=7 Exploring Operation: 155-85=70, Resulting Numbers: [92, 70] Generated Node #0,0,1: 97:[92, 70] Operation: 155-85=70 Exploring Operation: 92+85=177, Resulting Numbers: [155, 177] Generated Node #0,0,2: 97:[155, 177] Operation: 92+85=177 Exploring Operation: 155-92=63, Resulting Numbers: [85, 63] Generated Node #0,0,3: 97:[85, 63] Operation: 155-92=63 Exploring Operation: 85+155=240, Resulting Numbers: [92, 240] Generated Node #0,0,4: 97:[92, 240] Operation: 85+155=240 Moving to Node #0,0,1 Current State: 97:[92, 70], Operations: ['93+62=155', '155-85=70'] Exploring Operation: 92-70=22, Resulting Numbers: [22] 22,97 unequal: No Solution Exploring Operation: 92*70=6440, Resulting Numbers: [6440] 6440,97 unequal: No Solution Exploring Operation: 92+70=162, Resulting Numbers: [162] 162,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[85, 63], Operations: ['93+62=155', '155-92=63'] Exploring Operation: 85-63=22, Resulting Numbers: [22] 22,97 unequal: No Solution Exploring Operation: 85*63=5355, Resulting Numbers: [5355] 5355,97 unequal: No Solution Exploring Operation: 85+63=148, Resulting Numbers: [148] 148,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[155, 177], Operations: ['93+62=155', '92+85=177'] Exploring Operation: 155*177=27435, Resulting Numbers: [27435] 27435,97 unequal: No Solution Exploring Operation: 155+177=332, Resulting Numbers: [332] 332,97 unequal: No Solution Exploring Operation: 177-155=22, Resulting Numbers: [22] 22,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[155, 7], Operations: ['93+62=155', '92-85=7'] Exploring Operation: 155-7=148, Resulting Numbers: [148] 148,97 unequal: No Solution Exploring Operation: 155*7=1085, Resulting Numbers: [1085] 1085,97 unequal: No Solution Exploring Operation: 155+7=162, Resulting Numbers: [162] 162,97 unequal: No Solution Moving to Node #0,0,4 Current State: 97:[92, 240], Operations: ['93+62=155', '85+155=240'] Exploring Operation: 92*240=22080, Resulting Numbers: [22080] 22080,97 unequal: No Solution Exploring Operation: 92+240=332, Resulting Numbers: [332] 332,97 unequal: No Solution Exploring Operation: 240-92=148, Resulting Numbers: [148] 148,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[93, 85, 30], Operations: ['92-62=30'] Exploring Operation: 85+30=115, Resulting Numbers: [93, 115] Generated Node #0,1,0: 97:[93, 115] Operation: 85+30=115 Exploring Operation: 93+30=123, Resulting Numbers: [85, 123] Generated Node #0,1,1: 97:[85, 123] Operation: 93+30=123 Exploring Operation: 93-30=63, Resulting Numbers: [85, 63] Generated Node #0,1,2: 97:[85, 63] Operation: 93-30=63 Exploring Operation: 85-30=55, Resulting Numbers: [93, 55] Generated Node #0,1,3: 97:[93, 55] Operation: 85-30=55 Exploring Operation: 93+85=178, Resulting Numbers: [30, 178] Generated Node #0,1,4: 97:[30, 178] Operation: 93+85=178 Moving to Node #0,1,0 Current State: 97:[93, 115], Operations: ['92-62=30', '85+30=115'] Exploring Operation: 115-93=22, Resulting Numbers: [22] 22,97 unequal: No Solution Exploring Operation: 93*115=10695, Resulting Numbers: [10695] 10695,97 unequal: No Solution Exploring Operation: 93+115=208, Resulting Numbers: [208] 208,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[85, 123], Operations: ['92-62=30', '93+30=123'] Exploring Operation: 123-85=38, Resulting Numbers: [38] 38,97 unequal: No Solution Exploring Operation: 85*123=10455, Resulting Numbers: [10455] 10455,97 unequal: No Solution Exploring Operation: 85+123=208, Resulting Numbers: [208] 208,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[85, 63], Operations: ['92-62=30', '93-30=63'] Exploring Operation: 85-63=22, Resulting Numbers: [22] 22,97 unequal: No Solution Exploring Operation: 85+63=148, Resulting Numbers: [148] 148,97 unequal: No Solution Exploring Operation: 85*63=5355, Resulting Numbers: [5355] 5355,97 unequal: No Solution Moving to Node #0,1,3 Current State: 97:[93, 55], Operations: ['92-62=30', '85-30=55'] Exploring Operation: 93*55=5115, Resulting Numbers: [5115] 5115,97 unequal: No Solution Exploring Operation: 93-55=38, Resulting Numbers: [38] 38,97 unequal: No Solution Exploring Operation: 93+55=148, Resulting Numbers: [148] 148,97 unequal: No Solution Moving to Node #0,1,4 Current State: 97:[30, 178], Operations: ['92-62=30', '93+85=178'] Exploring Operation: 178-30=148, Resulting Numbers: [148] 148,97 unequal: No Solution Exploring Operation: 30*178=5340, Resulting Numbers: [5340] 5340,97 unequal: No Solution Exploring Operation: 30+178=208, Resulting Numbers: [208] 208,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[92, 85, 31], Operations: ['93-62=31'] Exploring Operation: 85+31=116, Resulting Numbers: [92, 116] Generated Node #0,2,0: 97:[92, 116] Operation: 85+31=116 Exploring Operation: 92+31=123, Resulting Numbers: [85, 123] Generated Node #0,2,1: 97:[85, 123] Operation: 92+31=123 Exploring Operation: 92-31=61, Resulting Numbers: [85, 61] Generated Node #0,2,2: 97:[85, 61] Operation: 92-31=61 Exploring Operation: 85-31=54, Resulting Numbers: [92, 54] Generated Node #0,2,3: 97:[92, 54] Operation: 85-31=54 Exploring Operation: 92+85=177, Resulting Numbers: [31, 177] Generated Node #0,2,4: 97:[31, 177] Operation: 92+85=177 Moving to Node #0,2,0 Current State: 97:[92, 116], Operations: ['93-62=31', '85+31=116'] Exploring Operation: 92+116=208, Resulting Numbers: [208] 208,97 unequal: No Solution Exploring Operation: 116-92=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 92*116=10672, Resulting Numbers: [10672] 10672,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[85, 123], Operations: ['93-62=31', '92+31=123'] Exploring Operation: 85*123=10455, Resulting Numbers: [10455] 10455,97 unequal: No Solution Exploring Operation: 85+123=208, Resulting Numbers: [208] 208,97 unequal: No Solution Exploring Operation: 123-85=38, Resulting Numbers: [38] 38,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[85, 61], Operations: ['93-62=31', '92-31=61'] Exploring Operation: 85+61=146, Resulting Numbers: [146] 146,97 unequal: No Solution Exploring Operation: 85*61=5185, Resulting Numbers: [5185] 5185,97 unequal: No Solution Exploring Operation: 85-61=24, Resulting Numbers: [24] 24,97 unequal: No Solution Moving to Node #0,2,3 Current State: 97:[92, 54], Operations: ['93-62=31', '85-31=54'] Exploring Operation: 92*54=4968, Resulting Numbers: [4968] 4968,97 unequal: No Solution Exploring Operation: 92-54=38, Resulting Numbers: [38] 38,97 unequal: No Solution Exploring Operation: 92+54=146, Resulting Numbers: [146] 146,97 unequal: No Solution Moving to Node #0,2,4 Current State: 97:[31, 177], Operations: ['93-62=31', '92+85=177'] Exploring Operation: 31*177=5487, Resulting Numbers: [5487] 5487,97 unequal: No Solution Exploring Operation: 31+177=208, Resulting Numbers: [208] 208,97 unequal: No Solution Exploring Operation: 177-31=146, Resulting Numbers: [146] 146,97 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
[ 26, 39, 9, 70 ]
47
[ "39-26=13", "9*13=117", "117-70=47" ]
Current State: 47:[26, 39, 9, 70], Operations: [] Exploring Operation: 39-26=13, Resulting Numbers: [9, 70, 13] Generated Node #2: [9, 70, 13] from Operation: 39-26=13 Current State: 47:[9, 70, 13], Operations: ['39-26=13'] Exploring Operation: 9*13=117, Resulting Numbers: [70, 117] Generated Node #3: [70, 117] from Operation: 9*13=117 Current State: 47:[70, 117], Operations: ['39-26=13', '9*13=117'] Exploring Operation: 117-70=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[26, 39, 9, 70], Operations: [] Exploring Operation: 26-9=17, Resulting Numbers: [39, 70, 17] Generated Node #0,0: 47:[39, 70, 17] Operation: 26-9=17 Exploring Operation: 39+9=48, Resulting Numbers: [26, 70, 48] Generated Node #0,1: 47:[26, 70, 48] Operation: 39+9=48 Exploring Operation: 70-9=61, Resulting Numbers: [26, 39, 61] Generated Node #0,2: 47:[26, 39, 61] Operation: 70-9=61 Exploring Operation: 26+9=35, Resulting Numbers: [39, 70, 35] Generated Node #0,3: 47:[39, 70, 35] Operation: 26+9=35 Exploring Operation: 70-26=44, Resulting Numbers: [39, 9, 44] Generated Node #0,4: 47:[39, 9, 44] Operation: 70-26=44 Moving to Node #0,2 Current State: 47:[26, 39, 61], Operations: ['70-9=61'] Exploring Operation: 39-26=13, Resulting Numbers: [61, 13] Generated Node #0,2,0: 47:[61, 13] Operation: 39-26=13 Exploring Operation: 26+39=65, Resulting Numbers: [61, 65] Generated Node #0,2,1: 47:[61, 65] Operation: 26+39=65 Exploring Operation: 26+61=87, Resulting Numbers: [39, 87] Generated Node #0,2,2: 47:[39, 87] Operation: 26+61=87 Exploring Operation: 61-39=22, Resulting Numbers: [26, 22] Generated Node #0,2,3: 47:[26, 22] Operation: 61-39=22 Exploring Operation: 61-26=35, Resulting Numbers: [39, 35] Generated Node #0,2,4: 47:[39, 35] Operation: 61-26=35 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 47:[39, 35], Operations: ['70-9=61', '61-26=35'] Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,47 unequal: No Solution Exploring Operation: 39*35=1365, Resulting Numbers: [1365] 1365,47 unequal: No Solution Exploring Operation: 39+35=74, Resulting Numbers: [74] 74,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 47:[61, 65], Operations: ['70-9=61', '26+39=65'] Exploring Operation: 61+65=126, Resulting Numbers: [126] 126,47 unequal: No Solution Exploring Operation: 61*65=3965, Resulting Numbers: [3965] 3965,47 unequal: No Solution Exploring Operation: 65-61=4, Resulting Numbers: [4] 4,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 47:[26, 22], Operations: ['70-9=61', '61-39=22'] Exploring Operation: 26*22=572, Resulting Numbers: [572] 572,47 unequal: No Solution Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,47 unequal: No Solution Exploring Operation: 26+22=48, Resulting Numbers: [48] 48,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 47:[61, 13], Operations: ['70-9=61', '39-26=13'] Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,47 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,47 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 47:[39, 87], Operations: ['70-9=61', '26+61=87'] Exploring Operation: 39*87=3393, Resulting Numbers: [3393] 3393,47 unequal: No Solution Exploring Operation: 87-39=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 39+87=126, Resulting Numbers: [126] 126,47 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: 47:[39, 70, 35], Operations: ['26+9=35'] Exploring Operation: 70-39=31, Resulting Numbers: [35, 31] Generated Node #0,3,0: 47:[35, 31] Operation: 70-39=31 Exploring Operation: 39+35=74, Resulting Numbers: [70, 74] Generated Node #0,3,1: 47:[70, 74] Operation: 39+35=74 Exploring Operation: 70/35=2, Resulting Numbers: [39, 2] Generated Node #0,3,2: 47:[39, 2] Operation: 70/35=2 Exploring Operation: 70-35=35, Resulting Numbers: [39, 35] Generated Node #0,3,3: 47:[39, 35] Operation: 70-35=35 Exploring Operation: 39-35=4, Resulting Numbers: [70, 4] Generated Node #0,3,4: 47:[70, 4] Operation: 39-35=4 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 47:[39, 35], Operations: ['26+9=35', '70-35=35'] Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,47 unequal: No Solution Exploring Operation: 39+35=74, Resulting Numbers: [74] 74,47 unequal: No Solution Exploring Operation: 39*35=1365, Resulting Numbers: [1365] 1365,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 47:[35, 31], Operations: ['26+9=35', '70-39=31'] Exploring Operation: 35-31=4, Resulting Numbers: [4] 4,47 unequal: No Solution Exploring Operation: 35*31=1085, Resulting Numbers: [1085] 1085,47 unequal: No Solution Exploring Operation: 35+31=66, Resulting Numbers: [66] 66,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 47:[70, 74], Operations: ['26+9=35', '39+35=74'] Exploring Operation: 74-70=4, Resulting Numbers: [4] 4,47 unequal: No Solution Exploring Operation: 70*74=5180, Resulting Numbers: [5180] 5180,47 unequal: No Solution Exploring Operation: 70+74=144, Resulting Numbers: [144] 144,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 47:[39, 2], Operations: ['26+9=35', '70/35=2'] Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,47 unequal: No Solution Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 47:[70, 4], Operations: ['26+9=35', '39-35=4'] Exploring Operation: 70*4=280, Resulting Numbers: [280] 280,47 unequal: No Solution Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,47 unequal: No Solution Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,47 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: 47:[26, 70, 48], Operations: ['39+9=48'] Exploring Operation: 70-48=22, Resulting Numbers: [26, 22] Generated Node #0,1,0: 47:[26, 22] Operation: 70-48=22 Exploring Operation: 26+70=96, Resulting Numbers: [48, 96] Generated Node #0,1,1: 47:[48, 96] Operation: 26+70=96 Exploring Operation: 26+48=74, Resulting Numbers: [70, 74] Generated Node #0,1,2: 47:[70, 74] Operation: 26+48=74 Exploring Operation: 48-26=22, Resulting Numbers: [70, 22] Generated Node #0,1,3: 47:[70, 22] Operation: 48-26=22 Exploring Operation: 70-26=44, Resulting Numbers: [48, 44] Generated Node #0,1,4: 47:[48, 44] Operation: 70-26=44 Moving to Node #0,4 Current State: 47:[39, 9, 44], Operations: ['70-26=44'] Exploring Operation: 39+9=48, Resulting Numbers: [44, 48] Generated Node #0,4,0: 47:[44, 48] Operation: 39+9=48 Exploring Operation: 39+44=83, Resulting Numbers: [9, 83] Generated Node #0,4,1: 47:[9, 83] Operation: 39+44=83 Exploring Operation: 39-9=30, Resulting Numbers: [44, 30] Generated Node #0,4,2: 47:[44, 30] Operation: 39-9=30 Exploring Operation: 9+44=53, Resulting Numbers: [39, 53] Generated Node #0,4,3: 47:[39, 53] Operation: 9+44=53 Exploring Operation: 44-9=35, Resulting Numbers: [39, 35] Generated Node #0,4,4: 47:[39, 35] Operation: 44-9=35 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 47:[44, 48], Operations: ['70-26=44', '39+9=48'] Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,47 unequal: No Solution Exploring Operation: 44*48=2112, Resulting Numbers: [2112] 2112,47 unequal: No Solution Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 47:[39, 53], Operations: ['70-26=44', '9+44=53'] Exploring Operation: 53-39=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 39+53=92, Resulting Numbers: [92] 92,47 unequal: No Solution Exploring Operation: 39*53=2067, Resulting Numbers: [2067] 2067,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 47:[44, 30], Operations: ['70-26=44', '39-9=30'] Exploring Operation: 44+30=74, Resulting Numbers: [74] 74,47 unequal: No Solution Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 44*30=1320, Resulting Numbers: [1320] 1320,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 47:[39, 35], Operations: ['70-26=44', '44-9=35'] Exploring Operation: 39+35=74, Resulting Numbers: [74] 74,47 unequal: No Solution Exploring Operation: 39*35=1365, Resulting Numbers: [1365] 1365,47 unequal: No Solution Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 47:[9, 83], Operations: ['70-26=44', '39+44=83'] Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,47 unequal: No Solution Exploring Operation: 9*83=747, Resulting Numbers: [747] 747,47 unequal: No Solution Exploring Operation: 9+83=92, Resulting Numbers: [92] 92,47 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: 47:[39, 70, 17], Operations: ['26-9=17'] Exploring Operation: 70+17=87, Resulting Numbers: [39, 87] Generated Node #0,0,0: 47:[39, 87] Operation: 70+17=87 Exploring Operation: 70-39=31, Resulting Numbers: [17, 31] Generated Node #0,0,1: 47:[17, 31] Operation: 70-39=31 Exploring Operation: 39-17=22, Resulting Numbers: [70, 22] Generated Node #0,0,2: 47:[70, 22] Operation: 39-17=22 Exploring Operation: 39+17=56, Resulting Numbers: [70, 56] Generated Node #0,0,3: 47:[70, 56] Operation: 39+17=56 Exploring Operation: 70-17=53, Resulting Numbers: [39, 53] Generated Node #0,0,4: 47:[39, 53] Operation: 70-17=53 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 47:[39, 53], Operations: ['26-9=17', '70-17=53'] Exploring Operation: 39*53=2067, Resulting Numbers: [2067] 2067,47 unequal: No Solution Exploring Operation: 53-39=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 39+53=92, Resulting Numbers: [92] 92,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 47:[70, 56], Operations: ['26-9=17', '39+17=56'] Exploring Operation: 70+56=126, Resulting Numbers: [126] 126,47 unequal: No Solution Exploring Operation: 70-56=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 70*56=3920, Resulting Numbers: [3920] 3920,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[17, 31], Operations: ['26-9=17', '70-39=31'] Exploring Operation: 31-17=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 17+31=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 17*31=527, Resulting Numbers: [527] 527,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[39, 87], Operations: ['26-9=17', '70+17=87'] Exploring Operation: 39+87=126, Resulting Numbers: [126] 126,47 unequal: No Solution Exploring Operation: 39*87=3393, Resulting Numbers: [3393] 3393,47 unequal: No Solution Exploring Operation: 87-39=48, Resulting Numbers: [48] 48,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[70, 22], Operations: ['26-9=17', '39-17=22'] Exploring Operation: 70+22=92, Resulting Numbers: [92] 92,47 unequal: No Solution Exploring Operation: 70-22=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 70*22=1540, Resulting Numbers: [1540] 1540,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,4 Current State: 47:[48, 44], Operations: ['39+9=48', '70-26=44'] Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,47 unequal: No Solution Exploring Operation: 48*44=2112, Resulting Numbers: [2112] 2112,47 unequal: No Solution Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[26, 22], Operations: ['39+9=48', '70-48=22'] Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,47 unequal: No Solution Exploring Operation: 26*22=572, Resulting Numbers: [572] 572,47 unequal: No Solution Exploring Operation: 26+22=48, Resulting Numbers: [48] 48,47 unequal: No Solution Moving to Node #0,1,3 Current State: 47:[70, 22], Operations: ['39+9=48', '48-26=22'] Exploring Operation: 70*22=1540, Resulting Numbers: [1540] 1540,47 unequal: No Solution Exploring Operation: 70+22=92, Resulting Numbers: [92] 92,47 unequal: No Solution Exploring Operation: 70-22=48, Resulting Numbers: [48] 48,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[48, 96], Operations: ['39+9=48', '26+70=96'] Exploring Operation: 96/48=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 48+96=144, Resulting Numbers: [144] 144,47 unequal: No Solution Exploring Operation: 96-48=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 48*96=4608, Resulting Numbers: [4608] 4608,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[70, 74], Operations: ['39+9=48', '26+48=74'] Exploring Operation: 74-70=4, Resulting Numbers: [4] 4,47 unequal: No Solution Exploring Operation: 70+74=144, Resulting Numbers: [144] 144,47 unequal: No Solution Exploring Operation: 70*74=5180, Resulting Numbers: [5180] 5180,47 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 54, 54, 30, 9 ]
59
[ "54/9=6", "30/6=5", "54+5=59" ]
Current State: 59:[54, 54, 30, 9], Operations: [] Exploring Operation: 54/9=6, Resulting Numbers: [30, 6] Generated Node #2: [30, 6] from Operation: 54/9=6 Current State: 59:[30, 6], Operations: ['54/9=6'] Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,59 equal: Goal Reached Exploring Operation: 54+5=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[54, 54, 30, 9], Operations: [] Exploring Operation: 54-9=45, Resulting Numbers: [54, 30, 45] Generated Node #0,0: 59:[54, 30, 45] Operation: 54-9=45 Exploring Operation: 54+9=63, Resulting Numbers: [54, 30, 63] Generated Node #0,1: 59:[54, 30, 63] Operation: 54+9=63 Exploring Operation: 54+9=63, Resulting Numbers: [54, 30, 63] Generated Node #0,2: 59:[54, 30, 63] Operation: 54+9=63 Exploring Operation: 30+9=39, Resulting Numbers: [54, 54, 39] Generated Node #0,3: 59:[54, 54, 39] Operation: 30+9=39 Moving to Node #0,3 Current State: 59:[54, 54, 39], Operations: ['30+9=39'] Exploring Operation: 54-39=15, Resulting Numbers: [54, 15] Generated Node #0,3,0: 59:[54, 15] Operation: 54-39=15 Exploring Operation: 54+39=93, Resulting Numbers: [54, 93] Generated Node #0,3,1: 59:[54, 93] Operation: 54+39=93 Exploring Operation: 54-39=15, Resulting Numbers: [54, 15] Generated Node #0,3,2: 59:[54, 15] Operation: 54-39=15 Exploring Operation: 54+39=93, Resulting Numbers: [54, 93] Generated Node #0,3,3: 59:[54, 93] Operation: 54+39=93 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 59:[54, 93], Operations: ['30+9=39', '54+39=93'] Exploring Operation: 54+93=147, Resulting Numbers: [147] 147,59 unequal: No Solution Exploring Operation: 54*93=5022, Resulting Numbers: [5022] 5022,59 unequal: No Solution Exploring Operation: 93-54=39, Resulting Numbers: [39] 39,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 59:[54, 93], Operations: ['30+9=39', '54+39=93'] Exploring Operation: 54*93=5022, Resulting Numbers: [5022] 5022,59 unequal: No Solution Exploring Operation: 54+93=147, Resulting Numbers: [147] 147,59 unequal: No Solution Exploring Operation: 93-54=39, Resulting Numbers: [39] 39,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 59:[54, 15], Operations: ['30+9=39', '54-39=15'] Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,59 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,59 unequal: No Solution Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 59:[54, 15], Operations: ['30+9=39', '54-39=15'] Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,59 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,59 unequal: No Solution Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 59:[54, 30, 63], Operations: ['54+9=63'] Exploring Operation: 54-30=24, Resulting Numbers: [63, 24] Generated Node #0,2,0: 59:[63, 24] Operation: 54-30=24 Exploring Operation: 54+30=84, Resulting Numbers: [63, 84] Generated Node #0,2,1: 59:[63, 84] Operation: 54+30=84 Exploring Operation: 63-30=33, Resulting Numbers: [54, 33] Generated Node #0,2,2: 59:[54, 33] Operation: 63-30=33 Exploring Operation: 30+63=93, Resulting Numbers: [54, 93] Generated Node #0,2,3: 59:[54, 93] Operation: 30+63=93 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[63, 84], Operations: ['54+9=63', '54+30=84'] Exploring Operation: 63+84=147, Resulting Numbers: [147] 147,59 unequal: No Solution Exploring Operation: 63*84=5292, Resulting Numbers: [5292] 5292,59 unequal: No Solution Exploring Operation: 84-63=21, Resulting Numbers: [21] 21,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[54, 33], Operations: ['54+9=63', '63-30=33'] Exploring Operation: 54-33=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 54+33=87, Resulting Numbers: [87] 87,59 unequal: No Solution Exploring Operation: 54*33=1782, Resulting Numbers: [1782] 1782,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[63, 24], Operations: ['54+9=63', '54-30=24'] Exploring Operation: 63*24=1512, Resulting Numbers: [1512] 1512,59 unequal: No Solution Exploring Operation: 63+24=87, Resulting Numbers: [87] 87,59 unequal: No Solution Exploring Operation: 63-24=39, Resulting Numbers: [39] 39,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 59:[54, 93], Operations: ['54+9=63', '30+63=93'] Exploring Operation: 93-54=39, Resulting Numbers: [39] 39,59 unequal: No Solution Exploring Operation: 54*93=5022, Resulting Numbers: [5022] 5022,59 unequal: No Solution Exploring Operation: 54+93=147, Resulting Numbers: [147] 147,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 59:[54, 30, 63], Operations: ['54+9=63'] Exploring Operation: 63-30=33, Resulting Numbers: [54, 33] Generated Node #0,1,0: 59:[54, 33] Operation: 63-30=33 Exploring Operation: 54-30=24, Resulting Numbers: [63, 24] Generated Node #0,1,1: 59:[63, 24] Operation: 54-30=24 Exploring Operation: 54+30=84, Resulting Numbers: [63, 84] Generated Node #0,1,2: 59:[63, 84] Operation: 54+30=84 Exploring Operation: 30+63=93, Resulting Numbers: [54, 93] Generated Node #0,1,3: 59:[54, 93] Operation: 30+63=93 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[63, 84], Operations: ['54+9=63', '54+30=84'] Exploring Operation: 84-63=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 63+84=147, Resulting Numbers: [147] 147,59 unequal: No Solution Exploring Operation: 63*84=5292, Resulting Numbers: [5292] 5292,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[54, 33], Operations: ['54+9=63', '63-30=33'] Exploring Operation: 54+33=87, Resulting Numbers: [87] 87,59 unequal: No Solution Exploring Operation: 54-33=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 54*33=1782, Resulting Numbers: [1782] 1782,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[63, 24], Operations: ['54+9=63', '54-30=24'] Exploring Operation: 63+24=87, Resulting Numbers: [87] 87,59 unequal: No Solution Exploring Operation: 63*24=1512, Resulting Numbers: [1512] 1512,59 unequal: No Solution Exploring Operation: 63-24=39, Resulting Numbers: [39] 39,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 59:[54, 93], Operations: ['54+9=63', '30+63=93'] Exploring Operation: 54*93=5022, Resulting Numbers: [5022] 5022,59 unequal: No Solution Exploring Operation: 93-54=39, Resulting Numbers: [39] 39,59 unequal: No Solution Exploring Operation: 54+93=147, Resulting Numbers: [147] 147,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 59:[54, 30, 45], Operations: ['54-9=45'] Exploring Operation: 54+30=84, Resulting Numbers: [45, 84] Generated Node #0,0,0: 59:[45, 84] Operation: 54+30=84 Exploring Operation: 54-30=24, Resulting Numbers: [45, 24] Generated Node #0,0,1: 59:[45, 24] Operation: 54-30=24 Exploring Operation: 45-30=15, Resulting Numbers: [54, 15] Generated Node #0,0,2: 59:[54, 15] Operation: 45-30=15 Exploring Operation: 30+45=75, Resulting Numbers: [54, 75] Generated Node #0,0,3: 59:[54, 75] Operation: 30+45=75 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 59:[54, 75], Operations: ['54-9=45', '30+45=75'] Exploring Operation: 54+75=129, Resulting Numbers: [129] 129,59 unequal: No Solution Exploring Operation: 54*75=4050, Resulting Numbers: [4050] 4050,59 unequal: No Solution Exploring Operation: 75-54=21, Resulting Numbers: [21] 21,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[45, 84], Operations: ['54-9=45', '54+30=84'] Exploring Operation: 45+84=129, Resulting Numbers: [129] 129,59 unequal: No Solution Exploring Operation: 45*84=3780, Resulting Numbers: [3780] 3780,59 unequal: No Solution Exploring Operation: 84-45=39, Resulting Numbers: [39] 39,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[45, 24], Operations: ['54-9=45', '54-30=24'] Exploring Operation: 45*24=1080, Resulting Numbers: [1080] 1080,59 unequal: No Solution Exploring Operation: 45+24=69, Resulting Numbers: [69] 69,59 unequal: No Solution Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 59:[54, 15], Operations: ['54-9=45', '45-30=15'] Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,59 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,59 unequal: No Solution Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 52, 61, 24, 58 ]
20
[ "61-58=3", "24*3=72", "72-52=20" ]
Current State: 20:[52, 61, 24, 58], Operations: [] Exploring Operation: 61-58=3, Resulting Numbers: [52, 24, 3] Generated Node #2: [52, 24, 3] from Operation: 61-58=3 Current State: 20:[52, 24, 3], Operations: ['61-58=3'] Exploring Operation: 24*3=72, Resulting Numbers: [52, 72] Generated Node #3: [52, 72] from Operation: 24*3=72 Current State: 20:[52, 72], Operations: ['61-58=3', '24*3=72'] Exploring Operation: 72-52=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[52, 61, 24, 58], Operations: [] Exploring Operation: 61-58=3, Resulting Numbers: [52, 24, 3] Generated Node #0,0: 20:[52, 24, 3] Operation: 61-58=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[52, 24, 3], Operations: ['61-58=3'] Exploring Operation: 52-24=28, Resulting Numbers: [3, 28] Generated Node #0,0,0: 20:[3, 28] Operation: 52-24=28 Moving to Node #0,0,0 Current State: 20:[3, 28], Operations: ['61-58=3', '52-24=28'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 92, 8, 47, 62 ]
99
[ "92-8=84", "62-47=15", "84+15=99" ]
Current State: 99:[92, 8, 47, 62], Operations: [] Exploring Operation: 92-8=84, Resulting Numbers: [47, 62, 84] Generated Node #2: [47, 62, 84] from Operation: 92-8=84 Current State: 99:[47, 62, 84], Operations: ['92-8=84'] Exploring Operation: 62-47=15, Resulting Numbers: [84, 15] Generated Node #3: [84, 15] from Operation: 62-47=15 Current State: 99:[84, 15], Operations: ['92-8=84', '62-47=15'] Exploring Operation: 84+15=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[92, 8, 47, 62], Operations: [] Exploring Operation: 92-47=45, Resulting Numbers: [8, 62, 45] Generated Node #0,0: 99:[8, 62, 45] Operation: 92-47=45 Exploring Operation: 47+62=109, Resulting Numbers: [92, 8, 109] Generated Node #0,1: 99:[92, 8, 109] Operation: 47+62=109 Exploring Operation: 62-47=15, Resulting Numbers: [92, 8, 15] Generated Node #0,2: 99:[92, 8, 15] Operation: 62-47=15 Exploring Operation: 92-62=30, Resulting Numbers: [8, 47, 30] Generated Node #0,3: 99:[8, 47, 30] Operation: 92-62=30 Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[92, 8, 15], Operations: ['62-47=15'] Exploring Operation: 8+15=23, Resulting Numbers: [92, 23] Generated Node #0,2,0: 99:[92, 23] Operation: 8+15=23 Exploring Operation: 92+15=107, Resulting Numbers: [8, 107] Generated Node #0,2,1: 99:[8, 107] Operation: 92+15=107 Exploring Operation: 15-8=7, Resulting Numbers: [92, 7] Generated Node #0,2,2: 99:[92, 7] Operation: 15-8=7 Exploring Operation: 92+8=100, Resulting Numbers: [15, 100] Generated Node #0,2,3: 99:[15, 100] Operation: 92+8=100 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 99:[15, 100], Operations: ['62-47=15', '92+8=100'] Exploring Operation: 100-15=85, Resulting Numbers: [85] 85,99 unequal: No Solution Exploring Operation: 15+100=115, Resulting Numbers: [115] 115,99 unequal: No Solution Exploring Operation: 15*100=1500, Resulting Numbers: [1500] 1500,99 unequal: No Solution No 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: 99:[8, 107], Operations: ['62-47=15', '92+15=107'] Exploring Operation: 107-8=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[92, 8, 47, 62], Operations: [] Exploring Operation: 62-47=15, Resulting Numbers: [92, 8, 15] Generated Node #0,2: 99:[92, 8, 15] Operation: 62-47=15 Moving to Node #0,2 Current State: 99:[92, 8, 15], Operations: ['62-47=15'] Exploring Operation: 92+15=107, Resulting Numbers: [8, 107] Generated Node #0,2,1: 99:[8, 107] Operation: 92+15=107 Moving to Node #0,2,1 Current State: 99:[8, 107], Operations: ['62-47=15', '92+15=107'] Exploring Operation: 107-8=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 87, 74, 11, 1 ]
23
[ "87-74=13", "11-1=10", "13+10=23" ]
Current State: 23:[87, 74, 11, 1], Operations: [] Exploring Operation: 87-74=13, Resulting Numbers: [11, 1, 13] Generated Node #2: [11, 1, 13] from Operation: 87-74=13 Current State: 23:[11, 1, 13], Operations: ['87-74=13'] Exploring Operation: 11-1=10, Resulting Numbers: [13, 10] Generated Node #3: [13, 10] from Operation: 11-1=10 Current State: 23:[13, 10], Operations: ['87-74=13', '11-1=10'] Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[87, 74, 11, 1], Operations: [] Exploring Operation: 87-11=76, Resulting Numbers: [74, 1, 76] Generated Node #0,0: 23:[74, 1, 76] Operation: 87-11=76 Exploring Operation: 87-74=13, Resulting Numbers: [11, 1, 13] Generated Node #0,1: 23:[11, 1, 13] Operation: 87-74=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[11, 1, 13], Operations: ['87-74=13'] Exploring Operation: 11+1=12, Resulting Numbers: [13, 12] Generated Node #0,1,0: 23:[13, 12] Operation: 11+1=12 Exploring Operation: 1+13=14, Resulting Numbers: [11, 14] Generated Node #0,1,1: 23:[11, 14] Operation: 1+13=14 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 23:[13, 12], Operations: ['87-74=13', '11+1=12'] Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 13+12=25, Resulting Numbers: [25] 25,23 unequal: No Solution No 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: 23:[11, 14], Operations: ['87-74=13', '1+13=14'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,23 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: 23:[74, 1, 76], Operations: ['87-11=76'] Exploring Operation: 76-74=2, Resulting Numbers: [1, 2] Generated Node #0,0,0: 23:[1, 2] Operation: 76-74=2 Exploring Operation: 74-1=73, Resulting Numbers: [76, 73] Generated Node #0,0,1: 23:[76, 73] Operation: 74-1=73 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[1, 2], Operations: ['87-11=76', '76-74=2'] Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,23 unequal: No Solution No 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: 23:[76, 73], Operations: ['87-11=76', '74-1=73'] Exploring Operation: 76-73=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 76+73=149, Resulting Numbers: [149] 149,23 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
[ 15, 82, 38, 30 ]
63
[ "15*38=570", "570/30=19", "82-19=63" ]
Current State: 63:[15, 82, 38, 30], Operations: [] Exploring Operation: 15*38=570, Resulting Numbers: [82, 30, 570] Generated Node #2: [82, 30, 570] from Operation: 15*38=570 Current State: 63:[82, 30, 570], Operations: ['15*38=570'] Exploring Operation: 570/30=19, Resulting Numbers: [82, 19] Generated Node #3: [82, 19] from Operation: 570/30=19 Current State: 63:[82, 19], Operations: ['15*38=570', '570/30=19'] Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[15, 82, 38, 30], Operations: [] Exploring Operation: 82-15=67, Resulting Numbers: [38, 30, 67] Generated Node #0,0: 63:[38, 30, 67] Operation: 82-15=67 Exploring Operation: 38-30=8, Resulting Numbers: [15, 82, 8] Generated Node #0,1: 63:[15, 82, 8] Operation: 38-30=8 Exploring Operation: 38-15=23, Resulting Numbers: [82, 30, 23] Generated Node #0,2: 63:[82, 30, 23] Operation: 38-15=23 Exploring Operation: 38+30=68, Resulting Numbers: [15, 82, 68] Generated Node #0,3: 63:[15, 82, 68] Operation: 38+30=68 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[15, 82, 8], Operations: ['38-30=8'] Exploring Operation: 15-8=7, Resulting Numbers: [82, 7] Generated Node #0,1,0: 63:[82, 7] Operation: 15-8=7 Exploring Operation: 15+8=23, Resulting Numbers: [82, 23] Generated Node #0,1,1: 63:[82, 23] Operation: 15+8=23 Exploring Operation: 82-8=74, Resulting Numbers: [15, 74] Generated Node #0,1,2: 63:[15, 74] Operation: 82-8=74 Exploring Operation: 82-15=67, Resulting Numbers: [8, 67] Generated Node #0,1,3: 63:[8, 67] Operation: 82-15=67 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 63:[8, 67], Operations: ['38-30=8', '82-15=67'] Exploring Operation: 8+67=75, Resulting Numbers: [75] 75,63 unequal: No Solution Exploring Operation: 8*67=536, Resulting Numbers: [536] 536,63 unequal: No Solution Exploring Operation: 67-8=59, Resulting Numbers: [59] 59,63 unequal: No Solution No 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: 63:[15, 74], Operations: ['38-30=8', '82-8=74'] Exploring Operation: 15*74=1110, Resulting Numbers: [1110] 1110,63 unequal: No Solution Exploring Operation: 74-15=59, Resulting Numbers: [59] 59,63 unequal: No Solution Exploring Operation: 15+74=89, Resulting Numbers: [89] 89,63 unequal: No Solution No 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: 63:[82, 7], Operations: ['38-30=8', '15-8=7'] Exploring Operation: 82+7=89, Resulting Numbers: [89] 89,63 unequal: No Solution Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,63 unequal: No Solution Exploring Operation: 82*7=574, Resulting Numbers: [574] 574,63 unequal: No Solution No 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: 63:[82, 23], Operations: ['38-30=8', '15+8=23'] Exploring Operation: 82+23=105, Resulting Numbers: [105] 105,63 unequal: No Solution Exploring Operation: 82*23=1886, Resulting Numbers: [1886] 1886,63 unequal: No Solution Exploring Operation: 82-23=59, Resulting Numbers: [59] 59,63 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: 63:[38, 30, 67], Operations: ['82-15=67'] Exploring Operation: 38+30=68, Resulting Numbers: [67, 68] Generated Node #0,0,0: 63:[67, 68] Operation: 38+30=68 Exploring Operation: 38-30=8, Resulting Numbers: [67, 8] Generated Node #0,0,1: 63:[67, 8] Operation: 38-30=8 Exploring Operation: 67-38=29, Resulting Numbers: [30, 29] Generated Node #0,0,2: 63:[30, 29] Operation: 67-38=29 Exploring Operation: 67-30=37, Resulting Numbers: [38, 37] Generated Node #0,0,3: 63:[38, 37] Operation: 67-30=37 Moving to Node #0,0,1 Current State: 63:[67, 8], Operations: ['82-15=67', '38-30=8'] Exploring Operation: 67-8=59, Resulting Numbers: [59] 59,63 unequal: No Solution Exploring Operation: 67*8=536, Resulting Numbers: [536] 536,63 unequal: No Solution Exploring Operation: 67+8=75, Resulting Numbers: [75] 75,63 unequal: No Solution Moving to Node #0,0,0 Current State: 63:[67, 68], Operations: ['82-15=67', '38+30=68'] Exploring Operation: 67*68=4556, Resulting Numbers: [4556] 4556,63 unequal: No Solution Exploring Operation: 68-67=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 67+68=135, Resulting Numbers: [135] 135,63 unequal: No Solution Moving to Node #0,0,2 Current State: 63:[30, 29], Operations: ['82-15=67', '67-38=29'] Exploring Operation: 30*29=870, Resulting Numbers: [870] 870,63 unequal: No Solution Exploring Operation: 30+29=59, Resulting Numbers: [59] 59,63 unequal: No Solution Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,63 unequal: No Solution Moving to Node #0,0,3 Current State: 63:[38, 37], Operations: ['82-15=67', '67-30=37'] Exploring Operation: 38+37=75, Resulting Numbers: [75] 75,63 unequal: No Solution Exploring Operation: 38*37=1406, Resulting Numbers: [1406] 1406,63 unequal: No Solution Exploring Operation: 38-37=1, Resulting Numbers: [1] 1,63 unequal: No Solution No 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: 63:[82, 30, 23], Operations: ['38-15=23'] Exploring Operation: 30+23=53, Resulting Numbers: [82, 53] Generated Node #0,2,0: 63:[82, 53] Operation: 30+23=53 Exploring Operation: 82-30=52, Resulting Numbers: [23, 52] Generated Node #0,2,1: 63:[23, 52] Operation: 82-30=52 Exploring Operation: 82-23=59, Resulting Numbers: [30, 59] Generated Node #0,2,2: 63:[30, 59] Operation: 82-23=59 Exploring Operation: 30-23=7, Resulting Numbers: [82, 7] Generated Node #0,2,3: 63:[82, 7] Operation: 30-23=7 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 63:[23, 52], Operations: ['38-15=23', '82-30=52'] Exploring Operation: 52-23=29, Resulting Numbers: [29] 29,63 unequal: No Solution Exploring Operation: 23+52=75, Resulting Numbers: [75] 75,63 unequal: No Solution Exploring Operation: 23*52=1196, Resulting Numbers: [1196] 1196,63 unequal: No Solution No 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: 63:[30, 59], Operations: ['38-15=23', '82-23=59'] Exploring Operation: 59-30=29, Resulting Numbers: [29] 29,63 unequal: No Solution Exploring Operation: 30+59=89, Resulting Numbers: [89] 89,63 unequal: No Solution Exploring Operation: 30*59=1770, Resulting Numbers: [1770] 1770,63 unequal: No Solution No 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: 63:[82, 7], Operations: ['38-15=23', '30-23=7'] Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,63 unequal: No Solution Exploring Operation: 82+7=89, Resulting Numbers: [89] 89,63 unequal: No Solution Exploring Operation: 82*7=574, Resulting Numbers: [574] 574,63 unequal: No Solution No 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: 63:[82, 53], Operations: ['38-15=23', '30+23=53'] Exploring Operation: 82-53=29, Resulting Numbers: [29] 29,63 unequal: No Solution Exploring Operation: 82+53=135, Resulting Numbers: [135] 135,63 unequal: No Solution Exploring Operation: 82*53=4346, Resulting Numbers: [4346] 4346,63 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: 63:[15, 82, 68], Operations: ['38+30=68'] Exploring Operation: 15+82=97, Resulting Numbers: [68, 97] Generated Node #0,3,0: 63:[68, 97] Operation: 15+82=97 Exploring Operation: 82-15=67, Resulting Numbers: [68, 67] Generated Node #0,3,1: 63:[68, 67] Operation: 82-15=67 Exploring Operation: 82-68=14, Resulting Numbers: [15, 14] Generated Node #0,3,2: 63:[15, 14] Operation: 82-68=14 Exploring Operation: 68-15=53, Resulting Numbers: [82, 53] Generated Node #0,3,3: 63:[82, 53] Operation: 68-15=53 Moving to Node #0,3,1 Current State: 63:[68, 67], Operations: ['38+30=68', '82-15=67'] Exploring Operation: 68*67=4556, Resulting Numbers: [4556] 4556,63 unequal: No Solution Exploring Operation: 68+67=135, Resulting Numbers: [135] 135,63 unequal: No Solution Exploring Operation: 68-67=1, Resulting Numbers: [1] 1,63 unequal: No Solution Moving to Node #0,3,2 Current State: 63:[15, 14], Operations: ['38+30=68', '82-68=14'] Exploring Operation: 15*14=210, Resulting Numbers: [210] 210,63 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,63 unequal: No Solution Moving to Node #0,3,3 Current State: 63:[82, 53], Operations: ['38+30=68', '68-15=53'] Exploring Operation: 82-53=29, Resulting Numbers: [29] 29,63 unequal: No Solution Exploring Operation: 82+53=135, Resulting Numbers: [135] 135,63 unequal: No Solution Exploring Operation: 82*53=4346, Resulting Numbers: [4346] 4346,63 unequal: No Solution Moving to Node #0,3,0 Current State: 63:[68, 97], Operations: ['38+30=68', '15+82=97'] Exploring Operation: 68+97=165, Resulting Numbers: [165] 165,63 unequal: No Solution Exploring Operation: 68*97=6596, Resulting Numbers: [6596] 6596,63 unequal: No Solution Exploring Operation: 97-68=29, Resulting Numbers: [29] 29,63 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
[ 74, 20, 56, 54 ]
55
[ "74-20=54", "54/54=1", "56-1=55" ]
Current State: 55:[74, 20, 56, 54], Operations: [] Exploring Operation: 74-20=54, Resulting Numbers: [56, 54, 54] Generated Node #2: [56, 54, 54] from Operation: 74-20=54 Current State: 55:[56, 54, 54], Operations: ['74-20=54'] Exploring Operation: 54/54=1, Resulting Numbers: [56, 1] Generated Node #3: [56, 1] from Operation: 54/54=1 Current State: 55:[56, 1], Operations: ['74-20=54', '54/54=1'] Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[74, 20, 56, 54], Operations: [] Exploring Operation: 74-56=18, Resulting Numbers: [20, 54, 18] Generated Node #0,0: 55:[20, 54, 18] Operation: 74-56=18 Exploring Operation: 74-20=54, Resulting Numbers: [56, 54, 54] Generated Node #0,1: 55:[56, 54, 54] Operation: 74-20=54 Exploring Operation: 74-54=20, Resulting Numbers: [20, 56, 20] Generated Node #0,2: 55:[20, 56, 20] Operation: 74-54=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[56, 54, 54], Operations: ['74-20=54'] Exploring Operation: 56-54=2, Resulting Numbers: [54, 2] Generated Node #0,1,0: 55:[54, 2] Operation: 56-54=2 Exploring Operation: 56-54=2, Resulting Numbers: [54, 2] Generated Node #0,1,1: 55:[54, 2] Operation: 56-54=2 Exploring Operation: 54/54=1, Resulting Numbers: [56, 1] Generated Node #0,1,2: 55:[56, 1] Operation: 54/54=1 Moving to Node #0,1,0 Current State: 55:[54, 2], Operations: ['74-20=54', '56-54=2'] Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,55 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,55 unequal: No Solution Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[54, 2], Operations: ['74-20=54', '56-54=2'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,55 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,55 unequal: No Solution Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,55 unequal: No Solution Moving to Node #0,1,2 Current State: 55:[56, 1], Operations: ['74-20=54', '54/54=1'] Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[74, 20, 56, 54], Operations: [] Exploring Operation: 74-20=54, Resulting Numbers: [56, 54, 54] Generated Node #0,1: 55:[56, 54, 54] Operation: 74-20=54 Moving to Node #0,1 Current State: 55:[56, 54, 54], Operations: ['74-20=54'] Exploring Operation: 54/54=1, Resulting Numbers: [56, 1] Generated Node #0,1,2: 55:[56, 1] Operation: 54/54=1 Moving to Node #0,1,2 Current State: 55:[56, 1], Operations: ['74-20=54', '54/54=1'] Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 33, 90, 68, 99 ]
38
[ "33*90=2970", "2970/99=30", "68-30=38" ]
Current State: 38:[33, 90, 68, 99], Operations: [] Exploring Operation: 33*90=2970, Resulting Numbers: [68, 99, 2970] Generated Node #2: [68, 99, 2970] from Operation: 33*90=2970 Current State: 38:[68, 99, 2970], Operations: ['33*90=2970'] Exploring Operation: 2970/99=30, Resulting Numbers: [68, 30] Generated Node #3: [68, 30] from Operation: 2970/99=30 Current State: 38:[68, 30], Operations: ['33*90=2970', '2970/99=30'] Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[33, 90, 68, 99], Operations: [] Exploring Operation: 99-90=9, Resulting Numbers: [33, 68, 9] Generated Node #0,0: 38:[33, 68, 9] Operation: 99-90=9 Moving to Node #0,0 Current State: 38:[33, 68, 9], Operations: ['99-90=9'] Exploring Operation: 68-33=35, Resulting Numbers: [9, 35] Generated Node #0,0,0: 38:[9, 35] Operation: 68-33=35 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[9, 35], Operations: ['99-90=9', '68-33=35'] Exploring Operation: 9+35=44, Resulting Numbers: [44] 44,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 71, 69, 52, 69 ]
86
[ "71-69=2", "69*2=138", "138-52=86" ]
Current State: 86:[71, 69, 52, 69], Operations: [] Exploring Operation: 71-69=2, Resulting Numbers: [52, 2] Generated Node #2: [52, 2] from Operation: 71-69=2 Current State: 86:[52, 2], Operations: ['71-69=2'] Exploring Operation: 69*2=138, Resulting Numbers: [52, 138] Generated Node #3: [52, 138] from Operation: 69*2=138 Current State: 86:[52, 138], Operations: ['71-69=2', '69*2=138'] Exploring Operation: 138-52=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[71, 69, 52, 69], Operations: [] Exploring Operation: 69/69=1, Resulting Numbers: [71, 52, 1] Generated Node #0,0: 86:[71, 52, 1] Operation: 69/69=1 Exploring Operation: 71-69=2, Resulting Numbers: [52, 69, 2] Generated Node #0,1: 86:[52, 69, 2] Operation: 71-69=2 Moving to Node #0,0 Current State: 86:[71, 52, 1], Operations: ['69/69=1'] Exploring Operation: 71+1=72, Resulting Numbers: [52, 72] Generated Node #0,0,0: 86:[52, 72] Operation: 71+1=72 Exploring Operation: 71-52=19, Resulting Numbers: [1, 19] Generated Node #0,0,1: 86:[1, 19] Operation: 71-52=19 Moving to Node #0,1 Current State: 86:[52, 69, 2], Operations: ['71-69=2'] Exploring Operation: 52-2=50, Resulting Numbers: [69, 50] Generated Node #0,1,0: 86:[69, 50] Operation: 52-2=50 Exploring Operation: 69-52=17, Resulting Numbers: [2, 17] Generated Node #0,1,1: 86:[2, 17] Operation: 69-52=17 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[2, 17], Operations: ['71-69=2', '69-52=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,86 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,86 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:[69, 50], Operations: ['71-69=2', '52-2=50'] Exploring Operation: 69+50=119, Resulting Numbers: [119] 119,86 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 86:[1, 19], Operations: ['69/69=1', '71-52=19'] Exploring Operation: 1*19=19, Resulting Numbers: [19] 19,86 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[52, 72], Operations: ['69/69=1', '71+1=72'] Exploring Operation: 72-52=20, Resulting Numbers: [20] 20,86 unequal: No Solution Exploring Operation: 52+72=124, Resulting Numbers: [124] 124,86 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 11, 55, 3, 27 ]
59
[ "11+27=38", "3*38=114", "114-55=59" ]
Current State: 59:[11, 55, 3, 27], Operations: [] Exploring Operation: 11+27=38, Resulting Numbers: [55, 3, 38] Generated Node #2: [55, 3, 38] from Operation: 11+27=38 Current State: 59:[55, 3, 38], Operations: ['11+27=38'] Exploring Operation: 3*38=114, Resulting Numbers: [55, 114] Generated Node #3: [55, 114] from Operation: 3*38=114 Current State: 59:[55, 114], Operations: ['11+27=38', '3*38=114'] Exploring Operation: 114-55=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[11, 55, 3, 27], Operations: [] Exploring Operation: 11*3=33, Resulting Numbers: [55, 27, 33] Generated Node #0,0: 59:[55, 27, 33] Operation: 11*3=33 Exploring Operation: 3*27=81, Resulting Numbers: [11, 55, 81] Generated Node #0,1: 59:[11, 55, 81] Operation: 3*27=81 Moving to Node #0,0 Current State: 59:[55, 27, 33], Operations: ['11*3=33'] Exploring Operation: 55+27=82, Resulting Numbers: [33, 82] Generated Node #0,0,0: 59:[33, 82] Operation: 55+27=82 Exploring Operation: 27+33=60, Resulting Numbers: [55, 60] Generated Node #0,0,1: 59:[55, 60] Operation: 27+33=60 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[55, 60], Operations: ['11*3=33', '27+33=60'] Exploring Operation: 55+60=115, Resulting Numbers: [115] 115,59 unequal: No Solution Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[33, 82], Operations: ['11*3=33', '55+27=82'] Exploring Operation: 82-33=49, Resulting Numbers: [49] 49,59 unequal: No Solution Exploring Operation: 33+82=115, Resulting Numbers: [115] 115,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 59:[11, 55, 81], Operations: ['3*27=81'] Exploring Operation: 81-11=70, Resulting Numbers: [55, 70] Generated Node #0,1,0: 59:[55, 70] Operation: 81-11=70 Exploring Operation: 11+55=66, Resulting Numbers: [81, 66] Generated Node #0,1,1: 59:[81, 66] Operation: 11+55=66 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[55, 70], Operations: ['3*27=81', '81-11=70'] Exploring Operation: 55+70=125, Resulting Numbers: [125] 125,59 unequal: No Solution Exploring Operation: 70-55=15, Resulting Numbers: [15] 15,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[81, 66], Operations: ['3*27=81', '11+55=66'] Exploring Operation: 81+66=147, Resulting Numbers: [147] 147,59 unequal: No Solution Exploring Operation: 81-66=15, Resulting Numbers: [15] 15,59 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
[ 23, 19, 82, 43 ]
81
[ "23+19=42", "82-43=39", "42+39=81" ]
Current State: 81:[23, 19, 82, 43], Operations: [] Exploring Operation: 23+19=42, Resulting Numbers: [82, 43, 42] Generated Node #2: [82, 43, 42] from Operation: 23+19=42 Current State: 81:[82, 43, 42], Operations: ['23+19=42'] Exploring Operation: 82-43=39, Resulting Numbers: [42, 39] Generated Node #3: [42, 39] from Operation: 82-43=39 Current State: 81:[42, 39], Operations: ['23+19=42', '82-43=39'] Exploring Operation: 42+39=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[23, 19, 82, 43], Operations: [] Exploring Operation: 43-19=24, Resulting Numbers: [23, 82, 24] Generated Node #0,0: 81:[23, 82, 24] Operation: 43-19=24 Exploring Operation: 23+43=66, Resulting Numbers: [19, 82, 66] Generated Node #0,1: 81:[19, 82, 66] Operation: 23+43=66 Exploring Operation: 43-23=20, Resulting Numbers: [19, 82, 20] Generated Node #0,2: 81:[19, 82, 20] Operation: 43-23=20 Exploring Operation: 23-19=4, Resulting Numbers: [82, 43, 4] Generated Node #0,3: 81:[82, 43, 4] Operation: 23-19=4 Exploring Operation: 19+43=62, Resulting Numbers: [23, 82, 62] Generated Node #0,4: 81:[23, 82, 62] Operation: 19+43=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[23, 82, 24], Operations: ['43-19=24'] Exploring Operation: 82-24=58, Resulting Numbers: [23, 58] Generated Node #0,0,0: 81:[23, 58] Operation: 82-24=58 Exploring Operation: 24-23=1, Resulting Numbers: [82, 1] Generated Node #0,0,1: 81:[82, 1] Operation: 24-23=1 Exploring Operation: 23+24=47, Resulting Numbers: [82, 47] Generated Node #0,0,2: 81:[82, 47] Operation: 23+24=47 Exploring Operation: 82-23=59, Resulting Numbers: [24, 59] Generated Node #0,0,3: 81:[24, 59] Operation: 82-23=59 Exploring Operation: 23+82=105, Resulting Numbers: [24, 105] Generated Node #0,0,4: 81:[24, 105] Operation: 23+82=105 Moving to Node #0,0,1 Current State: 81:[82, 1], Operations: ['43-19=24', '24-23=1'] Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[23, 19, 82, 43], Operations: [] Exploring Operation: 43-19=24, Resulting Numbers: [23, 82, 24] Generated Node #0,0: 81:[23, 82, 24] Operation: 43-19=24 Moving to Node #0,0 Current State: 81:[23, 82, 24], Operations: ['43-19=24'] Exploring Operation: 24-23=1, Resulting Numbers: [82, 1] Generated Node #0,0,1: 81:[82, 1] Operation: 24-23=1 Moving to Node #0,0,1 Current State: 81:[82, 1], Operations: ['43-19=24', '24-23=1'] Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 72, 16, 78, 90 ]
98
[ "16*90=1440", "1440/72=20", "78+20=98" ]
Current State: 98:[72, 16, 78, 90], Operations: [] Exploring Operation: 16*90=1440, Resulting Numbers: [72, 78, 1440] Generated Node #2: [72, 78, 1440] from Operation: 16*90=1440 Current State: 98:[72, 78, 1440], Operations: ['16*90=1440'] Exploring Operation: 1440/72=20, Resulting Numbers: [78, 20] Generated Node #3: [78, 20] from Operation: 1440/72=20 Current State: 98:[78, 20], Operations: ['16*90=1440', '1440/72=20'] Exploring Operation: 78+20=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[72, 16, 78, 90], Operations: [] Exploring Operation: 78-72=6, Resulting Numbers: [16, 90, 6] Generated Node #0,0: 98:[16, 90, 6] Operation: 78-72=6 Moving to Node #0,0 Current State: 98:[16, 90, 6], Operations: ['78-72=6'] Exploring Operation: 90/6=15, Resulting Numbers: [16, 15] Generated Node #0,0,0: 98:[16, 15] Operation: 90/6=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[16, 15], Operations: ['78-72=6', '90/6=15'] Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,98 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
[ 31, 2, 66, 14 ]
84
[ "66-31=35", "2*35=70", "14+70=84" ]
Current State: 84:[31, 2, 66, 14], Operations: [] Exploring Operation: 66-31=35, Resulting Numbers: [2, 14, 35] Generated Node #2: [2, 14, 35] from Operation: 66-31=35 Current State: 84:[2, 14, 35], Operations: ['66-31=35'] Exploring Operation: 2*35=70, Resulting Numbers: [14, 70] Generated Node #3: [14, 70] from Operation: 2*35=70 Current State: 84:[14, 70], Operations: ['66-31=35', '2*35=70'] Exploring Operation: 14+70=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[31, 2, 66, 14], Operations: [] Exploring Operation: 66-31=35, Resulting Numbers: [2, 14, 35] Generated Node #0,0: 84:[2, 14, 35] Operation: 66-31=35 Exploring Operation: 66+14=80, Resulting Numbers: [31, 2, 80] Generated Node #0,1: 84:[31, 2, 80] Operation: 66+14=80 Moving to Node #0,0 Current State: 84:[2, 14, 35], Operations: ['66-31=35'] Exploring Operation: 35-14=21, Resulting Numbers: [2, 21] Generated Node #0,0,0: 84:[2, 21] Operation: 35-14=21 Exploring Operation: 2+35=37, Resulting Numbers: [14, 37] Generated Node #0,0,1: 84:[14, 37] Operation: 2+35=37 Moving to Node #0,1 Current State: 84:[31, 2, 80], Operations: ['66+14=80'] Exploring Operation: 31-2=29, Resulting Numbers: [80, 29] Generated Node #0,1,0: 84:[80, 29] Operation: 31-2=29 Exploring Operation: 2+80=82, Resulting Numbers: [31, 82] Generated Node #0,1,1: 84:[31, 82] Operation: 2+80=82 Moving to Node #0,0,0 Current State: 84:[2, 21], Operations: ['66-31=35', '35-14=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,84 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[80, 29], Operations: ['66+14=80', '31-2=29'] Exploring Operation: 80+29=109, Resulting Numbers: [109] 109,84 unequal: No Solution Exploring Operation: 80-29=51, Resulting Numbers: [51] 51,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[14, 37], Operations: ['66-31=35', '2+35=37'] Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,84 unequal: No Solution Exploring Operation: 14+37=51, Resulting Numbers: [51] 51,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[31, 82], Operations: ['66+14=80', '2+80=82'] Exploring Operation: 31+82=113, Resulting Numbers: [113] 113,84 unequal: No Solution Exploring Operation: 82-31=51, Resulting Numbers: [51] 51,84 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 52, 2, 94, 23 ]
61
[ "94-52=42", "2*42=84", "84-23=61" ]
Current State: 61:[52, 2, 94, 23], Operations: [] Exploring Operation: 94-52=42, Resulting Numbers: [2, 23, 42] Generated Node #2: [2, 23, 42] from Operation: 94-52=42 Current State: 61:[2, 23, 42], Operations: ['94-52=42'] Exploring Operation: 2*42=84, Resulting Numbers: [23, 84] Generated Node #3: [23, 84] from Operation: 2*42=84 Current State: 61:[23, 84], Operations: ['94-52=42', '2*42=84'] Exploring Operation: 84-23=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[52, 2, 94, 23], Operations: [] Exploring Operation: 2+23=25, Resulting Numbers: [52, 94, 25] Generated Node #0,0: 61:[52, 94, 25] Operation: 2+23=25 Exploring Operation: 94/2=47, Resulting Numbers: [52, 23, 47] Generated Node #0,1: 61:[52, 23, 47] Operation: 94/2=47 Exploring Operation: 52+2=54, Resulting Numbers: [94, 23, 54] Generated Node #0,2: 61:[94, 23, 54] Operation: 52+2=54 Exploring Operation: 2*23=46, Resulting Numbers: [52, 94, 46] Generated Node #0,3: 61:[52, 94, 46] Operation: 2*23=46 Exploring Operation: 94-2=92, Resulting Numbers: [52, 23, 92] Generated Node #0,4: 61:[52, 23, 92] Operation: 94-2=92 Start Sub Search at level 1: Moving to Node #0,3 Current State: 61:[52, 94, 46], Operations: ['2*23=46'] Exploring Operation: 94+46=140, Resulting Numbers: [52, 140] Generated Node #0,3,0: 61:[52, 140] Operation: 94+46=140 Exploring Operation: 52-46=6, Resulting Numbers: [94, 6] Generated Node #0,3,1: 61:[94, 6] Operation: 52-46=6 Exploring Operation: 94-52=42, Resulting Numbers: [46, 42] Generated Node #0,3,2: 61:[46, 42] Operation: 94-52=42 Exploring Operation: 94-46=48, Resulting Numbers: [52, 48] Generated Node #0,3,3: 61:[52, 48] Operation: 94-46=48 Exploring Operation: 52+46=98, Resulting Numbers: [94, 98] Generated Node #0,3,4: 61:[94, 98] Operation: 52+46=98 Moving to Node #0,3,3 Current State: 61:[52, 48], Operations: ['2*23=46', '94-46=48'] Exploring Operation: 52+48=100, Resulting Numbers: [100] 100,61 unequal: No Solution Exploring Operation: 52-48=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 52*48=2496, Resulting Numbers: [2496] 2496,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[46, 42], Operations: ['2*23=46', '94-52=42'] Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 46+42=88, Resulting Numbers: [88] 88,61 unequal: No Solution Exploring Operation: 46*42=1932, Resulting Numbers: [1932] 1932,61 unequal: No Solution Moving to Node #0,3,4 Current State: 61:[94, 98], Operations: ['2*23=46', '52+46=98'] Exploring Operation: 94+98=192, Resulting Numbers: [192] 192,61 unequal: No Solution Exploring Operation: 98-94=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 94*98=9212, Resulting Numbers: [9212] 9212,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[52, 140], Operations: ['2*23=46', '94+46=140'] Exploring Operation: 52+140=192, Resulting Numbers: [192] 192,61 unequal: No Solution Exploring Operation: 52*140=7280, Resulting Numbers: [7280] 7280,61 unequal: No Solution Exploring Operation: 140-52=88, Resulting Numbers: [88] 88,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[94, 6], Operations: ['2*23=46', '52-46=6'] Exploring Operation: 94+6=100, Resulting Numbers: [100] 100,61 unequal: No Solution Exploring Operation: 94*6=564, Resulting Numbers: [564] 564,61 unequal: No Solution Exploring Operation: 94-6=88, Resulting Numbers: [88] 88,61 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 Current State: 61:[52, 23, 47], Operations: ['94/2=47'] Exploring Operation: 52+47=99, Resulting Numbers: [23, 99] Generated Node #0,1,0: 61:[23, 99] Operation: 52+47=99 Exploring Operation: 47-23=24, Resulting Numbers: [52, 24] Generated Node #0,1,1: 61:[52, 24] Operation: 47-23=24 Exploring Operation: 52-23=29, Resulting Numbers: [47, 29] Generated Node #0,1,2: 61:[47, 29] Operation: 52-23=29 Exploring Operation: 52+23=75, Resulting Numbers: [47, 75] Generated Node #0,1,3: 61:[47, 75] Operation: 52+23=75 Exploring Operation: 23+47=70, Resulting Numbers: [52, 70] Generated Node #0,1,4: 61:[52, 70] Operation: 23+47=70 Moving to Node #0,1,4 Current State: 61:[52, 70], Operations: ['94/2=47', '23+47=70'] Exploring Operation: 52*70=3640, Resulting Numbers: [3640] 3640,61 unequal: No Solution Exploring Operation: 52+70=122, Resulting Numbers: [122] 122,61 unequal: No Solution Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[47, 75], Operations: ['94/2=47', '52+23=75'] Exploring Operation: 47*75=3525, Resulting Numbers: [3525] 3525,61 unequal: No Solution Exploring Operation: 47+75=122, Resulting Numbers: [122] 122,61 unequal: No Solution Exploring Operation: 75-47=28, Resulting Numbers: [28] 28,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[52, 24], Operations: ['94/2=47', '47-23=24'] Exploring Operation: 52*24=1248, Resulting Numbers: [1248] 1248,61 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 52+24=76, Resulting Numbers: [76] 76,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[47, 29], Operations: ['94/2=47', '52-23=29'] Exploring Operation: 47*29=1363, Resulting Numbers: [1363] 1363,61 unequal: No Solution Exploring Operation: 47-29=18, Resulting Numbers: [18] 18,61 unequal: No Solution Exploring Operation: 47+29=76, Resulting Numbers: [76] 76,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[23, 99], Operations: ['94/2=47', '52+47=99'] Exploring Operation: 23+99=122, Resulting Numbers: [122] 122,61 unequal: No Solution Exploring Operation: 99-23=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 23*99=2277, Resulting Numbers: [2277] 2277,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[52, 94, 25], Operations: ['2+23=25'] Exploring Operation: 94+25=119, Resulting Numbers: [52, 119] Generated Node #0,0,0: 61:[52, 119] Operation: 94+25=119 Exploring Operation: 94-52=42, Resulting Numbers: [25, 42] Generated Node #0,0,1: 61:[25, 42] Operation: 94-52=42 Exploring Operation: 94-25=69, Resulting Numbers: [52, 69] Generated Node #0,0,2: 61:[52, 69] Operation: 94-25=69 Exploring Operation: 52+25=77, Resulting Numbers: [94, 77] Generated Node #0,0,3: 61:[94, 77] Operation: 52+25=77 Exploring Operation: 52-25=27, Resulting Numbers: [94, 27] Generated Node #0,0,4: 61:[94, 27] Operation: 52-25=27 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 61:[52, 69], Operations: ['2+23=25', '94-25=69'] Exploring Operation: 52+69=121, Resulting Numbers: [121] 121,61 unequal: No Solution Exploring Operation: 52*69=3588, Resulting Numbers: [3588] 3588,61 unequal: No Solution Exploring Operation: 69-52=17, Resulting Numbers: [17] 17,61 unequal: No Solution No 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: 61:[94, 77], Operations: ['2+23=25', '52+25=77'] Exploring Operation: 94*77=7238, Resulting Numbers: [7238] 7238,61 unequal: No Solution Exploring Operation: 94+77=171, Resulting Numbers: [171] 171,61 unequal: No Solution Exploring Operation: 94-77=17, Resulting Numbers: [17] 17,61 unequal: No Solution No 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: 61:[25, 42], Operations: ['2+23=25', '94-52=42'] Exploring Operation: 25*42=1050, Resulting Numbers: [1050] 1050,61 unequal: No Solution Exploring Operation: 25+42=67, Resulting Numbers: [67] 67,61 unequal: No Solution Exploring Operation: 42-25=17, Resulting Numbers: [17] 17,61 unequal: No Solution No 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: 61:[52, 119], Operations: ['2+23=25', '94+25=119'] Exploring Operation: 52*119=6188, Resulting Numbers: [6188] 6188,61 unequal: No Solution Exploring Operation: 119-52=67, Resulting Numbers: [67] 67,61 unequal: No Solution Exploring Operation: 52+119=171, Resulting Numbers: [171] 171,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 61:[94, 27], Operations: ['2+23=25', '52-25=27'] Exploring Operation: 94*27=2538, Resulting Numbers: [2538] 2538,61 unequal: No Solution Exploring Operation: 94-27=67, Resulting Numbers: [67] 67,61 unequal: No Solution Exploring Operation: 94+27=121, Resulting Numbers: [121] 121,61 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: 61:[94, 23, 54], Operations: ['52+2=54'] Exploring Operation: 54-23=31, Resulting Numbers: [94, 31] Generated Node #0,2,0: 61:[94, 31] Operation: 54-23=31 Exploring Operation: 94-23=71, Resulting Numbers: [54, 71] Generated Node #0,2,1: 61:[54, 71] Operation: 94-23=71 Exploring Operation: 23+54=77, Resulting Numbers: [94, 77] Generated Node #0,2,2: 61:[94, 77] Operation: 23+54=77 Exploring Operation: 94-54=40, Resulting Numbers: [23, 40] Generated Node #0,2,3: 61:[23, 40] Operation: 94-54=40 Exploring Operation: 94+23=117, Resulting Numbers: [54, 117] Generated Node #0,2,4: 61:[54, 117] Operation: 94+23=117 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 61:[54, 71], Operations: ['52+2=54', '94-23=71'] Exploring Operation: 54+71=125, Resulting Numbers: [125] 125,61 unequal: No Solution Exploring Operation: 54*71=3834, Resulting Numbers: [3834] 3834,61 unequal: No Solution Exploring Operation: 71-54=17, Resulting Numbers: [17] 17,61 unequal: No Solution No 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: 61:[94, 77], Operations: ['52+2=54', '23+54=77'] Exploring Operation: 94*77=7238, Resulting Numbers: [7238] 7238,61 unequal: No Solution Exploring Operation: 94+77=171, Resulting Numbers: [171] 171,61 unequal: No Solution Exploring Operation: 94-77=17, Resulting Numbers: [17] 17,61 unequal: No Solution No 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: 61:[23, 40], Operations: ['52+2=54', '94-54=40'] Exploring Operation: 23*40=920, Resulting Numbers: [920] 920,61 unequal: No Solution Exploring Operation: 23+40=63, Resulting Numbers: [63] 63,61 unequal: No Solution Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,61 unequal: No Solution No 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: 61:[94, 31], Operations: ['52+2=54', '54-23=31'] Exploring Operation: 94*31=2914, Resulting Numbers: [2914] 2914,61 unequal: No Solution Exploring Operation: 94-31=63, Resulting Numbers: [63] 63,61 unequal: No Solution Exploring Operation: 94+31=125, Resulting Numbers: [125] 125,61 unequal: No Solution No 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: 61:[54, 117], Operations: ['52+2=54', '94+23=117'] Exploring Operation: 54+117=171, Resulting Numbers: [171] 171,61 unequal: No Solution Exploring Operation: 54*117=6318, Resulting Numbers: [6318] 6318,61 unequal: No Solution Exploring Operation: 117-54=63, Resulting Numbers: [63] 63,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 61:[52, 23, 92], Operations: ['94-2=92'] Exploring Operation: 52+23=75, Resulting Numbers: [92, 75] Generated Node #0,4,0: 61:[92, 75] Operation: 52+23=75 Exploring Operation: 92-23=69, Resulting Numbers: [52, 69] Generated Node #0,4,1: 61:[52, 69] Operation: 92-23=69 Exploring Operation: 52-23=29, Resulting Numbers: [92, 29] Generated Node #0,4,2: 61:[92, 29] Operation: 52-23=29 Exploring Operation: 92-52=40, Resulting Numbers: [23, 40] Generated Node #0,4,3: 61:[23, 40] Operation: 92-52=40 Exploring Operation: 23+92=115, Resulting Numbers: [52, 115] Generated Node #0,4,4: 61:[52, 115] Operation: 23+92=115 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 61:[52, 69], Operations: ['94-2=92', '92-23=69'] Exploring Operation: 69-52=17, Resulting Numbers: [17] 17,61 unequal: No Solution Exploring Operation: 52+69=121, Resulting Numbers: [121] 121,61 unequal: No Solution Exploring Operation: 52*69=3588, Resulting Numbers: [3588] 3588,61 unequal: No Solution No 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: 61:[92, 75], Operations: ['94-2=92', '52+23=75'] Exploring Operation: 92+75=167, Resulting Numbers: [167] 167,61 unequal: No Solution Exploring Operation: 92*75=6900, Resulting Numbers: [6900] 6900,61 unequal: No Solution Exploring Operation: 92-75=17, Resulting Numbers: [17] 17,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 61:[23, 40], Operations: ['94-2=92', '92-52=40'] Exploring Operation: 23+40=63, Resulting Numbers: [63] 63,61 unequal: No Solution Exploring Operation: 23*40=920, Resulting Numbers: [920] 920,61 unequal: No Solution Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,61 unequal: No Solution No 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: 61:[92, 29], Operations: ['94-2=92', '52-23=29'] Exploring Operation: 92+29=121, Resulting Numbers: [121] 121,61 unequal: No Solution Exploring Operation: 92*29=2668, Resulting Numbers: [2668] 2668,61 unequal: No Solution Exploring Operation: 92-29=63, Resulting Numbers: [63] 63,61 unequal: No Solution No 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: 61:[52, 115], Operations: ['94-2=92', '23+92=115'] Exploring Operation: 52+115=167, Resulting Numbers: [167] 167,61 unequal: No Solution Exploring Operation: 52*115=5980, Resulting Numbers: [5980] 5980,61 unequal: No Solution Exploring Operation: 115-52=63, Resulting Numbers: [63] 63,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 88, 86, 88, 98 ]
86
[ "88-88=0", "98*0=0", "86+0=86" ]
Current State: 86:[88, 86, 88, 98], Operations: [] Exploring Operation: 88-88=0, Resulting Numbers: [86, 98, 0] Generated Node #2: [86, 98, 0] from Operation: 88-88=0 Current State: 86:[86, 98, 0], Operations: ['88-88=0'] Exploring Operation: 98*0=0, Resulting Numbers: [86, 0] Generated Node #3: [86, 0] from Operation: 98*0=0 Current State: 86:[86, 0], Operations: ['88-88=0', '98*0=0'] Exploring Operation: 86+0=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[88, 86, 88, 98], Operations: [] Exploring Operation: 98-88=10, Resulting Numbers: [86, 88, 10] Generated Node #0,0: 86:[86, 88, 10] Operation: 98-88=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[86, 88, 10], Operations: ['98-88=10'] Exploring Operation: 88-86=2, Resulting Numbers: [10, 2] Generated Node #0,0,0: 86:[10, 2] Operation: 88-86=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[10, 2], Operations: ['98-88=10', '88-86=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 63, 44, 98, 47 ]
56
[ "63+44=107", "98-47=51", "107-51=56" ]
Current State: 56:[63, 44, 98, 47], Operations: [] Exploring Operation: 63+44=107, Resulting Numbers: [98, 47, 107] Generated Node #2: [98, 47, 107] from Operation: 63+44=107 Current State: 56:[98, 47, 107], Operations: ['63+44=107'] Exploring Operation: 98-47=51, Resulting Numbers: [107, 51] Generated Node #3: [107, 51] from Operation: 98-47=51 Current State: 56:[107, 51], Operations: ['63+44=107', '98-47=51'] Exploring Operation: 107-51=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[63, 44, 98, 47], Operations: [] Exploring Operation: 98-44=54, Resulting Numbers: [63, 47, 54] Generated Node #0,0: 56:[63, 47, 54] Operation: 98-44=54 Exploring Operation: 98-47=51, Resulting Numbers: [63, 44, 51] Generated Node #0,1: 56:[63, 44, 51] Operation: 98-47=51 Exploring Operation: 98-63=35, Resulting Numbers: [44, 47, 35] Generated Node #0,2: 56:[44, 47, 35] Operation: 98-63=35 Exploring Operation: 47-44=3, Resulting Numbers: [63, 98, 3] Generated Node #0,3: 56:[63, 98, 3] Operation: 47-44=3 Moving to Node #0,0 Current State: 56:[63, 47, 54], Operations: ['98-44=54'] Exploring Operation: 54-47=7, Resulting Numbers: [63, 7] Generated Node #0,0,0: 56:[63, 7] Operation: 54-47=7 Exploring Operation: 47+54=101, Resulting Numbers: [63, 101] Generated Node #0,0,1: 56:[63, 101] Operation: 47+54=101 Exploring Operation: 63-54=9, Resulting Numbers: [47, 9] Generated Node #0,0,2: 56:[47, 9] Operation: 63-54=9 Exploring Operation: 63-47=16, Resulting Numbers: [54, 16] Generated Node #0,0,3: 56:[54, 16] Operation: 63-47=16 Moving to Node #0,1 Current State: 56:[63, 44, 51], Operations: ['98-47=51'] Exploring Operation: 51-44=7, Resulting Numbers: [63, 7] Generated Node #0,1,0: 56:[63, 7] Operation: 51-44=7 Exploring Operation: 63-51=12, Resulting Numbers: [44, 12] Generated Node #0,1,1: 56:[44, 12] Operation: 63-51=12 Exploring Operation: 63-44=19, Resulting Numbers: [51, 19] Generated Node #0,1,2: 56:[51, 19] Operation: 63-44=19 Exploring Operation: 44+51=95, Resulting Numbers: [63, 95] Generated Node #0,1,3: 56:[63, 95] Operation: 44+51=95 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 56:[63, 7], Operations: ['98-47=51', '51-44=7'] Exploring Operation: 63+7=70, Resulting Numbers: [70] 70,56 unequal: No Solution Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,56 unequal: No Solution Exploring Operation: 63*7=441, Resulting Numbers: [441] 441,56 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[63, 44, 98, 47], Operations: [] Exploring Operation: 98-47=51, Resulting Numbers: [63, 44, 51] Generated Node #0,1: 56:[63, 44, 51] Operation: 98-47=51 Moving to Node #0,1 Current State: 56:[63, 44, 51], Operations: ['98-47=51'] Exploring Operation: 51-44=7, Resulting Numbers: [63, 7] Generated Node #0,1,0: 56:[63, 7] Operation: 51-44=7 Moving to Node #0,1,0 Current State: 56:[63, 7], Operations: ['98-47=51', '51-44=7'] Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 66, 18, 12, 58 ]
22
[ "66-18=48", "12+58=70", "70-48=22" ]
Current State: 22:[66, 18, 12, 58], Operations: [] Exploring Operation: 66-18=48, Resulting Numbers: [12, 58, 48] Generated Node #2: [12, 58, 48] from Operation: 66-18=48 Current State: 22:[12, 58, 48], Operations: ['66-18=48'] Exploring Operation: 12+58=70, Resulting Numbers: [48, 70] Generated Node #3: [48, 70] from Operation: 12+58=70 Current State: 22:[48, 70], Operations: ['66-18=48', '12+58=70'] Exploring Operation: 70-48=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[66, 18, 12, 58], Operations: [] Exploring Operation: 58-18=40, Resulting Numbers: [66, 12, 40] Generated Node #0,0: 22:[66, 12, 40] Operation: 58-18=40 Exploring Operation: 66-18=48, Resulting Numbers: [12, 58, 48] Generated Node #0,1: 22:[12, 58, 48] Operation: 66-18=48 Exploring Operation: 66-58=8, Resulting Numbers: [18, 12, 8] Generated Node #0,2: 22:[18, 12, 8] Operation: 66-58=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[18, 12, 8], Operations: ['66-58=8'] Exploring Operation: 18+8=26, Resulting Numbers: [12, 26] Generated Node #0,2,0: 22:[12, 26] Operation: 18+8=26 Exploring Operation: 12+8=20, Resulting Numbers: [18, 20] Generated Node #0,2,1: 22:[18, 20] Operation: 12+8=20 Exploring Operation: 18-8=10, Resulting Numbers: [12, 10] Generated Node #0,2,2: 22:[12, 10] Operation: 18-8=10 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 22:[12, 10], Operations: ['66-58=8', '18-8=10'] Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 12*10=120, Resulting Numbers: [120] 120,22 unequal: No Solution Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[66, 18, 12, 58], Operations: [] Exploring Operation: 66-58=8, Resulting Numbers: [18, 12, 8] Generated Node #0,2: 22:[18, 12, 8] Operation: 66-58=8 Moving to Node #0,2 Current State: 22:[18, 12, 8], Operations: ['66-58=8'] Exploring Operation: 18-8=10, Resulting Numbers: [12, 10] Generated Node #0,2,2: 22:[12, 10] Operation: 18-8=10 Moving to Node #0,2,2 Current State: 22:[12, 10], Operations: ['66-58=8', '18-8=10'] Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 20, 18, 21, 29 ]
30
[ "20+18=38", "29-21=8", "38-8=30" ]
Current State: 30:[20, 18, 21, 29], Operations: [] Exploring Operation: 20+18=38, Resulting Numbers: [21, 29, 38] Generated Node #2: [21, 29, 38] from Operation: 20+18=38 Current State: 30:[21, 29, 38], Operations: ['20+18=38'] Exploring Operation: 29-21=8, Resulting Numbers: [38, 8] Generated Node #3: [38, 8] from Operation: 29-21=8 Current State: 30:[38, 8], Operations: ['20+18=38', '29-21=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[20, 18, 21, 29], Operations: [] Exploring Operation: 21-20=1, Resulting Numbers: [18, 29, 1] Generated Node #0,0: 30:[18, 29, 1] Operation: 21-20=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[18, 29, 1], Operations: ['21-20=1'] Exploring Operation: 29-18=11, Resulting Numbers: [1, 11] Generated Node #0,0,0: 30:[1, 11] Operation: 29-18=11 Moving to Node #0,0,0 Current State: 30:[1, 11], Operations: ['21-20=1', '29-18=11'] Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,30 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
[ 14, 19, 42, 7 ]
68
[ "14+19=33", "42-7=35", "33+35=68" ]
Current State: 68:[14, 19, 42, 7], Operations: [] Exploring Operation: 14+19=33, Resulting Numbers: [42, 7, 33] Generated Node #2: [42, 7, 33] from Operation: 14+19=33 Current State: 68:[42, 7, 33], Operations: ['14+19=33'] Exploring Operation: 42-7=35, Resulting Numbers: [33, 35] Generated Node #3: [33, 35] from Operation: 42-7=35 Current State: 68:[33, 35], Operations: ['14+19=33', '42-7=35'] Exploring Operation: 33+35=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[14, 19, 42, 7], Operations: [] Exploring Operation: 42/14=3, Resulting Numbers: [19, 7, 3] Generated Node #0,0: 68:[19, 7, 3] Operation: 42/14=3 Exploring Operation: 14/7=2, Resulting Numbers: [19, 42, 2] Generated Node #0,1: 68:[19, 42, 2] Operation: 14/7=2 Exploring Operation: 42/7=6, Resulting Numbers: [14, 19, 6] Generated Node #0,2: 68:[14, 19, 6] Operation: 42/7=6 Exploring Operation: 42-7=35, Resulting Numbers: [14, 19, 35] Generated Node #0,3: 68:[14, 19, 35] Operation: 42-7=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[19, 7, 3], Operations: ['42/14=3'] Exploring Operation: 7-3=4, Resulting Numbers: [19, 4] Generated Node #0,0,0: 68:[19, 4] Operation: 7-3=4 Exploring Operation: 19-7=12, Resulting Numbers: [3, 12] Generated Node #0,0,1: 68:[3, 12] Operation: 19-7=12 Exploring Operation: 19-3=16, Resulting Numbers: [7, 16] Generated Node #0,0,2: 68:[7, 16] Operation: 19-3=16 Exploring Operation: 7*3=21, Resulting Numbers: [19, 21] Generated Node #0,0,3: 68:[19, 21] Operation: 7*3=21 Moving to Node #0,0,0 Current State: 68:[19, 4], Operations: ['42/14=3', '7-3=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,68 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,68 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[7, 16], Operations: ['42/14=3', '19-3=16'] Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,68 unequal: No Solution Exploring Operation: 7*16=112, Resulting Numbers: [112] 112,68 unequal: No Solution Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,68 unequal: No Solution Moving to Node #0,0,3 Current State: 68:[19, 21], Operations: ['42/14=3', '7*3=21'] Exploring Operation: 21-19=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 19*21=399, Resulting Numbers: [399] 399,68 unequal: No Solution Exploring Operation: 19+21=40, Resulting Numbers: [40] 40,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[3, 12], Operations: ['42/14=3', '19-7=12'] Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,68 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,68 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,68 unequal: No Solution No 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: 68:[14, 19, 35], Operations: ['42-7=35'] Exploring Operation: 14+19=33, Resulting Numbers: [35, 33] Generated Node #0,3,0: 68:[35, 33] Operation: 14+19=33 Exploring Operation: 35-19=16, Resulting Numbers: [14, 16] Generated Node #0,3,1: 68:[14, 16] Operation: 35-19=16 Exploring Operation: 35-14=21, Resulting Numbers: [19, 21] Generated Node #0,3,2: 68:[19, 21] Operation: 35-14=21 Exploring Operation: 19-14=5, Resulting Numbers: [35, 5] Generated Node #0,3,3: 68:[35, 5] Operation: 19-14=5 Moving to Node #0,3,0 Current State: 68:[35, 33], Operations: ['42-7=35', '14+19=33'] Exploring Operation: 35*33=1155, Resulting Numbers: [1155] 1155,68 unequal: No Solution Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[14, 19, 42, 7], Operations: [] Exploring Operation: 42-7=35, Resulting Numbers: [14, 19, 35] Generated Node #0,3: 68:[14, 19, 35] Operation: 42-7=35 Moving to Node #0,3 Current State: 68:[14, 19, 35], Operations: ['42-7=35'] Exploring Operation: 14+19=33, Resulting Numbers: [35, 33] Generated Node #0,3,0: 68:[35, 33] Operation: 14+19=33 Moving to Node #0,3,0 Current State: 68:[35, 33], Operations: ['42-7=35', '14+19=33'] Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 89, 96, 15, 97 ]
24
[ "97-89=8", "15*8=120", "120-96=24" ]
Current State: 24:[89, 96, 15, 97], Operations: [] Exploring Operation: 97-89=8, Resulting Numbers: [96, 15, 8] Generated Node #2: [96, 15, 8] from Operation: 97-89=8 Current State: 24:[96, 15, 8], Operations: ['97-89=8'] Exploring Operation: 15*8=120, Resulting Numbers: [96, 120] Generated Node #3: [96, 120] from Operation: 15*8=120 Current State: 24:[96, 120], Operations: ['97-89=8', '15*8=120'] Exploring Operation: 120-96=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[89, 96, 15, 97], Operations: [] Exploring Operation: 97-96=1, Resulting Numbers: [89, 15, 1] Generated Node #0,0: 24:[89, 15, 1] Operation: 97-96=1 Exploring Operation: 97-89=8, Resulting Numbers: [96, 15, 8] Generated Node #0,1: 24:[96, 15, 8] Operation: 97-89=8 Moving to Node #0,0 Current State: 24:[89, 15, 1], Operations: ['97-96=1'] Exploring Operation: 89-1=88, Resulting Numbers: [15, 88] Generated Node #0,0,0: 24:[15, 88] Operation: 89-1=88 Exploring Operation: 89-15=74, Resulting Numbers: [1, 74] Generated Node #0,0,1: 24:[1, 74] Operation: 89-15=74 Moving to Node #0,1 Current State: 24:[96, 15, 8], Operations: ['97-89=8'] Exploring Operation: 96-15=81, Resulting Numbers: [8, 81] Generated Node #0,1,0: 24:[8, 81] Operation: 96-15=81 Exploring Operation: 96/8=12, Resulting Numbers: [15, 12] Generated Node #0,1,1: 24:[15, 12] Operation: 96/8=12 Moving to Node #0,1,1 Current State: 24:[15, 12], Operations: ['97-89=8', '96/8=12'] Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 15+12=27, Resulting Numbers: [27] 27,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[1, 74], Operations: ['97-96=1', '89-15=74'] Exploring Operation: 74-1=73, Resulting Numbers: [73] 73,24 unequal: No Solution Exploring Operation: 1*74=74, Resulting Numbers: [74] 74,24 unequal: No Solution Moving to Node #0,1,0 Current State: 24:[8, 81], Operations: ['97-89=8', '96-15=81'] Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,24 unequal: No Solution Exploring Operation: 8+81=89, Resulting Numbers: [89] 89,24 unequal: No Solution Moving to Node #0,0,0 Current State: 24:[15, 88], Operations: ['97-96=1', '89-1=88'] Exploring Operation: 15+88=103, Resulting Numbers: [103] 103,24 unequal: No Solution Exploring Operation: 88-15=73, Resulting Numbers: [73] 73,24 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 35, 22, 70, 15 ]
25
[ "22-15=7", "70/7=10", "35-10=25" ]
Current State: 25:[35, 22, 70, 15], Operations: [] Exploring Operation: 22-15=7, Resulting Numbers: [35, 70, 7] Generated Node #2: [35, 70, 7] from Operation: 22-15=7 Current State: 25:[35, 70, 7], Operations: ['22-15=7'] Exploring Operation: 70/7=10, Resulting Numbers: [35, 10] Generated Node #3: [35, 10] from Operation: 70/7=10 Current State: 25:[35, 10], Operations: ['22-15=7', '70/7=10'] Exploring Operation: 35-10=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[35, 22, 70, 15], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [22, 15, 2] Generated Node #0,0: 25:[22, 15, 2] Operation: 70/35=2 Moving to Node #0,0 Current State: 25:[22, 15, 2], Operations: ['70/35=2'] Exploring Operation: 22-15=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 25:[2, 7] Operation: 22-15=7 Moving to Node #0,0,0 Current State: 25:[2, 7], Operations: ['70/35=2', '22-15=7'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,25 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 46, 31, 87, 75 ]
27
[ "46-31=15", "87-75=12", "15+12=27" ]
Current State: 27:[46, 31, 87, 75], Operations: [] Exploring Operation: 46-31=15, Resulting Numbers: [87, 75, 15] Generated Node #2: [87, 75, 15] from Operation: 46-31=15 Current State: 27:[87, 75, 15], Operations: ['46-31=15'] Exploring Operation: 87-75=12, Resulting Numbers: [15, 12] Generated Node #3: [15, 12] from Operation: 87-75=12 Current State: 27:[15, 12], Operations: ['46-31=15', '87-75=12'] Exploring Operation: 15+12=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[46, 31, 87, 75], Operations: [] Exploring Operation: 87-75=12, Resulting Numbers: [46, 31, 12] Generated Node #0,0: 27:[46, 31, 12] Operation: 87-75=12 Exploring Operation: 75-46=29, Resulting Numbers: [31, 87, 29] Generated Node #0,1: 27:[31, 87, 29] Operation: 75-46=29 Exploring Operation: 87-46=41, Resulting Numbers: [31, 75, 41] Generated Node #0,2: 27:[31, 75, 41] Operation: 87-46=41 Moving to Node #0,0 Current State: 27:[46, 31, 12], Operations: ['87-75=12'] Exploring Operation: 46-31=15, Resulting Numbers: [12, 15] Generated Node #0,0,0: 27:[12, 15] Operation: 46-31=15 Exploring Operation: 46-12=34, Resulting Numbers: [31, 34] Generated Node #0,0,1: 27:[31, 34] Operation: 46-12=34 Exploring Operation: 31-12=19, Resulting Numbers: [46, 19] Generated Node #0,0,2: 27:[46, 19] Operation: 31-12=19 Moving to Node #0,1 Current State: 27:[31, 87, 29], Operations: ['75-46=29'] Exploring Operation: 87-31=56, Resulting Numbers: [29, 56] Generated Node #0,1,0: 27:[29, 56] Operation: 87-31=56 Exploring Operation: 87-29=58, Resulting Numbers: [31, 58] Generated Node #0,1,1: 27:[31, 58] Operation: 87-29=58 Exploring Operation: 87/29=3, Resulting Numbers: [31, 3] Generated Node #0,1,2: 27:[31, 3] Operation: 87/29=3 Moving to Node #0,2 Current State: 27:[31, 75, 41], Operations: ['87-46=41'] Exploring Operation: 75-31=44, Resulting Numbers: [41, 44] Generated Node #0,2,0: 27:[41, 44] Operation: 75-31=44 Exploring Operation: 41-31=10, Resulting Numbers: [75, 10] Generated Node #0,2,1: 27:[75, 10] Operation: 41-31=10 Exploring Operation: 75-41=34, Resulting Numbers: [31, 34] Generated Node #0,2,2: 27:[31, 34] Operation: 75-41=34 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 27:[31, 34], Operations: ['87-46=41', '75-41=34'] Exploring Operation: 34-31=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 31*34=1054, Resulting Numbers: [1054] 1054,27 unequal: No Solution Exploring Operation: 31+34=65, Resulting Numbers: [65] 65,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 27:[41, 44], Operations: ['87-46=41', '75-31=44'] Exploring Operation: 41+44=85, Resulting Numbers: [85] 85,27 unequal: No Solution Exploring Operation: 44-41=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 41*44=1804, Resulting Numbers: [1804] 1804,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 27:[75, 10], Operations: ['87-46=41', '41-31=10'] Exploring Operation: 75*10=750, Resulting Numbers: [750] 750,27 unequal: No Solution Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,27 unequal: No Solution Exploring Operation: 75+10=85, Resulting Numbers: [85] 85,27 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: 27:[31, 3], Operations: ['75-46=29', '87/29=3'] Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,27 unequal: No Solution Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[12, 15], Operations: ['87-75=12', '46-31=15'] Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,27 unequal: No Solution Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[46, 31, 87, 75], Operations: [] Exploring Operation: 87-75=12, Resulting Numbers: [46, 31, 12] Generated Node #0,0: 27:[46, 31, 12] Operation: 87-75=12 Moving to Node #0,0 Current State: 27:[46, 31, 12], Operations: ['87-75=12'] Exploring Operation: 46-31=15, Resulting Numbers: [12, 15] Generated Node #0,0,0: 27:[12, 15] Operation: 46-31=15 Moving to Node #0,0,0 Current State: 27:[12, 15], Operations: ['87-75=12', '46-31=15'] Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
0.973958
hs_3
sum_heuristic
[ 26, 98, 23, 27 ]
76
[ "98-26=72", "27-23=4", "72+4=76" ]
Current State: 76:[26, 98, 23, 27], Operations: [] Exploring Operation: 98-26=72, Resulting Numbers: [23, 27, 72] Generated Node #2: [23, 27, 72] from Operation: 98-26=72 Current State: 76:[23, 27, 72], Operations: ['98-26=72'] Exploring Operation: 27-23=4, Resulting Numbers: [72, 4] Generated Node #3: [72, 4] from Operation: 27-23=4 Current State: 76:[72, 4], Operations: ['98-26=72', '27-23=4'] Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[26, 98, 23, 27], Operations: [] Exploring Operation: 98-26=72, Resulting Numbers: [23, 27, 72] Generated Node #0,0: 76:[23, 27, 72] Operation: 98-26=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[23, 27, 72], Operations: ['98-26=72'] Exploring Operation: 27-23=4, Resulting Numbers: [72, 4] Generated Node #0,0,0: 76:[72, 4] Operation: 27-23=4 Moving to Node #0,0,0 Current State: 76:[72, 4], Operations: ['98-26=72', '27-23=4'] Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[26, 98, 23, 27], Operations: [] Exploring Operation: 98-26=72, Resulting Numbers: [23, 27, 72] Generated Node #0,0: 76:[23, 27, 72] Operation: 98-26=72 Moving to Node #0,0 Current State: 76:[23, 27, 72], Operations: ['98-26=72'] Exploring Operation: 27-23=4, Resulting Numbers: [72, 4] Generated Node #0,0,0: 76:[72, 4] Operation: 27-23=4 Moving to Node #0,0,0 Current State: 76:[72, 4], Operations: ['98-26=72', '27-23=4'] Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 24, 86, 56, 58 ]
67
[ "58-56=2", "86/2=43", "24+43=67" ]
Current State: 67:[24, 86, 56, 58], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [24, 86, 2] Generated Node #2: [24, 86, 2] from Operation: 58-56=2 Current State: 67:[24, 86, 2], Operations: ['58-56=2'] Exploring Operation: 86/2=43, Resulting Numbers: [24, 43] Generated Node #3: [24, 43] from Operation: 86/2=43 Current State: 67:[24, 43], Operations: ['58-56=2', '86/2=43'] Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[24, 86, 56, 58], Operations: [] Exploring Operation: 86-24=62, Resulting Numbers: [56, 58, 62] Generated Node #0,0: 67:[56, 58, 62] Operation: 86-24=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[56, 58, 62], Operations: ['86-24=62'] Exploring Operation: 56+58=114, Resulting Numbers: [62, 114] Generated Node #0,0,0: 67:[62, 114] Operation: 56+58=114 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[62, 114], Operations: ['86-24=62', '56+58=114'] Exploring Operation: 114-62=52, Resulting Numbers: [52] 52,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 39, 6, 74, 79 ]
19
[ "74-39=35", "79+35=114", "114/6=19" ]
Current State: 19:[39, 6, 74, 79], Operations: [] Exploring Operation: 74-39=35, Resulting Numbers: [6, 79, 35] Generated Node #2: [6, 79, 35] from Operation: 74-39=35 Current State: 19:[6, 79, 35], Operations: ['74-39=35'] Exploring Operation: 79+35=114, Resulting Numbers: [6, 114] Generated Node #3: [6, 114] from Operation: 79+35=114 Current State: 19:[6, 114], Operations: ['74-39=35', '79+35=114'] Exploring Operation: 114/6=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[39, 6, 74, 79], Operations: [] Exploring Operation: 79-39=40, Resulting Numbers: [6, 74, 40] Generated Node #0,0: 19:[6, 74, 40] Operation: 79-39=40 Exploring Operation: 79-74=5, Resulting Numbers: [39, 6, 5] Generated Node #0,1: 19:[39, 6, 5] Operation: 79-74=5 Exploring Operation: 74-39=35, Resulting Numbers: [6, 79, 35] Generated Node #0,2: 19:[6, 79, 35] Operation: 74-39=35 Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[39, 6, 5], Operations: ['79-74=5'] Exploring Operation: 39-6=33, Resulting Numbers: [5, 33] Generated Node #0,1,0: 19:[5, 33] Operation: 39-6=33 Exploring Operation: 6+5=11, Resulting Numbers: [39, 11] Generated Node #0,1,1: 19:[39, 11] Operation: 6+5=11 Exploring Operation: 39-5=34, Resulting Numbers: [6, 34] Generated Node #0,1,2: 19:[6, 34] Operation: 39-5=34 Moving to Node #0,1,0 Current State: 19:[5, 33], Operations: ['79-74=5', '39-6=33'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 5+33=38, Resulting Numbers: [38] 38,19 unequal: No Solution Exploring Operation: 5*33=165, Resulting Numbers: [165] 165,19 unequal: No Solution Moving to Node #0,1,1 Current State: 19:[39, 11], Operations: ['79-74=5', '6+5=11'] Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 39*11=429, Resulting Numbers: [429] 429,19 unequal: No Solution Exploring Operation: 39+11=50, Resulting Numbers: [50] 50,19 unequal: No Solution Moving to Node #0,1,2 Current State: 19:[6, 34], Operations: ['79-74=5', '39-5=34'] Exploring Operation: 6+34=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 6*34=204, Resulting Numbers: [204] 204,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[6, 74, 40], Operations: ['79-39=40'] Exploring Operation: 74-6=68, Resulting Numbers: [40, 68] Generated Node #0,0,0: 19:[40, 68] Operation: 74-6=68 Exploring Operation: 40-6=34, Resulting Numbers: [74, 34] Generated Node #0,0,1: 19:[74, 34] Operation: 40-6=34 Exploring Operation: 74-40=34, Resulting Numbers: [6, 34] Generated Node #0,0,2: 19:[6, 34] Operation: 74-40=34 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 19:[6, 34], Operations: ['79-39=40', '74-40=34'] Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 6+34=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 6*34=204, Resulting Numbers: [204] 204,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[40, 68], Operations: ['79-39=40', '74-6=68'] Exploring Operation: 40+68=108, Resulting Numbers: [108] 108,19 unequal: No Solution Exploring Operation: 40*68=2720, Resulting Numbers: [2720] 2720,19 unequal: No Solution Exploring Operation: 68-40=28, Resulting Numbers: [28] 28,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 19:[74, 34], Operations: ['79-39=40', '40-6=34'] Exploring Operation: 74-34=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 74*34=2516, Resulting Numbers: [2516] 2516,19 unequal: No Solution Exploring Operation: 74+34=108, Resulting Numbers: [108] 108,19 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:[6, 79, 35], Operations: ['74-39=35'] Exploring Operation: 35-6=29, Resulting Numbers: [79, 29] Generated Node #0,2,0: 19:[79, 29] Operation: 35-6=29 Exploring Operation: 79-35=44, Resulting Numbers: [6, 44] Generated Node #0,2,1: 19:[6, 44] Operation: 79-35=44 Exploring Operation: 79-6=73, Resulting Numbers: [35, 73] Generated Node #0,2,2: 19:[35, 73] Operation: 79-6=73 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 19:[6, 44], Operations: ['74-39=35', '79-35=44'] Exploring Operation: 6*44=264, Resulting Numbers: [264] 264,19 unequal: No Solution Exploring Operation: 6+44=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 19:[79, 29], Operations: ['74-39=35', '35-6=29'] Exploring Operation: 79+29=108, Resulting Numbers: [108] 108,19 unequal: No Solution Exploring Operation: 79*29=2291, Resulting Numbers: [2291] 2291,19 unequal: No Solution Exploring Operation: 79-29=50, Resulting Numbers: [50] 50,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 19:[35, 73], Operations: ['74-39=35', '79-6=73'] Exploring Operation: 35*73=2555, Resulting Numbers: [2555] 2555,19 unequal: No Solution Exploring Operation: 73-35=38, Resulting Numbers: [38] 38,19 unequal: No Solution Exploring Operation: 35+73=108, Resulting Numbers: [108] 108,19 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 No solution found.
0
hs_3
sum_heuristic
[ 65, 93, 66, 97 ]
68
[ "97-66=31", "93/31=3", "65+3=68" ]
Current State: 68:[65, 93, 66, 97], Operations: [] Exploring Operation: 97-66=31, Resulting Numbers: [65, 93, 31] Generated Node #2: [65, 93, 31] from Operation: 97-66=31 Current State: 68:[65, 93, 31], Operations: ['97-66=31'] Exploring Operation: 93/31=3, Resulting Numbers: [65, 3] Generated Node #3: [65, 3] from Operation: 93/31=3 Current State: 68:[65, 3], Operations: ['97-66=31', '93/31=3'] Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[65, 93, 66, 97], Operations: [] Exploring Operation: 97-66=31, Resulting Numbers: [65, 93, 31] Generated Node #0,0: 68:[65, 93, 31] Operation: 97-66=31 Exploring Operation: 97-65=32, Resulting Numbers: [93, 66, 32] Generated Node #0,1: 68:[93, 66, 32] Operation: 97-65=32 Exploring Operation: 97-93=4, Resulting Numbers: [65, 66, 4] Generated Node #0,2: 68:[65, 66, 4] Operation: 97-93=4 Moving to Node #0,2 Current State: 68:[65, 66, 4], Operations: ['97-93=4'] Exploring Operation: 65+4=69, Resulting Numbers: [66, 69] Generated Node #0,2,0: 68:[66, 69] Operation: 65+4=69 Exploring Operation: 66-65=1, Resulting Numbers: [4, 1] Generated Node #0,2,1: 68:[4, 1] Operation: 66-65=1 Exploring Operation: 66+4=70, Resulting Numbers: [65, 70] Generated Node #0,2,2: 68:[65, 70] Operation: 66+4=70 Moving to Node #0,1 Current State: 68:[93, 66, 32], Operations: ['97-65=32'] Exploring Operation: 93-66=27, Resulting Numbers: [32, 27] Generated Node #0,1,0: 68:[32, 27] Operation: 93-66=27 Exploring Operation: 66-32=34, Resulting Numbers: [93, 34] Generated Node #0,1,1: 68:[93, 34] Operation: 66-32=34 Exploring Operation: 93-32=61, Resulting Numbers: [66, 61] Generated Node #0,1,2: 68:[66, 61] Operation: 93-32=61 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 68:[32, 27], Operations: ['97-65=32', '93-66=27'] Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,68 unequal: No Solution Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,68 unequal: No Solution No 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: 68:[66, 61], Operations: ['97-65=32', '93-32=61'] Exploring Operation: 66-61=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 66+61=127, Resulting Numbers: [127] 127,68 unequal: No Solution Exploring Operation: 66*61=4026, Resulting Numbers: [4026] 4026,68 unequal: No Solution No 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: 68:[93, 34], Operations: ['97-65=32', '66-32=34'] Exploring Operation: 93+34=127, Resulting Numbers: [127] 127,68 unequal: No Solution Exploring Operation: 93-34=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 93*34=3162, Resulting Numbers: [3162] 3162,68 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: 68:[65, 93, 31], Operations: ['97-66=31'] Exploring Operation: 93/31=3, Resulting Numbers: [65, 3] Generated Node #0,0,0: 68:[65, 3] Operation: 93/31=3 Exploring Operation: 93-31=62, Resulting Numbers: [65, 62] Generated Node #0,0,1: 68:[65, 62] Operation: 93-31=62 Exploring Operation: 93-65=28, Resulting Numbers: [31, 28] Generated Node #0,0,2: 68:[31, 28] Operation: 93-65=28 Moving to Node #0,2,1 Current State: 68:[4, 1], Operations: ['97-93=4', '66-65=1'] Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,68 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[66, 69], Operations: ['97-93=4', '65+4=69'] Exploring Operation: 66*69=4554, Resulting Numbers: [4554] 4554,68 unequal: No Solution Exploring Operation: 69-66=3, Resulting Numbers: [3] 3,68 unequal: No Solution Exploring Operation: 66+69=135, Resulting Numbers: [135] 135,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[65, 3], Operations: ['97-66=31', '93/31=3'] Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[65, 93, 66, 97], Operations: [] Exploring Operation: 97-66=31, Resulting Numbers: [65, 93, 31] Generated Node #0,0: 68:[65, 93, 31] Operation: 97-66=31 Moving to Node #0,0 Current State: 68:[65, 93, 31], Operations: ['97-66=31'] Exploring Operation: 93/31=3, Resulting Numbers: [65, 3] Generated Node #0,0,0: 68:[65, 3] Operation: 93/31=3 Moving to Node #0,0,0 Current State: 68:[65, 3], Operations: ['97-66=31', '93/31=3'] Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
0.972222
hs_3
sum_heuristic
[ 25, 27, 16, 36 ]
34
[ "27-25=2", "36/2=18", "16+18=34" ]
Current State: 34:[25, 27, 16, 36], Operations: [] Exploring Operation: 27-25=2, Resulting Numbers: [16, 36, 2] Generated Node #2: [16, 36, 2] from Operation: 27-25=2 Current State: 34:[16, 36, 2], Operations: ['27-25=2'] Exploring Operation: 36/2=18, Resulting Numbers: [16, 18] Generated Node #3: [16, 18] from Operation: 36/2=18 Current State: 34:[16, 18], Operations: ['27-25=2', '36/2=18'] Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[25, 27, 16, 36], Operations: [] Exploring Operation: 27-16=11, Resulting Numbers: [25, 36, 11] Generated Node #0,0: 34:[25, 36, 11] Operation: 27-16=11 Exploring Operation: 25-16=9, Resulting Numbers: [27, 36, 9] Generated Node #0,1: 34:[27, 36, 9] Operation: 25-16=9 Exploring Operation: 36-25=11, Resulting Numbers: [27, 16, 11] Generated Node #0,2: 34:[27, 16, 11] Operation: 36-25=11 Exploring Operation: 25+16=41, Resulting Numbers: [27, 36, 41] Generated Node #0,3: 34:[27, 36, 41] Operation: 25+16=41 Exploring Operation: 27-25=2, Resulting Numbers: [16, 36, 2] Generated Node #0,4: 34:[16, 36, 2] Operation: 27-25=2 Moving to Node #0,4 Current State: 34:[16, 36, 2], Operations: ['27-25=2'] Exploring Operation: 36/2=18, Resulting Numbers: [16, 18] Generated Node #0,4,0: 34:[16, 18] Operation: 36/2=18 Exploring Operation: 16*2=32, Resulting Numbers: [36, 32] Generated Node #0,4,1: 34:[36, 32] Operation: 16*2=32 Exploring Operation: 16+2=18, Resulting Numbers: [36, 18] Generated Node #0,4,2: 34:[36, 18] Operation: 16+2=18 Exploring Operation: 36-16=20, Resulting Numbers: [2, 20] Generated Node #0,4,3: 34:[2, 20] Operation: 36-16=20 Exploring Operation: 36-2=34, Resulting Numbers: [16, 34] Generated Node #0,4,4: 34:[16, 34] Operation: 36-2=34 Moving to Node #0,2 Current State: 34:[27, 16, 11], Operations: ['36-25=11'] Exploring Operation: 16-11=5, Resulting Numbers: [27, 5] Generated Node #0,2,0: 34:[27, 5] Operation: 16-11=5 Exploring Operation: 27-11=16, Resulting Numbers: [16, 16] Generated Node #0,2,1: 34:[16, 16] Operation: 27-11=16 Exploring Operation: 16+11=27, Resulting Numbers: [27, 27] Generated Node #0,2,2: 34:[27, 27] Operation: 16+11=27 Exploring Operation: 27+11=38, Resulting Numbers: [16, 38] Generated Node #0,2,3: 34:[16, 38] Operation: 27+11=38 Exploring Operation: 27-16=11, Resulting Numbers: [11, 11] Generated Node #0,2,4: 34:[11, 11] Operation: 27-16=11 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 34:[16, 16], Operations: ['36-25=11', '27-11=16'] Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,34 unequal: No Solution Exploring Operation: 16-16=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 16*16=256, Resulting Numbers: [256] 256,34 unequal: No Solution Exploring Operation: 16/16=1, Resulting Numbers: [1] 1,34 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 #0,2,3 Current State: 34:[16, 38], Operations: ['36-25=11', '27+11=38'] Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 16+38=54, Resulting Numbers: [54] 54,34 unequal: No Solution Exploring Operation: 16*38=608, Resulting Numbers: [608] 608,34 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 #0,2,0 Current State: 34:[27, 5], Operations: ['36-25=11', '16-11=5'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,34 unequal: No Solution Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,34 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 #0,2,4 Current State: 34:[11, 11], Operations: ['36-25=11', '27-16=11'] Exploring Operation: 11*11=121, Resulting Numbers: [121] 121,34 unequal: No Solution Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 11-11=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 #0,2,2 Current State: 34:[27, 27], Operations: ['36-25=11', '16+11=27'] Exploring Operation: 27/27=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 27-27=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 27+27=54, Resulting Numbers: [54] 54,34 unequal: No Solution Exploring Operation: 27*27=729, Resulting Numbers: [729] 729,34 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: 34:[25, 36, 11], Operations: ['27-16=11'] Exploring Operation: 36-11=25, Resulting Numbers: [25, 25] Generated Node #0,0,0: 34:[25, 25] Operation: 36-11=25 Exploring Operation: 25+11=36, Resulting Numbers: [36, 36] Generated Node #0,0,1: 34:[36, 36] Operation: 25+11=36 Exploring Operation: 25-11=14, Resulting Numbers: [36, 14] Generated Node #0,0,2: 34:[36, 14] Operation: 25-11=14 Exploring Operation: 36+11=47, Resulting Numbers: [25, 47] Generated Node #0,0,3: 34:[25, 47] Operation: 36+11=47 Exploring Operation: 36-25=11, Resulting Numbers: [11, 11] Generated Node #0,0,4: 34:[11, 11] Operation: 36-25=11 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 34:[36, 36], Operations: ['27-16=11', '25+11=36'] Exploring Operation: 36/36=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 36+36=72, Resulting Numbers: [72] 72,34 unequal: No Solution Exploring Operation: 36-36=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 36*36=1296, Resulting Numbers: [1296] 1296,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 34:[36, 14], Operations: ['27-16=11', '25-11=14'] Exploring Operation: 36+14=50, Resulting Numbers: [50] 50,34 unequal: No Solution Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 36*14=504, Resulting Numbers: [504] 504,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 34:[11, 11], Operations: ['27-16=11', '36-25=11'] Exploring Operation: 11-11=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 11*11=121, Resulting Numbers: [121] 121,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 34:[25, 25], Operations: ['27-16=11', '36-11=25'] Exploring Operation: 25-25=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 25/25=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 25*25=625, Resulting Numbers: [625] 625,34 unequal: No Solution Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 34:[25, 47], Operations: ['27-16=11', '36+11=47'] Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 25*47=1175, Resulting Numbers: [1175] 1175,34 unequal: No Solution Exploring Operation: 25+47=72, Resulting Numbers: [72] 72,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 34:[27, 36, 9], Operations: ['25-16=9'] Exploring Operation: 27-9=18, Resulting Numbers: [36, 18] Generated Node #0,1,0: 34:[36, 18] Operation: 27-9=18 Exploring Operation: 27+9=36, Resulting Numbers: [36, 36] Generated Node #0,1,1: 34:[36, 36] Operation: 27+9=36 Exploring Operation: 36-27=9, Resulting Numbers: [9, 9] Generated Node #0,1,2: 34:[9, 9] Operation: 36-27=9 Exploring Operation: 27/9=3, Resulting Numbers: [36, 3] Generated Node #0,1,3: 34:[36, 3] Operation: 27/9=3 Exploring Operation: 36/9=4, Resulting Numbers: [27, 4] Generated Node #0,1,4: 34:[27, 4] Operation: 36/9=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 34:[36, 18], Operations: ['25-16=9', '27-9=18'] Exploring Operation: 36/18=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 36+18=54, Resulting Numbers: [54] 54,34 unequal: No Solution Exploring Operation: 36*18=648, Resulting Numbers: [648] 648,34 unequal: No Solution Exploring Operation: 36-18=18, Resulting Numbers: [18] 18,34 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 #0,1,3 Current State: 34:[36, 3], Operations: ['25-16=9', '27/9=3'] Exploring Operation: 36+3=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 36*3=108, Resulting Numbers: [108] 108,34 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,34 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 #0,1,1 Current State: 34:[36, 36], Operations: ['25-16=9', '27+9=36'] Exploring Operation: 36+36=72, Resulting Numbers: [72] 72,34 unequal: No Solution Exploring Operation: 36/36=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 36-36=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 36*36=1296, Resulting Numbers: [1296] 1296,34 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 #0,1,4 Current State: 34:[27, 4], Operations: ['25-16=9', '36/9=4'] Exploring Operation: 27*4=108, Resulting Numbers: [108] 108,34 unequal: No Solution Exploring Operation: 27+4=31, Resulting Numbers: [31] 31,34 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,34 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 #0,1,2 Current State: 34:[9, 9], Operations: ['25-16=9', '36-27=9'] Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,34 unequal: No Solution Exploring Operation: 9*9=81, Resulting Numbers: [81] 81,34 unequal: No Solution Exploring Operation: 9/9=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 9-9=0, Resulting Numbers: [0] 0,34 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: 34:[27, 36, 41], Operations: ['25+16=41'] Exploring Operation: 41-36=5, Resulting Numbers: [27, 5] Generated Node #0,3,0: 34:[27, 5] Operation: 41-36=5 Exploring Operation: 27+41=68, Resulting Numbers: [36, 68] Generated Node #0,3,1: 34:[36, 68] Operation: 27+41=68 Exploring Operation: 36-27=9, Resulting Numbers: [41, 9] Generated Node #0,3,2: 34:[41, 9] Operation: 36-27=9 Exploring Operation: 41-27=14, Resulting Numbers: [36, 14] Generated Node #0,3,3: 34:[36, 14] Operation: 41-27=14 Exploring Operation: 27+36=63, Resulting Numbers: [41, 63] Generated Node #0,3,4: 34:[41, 63] Operation: 27+36=63 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 34:[36, 14], Operations: ['25+16=41', '41-27=14'] Exploring Operation: 36*14=504, Resulting Numbers: [504] 504,34 unequal: No Solution Exploring Operation: 36+14=50, Resulting Numbers: [50] 50,34 unequal: No Solution Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 34:[27, 5], Operations: ['25+16=41', '41-36=5'] Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,34 unequal: No Solution Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,34 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 34:[41, 9], Operations: ['25+16=41', '36-27=9'] Exploring Operation: 41+9=50, Resulting Numbers: [50] 50,34 unequal: No Solution Exploring Operation: 41*9=369, Resulting Numbers: [369] 369,34 unequal: No Solution Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 34:[36, 68], Operations: ['25+16=41', '27+41=68'] Exploring Operation: 36+68=104, Resulting Numbers: [104] 104,34 unequal: No Solution Exploring Operation: 36*68=2448, Resulting Numbers: [2448] 2448,34 unequal: No Solution Exploring Operation: 68-36=32, Resulting Numbers: [32] 32,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 34:[41, 63], Operations: ['25+16=41', '27+36=63'] Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 41+63=104, Resulting Numbers: [104] 104,34 unequal: No Solution Exploring Operation: 41*63=2583, Resulting Numbers: [2583] 2583,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,4 Current State: 34:[16, 34], Operations: ['27-25=2', '36-2=34'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,34 unequal: No Solution Exploring Operation: 16*34=544, Resulting Numbers: [544] 544,34 unequal: No Solution Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,34 unequal: No Solution Moving to Node #0,4,0 Current State: 34:[16, 18], Operations: ['27-25=2', '36/2=18'] Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[25, 27, 16, 36], Operations: [] Exploring Operation: 27-25=2, Resulting Numbers: [16, 36, 2] Generated Node #0,4: 34:[16, 36, 2] Operation: 27-25=2 Moving to Node #0,4 Current State: 34:[16, 36, 2], Operations: ['27-25=2'] Exploring Operation: 36/2=18, Resulting Numbers: [16, 18] Generated Node #0,4,0: 34:[16, 18] Operation: 36/2=18 Moving to Node #0,4,0 Current State: 34:[16, 18], Operations: ['27-25=2', '36/2=18'] Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
0.90625
hs_5
sum_heuristic
[ 67, 44, 28, 82 ]
57
[ "67+44=111", "82-28=54", "111-54=57" ]
Current State: 57:[67, 44, 28, 82], Operations: [] Exploring Operation: 67+44=111, Resulting Numbers: [28, 82, 111] Generated Node #2: [28, 82, 111] from Operation: 67+44=111 Current State: 57:[28, 82, 111], Operations: ['67+44=111'] Exploring Operation: 82-28=54, Resulting Numbers: [111, 54] Generated Node #3: [111, 54] from Operation: 82-28=54 Current State: 57:[111, 54], Operations: ['67+44=111', '82-28=54'] Exploring Operation: 111-54=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[67, 44, 28, 82], Operations: [] Exploring Operation: 67-44=23, Resulting Numbers: [28, 82, 23] Generated Node #0,0: 57:[28, 82, 23] Operation: 67-44=23 Exploring Operation: 82-67=15, Resulting Numbers: [44, 28, 15] Generated Node #0,1: 57:[44, 28, 15] Operation: 82-67=15 Exploring Operation: 82-28=54, Resulting Numbers: [67, 44, 54] Generated Node #0,2: 57:[67, 44, 54] Operation: 82-28=54 Exploring Operation: 44-28=16, Resulting Numbers: [67, 82, 16] Generated Node #0,3: 57:[67, 82, 16] Operation: 44-28=16 Moving to Node #0,1 Current State: 57:[44, 28, 15], Operations: ['82-67=15'] Exploring Operation: 44+28=72, Resulting Numbers: [15, 72] Generated Node #0,1,0: 57:[15, 72] Operation: 44+28=72 Exploring Operation: 44+15=59, Resulting Numbers: [28, 59] Generated Node #0,1,1: 57:[28, 59] Operation: 44+15=59 Exploring Operation: 44-15=29, Resulting Numbers: [28, 29] Generated Node #0,1,2: 57:[28, 29] Operation: 44-15=29 Exploring Operation: 44-28=16, Resulting Numbers: [15, 16] Generated Node #0,1,3: 57:[15, 16] Operation: 44-28=16 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 57:[15, 16], Operations: ['82-67=15', '44-28=16'] Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,57 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,57 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:[28, 59], Operations: ['82-67=15', '44+15=59'] Exploring Operation: 28+59=87, Resulting Numbers: [87] 87,57 unequal: No Solution Exploring Operation: 59-28=31, Resulting Numbers: [31] 31,57 unequal: No Solution Exploring Operation: 28*59=1652, Resulting Numbers: [1652] 1652,57 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 #0,1,0 Current State: 57:[15, 72], Operations: ['82-67=15', '44+28=72'] Exploring Operation: 15+72=87, Resulting Numbers: [87] 87,57 unequal: No Solution Exploring Operation: 15*72=1080, Resulting Numbers: [1080] 1080,57 unequal: No Solution Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[67, 44, 28, 82], Operations: [] Exploring Operation: 82-67=15, Resulting Numbers: [44, 28, 15] Generated Node #0,1: 57:[44, 28, 15] Operation: 82-67=15 Moving to Node #0,1 Current State: 57:[44, 28, 15], Operations: ['82-67=15'] Exploring Operation: 44+28=72, Resulting Numbers: [15, 72] Generated Node #0,1,0: 57:[15, 72] Operation: 44+28=72 Moving to Node #0,1,0 Current State: 57:[15, 72], Operations: ['82-67=15', '44+28=72'] Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 6, 54, 59, 57 ]
50
[ "54-6=48", "59-57=2", "48+2=50" ]
Current State: 50:[6, 54, 59, 57], Operations: [] Exploring Operation: 54-6=48, Resulting Numbers: [59, 57, 48] Generated Node #2: [59, 57, 48] from Operation: 54-6=48 Current State: 50:[59, 57, 48], Operations: ['54-6=48'] Exploring Operation: 59-57=2, Resulting Numbers: [48, 2] Generated Node #3: [48, 2] from Operation: 59-57=2 Current State: 50:[48, 2], Operations: ['54-6=48', '59-57=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[6, 54, 59, 57], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [6, 54, 2] Generated Node #0,0: 50:[6, 54, 2] Operation: 59-57=2 Exploring Operation: 59-54=5, Resulting Numbers: [6, 57, 5] Generated Node #0,1: 50:[6, 57, 5] Operation: 59-54=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[6, 54, 2], Operations: ['59-57=2'] Exploring Operation: 54/6=9, Resulting Numbers: [2, 9] Generated Node #0,0,0: 50:[2, 9] Operation: 54/6=9 Exploring Operation: 54-6=48, Resulting Numbers: [2, 48] Generated Node #0,0,1: 50:[2, 48] Operation: 54-6=48 Moving to Node #0,0,0 Current State: 50:[2, 9], Operations: ['59-57=2', '54/6=9'] Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,50 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[2, 48], Operations: ['59-57=2', '54-6=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[6, 54, 59, 57], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [6, 54, 2] Generated Node #0,0: 50:[6, 54, 2] Operation: 59-57=2 Moving to Node #0,0 Current State: 50:[6, 54, 2], Operations: ['59-57=2'] Exploring Operation: 54-6=48, Resulting Numbers: [2, 48] Generated Node #0,0,1: 50:[2, 48] Operation: 54-6=48 Moving to Node #0,0,1 Current State: 50:[2, 48], Operations: ['59-57=2', '54-6=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 9, 30, 57, 63 ]
84
[ "63-57=6", "9*6=54", "30+54=84" ]
Current State: 84:[9, 30, 57, 63], Operations: [] Exploring Operation: 63-57=6, Resulting Numbers: [9, 30, 6] Generated Node #2: [9, 30, 6] from Operation: 63-57=6 Current State: 84:[9, 30, 6], Operations: ['63-57=6'] Exploring Operation: 9*6=54, Resulting Numbers: [30, 54] Generated Node #3: [30, 54] from Operation: 9*6=54 Current State: 84:[30, 54], Operations: ['63-57=6', '9*6=54'] Exploring Operation: 30+54=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[9, 30, 57, 63], Operations: [] Exploring Operation: 63-57=6, Resulting Numbers: [9, 30, 6] Generated Node #0,0: 84:[9, 30, 6] Operation: 63-57=6 Moving to Node #0,0 Current State: 84:[9, 30, 6], Operations: ['63-57=6'] Exploring Operation: 30-9=21, Resulting Numbers: [6, 21] Generated Node #0,0,0: 84:[6, 21] Operation: 30-9=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[6, 21], Operations: ['63-57=6', '30-9=21'] Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 15, 71, 98, 12 ]
54
[ "71-15=56", "98+12=110", "110-56=54" ]
Current State: 54:[15, 71, 98, 12], Operations: [] Exploring Operation: 71-15=56, Resulting Numbers: [98, 12, 56] Generated Node #2: [98, 12, 56] from Operation: 71-15=56 Current State: 54:[98, 12, 56], Operations: ['71-15=56'] Exploring Operation: 98+12=110, Resulting Numbers: [56, 110] Generated Node #3: [56, 110] from Operation: 98+12=110 Current State: 54:[56, 110], Operations: ['71-15=56', '98+12=110'] Exploring Operation: 110-56=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[15, 71, 98, 12], Operations: [] Exploring Operation: 98-12=86, Resulting Numbers: [15, 71, 86] Generated Node #0,0: 54:[15, 71, 86] Operation: 98-12=86 Exploring Operation: 98-15=83, Resulting Numbers: [71, 12, 83] Generated Node #0,1: 54:[71, 12, 83] Operation: 98-15=83 Exploring Operation: 71-15=56, Resulting Numbers: [98, 12, 56] Generated Node #0,2: 54:[98, 12, 56] Operation: 71-15=56 Exploring Operation: 98-71=27, Resulting Numbers: [15, 12, 27] Generated Node #0,3: 54:[15, 12, 27] Operation: 98-71=27 Exploring Operation: 71-12=59, Resulting Numbers: [15, 98, 59] Generated Node #0,4: 54:[15, 98, 59] Operation: 71-12=59 Start Sub Search at level 1: Moving to Node #0,3 Current State: 54:[15, 12, 27], Operations: ['98-71=27'] Exploring Operation: 15+12=27, Resulting Numbers: [27, 27] Generated Node #0,3,0: 54:[27, 27] Operation: 15+12=27 Exploring Operation: 15-12=3, Resulting Numbers: [27, 3] Generated Node #0,3,1: 54:[27, 3] Operation: 15-12=3 Exploring Operation: 15+27=42, Resulting Numbers: [12, 42] Generated Node #0,3,2: 54:[12, 42] Operation: 15+27=42 Exploring Operation: 27-12=15, Resulting Numbers: [15, 15] Generated Node #0,3,3: 54:[15, 15] Operation: 27-12=15 Exploring Operation: 27-15=12, Resulting Numbers: [12, 12] Generated Node #0,3,4: 54:[12, 12] Operation: 27-15=12 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 54:[27, 27], Operations: ['98-71=27', '15+12=27'] Exploring Operation: 27/27=1, Resulting Numbers: [1] 1,54 unequal: No Solution Exploring Operation: 27-27=0, Resulting Numbers: [0] 0,54 unequal: No Solution Exploring Operation: 27*27=729, Resulting Numbers: [729] 729,54 unequal: No Solution Exploring Operation: 27+27=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[15, 71, 98, 12], Operations: [] Exploring Operation: 98-71=27, Resulting Numbers: [15, 12, 27] Generated Node #0,3: 54:[15, 12, 27] Operation: 98-71=27 Moving to Node #0,3 Current State: 54:[15, 12, 27], Operations: ['98-71=27'] Exploring Operation: 15+12=27, Resulting Numbers: [27, 27] Generated Node #0,3,0: 54:[27, 27] Operation: 15+12=27 Moving to Node #0,3,0 Current State: 54:[27, 27], Operations: ['98-71=27', '15+12=27'] Exploring Operation: 27+27=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic