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
[ 83, 3, 97, 82 ]
70
[ "83*3=249", "97+82=179", "249-179=70" ]
Current State: 70:[83, 3, 97, 82], Operations: [] Exploring Operation: 83*3=249, Resulting Numbers: [97, 82, 249] Generated Node #2: [97, 82, 249] from Operation: 83*3=249 Current State: 70:[97, 82, 249], Operations: ['83*3=249'] Exploring Operation: 97+82=179, Resulting Numbers: [249, 179] Generated Node #3: [249, 179] from Operation: 97+82=179 Current State: 70:[249, 179], Operations: ['83*3=249', '97+82=179'] Exploring Operation: 249-179=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[83, 3, 97, 82], Operations: [] Exploring Operation: 97-83=14, Resulting Numbers: [3, 82, 14] Generated Node #0,0: 70:[3, 82, 14] Operation: 97-83=14 Moving to Node #0,0 Current State: 70:[3, 82, 14], Operations: ['97-83=14'] Exploring Operation: 82-14=68, Resulting Numbers: [3, 68] Generated Node #0,0,0: 70:[3, 68] Operation: 82-14=68 Moving to Node #0,0,0 Current State: 70:[3, 68], Operations: ['97-83=14', '82-14=68'] Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,70 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 12, 75, 13, 84 ]
95
[ "84/12=7", "75+13=88", "7+88=95" ]
Current State: 95:[12, 75, 13, 84], Operations: [] Exploring Operation: 84/12=7, Resulting Numbers: [75, 13, 7] Generated Node #2: [75, 13, 7] from Operation: 84/12=7 Current State: 95:[75, 13, 7], Operations: ['84/12=7'] Exploring Operation: 75+13=88, Resulting Numbers: [7, 88] Generated Node #3: [7, 88] from Operation: 75+13=88 Current State: 95:[7, 88], Operations: ['84/12=7', '75+13=88'] Exploring Operation: 7+88=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[12, 75, 13, 84], Operations: [] Exploring Operation: 84-75=9, Resulting Numbers: [12, 13, 9] Generated Node #0,0: 95:[12, 13, 9] Operation: 84-75=9 Exploring Operation: 12+75=87, Resulting Numbers: [13, 84, 87] Generated Node #0,1: 95:[13, 84, 87] Operation: 12+75=87 Moving to Node #0,0 Current State: 95:[12, 13, 9], Operations: ['84-75=9'] Exploring Operation: 13-12=1, Resulting Numbers: [9, 1] Generated Node #0,0,0: 95:[9, 1] Operation: 13-12=1 Exploring Operation: 12+9=21, Resulting Numbers: [13, 21] Generated Node #0,0,1: 95:[13, 21] Operation: 12+9=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[9, 1], Operations: ['84-75=9', '13-12=1'] Exploring Operation: 9*1=9, Resulting Numbers: [9] 9,95 unequal: No Solution Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,95 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 #0,0,1 Current State: 95:[13, 21], Operations: ['84-75=9', '12+9=21'] Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,95 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: 95:[13, 84, 87], Operations: ['12+75=87'] Exploring Operation: 87-84=3, Resulting Numbers: [13, 3] Generated Node #0,1,0: 95:[13, 3] Operation: 87-84=3 Exploring Operation: 13+84=97, Resulting Numbers: [87, 97] Generated Node #0,1,1: 95:[87, 97] Operation: 13+84=97 Moving to Node #0,1,0 Current State: 95:[13, 3], Operations: ['12+75=87', '87-84=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[87, 97], Operations: ['12+75=87', '13+84=97'] Exploring Operation: 97-87=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 87+97=184, Resulting Numbers: [184] 184,95 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 53, 31, 72, 17 ]
62
[ "72-53=19", "19-17=2", "31*2=62" ]
Current State: 62:[53, 31, 72, 17], Operations: [] Exploring Operation: 72-53=19, Resulting Numbers: [31, 17, 19] Generated Node #2: [31, 17, 19] from Operation: 72-53=19 Current State: 62:[31, 17, 19], Operations: ['72-53=19'] Exploring Operation: 19-17=2, Resulting Numbers: [31, 2] Generated Node #3: [31, 2] from Operation: 19-17=2 Current State: 62:[31, 2], Operations: ['72-53=19', '19-17=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[53, 31, 72, 17], Operations: [] Exploring Operation: 53-17=36, Resulting Numbers: [31, 72, 36] Generated Node #0,0: 62:[31, 72, 36] Operation: 53-17=36 Moving to Node #0,0 Current State: 62:[31, 72, 36], Operations: ['53-17=36'] Exploring Operation: 72/36=2, Resulting Numbers: [31, 2] Generated Node #0,0,0: 62:[31, 2] Operation: 72/36=2 Moving to Node #0,0,0 Current State: 62:[31, 2], Operations: ['53-17=36', '72/36=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[53, 31, 72, 17], Operations: [] Exploring Operation: 53-17=36, Resulting Numbers: [31, 72, 36] Generated Node #0,0: 62:[31, 72, 36] Operation: 53-17=36 Moving to Node #0,0 Current State: 62:[31, 72, 36], Operations: ['53-17=36'] Exploring Operation: 72/36=2, Resulting Numbers: [31, 2] Generated Node #0,0,0: 62:[31, 2] Operation: 72/36=2 Moving to Node #0,0,0 Current State: 62:[31, 2], Operations: ['53-17=36', '72/36=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 81, 59, 4, 48 ]
37
[ "59-48=11", "4*11=44", "81-44=37" ]
Current State: 37:[81, 59, 4, 48], Operations: [] Exploring Operation: 59-48=11, Resulting Numbers: [81, 4, 11] Generated Node #2: [81, 4, 11] from Operation: 59-48=11 Current State: 37:[81, 4, 11], Operations: ['59-48=11'] Exploring Operation: 4*11=44, Resulting Numbers: [81, 44] Generated Node #3: [81, 44] from Operation: 4*11=44 Current State: 37:[81, 44], Operations: ['59-48=11', '4*11=44'] Exploring Operation: 81-44=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[81, 59, 4, 48], Operations: [] Exploring Operation: 81-59=22, Resulting Numbers: [4, 48, 22] Generated Node #0,0: 37:[4, 48, 22] Operation: 81-59=22 Exploring Operation: 81-4=77, Resulting Numbers: [59, 48, 77] Generated Node #0,1: 37:[59, 48, 77] Operation: 81-4=77 Exploring Operation: 81-48=33, Resulting Numbers: [59, 4, 33] Generated Node #0,2: 37:[59, 4, 33] Operation: 81-48=33 Moving to Node #0,0 Current State: 37:[4, 48, 22], Operations: ['81-59=22'] Exploring Operation: 4+22=26, Resulting Numbers: [48, 26] Generated Node #0,0,0: 37:[48, 26] Operation: 4+22=26 Exploring Operation: 4+48=52, Resulting Numbers: [22, 52] Generated Node #0,0,1: 37:[22, 52] Operation: 4+48=52 Exploring Operation: 48-4=44, Resulting Numbers: [22, 44] Generated Node #0,0,2: 37:[22, 44] Operation: 48-4=44 Moving to Node #0,2 Current State: 37:[59, 4, 33], Operations: ['81-48=33'] Exploring Operation: 4+33=37, Resulting Numbers: [59, 37] Generated Node #0,2,0: 37:[59, 37] Operation: 4+33=37 Exploring Operation: 59-4=55, Resulting Numbers: [33, 55] Generated Node #0,2,1: 37:[33, 55] Operation: 59-4=55 Exploring Operation: 59+4=63, Resulting Numbers: [33, 63] Generated Node #0,2,2: 37:[33, 63] Operation: 59+4=63 Moving to Node #0,1 Current State: 37:[59, 48, 77], Operations: ['81-4=77'] Exploring Operation: 77-59=18, Resulting Numbers: [48, 18] Generated Node #0,1,0: 37:[48, 18] Operation: 77-59=18 Exploring Operation: 77-48=29, Resulting Numbers: [59, 29] Generated Node #0,1,1: 37:[59, 29] Operation: 77-48=29 Exploring Operation: 59-48=11, Resulting Numbers: [77, 11] Generated Node #0,1,2: 37:[77, 11] Operation: 59-48=11 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[48, 18], Operations: ['81-4=77', '77-59=18'] Exploring Operation: 48*18=864, Resulting Numbers: [864] 864,37 unequal: No Solution Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,37 unequal: No Solution Exploring Operation: 48+18=66, Resulting Numbers: [66] 66,37 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 #0,1,1 Current State: 37:[59, 29], Operations: ['81-4=77', '77-48=29'] Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,37 unequal: No Solution Exploring Operation: 59+29=88, Resulting Numbers: [88] 88,37 unequal: No Solution Exploring Operation: 59*29=1711, Resulting Numbers: [1711] 1711,37 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 #0,1,2 Current State: 37:[77, 11], Operations: ['81-4=77', '59-48=11'] Exploring Operation: 77-11=66, Resulting Numbers: [66] 66,37 unequal: No Solution Exploring Operation: 77/11=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 77+11=88, Resulting Numbers: [88] 88,37 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: 37:[48, 26], Operations: ['81-59=22', '4+22=26'] Exploring Operation: 48-26=22, Resulting Numbers: [22] 22,37 unequal: No Solution Exploring Operation: 48*26=1248, Resulting Numbers: [1248] 1248,37 unequal: No Solution Exploring Operation: 48+26=74, Resulting Numbers: [74] 74,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[22, 44], Operations: ['81-59=22', '48-4=44'] Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,37 unequal: No Solution Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,37 unequal: No Solution Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[33, 55], Operations: ['81-48=33', '59-4=55'] Exploring Operation: 33+55=88, Resulting Numbers: [88] 88,37 unequal: No Solution Exploring Operation: 55-33=22, Resulting Numbers: [22] 22,37 unequal: No Solution Exploring Operation: 33*55=1815, Resulting Numbers: [1815] 1815,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[59, 37], Operations: ['81-48=33', '4+33=37'] Exploring Operation: 59*37=2183, Resulting Numbers: [2183] 2183,37 unequal: No Solution Exploring Operation: 59+37=96, Resulting Numbers: [96] 96,37 unequal: No Solution Exploring Operation: 59-37=22, Resulting Numbers: [22] 22,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[33, 63], Operations: ['81-48=33', '59+4=63'] Exploring Operation: 33+63=96, Resulting Numbers: [96] 96,37 unequal: No Solution Exploring Operation: 33*63=2079, Resulting Numbers: [2079] 2079,37 unequal: No Solution Exploring Operation: 63-33=30, Resulting Numbers: [30] 30,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[22, 52], Operations: ['81-59=22', '4+48=52'] Exploring Operation: 22+52=74, Resulting Numbers: [74] 74,37 unequal: No Solution Exploring Operation: 52-22=30, Resulting Numbers: [30] 30,37 unequal: No Solution Exploring Operation: 22*52=1144, Resulting Numbers: [1144] 1144,37 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 2, 15, 40, 45 ]
77
[ "2*40=80", "45/15=3", "80-3=77" ]
Current State: 77:[2, 15, 40, 45], Operations: [] Exploring Operation: 2*40=80, Resulting Numbers: [15, 45, 80] Generated Node #2: [15, 45, 80] from Operation: 2*40=80 Current State: 77:[15, 45, 80], Operations: ['2*40=80'] Exploring Operation: 45/15=3, Resulting Numbers: [80, 3] Generated Node #3: [80, 3] from Operation: 45/15=3 Current State: 77:[80, 3], Operations: ['2*40=80', '45/15=3'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[2, 15, 40, 45], Operations: [] Exploring Operation: 40+45=85, Resulting Numbers: [2, 15, 85] Generated Node #0,0: 77:[2, 15, 85] Operation: 40+45=85 Exploring Operation: 45-40=5, Resulting Numbers: [2, 15, 5] Generated Node #0,1: 77:[2, 15, 5] Operation: 45-40=5 Moving to Node #0,1 Current State: 77:[2, 15, 5], Operations: ['45-40=5'] Exploring Operation: 15-2=13, Resulting Numbers: [5, 13] Generated Node #0,1,0: 77:[5, 13] Operation: 15-2=13 Exploring Operation: 2+5=7, Resulting Numbers: [15, 7] Generated Node #0,1,1: 77:[15, 7] Operation: 2+5=7 Moving to Node #0,0 Current State: 77:[2, 15, 85], Operations: ['40+45=85'] Exploring Operation: 85-2=83, Resulting Numbers: [15, 83] Generated Node #0,0,0: 77:[15, 83] Operation: 85-2=83 Exploring Operation: 15-2=13, Resulting Numbers: [85, 13] Generated Node #0,0,1: 77:[85, 13] Operation: 15-2=13 Moving to Node #0,1,0 Current State: 77:[5, 13], Operations: ['45-40=5', '15-2=13'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[15, 7], Operations: ['45-40=5', '2+5=7'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[85, 13], Operations: ['40+45=85', '15-2=13'] Exploring Operation: 85+13=98, Resulting Numbers: [98] 98,77 unequal: No Solution Exploring Operation: 85-13=72, Resulting Numbers: [72] 72,77 unequal: No Solution Moving to Node #0,0,0 Current State: 77:[15, 83], Operations: ['40+45=85', '85-2=83'] Exploring Operation: 15+83=98, Resulting Numbers: [98] 98,77 unequal: No Solution Exploring Operation: 83-15=68, Resulting Numbers: [68] 68,77 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 21, 11, 67, 65 ]
12
[ "21-11=10", "67-65=2", "10+2=12" ]
Current State: 12:[21, 11, 67, 65], Operations: [] Exploring Operation: 21-11=10, Resulting Numbers: [67, 65, 10] Generated Node #2: [67, 65, 10] from Operation: 21-11=10 Current State: 12:[67, 65, 10], Operations: ['21-11=10'] Exploring Operation: 67-65=2, Resulting Numbers: [10, 2] Generated Node #3: [10, 2] from Operation: 67-65=2 Current State: 12:[10, 2], Operations: ['21-11=10', '67-65=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[21, 11, 67, 65], Operations: [] Exploring Operation: 65-21=44, Resulting Numbers: [11, 67, 44] Generated Node #0,0: 12:[11, 67, 44] Operation: 65-21=44 Exploring Operation: 67-21=46, Resulting Numbers: [11, 65, 46] Generated Node #0,1: 12:[11, 65, 46] Operation: 67-21=46 Exploring Operation: 67-65=2, Resulting Numbers: [21, 11, 2] Generated Node #0,2: 12:[21, 11, 2] Operation: 67-65=2 Exploring Operation: 67-11=56, Resulting Numbers: [21, 65, 56] Generated Node #0,3: 12:[21, 65, 56] Operation: 67-11=56 Moving to Node #0,2 Current State: 12:[21, 11, 2], Operations: ['67-65=2'] Exploring Operation: 11+2=13, Resulting Numbers: [21, 13] Generated Node #0,2,0: 12:[21, 13] Operation: 11+2=13 Exploring Operation: 21-2=19, Resulting Numbers: [11, 19] Generated Node #0,2,1: 12:[11, 19] Operation: 21-2=19 Exploring Operation: 21-11=10, Resulting Numbers: [2, 10] Generated Node #0,2,2: 12:[2, 10] Operation: 21-11=10 Exploring Operation: 21+2=23, Resulting Numbers: [11, 23] Generated Node #0,2,3: 12:[11, 23] Operation: 21+2=23 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 12:[2, 10], Operations: ['67-65=2', '21-11=10'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[21, 11, 67, 65], Operations: [] Exploring Operation: 67-65=2, Resulting Numbers: [21, 11, 2] Generated Node #0,2: 12:[21, 11, 2] Operation: 67-65=2 Moving to Node #0,2 Current State: 12:[21, 11, 2], Operations: ['67-65=2'] Exploring Operation: 21-11=10, Resulting Numbers: [2, 10] Generated Node #0,2,2: 12:[2, 10] Operation: 21-11=10 Moving to Node #0,2,2 Current State: 12:[2, 10], Operations: ['67-65=2', '21-11=10'] Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 51, 54, 46, 40 ]
19
[ "51+54=105", "46+40=86", "105-86=19" ]
Current State: 19:[51, 54, 46, 40], Operations: [] Exploring Operation: 51+54=105, Resulting Numbers: [46, 40, 105] Generated Node #2: [46, 40, 105] from Operation: 51+54=105 Current State: 19:[46, 40, 105], Operations: ['51+54=105'] Exploring Operation: 46+40=86, Resulting Numbers: [105, 86] Generated Node #3: [105, 86] from Operation: 46+40=86 Current State: 19:[105, 86], Operations: ['51+54=105', '46+40=86'] Exploring Operation: 105-86=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[51, 54, 46, 40], Operations: [] Exploring Operation: 54-51=3, Resulting Numbers: [46, 40, 3] Generated Node #0,0: 19:[46, 40, 3] Operation: 54-51=3 Moving to Node #0,0 Current State: 19:[46, 40, 3], Operations: ['54-51=3'] Exploring Operation: 46-40=6, Resulting Numbers: [3, 6] Generated Node #0,0,0: 19:[3, 6] Operation: 46-40=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[3, 6], Operations: ['54-51=3', '46-40=6'] Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 52, 2, 31, 78 ]
97
[ "52-2=50", "78-31=47", "50+47=97" ]
Current State: 97:[52, 2, 31, 78], Operations: [] Exploring Operation: 52-2=50, Resulting Numbers: [31, 78, 50] Generated Node #2: [31, 78, 50] from Operation: 52-2=50 Current State: 97:[31, 78, 50], Operations: ['52-2=50'] Exploring Operation: 78-31=47, Resulting Numbers: [50, 47] Generated Node #3: [50, 47] from Operation: 78-31=47 Current State: 97:[50, 47], Operations: ['52-2=50', '78-31=47'] Exploring Operation: 50+47=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[52, 2, 31, 78], Operations: [] Exploring Operation: 52+2=54, Resulting Numbers: [31, 78, 54] Generated Node #0,0: 97:[31, 78, 54] Operation: 52+2=54 Exploring Operation: 52*2=104, Resulting Numbers: [31, 78, 104] Generated Node #0,1: 97:[31, 78, 104] Operation: 52*2=104 Exploring Operation: 2*31=62, Resulting Numbers: [52, 78, 62] Generated Node #0,2: 97:[52, 78, 62] Operation: 2*31=62 Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[31, 78, 104], Operations: ['52*2=104'] Exploring Operation: 31+78=109, Resulting Numbers: [104, 109] Generated Node #0,1,0: 97:[104, 109] Operation: 31+78=109 Exploring Operation: 78-31=47, Resulting Numbers: [104, 47] Generated Node #0,1,1: 97:[104, 47] Operation: 78-31=47 Exploring Operation: 104-31=73, Resulting Numbers: [78, 73] Generated Node #0,1,2: 97:[78, 73] Operation: 104-31=73 Moving to Node #0,1,0 Current State: 97:[104, 109], Operations: ['52*2=104', '31+78=109'] Exploring Operation: 104+109=213, Resulting Numbers: [213] 213,97 unequal: No Solution Exploring Operation: 109-104=5, Resulting Numbers: [5] 5,97 unequal: No Solution Exploring Operation: 104*109=11336, Resulting Numbers: [11336] 11336,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[78, 73], Operations: ['52*2=104', '104-31=73'] Exploring Operation: 78-73=5, Resulting Numbers: [5] 5,97 unequal: No Solution Exploring Operation: 78+73=151, Resulting Numbers: [151] 151,97 unequal: No Solution Exploring Operation: 78*73=5694, Resulting Numbers: [5694] 5694,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[104, 47], Operations: ['52*2=104', '78-31=47'] Exploring Operation: 104*47=4888, Resulting Numbers: [4888] 4888,97 unequal: No Solution Exploring Operation: 104+47=151, Resulting Numbers: [151] 151,97 unequal: No Solution Exploring Operation: 104-47=57, Resulting Numbers: [57] 57,97 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:[52, 78, 62], Operations: ['2*31=62'] Exploring Operation: 52+78=130, Resulting Numbers: [62, 130] Generated Node #0,2,0: 97:[62, 130] Operation: 52+78=130 Exploring Operation: 78+62=140, Resulting Numbers: [52, 140] Generated Node #0,2,1: 97:[52, 140] Operation: 78+62=140 Exploring Operation: 52+62=114, Resulting Numbers: [78, 114] Generated Node #0,2,2: 97:[78, 114] Operation: 52+62=114 Moving to Node #0,2,2 Current State: 97:[78, 114], Operations: ['2*31=62', '52+62=114'] Exploring Operation: 114-78=36, Resulting Numbers: [36] 36,97 unequal: No Solution Exploring Operation: 78*114=8892, Resulting Numbers: [8892] 8892,97 unequal: No Solution Exploring Operation: 78+114=192, Resulting Numbers: [192] 192,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[62, 130], Operations: ['2*31=62', '52+78=130'] Exploring Operation: 62*130=8060, Resulting Numbers: [8060] 8060,97 unequal: No Solution Exploring Operation: 62+130=192, Resulting Numbers: [192] 192,97 unequal: No Solution Exploring Operation: 130-62=68, Resulting Numbers: [68] 68,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[52, 140], Operations: ['2*31=62', '78+62=140'] Exploring Operation: 140-52=88, Resulting Numbers: [88] 88,97 unequal: No Solution Exploring Operation: 52+140=192, Resulting Numbers: [192] 192,97 unequal: No Solution Exploring Operation: 52*140=7280, Resulting Numbers: [7280] 7280,97 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:[31, 78, 54], Operations: ['52+2=54'] Exploring Operation: 78-31=47, Resulting Numbers: [54, 47] Generated Node #0,0,0: 97:[54, 47] Operation: 78-31=47 Exploring Operation: 31+78=109, Resulting Numbers: [54, 109] Generated Node #0,0,1: 97:[54, 109] Operation: 31+78=109 Exploring Operation: 31+54=85, Resulting Numbers: [78, 85] Generated Node #0,0,2: 97:[78, 85] Operation: 31+54=85 Moving to Node #0,0,2 Current State: 97:[78, 85], Operations: ['52+2=54', '31+54=85'] Exploring Operation: 85-78=7, Resulting Numbers: [7] 7,97 unequal: No Solution Exploring Operation: 78+85=163, Resulting Numbers: [163] 163,97 unequal: No Solution Exploring Operation: 78*85=6630, Resulting Numbers: [6630] 6630,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[54, 109], Operations: ['52+2=54', '31+78=109'] Exploring Operation: 54+109=163, Resulting Numbers: [163] 163,97 unequal: No Solution Exploring Operation: 109-54=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 54*109=5886, Resulting Numbers: [5886] 5886,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[54, 47], Operations: ['52+2=54', '78-31=47'] Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,97 unequal: No Solution Exploring Operation: 54+47=101, Resulting Numbers: [101] 101,97 unequal: No Solution Exploring Operation: 54*47=2538, Resulting Numbers: [2538] 2538,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 32, 83, 75, 35 ]
91
[ "83-32=51", "75-35=40", "51+40=91" ]
Current State: 91:[32, 83, 75, 35], Operations: [] Exploring Operation: 83-32=51, Resulting Numbers: [75, 35, 51] Generated Node #2: [75, 35, 51] from Operation: 83-32=51 Current State: 91:[75, 35, 51], Operations: ['83-32=51'] Exploring Operation: 75-35=40, Resulting Numbers: [51, 40] Generated Node #3: [51, 40] from Operation: 75-35=40 Current State: 91:[51, 40], Operations: ['83-32=51', '75-35=40'] Exploring Operation: 51+40=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[32, 83, 75, 35], Operations: [] Exploring Operation: 35-32=3, Resulting Numbers: [83, 75, 3] Generated Node #0,0: 91:[83, 75, 3] Operation: 35-32=3 Exploring Operation: 32+75=107, Resulting Numbers: [83, 35, 107] Generated Node #0,1: 91:[83, 35, 107] Operation: 32+75=107 Exploring Operation: 83-75=8, Resulting Numbers: [32, 35, 8] Generated Node #0,2: 91:[32, 35, 8] Operation: 83-75=8 Exploring Operation: 75+35=110, Resulting Numbers: [32, 83, 110] Generated Node #0,3: 91:[32, 83, 110] Operation: 75+35=110 Moving to Node #0,0 Current State: 91:[83, 75, 3], Operations: ['35-32=3'] Exploring Operation: 83+3=86, Resulting Numbers: [75, 86] Generated Node #0,0,0: 91:[75, 86] Operation: 83+3=86 Exploring Operation: 83-75=8, Resulting Numbers: [3, 8] Generated Node #0,0,1: 91:[3, 8] Operation: 83-75=8 Exploring Operation: 75/3=25, Resulting Numbers: [83, 25] Generated Node #0,0,2: 91:[83, 25] Operation: 75/3=25 Exploring Operation: 75+3=78, Resulting Numbers: [83, 78] Generated Node #0,0,3: 91:[83, 78] Operation: 75+3=78 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 91:[3, 8], Operations: ['35-32=3', '83-75=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,91 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,91 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 91:[83, 25], Operations: ['35-32=3', '75/3=25'] Exploring Operation: 83*25=2075, Resulting Numbers: [2075] 2075,91 unequal: No Solution Exploring Operation: 83-25=58, Resulting Numbers: [58] 58,91 unequal: No Solution Exploring Operation: 83+25=108, Resulting Numbers: [108] 108,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 91:[75, 86], Operations: ['35-32=3', '83+3=86'] Exploring Operation: 75+86=161, Resulting Numbers: [161] 161,91 unequal: No Solution Exploring Operation: 75*86=6450, Resulting Numbers: [6450] 6450,91 unequal: No Solution Exploring Operation: 86-75=11, Resulting Numbers: [11] 11,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 91:[83, 78], Operations: ['35-32=3', '75+3=78'] Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,91 unequal: No Solution Exploring Operation: 83*78=6474, Resulting Numbers: [6474] 6474,91 unequal: No Solution Exploring Operation: 83+78=161, Resulting Numbers: [161] 161,91 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: 91:[32, 35, 8], Operations: ['83-75=8'] Exploring Operation: 32/8=4, Resulting Numbers: [35, 4] Generated Node #0,2,0: 91:[35, 4] Operation: 32/8=4 Exploring Operation: 32+35=67, Resulting Numbers: [8, 67] Generated Node #0,2,1: 91:[8, 67] Operation: 32+35=67 Exploring Operation: 32-8=24, Resulting Numbers: [35, 24] Generated Node #0,2,2: 91:[35, 24] Operation: 32-8=24 Exploring Operation: 35-32=3, Resulting Numbers: [8, 3] Generated Node #0,2,3: 91:[8, 3] Operation: 35-32=3 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 91:[8, 3], Operations: ['83-75=8', '35-32=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,91 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,91 unequal: No Solution Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 91:[35, 4], Operations: ['83-75=8', '32/8=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,91 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,91 unequal: No Solution Exploring Operation: 35*4=140, Resulting Numbers: [140] 140,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 91:[8, 67], Operations: ['83-75=8', '32+35=67'] Exploring Operation: 8+67=75, Resulting Numbers: [75] 75,91 unequal: No Solution Exploring Operation: 67-8=59, Resulting Numbers: [59] 59,91 unequal: No Solution Exploring Operation: 8*67=536, Resulting Numbers: [536] 536,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 91:[35, 24], Operations: ['83-75=8', '32-8=24'] Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 35*24=840, Resulting Numbers: [840] 840,91 unequal: No Solution Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,91 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: 91:[32, 83, 110], Operations: ['75+35=110'] Exploring Operation: 110-32=78, Resulting Numbers: [83, 78] Generated Node #0,3,0: 91:[83, 78] Operation: 110-32=78 Exploring Operation: 110-83=27, Resulting Numbers: [32, 27] Generated Node #0,3,1: 91:[32, 27] Operation: 110-83=27 Exploring Operation: 83-32=51, Resulting Numbers: [110, 51] Generated Node #0,3,2: 91:[110, 51] Operation: 83-32=51 Exploring Operation: 32+83=115, Resulting Numbers: [110, 115] Generated Node #0,3,3: 91:[110, 115] Operation: 32+83=115 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 91:[83, 78], Operations: ['75+35=110', '110-32=78'] Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,91 unequal: No Solution Exploring Operation: 83+78=161, Resulting Numbers: [161] 161,91 unequal: No Solution Exploring Operation: 83*78=6474, Resulting Numbers: [6474] 6474,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 91:[32, 27], Operations: ['75+35=110', '110-83=27'] Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,91 unequal: No Solution Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,91 unequal: No Solution Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 91:[110, 115], Operations: ['75+35=110', '32+83=115'] Exploring Operation: 110+115=225, Resulting Numbers: [225] 225,91 unequal: No Solution Exploring Operation: 110*115=12650, Resulting Numbers: [12650] 12650,91 unequal: No Solution Exploring Operation: 115-110=5, Resulting Numbers: [5] 5,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 91:[110, 51], Operations: ['75+35=110', '83-32=51'] Exploring Operation: 110+51=161, Resulting Numbers: [161] 161,91 unequal: No Solution Exploring Operation: 110-51=59, Resulting Numbers: [59] 59,91 unequal: No Solution Exploring Operation: 110*51=5610, Resulting Numbers: [5610] 5610,91 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: 91:[83, 35, 107], Operations: ['32+75=107'] Exploring Operation: 83+35=118, Resulting Numbers: [107, 118] Generated Node #0,1,0: 91:[107, 118] Operation: 83+35=118 Exploring Operation: 83-35=48, Resulting Numbers: [107, 48] Generated Node #0,1,1: 91:[107, 48] Operation: 83-35=48 Exploring Operation: 107-35=72, Resulting Numbers: [83, 72] Generated Node #0,1,2: 91:[83, 72] Operation: 107-35=72 Exploring Operation: 107-83=24, Resulting Numbers: [35, 24] Generated Node #0,1,3: 91:[35, 24] Operation: 107-83=24 Moving to Node #0,1,2 Current State: 91:[83, 72], Operations: ['32+75=107', '107-35=72'] Exploring Operation: 83-72=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 83+72=155, Resulting Numbers: [155] 155,91 unequal: No Solution Exploring Operation: 83*72=5976, Resulting Numbers: [5976] 5976,91 unequal: No Solution Moving to Node #0,1,3 Current State: 91:[35, 24], Operations: ['32+75=107', '107-83=24'] Exploring Operation: 35*24=840, Resulting Numbers: [840] 840,91 unequal: No Solution Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,91 unequal: No Solution Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,91 unequal: No Solution Moving to Node #0,1,0 Current State: 91:[107, 118], Operations: ['32+75=107', '83+35=118'] Exploring Operation: 107*118=12626, Resulting Numbers: [12626] 12626,91 unequal: No Solution Exploring Operation: 107+118=225, Resulting Numbers: [225] 225,91 unequal: No Solution Exploring Operation: 118-107=11, Resulting Numbers: [11] 11,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[107, 48], Operations: ['32+75=107', '83-35=48'] Exploring Operation: 107*48=5136, Resulting Numbers: [5136] 5136,91 unequal: No Solution Exploring Operation: 107+48=155, Resulting Numbers: [155] 155,91 unequal: No Solution Exploring Operation: 107-48=59, Resulting Numbers: [59] 59,91 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 2, 13, 1, 23 ]
24
[ "23-1=22", "22/2=11", "13+11=24" ]
Current State: 24:[2, 13, 1, 23], Operations: [] Exploring Operation: 23-1=22, Resulting Numbers: [2, 13, 22] Generated Node #2: [2, 13, 22] from Operation: 23-1=22 Current State: 24:[2, 13, 22], Operations: ['23-1=22'] Exploring Operation: 22/2=11, Resulting Numbers: [13, 11] Generated Node #3: [13, 11] from Operation: 22/2=11 Current State: 24:[13, 11], Operations: ['23-1=22', '22/2=11'] Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[2, 13, 1, 23], Operations: [] Exploring Operation: 13-1=12, Resulting Numbers: [2, 23, 12] Generated Node #0,0: 24:[2, 23, 12] Operation: 13-1=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[2, 23, 12], Operations: ['13-1=12'] Exploring Operation: 2+23=25, Resulting Numbers: [12, 25] Generated Node #0,0,0: 24:[12, 25] Operation: 2+23=25 Moving to Node #0,0,0 Current State: 24:[12, 25], Operations: ['13-1=12', '2+23=25'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,24 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
[ 55, 41, 18, 38 ]
61
[ "41-38=3", "18/3=6", "55+6=61" ]
Current State: 61:[55, 41, 18, 38], Operations: [] Exploring Operation: 41-38=3, Resulting Numbers: [55, 18, 3] Generated Node #2: [55, 18, 3] from Operation: 41-38=3 Current State: 61:[55, 18, 3], Operations: ['41-38=3'] Exploring Operation: 18/3=6, Resulting Numbers: [55, 6] Generated Node #3: [55, 6] from Operation: 18/3=6 Current State: 61:[55, 6], Operations: ['41-38=3', '18/3=6'] Exploring Operation: 55+6=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[55, 41, 18, 38], Operations: [] Exploring Operation: 41+18=59, Resulting Numbers: [55, 38, 59] Generated Node #0,0: 61:[55, 38, 59] Operation: 41+18=59 Exploring Operation: 18+38=56, Resulting Numbers: [55, 41, 56] Generated Node #0,1: 61:[55, 41, 56] Operation: 18+38=56 Exploring Operation: 41-18=23, Resulting Numbers: [55, 38, 23] Generated Node #0,2: 61:[55, 38, 23] Operation: 41-18=23 Exploring Operation: 55-18=37, Resulting Numbers: [41, 38, 37] Generated Node #0,3: 61:[41, 38, 37] Operation: 55-18=37 Exploring Operation: 55+18=73, Resulting Numbers: [41, 38, 73] Generated Node #0,4: 61:[41, 38, 73] Operation: 55+18=73 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[55, 38, 59], Operations: ['41+18=59'] Exploring Operation: 55+59=114, Resulting Numbers: [38, 114] Generated Node #0,0,0: 61:[38, 114] Operation: 55+59=114 Exploring Operation: 55-38=17, Resulting Numbers: [59, 17] Generated Node #0,0,1: 61:[59, 17] Operation: 55-38=17 Exploring Operation: 38+59=97, Resulting Numbers: [55, 97] Generated Node #0,0,2: 61:[55, 97] Operation: 38+59=97 Exploring Operation: 55+38=93, Resulting Numbers: [59, 93] Generated Node #0,0,3: 61:[59, 93] Operation: 55+38=93 Exploring Operation: 59-38=21, Resulting Numbers: [55, 21] Generated Node #0,0,4: 61:[55, 21] Operation: 59-38=21 Moving to Node #0,0,3 Current State: 61:[59, 93], Operations: ['41+18=59', '55+38=93'] Exploring Operation: 59*93=5487, Resulting Numbers: [5487] 5487,61 unequal: No Solution Exploring Operation: 93-59=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 59+93=152, Resulting Numbers: [152] 152,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[55, 97], Operations: ['41+18=59', '38+59=97'] Exploring Operation: 97-55=42, Resulting Numbers: [42] 42,61 unequal: No Solution Exploring Operation: 55+97=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 55*97=5335, Resulting Numbers: [5335] 5335,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[59, 17], Operations: ['41+18=59', '55-38=17'] Exploring Operation: 59+17=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 59*17=1003, Resulting Numbers: [1003] 1003,61 unequal: No Solution Exploring Operation: 59-17=42, Resulting Numbers: [42] 42,61 unequal: No Solution Moving to Node #0,0,4 Current State: 61:[55, 21], Operations: ['41+18=59', '59-38=21'] Exploring Operation: 55+21=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 55-21=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 55*21=1155, Resulting Numbers: [1155] 1155,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[38, 114], Operations: ['41+18=59', '55+59=114'] Exploring Operation: 38+114=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 114-38=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 38*114=4332, Resulting Numbers: [4332] 4332,61 unequal: No Solution Exploring Operation: 114/38=3, Resulting Numbers: [3] 3,61 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:[55, 41, 56], Operations: ['18+38=56'] Exploring Operation: 55+56=111, Resulting Numbers: [41, 111] Generated Node #0,1,0: 61:[41, 111] Operation: 55+56=111 Exploring Operation: 41+56=97, Resulting Numbers: [55, 97] Generated Node #0,1,1: 61:[55, 97] Operation: 41+56=97 Exploring Operation: 56-41=15, Resulting Numbers: [55, 15] Generated Node #0,1,2: 61:[55, 15] Operation: 56-41=15 Exploring Operation: 55-41=14, Resulting Numbers: [56, 14] Generated Node #0,1,3: 61:[56, 14] Operation: 55-41=14 Exploring Operation: 55+41=96, Resulting Numbers: [56, 96] Generated Node #0,1,4: 61:[56, 96] Operation: 55+41=96 Moving to Node #0,1,4 Current State: 61:[56, 96], Operations: ['18+38=56', '55+41=96'] Exploring Operation: 96-56=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 56+96=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 56*96=5376, Resulting Numbers: [5376] 5376,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[55, 97], Operations: ['18+38=56', '41+56=97'] Exploring Operation: 55+97=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 97-55=42, Resulting Numbers: [42] 42,61 unequal: No Solution Exploring Operation: 55*97=5335, Resulting Numbers: [5335] 5335,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[55, 15], Operations: ['18+38=56', '56-41=15'] Exploring Operation: 55+15=70, Resulting Numbers: [70] 70,61 unequal: No Solution Exploring Operation: 55*15=825, Resulting Numbers: [825] 825,61 unequal: No Solution Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[56, 14], Operations: ['18+38=56', '55-41=14'] Exploring Operation: 56*14=784, Resulting Numbers: [784] 784,61 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,61 unequal: No Solution Exploring Operation: 56+14=70, Resulting Numbers: [70] 70,61 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[41, 111], Operations: ['18+38=56', '55+56=111'] Exploring Operation: 41+111=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 41*111=4551, Resulting Numbers: [4551] 4551,61 unequal: No Solution Exploring Operation: 111-41=70, Resulting Numbers: [70] 70,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 61:[41, 38, 73], Operations: ['55+18=73'] Exploring Operation: 38+73=111, Resulting Numbers: [41, 111] Generated Node #0,4,0: 61:[41, 111] Operation: 38+73=111 Exploring Operation: 73-41=32, Resulting Numbers: [38, 32] Generated Node #0,4,1: 61:[38, 32] Operation: 73-41=32 Exploring Operation: 73-38=35, Resulting Numbers: [41, 35] Generated Node #0,4,2: 61:[41, 35] Operation: 73-38=35 Exploring Operation: 41-38=3, Resulting Numbers: [73, 3] Generated Node #0,4,3: 61:[73, 3] Operation: 41-38=3 Exploring Operation: 41+38=79, Resulting Numbers: [73, 79] Generated Node #0,4,4: 61:[73, 79] Operation: 41+38=79 Moving to Node #0,4,4 Current State: 61:[73, 79], Operations: ['55+18=73', '41+38=79'] Exploring Operation: 73*79=5767, Resulting Numbers: [5767] 5767,61 unequal: No Solution Exploring Operation: 73+79=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 79-73=6, Resulting Numbers: [6] 6,61 unequal: No Solution Moving to Node #0,4,2 Current State: 61:[41, 35], Operations: ['55+18=73', '73-38=35'] Exploring Operation: 41+35=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 41*35=1435, Resulting Numbers: [1435] 1435,61 unequal: No Solution Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,61 unequal: No Solution Moving to Node #0,4,1 Current State: 61:[38, 32], Operations: ['55+18=73', '73-41=32'] Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,61 unequal: No Solution Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,61 unequal: No Solution Moving to Node #0,4,0 Current State: 61:[41, 111], Operations: ['55+18=73', '38+73=111'] Exploring Operation: 41*111=4551, Resulting Numbers: [4551] 4551,61 unequal: No Solution Exploring Operation: 41+111=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 111-41=70, Resulting Numbers: [70] 70,61 unequal: No Solution Moving to Node #0,4,3 Current State: 61:[73, 3], Operations: ['55+18=73', '41-38=3'] Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,61 unequal: No Solution Exploring Operation: 73*3=219, Resulting Numbers: [219] 219,61 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:[55, 38, 23], Operations: ['41-18=23'] Exploring Operation: 55+23=78, Resulting Numbers: [38, 78] Generated Node #0,2,0: 61:[38, 78] Operation: 55+23=78 Exploring Operation: 55-23=32, Resulting Numbers: [38, 32] Generated Node #0,2,1: 61:[38, 32] Operation: 55-23=32 Exploring Operation: 38+23=61, Resulting Numbers: [55, 61] Generated Node #0,2,2: 61:[55, 61] Operation: 38+23=61 Exploring Operation: 55+38=93, Resulting Numbers: [23, 93] Generated Node #0,2,3: 61:[23, 93] Operation: 55+38=93 Exploring Operation: 38-23=15, Resulting Numbers: [55, 15] Generated Node #0,2,4: 61:[55, 15] Operation: 38-23=15 Moving to Node #0,2,2 Current State: 61:[55, 61], Operations: ['41-18=23', '38+23=61'] Exploring Operation: 55*61=3355, Resulting Numbers: [3355] 3355,61 unequal: No Solution Exploring Operation: 61-55=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 55+61=116, Resulting Numbers: [116] 116,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[38, 78], Operations: ['41-18=23', '55+23=78'] Exploring Operation: 38*78=2964, Resulting Numbers: [2964] 2964,61 unequal: No Solution Exploring Operation: 38+78=116, Resulting Numbers: [116] 116,61 unequal: No Solution Exploring Operation: 78-38=40, Resulting Numbers: [40] 40,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[38, 32], Operations: ['41-18=23', '55-23=32'] Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,61 unequal: No Solution Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,61 unequal: No Solution Moving to Node #0,2,4 Current State: 61:[55, 15], Operations: ['41-18=23', '38-23=15'] Exploring Operation: 55+15=70, Resulting Numbers: [70] 70,61 unequal: No Solution Exploring Operation: 55*15=825, Resulting Numbers: [825] 825,61 unequal: No Solution Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,61 unequal: No Solution Moving to Node #0,2,3 Current State: 61:[23, 93], Operations: ['41-18=23', '55+38=93'] Exploring Operation: 23+93=116, Resulting Numbers: [116] 116,61 unequal: No Solution Exploring Operation: 23*93=2139, Resulting Numbers: [2139] 2139,61 unequal: No Solution Exploring Operation: 93-23=70, Resulting Numbers: [70] 70,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 61:[41, 38, 37], Operations: ['55-18=37'] Exploring Operation: 38+37=75, Resulting Numbers: [41, 75] Generated Node #0,3,0: 61:[41, 75] Operation: 38+37=75 Exploring Operation: 41+37=78, Resulting Numbers: [38, 78] Generated Node #0,3,1: 61:[38, 78] Operation: 41+37=78 Exploring Operation: 41+38=79, Resulting Numbers: [37, 79] Generated Node #0,3,2: 61:[37, 79] Operation: 41+38=79 Exploring Operation: 41-37=4, Resulting Numbers: [38, 4] Generated Node #0,3,3: 61:[38, 4] Operation: 41-37=4 Exploring Operation: 38-37=1, Resulting Numbers: [41, 1] Generated Node #0,3,4: 61:[41, 1] Operation: 38-37=1 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 61:[41, 75], Operations: ['55-18=37', '38+37=75'] Exploring Operation: 75-41=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 41+75=116, Resulting Numbers: [116] 116,61 unequal: No Solution Exploring Operation: 41*75=3075, Resulting Numbers: [3075] 3075,61 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 #0,3,1 Current State: 61:[38, 78], Operations: ['55-18=37', '41+37=78'] Exploring Operation: 38*78=2964, Resulting Numbers: [2964] 2964,61 unequal: No Solution Exploring Operation: 78-38=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 38+78=116, Resulting Numbers: [116] 116,61 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 #0,3,2 Current State: 61:[37, 79], Operations: ['55-18=37', '41+38=79'] Exploring Operation: 37+79=116, Resulting Numbers: [116] 116,61 unequal: No Solution Exploring Operation: 79-37=42, Resulting Numbers: [42] 42,61 unequal: No Solution Exploring Operation: 37*79=2923, Resulting Numbers: [2923] 2923,61 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 #0,3,3 Current State: 61:[38, 4], Operations: ['55-18=37', '41-37=4'] Exploring Operation: 38*4=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 38+4=42, Resulting Numbers: [42] 42,61 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 #0,3,4 Current State: 61:[41, 1], Operations: ['55-18=37', '38-37=1'] Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,61 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,61 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
sum_heuristic
[ 8, 38, 36, 60 ]
54
[ "38-8=30", "60-36=24", "30+24=54" ]
Current State: 54:[8, 38, 36, 60], Operations: [] Exploring Operation: 38-8=30, Resulting Numbers: [36, 60, 30] Generated Node #2: [36, 60, 30] from Operation: 38-8=30 Current State: 54:[36, 60, 30], Operations: ['38-8=30'] Exploring Operation: 60-36=24, Resulting Numbers: [30, 24] Generated Node #3: [30, 24] from Operation: 60-36=24 Current State: 54:[30, 24], Operations: ['38-8=30', '60-36=24'] Exploring Operation: 30+24=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[8, 38, 36, 60], Operations: [] Exploring Operation: 38-36=2, Resulting Numbers: [8, 60, 2] Generated Node #0,0: 54:[8, 60, 2] Operation: 38-36=2 Exploring Operation: 60-36=24, Resulting Numbers: [8, 38, 24] Generated Node #0,1: 54:[8, 38, 24] Operation: 60-36=24 Exploring Operation: 60-38=22, Resulting Numbers: [8, 36, 22] Generated Node #0,2: 54:[8, 36, 22] Operation: 60-38=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[8, 60, 2], Operations: ['38-36=2'] Exploring Operation: 60-2=58, Resulting Numbers: [8, 58] Generated Node #0,0,0: 54:[8, 58] Operation: 60-2=58 Exploring Operation: 60/2=30, Resulting Numbers: [8, 30] Generated Node #0,0,1: 54:[8, 30] Operation: 60/2=30 Exploring Operation: 60-8=52, Resulting Numbers: [2, 52] Generated Node #0,0,2: 54:[2, 52] Operation: 60-8=52 Moving to Node #0,0,2 Current State: 54:[2, 52], Operations: ['38-36=2', '60-8=52'] Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,54 unequal: No Solution Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[8, 38, 36, 60], Operations: [] Exploring Operation: 38-36=2, Resulting Numbers: [8, 60, 2] Generated Node #0,0: 54:[8, 60, 2] Operation: 38-36=2 Moving to Node #0,0 Current State: 54:[8, 60, 2], Operations: ['38-36=2'] Exploring Operation: 60-8=52, Resulting Numbers: [2, 52] Generated Node #0,0,2: 54:[2, 52] Operation: 60-8=52 Moving to Node #0,0,2 Current State: 54:[2, 52], Operations: ['38-36=2', '60-8=52'] Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 81, 1, 10, 95 ]
25
[ "81-1=80", "10+95=105", "105-80=25" ]
Current State: 25:[81, 1, 10, 95], Operations: [] Exploring Operation: 81-1=80, Resulting Numbers: [10, 95, 80] Generated Node #2: [10, 95, 80] from Operation: 81-1=80 Current State: 25:[10, 95, 80], Operations: ['81-1=80'] Exploring Operation: 10+95=105, Resulting Numbers: [80, 105] Generated Node #3: [80, 105] from Operation: 10+95=105 Current State: 25:[80, 105], Operations: ['81-1=80', '10+95=105'] Exploring Operation: 105-80=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[81, 1, 10, 95], Operations: [] Exploring Operation: 10-1=9, Resulting Numbers: [81, 95, 9] Generated Node #0,0: 25:[81, 95, 9] Operation: 10-1=9 Exploring Operation: 81-10=71, Resulting Numbers: [1, 95, 71] Generated Node #0,1: 25:[1, 95, 71] Operation: 81-10=71 Exploring Operation: 95-81=14, Resulting Numbers: [1, 10, 14] Generated Node #0,2: 25:[1, 10, 14] Operation: 95-81=14 Exploring Operation: 81-1=80, Resulting Numbers: [10, 95, 80] Generated Node #0,3: 25:[10, 95, 80] Operation: 81-1=80 Exploring Operation: 95-10=85, Resulting Numbers: [81, 1, 85] Generated Node #0,4: 25:[81, 1, 85] Operation: 95-10=85 Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[1, 10, 14], Operations: ['95-81=14'] Exploring Operation: 10-1=9, Resulting Numbers: [14, 9] Generated Node #0,2,0: 25:[14, 9] Operation: 10-1=9 Exploring Operation: 10+14=24, Resulting Numbers: [1, 24] Generated Node #0,2,1: 25:[1, 24] Operation: 10+14=24 Exploring Operation: 14-10=4, Resulting Numbers: [1, 4] Generated Node #0,2,2: 25:[1, 4] Operation: 14-10=4 Exploring Operation: 14-1=13, Resulting Numbers: [10, 13] Generated Node #0,2,3: 25:[10, 13] Operation: 14-1=13 Exploring Operation: 1*10=10, Resulting Numbers: [14, 10] Generated Node #0,2,4: 25:[14, 10] Operation: 1*10=10 Moving to Node #0,2,1 Current State: 25:[1, 24], Operations: ['95-81=14', '10+14=24'] Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[81, 1, 10, 95], Operations: [] Exploring Operation: 95-81=14, Resulting Numbers: [1, 10, 14] Generated Node #0,2: 25:[1, 10, 14] Operation: 95-81=14 Moving to Node #0,2 Current State: 25:[1, 10, 14], Operations: ['95-81=14'] Exploring Operation: 10+14=24, Resulting Numbers: [1, 24] Generated Node #0,2,1: 25:[1, 24] Operation: 10+14=24 Moving to Node #0,2,1 Current State: 25:[1, 24], Operations: ['95-81=14', '10+14=24'] Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 28, 33, 30, 99 ]
61
[ "28+30=58", "99/33=3", "58+3=61" ]
Current State: 61:[28, 33, 30, 99], Operations: [] Exploring Operation: 28+30=58, Resulting Numbers: [33, 99, 58] Generated Node #2: [33, 99, 58] from Operation: 28+30=58 Current State: 61:[33, 99, 58], Operations: ['28+30=58'] Exploring Operation: 99/33=3, Resulting Numbers: [58, 3] Generated Node #3: [58, 3] from Operation: 99/33=3 Current State: 61:[58, 3], Operations: ['28+30=58', '99/33=3'] Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[28, 33, 30, 99], Operations: [] Exploring Operation: 99-30=69, Resulting Numbers: [28, 33, 69] Generated Node #0,0: 61:[28, 33, 69] Operation: 99-30=69 Exploring Operation: 99-33=66, Resulting Numbers: [28, 30, 66] Generated Node #0,1: 61:[28, 30, 66] Operation: 99-33=66 Exploring Operation: 99-28=71, Resulting Numbers: [33, 30, 71] Generated Node #0,2: 61:[33, 30, 71] Operation: 99-28=71 Exploring Operation: 28+30=58, Resulting Numbers: [33, 99, 58] Generated Node #0,3: 61:[33, 99, 58] Operation: 28+30=58 Exploring Operation: 28+33=61, Resulting Numbers: [30, 99, 61] Generated Node #0,4: 61:[30, 99, 61] Operation: 28+33=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[28, 33, 69], Operations: ['99-30=69'] Exploring Operation: 69-33=36, Resulting Numbers: [28, 36] Generated Node #0,0,0: 61:[28, 36] Operation: 69-33=36 Exploring Operation: 69-28=41, Resulting Numbers: [33, 41] Generated Node #0,0,1: 61:[33, 41] Operation: 69-28=41 Exploring Operation: 28+69=97, Resulting Numbers: [33, 97] Generated Node #0,0,2: 61:[33, 97] Operation: 28+69=97 Exploring Operation: 28+33=61, Resulting Numbers: [69, 61] Generated Node #0,0,3: 61:[69, 61] Operation: 28+33=61 Exploring Operation: 33-28=5, Resulting Numbers: [69, 5] Generated Node #0,0,4: 61:[69, 5] Operation: 33-28=5 Moving to Node #0,0,3 Current State: 61:[69, 61], Operations: ['99-30=69', '28+33=61'] Exploring Operation: 69+61=130, Resulting Numbers: [130] 130,61 unequal: No Solution Exploring Operation: 69*61=4209, Resulting Numbers: [4209] 4209,61 unequal: No Solution Exploring Operation: 69-61=8, Resulting Numbers: [8] 8,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[33, 41], Operations: ['99-30=69', '69-28=41'] Exploring Operation: 33+41=74, Resulting Numbers: [74] 74,61 unequal: No Solution Exploring Operation: 41-33=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 33*41=1353, Resulting Numbers: [1353] 1353,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[28, 36], Operations: ['99-30=69', '69-33=36'] Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 28+36=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 28*36=1008, Resulting Numbers: [1008] 1008,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[33, 97], Operations: ['99-30=69', '28+69=97'] Exploring Operation: 33*97=3201, Resulting Numbers: [3201] 3201,61 unequal: No Solution Exploring Operation: 97-33=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 33+97=130, Resulting Numbers: [130] 130,61 unequal: No Solution Moving to Node #0,0,4 Current State: 61:[69, 5], Operations: ['99-30=69', '33-28=5'] Exploring Operation: 69*5=345, Resulting Numbers: [345] 345,61 unequal: No Solution Exploring Operation: 69-5=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 69+5=74, Resulting Numbers: [74] 74,61 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:[28, 30, 66], Operations: ['99-33=66'] Exploring Operation: 28+66=94, Resulting Numbers: [30, 94] Generated Node #0,1,0: 61:[30, 94] Operation: 28+66=94 Exploring Operation: 28+30=58, Resulting Numbers: [66, 58] Generated Node #0,1,1: 61:[66, 58] Operation: 28+30=58 Exploring Operation: 66-30=36, Resulting Numbers: [28, 36] Generated Node #0,1,2: 61:[28, 36] Operation: 66-30=36 Exploring Operation: 66-28=38, Resulting Numbers: [30, 38] Generated Node #0,1,3: 61:[30, 38] Operation: 66-28=38 Exploring Operation: 30-28=2, Resulting Numbers: [66, 2] Generated Node #0,1,4: 61:[66, 2] Operation: 30-28=2 Moving to Node #0,1,1 Current State: 61:[66, 58], Operations: ['99-33=66', '28+30=58'] Exploring Operation: 66+58=124, Resulting Numbers: [124] 124,61 unequal: No Solution Exploring Operation: 66-58=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 66*58=3828, Resulting Numbers: [3828] 3828,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[30, 38], Operations: ['99-33=66', '66-28=38'] Exploring Operation: 30+38=68, Resulting Numbers: [68] 68,61 unequal: No Solution Exploring Operation: 30*38=1140, Resulting Numbers: [1140] 1140,61 unequal: No Solution Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[28, 36], Operations: ['99-33=66', '66-30=36'] Exploring Operation: 28+36=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 28*36=1008, Resulting Numbers: [1008] 1008,61 unequal: No Solution Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[30, 94], Operations: ['99-33=66', '28+66=94'] Exploring Operation: 30*94=2820, Resulting Numbers: [2820] 2820,61 unequal: No Solution Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 30+94=124, Resulting Numbers: [124] 124,61 unequal: No Solution Moving to Node #0,1,4 Current State: 61:[66, 2], Operations: ['99-33=66', '30-28=2'] Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,61 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 66*2=132, Resulting Numbers: [132] 132,61 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[33, 30, 71], Operations: ['99-28=71'] Exploring Operation: 71-30=41, Resulting Numbers: [33, 41] Generated Node #0,2,0: 61:[33, 41] Operation: 71-30=41 Exploring Operation: 33+30=63, Resulting Numbers: [71, 63] Generated Node #0,2,1: 61:[71, 63] Operation: 33+30=63 Exploring Operation: 71-33=38, Resulting Numbers: [30, 38] Generated Node #0,2,2: 61:[30, 38] Operation: 71-33=38 Exploring Operation: 30+71=101, Resulting Numbers: [33, 101] Generated Node #0,2,3: 61:[33, 101] Operation: 30+71=101 Exploring Operation: 33-30=3, Resulting Numbers: [71, 3] Generated Node #0,2,4: 61:[71, 3] Operation: 33-30=3 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 61:[71, 63], Operations: ['99-28=71', '33+30=63'] Exploring Operation: 71+63=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 71-63=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 71*63=4473, Resulting Numbers: [4473] 4473,61 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:[33, 41], Operations: ['99-28=71', '71-30=41'] Exploring Operation: 41-33=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 33+41=74, Resulting Numbers: [74] 74,61 unequal: No Solution Exploring Operation: 33*41=1353, Resulting Numbers: [1353] 1353,61 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:[30, 38], Operations: ['99-28=71', '71-33=38'] Exploring Operation: 30*38=1140, Resulting Numbers: [1140] 1140,61 unequal: No Solution Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 30+38=68, Resulting Numbers: [68] 68,61 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:[33, 101], Operations: ['99-28=71', '30+71=101'] Exploring Operation: 33+101=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 33*101=3333, Resulting Numbers: [3333] 3333,61 unequal: No Solution Exploring Operation: 101-33=68, Resulting Numbers: [68] 68,61 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:[71, 3], Operations: ['99-28=71', '33-30=3'] Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,61 unequal: No Solution Exploring Operation: 71+3=74, Resulting Numbers: [74] 74,61 unequal: No Solution Exploring Operation: 71*3=213, Resulting Numbers: [213] 213,61 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:[33, 99, 58], Operations: ['28+30=58'] Exploring Operation: 99-33=66, Resulting Numbers: [58, 66] Generated Node #0,3,0: 61:[58, 66] Operation: 99-33=66 Exploring Operation: 99-58=41, Resulting Numbers: [33, 41] Generated Node #0,3,1: 61:[33, 41] Operation: 99-58=41 Exploring Operation: 33+99=132, Resulting Numbers: [58, 132] Generated Node #0,3,2: 61:[58, 132] Operation: 33+99=132 Exploring Operation: 33+58=91, Resulting Numbers: [99, 91] Generated Node #0,3,3: 61:[99, 91] Operation: 33+58=91 Exploring Operation: 99/33=3, Resulting Numbers: [58, 3] Generated Node #0,3,4: 61:[58, 3] Operation: 99/33=3 Moving to Node #0,3,0 Current State: 61:[58, 66], Operations: ['28+30=58', '99-33=66'] Exploring Operation: 58*66=3828, Resulting Numbers: [3828] 3828,61 unequal: No Solution Exploring Operation: 58+66=124, Resulting Numbers: [124] 124,61 unequal: No Solution Exploring Operation: 66-58=8, Resulting Numbers: [8] 8,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[33, 41], Operations: ['28+30=58', '99-58=41'] Exploring Operation: 33*41=1353, Resulting Numbers: [1353] 1353,61 unequal: No Solution Exploring Operation: 41-33=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 33+41=74, Resulting Numbers: [74] 74,61 unequal: No Solution Moving to Node #0,3,4 Current State: 61:[58, 3], Operations: ['28+30=58', '99/33=3'] Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,61 unequal: No Solution Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[28, 33, 30, 99], Operations: [] Exploring Operation: 28+30=58, Resulting Numbers: [33, 99, 58] Generated Node #0,3: 61:[33, 99, 58] Operation: 28+30=58 Moving to Node #0,3 Current State: 61:[33, 99, 58], Operations: ['28+30=58'] Exploring Operation: 99/33=3, Resulting Numbers: [58, 3] Generated Node #0,3,4: 61:[58, 3] Operation: 99/33=3 Moving to Node #0,3,4 Current State: 61:[58, 3], Operations: ['28+30=58', '99/33=3'] Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.927951
hs_5
sum_heuristic
[ 68, 19, 68, 20 ]
38
[ "68/68=1", "19+20=39", "39-1=38" ]
Current State: 38:[68, 19, 68, 20], Operations: [] Exploring Operation: 68/68=1, Resulting Numbers: [19, 20, 1] Generated Node #2: [19, 20, 1] from Operation: 68/68=1 Current State: 38:[19, 20, 1], Operations: ['68/68=1'] Exploring Operation: 19+20=39, Resulting Numbers: [1, 39] Generated Node #3: [1, 39] from Operation: 19+20=39 Current State: 38:[1, 39], Operations: ['68/68=1', '19+20=39'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[68, 19, 68, 20], Operations: [] Exploring Operation: 68/68=1, Resulting Numbers: [19, 20, 1] Generated Node #0,0: 38:[19, 20, 1] Operation: 68/68=1 Exploring Operation: 68-68=0, Resulting Numbers: [19, 20, 0] Generated Node #0,1: 38:[19, 20, 0] Operation: 68-68=0 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[19, 20, 1], Operations: ['68/68=1'] Exploring Operation: 19*1=19, Resulting Numbers: [20, 19] Generated Node #0,0,0: 38:[20, 19] Operation: 19*1=19 Exploring Operation: 20-1=19, Resulting Numbers: [19, 19] Generated Node #0,0,1: 38:[19, 19] Operation: 20-1=19 Moving to Node #0,0,1 Current State: 38:[19, 19], Operations: ['68/68=1', '20-1=19'] Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[68, 19, 68, 20], Operations: [] Exploring Operation: 68/68=1, Resulting Numbers: [19, 20, 1] Generated Node #0,0: 38:[19, 20, 1] Operation: 68/68=1 Moving to Node #0,0 Current State: 38:[19, 20, 1], Operations: ['68/68=1'] Exploring Operation: 20-1=19, Resulting Numbers: [19, 19] Generated Node #0,0,1: 38:[19, 19] Operation: 20-1=19 Moving to Node #0,0,1 Current State: 38:[19, 19], Operations: ['68/68=1', '20-1=19'] Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 2, 85, 43, 13 ]
53
[ "85-2=83", "43-13=30", "83-30=53" ]
Current State: 53:[2, 85, 43, 13], Operations: [] Exploring Operation: 85-2=83, Resulting Numbers: [43, 13, 83] Generated Node #2: [43, 13, 83] from Operation: 85-2=83 Current State: 53:[43, 13, 83], Operations: ['85-2=83'] Exploring Operation: 43-13=30, Resulting Numbers: [83, 30] Generated Node #3: [83, 30] from Operation: 43-13=30 Current State: 53:[83, 30], Operations: ['85-2=83', '43-13=30'] Exploring Operation: 83-30=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[2, 85, 43, 13], Operations: [] Exploring Operation: 2*13=26, Resulting Numbers: [85, 43, 26] Generated Node #0,0: 53:[85, 43, 26] Operation: 2*13=26 Exploring Operation: 2+43=45, Resulting Numbers: [85, 13, 45] Generated Node #0,1: 53:[85, 13, 45] Operation: 2+43=45 Exploring Operation: 85-2=83, Resulting Numbers: [43, 13, 83] Generated Node #0,2: 53:[43, 13, 83] Operation: 85-2=83 Moving to Node #0,0 Current State: 53:[85, 43, 26], Operations: ['2*13=26'] Exploring Operation: 85-26=59, Resulting Numbers: [43, 59] Generated Node #0,0,0: 53:[43, 59] Operation: 85-26=59 Exploring Operation: 85-43=42, Resulting Numbers: [26, 42] Generated Node #0,0,1: 53:[26, 42] Operation: 85-43=42 Exploring Operation: 43+26=69, Resulting Numbers: [85, 69] Generated Node #0,0,2: 53:[85, 69] Operation: 43+26=69 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[43, 59], Operations: ['2*13=26', '85-26=59'] Exploring Operation: 43+59=102, Resulting Numbers: [102] 102,53 unequal: No Solution Exploring Operation: 59-43=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 43*59=2537, Resulting Numbers: [2537] 2537,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[26, 42], Operations: ['2*13=26', '85-43=42'] Exploring Operation: 26+42=68, Resulting Numbers: [68] 68,53 unequal: No Solution Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 26*42=1092, Resulting Numbers: [1092] 1092,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 53:[85, 69], Operations: ['2*13=26', '43+26=69'] Exploring Operation: 85-69=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 85*69=5865, Resulting Numbers: [5865] 5865,53 unequal: No Solution Exploring Operation: 85+69=154, Resulting Numbers: [154] 154,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 53:[85, 13, 45], Operations: ['2+43=45'] Exploring Operation: 85+13=98, Resulting Numbers: [45, 98] Generated Node #0,1,0: 53:[45, 98] Operation: 85+13=98 Exploring Operation: 85-13=72, Resulting Numbers: [45, 72] Generated Node #0,1,1: 53:[45, 72] Operation: 85-13=72 Exploring Operation: 13+45=58, Resulting Numbers: [85, 58] Generated Node #0,1,2: 53:[85, 58] Operation: 13+45=58 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 53:[45, 72], Operations: ['2+43=45', '85-13=72'] Exploring Operation: 45*72=3240, Resulting Numbers: [3240] 3240,53 unequal: No Solution Exploring Operation: 72-45=27, Resulting Numbers: [27] 27,53 unequal: No Solution Exploring Operation: 45+72=117, Resulting Numbers: [117] 117,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 53:[85, 58], Operations: ['2+43=45', '13+45=58'] Exploring Operation: 85-58=27, Resulting Numbers: [27] 27,53 unequal: No Solution Exploring Operation: 85+58=143, Resulting Numbers: [143] 143,53 unequal: No Solution Exploring Operation: 85*58=4930, Resulting Numbers: [4930] 4930,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[45, 98], Operations: ['2+43=45', '85+13=98'] Exploring Operation: 45*98=4410, Resulting Numbers: [4410] 4410,53 unequal: No Solution Exploring Operation: 45+98=143, Resulting Numbers: [143] 143,53 unequal: No Solution Exploring Operation: 98-45=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[2, 85, 43, 13], Operations: [] Exploring Operation: 2+43=45, Resulting Numbers: [85, 13, 45] Generated Node #0,1: 53:[85, 13, 45] Operation: 2+43=45 Moving to Node #0,1 Current State: 53:[85, 13, 45], Operations: ['2+43=45'] Exploring Operation: 85+13=98, Resulting Numbers: [45, 98] Generated Node #0,1,0: 53:[45, 98] Operation: 85+13=98 Moving to Node #0,1,0 Current State: 53:[45, 98], Operations: ['2+43=45', '85+13=98'] Exploring Operation: 98-45=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_3
sum_heuristic
[ 81, 31, 93, 78 ]
38
[ "31*93=2883", "81+2883=2964", "2964/78=38" ]
Current State: 38:[81, 31, 93, 78], Operations: [] Exploring Operation: 31*93=2883, Resulting Numbers: [81, 78, 2883] Generated Node #2: [81, 78, 2883] from Operation: 31*93=2883 Current State: 38:[81, 78, 2883], Operations: ['31*93=2883'] Exploring Operation: 81+2883=2964, Resulting Numbers: [78, 2964] Generated Node #3: [78, 2964] from Operation: 81+2883=2964 Current State: 38:[78, 2964], Operations: ['31*93=2883', '81+2883=2964'] Exploring Operation: 2964/78=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[81, 31, 93, 78], Operations: [] Exploring Operation: 93-81=12, Resulting Numbers: [31, 78, 12] Generated Node #0,0: 38:[31, 78, 12] Operation: 93-81=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[31, 78, 12], Operations: ['93-81=12'] Exploring Operation: 78-31=47, Resulting Numbers: [12, 47] Generated Node #0,0,0: 38:[12, 47] Operation: 78-31=47 Moving to Node #0,0,0 Current State: 38:[12, 47], Operations: ['93-81=12', '78-31=47'] Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,38 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
[ 19, 49, 6, 53 ]
90
[ "19+49=68", "68-53=15", "6*15=90" ]
Current State: 90:[19, 49, 6, 53], Operations: [] Exploring Operation: 19+49=68, Resulting Numbers: [6, 53, 68] Generated Node #2: [6, 53, 68] from Operation: 19+49=68 Current State: 90:[6, 53, 68], Operations: ['19+49=68'] Exploring Operation: 68-53=15, Resulting Numbers: [6, 15] Generated Node #3: [6, 15] from Operation: 68-53=15 Current State: 90:[6, 15], Operations: ['19+49=68', '68-53=15'] Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[19, 49, 6, 53], Operations: [] Exploring Operation: 53-49=4, Resulting Numbers: [19, 6, 4] Generated Node #0,0: 90:[19, 6, 4] Operation: 53-49=4 Exploring Operation: 53-6=47, Resulting Numbers: [19, 49, 47] Generated Node #0,1: 90:[19, 49, 47] Operation: 53-6=47 Exploring Operation: 49-19=30, Resulting Numbers: [6, 53, 30] Generated Node #0,2: 90:[6, 53, 30] Operation: 49-19=30 Exploring Operation: 49-6=43, Resulting Numbers: [19, 53, 43] Generated Node #0,3: 90:[19, 53, 43] Operation: 49-6=43 Exploring Operation: 53-19=34, Resulting Numbers: [49, 6, 34] Generated Node #0,4: 90:[49, 6, 34] Operation: 53-19=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[19, 6, 4], Operations: ['53-49=4'] Exploring Operation: 19-6=13, Resulting Numbers: [4, 13] Generated Node #0,0,0: 90:[4, 13] Operation: 19-6=13 Exploring Operation: 19+4=23, Resulting Numbers: [6, 23] Generated Node #0,0,1: 90:[6, 23] Operation: 19+4=23 Exploring Operation: 6+4=10, Resulting Numbers: [19, 10] Generated Node #0,0,2: 90:[19, 10] Operation: 6+4=10 Exploring Operation: 6-4=2, Resulting Numbers: [19, 2] Generated Node #0,0,3: 90:[19, 2] Operation: 6-4=2 Exploring Operation: 19-4=15, Resulting Numbers: [6, 15] Generated Node #0,0,4: 90:[6, 15] Operation: 19-4=15 Moving to Node #0,0,4 Current State: 90:[6, 15], Operations: ['53-49=4', '19-4=15'] Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,90 unequal: No Solution Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[19, 49, 6, 53], Operations: [] Exploring Operation: 53-49=4, Resulting Numbers: [19, 6, 4] Generated Node #0,0: 90:[19, 6, 4] Operation: 53-49=4 Moving to Node #0,0 Current State: 90:[19, 6, 4], Operations: ['53-49=4'] Exploring Operation: 19-4=15, Resulting Numbers: [6, 15] Generated Node #0,0,4: 90:[6, 15] Operation: 19-4=15 Moving to Node #0,0,4 Current State: 90:[6, 15], Operations: ['53-49=4', '19-4=15'] Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 38, 4, 21, 23 ]
33
[ "38+21=59", "4*23=92", "92-59=33" ]
Current State: 33:[38, 4, 21, 23], Operations: [] Exploring Operation: 38+21=59, Resulting Numbers: [4, 23, 59] Generated Node #2: [4, 23, 59] from Operation: 38+21=59 Current State: 33:[4, 23, 59], Operations: ['38+21=59'] Exploring Operation: 4*23=92, Resulting Numbers: [59, 92] Generated Node #3: [59, 92] from Operation: 4*23=92 Current State: 33:[59, 92], Operations: ['38+21=59', '4*23=92'] Exploring Operation: 92-59=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[38, 4, 21, 23], Operations: [] Exploring Operation: 38-21=17, Resulting Numbers: [4, 23, 17] Generated Node #0,0: 33:[4, 23, 17] Operation: 38-21=17 Exploring Operation: 38-23=15, Resulting Numbers: [4, 21, 15] Generated Node #0,1: 33:[4, 21, 15] Operation: 38-23=15 Exploring Operation: 23-21=2, Resulting Numbers: [38, 4, 2] Generated Node #0,2: 33:[38, 4, 2] Operation: 23-21=2 Moving to Node #0,2 Current State: 33:[38, 4, 2], Operations: ['23-21=2'] Exploring Operation: 38-4=34, Resulting Numbers: [2, 34] Generated Node #0,2,0: 33:[2, 34] Operation: 38-4=34 Exploring Operation: 4-2=2, Resulting Numbers: [38, 2] Generated Node #0,2,1: 33:[38, 2] Operation: 4-2=2 Exploring Operation: 38-2=36, Resulting Numbers: [4, 36] Generated Node #0,2,2: 33:[4, 36] Operation: 38-2=36 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 33:[2, 34], Operations: ['23-21=2', '38-4=34'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,33 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,33 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 33:[4, 36], Operations: ['23-21=2', '38-2=36'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,33 unequal: No Solution Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,33 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 33:[38, 2], Operations: ['23-21=2', '4-2=2'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,33 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 33:[4, 21, 15], Operations: ['38-23=15'] Exploring Operation: 21+15=36, Resulting Numbers: [4, 36] Generated Node #0,1,0: 33:[4, 36] Operation: 21+15=36 Exploring Operation: 21-15=6, Resulting Numbers: [4, 6] Generated Node #0,1,1: 33:[4, 6] Operation: 21-15=6 Exploring Operation: 21-4=17, Resulting Numbers: [15, 17] Generated Node #0,1,2: 33:[15, 17] Operation: 21-4=17 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 33:[4, 36], Operations: ['38-23=15', '21+15=36'] Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,33 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,33 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,33 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 #0,1,1 Current State: 33:[4, 6], Operations: ['38-23=15', '21-15=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 33:[15, 17], Operations: ['38-23=15', '21-4=17'] Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,33 unequal: No Solution Exploring Operation: 15*17=255, Resulting Numbers: [255] 255,33 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,33 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: 33:[4, 23, 17], Operations: ['38-21=17'] Exploring Operation: 23-17=6, Resulting Numbers: [4, 6] Generated Node #0,0,0: 33:[4, 6] Operation: 23-17=6 Exploring Operation: 23+17=40, Resulting Numbers: [4, 40] Generated Node #0,0,1: 33:[4, 40] Operation: 23+17=40 Exploring Operation: 4+23=27, Resulting Numbers: [17, 27] Generated Node #0,0,2: 33:[17, 27] Operation: 4+23=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[4, 6], Operations: ['38-21=17', '23-17=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 33:[4, 40], Operations: ['38-21=17', '23+17=40'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 4+40=44, Resulting Numbers: [44] 44,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 33:[17, 27], Operations: ['38-21=17', '4+23=27'] Exploring Operation: 17*27=459, Resulting Numbers: [459] 459,33 unequal: No Solution Exploring Operation: 17+27=44, Resulting Numbers: [44] 44,33 unequal: No Solution Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 26, 35, 2, 66 ]
55
[ "35-26=9", "66-2=64", "64-9=55" ]
Current State: 55:[26, 35, 2, 66], Operations: [] Exploring Operation: 35-26=9, Resulting Numbers: [2, 66, 9] Generated Node #2: [2, 66, 9] from Operation: 35-26=9 Current State: 55:[2, 66, 9], Operations: ['35-26=9'] Exploring Operation: 66-2=64, Resulting Numbers: [9, 64] Generated Node #3: [9, 64] from Operation: 66-2=64 Current State: 55:[9, 64], Operations: ['35-26=9', '66-2=64'] Exploring Operation: 64-9=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[26, 35, 2, 66], Operations: [] Exploring Operation: 35-26=9, Resulting Numbers: [2, 66, 9] Generated Node #0,0: 55:[2, 66, 9] Operation: 35-26=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[2, 66, 9], Operations: ['35-26=9'] Exploring Operation: 66-9=57, Resulting Numbers: [2, 57] Generated Node #0,0,0: 55:[2, 57] Operation: 66-9=57 Moving to Node #0,0,0 Current State: 55:[2, 57], Operations: ['35-26=9', '66-9=57'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[26, 35, 2, 66], Operations: [] Exploring Operation: 35-26=9, Resulting Numbers: [2, 66, 9] Generated Node #0,0: 55:[2, 66, 9] Operation: 35-26=9 Moving to Node #0,0 Current State: 55:[2, 66, 9], Operations: ['35-26=9'] Exploring Operation: 66-9=57, Resulting Numbers: [2, 57] Generated Node #0,0,0: 55:[2, 57] Operation: 66-9=57 Moving to Node #0,0,0 Current State: 55:[2, 57], Operations: ['35-26=9', '66-9=57'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 83, 52, 55, 24 ]
75
[ "55-52=3", "24/3=8", "83-8=75" ]
Current State: 75:[83, 52, 55, 24], Operations: [] Exploring Operation: 55-52=3, Resulting Numbers: [83, 24, 3] Generated Node #2: [83, 24, 3] from Operation: 55-52=3 Current State: 75:[83, 24, 3], Operations: ['55-52=3'] Exploring Operation: 24/3=8, Resulting Numbers: [83, 8] Generated Node #3: [83, 8] from Operation: 24/3=8 Current State: 75:[83, 8], Operations: ['55-52=3', '24/3=8'] Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[83, 52, 55, 24], Operations: [] Exploring Operation: 55-52=3, Resulting Numbers: [83, 24, 3] Generated Node #0,0: 75:[83, 24, 3] Operation: 55-52=3 Moving to Node #0,0 Current State: 75:[83, 24, 3], Operations: ['55-52=3'] Exploring Operation: 83-3=80, Resulting Numbers: [24, 80] Generated Node #0,0,0: 75:[24, 80] Operation: 83-3=80 Moving to Node #0,0,0 Current State: 75:[24, 80], Operations: ['55-52=3', '83-3=80'] Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,75 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 19, 50, 53, 98 ]
82
[ "19+50=69", "53+98=151", "151-69=82" ]
Current State: 82:[19, 50, 53, 98], Operations: [] Exploring Operation: 19+50=69, Resulting Numbers: [53, 98, 69] Generated Node #2: [53, 98, 69] from Operation: 19+50=69 Current State: 82:[53, 98, 69], Operations: ['19+50=69'] Exploring Operation: 53+98=151, Resulting Numbers: [69, 151] Generated Node #3: [69, 151] from Operation: 53+98=151 Current State: 82:[69, 151], Operations: ['19+50=69', '53+98=151'] Exploring Operation: 151-69=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[19, 50, 53, 98], Operations: [] Exploring Operation: 98-19=79, Resulting Numbers: [50, 53, 79] Generated Node #0,0: 82:[50, 53, 79] Operation: 98-19=79 Moving to Node #0,0 Current State: 82:[50, 53, 79], Operations: ['98-19=79'] Exploring Operation: 53-50=3, Resulting Numbers: [79, 3] Generated Node #0,0,0: 82:[79, 3] Operation: 53-50=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 82:[79, 3], Operations: ['98-19=79', '53-50=3'] Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[19, 50, 53, 98], Operations: [] Exploring Operation: 98-19=79, Resulting Numbers: [50, 53, 79] Generated Node #0,0: 82:[50, 53, 79] Operation: 98-19=79 Moving to Node #0,0 Current State: 82:[50, 53, 79], Operations: ['98-19=79'] Exploring Operation: 53-50=3, Resulting Numbers: [79, 3] Generated Node #0,0,0: 82:[79, 3] Operation: 53-50=3 Moving to Node #0,0,0 Current State: 82:[79, 3], Operations: ['98-19=79', '53-50=3'] Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 21, 42, 75, 8 ]
71
[ "42/21=2", "8/2=4", "75-4=71" ]
Current State: 71:[21, 42, 75, 8], Operations: [] Exploring Operation: 42/21=2, Resulting Numbers: [75, 8, 2] Generated Node #2: [75, 8, 2] from Operation: 42/21=2 Current State: 71:[75, 8, 2], Operations: ['42/21=2'] Exploring Operation: 8/2=4, Resulting Numbers: [75, 4] Generated Node #3: [75, 4] from Operation: 8/2=4 Current State: 71:[75, 4], Operations: ['42/21=2', '8/2=4'] Exploring Operation: 75-4=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[21, 42, 75, 8], Operations: [] Exploring Operation: 21+42=63, Resulting Numbers: [75, 8, 63] Generated Node #0,0: 71:[75, 8, 63] Operation: 21+42=63 Exploring Operation: 42+8=50, Resulting Numbers: [21, 75, 50] Generated Node #0,1: 71:[21, 75, 50] Operation: 42+8=50 Exploring Operation: 21+8=29, Resulting Numbers: [42, 75, 29] Generated Node #0,2: 71:[42, 75, 29] Operation: 21+8=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[75, 8, 63], Operations: ['21+42=63'] Exploring Operation: 8+63=71, Resulting Numbers: [75, 71] Generated Node #0,0,0: 71:[75, 71] Operation: 8+63=71 Exploring Operation: 75-8=67, Resulting Numbers: [63, 67] Generated Node #0,0,1: 71:[63, 67] Operation: 75-8=67 Exploring Operation: 75+8=83, Resulting Numbers: [63, 83] Generated Node #0,0,2: 71:[63, 83] Operation: 75+8=83 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[75, 71], Operations: ['21+42=63', '8+63=71'] Exploring Operation: 75*71=5325, Resulting Numbers: [5325] 5325,71 unequal: No Solution Exploring Operation: 75-71=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 75+71=146, Resulting Numbers: [146] 146,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 71:[63, 67], Operations: ['21+42=63', '75-8=67'] Exploring Operation: 67-63=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 63+67=130, Resulting Numbers: [130] 130,71 unequal: No Solution Exploring Operation: 63*67=4221, Resulting Numbers: [4221] 4221,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 71:[63, 83], Operations: ['21+42=63', '75+8=83'] Exploring Operation: 83-63=20, Resulting Numbers: [20] 20,71 unequal: No Solution Exploring Operation: 63+83=146, Resulting Numbers: [146] 146,71 unequal: No Solution Exploring Operation: 63*83=5229, Resulting Numbers: [5229] 5229,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[21, 75, 50], Operations: ['42+8=50'] Exploring Operation: 75-21=54, Resulting Numbers: [50, 54] Generated Node #0,1,0: 71:[50, 54] Operation: 75-21=54 Exploring Operation: 21+75=96, Resulting Numbers: [50, 96] Generated Node #0,1,1: 71:[50, 96] Operation: 21+75=96 Exploring Operation: 21+50=71, Resulting Numbers: [75, 71] Generated Node #0,1,2: 71:[75, 71] Operation: 21+50=71 Moving to Node #0,1,2 Current State: 71:[75, 71], Operations: ['42+8=50', '21+50=71'] Exploring Operation: 75*71=5325, Resulting Numbers: [5325] 5325,71 unequal: No Solution Exploring Operation: 75+71=146, Resulting Numbers: [146] 146,71 unequal: No Solution Exploring Operation: 75-71=4, Resulting Numbers: [4] 4,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[50, 54], Operations: ['42+8=50', '75-21=54'] Exploring Operation: 50+54=104, Resulting Numbers: [104] 104,71 unequal: No Solution Exploring Operation: 50*54=2700, Resulting Numbers: [2700] 2700,71 unequal: No Solution Exploring Operation: 54-50=4, Resulting Numbers: [4] 4,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[50, 96], Operations: ['42+8=50', '21+75=96'] Exploring Operation: 96-50=46, Resulting Numbers: [46] 46,71 unequal: No Solution Exploring Operation: 50*96=4800, Resulting Numbers: [4800] 4800,71 unequal: No Solution Exploring Operation: 50+96=146, Resulting Numbers: [146] 146,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[42, 75, 29], Operations: ['21+8=29'] Exploring Operation: 42-29=13, Resulting Numbers: [75, 13] Generated Node #0,2,0: 71:[75, 13] Operation: 42-29=13 Exploring Operation: 75-29=46, Resulting Numbers: [42, 46] Generated Node #0,2,1: 71:[42, 46] Operation: 75-29=46 Exploring Operation: 42+29=71, Resulting Numbers: [75, 71] Generated Node #0,2,2: 71:[75, 71] Operation: 42+29=71 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 71:[75, 71], Operations: ['21+8=29', '42+29=71'] Exploring Operation: 75-71=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 75*71=5325, Resulting Numbers: [5325] 5325,71 unequal: No Solution Exploring Operation: 75+71=146, Resulting Numbers: [146] 146,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 71:[42, 46], Operations: ['21+8=29', '75-29=46'] Exploring Operation: 42*46=1932, Resulting Numbers: [1932] 1932,71 unequal: No Solution Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 42+46=88, Resulting Numbers: [88] 88,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 71:[75, 13], Operations: ['21+8=29', '42-29=13'] Exploring Operation: 75-13=62, Resulting Numbers: [62] 62,71 unequal: No Solution Exploring Operation: 75*13=975, Resulting Numbers: [975] 975,71 unequal: No Solution Exploring Operation: 75+13=88, Resulting Numbers: [88] 88,71 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_3
sum_heuristic
[ 30, 20, 62, 70 ]
58
[ "30+20=50", "70-62=8", "50+8=58" ]
Current State: 58:[30, 20, 62, 70], Operations: [] Exploring Operation: 30+20=50, Resulting Numbers: [62, 70, 50] Generated Node #2: [62, 70, 50] from Operation: 30+20=50 Current State: 58:[62, 70, 50], Operations: ['30+20=50'] Exploring Operation: 70-62=8, Resulting Numbers: [50, 8] Generated Node #3: [50, 8] from Operation: 70-62=8 Current State: 58:[50, 8], Operations: ['30+20=50', '70-62=8'] Exploring Operation: 50+8=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[30, 20, 62, 70], Operations: [] Exploring Operation: 30+20=50, Resulting Numbers: [62, 70, 50] Generated Node #0,0: 58:[62, 70, 50] Operation: 30+20=50 Exploring Operation: 30-20=10, Resulting Numbers: [62, 70, 10] Generated Node #0,1: 58:[62, 70, 10] Operation: 30-20=10 Exploring Operation: 70-62=8, Resulting Numbers: [30, 20, 8] Generated Node #0,2: 58:[30, 20, 8] Operation: 70-62=8 Exploring Operation: 70-20=50, Resulting Numbers: [30, 62, 50] Generated Node #0,3: 58:[30, 62, 50] Operation: 70-20=50 Moving to Node #0,3 Current State: 58:[30, 62, 50], Operations: ['70-20=50'] Exploring Operation: 62-50=12, Resulting Numbers: [30, 12] Generated Node #0,3,0: 58:[30, 12] Operation: 62-50=12 Exploring Operation: 62-30=32, Resulting Numbers: [50, 32] Generated Node #0,3,1: 58:[50, 32] Operation: 62-30=32 Exploring Operation: 30+50=80, Resulting Numbers: [62, 80] Generated Node #0,3,2: 58:[62, 80] Operation: 30+50=80 Exploring Operation: 50-30=20, Resulting Numbers: [62, 20] Generated Node #0,3,3: 58:[62, 20] Operation: 50-30=20 Moving to Node #0,2 Current State: 58:[30, 20, 8], Operations: ['70-62=8'] Exploring Operation: 30-20=10, Resulting Numbers: [8, 10] Generated Node #0,2,0: 58:[8, 10] Operation: 30-20=10 Exploring Operation: 20+8=28, Resulting Numbers: [30, 28] Generated Node #0,2,1: 58:[30, 28] Operation: 20+8=28 Exploring Operation: 20-8=12, Resulting Numbers: [30, 12] Generated Node #0,2,2: 58:[30, 12] Operation: 20-8=12 Exploring Operation: 30+20=50, Resulting Numbers: [8, 50] Generated Node #0,2,3: 58:[8, 50] Operation: 30+20=50 Moving to Node #0,1 Current State: 58:[62, 70, 10], Operations: ['30-20=10'] Exploring Operation: 70/10=7, Resulting Numbers: [62, 7] Generated Node #0,1,0: 58:[62, 7] Operation: 70/10=7 Exploring Operation: 62-10=52, Resulting Numbers: [70, 52] Generated Node #0,1,1: 58:[70, 52] Operation: 62-10=52 Exploring Operation: 70-62=8, Resulting Numbers: [10, 8] Generated Node #0,1,2: 58:[10, 8] Operation: 70-62=8 Exploring Operation: 70-10=60, Resulting Numbers: [62, 60] Generated Node #0,1,3: 58:[62, 60] Operation: 70-10=60 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 58:[62, 60], Operations: ['30-20=10', '70-10=60'] Exploring Operation: 62*60=3720, Resulting Numbers: [3720] 3720,58 unequal: No Solution Exploring Operation: 62+60=122, Resulting Numbers: [122] 122,58 unequal: No Solution Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 58:[62, 7], Operations: ['30-20=10', '70/10=7'] Exploring Operation: 62+7=69, Resulting Numbers: [69] 69,58 unequal: No Solution Exploring Operation: 62*7=434, Resulting Numbers: [434] 434,58 unequal: No Solution Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 58:[10, 8], Operations: ['30-20=10', '70-62=8'] Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,58 unequal: No Solution Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,58 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 58:[70, 52], Operations: ['30-20=10', '62-10=52'] Exploring Operation: 70*52=3640, Resulting Numbers: [3640] 3640,58 unequal: No Solution Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,58 unequal: No Solution Exploring Operation: 70+52=122, Resulting Numbers: [122] 122,58 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: 58:[62, 70, 50], Operations: ['30+20=50'] Exploring Operation: 70-50=20, Resulting Numbers: [62, 20] Generated Node #0,0,0: 58:[62, 20] Operation: 70-50=20 Exploring Operation: 62+50=112, Resulting Numbers: [70, 112] Generated Node #0,0,1: 58:[70, 112] Operation: 62+50=112 Exploring Operation: 70-62=8, Resulting Numbers: [50, 8] Generated Node #0,0,2: 58:[50, 8] Operation: 70-62=8 Exploring Operation: 62-50=12, Resulting Numbers: [70, 12] Generated Node #0,0,3: 58:[70, 12] Operation: 62-50=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[62, 20], Operations: ['30+20=50', '70-50=20'] Exploring Operation: 62*20=1240, Resulting Numbers: [1240] 1240,58 unequal: No Solution Exploring Operation: 62+20=82, Resulting Numbers: [82] 82,58 unequal: No Solution Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 58:[50, 8], Operations: ['30+20=50', '70-62=8'] Exploring Operation: 50+8=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[30, 20, 62, 70], Operations: [] Exploring Operation: 30+20=50, Resulting Numbers: [62, 70, 50] Generated Node #0,0: 58:[62, 70, 50] Operation: 30+20=50 Moving to Node #0,0 Current State: 58:[62, 70, 50], Operations: ['30+20=50'] Exploring Operation: 70-62=8, Resulting Numbers: [50, 8] Generated Node #0,0,2: 58:[50, 8] Operation: 70-62=8 Moving to Node #0,0,2 Current State: 58:[50, 8], Operations: ['30+20=50', '70-62=8'] Exploring Operation: 50+8=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_4
sum_heuristic
[ 68, 86, 5, 89 ]
66
[ "86-68=18", "89-5=84", "84-18=66" ]
Current State: 66:[68, 86, 5, 89], Operations: [] Exploring Operation: 86-68=18, Resulting Numbers: [5, 89, 18] Generated Node #2: [5, 89, 18] from Operation: 86-68=18 Current State: 66:[5, 89, 18], Operations: ['86-68=18'] Exploring Operation: 89-5=84, Resulting Numbers: [18, 84] Generated Node #3: [18, 84] from Operation: 89-5=84 Current State: 66:[18, 84], Operations: ['86-68=18', '89-5=84'] Exploring Operation: 84-18=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[68, 86, 5, 89], Operations: [] Exploring Operation: 89-68=21, Resulting Numbers: [86, 5, 21] Generated Node #0,0: 66:[86, 5, 21] Operation: 89-68=21 Exploring Operation: 89-86=3, Resulting Numbers: [68, 5, 3] Generated Node #0,1: 66:[68, 5, 3] Operation: 89-86=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[68, 5, 3], Operations: ['89-86=3'] Exploring Operation: 68-3=65, Resulting Numbers: [5, 65] Generated Node #0,1,0: 66:[5, 65] Operation: 68-3=65 Exploring Operation: 5-3=2, Resulting Numbers: [68, 2] Generated Node #0,1,1: 66:[68, 2] Operation: 5-3=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 66:[5, 65], Operations: ['89-86=3', '68-3=65'] Exploring Operation: 5+65=70, Resulting Numbers: [70] 70,66 unequal: No Solution Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,66 unequal: No Solution No 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: 66:[68, 2], Operations: ['89-86=3', '5-3=2'] Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[68, 86, 5, 89], Operations: [] Exploring Operation: 89-86=3, Resulting Numbers: [68, 5, 3] Generated Node #0,1: 66:[68, 5, 3] Operation: 89-86=3 Moving to Node #0,1 Current State: 66:[68, 5, 3], Operations: ['89-86=3'] Exploring Operation: 5-3=2, Resulting Numbers: [68, 2] Generated Node #0,1,1: 66:[68, 2] Operation: 5-3=2 Moving to Node #0,1,1 Current State: 66:[68, 2], Operations: ['89-86=3', '5-3=2'] Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 61, 59, 34, 62 ]
65
[ "61-59=2", "62/2=31", "34+31=65" ]
Current State: 65:[61, 59, 34, 62], Operations: [] Exploring Operation: 61-59=2, Resulting Numbers: [34, 62, 2] Generated Node #2: [34, 62, 2] from Operation: 61-59=2 Current State: 65:[34, 62, 2], Operations: ['61-59=2'] Exploring Operation: 62/2=31, Resulting Numbers: [34, 31] Generated Node #3: [34, 31] from Operation: 62/2=31 Current State: 65:[34, 31], Operations: ['61-59=2', '62/2=31'] Exploring Operation: 34+31=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[61, 59, 34, 62], Operations: [] Exploring Operation: 61-34=27, Resulting Numbers: [59, 62, 27] Generated Node #0,0: 65:[59, 62, 27] Operation: 61-34=27 Exploring Operation: 59-34=25, Resulting Numbers: [61, 62, 25] Generated Node #0,1: 65:[61, 62, 25] Operation: 59-34=25 Exploring Operation: 62-34=28, Resulting Numbers: [61, 59, 28] Generated Node #0,2: 65:[61, 59, 28] Operation: 62-34=28 Moving to Node #0,1 Current State: 65:[61, 62, 25], Operations: ['59-34=25'] Exploring Operation: 61+25=86, Resulting Numbers: [62, 86] Generated Node #0,1,0: 65:[62, 86] Operation: 61+25=86 Exploring Operation: 61-25=36, Resulting Numbers: [62, 36] Generated Node #0,1,1: 65:[62, 36] Operation: 61-25=36 Exploring Operation: 62-61=1, Resulting Numbers: [25, 1] Generated Node #0,1,2: 65:[25, 1] Operation: 62-61=1 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[25, 1], Operations: ['59-34=25', '62-61=1'] Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,65 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:[62, 86], Operations: ['59-34=25', '61+25=86'] Exploring Operation: 62+86=148, Resulting Numbers: [148] 148,65 unequal: No Solution Exploring Operation: 62*86=5332, Resulting Numbers: [5332] 5332,65 unequal: No Solution Exploring Operation: 86-62=24, Resulting Numbers: [24] 24,65 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:[62, 36], Operations: ['59-34=25', '61-25=36'] Exploring Operation: 62*36=2232, Resulting Numbers: [2232] 2232,65 unequal: No Solution Exploring Operation: 62+36=98, Resulting Numbers: [98] 98,65 unequal: No Solution Exploring Operation: 62-36=26, Resulting Numbers: [26] 26,65 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:[59, 62, 27], Operations: ['61-34=27'] Exploring Operation: 59-27=32, Resulting Numbers: [62, 32] Generated Node #0,0,0: 65:[62, 32] Operation: 59-27=32 Exploring Operation: 59+27=86, Resulting Numbers: [62, 86] Generated Node #0,0,1: 65:[62, 86] Operation: 59+27=86 Exploring Operation: 62-59=3, Resulting Numbers: [27, 3] Generated Node #0,0,2: 65:[27, 3] Operation: 62-59=3 Moving to Node #0,2 Current State: 65:[61, 59, 28], Operations: ['62-34=28'] Exploring Operation: 61-28=33, Resulting Numbers: [59, 33] Generated Node #0,2,0: 65:[59, 33] Operation: 61-28=33 Exploring Operation: 59-28=31, Resulting Numbers: [61, 31] Generated Node #0,2,1: 65:[61, 31] Operation: 59-28=31 Exploring Operation: 61-59=2, Resulting Numbers: [28, 2] Generated Node #0,2,2: 65:[28, 2] Operation: 61-59=2 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 65:[28, 2], Operations: ['62-34=28', '61-59=2'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 28*2=56, Resulting Numbers: [56] 56,65 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 #0,2,1 Current State: 65:[61, 31], Operations: ['62-34=28', '59-28=31'] Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 61+31=92, Resulting Numbers: [92] 92,65 unequal: No Solution Exploring Operation: 61*31=1891, Resulting Numbers: [1891] 1891,65 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 #0,2,0 Current State: 65:[59, 33], Operations: ['62-34=28', '61-28=33'] Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 59*33=1947, Resulting Numbers: [1947] 1947,65 unequal: No Solution Exploring Operation: 59+33=92, Resulting Numbers: [92] 92,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 65:[27, 3], Operations: ['61-34=27', '62-59=3'] Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,65 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[62, 32], Operations: ['61-34=27', '59-27=32'] Exploring Operation: 62+32=94, Resulting Numbers: [94] 94,65 unequal: No Solution Exploring Operation: 62-32=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 62*32=1984, Resulting Numbers: [1984] 1984,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[62, 86], Operations: ['61-34=27', '59+27=86'] Exploring Operation: 86-62=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 62*86=5332, Resulting Numbers: [5332] 5332,65 unequal: No Solution Exploring Operation: 62+86=148, Resulting Numbers: [148] 148,65 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 50, 36, 71, 11 ]
96
[ "50-36=14", "71+11=82", "14+82=96" ]
Current State: 96:[50, 36, 71, 11], Operations: [] Exploring Operation: 50-36=14, Resulting Numbers: [71, 11, 14] Generated Node #2: [71, 11, 14] from Operation: 50-36=14 Current State: 96:[71, 11, 14], Operations: ['50-36=14'] Exploring Operation: 71+11=82, Resulting Numbers: [14, 82] Generated Node #3: [14, 82] from Operation: 71+11=82 Current State: 96:[14, 82], Operations: ['50-36=14', '71+11=82'] Exploring Operation: 14+82=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[50, 36, 71, 11], Operations: [] Exploring Operation: 71-50=21, Resulting Numbers: [36, 11, 21] Generated Node #0,0: 96:[36, 11, 21] Operation: 71-50=21 Exploring Operation: 71-36=35, Resulting Numbers: [50, 11, 35] Generated Node #0,1: 96:[50, 11, 35] Operation: 71-36=35 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[50, 11, 35], Operations: ['71-36=35'] Exploring Operation: 50-35=15, Resulting Numbers: [11, 15] Generated Node #0,1,0: 96:[11, 15] Operation: 50-35=15 Exploring Operation: 35-11=24, Resulting Numbers: [50, 24] Generated Node #0,1,1: 96:[50, 24] Operation: 35-11=24 Moving to Node #0,1,0 Current State: 96:[11, 15], Operations: ['71-36=35', '50-35=15'] Exploring Operation: 11+15=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[50, 24], Operations: ['71-36=35', '35-11=24'] Exploring Operation: 50+24=74, Resulting Numbers: [74] 74,96 unequal: No Solution Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[36, 11, 21], Operations: ['71-50=21'] Exploring Operation: 36-21=15, Resulting Numbers: [11, 15] Generated Node #0,0,0: 96:[11, 15] Operation: 36-21=15 Exploring Operation: 36+11=47, Resulting Numbers: [21, 47] Generated Node #0,0,1: 96:[21, 47] Operation: 36+11=47 Moving to Node #0,0,0 Current State: 96:[11, 15], Operations: ['71-50=21', '36-21=15'] Exploring Operation: 11+15=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[21, 47], Operations: ['71-50=21', '36+11=47'] Exploring Operation: 47-21=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 21+47=68, Resulting Numbers: [68] 68,96 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
[ 5, 81, 8, 49 ]
22
[ "8-5=3", "81/3=27", "49-27=22" ]
Current State: 22:[5, 81, 8, 49], Operations: [] Exploring Operation: 8-5=3, Resulting Numbers: [81, 49, 3] Generated Node #2: [81, 49, 3] from Operation: 8-5=3 Current State: 22:[81, 49, 3], Operations: ['8-5=3'] Exploring Operation: 81/3=27, Resulting Numbers: [49, 27] Generated Node #3: [49, 27] from Operation: 81/3=27 Current State: 22:[49, 27], Operations: ['8-5=3', '81/3=27'] Exploring Operation: 49-27=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[5, 81, 8, 49], Operations: [] Exploring Operation: 49-5=44, Resulting Numbers: [81, 8, 44] Generated Node #0,0: 22:[81, 8, 44] Operation: 49-5=44 Exploring Operation: 81-5=76, Resulting Numbers: [8, 49, 76] Generated Node #0,1: 22:[8, 49, 76] Operation: 81-5=76 Exploring Operation: 81-49=32, Resulting Numbers: [5, 8, 32] Generated Node #0,2: 22:[5, 8, 32] Operation: 81-49=32 Exploring Operation: 49-8=41, Resulting Numbers: [5, 81, 41] Generated Node #0,3: 22:[5, 81, 41] Operation: 49-8=41 Exploring Operation: 81-8=73, Resulting Numbers: [5, 49, 73] Generated Node #0,4: 22:[5, 49, 73] Operation: 81-8=73 Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[5, 8, 32], Operations: ['81-49=32'] Exploring Operation: 5+8=13, Resulting Numbers: [32, 13] Generated Node #0,2,0: 22:[32, 13] Operation: 5+8=13 Exploring Operation: 32-8=24, Resulting Numbers: [5, 24] Generated Node #0,2,1: 22:[5, 24] Operation: 32-8=24 Exploring Operation: 32-5=27, Resulting Numbers: [8, 27] Generated Node #0,2,2: 22:[8, 27] Operation: 32-5=27 Exploring Operation: 32/8=4, Resulting Numbers: [5, 4] Generated Node #0,2,3: 22:[5, 4] Operation: 32/8=4 Exploring Operation: 8-5=3, Resulting Numbers: [32, 3] Generated Node #0,2,4: 22:[32, 3] Operation: 8-5=3 Moving to Node #0,2,1 Current State: 22:[5, 24], Operations: ['81-49=32', '32-8=24'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,22 unequal: No Solution Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,22 unequal: No Solution Moving to Node #0,2,3 Current State: 22:[5, 4], Operations: ['81-49=32', '32/8=4'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,22 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[8, 27], Operations: ['81-49=32', '32-5=27'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,22 unequal: No Solution Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,22 unequal: No Solution Moving to Node #0,2,4 Current State: 22:[32, 3], Operations: ['81-49=32', '8-5=3'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 32*3=96, Resulting Numbers: [96] 96,22 unequal: No Solution Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,22 unequal: No Solution Moving to Node #0,2,0 Current State: 22:[32, 13], Operations: ['81-49=32', '5+8=13'] Exploring Operation: 32-13=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 32*13=416, Resulting Numbers: [416] 416,22 unequal: No Solution Exploring Operation: 32+13=45, Resulting Numbers: [45] 45,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 22:[5, 81, 41], Operations: ['49-8=41'] Exploring Operation: 5+81=86, Resulting Numbers: [41, 86] Generated Node #0,3,0: 22:[41, 86] Operation: 5+81=86 Exploring Operation: 5+41=46, Resulting Numbers: [81, 46] Generated Node #0,3,1: 22:[81, 46] Operation: 5+41=46 Exploring Operation: 81-5=76, Resulting Numbers: [41, 76] Generated Node #0,3,2: 22:[41, 76] Operation: 81-5=76 Exploring Operation: 41-5=36, Resulting Numbers: [81, 36] Generated Node #0,3,3: 22:[81, 36] Operation: 41-5=36 Exploring Operation: 81-41=40, Resulting Numbers: [5, 40] Generated Node #0,3,4: 22:[5, 40] Operation: 81-41=40 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 22:[5, 40], Operations: ['49-8=41', '81-41=40'] Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,22 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,22 unequal: No Solution Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,22 unequal: No Solution Exploring Operation: 5*40=200, Resulting Numbers: [200] 200,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 22:[41, 76], Operations: ['49-8=41', '81-5=76'] Exploring Operation: 76-41=35, Resulting Numbers: [35] 35,22 unequal: No Solution Exploring Operation: 41+76=117, Resulting Numbers: [117] 117,22 unequal: No Solution Exploring Operation: 41*76=3116, Resulting Numbers: [3116] 3116,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 22:[81, 36], Operations: ['49-8=41', '41-5=36'] Exploring Operation: 81+36=117, Resulting Numbers: [117] 117,22 unequal: No Solution Exploring Operation: 81*36=2916, Resulting Numbers: [2916] 2916,22 unequal: No Solution Exploring Operation: 81-36=45, Resulting Numbers: [45] 45,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 22:[41, 86], Operations: ['49-8=41', '5+81=86'] Exploring Operation: 41+86=127, Resulting Numbers: [127] 127,22 unequal: No Solution Exploring Operation: 41*86=3526, Resulting Numbers: [3526] 3526,22 unequal: No Solution Exploring Operation: 86-41=45, Resulting Numbers: [45] 45,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 22:[81, 46], Operations: ['49-8=41', '5+41=46'] Exploring Operation: 81+46=127, Resulting Numbers: [127] 127,22 unequal: No Solution Exploring Operation: 81*46=3726, Resulting Numbers: [3726] 3726,22 unequal: No Solution Exploring Operation: 81-46=35, Resulting Numbers: [35] 35,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 22:[5, 49, 73], Operations: ['81-8=73'] Exploring Operation: 5+49=54, Resulting Numbers: [73, 54] Generated Node #0,4,0: 22:[73, 54] Operation: 5+49=54 Exploring Operation: 73-5=68, Resulting Numbers: [49, 68] Generated Node #0,4,1: 22:[49, 68] Operation: 73-5=68 Exploring Operation: 73-49=24, Resulting Numbers: [5, 24] Generated Node #0,4,2: 22:[5, 24] Operation: 73-49=24 Exploring Operation: 49-5=44, Resulting Numbers: [73, 44] Generated Node #0,4,3: 22:[73, 44] Operation: 49-5=44 Exploring Operation: 5+73=78, Resulting Numbers: [49, 78] Generated Node #0,4,4: 22:[49, 78] Operation: 5+73=78 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 22:[5, 24], Operations: ['81-8=73', '73-49=24'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,22 unequal: No Solution Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 22:[49, 68], Operations: ['81-8=73', '73-5=68'] Exploring Operation: 49+68=117, Resulting Numbers: [117] 117,22 unequal: No Solution Exploring Operation: 68-49=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 49*68=3332, Resulting Numbers: [3332] 3332,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 22:[73, 44], Operations: ['81-8=73', '49-5=44'] Exploring Operation: 73-44=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 73+44=117, Resulting Numbers: [117] 117,22 unequal: No Solution Exploring Operation: 73*44=3212, Resulting Numbers: [3212] 3212,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 22:[73, 54], Operations: ['81-8=73', '5+49=54'] Exploring Operation: 73*54=3942, Resulting Numbers: [3942] 3942,22 unequal: No Solution Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 73+54=127, Resulting Numbers: [127] 127,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 22:[49, 78], Operations: ['81-8=73', '5+73=78'] Exploring Operation: 49+78=127, Resulting Numbers: [127] 127,22 unequal: No Solution Exploring Operation: 49*78=3822, Resulting Numbers: [3822] 3822,22 unequal: No Solution Exploring Operation: 78-49=29, Resulting Numbers: [29] 29,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[81, 8, 44], Operations: ['49-5=44'] Exploring Operation: 81+8=89, Resulting Numbers: [44, 89] Generated Node #0,0,0: 22:[44, 89] Operation: 81+8=89 Exploring Operation: 81-8=73, Resulting Numbers: [44, 73] Generated Node #0,0,1: 22:[44, 73] Operation: 81-8=73 Exploring Operation: 8+44=52, Resulting Numbers: [81, 52] Generated Node #0,0,2: 22:[81, 52] Operation: 8+44=52 Exploring Operation: 44-8=36, Resulting Numbers: [81, 36] Generated Node #0,0,3: 22:[81, 36] Operation: 44-8=36 Exploring Operation: 81-44=37, Resulting Numbers: [8, 37] Generated Node #0,0,4: 22:[8, 37] Operation: 81-44=37 Moving to Node #0,0,4 Current State: 22:[8, 37], Operations: ['49-5=44', '81-44=37'] Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 8*37=296, Resulting Numbers: [296] 296,22 unequal: No Solution Exploring Operation: 8+37=45, Resulting Numbers: [45] 45,22 unequal: No Solution Moving to Node #0,0,3 Current State: 22:[81, 36], Operations: ['49-5=44', '44-8=36'] Exploring Operation: 81*36=2916, Resulting Numbers: [2916] 2916,22 unequal: No Solution Exploring Operation: 81+36=117, Resulting Numbers: [117] 117,22 unequal: No Solution Exploring Operation: 81-36=45, Resulting Numbers: [45] 45,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[44, 73], Operations: ['49-5=44', '81-8=73'] Exploring Operation: 44+73=117, Resulting Numbers: [117] 117,22 unequal: No Solution Exploring Operation: 73-44=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 44*73=3212, Resulting Numbers: [3212] 3212,22 unequal: No Solution Moving to Node #0,0,0 Current State: 22:[44, 89], Operations: ['49-5=44', '81+8=89'] Exploring Operation: 89-44=45, Resulting Numbers: [45] 45,22 unequal: No Solution Exploring Operation: 44*89=3916, Resulting Numbers: [3916] 3916,22 unequal: No Solution Exploring Operation: 44+89=133, Resulting Numbers: [133] 133,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[81, 52], Operations: ['49-5=44', '8+44=52'] Exploring Operation: 81-52=29, Resulting Numbers: [29] 29,22 unequal: No Solution Exploring Operation: 81+52=133, Resulting Numbers: [133] 133,22 unequal: No Solution Exploring Operation: 81*52=4212, Resulting Numbers: [4212] 4212,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[8, 49, 76], Operations: ['81-5=76'] Exploring Operation: 76-49=27, Resulting Numbers: [8, 27] Generated Node #0,1,0: 22:[8, 27] Operation: 76-49=27 Exploring Operation: 76-8=68, Resulting Numbers: [49, 68] Generated Node #0,1,1: 22:[49, 68] Operation: 76-8=68 Exploring Operation: 49-8=41, Resulting Numbers: [76, 41] Generated Node #0,1,2: 22:[76, 41] Operation: 49-8=41 Exploring Operation: 8+76=84, Resulting Numbers: [49, 84] Generated Node #0,1,3: 22:[49, 84] Operation: 8+76=84 Exploring Operation: 8+49=57, Resulting Numbers: [76, 57] Generated Node #0,1,4: 22:[76, 57] Operation: 8+49=57 Moving to Node #0,1,0 Current State: 22:[8, 27], Operations: ['81-5=76', '76-49=27'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,22 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[76, 41], Operations: ['81-5=76', '49-8=41'] Exploring Operation: 76+41=117, Resulting Numbers: [117] 117,22 unequal: No Solution Exploring Operation: 76*41=3116, Resulting Numbers: [3116] 3116,22 unequal: No Solution Exploring Operation: 76-41=35, Resulting Numbers: [35] 35,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[49, 68], Operations: ['81-5=76', '76-8=68'] Exploring Operation: 49*68=3332, Resulting Numbers: [3332] 3332,22 unequal: No Solution Exploring Operation: 68-49=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 49+68=117, Resulting Numbers: [117] 117,22 unequal: No Solution Moving to Node #0,1,3 Current State: 22:[49, 84], Operations: ['81-5=76', '8+76=84'] Exploring Operation: 49*84=4116, Resulting Numbers: [4116] 4116,22 unequal: No Solution Exploring Operation: 84-49=35, Resulting Numbers: [35] 35,22 unequal: No Solution Exploring Operation: 49+84=133, Resulting Numbers: [133] 133,22 unequal: No Solution Moving to Node #0,1,4 Current State: 22:[76, 57], Operations: ['81-5=76', '8+49=57'] Exploring Operation: 76*57=4332, Resulting Numbers: [4332] 4332,22 unequal: No Solution Exploring Operation: 76-57=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 76+57=133, Resulting Numbers: [133] 133,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 39, 94, 97, 61 ]
91
[ "94-39=55", "97-61=36", "55+36=91" ]
Current State: 91:[39, 94, 97, 61], Operations: [] Exploring Operation: 94-39=55, Resulting Numbers: [97, 61, 55] Generated Node #2: [97, 61, 55] from Operation: 94-39=55 Current State: 91:[97, 61, 55], Operations: ['94-39=55'] Exploring Operation: 97-61=36, Resulting Numbers: [55, 36] Generated Node #3: [55, 36] from Operation: 97-61=36 Current State: 91:[55, 36], Operations: ['94-39=55', '97-61=36'] Exploring Operation: 55+36=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[39, 94, 97, 61], Operations: [] Exploring Operation: 39+61=100, Resulting Numbers: [94, 97, 100] Generated Node #0,0: 91:[94, 97, 100] Operation: 39+61=100 Exploring Operation: 61-39=22, Resulting Numbers: [94, 97, 22] Generated Node #0,1: 91:[94, 97, 22] Operation: 61-39=22 Moving to Node #0,0 Current State: 91:[94, 97, 100], Operations: ['39+61=100'] Exploring Operation: 100-97=3, Resulting Numbers: [94, 3] Generated Node #0,0,0: 91:[94, 3] Operation: 100-97=3 Exploring Operation: 100-94=6, Resulting Numbers: [97, 6] Generated Node #0,0,1: 91:[97, 6] Operation: 100-94=6 Moving to Node #0,1 Current State: 91:[94, 97, 22], Operations: ['61-39=22'] Exploring Operation: 97-22=75, Resulting Numbers: [94, 75] Generated Node #0,1,0: 91:[94, 75] Operation: 97-22=75 Exploring Operation: 97-94=3, Resulting Numbers: [22, 3] Generated Node #0,1,1: 91:[22, 3] Operation: 97-94=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 91:[22, 3], Operations: ['61-39=22', '97-94=3'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,91 unequal: No Solution Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 91:[94, 75], Operations: ['61-39=22', '97-22=75'] Exploring Operation: 94-75=19, Resulting Numbers: [19] 19,91 unequal: No Solution Exploring Operation: 94+75=169, Resulting Numbers: [169] 169,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 91:[94, 3], Operations: ['39+61=100', '100-97=3'] Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[39, 94, 97, 61], Operations: [] Exploring Operation: 39+61=100, Resulting Numbers: [94, 97, 100] Generated Node #0,0: 91:[94, 97, 100] Operation: 39+61=100 Moving to Node #0,0 Current State: 91:[94, 97, 100], Operations: ['39+61=100'] Exploring Operation: 100-97=3, Resulting Numbers: [94, 3] Generated Node #0,0,0: 91:[94, 3] Operation: 100-97=3 Moving to Node #0,0,0 Current State: 91:[94, 3], Operations: ['39+61=100', '100-97=3'] Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 37, 63, 63, 51 ]
38
[ "63-37=26", "63-51=12", "26+12=38" ]
Current State: 38:[37, 63, 63, 51], Operations: [] Exploring Operation: 63-37=26, Resulting Numbers: [51, 26] Generated Node #2: [51, 26] from Operation: 63-37=26 Current State: 38:[51, 26], Operations: ['63-37=26'] Exploring Operation: 63-51=12, Resulting Numbers: [26, 12] Generated Node #3: [26, 12] from Operation: 63-51=12 Current State: 38:[26, 12], Operations: ['63-37=26', '63-51=12'] Exploring Operation: 26+12=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[37, 63, 63, 51], Operations: [] Exploring Operation: 63-63=0, Resulting Numbers: [37, 51, 0] Generated Node #0,0: 38:[37, 51, 0] Operation: 63-63=0 Exploring Operation: 63/63=1, Resulting Numbers: [37, 51, 1] Generated Node #0,1: 38:[37, 51, 1] Operation: 63/63=1 Moving to Node #0,1 Current State: 38:[37, 51, 1], Operations: ['63/63=1'] Exploring Operation: 51-37=14, Resulting Numbers: [1, 14] Generated Node #0,1,0: 38:[1, 14] Operation: 51-37=14 Exploring Operation: 37+1=38, Resulting Numbers: [51, 38] Generated Node #0,1,1: 38:[51, 38] Operation: 37+1=38 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 38:[1, 14], Operations: ['63/63=1', '51-37=14'] Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,38 unequal: No Solution Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 38:[51, 38], Operations: ['63/63=1', '37+1=38'] Exploring Operation: 51-38=13, Resulting Numbers: [13] 13,38 unequal: No Solution Exploring Operation: 51+38=89, Resulting Numbers: [89] 89,38 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: 38:[37, 51, 0], Operations: ['63-63=0'] Exploring Operation: 51*0=0, Resulting Numbers: [37, 0] Generated Node #0,0,0: 38:[37, 0] Operation: 51*0=0 Exploring Operation: 51-37=14, Resulting Numbers: [0, 14] Generated Node #0,0,1: 38:[0, 14] Operation: 51-37=14 Moving to Node #0,0,0 Current State: 38:[37, 0], Operations: ['63-63=0', '51*0=0'] Exploring Operation: 37-0=37, Resulting Numbers: [37] 37,38 unequal: No Solution Exploring Operation: 37+0=37, Resulting Numbers: [37] 37,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[0, 14], Operations: ['63-63=0', '51-37=14'] Exploring Operation: 0*14=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 0+14=14, Resulting Numbers: [14] 14,38 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 70, 15, 84, 42 ]
87
[ "70+15=85", "84/42=2", "85+2=87" ]
Current State: 87:[70, 15, 84, 42], Operations: [] Exploring Operation: 70+15=85, Resulting Numbers: [84, 42, 85] Generated Node #2: [84, 42, 85] from Operation: 70+15=85 Current State: 87:[84, 42, 85], Operations: ['70+15=85'] Exploring Operation: 84/42=2, Resulting Numbers: [85, 2] Generated Node #3: [85, 2] from Operation: 84/42=2 Current State: 87:[85, 2], Operations: ['70+15=85', '84/42=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[70, 15, 84, 42], Operations: [] Exploring Operation: 70+15=85, Resulting Numbers: [84, 42, 85] Generated Node #0,0: 87:[84, 42, 85] Operation: 70+15=85 Exploring Operation: 70-42=28, Resulting Numbers: [15, 84, 28] Generated Node #0,1: 87:[15, 84, 28] Operation: 70-42=28 Moving to Node #0,1 Current State: 87:[15, 84, 28], Operations: ['70-42=28'] Exploring Operation: 84/28=3, Resulting Numbers: [15, 3] Generated Node #0,1,0: 87:[15, 3] Operation: 84/28=3 Exploring Operation: 15+84=99, Resulting Numbers: [28, 99] Generated Node #0,1,1: 87:[28, 99] Operation: 15+84=99 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 87:[15, 3], Operations: ['70-42=28', '84/28=3'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,87 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 87:[28, 99], Operations: ['70-42=28', '15+84=99'] Exploring Operation: 28+99=127, Resulting Numbers: [127] 127,87 unequal: No Solution Exploring Operation: 99-28=71, Resulting Numbers: [71] 71,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 87:[84, 42, 85], Operations: ['70+15=85'] Exploring Operation: 84/42=2, Resulting Numbers: [85, 2] Generated Node #0,0,0: 87:[85, 2] Operation: 84/42=2 Exploring Operation: 84-42=42, Resulting Numbers: [85, 42] Generated Node #0,0,1: 87:[85, 42] Operation: 84-42=42 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[85, 2], Operations: ['70+15=85', '84/42=2'] Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,87 unequal: No Solution Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[70, 15, 84, 42], Operations: [] Exploring Operation: 70+15=85, Resulting Numbers: [84, 42, 85] Generated Node #0,0: 87:[84, 42, 85] Operation: 70+15=85 Moving to Node #0,0 Current State: 87:[84, 42, 85], Operations: ['70+15=85'] Exploring Operation: 84/42=2, Resulting Numbers: [85, 2] Generated Node #0,0,0: 87:[85, 2] Operation: 84/42=2 Moving to Node #0,0,0 Current State: 87:[85, 2], Operations: ['70+15=85', '84/42=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 90, 87, 92, 31 ]
54
[ "90+87=177", "92+31=123", "177-123=54" ]
Current State: 54:[90, 87, 92, 31], Operations: [] Exploring Operation: 90+87=177, Resulting Numbers: [92, 31, 177] Generated Node #2: [92, 31, 177] from Operation: 90+87=177 Current State: 54:[92, 31, 177], Operations: ['90+87=177'] Exploring Operation: 92+31=123, Resulting Numbers: [177, 123] Generated Node #3: [177, 123] from Operation: 92+31=123 Current State: 54:[177, 123], Operations: ['90+87=177', '92+31=123'] Exploring Operation: 177-123=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[90, 87, 92, 31], Operations: [] Exploring Operation: 90-31=59, Resulting Numbers: [87, 92, 59] Generated Node #0,0: 54:[87, 92, 59] Operation: 90-31=59 Exploring Operation: 92-90=2, Resulting Numbers: [87, 31, 2] Generated Node #0,1: 54:[87, 31, 2] Operation: 92-90=2 Exploring Operation: 90-87=3, Resulting Numbers: [92, 31, 3] Generated Node #0,2: 54:[92, 31, 3] Operation: 90-87=3 Exploring Operation: 92-87=5, Resulting Numbers: [90, 31, 5] Generated Node #0,3: 54:[90, 31, 5] Operation: 92-87=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[87, 31, 2], Operations: ['92-90=2'] Exploring Operation: 87-31=56, Resulting Numbers: [2, 56] Generated Node #0,1,0: 54:[2, 56] Operation: 87-31=56 Exploring Operation: 31-2=29, Resulting Numbers: [87, 29] Generated Node #0,1,1: 54:[87, 29] Operation: 31-2=29 Exploring Operation: 87-2=85, Resulting Numbers: [31, 85] Generated Node #0,1,2: 54:[31, 85] Operation: 87-2=85 Exploring Operation: 87+2=89, Resulting Numbers: [31, 89] Generated Node #0,1,3: 54:[31, 89] Operation: 87+2=89 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 54:[2, 56], Operations: ['92-90=2', '87-31=56'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 2*56=112, Resulting Numbers: [112] 112,54 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[90, 87, 92, 31], Operations: [] Exploring Operation: 92-90=2, Resulting Numbers: [87, 31, 2] Generated Node #0,1: 54:[87, 31, 2] Operation: 92-90=2 Moving to Node #0,1 Current State: 54:[87, 31, 2], Operations: ['92-90=2'] Exploring Operation: 87-31=56, Resulting Numbers: [2, 56] Generated Node #0,1,0: 54:[2, 56] Operation: 87-31=56 Moving to Node #0,1,0 Current State: 54:[2, 56], Operations: ['92-90=2', '87-31=56'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 17, 38, 65, 32 ]
76
[ "38-17=21", "65+32=97", "97-21=76" ]
Current State: 76:[17, 38, 65, 32], Operations: [] Exploring Operation: 38-17=21, Resulting Numbers: [65, 32, 21] Generated Node #2: [65, 32, 21] from Operation: 38-17=21 Current State: 76:[65, 32, 21], Operations: ['38-17=21'] Exploring Operation: 65+32=97, Resulting Numbers: [21, 97] Generated Node #3: [21, 97] from Operation: 65+32=97 Current State: 76:[21, 97], Operations: ['38-17=21', '65+32=97'] Exploring Operation: 97-21=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[17, 38, 65, 32], Operations: [] Exploring Operation: 32-17=15, Resulting Numbers: [38, 65, 15] Generated Node #0,0: 76:[38, 65, 15] Operation: 32-17=15 Exploring Operation: 65-32=33, Resulting Numbers: [17, 38, 33] Generated Node #0,1: 76:[17, 38, 33] Operation: 65-32=33 Exploring Operation: 17+65=82, Resulting Numbers: [38, 32, 82] Generated Node #0,2: 76:[38, 32, 82] Operation: 17+65=82 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[17, 38, 33], Operations: ['65-32=33'] Exploring Operation: 38-17=21, Resulting Numbers: [33, 21] Generated Node #0,1,0: 76:[33, 21] Operation: 38-17=21 Exploring Operation: 38-33=5, Resulting Numbers: [17, 5] Generated Node #0,1,1: 76:[17, 5] Operation: 38-33=5 Exploring Operation: 33-17=16, Resulting Numbers: [38, 16] Generated Node #0,1,2: 76:[38, 16] Operation: 33-17=16 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 76:[17, 5], Operations: ['65-32=33', '38-33=5'] Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,76 unequal: No Solution Exploring Operation: 17*5=85, Resulting Numbers: [85] 85,76 unequal: No Solution Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 76:[38, 16], Operations: ['65-32=33', '33-17=16'] Exploring Operation: 38*16=608, Resulting Numbers: [608] 608,76 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,76 unequal: No Solution Exploring Operation: 38+16=54, Resulting Numbers: [54] 54,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 76:[33, 21], Operations: ['65-32=33', '38-17=21'] Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 33*21=693, Resulting Numbers: [693] 693,76 unequal: No Solution Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[38, 32, 82], Operations: ['17+65=82'] Exploring Operation: 38+32=70, Resulting Numbers: [82, 70] Generated Node #0,2,0: 76:[82, 70] Operation: 38+32=70 Exploring Operation: 38-32=6, Resulting Numbers: [82, 6] Generated Node #0,2,1: 76:[82, 6] Operation: 38-32=6 Exploring Operation: 82-38=44, Resulting Numbers: [32, 44] Generated Node #0,2,2: 76:[32, 44] Operation: 82-38=44 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 76:[82, 6], Operations: ['17+65=82', '38-32=6'] Exploring Operation: 82-6=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[17, 38, 65, 32], Operations: [] Exploring Operation: 17+65=82, Resulting Numbers: [38, 32, 82] Generated Node #0,2: 76:[38, 32, 82] Operation: 17+65=82 Moving to Node #0,2 Current State: 76:[38, 32, 82], Operations: ['17+65=82'] Exploring Operation: 38-32=6, Resulting Numbers: [82, 6] Generated Node #0,2,1: 76:[82, 6] Operation: 38-32=6 Moving to Node #0,2,1 Current State: 76:[82, 6], Operations: ['17+65=82', '38-32=6'] Exploring Operation: 82-6=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 83, 18, 13, 15 ]
73
[ "83+18=101", "13+15=28", "101-28=73" ]
Current State: 73:[83, 18, 13, 15], Operations: [] Exploring Operation: 83+18=101, Resulting Numbers: [13, 15, 101] Generated Node #2: [13, 15, 101] from Operation: 83+18=101 Current State: 73:[13, 15, 101], Operations: ['83+18=101'] Exploring Operation: 13+15=28, Resulting Numbers: [101, 28] Generated Node #3: [101, 28] from Operation: 13+15=28 Current State: 73:[101, 28], Operations: ['83+18=101', '13+15=28'] Exploring Operation: 101-28=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[83, 18, 13, 15], Operations: [] Exploring Operation: 18+15=33, Resulting Numbers: [83, 13, 33] Generated Node #0,0: 73:[83, 13, 33] Operation: 18+15=33 Exploring Operation: 18+13=31, Resulting Numbers: [83, 15, 31] Generated Node #0,1: 73:[83, 15, 31] Operation: 18+13=31 Moving to Node #0,0 Current State: 73:[83, 13, 33], Operations: ['18+15=33'] Exploring Operation: 13+33=46, Resulting Numbers: [83, 46] Generated Node #0,0,0: 73:[83, 46] Operation: 13+33=46 Exploring Operation: 83-13=70, Resulting Numbers: [33, 70] Generated Node #0,0,1: 73:[33, 70] Operation: 83-13=70 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[83, 46], Operations: ['18+15=33', '13+33=46'] Exploring Operation: 83-46=37, Resulting Numbers: [37] 37,73 unequal: No Solution Exploring Operation: 83+46=129, Resulting Numbers: [129] 129,73 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 #0,0,1 Current State: 73:[33, 70], Operations: ['18+15=33', '83-13=70'] Exploring Operation: 70-33=37, Resulting Numbers: [37] 37,73 unequal: No Solution Exploring Operation: 33+70=103, Resulting Numbers: [103] 103,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 73:[83, 15, 31], Operations: ['18+13=31'] Exploring Operation: 15+31=46, Resulting Numbers: [83, 46] Generated Node #0,1,0: 73:[83, 46] Operation: 15+31=46 Exploring Operation: 83-15=68, Resulting Numbers: [31, 68] Generated Node #0,1,1: 73:[31, 68] Operation: 83-15=68 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[83, 46], Operations: ['18+13=31', '15+31=46'] Exploring Operation: 83-46=37, Resulting Numbers: [37] 37,73 unequal: No Solution Exploring Operation: 83+46=129, Resulting Numbers: [129] 129,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[31, 68], Operations: ['18+13=31', '83-15=68'] Exploring Operation: 68-31=37, Resulting Numbers: [37] 37,73 unequal: No Solution Exploring Operation: 31+68=99, Resulting Numbers: [99] 99,73 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
[ 44, 39, 84, 76 ]
76
[ "44+39=83", "84-83=1", "76*1=76" ]
Current State: 76:[44, 39, 84, 76], Operations: [] Exploring Operation: 44+39=83, Resulting Numbers: [84, 76, 83] Generated Node #2: [84, 76, 83] from Operation: 44+39=83 Current State: 76:[84, 76, 83], Operations: ['44+39=83'] Exploring Operation: 84-83=1, Resulting Numbers: [76, 1] Generated Node #3: [76, 1] from Operation: 84-83=1 Current State: 76:[76, 1], Operations: ['44+39=83', '84-83=1'] Exploring Operation: 76*1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[44, 39, 84, 76], Operations: [] Exploring Operation: 84-39=45, Resulting Numbers: [44, 76, 45] Generated Node #0,0: 76:[44, 76, 45] Operation: 84-39=45 Exploring Operation: 84-76=8, Resulting Numbers: [44, 39, 8] Generated Node #0,1: 76:[44, 39, 8] Operation: 84-76=8 Exploring Operation: 44-39=5, Resulting Numbers: [84, 76, 5] Generated Node #0,2: 76:[84, 76, 5] Operation: 44-39=5 Exploring Operation: 44+39=83, Resulting Numbers: [84, 76, 83] Generated Node #0,3: 76:[84, 76, 83] Operation: 44+39=83 Exploring Operation: 84-44=40, Resulting Numbers: [39, 76, 40] Generated Node #0,4: 76:[39, 76, 40] Operation: 84-44=40 Start Sub Search at level 1: Moving to Node #0,4 Current State: 76:[39, 76, 40], Operations: ['84-44=40'] Exploring Operation: 76-39=37, Resulting Numbers: [40, 37] Generated Node #0,4,0: 76:[40, 37] Operation: 76-39=37 Exploring Operation: 39+40=79, Resulting Numbers: [76, 79] Generated Node #0,4,1: 76:[76, 79] Operation: 39+40=79 Exploring Operation: 76-40=36, Resulting Numbers: [39, 36] Generated Node #0,4,2: 76:[39, 36] Operation: 76-40=36 Exploring Operation: 39+76=115, Resulting Numbers: [40, 115] Generated Node #0,4,3: 76:[40, 115] Operation: 39+76=115 Exploring Operation: 40-39=1, Resulting Numbers: [76, 1] Generated Node #0,4,4: 76:[76, 1] Operation: 40-39=1 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 76:[76, 1], Operations: ['84-44=40', '40-39=1'] Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[44, 39, 84, 76], Operations: [] Exploring Operation: 84-44=40, Resulting Numbers: [39, 76, 40] Generated Node #0,4: 76:[39, 76, 40] Operation: 84-44=40 Moving to Node #0,4 Current State: 76:[39, 76, 40], Operations: ['84-44=40'] Exploring Operation: 40-39=1, Resulting Numbers: [76, 1] Generated Node #0,4,4: 76:[76, 1] Operation: 40-39=1 Moving to Node #0,4,4 Current State: 76:[76, 1], Operations: ['84-44=40', '40-39=1'] Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 49, 42, 35, 58 ]
71
[ "42*58=2436", "49+2436=2485", "2485/35=71" ]
Current State: 71:[49, 42, 35, 58], Operations: [] Exploring Operation: 42*58=2436, Resulting Numbers: [49, 35, 2436] Generated Node #2: [49, 35, 2436] from Operation: 42*58=2436 Current State: 71:[49, 35, 2436], Operations: ['42*58=2436'] Exploring Operation: 49+2436=2485, Resulting Numbers: [35, 2485] Generated Node #3: [35, 2485] from Operation: 49+2436=2485 Current State: 71:[35, 2485], Operations: ['42*58=2436', '49+2436=2485'] Exploring Operation: 2485/35=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[49, 42, 35, 58], Operations: [] Exploring Operation: 49+35=84, Resulting Numbers: [42, 58, 84] Generated Node #0,0: 71:[42, 58, 84] Operation: 49+35=84 Exploring Operation: 42+35=77, Resulting Numbers: [49, 58, 77] Generated Node #0,1: 71:[49, 58, 77] Operation: 42+35=77 Moving to Node #0,1 Current State: 71:[49, 58, 77], Operations: ['42+35=77'] Exploring Operation: 49+58=107, Resulting Numbers: [77, 107] Generated Node #0,1,0: 71:[77, 107] Operation: 49+58=107 Exploring Operation: 77-49=28, Resulting Numbers: [58, 28] Generated Node #0,1,1: 71:[58, 28] Operation: 77-49=28 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 71:[77, 107], Operations: ['42+35=77', '49+58=107'] Exploring Operation: 107-77=30, Resulting Numbers: [30] 30,71 unequal: No Solution Exploring Operation: 77+107=184, Resulting Numbers: [184] 184,71 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:[58, 28], Operations: ['42+35=77', '77-49=28'] Exploring Operation: 58-28=30, Resulting Numbers: [30] 30,71 unequal: No Solution Exploring Operation: 58+28=86, Resulting Numbers: [86] 86,71 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: 71:[42, 58, 84], Operations: ['49+35=84'] Exploring Operation: 42+58=100, Resulting Numbers: [84, 100] Generated Node #0,0,0: 71:[84, 100] Operation: 42+58=100 Exploring Operation: 84-42=42, Resulting Numbers: [58, 42] Generated Node #0,0,1: 71:[58, 42] Operation: 84-42=42 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[84, 100], Operations: ['49+35=84', '42+58=100'] Exploring Operation: 84+100=184, Resulting Numbers: [184] 184,71 unequal: No Solution Exploring Operation: 100-84=16, Resulting Numbers: [16] 16,71 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:[58, 42], Operations: ['49+35=84', '84-42=42'] Exploring Operation: 58+42=100, Resulting Numbers: [100] 100,71 unequal: No Solution Exploring Operation: 58-42=16, Resulting Numbers: [16] 16,71 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
[ 12, 17, 33, 19 ]
36
[ "33-17=16", "19-16=3", "12*3=36" ]
Current State: 36:[12, 17, 33, 19], Operations: [] Exploring Operation: 33-17=16, Resulting Numbers: [12, 19, 16] Generated Node #2: [12, 19, 16] from Operation: 33-17=16 Current State: 36:[12, 19, 16], Operations: ['33-17=16'] Exploring Operation: 19-16=3, Resulting Numbers: [12, 3] Generated Node #3: [12, 3] from Operation: 19-16=3 Current State: 36:[12, 3], Operations: ['33-17=16', '19-16=3'] Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[12, 17, 33, 19], Operations: [] Exploring Operation: 17+19=36, Resulting Numbers: [12, 33, 36] Generated Node #0,0: 36:[12, 33, 36] Operation: 17+19=36 Exploring Operation: 33-17=16, Resulting Numbers: [12, 19, 16] Generated Node #0,1: 36:[12, 19, 16] Operation: 33-17=16 Exploring Operation: 19-17=2, Resulting Numbers: [12, 33, 2] Generated Node #0,2: 36:[12, 33, 2] Operation: 19-17=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[12, 33, 36], Operations: ['17+19=36'] Exploring Operation: 36-33=3, Resulting Numbers: [12, 3] Generated Node #0,0,0: 36:[12, 3] Operation: 36-33=3 Exploring Operation: 36/12=3, Resulting Numbers: [33, 3] Generated Node #0,0,1: 36:[33, 3] Operation: 36/12=3 Exploring Operation: 33-12=21, Resulting Numbers: [36, 21] Generated Node #0,0,2: 36:[36, 21] Operation: 33-12=21 Moving to Node #0,0,0 Current State: 36:[12, 3], Operations: ['17+19=36', '36-33=3'] Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,36 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[12, 17, 33, 19], Operations: [] Exploring Operation: 17+19=36, Resulting Numbers: [12, 33, 36] Generated Node #0,0: 36:[12, 33, 36] Operation: 17+19=36 Moving to Node #0,0 Current State: 36:[12, 33, 36], Operations: ['17+19=36'] Exploring Operation: 36-33=3, Resulting Numbers: [12, 3] Generated Node #0,0,0: 36:[12, 3] Operation: 36-33=3 Moving to Node #0,0,0 Current State: 36:[12, 3], Operations: ['17+19=36', '36-33=3'] Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 30, 33, 33, 15 ]
44
[ "30+15=45", "33/33=1", "45-1=44" ]
Current State: 44:[30, 33, 33, 15], Operations: [] Exploring Operation: 30+15=45, Resulting Numbers: [33, 33, 45] Generated Node #2: [33, 33, 45] from Operation: 30+15=45 Current State: 44:[33, 33, 45], Operations: ['30+15=45'] Exploring Operation: 33/33=1, Resulting Numbers: [45, 1] Generated Node #3: [45, 1] from Operation: 33/33=1 Current State: 44:[45, 1], Operations: ['30+15=45', '33/33=1'] Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[30, 33, 33, 15], Operations: [] Exploring Operation: 33/33=1, Resulting Numbers: [30, 15, 1] Generated Node #0,0: 44:[30, 15, 1] Operation: 33/33=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[30, 15, 1], Operations: ['33/33=1'] Exploring Operation: 30/15=2, Resulting Numbers: [1, 2] Generated Node #0,0,0: 44:[1, 2] Operation: 30/15=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[1, 2], Operations: ['33/33=1', '30/15=2'] Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,44 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
[ 26, 81, 2, 19 ]
37
[ "81-26=55", "19+55=74", "74/2=37" ]
Current State: 37:[26, 81, 2, 19], Operations: [] Exploring Operation: 81-26=55, Resulting Numbers: [2, 19, 55] Generated Node #2: [2, 19, 55] from Operation: 81-26=55 Current State: 37:[2, 19, 55], Operations: ['81-26=55'] Exploring Operation: 19+55=74, Resulting Numbers: [2, 74] Generated Node #3: [2, 74] from Operation: 19+55=74 Current State: 37:[2, 74], Operations: ['81-26=55', '19+55=74'] Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[26, 81, 2, 19], Operations: [] Exploring Operation: 2*19=38, Resulting Numbers: [26, 81, 38] Generated Node #0,0: 37:[26, 81, 38] Operation: 2*19=38 Exploring Operation: 26+2=28, Resulting Numbers: [81, 19, 28] Generated Node #0,1: 37:[81, 19, 28] Operation: 26+2=28 Exploring Operation: 81-26=55, Resulting Numbers: [2, 19, 55] Generated Node #0,2: 37:[2, 19, 55] Operation: 81-26=55 Exploring Operation: 81-2=79, Resulting Numbers: [26, 19, 79] Generated Node #0,3: 37:[26, 19, 79] Operation: 81-2=79 Exploring Operation: 81-19=62, Resulting Numbers: [26, 2, 62] Generated Node #0,4: 37:[26, 2, 62] Operation: 81-19=62 Moving to Node #0,0 Current State: 37:[26, 81, 38], Operations: ['2*19=38'] Exploring Operation: 81-26=55, Resulting Numbers: [38, 55] Generated Node #0,0,0: 37:[38, 55] Operation: 81-26=55 Exploring Operation: 38-26=12, Resulting Numbers: [81, 12] Generated Node #0,0,1: 37:[81, 12] Operation: 38-26=12 Exploring Operation: 26+38=64, Resulting Numbers: [81, 64] Generated Node #0,0,2: 37:[81, 64] Operation: 26+38=64 Exploring Operation: 81-38=43, Resulting Numbers: [26, 43] Generated Node #0,0,3: 37:[26, 43] Operation: 81-38=43 Exploring Operation: 26+81=107, Resulting Numbers: [38, 107] Generated Node #0,0,4: 37:[38, 107] Operation: 26+81=107 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 37:[26, 43], Operations: ['2*19=38', '81-38=43'] Exploring Operation: 43-26=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 26*43=1118, Resulting Numbers: [1118] 1118,37 unequal: No Solution Exploring Operation: 26+43=69, Resulting Numbers: [69] 69,37 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:[38, 55], Operations: ['2*19=38', '81-26=55'] Exploring Operation: 38+55=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 38*55=2090, Resulting Numbers: [2090] 2090,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[81, 12], Operations: ['2*19=38', '38-26=12'] Exploring Operation: 81+12=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 81*12=972, Resulting Numbers: [972] 972,37 unequal: No Solution Exploring Operation: 81-12=69, Resulting Numbers: [69] 69,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 37:[81, 64], Operations: ['2*19=38', '26+38=64'] Exploring Operation: 81*64=5184, Resulting Numbers: [5184] 5184,37 unequal: No Solution Exploring Operation: 81+64=145, Resulting Numbers: [145] 145,37 unequal: No Solution Exploring Operation: 81-64=17, Resulting Numbers: [17] 17,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 37:[38, 107], Operations: ['2*19=38', '26+81=107'] Exploring Operation: 38+107=145, Resulting Numbers: [145] 145,37 unequal: No Solution Exploring Operation: 107-38=69, Resulting Numbers: [69] 69,37 unequal: No Solution Exploring Operation: 38*107=4066, Resulting Numbers: [4066] 4066,37 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: 37:[2, 19, 55], Operations: ['81-26=55'] Exploring Operation: 55-19=36, Resulting Numbers: [2, 36] Generated Node #0,2,0: 37:[2, 36] Operation: 55-19=36 Exploring Operation: 2*19=38, Resulting Numbers: [55, 38] Generated Node #0,2,1: 37:[55, 38] Operation: 2*19=38 Exploring Operation: 2+19=21, Resulting Numbers: [55, 21] Generated Node #0,2,2: 37:[55, 21] Operation: 2+19=21 Exploring Operation: 19-2=17, Resulting Numbers: [55, 17] Generated Node #0,2,3: 37:[55, 17] Operation: 19-2=17 Exploring Operation: 55-2=53, Resulting Numbers: [19, 53] Generated Node #0,2,4: 37:[19, 53] Operation: 55-2=53 Moving to Node #0,4 Current State: 37:[26, 2, 62], Operations: ['81-19=62'] Exploring Operation: 26-2=24, Resulting Numbers: [62, 24] Generated Node #0,4,0: 37:[62, 24] Operation: 26-2=24 Exploring Operation: 62-26=36, Resulting Numbers: [2, 36] Generated Node #0,4,1: 37:[2, 36] Operation: 62-26=36 Exploring Operation: 26+2=28, Resulting Numbers: [62, 28] Generated Node #0,4,2: 37:[62, 28] Operation: 26+2=28 Exploring Operation: 62/2=31, Resulting Numbers: [26, 31] Generated Node #0,4,3: 37:[26, 31] Operation: 62/2=31 Exploring Operation: 62-2=60, Resulting Numbers: [26, 60] Generated Node #0,4,4: 37:[26, 60] Operation: 62-2=60 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 37:[26, 31], Operations: ['81-19=62', '62/2=31'] Exploring Operation: 31-26=5, Resulting Numbers: [5] 5,37 unequal: No Solution Exploring Operation: 26*31=806, Resulting Numbers: [806] 806,37 unequal: No Solution Exploring Operation: 26+31=57, Resulting Numbers: [57] 57,37 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 #0,4,2 Current State: 37:[62, 28], Operations: ['81-19=62', '26+2=28'] Exploring Operation: 62-28=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 62+28=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 62*28=1736, Resulting Numbers: [1736] 1736,37 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 #0,4,4 Current State: 37:[26, 60], Operations: ['81-19=62', '62-2=60'] Exploring Operation: 26*60=1560, Resulting Numbers: [1560] 1560,37 unequal: No Solution Exploring Operation: 26+60=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,37 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 #0,4,1 Current State: 37:[2, 36], Operations: ['81-19=62', '62-26=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,37 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,37 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,37 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 #0,4,0 Current State: 37:[62, 24], Operations: ['81-19=62', '26-2=24'] Exploring Operation: 62*24=1488, Resulting Numbers: [1488] 1488,37 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 62+24=86, Resulting Numbers: [86] 86,37 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:[81, 19, 28], Operations: ['26+2=28'] Exploring Operation: 19+28=47, Resulting Numbers: [81, 47] Generated Node #0,1,0: 37:[81, 47] Operation: 19+28=47 Exploring Operation: 81+19=100, Resulting Numbers: [28, 100] Generated Node #0,1,1: 37:[28, 100] Operation: 81+19=100 Exploring Operation: 28-19=9, Resulting Numbers: [81, 9] Generated Node #0,1,2: 37:[81, 9] Operation: 28-19=9 Exploring Operation: 81-19=62, Resulting Numbers: [28, 62] Generated Node #0,1,3: 37:[28, 62] Operation: 81-19=62 Exploring Operation: 81-28=53, Resulting Numbers: [19, 53] Generated Node #0,1,4: 37:[19, 53] Operation: 81-28=53 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 37:[28, 62], Operations: ['26+2=28', '81-19=62'] Exploring Operation: 28*62=1736, Resulting Numbers: [1736] 1736,37 unequal: No Solution Exploring Operation: 28+62=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 62-28=34, Resulting Numbers: [34] 34,37 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 #0,1,4 Current State: 37:[19, 53], Operations: ['26+2=28', '81-28=53'] Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,37 unequal: No Solution Exploring Operation: 19*53=1007, Resulting Numbers: [1007] 1007,37 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:[81, 47], Operations: ['26+2=28', '19+28=47'] Exploring Operation: 81*47=3807, Resulting Numbers: [3807] 3807,37 unequal: No Solution Exploring Operation: 81-47=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 81+47=128, Resulting Numbers: [128] 128,37 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 #0,1,1 Current State: 37:[28, 100], Operations: ['26+2=28', '81+19=100'] Exploring Operation: 28*100=2800, Resulting Numbers: [2800] 2800,37 unequal: No Solution Exploring Operation: 100-28=72, Resulting Numbers: [72] 72,37 unequal: No Solution Exploring Operation: 28+100=128, Resulting Numbers: [128] 128,37 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 #0,1,2 Current State: 37:[81, 9], Operations: ['26+2=28', '28-19=9'] Exploring Operation: 81*9=729, Resulting Numbers: [729] 729,37 unequal: No Solution Exploring Operation: 81/9=9, Resulting Numbers: [9] 9,37 unequal: No Solution Exploring Operation: 81+9=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 81-9=72, Resulting Numbers: [72] 72,37 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: 37:[26, 19, 79], Operations: ['81-2=79'] Exploring Operation: 26-19=7, Resulting Numbers: [79, 7] Generated Node #0,3,0: 37:[79, 7] Operation: 26-19=7 Exploring Operation: 26+19=45, Resulting Numbers: [79, 45] Generated Node #0,3,1: 37:[79, 45] Operation: 26+19=45 Exploring Operation: 79-19=60, Resulting Numbers: [26, 60] Generated Node #0,3,2: 37:[26, 60] Operation: 79-19=60 Exploring Operation: 79-26=53, Resulting Numbers: [19, 53] Generated Node #0,3,3: 37:[19, 53] Operation: 79-26=53 Exploring Operation: 19+79=98, Resulting Numbers: [26, 98] Generated Node #0,3,4: 37:[26, 98] Operation: 19+79=98 Moving to Node #0,2,1 Current State: 37:[55, 38], Operations: ['81-26=55', '2*19=38'] Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 55+38=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 55*38=2090, Resulting Numbers: [2090] 2090,37 unequal: No Solution Moving to Node #0,2,4 Current State: 37:[19, 53], Operations: ['81-26=55', '55-2=53'] Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,37 unequal: No Solution Exploring Operation: 19*53=1007, Resulting Numbers: [1007] 1007,37 unequal: No Solution Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,37 unequal: No Solution Moving to Node #0,3,3 Current State: 37:[19, 53], Operations: ['81-2=79', '79-26=53'] Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,37 unequal: No Solution Exploring Operation: 19*53=1007, Resulting Numbers: [1007] 1007,37 unequal: No Solution Moving to Node #0,3,2 Current State: 37:[26, 60], Operations: ['81-2=79', '79-19=60'] Exploring Operation: 26+60=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 26*60=1560, Resulting Numbers: [1560] 1560,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[55, 21], Operations: ['81-26=55', '2+19=21'] Exploring Operation: 55*21=1155, Resulting Numbers: [1155] 1155,37 unequal: No Solution Exploring Operation: 55-21=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 55+21=76, Resulting Numbers: [76] 76,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[2, 36], Operations: ['81-26=55', '55-19=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,37 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[55, 17], Operations: ['81-26=55', '19-2=17'] Exploring Operation: 55*17=935, Resulting Numbers: [935] 935,37 unequal: No Solution Exploring Operation: 55-17=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 55+17=72, Resulting Numbers: [72] 72,37 unequal: No Solution Moving to Node #0,3,1 Current State: 37:[79, 45], Operations: ['81-2=79', '26+19=45'] Exploring Operation: 79+45=124, Resulting Numbers: [124] 124,37 unequal: No Solution Exploring Operation: 79-45=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 79*45=3555, Resulting Numbers: [3555] 3555,37 unequal: No Solution Moving to Node #0,3,4 Current State: 37:[26, 98], Operations: ['81-2=79', '19+79=98'] Exploring Operation: 26*98=2548, Resulting Numbers: [2548] 2548,37 unequal: No Solution Exploring Operation: 26+98=124, Resulting Numbers: [124] 124,37 unequal: No Solution Exploring Operation: 98-26=72, Resulting Numbers: [72] 72,37 unequal: No Solution Moving to Node #0,3,0 Current State: 37:[79, 7], Operations: ['81-2=79', '26-19=7'] Exploring Operation: 79+7=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 79*7=553, Resulting Numbers: [553] 553,37 unequal: No Solution Exploring Operation: 79-7=72, Resulting Numbers: [72] 72,37 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 46, 19, 10, 19 ]
99
[ "46*10=460", "19*19=361", "460-361=99" ]
Current State: 99:[46, 19, 10, 19], Operations: [] Exploring Operation: 46*10=460, Resulting Numbers: [19, 19, 460] Generated Node #2: [19, 19, 460] from Operation: 46*10=460 Current State: 99:[19, 19, 460], Operations: ['46*10=460'] Exploring Operation: 19*19=361, Resulting Numbers: [460, 361] Generated Node #3: [460, 361] from Operation: 19*19=361 Current State: 99:[460, 361], Operations: ['46*10=460', '19*19=361'] Exploring Operation: 460-361=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[46, 19, 10, 19], Operations: [] Exploring Operation: 46-19=27, Resulting Numbers: [19, 10, 27] Generated Node #0,0: 99:[19, 10, 27] Operation: 46-19=27 Exploring Operation: 46-19=27, Resulting Numbers: [10, 19, 27] Generated Node #0,1: 99:[10, 19, 27] Operation: 46-19=27 Moving to Node #0,0 Current State: 99:[19, 10, 27], Operations: ['46-19=27'] Exploring Operation: 19-10=9, Resulting Numbers: [27, 9] Generated Node #0,0,0: 99:[27, 9] Operation: 19-10=9 Exploring Operation: 27-19=8, Resulting Numbers: [10, 8] Generated Node #0,0,1: 99:[10, 8] Operation: 27-19=8 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[10, 8], Operations: ['46-19=27', '27-19=8'] Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,99 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[27, 9], Operations: ['46-19=27', '19-10=9'] Exploring Operation: 27+9=36, Resulting Numbers: [36] 36,99 unequal: No Solution Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 99:[10, 19, 27], Operations: ['46-19=27'] Exploring Operation: 19-10=9, Resulting Numbers: [27, 9] Generated Node #0,1,0: 99:[27, 9] Operation: 19-10=9 Exploring Operation: 27-19=8, Resulting Numbers: [10, 8] Generated Node #0,1,1: 99:[10, 8] Operation: 27-19=8 Moving to Node #0,1,1 Current State: 99:[10, 8], Operations: ['46-19=27', '27-19=8'] Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,99 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[27, 9], Operations: ['46-19=27', '19-10=9'] Exploring Operation: 27+9=36, Resulting Numbers: [36] 36,99 unequal: No Solution Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,99 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 2, 94, 44, 77 ]
25
[ "2+94=96", "44+77=121", "121-96=25" ]
Current State: 25:[2, 94, 44, 77], Operations: [] Exploring Operation: 2+94=96, Resulting Numbers: [44, 77, 96] Generated Node #2: [44, 77, 96] from Operation: 2+94=96 Current State: 25:[44, 77, 96], Operations: ['2+94=96'] Exploring Operation: 44+77=121, Resulting Numbers: [96, 121] Generated Node #3: [96, 121] from Operation: 44+77=121 Current State: 25:[96, 121], Operations: ['2+94=96', '44+77=121'] Exploring Operation: 121-96=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[2, 94, 44, 77], Operations: [] Exploring Operation: 94-44=50, Resulting Numbers: [2, 77, 50] Generated Node #0,0: 25:[2, 77, 50] Operation: 94-44=50 Exploring Operation: 94-77=17, Resulting Numbers: [2, 44, 17] Generated Node #0,1: 25:[2, 44, 17] Operation: 94-77=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[2, 44, 17], Operations: ['94-77=17'] Exploring Operation: 44-17=27, Resulting Numbers: [2, 27] Generated Node #0,1,0: 25:[2, 27] Operation: 44-17=27 Exploring Operation: 44/2=22, Resulting Numbers: [17, 22] Generated Node #0,1,1: 25:[17, 22] Operation: 44/2=22 Moving to Node #0,1,0 Current State: 25:[2, 27], Operations: ['94-77=17', '44-17=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[2, 94, 44, 77], Operations: [] Exploring Operation: 94-77=17, Resulting Numbers: [2, 44, 17] Generated Node #0,1: 25:[2, 44, 17] Operation: 94-77=17 Moving to Node #0,1 Current State: 25:[2, 44, 17], Operations: ['94-77=17'] Exploring Operation: 44-17=27, Resulting Numbers: [2, 27] Generated Node #0,1,0: 25:[2, 27] Operation: 44-17=27 Moving to Node #0,1,0 Current State: 25:[2, 27], Operations: ['94-77=17', '44-17=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 46, 69, 82, 30 ]
63
[ "46+69=115", "82-30=52", "115-52=63" ]
Current State: 63:[46, 69, 82, 30], Operations: [] Exploring Operation: 46+69=115, Resulting Numbers: [82, 30, 115] Generated Node #2: [82, 30, 115] from Operation: 46+69=115 Current State: 63:[82, 30, 115], Operations: ['46+69=115'] Exploring Operation: 82-30=52, Resulting Numbers: [115, 52] Generated Node #3: [115, 52] from Operation: 82-30=52 Current State: 63:[115, 52], Operations: ['46+69=115', '82-30=52'] Exploring Operation: 115-52=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[46, 69, 82, 30], Operations: [] Exploring Operation: 69-46=23, Resulting Numbers: [82, 30, 23] Generated Node #0,0: 63:[82, 30, 23] Operation: 69-46=23 Exploring Operation: 82-46=36, Resulting Numbers: [69, 30, 36] Generated Node #0,1: 63:[69, 30, 36] Operation: 82-46=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[82, 30, 23], Operations: ['69-46=23'] Exploring Operation: 82-30=52, Resulting Numbers: [23, 52] Generated Node #0,0,0: 63:[23, 52] Operation: 82-30=52 Exploring Operation: 82-23=59, Resulting Numbers: [30, 59] Generated Node #0,0,1: 63:[30, 59] Operation: 82-23=59 Moving to Node #0,0,0 Current State: 63:[23, 52], Operations: ['69-46=23', '82-30=52'] Exploring Operation: 23+52=75, Resulting Numbers: [75] 75,63 unequal: No Solution Exploring Operation: 52-23=29, Resulting Numbers: [29] 29,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[30, 59], Operations: ['69-46=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 No 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: 63:[69, 30, 36], Operations: ['82-46=36'] Exploring Operation: 30+36=66, Resulting Numbers: [69, 66] Generated Node #0,1,0: 63:[69, 66] Operation: 30+36=66 Exploring Operation: 36-30=6, Resulting Numbers: [69, 6] Generated Node #0,1,1: 63:[69, 6] Operation: 36-30=6 Moving to Node #0,1,1 Current State: 63:[69, 6], Operations: ['82-46=36', '36-30=6'] Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[46, 69, 82, 30], Operations: [] Exploring Operation: 82-46=36, Resulting Numbers: [69, 30, 36] Generated Node #0,1: 63:[69, 30, 36] Operation: 82-46=36 Moving to Node #0,1 Current State: 63:[69, 30, 36], Operations: ['82-46=36'] Exploring Operation: 36-30=6, Resulting Numbers: [69, 6] Generated Node #0,1,1: 63:[69, 6] Operation: 36-30=6 Moving to Node #0,1,1 Current State: 63:[69, 6], Operations: ['82-46=36', '36-30=6'] Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 13, 34, 52, 36 ]
39
[ "36-34=2", "52/2=26", "13+26=39" ]
Current State: 39:[13, 34, 52, 36], Operations: [] Exploring Operation: 36-34=2, Resulting Numbers: [13, 52, 2] Generated Node #2: [13, 52, 2] from Operation: 36-34=2 Current State: 39:[13, 52, 2], Operations: ['36-34=2'] Exploring Operation: 52/2=26, Resulting Numbers: [13, 26] Generated Node #3: [13, 26] from Operation: 52/2=26 Current State: 39:[13, 26], Operations: ['36-34=2', '52/2=26'] Exploring Operation: 13+26=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[13, 34, 52, 36], Operations: [] Exploring Operation: 52-34=18, Resulting Numbers: [13, 36, 18] Generated Node #0,0: 39:[13, 36, 18] Operation: 52-34=18 Exploring Operation: 52-36=16, Resulting Numbers: [13, 34, 16] Generated Node #0,1: 39:[13, 34, 16] Operation: 52-36=16 Exploring Operation: 52-13=39, Resulting Numbers: [34, 36, 39] Generated Node #0,2: 39:[34, 36, 39] Operation: 52-13=39 Exploring Operation: 52/13=4, Resulting Numbers: [34, 36, 4] Generated Node #0,3: 39:[34, 36, 4] Operation: 52/13=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[13, 36, 18], Operations: ['52-34=18'] Exploring Operation: 36/18=2, Resulting Numbers: [13, 2] Generated Node #0,0,0: 39:[13, 2] Operation: 36/18=2 Exploring Operation: 18-13=5, Resulting Numbers: [36, 5] Generated Node #0,0,1: 39:[36, 5] Operation: 18-13=5 Exploring Operation: 36-18=18, Resulting Numbers: [13, 18] Generated Node #0,0,2: 39:[13, 18] Operation: 36-18=18 Exploring Operation: 13+18=31, Resulting Numbers: [36, 31] Generated Node #0,0,3: 39:[36, 31] Operation: 13+18=31 Moving to Node #0,0,0 Current State: 39:[13, 2], Operations: ['52-34=18', '36/18=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[13, 18], Operations: ['52-34=18', '36-18=18'] Exploring Operation: 13*18=234, Resulting Numbers: [234] 234,39 unequal: No Solution Exploring Operation: 18-13=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 13+18=31, Resulting Numbers: [31] 31,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[36, 5], Operations: ['52-34=18', '18-13=5'] Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 36+5=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 36*5=180, Resulting Numbers: [180] 180,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[36, 31], Operations: ['52-34=18', '13+18=31'] Exploring Operation: 36*31=1116, Resulting Numbers: [1116] 1116,39 unequal: No Solution Exploring Operation: 36+31=67, Resulting Numbers: [67] 67,39 unequal: No Solution Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,39 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:[13, 34, 16], Operations: ['52-36=16'] Exploring Operation: 13+34=47, Resulting Numbers: [16, 47] Generated Node #0,1,0: 39:[16, 47] Operation: 13+34=47 Exploring Operation: 34-13=21, Resulting Numbers: [16, 21] Generated Node #0,1,1: 39:[16, 21] Operation: 34-13=21 Exploring Operation: 16-13=3, Resulting Numbers: [34, 3] Generated Node #0,1,2: 39:[34, 3] Operation: 16-13=3 Exploring Operation: 34-16=18, Resulting Numbers: [13, 18] Generated Node #0,1,3: 39:[13, 18] Operation: 34-16=18 Moving to Node #0,1,2 Current State: 39:[34, 3], Operations: ['52-36=16', '16-13=3'] Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 34*3=102, Resulting Numbers: [102] 102,39 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,39 unequal: No Solution Moving to Node #0,1,3 Current State: 39:[13, 18], Operations: ['52-36=16', '34-16=18'] Exploring Operation: 13+18=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 18-13=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 13*18=234, Resulting Numbers: [234] 234,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[16, 21], Operations: ['52-36=16', '34-13=21'] Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 16*21=336, Resulting Numbers: [336] 336,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[16, 47], Operations: ['52-36=16', '13+34=47'] Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 16*47=752, Resulting Numbers: [752] 752,39 unequal: No Solution Exploring Operation: 16+47=63, Resulting Numbers: [63] 63,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[34, 36, 39], Operations: ['52-13=39'] Exploring Operation: 39-34=5, Resulting Numbers: [36, 5] Generated Node #0,2,0: 39:[36, 5] Operation: 39-34=5 Exploring Operation: 36-34=2, Resulting Numbers: [39, 2] Generated Node #0,2,1: 39:[39, 2] Operation: 36-34=2 Exploring Operation: 34+36=70, Resulting Numbers: [39, 70] Generated Node #0,2,2: 39:[39, 70] Operation: 34+36=70 Exploring Operation: 39-36=3, Resulting Numbers: [34, 3] Generated Node #0,2,3: 39:[34, 3] Operation: 39-36=3 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 39:[39, 2], Operations: ['52-13=39', '36-34=2'] Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,39 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,39 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 #0,2,0 Current State: 39:[36, 5], Operations: ['52-13=39', '39-34=5'] Exploring Operation: 36+5=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 36*5=180, Resulting Numbers: [180] 180,39 unequal: No Solution Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,39 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 #0,2,3 Current State: 39:[34, 3], Operations: ['52-13=39', '39-36=3'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 34*3=102, Resulting Numbers: [102] 102,39 unequal: No Solution Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,39 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 #0,2,2 Current State: 39:[39, 70], Operations: ['52-13=39', '34+36=70'] Exploring Operation: 70-39=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 39+70=109, Resulting Numbers: [109] 109,39 unequal: No Solution Exploring Operation: 39*70=2730, Resulting Numbers: [2730] 2730,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 39:[34, 36, 4], Operations: ['52/13=4'] Exploring Operation: 34+4=38, Resulting Numbers: [36, 38] Generated Node #0,3,0: 39:[36, 38] Operation: 34+4=38 Exploring Operation: 36+4=40, Resulting Numbers: [34, 40] Generated Node #0,3,1: 39:[34, 40] Operation: 36+4=40 Exploring Operation: 36/4=9, Resulting Numbers: [34, 9] Generated Node #0,3,2: 39:[34, 9] Operation: 36/4=9 Exploring Operation: 36-34=2, Resulting Numbers: [4, 2] Generated Node #0,3,3: 39:[4, 2] Operation: 36-34=2 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 39:[4, 2], Operations: ['52/13=4', '36-34=2'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,39 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,39 unequal: No Solution No 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: 39:[36, 38], Operations: ['52/13=4', '34+4=38'] Exploring Operation: 36+38=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 36*38=1368, Resulting Numbers: [1368] 1368,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 39:[34, 40], Operations: ['52/13=4', '36+4=40'] Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 34*40=1360, Resulting Numbers: [1360] 1360,39 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 39:[34, 9], Operations: ['52/13=4', '36/4=9'] Exploring Operation: 34+9=43, Resulting Numbers: [43] 43,39 unequal: No Solution Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 34*9=306, Resulting Numbers: [306] 306,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 94, 33, 5, 79 ]
42
[ "94-79=15", "5*15=75", "75-33=42" ]
Current State: 42:[94, 33, 5, 79], Operations: [] Exploring Operation: 94-79=15, Resulting Numbers: [33, 5, 15] Generated Node #2: [33, 5, 15] from Operation: 94-79=15 Current State: 42:[33, 5, 15], Operations: ['94-79=15'] Exploring Operation: 5*15=75, Resulting Numbers: [33, 75] Generated Node #3: [33, 75] from Operation: 5*15=75 Current State: 42:[33, 75], Operations: ['94-79=15', '5*15=75'] Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[94, 33, 5, 79], Operations: [] Exploring Operation: 94-5=89, Resulting Numbers: [33, 79, 89] Generated Node #0,0: 42:[33, 79, 89] Operation: 94-5=89 Exploring Operation: 79-33=46, Resulting Numbers: [94, 5, 46] Generated Node #0,1: 42:[94, 5, 46] Operation: 79-33=46 Exploring Operation: 94-79=15, Resulting Numbers: [33, 5, 15] Generated Node #0,2: 42:[33, 5, 15] Operation: 94-79=15 Exploring Operation: 94-33=61, Resulting Numbers: [5, 79, 61] Generated Node #0,3: 42:[5, 79, 61] Operation: 94-33=61 Moving to Node #0,2 Current State: 42:[33, 5, 15], Operations: ['94-79=15'] Exploring Operation: 33-5=28, Resulting Numbers: [15, 28] Generated Node #0,2,0: 42:[15, 28] Operation: 33-5=28 Exploring Operation: 33+15=48, Resulting Numbers: [5, 48] Generated Node #0,2,1: 42:[5, 48] Operation: 33+15=48 Exploring Operation: 33-15=18, Resulting Numbers: [5, 18] Generated Node #0,2,2: 42:[5, 18] Operation: 33-15=18 Exploring Operation: 33+5=38, Resulting Numbers: [15, 38] Generated Node #0,2,3: 42:[15, 38] Operation: 33+5=38 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 42:[5, 18], Operations: ['94-79=15', '33-15=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 42:[15, 38], Operations: ['94-79=15', '33+5=38'] Exploring Operation: 15+38=53, Resulting Numbers: [53] 53,42 unequal: No Solution Exploring Operation: 38-15=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 15*38=570, Resulting Numbers: [570] 570,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 42:[5, 48], Operations: ['94-79=15', '33+15=48'] Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,42 unequal: No Solution Exploring Operation: 5*48=240, Resulting Numbers: [240] 240,42 unequal: No Solution Exploring Operation: 5+48=53, Resulting Numbers: [53] 53,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 42:[15, 28], Operations: ['94-79=15', '33-5=28'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,42 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,42 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: 42:[5, 79, 61], Operations: ['94-33=61'] Exploring Operation: 61-5=56, Resulting Numbers: [79, 56] Generated Node #0,3,0: 42:[79, 56] Operation: 61-5=56 Exploring Operation: 79-5=74, Resulting Numbers: [61, 74] Generated Node #0,3,1: 42:[61, 74] Operation: 79-5=74 Exploring Operation: 79-61=18, Resulting Numbers: [5, 18] Generated Node #0,3,2: 42:[5, 18] Operation: 79-61=18 Exploring Operation: 5+79=84, Resulting Numbers: [61, 84] Generated Node #0,3,3: 42:[61, 84] Operation: 5+79=84 Moving to Node #0,1 Current State: 42:[94, 5, 46], Operations: ['79-33=46'] Exploring Operation: 46-5=41, Resulting Numbers: [94, 41] Generated Node #0,1,0: 42:[94, 41] Operation: 46-5=41 Exploring Operation: 94+5=99, Resulting Numbers: [46, 99] Generated Node #0,1,1: 42:[46, 99] Operation: 94+5=99 Exploring Operation: 94-46=48, Resulting Numbers: [5, 48] Generated Node #0,1,2: 42:[5, 48] Operation: 94-46=48 Exploring Operation: 94-5=89, Resulting Numbers: [46, 89] Generated Node #0,1,3: 42:[46, 89] Operation: 94-5=89 Moving to Node #0,0 Current State: 42:[33, 79, 89], Operations: ['94-5=89'] Exploring Operation: 89-33=56, Resulting Numbers: [79, 56] Generated Node #0,0,0: 42:[79, 56] Operation: 89-33=56 Exploring Operation: 79-33=46, Resulting Numbers: [89, 46] Generated Node #0,0,1: 42:[89, 46] Operation: 79-33=46 Exploring Operation: 33+79=112, Resulting Numbers: [89, 112] Generated Node #0,0,2: 42:[89, 112] Operation: 33+79=112 Exploring Operation: 89-79=10, Resulting Numbers: [33, 10] Generated Node #0,0,3: 42:[33, 10] Operation: 89-79=10 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 42:[33, 10], Operations: ['94-5=89', '89-79=10'] Exploring Operation: 33*10=330, Resulting Numbers: [330] 330,42 unequal: No Solution Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 33+10=43, Resulting Numbers: [43] 43,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[79, 56], Operations: ['94-5=89', '89-33=56'] Exploring Operation: 79+56=135, Resulting Numbers: [135] 135,42 unequal: No Solution Exploring Operation: 79-56=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 79*56=4424, Resulting Numbers: [4424] 4424,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 42:[89, 46], Operations: ['94-5=89', '79-33=46'] Exploring Operation: 89*46=4094, Resulting Numbers: [4094] 4094,42 unequal: No Solution Exploring Operation: 89+46=135, Resulting Numbers: [135] 135,42 unequal: No Solution Exploring Operation: 89-46=43, Resulting Numbers: [43] 43,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 42:[89, 112], Operations: ['94-5=89', '33+79=112'] Exploring Operation: 112-89=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 89*112=9968, Resulting Numbers: [9968] 9968,42 unequal: No Solution Exploring Operation: 89+112=201, Resulting Numbers: [201] 201,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 42:[5, 18], Operations: ['94-33=61', '79-61=18'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,42 unequal: No Solution Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[5, 48], Operations: ['79-33=46', '94-46=48'] Exploring Operation: 5+48=53, Resulting Numbers: [53] 53,42 unequal: No Solution Exploring Operation: 5*48=240, Resulting Numbers: [240] 240,42 unequal: No Solution Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,42 unequal: No Solution Moving to Node #0,3,1 Current State: 42:[61, 74], Operations: ['94-33=61', '79-5=74'] Exploring Operation: 61+74=135, Resulting Numbers: [135] 135,42 unequal: No Solution Exploring Operation: 61*74=4514, Resulting Numbers: [4514] 4514,42 unequal: No Solution Exploring Operation: 74-61=13, Resulting Numbers: [13] 13,42 unequal: No Solution Moving to Node #0,1,3 Current State: 42:[46, 89], Operations: ['79-33=46', '94-5=89'] Exploring Operation: 46*89=4094, Resulting Numbers: [4094] 4094,42 unequal: No Solution Exploring Operation: 46+89=135, Resulting Numbers: [135] 135,42 unequal: No Solution Exploring Operation: 89-46=43, Resulting Numbers: [43] 43,42 unequal: No Solution Moving to Node #0,3,0 Current State: 42:[79, 56], Operations: ['94-33=61', '61-5=56'] Exploring Operation: 79*56=4424, Resulting Numbers: [4424] 4424,42 unequal: No Solution Exploring Operation: 79+56=135, Resulting Numbers: [135] 135,42 unequal: No Solution Exploring Operation: 79-56=23, Resulting Numbers: [23] 23,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[94, 41], Operations: ['79-33=46', '46-5=41'] Exploring Operation: 94*41=3854, Resulting Numbers: [3854] 3854,42 unequal: No Solution Exploring Operation: 94-41=53, Resulting Numbers: [53] 53,42 unequal: No Solution Exploring Operation: 94+41=135, Resulting Numbers: [135] 135,42 unequal: No Solution Moving to Node #0,3,3 Current State: 42:[61, 84], Operations: ['94-33=61', '5+79=84'] Exploring Operation: 61+84=145, Resulting Numbers: [145] 145,42 unequal: No Solution Exploring Operation: 61*84=5124, Resulting Numbers: [5124] 5124,42 unequal: No Solution Exploring Operation: 84-61=23, Resulting Numbers: [23] 23,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[46, 99], Operations: ['79-33=46', '94+5=99'] Exploring Operation: 46*99=4554, Resulting Numbers: [4554] 4554,42 unequal: No Solution Exploring Operation: 46+99=145, Resulting Numbers: [145] 145,42 unequal: No Solution Exploring Operation: 99-46=53, Resulting Numbers: [53] 53,42 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 5, 45, 68, 30 ]
47
[ "45/5=9", "68-30=38", "9+38=47" ]
Current State: 47:[5, 45, 68, 30], Operations: [] Exploring Operation: 45/5=9, Resulting Numbers: [68, 30, 9] Generated Node #2: [68, 30, 9] from Operation: 45/5=9 Current State: 47:[68, 30, 9], Operations: ['45/5=9'] Exploring Operation: 68-30=38, Resulting Numbers: [9, 38] Generated Node #3: [9, 38] from Operation: 68-30=38 Current State: 47:[9, 38], Operations: ['45/5=9', '68-30=38'] Exploring Operation: 9+38=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[5, 45, 68, 30], Operations: [] Exploring Operation: 45-5=40, Resulting Numbers: [68, 30, 40] Generated Node #0,0: 47:[68, 30, 40] Operation: 45-5=40 Exploring Operation: 68-5=63, Resulting Numbers: [45, 30, 63] Generated Node #0,1: 47:[45, 30, 63] Operation: 68-5=63 Exploring Operation: 5+30=35, Resulting Numbers: [45, 68, 35] Generated Node #0,2: 47:[45, 68, 35] Operation: 5+30=35 Exploring Operation: 5+45=50, Resulting Numbers: [68, 30, 50] Generated Node #0,3: 47:[68, 30, 50] Operation: 5+45=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[45, 30, 63], Operations: ['68-5=63'] Exploring Operation: 45+30=75, Resulting Numbers: [63, 75] Generated Node #0,1,0: 47:[63, 75] Operation: 45+30=75 Exploring Operation: 63-30=33, Resulting Numbers: [45, 33] Generated Node #0,1,1: 47:[45, 33] Operation: 63-30=33 Exploring Operation: 45-30=15, Resulting Numbers: [63, 15] Generated Node #0,1,2: 47:[63, 15] Operation: 45-30=15 Exploring Operation: 63-45=18, Resulting Numbers: [30, 18] Generated Node #0,1,3: 47:[30, 18] Operation: 63-45=18 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 47:[45, 33], Operations: ['68-5=63', '63-30=33'] Exploring Operation: 45+33=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 45*33=1485, Resulting Numbers: [1485] 1485,47 unequal: No Solution Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,47 unequal: No Solution No 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: 47:[63, 75], Operations: ['68-5=63', '45+30=75'] Exploring Operation: 63*75=4725, Resulting Numbers: [4725] 4725,47 unequal: No Solution Exploring Operation: 75-63=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 63+75=138, Resulting Numbers: [138] 138,47 unequal: No Solution No 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: 47:[30, 18], Operations: ['68-5=63', '63-45=18'] Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 30*18=540, Resulting Numbers: [540] 540,47 unequal: No Solution Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,47 unequal: No Solution No 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: 47:[63, 15], Operations: ['68-5=63', '45-30=15'] Exploring Operation: 63+15=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 63*15=945, Resulting Numbers: [945] 945,47 unequal: No Solution Exploring Operation: 63-15=48, Resulting Numbers: [48] 48,47 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 47:[45, 68, 35], Operations: ['5+30=35'] Exploring Operation: 68-45=23, Resulting Numbers: [35, 23] Generated Node #0,2,0: 47:[35, 23] Operation: 68-45=23 Exploring Operation: 68-35=33, Resulting Numbers: [45, 33] Generated Node #0,2,1: 47:[45, 33] Operation: 68-35=33 Exploring Operation: 45-35=10, Resulting Numbers: [68, 10] Generated Node #0,2,2: 47:[68, 10] Operation: 45-35=10 Exploring Operation: 45+35=80, Resulting Numbers: [68, 80] Generated Node #0,2,3: 47:[68, 80] Operation: 45+35=80 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 47:[45, 33], Operations: ['5+30=35', '68-35=33'] Exploring Operation: 45*33=1485, Resulting Numbers: [1485] 1485,47 unequal: No Solution Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 45+33=78, Resulting Numbers: [78] 78,47 unequal: No Solution No 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: 47:[35, 23], Operations: ['5+30=35', '68-45=23'] Exploring Operation: 35*23=805, Resulting Numbers: [805] 805,47 unequal: No Solution Exploring Operation: 35+23=58, Resulting Numbers: [58] 58,47 unequal: No Solution Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,47 unequal: No Solution No 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: 47:[68, 80], Operations: ['5+30=35', '45+35=80'] Exploring Operation: 68+80=148, Resulting Numbers: [148] 148,47 unequal: No Solution Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 68*80=5440, Resulting Numbers: [5440] 5440,47 unequal: No Solution No 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: 47:[68, 10], Operations: ['5+30=35', '45-35=10'] Exploring Operation: 68+10=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,47 unequal: No Solution Exploring Operation: 68*10=680, Resulting Numbers: [680] 680,47 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 Start Sub Search at level 1: Moving to Node #0,3 Current State: 47:[68, 30, 50], Operations: ['5+45=50'] Exploring Operation: 68-30=38, Resulting Numbers: [50, 38] Generated Node #0,3,0: 47:[50, 38] Operation: 68-30=38 Exploring Operation: 50-30=20, Resulting Numbers: [68, 20] Generated Node #0,3,1: 47:[68, 20] Operation: 50-30=20 Exploring Operation: 68-50=18, Resulting Numbers: [30, 18] Generated Node #0,3,2: 47:[30, 18] Operation: 68-50=18 Exploring Operation: 68+30=98, Resulting Numbers: [50, 98] Generated Node #0,3,3: 47:[50, 98] Operation: 68+30=98 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 47:[50, 38], Operations: ['5+45=50', '68-30=38'] Exploring Operation: 50+38=88, Resulting Numbers: [88] 88,47 unequal: No Solution Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 50*38=1900, Resulting Numbers: [1900] 1900,47 unequal: No Solution No 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: 47:[30, 18], Operations: ['5+45=50', '68-50=18'] Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 30*18=540, Resulting Numbers: [540] 540,47 unequal: No Solution Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 47:[68, 20], Operations: ['5+45=50', '50-30=20'] Exploring Operation: 68*20=1360, Resulting Numbers: [1360] 1360,47 unequal: No Solution Exploring Operation: 68+20=88, Resulting Numbers: [88] 88,47 unequal: No Solution Exploring Operation: 68-20=48, Resulting Numbers: [48] 48,47 unequal: No Solution No 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: 47:[50, 98], Operations: ['5+45=50', '68+30=98'] Exploring Operation: 50*98=4900, Resulting Numbers: [4900] 4900,47 unequal: No Solution Exploring Operation: 98-50=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 50+98=148, Resulting Numbers: [148] 148,47 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[68, 30, 40], Operations: ['45-5=40'] Exploring Operation: 68-30=38, Resulting Numbers: [40, 38] Generated Node #0,0,0: 47:[40, 38] Operation: 68-30=38 Exploring Operation: 68+30=98, Resulting Numbers: [40, 98] Generated Node #0,0,1: 47:[40, 98] Operation: 68+30=98 Exploring Operation: 68-40=28, Resulting Numbers: [30, 28] Generated Node #0,0,2: 47:[30, 28] Operation: 68-40=28 Exploring Operation: 30+40=70, Resulting Numbers: [68, 70] Generated Node #0,0,3: 47:[68, 70] Operation: 30+40=70 Moving to Node #0,0,0 Current State: 47:[40, 38], Operations: ['45-5=40', '68-30=38'] Exploring Operation: 40-38=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 40*38=1520, Resulting Numbers: [1520] 1520,47 unequal: No Solution Exploring Operation: 40+38=78, Resulting Numbers: [78] 78,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[30, 28], Operations: ['45-5=40', '68-40=28'] Exploring Operation: 30*28=840, Resulting Numbers: [840] 840,47 unequal: No Solution Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,47 unequal: No Solution Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,47 unequal: No Solution Moving to Node #0,0,3 Current State: 47:[68, 70], Operations: ['45-5=40', '30+40=70'] Exploring Operation: 68*70=4760, Resulting Numbers: [4760] 4760,47 unequal: No Solution Exploring Operation: 68+70=138, Resulting Numbers: [138] 138,47 unequal: No Solution Exploring Operation: 70-68=2, Resulting Numbers: [2] 2,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[40, 98], Operations: ['45-5=40', '68+30=98'] Exploring Operation: 40+98=138, Resulting Numbers: [138] 138,47 unequal: No Solution Exploring Operation: 40*98=3920, Resulting Numbers: [3920] 3920,47 unequal: No Solution Exploring Operation: 98-40=58, Resulting Numbers: [58] 58,47 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
[ 66, 3, 90, 5 ]
42
[ "5-3=2", "66*2=132", "132-90=42" ]
Current State: 42:[66, 3, 90, 5], Operations: [] Exploring Operation: 5-3=2, Resulting Numbers: [66, 90, 2] Generated Node #2: [66, 90, 2] from Operation: 5-3=2 Current State: 42:[66, 90, 2], Operations: ['5-3=2'] Exploring Operation: 66*2=132, Resulting Numbers: [90, 132] Generated Node #3: [90, 132] from Operation: 66*2=132 Current State: 42:[90, 132], Operations: ['5-3=2', '66*2=132'] Exploring Operation: 132-90=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[66, 3, 90, 5], Operations: [] Exploring Operation: 90-66=24, Resulting Numbers: [3, 5, 24] Generated Node #0,0: 42:[3, 5, 24] Operation: 90-66=24 Exploring Operation: 90/5=18, Resulting Numbers: [66, 3, 18] Generated Node #0,1: 42:[66, 3, 18] Operation: 90/5=18 Exploring Operation: 90/3=30, Resulting Numbers: [66, 5, 30] Generated Node #0,2: 42:[66, 5, 30] Operation: 90/3=30 Exploring Operation: 66/3=22, Resulting Numbers: [90, 5, 22] Generated Node #0,3: 42:[90, 5, 22] Operation: 66/3=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[3, 5, 24], Operations: ['90-66=24'] Exploring Operation: 24-3=21, Resulting Numbers: [5, 21] Generated Node #0,0,0: 42:[5, 21] Operation: 24-3=21 Exploring Operation: 24-5=19, Resulting Numbers: [3, 19] Generated Node #0,0,1: 42:[3, 19] Operation: 24-5=19 Exploring Operation: 5-3=2, Resulting Numbers: [24, 2] Generated Node #0,0,2: 42:[24, 2] Operation: 5-3=2 Exploring Operation: 24/3=8, Resulting Numbers: [5, 8] Generated Node #0,0,3: 42:[5, 8] Operation: 24/3=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[5, 21], Operations: ['90-66=24', '24-3=21'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,42 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 42:[3, 19], Operations: ['90-66=24', '24-5=19'] Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 42:[5, 8], Operations: ['90-66=24', '24/3=8'] Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,42 unequal: No Solution Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 42:[24, 2], Operations: ['90-66=24', '5-3=2'] Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,42 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[66, 3, 18], Operations: ['90/5=18'] Exploring Operation: 66-18=48, Resulting Numbers: [3, 48] Generated Node #0,1,0: 42:[3, 48] Operation: 66-18=48 Exploring Operation: 3+18=21, Resulting Numbers: [66, 21] Generated Node #0,1,1: 42:[66, 21] Operation: 3+18=21 Exploring Operation: 66/3=22, Resulting Numbers: [18, 22] Generated Node #0,1,2: 42:[18, 22] Operation: 66/3=22 Exploring Operation: 66-3=63, Resulting Numbers: [18, 63] Generated Node #0,1,3: 42:[18, 63] Operation: 66-3=63 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 42:[18, 22], Operations: ['90/5=18', '66/3=22'] Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,42 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 18*22=396, Resulting Numbers: [396] 396,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 42:[3, 48], Operations: ['90/5=18', '66-18=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,42 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,42 unequal: No Solution Exploring Operation: 3*48=144, Resulting Numbers: [144] 144,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 42:[66, 21], Operations: ['90/5=18', '3+18=21'] Exploring Operation: 66+21=87, Resulting Numbers: [87] 87,42 unequal: No Solution Exploring Operation: 66*21=1386, Resulting Numbers: [1386] 1386,42 unequal: No Solution Exploring Operation: 66-21=45, Resulting Numbers: [45] 45,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 42:[18, 63], Operations: ['90/5=18', '66-3=63'] Exploring Operation: 18+63=81, Resulting Numbers: [81] 81,42 unequal: No Solution Exploring Operation: 18*63=1134, Resulting Numbers: [1134] 1134,42 unequal: No Solution Exploring Operation: 63-18=45, Resulting Numbers: [45] 45,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 42:[66, 5, 30], Operations: ['90/3=30'] Exploring Operation: 66-5=61, Resulting Numbers: [30, 61] Generated Node #0,2,0: 42:[30, 61] Operation: 66-5=61 Exploring Operation: 30-5=25, Resulting Numbers: [66, 25] Generated Node #0,2,1: 42:[66, 25] Operation: 30-5=25 Exploring Operation: 66-30=36, Resulting Numbers: [5, 36] Generated Node #0,2,2: 42:[5, 36] Operation: 66-30=36 Exploring Operation: 30/5=6, Resulting Numbers: [66, 6] Generated Node #0,2,3: 42:[66, 6] Operation: 30/5=6 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 42:[5, 36], Operations: ['90/3=30', '66-30=36'] Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,42 unequal: No Solution Exploring Operation: 5+36=41, Resulting Numbers: [41] 41,42 unequal: No Solution Exploring Operation: 5*36=180, Resulting Numbers: [180] 180,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 42:[66, 6], Operations: ['90/3=30', '30/5=6'] Exploring Operation: 66-6=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 66+6=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,42 unequal: No Solution Exploring Operation: 66*6=396, Resulting Numbers: [396] 396,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 42:[30, 61], Operations: ['90/3=30', '66-5=61'] Exploring Operation: 30*61=1830, Resulting Numbers: [1830] 1830,42 unequal: No Solution Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,42 unequal: No Solution Exploring Operation: 30+61=91, Resulting Numbers: [91] 91,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 42:[66, 25], Operations: ['90/3=30', '30-5=25'] Exploring Operation: 66-25=41, Resulting Numbers: [41] 41,42 unequal: No Solution Exploring Operation: 66*25=1650, Resulting Numbers: [1650] 1650,42 unequal: No Solution Exploring Operation: 66+25=91, Resulting Numbers: [91] 91,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 42:[90, 5, 22], Operations: ['66/3=22'] Exploring Operation: 22-5=17, Resulting Numbers: [90, 17] Generated Node #0,3,0: 42:[90, 17] Operation: 22-5=17 Exploring Operation: 90-5=85, Resulting Numbers: [22, 85] Generated Node #0,3,1: 42:[22, 85] Operation: 90-5=85 Exploring Operation: 90/5=18, Resulting Numbers: [22, 18] Generated Node #0,3,2: 42:[22, 18] Operation: 90/5=18 Exploring Operation: 90-22=68, Resulting Numbers: [5, 68] Generated Node #0,3,3: 42:[5, 68] Operation: 90-22=68 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 42:[22, 18], Operations: ['66/3=22', '90/5=18'] Exploring Operation: 22+18=40, Resulting Numbers: [40] 40,42 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 22*18=396, Resulting Numbers: [396] 396,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 42:[5, 68], Operations: ['66/3=22', '90-22=68'] Exploring Operation: 5+68=73, Resulting Numbers: [73] 73,42 unequal: No Solution Exploring Operation: 5*68=340, Resulting Numbers: [340] 340,42 unequal: No Solution Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 42:[22, 85], Operations: ['66/3=22', '90-5=85'] Exploring Operation: 85-22=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 22+85=107, Resulting Numbers: [107] 107,42 unequal: No Solution Exploring Operation: 22*85=1870, Resulting Numbers: [1870] 1870,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 42:[90, 17], Operations: ['66/3=22', '22-5=17'] Exploring Operation: 90-17=73, Resulting Numbers: [73] 73,42 unequal: No Solution Exploring Operation: 90+17=107, Resulting Numbers: [107] 107,42 unequal: No Solution Exploring Operation: 90*17=1530, Resulting Numbers: [1530] 1530,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 12, 14, 88, 62 ]
24
[ "14-12=2", "88-62=26", "26-2=24" ]
Current State: 24:[12, 14, 88, 62], Operations: [] Exploring Operation: 14-12=2, Resulting Numbers: [88, 62, 2] Generated Node #2: [88, 62, 2] from Operation: 14-12=2 Current State: 24:[88, 62, 2], Operations: ['14-12=2'] Exploring Operation: 88-62=26, Resulting Numbers: [2, 26] Generated Node #3: [2, 26] from Operation: 88-62=26 Current State: 24:[2, 26], Operations: ['14-12=2', '88-62=26'] Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[12, 14, 88, 62], Operations: [] Exploring Operation: 88-62=26, Resulting Numbers: [12, 14, 26] Generated Node #0,0: 24:[12, 14, 26] Operation: 88-62=26 Exploring Operation: 88-14=74, Resulting Numbers: [12, 62, 74] Generated Node #0,1: 24:[12, 62, 74] Operation: 88-14=74 Exploring Operation: 88-12=76, Resulting Numbers: [14, 62, 76] Generated Node #0,2: 24:[14, 62, 76] Operation: 88-12=76 Exploring Operation: 62-14=48, Resulting Numbers: [12, 88, 48] Generated Node #0,3: 24:[12, 88, 48] Operation: 62-14=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[12, 14, 26], Operations: ['88-62=26'] Exploring Operation: 14-12=2, Resulting Numbers: [26, 2] Generated Node #0,0,0: 24:[26, 2] Operation: 14-12=2 Exploring Operation: 12+14=26, Resulting Numbers: [26, 26] Generated Node #0,0,1: 24:[26, 26] Operation: 12+14=26 Exploring Operation: 26-12=14, Resulting Numbers: [14, 14] Generated Node #0,0,2: 24:[14, 14] Operation: 26-12=14 Exploring Operation: 26-14=12, Resulting Numbers: [12, 12] Generated Node #0,0,3: 24:[12, 12] Operation: 26-14=12 Moving to Node #0,0,3 Current State: 24:[12, 12], Operations: ['88-62=26', '26-14=12'] Exploring Operation: 12-12=0, Resulting Numbers: [0] 0,24 unequal: No Solution Exploring Operation: 12+12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[12, 14, 88, 62], Operations: [] Exploring Operation: 88-62=26, Resulting Numbers: [12, 14, 26] Generated Node #0,0: 24:[12, 14, 26] Operation: 88-62=26 Moving to Node #0,0 Current State: 24:[12, 14, 26], Operations: ['88-62=26'] Exploring Operation: 26-14=12, Resulting Numbers: [12, 12] Generated Node #0,0,3: 24:[12, 12] Operation: 26-14=12 Moving to Node #0,0,3 Current State: 24:[12, 12], Operations: ['88-62=26', '26-14=12'] Exploring Operation: 12+12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 6, 69, 8, 19 ]
98
[ "6*8=48", "69-19=50", "48+50=98" ]
Current State: 98:[6, 69, 8, 19], Operations: [] Exploring Operation: 6*8=48, Resulting Numbers: [69, 19, 48] Generated Node #2: [69, 19, 48] from Operation: 6*8=48 Current State: 98:[69, 19, 48], Operations: ['6*8=48'] Exploring Operation: 69-19=50, Resulting Numbers: [48, 50] Generated Node #3: [48, 50] from Operation: 69-19=50 Current State: 98:[48, 50], Operations: ['6*8=48', '69-19=50'] Exploring Operation: 48+50=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[6, 69, 8, 19], Operations: [] Exploring Operation: 69-19=50, Resulting Numbers: [6, 8, 50] Generated Node #0,0: 98:[6, 8, 50] Operation: 69-19=50 Exploring Operation: 69-6=63, Resulting Numbers: [8, 19, 63] Generated Node #0,1: 98:[8, 19, 63] Operation: 69-6=63 Exploring Operation: 69-8=61, Resulting Numbers: [6, 19, 61] Generated Node #0,2: 98:[6, 19, 61] Operation: 69-8=61 Exploring Operation: 69+19=88, Resulting Numbers: [6, 8, 88] Generated Node #0,3: 98:[6, 8, 88] Operation: 69+19=88 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[6, 8, 50], Operations: ['69-19=50'] Exploring Operation: 6*8=48, Resulting Numbers: [50, 48] Generated Node #0,0,0: 98:[50, 48] Operation: 6*8=48 Exploring Operation: 50-6=44, Resulting Numbers: [8, 44] Generated Node #0,0,1: 98:[8, 44] Operation: 50-6=44 Exploring Operation: 6+8=14, Resulting Numbers: [50, 14] Generated Node #0,0,2: 98:[50, 14] Operation: 6+8=14 Exploring Operation: 8-6=2, Resulting Numbers: [50, 2] Generated Node #0,0,3: 98:[50, 2] Operation: 8-6=2 Moving to Node #0,0,2 Current State: 98:[50, 14], Operations: ['69-19=50', '6+8=14'] Exploring Operation: 50*14=700, Resulting Numbers: [700] 700,98 unequal: No Solution Exploring Operation: 50+14=64, Resulting Numbers: [64] 64,98 unequal: No Solution Exploring Operation: 50-14=36, Resulting Numbers: [36] 36,98 unequal: No Solution Moving to Node #0,0,3 Current State: 98:[50, 2], Operations: ['69-19=50', '8-6=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,98 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,98 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,98 unequal: No Solution Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[50, 48], Operations: ['69-19=50', '6*8=48'] Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,98 unequal: No Solution Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[6, 69, 8, 19], Operations: [] Exploring Operation: 69-19=50, Resulting Numbers: [6, 8, 50] Generated Node #0,0: 98:[6, 8, 50] Operation: 69-19=50 Moving to Node #0,0 Current State: 98:[6, 8, 50], Operations: ['69-19=50'] Exploring Operation: 6*8=48, Resulting Numbers: [50, 48] Generated Node #0,0,0: 98:[50, 48] Operation: 6*8=48 Moving to Node #0,0,0 Current State: 98:[50, 48], Operations: ['69-19=50', '6*8=48'] Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
sum_heuristic
[ 74, 55, 1, 10 ]
13
[ "74+55=129", "1+129=130", "130/10=13" ]
Current State: 13:[74, 55, 1, 10], Operations: [] Exploring Operation: 74+55=129, Resulting Numbers: [1, 10, 129] Generated Node #2: [1, 10, 129] from Operation: 74+55=129 Current State: 13:[1, 10, 129], Operations: ['74+55=129'] Exploring Operation: 1+129=130, Resulting Numbers: [10, 130] Generated Node #3: [10, 130] from Operation: 1+129=130 Current State: 13:[10, 130], Operations: ['74+55=129', '1+129=130'] Exploring Operation: 130/10=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[74, 55, 1, 10], Operations: [] Exploring Operation: 74-10=64, Resulting Numbers: [55, 1, 64] Generated Node #0,0: 13:[55, 1, 64] Operation: 74-10=64 Exploring Operation: 74-55=19, Resulting Numbers: [1, 10, 19] Generated Node #0,1: 13:[1, 10, 19] Operation: 74-55=19 Exploring Operation: 74-1=73, Resulting Numbers: [55, 10, 73] Generated Node #0,2: 13:[55, 10, 73] Operation: 74-1=73 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[1, 10, 19], Operations: ['74-55=19'] Exploring Operation: 1*10=10, Resulting Numbers: [19, 10] Generated Node #0,1,0: 13:[19, 10] Operation: 1*10=10 Exploring Operation: 1+10=11, Resulting Numbers: [19, 11] Generated Node #0,1,1: 13:[19, 11] Operation: 1+10=11 Exploring Operation: 19-1=18, Resulting Numbers: [10, 18] Generated Node #0,1,2: 13:[10, 18] Operation: 19-1=18 Moving to Node #0,1,1 Current State: 13:[19, 11], Operations: ['74-55=19', '1+10=11'] Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 19*11=209, Resulting Numbers: [209] 209,13 unequal: No Solution Exploring Operation: 19+11=30, Resulting Numbers: [30] 30,13 unequal: No Solution Moving to Node #0,1,2 Current State: 13:[10, 18], Operations: ['74-55=19', '19-1=18'] Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,13 unequal: No Solution Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,13 unequal: No Solution Moving to Node #0,1,0 Current State: 13:[19, 10], Operations: ['74-55=19', '1*10=10'] Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,13 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,13 unequal: No Solution No 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: 13:[55, 1, 64], Operations: ['74-10=64'] Exploring Operation: 64-1=63, Resulting Numbers: [55, 63] Generated Node #0,0,0: 13:[55, 63] Operation: 64-1=63 Exploring Operation: 64-55=9, Resulting Numbers: [1, 9] Generated Node #0,0,1: 13:[1, 9] Operation: 64-55=9 Exploring Operation: 55-1=54, Resulting Numbers: [64, 54] Generated Node #0,0,2: 13:[64, 54] Operation: 55-1=54 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 13:[1, 9], Operations: ['74-10=64', '64-55=9'] Exploring Operation: 1*9=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 9/1=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 1+9=10, Resulting Numbers: [10] 10,13 unequal: No Solution No 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: 13:[55, 63], Operations: ['74-10=64', '64-1=63'] Exploring Operation: 55*63=3465, Resulting Numbers: [3465] 3465,13 unequal: No Solution Exploring Operation: 55+63=118, Resulting Numbers: [118] 118,13 unequal: No Solution Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,13 unequal: No Solution No 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: 13:[64, 54], Operations: ['74-10=64', '55-1=54'] Exploring Operation: 64*54=3456, Resulting Numbers: [3456] 3456,13 unequal: No Solution Exploring Operation: 64-54=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 64+54=118, Resulting Numbers: [118] 118,13 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: 13:[55, 10, 73], Operations: ['74-1=73'] Exploring Operation: 73-10=63, Resulting Numbers: [55, 63] Generated Node #0,2,0: 13:[55, 63] Operation: 73-10=63 Exploring Operation: 55-10=45, Resulting Numbers: [73, 45] Generated Node #0,2,1: 13:[73, 45] Operation: 55-10=45 Exploring Operation: 73-55=18, Resulting Numbers: [10, 18] Generated Node #0,2,2: 13:[10, 18] Operation: 73-55=18 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 13:[10, 18], Operations: ['74-1=73', '73-55=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,13 unequal: No Solution No 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: 13:[55, 63], Operations: ['74-1=73', '73-10=63'] Exploring Operation: 55+63=118, Resulting Numbers: [118] 118,13 unequal: No Solution Exploring Operation: 55*63=3465, Resulting Numbers: [3465] 3465,13 unequal: No Solution Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,13 unequal: No Solution No 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: 13:[73, 45], Operations: ['74-1=73', '55-10=45'] Exploring Operation: 73-45=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 73+45=118, Resulting Numbers: [118] 118,13 unequal: No Solution Exploring Operation: 73*45=3285, Resulting Numbers: [3285] 3285,13 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
[ 32, 64, 79, 94 ]
32
[ "64/32=2", "94/2=47", "79-47=32" ]
Current State: 32:[32, 64, 79, 94], Operations: [] Exploring Operation: 64/32=2, Resulting Numbers: [79, 94, 2] Generated Node #2: [79, 94, 2] from Operation: 64/32=2 Current State: 32:[79, 94, 2], Operations: ['64/32=2'] Exploring Operation: 94/2=47, Resulting Numbers: [79, 47] Generated Node #3: [79, 47] from Operation: 94/2=47 Current State: 32:[79, 47], Operations: ['64/32=2', '94/2=47'] Exploring Operation: 79-47=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[32, 64, 79, 94], Operations: [] Exploring Operation: 94-79=15, Resulting Numbers: [32, 64, 15] Generated Node #0,0: 32:[32, 64, 15] Operation: 94-79=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[32, 64, 15], Operations: ['94-79=15'] Exploring Operation: 64-32=32, Resulting Numbers: [15, 32] Generated Node #0,0,0: 32:[15, 32] Operation: 64-32=32 Moving to Node #0,0,0 Current State: 32:[15, 32], Operations: ['94-79=15', '64-32=32'] Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 96, 4, 87, 98 ]
81
[ "96-4=92", "98-87=11", "92-11=81" ]
Current State: 81:[96, 4, 87, 98], Operations: [] Exploring Operation: 96-4=92, Resulting Numbers: [87, 98, 92] Generated Node #2: [87, 98, 92] from Operation: 96-4=92 Current State: 81:[87, 98, 92], Operations: ['96-4=92'] Exploring Operation: 98-87=11, Resulting Numbers: [92, 11] Generated Node #3: [92, 11] from Operation: 98-87=11 Current State: 81:[92, 11], Operations: ['96-4=92', '98-87=11'] Exploring Operation: 92-11=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[96, 4, 87, 98], Operations: [] Exploring Operation: 98-87=11, Resulting Numbers: [96, 4, 11] Generated Node #0,0: 81:[96, 4, 11] Operation: 98-87=11 Exploring Operation: 96-87=9, Resulting Numbers: [4, 98, 9] Generated Node #0,1: 81:[4, 98, 9] Operation: 96-87=9 Exploring Operation: 96/4=24, Resulting Numbers: [87, 98, 24] Generated Node #0,2: 81:[87, 98, 24] Operation: 96/4=24 Exploring Operation: 98-96=2, Resulting Numbers: [4, 87, 2] Generated Node #0,3: 81:[4, 87, 2] Operation: 98-96=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 81:[4, 87, 2], Operations: ['98-96=2'] Exploring Operation: 4*2=8, Resulting Numbers: [87, 8] Generated Node #0,3,0: 81:[87, 8] Operation: 4*2=8 Exploring Operation: 87-4=83, Resulting Numbers: [2, 83] Generated Node #0,3,1: 81:[2, 83] Operation: 87-4=83 Exploring Operation: 87-2=85, Resulting Numbers: [4, 85] Generated Node #0,3,2: 81:[4, 85] Operation: 87-2=85 Exploring Operation: 4-2=2, Resulting Numbers: [87, 2] Generated Node #0,3,3: 81:[87, 2] Operation: 4-2=2 Moving to Node #0,3,1 Current State: 81:[2, 83], Operations: ['98-96=2', '87-4=83'] Exploring Operation: 2*83=166, Resulting Numbers: [166] 166,81 unequal: No Solution Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[96, 4, 87, 98], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [4, 87, 2] Generated Node #0,3: 81:[4, 87, 2] Operation: 98-96=2 Moving to Node #0,3 Current State: 81:[4, 87, 2], Operations: ['98-96=2'] Exploring Operation: 87-4=83, Resulting Numbers: [2, 83] Generated Node #0,3,1: 81:[2, 83] Operation: 87-4=83 Moving to Node #0,3,1 Current State: 81:[2, 83], Operations: ['98-96=2', '87-4=83'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 51, 16, 82, 3 ]
55
[ "51*3=153", "16+82=98", "153-98=55" ]
Current State: 55:[51, 16, 82, 3], Operations: [] Exploring Operation: 51*3=153, Resulting Numbers: [16, 82, 153] Generated Node #2: [16, 82, 153] from Operation: 51*3=153 Current State: 55:[16, 82, 153], Operations: ['51*3=153'] Exploring Operation: 16+82=98, Resulting Numbers: [153, 98] Generated Node #3: [153, 98] from Operation: 16+82=98 Current State: 55:[153, 98], Operations: ['51*3=153', '16+82=98'] Exploring Operation: 153-98=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[51, 16, 82, 3], Operations: [] Exploring Operation: 82-16=66, Resulting Numbers: [51, 3, 66] Generated Node #0,0: 55:[51, 3, 66] Operation: 82-16=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[51, 3, 66], Operations: ['82-16=66'] Exploring Operation: 66-51=15, Resulting Numbers: [3, 15] Generated Node #0,0,0: 55:[3, 15] Operation: 66-51=15 Moving to Node #0,0,0 Current State: 55:[3, 15], Operations: ['82-16=66', '66-51=15'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,55 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
[ 9, 48, 23, 16 ]
35
[ "9+23=32", "48/16=3", "32+3=35" ]
Current State: 35:[9, 48, 23, 16], Operations: [] Exploring Operation: 9+23=32, Resulting Numbers: [48, 16, 32] Generated Node #2: [48, 16, 32] from Operation: 9+23=32 Current State: 35:[48, 16, 32], Operations: ['9+23=32'] Exploring Operation: 48/16=3, Resulting Numbers: [32, 3] Generated Node #3: [32, 3] from Operation: 48/16=3 Current State: 35:[32, 3], Operations: ['9+23=32', '48/16=3'] Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[9, 48, 23, 16], Operations: [] Exploring Operation: 23-16=7, Resulting Numbers: [9, 48, 7] Generated Node #0,0: 35:[9, 48, 7] Operation: 23-16=7 Exploring Operation: 48/16=3, Resulting Numbers: [9, 23, 3] Generated Node #0,1: 35:[9, 23, 3] Operation: 48/16=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[9, 48, 7], Operations: ['23-16=7'] Exploring Operation: 48-9=39, Resulting Numbers: [7, 39] Generated Node #0,0,0: 35:[7, 39] Operation: 48-9=39 Exploring Operation: 48-7=41, Resulting Numbers: [9, 41] Generated Node #0,0,1: 35:[9, 41] Operation: 48-7=41 Moving to Node #0,0,0 Current State: 35:[7, 39], Operations: ['23-16=7', '48-9=39'] Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,35 unequal: No Solution Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[9, 41], Operations: ['23-16=7', '48-7=41'] Exploring Operation: 9+41=50, Resulting Numbers: [50] 50,35 unequal: No Solution Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[9, 23, 3], Operations: ['48/16=3'] Exploring Operation: 23-9=14, Resulting Numbers: [3, 14] Generated Node #0,1,0: 35:[3, 14] Operation: 23-9=14 Exploring Operation: 9+23=32, Resulting Numbers: [3, 32] Generated Node #0,1,1: 35:[3, 32] Operation: 9+23=32 Moving to Node #0,1,1 Current State: 35:[3, 32], Operations: ['48/16=3', '9+23=32'] Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[9, 48, 23, 16], Operations: [] Exploring Operation: 48/16=3, Resulting Numbers: [9, 23, 3] Generated Node #0,1: 35:[9, 23, 3] Operation: 48/16=3 Moving to Node #0,1 Current State: 35:[9, 23, 3], Operations: ['48/16=3'] Exploring Operation: 9+23=32, Resulting Numbers: [3, 32] Generated Node #0,1,1: 35:[3, 32] Operation: 9+23=32 Moving to Node #0,1,1 Current State: 35:[3, 32], Operations: ['48/16=3', '9+23=32'] Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 94, 2, 97, 87 ]
93
[ "97-94=3", "2*3=6", "87+6=93" ]
Current State: 93:[94, 2, 97, 87], Operations: [] Exploring Operation: 97-94=3, Resulting Numbers: [2, 87, 3] Generated Node #2: [2, 87, 3] from Operation: 97-94=3 Current State: 93:[2, 87, 3], Operations: ['97-94=3'] Exploring Operation: 2*3=6, Resulting Numbers: [87, 6] Generated Node #3: [87, 6] from Operation: 2*3=6 Current State: 93:[87, 6], Operations: ['97-94=3', '2*3=6'] Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[94, 2, 97, 87], Operations: [] Exploring Operation: 94-87=7, Resulting Numbers: [2, 97, 7] Generated Node #0,0: 93:[2, 97, 7] Operation: 94-87=7 Exploring Operation: 2+87=89, Resulting Numbers: [94, 97, 89] Generated Node #0,1: 93:[94, 97, 89] Operation: 2+87=89 Exploring Operation: 97-87=10, Resulting Numbers: [94, 2, 10] Generated Node #0,2: 93:[94, 2, 10] Operation: 97-87=10 Exploring Operation: 97-2=95, Resulting Numbers: [94, 87, 95] Generated Node #0,3: 93:[94, 87, 95] Operation: 97-2=95 Exploring Operation: 97-94=3, Resulting Numbers: [2, 87, 3] Generated Node #0,4: 93:[2, 87, 3] Operation: 97-94=3 Start Sub Search at level 1: Moving to Node #0,4 Current State: 93:[2, 87, 3], Operations: ['97-94=3'] Exploring Operation: 87+3=90, Resulting Numbers: [2, 90] Generated Node #0,4,0: 93:[2, 90] Operation: 87+3=90 Exploring Operation: 87/3=29, Resulting Numbers: [2, 29] Generated Node #0,4,1: 93:[2, 29] Operation: 87/3=29 Exploring Operation: 2+87=89, Resulting Numbers: [3, 89] Generated Node #0,4,2: 93:[3, 89] Operation: 2+87=89 Exploring Operation: 2+3=5, Resulting Numbers: [87, 5] Generated Node #0,4,3: 93:[87, 5] Operation: 2+3=5 Exploring Operation: 87-2=85, Resulting Numbers: [3, 85] Generated Node #0,4,4: 93:[3, 85] Operation: 87-2=85 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 93:[2, 29], Operations: ['97-94=3', '87/3=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,93 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,93 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 93:[2, 90], Operations: ['97-94=3', '87+3=90'] Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 2*90=180, Resulting Numbers: [180] 180,93 unequal: No Solution Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,93 unequal: No Solution Exploring Operation: 2+90=92, Resulting Numbers: [92] 92,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 93:[3, 89], Operations: ['97-94=3', '2+87=89'] Exploring Operation: 3+89=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 3*89=267, Resulting Numbers: [267] 267,93 unequal: No Solution Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 93:[87, 5], Operations: ['97-94=3', '2+3=5'] Exploring Operation: 87-5=82, Resulting Numbers: [82] 82,93 unequal: No Solution Exploring Operation: 87*5=435, Resulting Numbers: [435] 435,93 unequal: No Solution Exploring Operation: 87+5=92, Resulting Numbers: [92] 92,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 93:[3, 85], Operations: ['97-94=3', '87-2=85'] Exploring Operation: 3+85=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 3*85=255, Resulting Numbers: [255] 255,93 unequal: No Solution Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[2, 97, 7], Operations: ['94-87=7'] Exploring Operation: 2+7=9, Resulting Numbers: [97, 9] Generated Node #0,0,0: 93:[97, 9] Operation: 2+7=9 Exploring Operation: 2+97=99, Resulting Numbers: [7, 99] Generated Node #0,0,1: 93:[7, 99] Operation: 2+97=99 Exploring Operation: 97-7=90, Resulting Numbers: [2, 90] Generated Node #0,0,2: 93:[2, 90] Operation: 97-7=90 Exploring Operation: 7-2=5, Resulting Numbers: [97, 5] Generated Node #0,0,3: 93:[97, 5] Operation: 7-2=5 Exploring Operation: 97-2=95, Resulting Numbers: [7, 95] Generated Node #0,0,4: 93:[7, 95] Operation: 97-2=95 Moving to Node #0,0,2 Current State: 93:[2, 90], Operations: ['94-87=7', '97-7=90'] Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,93 unequal: No Solution Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 2+90=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 2*90=180, Resulting Numbers: [180] 180,93 unequal: No Solution Moving to Node #0,0,4 Current State: 93:[7, 95], Operations: ['94-87=7', '97-2=95'] Exploring Operation: 95-7=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 7*95=665, Resulting Numbers: [665] 665,93 unequal: No Solution Exploring Operation: 7+95=102, Resulting Numbers: [102] 102,93 unequal: No Solution Moving to Node #0,0,3 Current State: 93:[97, 5], Operations: ['94-87=7', '7-2=5'] Exploring Operation: 97-5=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 97*5=485, Resulting Numbers: [485] 485,93 unequal: No Solution Exploring Operation: 97+5=102, Resulting Numbers: [102] 102,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[97, 9], Operations: ['94-87=7', '2+7=9'] Exploring Operation: 97*9=873, Resulting Numbers: [873] 873,93 unequal: No Solution Exploring Operation: 97+9=106, Resulting Numbers: [106] 106,93 unequal: No Solution Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[7, 99], Operations: ['94-87=7', '2+97=99'] Exploring Operation: 7*99=693, Resulting Numbers: [693] 693,93 unequal: No Solution Exploring Operation: 7+99=106, Resulting Numbers: [106] 106,93 unequal: No Solution Exploring Operation: 99-7=92, Resulting Numbers: [92] 92,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[94, 97, 89], Operations: ['2+87=89'] Exploring Operation: 97-94=3, Resulting Numbers: [89, 3] Generated Node #0,1,0: 93:[89, 3] Operation: 97-94=3 Exploring Operation: 97+89=186, Resulting Numbers: [94, 186] Generated Node #0,1,1: 93:[94, 186] Operation: 97+89=186 Exploring Operation: 94-89=5, Resulting Numbers: [97, 5] Generated Node #0,1,2: 93:[97, 5] Operation: 94-89=5 Exploring Operation: 94+89=183, Resulting Numbers: [97, 183] Generated Node #0,1,3: 93:[97, 183] Operation: 94+89=183 Exploring Operation: 97-89=8, Resulting Numbers: [94, 8] Generated Node #0,1,4: 93:[94, 8] Operation: 97-89=8 Moving to Node #0,1,0 Current State: 93:[89, 3], Operations: ['2+87=89', '97-94=3'] Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 89*3=267, Resulting Numbers: [267] 267,93 unequal: No Solution Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,93 unequal: No Solution Moving to Node #0,1,4 Current State: 93:[94, 8], Operations: ['2+87=89', '97-89=8'] Exploring Operation: 94+8=102, Resulting Numbers: [102] 102,93 unequal: No Solution Exploring Operation: 94-8=86, Resulting Numbers: [86] 86,93 unequal: No Solution Exploring Operation: 94*8=752, Resulting Numbers: [752] 752,93 unequal: No Solution Moving to Node #0,1,2 Current State: 93:[97, 5], Operations: ['2+87=89', '94-89=5'] Exploring Operation: 97-5=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 97*5=485, Resulting Numbers: [485] 485,93 unequal: No Solution Exploring Operation: 97+5=102, Resulting Numbers: [102] 102,93 unequal: No Solution Moving to Node #0,1,1 Current State: 93:[94, 186], Operations: ['2+87=89', '97+89=186'] Exploring Operation: 94*186=17484, Resulting Numbers: [17484] 17484,93 unequal: No Solution Exploring Operation: 186-94=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 94+186=280, Resulting Numbers: [280] 280,93 unequal: No Solution Moving to Node #0,1,3 Current State: 93:[97, 183], Operations: ['2+87=89', '94+89=183'] Exploring Operation: 97+183=280, Resulting Numbers: [280] 280,93 unequal: No Solution Exploring Operation: 183-97=86, Resulting Numbers: [86] 86,93 unequal: No Solution Exploring Operation: 97*183=17751, Resulting Numbers: [17751] 17751,93 unequal: No Solution No 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: 93:[94, 2, 10], Operations: ['97-87=10'] Exploring Operation: 10/2=5, Resulting Numbers: [94, 5] Generated Node #0,2,0: 93:[94, 5] Operation: 10/2=5 Exploring Operation: 10-2=8, Resulting Numbers: [94, 8] Generated Node #0,2,1: 93:[94, 8] Operation: 10-2=8 Exploring Operation: 94-2=92, Resulting Numbers: [10, 92] Generated Node #0,2,2: 93:[10, 92] Operation: 94-2=92 Exploring Operation: 94+2=96, Resulting Numbers: [10, 96] Generated Node #0,2,3: 93:[10, 96] Operation: 94+2=96 Exploring Operation: 94-10=84, Resulting Numbers: [2, 84] Generated Node #0,2,4: 93:[2, 84] Operation: 94-10=84 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 93:[94, 5], Operations: ['97-87=10', '10/2=5'] Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,93 unequal: No Solution Exploring Operation: 94*5=470, Resulting Numbers: [470] 470,93 unequal: No Solution Exploring Operation: 94+5=99, Resulting Numbers: [99] 99,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 93:[94, 8], Operations: ['97-87=10', '10-2=8'] Exploring Operation: 94-8=86, Resulting Numbers: [86] 86,93 unequal: No Solution Exploring Operation: 94+8=102, Resulting Numbers: [102] 102,93 unequal: No Solution Exploring Operation: 94*8=752, Resulting Numbers: [752] 752,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 93:[10, 92], Operations: ['97-87=10', '94-2=92'] Exploring Operation: 10*92=920, Resulting Numbers: [920] 920,93 unequal: No Solution Exploring Operation: 92-10=82, Resulting Numbers: [82] 82,93 unequal: No Solution Exploring Operation: 10+92=102, Resulting Numbers: [102] 102,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 93:[10, 96], Operations: ['97-87=10', '94+2=96'] Exploring Operation: 10+96=106, Resulting Numbers: [106] 106,93 unequal: No Solution Exploring Operation: 96-10=86, Resulting Numbers: [86] 86,93 unequal: No Solution Exploring Operation: 10*96=960, Resulting Numbers: [960] 960,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 93:[2, 84], Operations: ['97-87=10', '94-10=84'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,93 unequal: No Solution Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,93 unequal: No Solution Exploring Operation: 2*84=168, Resulting Numbers: [168] 168,93 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 93:[94, 87, 95], Operations: ['97-2=95'] Exploring Operation: 95-87=8, Resulting Numbers: [94, 8] Generated Node #0,3,0: 93:[94, 8] Operation: 95-87=8 Exploring Operation: 95-94=1, Resulting Numbers: [87, 1] Generated Node #0,3,1: 93:[87, 1] Operation: 95-94=1 Exploring Operation: 94-87=7, Resulting Numbers: [95, 7] Generated Node #0,3,2: 93:[95, 7] Operation: 94-87=7 Exploring Operation: 87+95=182, Resulting Numbers: [94, 182] Generated Node #0,3,3: 93:[94, 182] Operation: 87+95=182 Exploring Operation: 94+87=181, Resulting Numbers: [95, 181] Generated Node #0,3,4: 93:[95, 181] Operation: 94+87=181 Moving to Node #0,3,0 Current State: 93:[94, 8], Operations: ['97-2=95', '95-87=8'] Exploring Operation: 94+8=102, Resulting Numbers: [102] 102,93 unequal: No Solution Exploring Operation: 94*8=752, Resulting Numbers: [752] 752,93 unequal: No Solution Exploring Operation: 94-8=86, Resulting Numbers: [86] 86,93 unequal: No Solution Moving to Node #0,3,2 Current State: 93:[95, 7], Operations: ['97-2=95', '94-87=7'] Exploring Operation: 95+7=102, Resulting Numbers: [102] 102,93 unequal: No Solution Exploring Operation: 95-7=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 95*7=665, Resulting Numbers: [665] 665,93 unequal: No Solution Moving to Node #0,3,1 Current State: 93:[87, 1], Operations: ['97-2=95', '95-94=1'] Exploring Operation: 87-1=86, Resulting Numbers: [86] 86,93 unequal: No Solution Exploring Operation: 87+1=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 87/1=87, Resulting Numbers: [87] 87,93 unequal: No Solution Exploring Operation: 87*1=87, Resulting Numbers: [87] 87,93 unequal: No Solution Moving to Node #0,3,3 Current State: 93:[94, 182], Operations: ['97-2=95', '87+95=182'] Exploring Operation: 182-94=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 94+182=276, Resulting Numbers: [276] 276,93 unequal: No Solution Exploring Operation: 94*182=17108, Resulting Numbers: [17108] 17108,93 unequal: No Solution Moving to Node #0,3,4 Current State: 93:[95, 181], Operations: ['97-2=95', '94+87=181'] Exploring Operation: 95*181=17195, Resulting Numbers: [17195] 17195,93 unequal: No Solution Exploring Operation: 181-95=86, Resulting Numbers: [86] 86,93 unequal: No Solution Exploring Operation: 95+181=276, Resulting Numbers: [276] 276,93 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
[ 64, 69, 4, 66 ]
13
[ "64/4=16", "69-66=3", "16-3=13" ]
Current State: 13:[64, 69, 4, 66], Operations: [] Exploring Operation: 64/4=16, Resulting Numbers: [69, 66, 16] Generated Node #2: [69, 66, 16] from Operation: 64/4=16 Current State: 13:[69, 66, 16], Operations: ['64/4=16'] Exploring Operation: 69-66=3, Resulting Numbers: [16, 3] Generated Node #3: [16, 3] from Operation: 69-66=3 Current State: 13:[16, 3], Operations: ['64/4=16', '69-66=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[64, 69, 4, 66], Operations: [] Exploring Operation: 69-64=5, Resulting Numbers: [4, 66, 5] Generated Node #0,0: 13:[4, 66, 5] Operation: 69-64=5 Exploring Operation: 64/4=16, Resulting Numbers: [69, 66, 16] Generated Node #0,1: 13:[69, 66, 16] Operation: 64/4=16 Exploring Operation: 69-66=3, Resulting Numbers: [64, 4, 3] Generated Node #0,2: 13:[64, 4, 3] Operation: 69-66=3 Exploring Operation: 66-64=2, Resulting Numbers: [69, 4, 2] Generated Node #0,3: 13:[69, 4, 2] Operation: 66-64=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[4, 66, 5], Operations: ['69-64=5'] Exploring Operation: 66-5=61, Resulting Numbers: [4, 61] Generated Node #0,0,0: 13:[4, 61] Operation: 66-5=61 Exploring Operation: 4*5=20, Resulting Numbers: [66, 20] Generated Node #0,0,1: 13:[66, 20] Operation: 4*5=20 Exploring Operation: 66-4=62, Resulting Numbers: [5, 62] Generated Node #0,0,2: 13:[5, 62] Operation: 66-4=62 Exploring Operation: 4+5=9, Resulting Numbers: [66, 9] Generated Node #0,0,3: 13:[66, 9] Operation: 4+5=9 Moving to Node #0,0,0 Current State: 13:[4, 61], Operations: ['69-64=5', '66-5=61'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,13 unequal: No Solution Exploring Operation: 4+61=65, Resulting Numbers: [65] 65,13 unequal: No Solution Exploring Operation: 4*61=244, Resulting Numbers: [244] 244,13 unequal: No Solution Moving to Node #0,0,3 Current State: 13:[66, 9], Operations: ['69-64=5', '4+5=9'] Exploring Operation: 66+9=75, Resulting Numbers: [75] 75,13 unequal: No Solution Exploring Operation: 66*9=594, Resulting Numbers: [594] 594,13 unequal: No Solution Exploring Operation: 66-9=57, Resulting Numbers: [57] 57,13 unequal: No Solution Moving to Node #0,0,2 Current State: 13:[5, 62], Operations: ['69-64=5', '66-4=62'] Exploring Operation: 62-5=57, Resulting Numbers: [57] 57,13 unequal: No Solution Exploring Operation: 5*62=310, Resulting Numbers: [310] 310,13 unequal: No Solution Exploring Operation: 5+62=67, Resulting Numbers: [67] 67,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[66, 20], Operations: ['69-64=5', '4*5=20'] Exploring Operation: 66*20=1320, Resulting Numbers: [1320] 1320,13 unequal: No Solution Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,13 unequal: No Solution Exploring Operation: 66+20=86, Resulting Numbers: [86] 86,13 unequal: No Solution No 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: 13:[64, 4, 3], Operations: ['69-66=3'] Exploring Operation: 64/4=16, Resulting Numbers: [3, 16] Generated Node #0,2,0: 13:[3, 16] Operation: 64/4=16 Exploring Operation: 64-4=60, Resulting Numbers: [3, 60] Generated Node #0,2,1: 13:[3, 60] Operation: 64-4=60 Exploring Operation: 64-3=61, Resulting Numbers: [4, 61] Generated Node #0,2,2: 13:[4, 61] Operation: 64-3=61 Exploring Operation: 4*3=12, Resulting Numbers: [64, 12] Generated Node #0,2,3: 13:[64, 12] Operation: 4*3=12 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 13:[3, 16], Operations: ['69-66=3', '64/4=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[64, 69, 4, 66], Operations: [] Exploring Operation: 69-66=3, Resulting Numbers: [64, 4, 3] Generated Node #0,2: 13:[64, 4, 3] Operation: 69-66=3 Moving to Node #0,2 Current State: 13:[64, 4, 3], Operations: ['69-66=3'] Exploring Operation: 64/4=16, Resulting Numbers: [3, 16] Generated Node #0,2,0: 13:[3, 16] Operation: 64/4=16 Moving to Node #0,2,0 Current State: 13:[3, 16], Operations: ['69-66=3', '64/4=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic
[ 91, 24, 49, 85 ]
19
[ "91+24=115", "49+85=134", "134-115=19" ]
Current State: 19:[91, 24, 49, 85], Operations: [] Exploring Operation: 91+24=115, Resulting Numbers: [49, 85, 115] Generated Node #2: [49, 85, 115] from Operation: 91+24=115 Current State: 19:[49, 85, 115], Operations: ['91+24=115'] Exploring Operation: 49+85=134, Resulting Numbers: [115, 134] Generated Node #3: [115, 134] from Operation: 49+85=134 Current State: 19:[115, 134], Operations: ['91+24=115', '49+85=134'] Exploring Operation: 134-115=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[91, 24, 49, 85], Operations: [] Exploring Operation: 91-85=6, Resulting Numbers: [24, 49, 6] Generated Node #0,0: 19:[24, 49, 6] Operation: 91-85=6 Moving to Node #0,0 Current State: 19:[24, 49, 6], Operations: ['91-85=6'] Exploring Operation: 49-24=25, Resulting Numbers: [6, 25] Generated Node #0,0,0: 19:[6, 25] Operation: 49-24=25 Moving to Node #0,0,0 Current State: 19:[6, 25], Operations: ['91-85=6', '49-24=25'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[91, 24, 49, 85], Operations: [] Exploring Operation: 91-85=6, Resulting Numbers: [24, 49, 6] Generated Node #0,0: 19:[24, 49, 6] Operation: 91-85=6 Moving to Node #0,0 Current State: 19:[24, 49, 6], Operations: ['91-85=6'] Exploring Operation: 49-24=25, Resulting Numbers: [6, 25] Generated Node #0,0,0: 19:[6, 25] Operation: 49-24=25 Moving to Node #0,0,0 Current State: 19:[6, 25], Operations: ['91-85=6', '49-24=25'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 60, 1, 21, 4 ]
84
[ "60-1=59", "21+4=25", "59+25=84" ]
Current State: 84:[60, 1, 21, 4], Operations: [] Exploring Operation: 60-1=59, Resulting Numbers: [21, 4, 59] Generated Node #2: [21, 4, 59] from Operation: 60-1=59 Current State: 84:[21, 4, 59], Operations: ['60-1=59'] Exploring Operation: 21+4=25, Resulting Numbers: [59, 25] Generated Node #3: [59, 25] from Operation: 21+4=25 Current State: 84:[59, 25], Operations: ['60-1=59', '21+4=25'] Exploring Operation: 59+25=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[60, 1, 21, 4], Operations: [] Exploring Operation: 60/4=15, Resulting Numbers: [1, 21, 15] Generated Node #0,0: 84:[1, 21, 15] Operation: 60/4=15 Exploring Operation: 60-21=39, Resulting Numbers: [1, 4, 39] Generated Node #0,1: 84:[1, 4, 39] Operation: 60-21=39 Exploring Operation: 60-4=56, Resulting Numbers: [1, 21, 56] Generated Node #0,2: 84:[1, 21, 56] Operation: 60-4=56 Exploring Operation: 60+21=81, Resulting Numbers: [1, 4, 81] Generated Node #0,3: 84:[1, 4, 81] Operation: 60+21=81 Exploring Operation: 60-1=59, Resulting Numbers: [21, 4, 59] Generated Node #0,4: 84:[21, 4, 59] Operation: 60-1=59 Moving to Node #0,0 Current State: 84:[1, 21, 15], Operations: ['60/4=15'] Exploring Operation: 1*21=21, Resulting Numbers: [15, 21] Generated Node #0,0,0: 84:[15, 21] Operation: 1*21=21 Exploring Operation: 15/1=15, Resulting Numbers: [21, 15] Generated Node #0,0,1: 84:[21, 15] Operation: 15/1=15 Exploring Operation: 21/1=21, Resulting Numbers: [15, 21] Generated Node #0,0,2: 84:[15, 21] Operation: 21/1=21 Exploring Operation: 15-1=14, Resulting Numbers: [21, 14] Generated Node #0,0,3: 84:[21, 14] Operation: 15-1=14 Exploring Operation: 1*15=15, Resulting Numbers: [21, 15] Generated Node #0,0,4: 84:[21, 15] Operation: 1*15=15 Moving to Node #0,3 Current State: 84:[1, 4, 81], Operations: ['60+21=81'] Exploring Operation: 4/1=4, Resulting Numbers: [81, 4] Generated Node #0,3,0: 84:[81, 4] Operation: 4/1=4 Exploring Operation: 1*4=4, Resulting Numbers: [81, 4] Generated Node #0,3,1: 84:[81, 4] Operation: 1*4=4 Exploring Operation: 1+81=82, Resulting Numbers: [4, 82] Generated Node #0,3,2: 84:[4, 82] Operation: 1+81=82 Exploring Operation: 4-1=3, Resulting Numbers: [81, 3] Generated Node #0,3,3: 84:[81, 3] Operation: 4-1=3 Exploring Operation: 4+81=85, Resulting Numbers: [1, 85] Generated Node #0,3,4: 84:[1, 85] Operation: 4+81=85 Moving to Node #0,1 Current State: 84:[1, 4, 39], Operations: ['60-21=39'] Exploring Operation: 4/1=4, Resulting Numbers: [39, 4] Generated Node #0,1,0: 84:[39, 4] Operation: 4/1=4 Exploring Operation: 1+39=40, Resulting Numbers: [4, 40] Generated Node #0,1,1: 84:[4, 40] Operation: 1+39=40 Exploring Operation: 4+39=43, Resulting Numbers: [1, 43] Generated Node #0,1,2: 84:[1, 43] Operation: 4+39=43 Exploring Operation: 4-1=3, Resulting Numbers: [39, 3] Generated Node #0,1,3: 84:[39, 3] Operation: 4-1=3 Exploring Operation: 1*4=4, Resulting Numbers: [39, 4] Generated Node #0,1,4: 84:[39, 4] Operation: 1*4=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[4, 40], Operations: ['60-21=39', '1+39=40'] Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 4*40=160, Resulting Numbers: [160] 160,84 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,84 unequal: No Solution Exploring Operation: 4+40=44, Resulting Numbers: [44] 44,84 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 #0,1,2 Current State: 84:[1, 43], Operations: ['60-21=39', '4+39=43'] Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,84 unequal: No Solution Exploring Operation: 1*43=43, Resulting Numbers: [43] 43,84 unequal: No Solution Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,84 unequal: No Solution Exploring Operation: 1+43=44, Resulting Numbers: [44] 44,84 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 #0,1,0 Current State: 84:[39, 4], Operations: ['60-21=39', '4/1=4'] Exploring Operation: 39*4=156, Resulting Numbers: [156] 156,84 unequal: No Solution Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,84 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,84 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 #0,1,3 Current State: 84:[39, 3], Operations: ['60-21=39', '4-1=3'] Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,84 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 39*3=117, Resulting Numbers: [117] 117,84 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 #0,1,4 Current State: 84:[39, 4], Operations: ['60-21=39', '1*4=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,84 unequal: No Solution Exploring Operation: 39*4=156, Resulting Numbers: [156] 156,84 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,84 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: 84:[1, 21, 56], Operations: ['60-4=56'] Exploring Operation: 21+56=77, Resulting Numbers: [1, 77] Generated Node #0,2,0: 84:[1, 77] Operation: 21+56=77 Exploring Operation: 56-21=35, Resulting Numbers: [1, 35] Generated Node #0,2,1: 84:[1, 35] Operation: 56-21=35 Exploring Operation: 21/1=21, Resulting Numbers: [56, 21] Generated Node #0,2,2: 84:[56, 21] Operation: 21/1=21 Exploring Operation: 1*21=21, Resulting Numbers: [56, 21] Generated Node #0,2,3: 84:[56, 21] Operation: 1*21=21 Exploring Operation: 56-1=55, Resulting Numbers: [21, 55] Generated Node #0,2,4: 84:[21, 55] Operation: 56-1=55 Moving to Node #0,4 Current State: 84:[21, 4, 59], Operations: ['60-1=59'] Exploring Operation: 21+59=80, Resulting Numbers: [4, 80] Generated Node #0,4,0: 84:[4, 80] Operation: 21+59=80 Exploring Operation: 21+4=25, Resulting Numbers: [59, 25] Generated Node #0,4,1: 84:[59, 25] Operation: 21+4=25 Exploring Operation: 21*4=84, Resulting Numbers: [59, 84] Generated Node #0,4,2: 84:[59, 84] Operation: 21*4=84 Exploring Operation: 59-21=38, Resulting Numbers: [4, 38] Generated Node #0,4,3: 84:[4, 38] Operation: 59-21=38 Exploring Operation: 59-4=55, Resulting Numbers: [21, 55] Generated Node #0,4,4: 84:[21, 55] Operation: 59-4=55 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 84:[4, 80], Operations: ['60-1=59', '21+59=80'] Exploring Operation: 4*80=320, Resulting Numbers: [320] 320,84 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,84 unequal: No Solution Exploring Operation: 4+80=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[60, 1, 21, 4], Operations: [] Exploring Operation: 60-1=59, Resulting Numbers: [21, 4, 59] Generated Node #0,4: 84:[21, 4, 59] Operation: 60-1=59 Moving to Node #0,4 Current State: 84:[21, 4, 59], Operations: ['60-1=59'] Exploring Operation: 21+59=80, Resulting Numbers: [4, 80] Generated Node #0,4,0: 84:[4, 80] Operation: 21+59=80 Moving to Node #0,4,0 Current State: 84:[4, 80], Operations: ['60-1=59', '21+59=80'] Exploring Operation: 4+80=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.951389
hs_5
mult_heuristic
[ 25, 49, 33, 72 ]
97
[ "33*72=2376", "49+2376=2425", "2425/25=97" ]
Current State: 97:[25, 49, 33, 72], Operations: [] Exploring Operation: 33*72=2376, Resulting Numbers: [25, 49, 2376] Generated Node #2: [25, 49, 2376] from Operation: 33*72=2376 Current State: 97:[25, 49, 2376], Operations: ['33*72=2376'] Exploring Operation: 49+2376=2425, Resulting Numbers: [25, 2425] Generated Node #3: [25, 2425] from Operation: 49+2376=2425 Current State: 97:[25, 2425], Operations: ['33*72=2376', '49+2376=2425'] Exploring Operation: 2425/25=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[25, 49, 33, 72], Operations: [] Exploring Operation: 25+72=97, Resulting Numbers: [49, 33, 97] Generated Node #0,0: 97:[49, 33, 97] Operation: 25+72=97 Exploring Operation: 33+72=105, Resulting Numbers: [25, 49, 105] Generated Node #0,1: 97:[25, 49, 105] Operation: 33+72=105 Exploring Operation: 25+33=58, Resulting Numbers: [49, 72, 58] Generated Node #0,2: 97:[49, 72, 58] Operation: 25+33=58 Exploring Operation: 25+49=74, Resulting Numbers: [33, 72, 74] Generated Node #0,3: 97:[33, 72, 74] Operation: 25+49=74 Exploring Operation: 49+33=82, Resulting Numbers: [25, 72, 82] Generated Node #0,4: 97:[25, 72, 82] Operation: 49+33=82 Moving to Node #0,0 Current State: 97:[49, 33, 97], Operations: ['25+72=97'] Exploring Operation: 33+97=130, Resulting Numbers: [49, 130] Generated Node #0,0,0: 97:[49, 130] Operation: 33+97=130 Exploring Operation: 49+33=82, Resulting Numbers: [97, 82] Generated Node #0,0,1: 97:[97, 82] Operation: 49+33=82 Exploring Operation: 49-33=16, Resulting Numbers: [97, 16] Generated Node #0,0,2: 97:[97, 16] Operation: 49-33=16 Exploring Operation: 97-33=64, Resulting Numbers: [49, 64] Generated Node #0,0,3: 97:[49, 64] Operation: 97-33=64 Exploring Operation: 49+97=146, Resulting Numbers: [33, 146] Generated Node #0,0,4: 97:[33, 146] Operation: 49+97=146 Moving to Node #0,3 Current State: 97:[33, 72, 74], Operations: ['25+49=74'] Exploring Operation: 33+72=105, Resulting Numbers: [74, 105] Generated Node #0,3,0: 97:[74, 105] Operation: 33+72=105 Exploring Operation: 33+74=107, Resulting Numbers: [72, 107] Generated Node #0,3,1: 97:[72, 107] Operation: 33+74=107 Exploring Operation: 74-33=41, Resulting Numbers: [72, 41] Generated Node #0,3,2: 97:[72, 41] Operation: 74-33=41 Exploring Operation: 72+74=146, Resulting Numbers: [33, 146] Generated Node #0,3,3: 97:[33, 146] Operation: 72+74=146 Exploring Operation: 72-33=39, Resulting Numbers: [74, 39] Generated Node #0,3,4: 97:[74, 39] Operation: 72-33=39 Moving to Node #0,2 Current State: 97:[49, 72, 58], Operations: ['25+33=58'] Exploring Operation: 58-49=9, Resulting Numbers: [72, 9] Generated Node #0,2,0: 97:[72, 9] Operation: 58-49=9 Exploring Operation: 49+72=121, Resulting Numbers: [58, 121] Generated Node #0,2,1: 97:[58, 121] Operation: 49+72=121 Exploring Operation: 49+58=107, Resulting Numbers: [72, 107] Generated Node #0,2,2: 97:[72, 107] Operation: 49+58=107 Exploring Operation: 72+58=130, Resulting Numbers: [49, 130] Generated Node #0,2,3: 97:[49, 130] Operation: 72+58=130 Exploring Operation: 72-49=23, Resulting Numbers: [58, 23] Generated Node #0,2,4: 97:[58, 23] Operation: 72-49=23 Moving to Node #0,4 Current State: 97:[25, 72, 82], Operations: ['49+33=82'] Exploring Operation: 72+82=154, Resulting Numbers: [25, 154] Generated Node #0,4,0: 97:[25, 154] Operation: 72+82=154 Exploring Operation: 25+82=107, Resulting Numbers: [72, 107] Generated Node #0,4,1: 97:[72, 107] Operation: 25+82=107 Exploring Operation: 72-25=47, Resulting Numbers: [82, 47] Generated Node #0,4,2: 97:[82, 47] Operation: 72-25=47 Exploring Operation: 25+72=97, Resulting Numbers: [82, 97] Generated Node #0,4,3: 97:[82, 97] Operation: 25+72=97 Exploring Operation: 82-25=57, Resulting Numbers: [72, 57] Generated Node #0,4,4: 97:[72, 57] Operation: 82-25=57 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 97:[82, 97], Operations: ['49+33=82', '25+72=97'] Exploring Operation: 82*97=7954, Resulting Numbers: [7954] 7954,97 unequal: No Solution Exploring Operation: 82+97=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 97-82=15, Resulting Numbers: [15] 15,97 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 #0,4,1 Current State: 97:[72, 107], Operations: ['49+33=82', '25+82=107'] Exploring Operation: 72+107=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 107-72=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 72*107=7704, Resulting Numbers: [7704] 7704,97 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 #0,4,2 Current State: 97:[82, 47], Operations: ['49+33=82', '72-25=47'] Exploring Operation: 82-47=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 82+47=129, Resulting Numbers: [129] 129,97 unequal: No Solution Exploring Operation: 82*47=3854, Resulting Numbers: [3854] 3854,97 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 #0,4,4 Current State: 97:[72, 57], Operations: ['49+33=82', '82-25=57'] Exploring Operation: 72*57=4104, Resulting Numbers: [4104] 4104,97 unequal: No Solution Exploring Operation: 72+57=129, Resulting Numbers: [129] 129,97 unequal: No Solution Exploring Operation: 72-57=15, Resulting Numbers: [15] 15,97 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 #0,4,0 Current State: 97:[25, 154], Operations: ['49+33=82', '72+82=154'] Exploring Operation: 25*154=3850, Resulting Numbers: [3850] 3850,97 unequal: No Solution Exploring Operation: 154-25=129, Resulting Numbers: [129] 129,97 unequal: No Solution Exploring Operation: 25+154=179, Resulting Numbers: [179] 179,97 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: 97:[25, 49, 105], Operations: ['33+72=105'] Exploring Operation: 105-49=56, Resulting Numbers: [25, 56] Generated Node #0,1,0: 97:[25, 56] Operation: 105-49=56 Exploring Operation: 25+49=74, Resulting Numbers: [105, 74] Generated Node #0,1,1: 97:[105, 74] Operation: 25+49=74 Exploring Operation: 25+105=130, Resulting Numbers: [49, 130] Generated Node #0,1,2: 97:[49, 130] Operation: 25+105=130 Exploring Operation: 49-25=24, Resulting Numbers: [105, 24] Generated Node #0,1,3: 97:[105, 24] Operation: 49-25=24 Exploring Operation: 105-25=80, Resulting Numbers: [49, 80] Generated Node #0,1,4: 97:[49, 80] Operation: 105-25=80 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[105, 74], Operations: ['33+72=105', '25+49=74'] Exploring Operation: 105+74=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 105*74=7770, Resulting Numbers: [7770] 7770,97 unequal: No Solution Exploring Operation: 105-74=31, Resulting Numbers: [31] 31,97 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 #0,1,4 Current State: 97:[49, 80], Operations: ['33+72=105', '105-25=80'] Exploring Operation: 80-49=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 49*80=3920, Resulting Numbers: [3920] 3920,97 unequal: No Solution Exploring Operation: 49+80=129, Resulting Numbers: [129] 129,97 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 #0,1,2 Current State: 97:[49, 130], Operations: ['33+72=105', '25+105=130'] Exploring Operation: 49+130=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 130-49=81, Resulting Numbers: [81] 81,97 unequal: No Solution Exploring Operation: 49*130=6370, Resulting Numbers: [6370] 6370,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 97:[105, 24], Operations: ['33+72=105', '49-25=24'] Exploring Operation: 105*24=2520, Resulting Numbers: [2520] 2520,97 unequal: No Solution Exploring Operation: 105-24=81, Resulting Numbers: [81] 81,97 unequal: No Solution Exploring Operation: 105+24=129, Resulting Numbers: [129] 129,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[25, 56], Operations: ['33+72=105', '105-49=56'] Exploring Operation: 25*56=1400, Resulting Numbers: [1400] 1400,97 unequal: No Solution Exploring Operation: 25+56=81, Resulting Numbers: [81] 81,97 unequal: No Solution Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,97 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: 97:[97, 82], Operations: ['25+72=97', '49+33=82'] Exploring Operation: 97+82=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 97*82=7954, Resulting Numbers: [7954] 7954,97 unequal: No Solution Exploring Operation: 97-82=15, Resulting Numbers: [15] 15,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[74, 105], Operations: ['25+49=74', '33+72=105'] Exploring Operation: 105-74=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 74+105=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 74*105=7770, Resulting Numbers: [7770] 7770,97 unequal: No Solution Moving to Node #0,3,1 Current State: 97:[72, 107], Operations: ['25+49=74', '33+74=107'] Exploring Operation: 107-72=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 72*107=7704, Resulting Numbers: [7704] 7704,97 unequal: No Solution Exploring Operation: 72+107=179, Resulting Numbers: [179] 179,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[72, 107], Operations: ['25+33=58', '49+58=107'] Exploring Operation: 72*107=7704, Resulting Numbers: [7704] 7704,97 unequal: No Solution Exploring Operation: 72+107=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 107-72=35, Resulting Numbers: [35] 35,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[58, 121], Operations: ['25+33=58', '49+72=121'] Exploring Operation: 121-58=63, Resulting Numbers: [63] 63,97 unequal: No Solution Exploring Operation: 58+121=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 58*121=7018, Resulting Numbers: [7018] 7018,97 unequal: No Solution Moving to Node #0,2,3 Current State: 97:[49, 130], Operations: ['25+33=58', '72+58=130'] Exploring Operation: 49*130=6370, Resulting Numbers: [6370] 6370,97 unequal: No Solution Exploring Operation: 49+130=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 130-49=81, Resulting Numbers: [81] 81,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[97, 16], Operations: ['25+72=97', '49-33=16'] Exploring Operation: 97-16=81, Resulting Numbers: [81] 81,97 unequal: No Solution Exploring Operation: 97+16=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 97*16=1552, Resulting Numbers: [1552] 1552,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[49, 130], Operations: ['25+72=97', '33+97=130'] Exploring Operation: 49*130=6370, Resulting Numbers: [6370] 6370,97 unequal: No Solution Exploring Operation: 49+130=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 130-49=81, Resulting Numbers: [81] 81,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[49, 64], Operations: ['25+72=97', '97-33=64'] Exploring Operation: 49+64=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,97 unequal: No Solution Exploring Operation: 49*64=3136, Resulting Numbers: [3136] 3136,97 unequal: No Solution Moving to Node #0,3,2 Current State: 97:[72, 41], Operations: ['25+49=74', '74-33=41'] Exploring Operation: 72+41=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 72-41=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 72*41=2952, Resulting Numbers: [2952] 2952,97 unequal: No Solution Moving to Node #0,3,4 Current State: 97:[74, 39], Operations: ['25+49=74', '72-33=39'] Exploring Operation: 74-39=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 74+39=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 74*39=2886, Resulting Numbers: [2886] 2886,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[72, 9], Operations: ['25+33=58', '58-49=9'] Exploring Operation: 72/9=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 72+9=81, Resulting Numbers: [81] 81,97 unequal: No Solution Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,97 unequal: No Solution Exploring Operation: 72*9=648, Resulting Numbers: [648] 648,97 unequal: No Solution Moving to Node #0,2,4 Current State: 97:[58, 23], Operations: ['25+33=58', '72-49=23'] Exploring Operation: 58*23=1334, Resulting Numbers: [1334] 1334,97 unequal: No Solution Exploring Operation: 58-23=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 58+23=81, Resulting Numbers: [81] 81,97 unequal: No Solution Moving to Node #0,0,4 Current State: 97:[33, 146], Operations: ['25+72=97', '49+97=146'] Exploring Operation: 146-33=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 33+146=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 33*146=4818, Resulting Numbers: [4818] 4818,97 unequal: No Solution Moving to Node #0,3,3 Current State: 97:[33, 146], Operations: ['25+49=74', '72+74=146'] Exploring Operation: 146-33=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 33+146=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 33*146=4818, Resulting Numbers: [4818] 4818,97 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 37, 13, 47, 1 ]
23
[ "37-13=24", "47*1=47", "47-24=23" ]
Current State: 23:[37, 13, 47, 1], Operations: [] Exploring Operation: 37-13=24, Resulting Numbers: [47, 1, 24] Generated Node #2: [47, 1, 24] from Operation: 37-13=24 Current State: 23:[47, 1, 24], Operations: ['37-13=24'] Exploring Operation: 47*1=47, Resulting Numbers: [24, 47] Generated Node #3: [24, 47] from Operation: 47*1=47 Current State: 23:[24, 47], Operations: ['37-13=24', '47*1=47'] Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[37, 13, 47, 1], Operations: [] Exploring Operation: 37-13=24, Resulting Numbers: [47, 1, 24] Generated Node #0,0: 23:[47, 1, 24] Operation: 37-13=24 Exploring Operation: 37-1=36, Resulting Numbers: [13, 47, 36] Generated Node #0,1: 23:[13, 47, 36] Operation: 37-1=36 Exploring Operation: 47-37=10, Resulting Numbers: [13, 1, 10] Generated Node #0,2: 23:[13, 1, 10] Operation: 47-37=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[13, 1, 10], Operations: ['47-37=10'] Exploring Operation: 1+10=11, Resulting Numbers: [13, 11] Generated Node #0,2,0: 23:[13, 11] Operation: 1+10=11 Exploring Operation: 13+10=23, Resulting Numbers: [1, 23] Generated Node #0,2,1: 23:[1, 23] Operation: 13+10=23 Exploring Operation: 13+1=14, Resulting Numbers: [10, 14] Generated Node #0,2,2: 23:[10, 14] Operation: 13+1=14 Moving to Node #0,2,0 Current State: 23:[13, 11], Operations: ['47-37=10', '1+10=11'] Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 13*11=143, Resulting Numbers: [143] 143,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[1, 23], Operations: ['47-37=10', '13+10=23'] Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 1*23=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[37, 13, 47, 1], Operations: [] Exploring Operation: 47-37=10, Resulting Numbers: [13, 1, 10] Generated Node #0,2: 23:[13, 1, 10] Operation: 47-37=10 Moving to Node #0,2 Current State: 23:[13, 1, 10], Operations: ['47-37=10'] Exploring Operation: 13+10=23, Resulting Numbers: [1, 23] Generated Node #0,2,1: 23:[1, 23] Operation: 13+10=23 Moving to Node #0,2,1 Current State: 23:[1, 23], Operations: ['47-37=10', '13+10=23'] Exploring Operation: 1*23=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 74, 50, 70, 70 ]
30
[ "74-70=4", "50+70=120", "120/4=30" ]
Current State: 30:[74, 50, 70, 70], Operations: [] Exploring Operation: 74-70=4, Resulting Numbers: [50, 4] Generated Node #2: [50, 4] from Operation: 74-70=4 Current State: 30:[50, 4], Operations: ['74-70=4'] Exploring Operation: 50+70=120, Resulting Numbers: [4, 120] Generated Node #3: [4, 120] from Operation: 50+70=120 Current State: 30:[4, 120], Operations: ['74-70=4', '50+70=120'] Exploring Operation: 120/4=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[74, 50, 70, 70], Operations: [] Exploring Operation: 74-70=4, Resulting Numbers: [50, 70, 4] Generated Node #0,0: 30:[50, 70, 4] Operation: 74-70=4 Exploring Operation: 74-50=24, Resulting Numbers: [70, 70, 24] Generated Node #0,1: 30:[70, 70, 24] Operation: 74-50=24 Exploring Operation: 74-70=4, Resulting Numbers: [50, 70, 4] Generated Node #0,2: 30:[50, 70, 4] Operation: 74-70=4 Exploring Operation: 70-70=0, Resulting Numbers: [74, 50, 0] Generated Node #0,3: 30:[74, 50, 0] Operation: 70-70=0 Exploring Operation: 70/70=1, Resulting Numbers: [74, 50, 1] Generated Node #0,4: 30:[74, 50, 1] Operation: 70/70=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[50, 70, 4], Operations: ['74-70=4'] Exploring Operation: 50-4=46, Resulting Numbers: [70, 46] Generated Node #0,0,0: 30:[70, 46] Operation: 50-4=46 Exploring Operation: 70-4=66, Resulting Numbers: [50, 66] Generated Node #0,0,1: 30:[50, 66] Operation: 70-4=66 Exploring Operation: 70-50=20, Resulting Numbers: [4, 20] Generated Node #0,0,2: 30:[4, 20] Operation: 70-50=20 Exploring Operation: 50+4=54, Resulting Numbers: [70, 54] Generated Node #0,0,3: 30:[70, 54] Operation: 50+4=54 Exploring Operation: 70+4=74, Resulting Numbers: [50, 74] Generated Node #0,0,4: 30:[50, 74] Operation: 70+4=74 Moving to Node #0,0,2 Current State: 30:[4, 20], Operations: ['74-70=4', '70-50=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,30 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,30 unequal: No Solution Moving to Node #0,0,1 Current State: 30:[50, 66], Operations: ['74-70=4', '70-4=66'] Exploring Operation: 50*66=3300, Resulting Numbers: [3300] 3300,30 unequal: No Solution Exploring Operation: 66-50=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 50+66=116, Resulting Numbers: [116] 116,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[70, 46], Operations: ['74-70=4', '50-4=46'] Exploring Operation: 70+46=116, Resulting Numbers: [116] 116,30 unequal: No Solution Exploring Operation: 70-46=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 70*46=3220, Resulting Numbers: [3220] 3220,30 unequal: No Solution Moving to Node #0,0,3 Current State: 30:[70, 54], Operations: ['74-70=4', '50+4=54'] Exploring Operation: 70-54=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 70*54=3780, Resulting Numbers: [3780] 3780,30 unequal: No Solution Exploring Operation: 70+54=124, Resulting Numbers: [124] 124,30 unequal: No Solution Moving to Node #0,0,4 Current State: 30:[50, 74], Operations: ['74-70=4', '70+4=74'] Exploring Operation: 74-50=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 50*74=3700, Resulting Numbers: [3700] 3700,30 unequal: No Solution Exploring Operation: 50+74=124, Resulting Numbers: [124] 124,30 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:[50, 70, 4], Operations: ['74-70=4'] Exploring Operation: 50-4=46, Resulting Numbers: [70, 46] Generated Node #0,2,0: 30:[70, 46] Operation: 50-4=46 Exploring Operation: 70-4=66, Resulting Numbers: [50, 66] Generated Node #0,2,1: 30:[50, 66] Operation: 70-4=66 Exploring Operation: 70-50=20, Resulting Numbers: [4, 20] Generated Node #0,2,2: 30:[4, 20] Operation: 70-50=20 Exploring Operation: 50+4=54, Resulting Numbers: [70, 54] Generated Node #0,2,3: 30:[70, 54] Operation: 50+4=54 Exploring Operation: 70+4=74, Resulting Numbers: [50, 74] Generated Node #0,2,4: 30:[50, 74] Operation: 70+4=74 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 30:[4, 20], Operations: ['74-70=4', '70-50=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,30 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 30:[70, 46], Operations: ['74-70=4', '50-4=46'] Exploring Operation: 70-46=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 70+46=116, Resulting Numbers: [116] 116,30 unequal: No Solution Exploring Operation: 70*46=3220, Resulting Numbers: [3220] 3220,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 30:[50, 66], Operations: ['74-70=4', '70-4=66'] Exploring Operation: 50*66=3300, Resulting Numbers: [3300] 3300,30 unequal: No Solution Exploring Operation: 50+66=116, Resulting Numbers: [116] 116,30 unequal: No Solution Exploring Operation: 66-50=16, Resulting Numbers: [16] 16,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 30:[70, 54], Operations: ['74-70=4', '50+4=54'] Exploring Operation: 70+54=124, Resulting Numbers: [124] 124,30 unequal: No Solution Exploring Operation: 70*54=3780, Resulting Numbers: [3780] 3780,30 unequal: No Solution Exploring Operation: 70-54=16, Resulting Numbers: [16] 16,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 30:[50, 74], Operations: ['74-70=4', '70+4=74'] Exploring Operation: 50*74=3700, Resulting Numbers: [3700] 3700,30 unequal: No Solution Exploring Operation: 74-50=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 50+74=124, Resulting Numbers: [124] 124,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 30:[74, 50, 1], Operations: ['70/70=1'] Exploring Operation: 74*1=74, Resulting Numbers: [50, 74] Generated Node #0,4,0: 30:[50, 74] Operation: 74*1=74 Exploring Operation: 74-50=24, Resulting Numbers: [1, 24] Generated Node #0,4,1: 30:[1, 24] Operation: 74-50=24 Exploring Operation: 74/1=74, Resulting Numbers: [50, 74] Generated Node #0,4,2: 30:[50, 74] Operation: 74/1=74 Exploring Operation: 50-1=49, Resulting Numbers: [74, 49] Generated Node #0,4,3: 30:[74, 49] Operation: 50-1=49 Exploring Operation: 74-1=73, Resulting Numbers: [50, 73] Generated Node #0,4,4: 30:[50, 73] Operation: 74-1=73 Moving to Node #0,4,1 Current State: 30:[1, 24], Operations: ['70/70=1', '74-50=24'] Exploring Operation: 1*24=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,30 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,30 unequal: No Solution Moving to Node #0,4,4 Current State: 30:[50, 73], Operations: ['70/70=1', '74-1=73'] Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,30 unequal: No Solution Exploring Operation: 50*73=3650, Resulting Numbers: [3650] 3650,30 unequal: No Solution Exploring Operation: 50+73=123, Resulting Numbers: [123] 123,30 unequal: No Solution Moving to Node #0,4,3 Current State: 30:[74, 49], Operations: ['70/70=1', '50-1=49'] Exploring Operation: 74-49=25, Resulting Numbers: [25] 25,30 unequal: No Solution Exploring Operation: 74*49=3626, Resulting Numbers: [3626] 3626,30 unequal: No Solution Exploring Operation: 74+49=123, Resulting Numbers: [123] 123,30 unequal: No Solution Moving to Node #0,4,0 Current State: 30:[50, 74], Operations: ['70/70=1', '74*1=74'] Exploring Operation: 50*74=3700, Resulting Numbers: [3700] 3700,30 unequal: No Solution Exploring Operation: 50+74=124, Resulting Numbers: [124] 124,30 unequal: No Solution Exploring Operation: 74-50=24, Resulting Numbers: [24] 24,30 unequal: No Solution Moving to Node #0,4,2 Current State: 30:[50, 74], Operations: ['70/70=1', '74/1=74'] Exploring Operation: 50*74=3700, Resulting Numbers: [3700] 3700,30 unequal: No Solution Exploring Operation: 50+74=124, Resulting Numbers: [124] 124,30 unequal: No Solution Exploring Operation: 74-50=24, Resulting Numbers: [24] 24,30 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 #0,3 Current State: 30:[74, 50, 0], Operations: ['70-70=0'] Exploring Operation: 74-50=24, Resulting Numbers: [0, 24] Generated Node #0,3,0: 30:[0, 24] Operation: 74-50=24 Exploring Operation: 50*0=0, Resulting Numbers: [74, 0] Generated Node #0,3,1: 30:[74, 0] Operation: 50*0=0 Exploring Operation: 74+0=74, Resulting Numbers: [50, 74] Generated Node #0,3,2: 30:[50, 74] Operation: 74+0=74 Exploring Operation: 74*0=0, Resulting Numbers: [50, 0] Generated Node #0,3,3: 30:[50, 0] Operation: 74*0=0 Exploring Operation: 74-0=74, Resulting Numbers: [50, 74] Generated Node #0,3,4: 30:[50, 74] Operation: 74-0=74 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 30:[0, 24], Operations: ['70-70=0', '74-50=24'] Exploring Operation: 24-0=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 0*24=0, Resulting Numbers: [0] 0,30 unequal: No Solution Exploring Operation: 0+24=24, Resulting Numbers: [24] 24,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 30:[50, 0], Operations: ['70-70=0', '74*0=0'] Exploring Operation: 50-0=50, Resulting Numbers: [50] 50,30 unequal: No Solution Exploring Operation: 50*0=0, Resulting Numbers: [0] 0,30 unequal: No Solution Exploring Operation: 50+0=50, Resulting Numbers: [50] 50,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 30:[74, 0], Operations: ['70-70=0', '50*0=0'] Exploring Operation: 74*0=0, Resulting Numbers: [0] 0,30 unequal: No Solution Exploring Operation: 74-0=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 74+0=74, Resulting Numbers: [74] 74,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 30:[50, 74], Operations: ['70-70=0', '74+0=74'] Exploring Operation: 74-50=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 50+74=124, Resulting Numbers: [124] 124,30 unequal: No Solution Exploring Operation: 50*74=3700, Resulting Numbers: [3700] 3700,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 30:[50, 74], Operations: ['70-70=0', '74-0=74'] Exploring Operation: 74-50=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 50*74=3700, Resulting Numbers: [3700] 3700,30 unequal: No Solution Exploring Operation: 50+74=124, Resulting Numbers: [124] 124,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[70, 70, 24], Operations: ['74-50=24'] Exploring Operation: 70-24=46, Resulting Numbers: [70, 46] Generated Node #0,1,0: 30:[70, 46] Operation: 70-24=46 Exploring Operation: 70/70=1, Resulting Numbers: [24, 1] Generated Node #0,1,1: 30:[24, 1] Operation: 70/70=1 Exploring Operation: 70-24=46, Resulting Numbers: [70, 46] Generated Node #0,1,2: 30:[70, 46] Operation: 70-24=46 Exploring Operation: 70-70=0, Resulting Numbers: [24, 0] Generated Node #0,1,3: 30:[24, 0] Operation: 70-70=0 Exploring Operation: 70+24=94, Resulting Numbers: [70, 94] Generated Node #0,1,4: 30:[70, 94] Operation: 70+24=94 Moving to Node #0,1,1 Current State: 30:[24, 1], Operations: ['74-50=24', '70/70=1'] Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,30 unequal: No Solution Exploring Operation: 24*1=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,30 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,30 unequal: No Solution Moving to Node #0,1,3 Current State: 30:[24, 0], Operations: ['74-50=24', '70-70=0'] Exploring Operation: 24*0=0, Resulting Numbers: [0] 0,30 unequal: No Solution Exploring Operation: 24+0=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 24-0=24, Resulting Numbers: [24] 24,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[70, 46], Operations: ['74-50=24', '70-24=46'] Exploring Operation: 70-46=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 70*46=3220, Resulting Numbers: [3220] 3220,30 unequal: No Solution Exploring Operation: 70+46=116, Resulting Numbers: [116] 116,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[70, 46], Operations: ['74-50=24', '70-24=46'] Exploring Operation: 70+46=116, Resulting Numbers: [116] 116,30 unequal: No Solution Exploring Operation: 70*46=3220, Resulting Numbers: [3220] 3220,30 unequal: No Solution Exploring Operation: 70-46=24, Resulting Numbers: [24] 24,30 unequal: No Solution Moving to Node #0,1,4 Current State: 30:[70, 94], Operations: ['74-50=24', '70+24=94'] Exploring Operation: 70*94=6580, Resulting Numbers: [6580] 6580,30 unequal: No Solution Exploring Operation: 70+94=164, Resulting Numbers: [164] 164,30 unequal: No Solution Exploring Operation: 94-70=24, Resulting Numbers: [24] 24,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 47, 8, 22, 40 ]
23
[ "47-8=39", "22+40=62", "62-39=23" ]
Current State: 23:[47, 8, 22, 40], Operations: [] Exploring Operation: 47-8=39, Resulting Numbers: [22, 40, 39] Generated Node #2: [22, 40, 39] from Operation: 47-8=39 Current State: 23:[22, 40, 39], Operations: ['47-8=39'] Exploring Operation: 22+40=62, Resulting Numbers: [39, 62] Generated Node #3: [39, 62] from Operation: 22+40=62 Current State: 23:[39, 62], Operations: ['47-8=39', '22+40=62'] Exploring Operation: 62-39=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[47, 8, 22, 40], Operations: [] Exploring Operation: 47-22=25, Resulting Numbers: [8, 40, 25] Generated Node #0,0: 23:[8, 40, 25] Operation: 47-22=25 Exploring Operation: 40-8=32, Resulting Numbers: [47, 22, 32] Generated Node #0,1: 23:[47, 22, 32] Operation: 40-8=32 Exploring Operation: 47-8=39, Resulting Numbers: [22, 40, 39] Generated Node #0,2: 23:[22, 40, 39] Operation: 47-8=39 Exploring Operation: 47-40=7, Resulting Numbers: [8, 22, 7] Generated Node #0,3: 23:[8, 22, 7] Operation: 47-40=7 Start Sub Search at level 1: Moving to Node #0,3 Current State: 23:[8, 22, 7], Operations: ['47-40=7'] Exploring Operation: 8+22=30, Resulting Numbers: [7, 30] Generated Node #0,3,0: 23:[7, 30] Operation: 8+22=30 Exploring Operation: 8-7=1, Resulting Numbers: [22, 1] Generated Node #0,3,1: 23:[22, 1] Operation: 8-7=1 Exploring Operation: 8+7=15, Resulting Numbers: [22, 15] Generated Node #0,3,2: 23:[22, 15] Operation: 8+7=15 Exploring Operation: 22+7=29, Resulting Numbers: [8, 29] Generated Node #0,3,3: 23:[8, 29] Operation: 22+7=29 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 23:[22, 15], Operations: ['47-40=7', '8+7=15'] Exploring Operation: 22*15=330, Resulting Numbers: [330] 330,23 unequal: No Solution Exploring Operation: 22+15=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,23 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 #0,3,3 Current State: 23:[8, 29], Operations: ['47-40=7', '22+7=29'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,23 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 #0,3,0 Current State: 23:[7, 30], Operations: ['47-40=7', '8+22=30'] Exploring Operation: 7*30=210, Resulting Numbers: [210] 210,23 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[47, 8, 22, 40], Operations: [] Exploring Operation: 47-40=7, Resulting Numbers: [8, 22, 7] Generated Node #0,3: 23:[8, 22, 7] Operation: 47-40=7 Moving to Node #0,3 Current State: 23:[8, 22, 7], Operations: ['47-40=7'] Exploring Operation: 8+22=30, Resulting Numbers: [7, 30] Generated Node #0,3,0: 23:[7, 30] Operation: 8+22=30 Moving to Node #0,3,0 Current State: 23:[7, 30], Operations: ['47-40=7', '8+22=30'] Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 99, 83, 5, 69 ]
29
[ "83-69=14", "5*14=70", "99-70=29" ]
Current State: 29:[99, 83, 5, 69], Operations: [] Exploring Operation: 83-69=14, Resulting Numbers: [99, 5, 14] Generated Node #2: [99, 5, 14] from Operation: 83-69=14 Current State: 29:[99, 5, 14], Operations: ['83-69=14'] Exploring Operation: 5*14=70, Resulting Numbers: [99, 70] Generated Node #3: [99, 70] from Operation: 5*14=70 Current State: 29:[99, 70], Operations: ['83-69=14', '5*14=70'] Exploring Operation: 99-70=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[99, 83, 5, 69], Operations: [] Exploring Operation: 99-83=16, Resulting Numbers: [5, 69, 16] Generated Node #0,0: 29:[5, 69, 16] Operation: 99-83=16 Exploring Operation: 83-69=14, Resulting Numbers: [99, 5, 14] Generated Node #0,1: 29:[99, 5, 14] Operation: 83-69=14 Exploring Operation: 99-69=30, Resulting Numbers: [83, 5, 30] Generated Node #0,2: 29:[83, 5, 30] Operation: 99-69=30 Moving to Node #0,0 Current State: 29:[5, 69, 16], Operations: ['99-83=16'] Exploring Operation: 69-16=53, Resulting Numbers: [5, 53] Generated Node #0,0,0: 29:[5, 53] Operation: 69-16=53 Exploring Operation: 5+16=21, Resulting Numbers: [69, 21] Generated Node #0,0,1: 29:[69, 21] Operation: 5+16=21 Exploring Operation: 69-5=64, Resulting Numbers: [16, 64] Generated Node #0,0,2: 29:[16, 64] Operation: 69-5=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[5, 53], Operations: ['99-83=16', '69-16=53'] Exploring Operation: 5+53=58, Resulting Numbers: [58] 58,29 unequal: No Solution Exploring Operation: 5*53=265, Resulting Numbers: [265] 265,29 unequal: No Solution Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 29:[69, 21], Operations: ['99-83=16', '5+16=21'] Exploring Operation: 69-21=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 69+21=90, Resulting Numbers: [90] 90,29 unequal: No Solution Exploring Operation: 69*21=1449, Resulting Numbers: [1449] 1449,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 29:[16, 64], Operations: ['99-83=16', '69-5=64'] Exploring Operation: 16+64=80, Resulting Numbers: [80] 80,29 unequal: No Solution Exploring Operation: 64/16=4, Resulting Numbers: [4] 4,29 unequal: No Solution Exploring Operation: 64-16=48, Resulting Numbers: [48] 48,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 29:[83, 5, 30], Operations: ['99-69=30'] Exploring Operation: 83-30=53, Resulting Numbers: [5, 53] Generated Node #0,2,0: 29:[5, 53] Operation: 83-30=53 Exploring Operation: 83-5=78, Resulting Numbers: [30, 78] Generated Node #0,2,1: 29:[30, 78] Operation: 83-5=78 Exploring Operation: 30-5=25, Resulting Numbers: [83, 25] Generated Node #0,2,2: 29:[83, 25] Operation: 30-5=25 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[5, 53], Operations: ['99-69=30', '83-30=53'] Exploring Operation: 5+53=58, Resulting Numbers: [58] 58,29 unequal: No Solution Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 5*53=265, Resulting Numbers: [265] 265,29 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 #0,2,1 Current State: 29:[30, 78], Operations: ['99-69=30', '83-5=78'] Exploring Operation: 30+78=108, Resulting Numbers: [108] 108,29 unequal: No Solution Exploring Operation: 30*78=2340, Resulting Numbers: [2340] 2340,29 unequal: No Solution Exploring Operation: 78-30=48, Resulting Numbers: [48] 48,29 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 #0,2,2 Current State: 29:[83, 25], Operations: ['99-69=30', '30-5=25'] Exploring Operation: 83*25=2075, Resulting Numbers: [2075] 2075,29 unequal: No Solution Exploring Operation: 83+25=108, Resulting Numbers: [108] 108,29 unequal: No Solution Exploring Operation: 83-25=58, Resulting Numbers: [58] 58,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 29:[99, 5, 14], Operations: ['83-69=14'] Exploring Operation: 5+14=19, Resulting Numbers: [99, 19] Generated Node #0,1,0: 29:[99, 19] Operation: 5+14=19 Exploring Operation: 99-14=85, Resulting Numbers: [5, 85] Generated Node #0,1,1: 29:[5, 85] Operation: 99-14=85 Exploring Operation: 99-5=94, Resulting Numbers: [14, 94] Generated Node #0,1,2: 29:[14, 94] Operation: 99-5=94 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 29:[99, 19], Operations: ['83-69=14', '5+14=19'] Exploring Operation: 99+19=118, Resulting Numbers: [118] 118,29 unequal: No Solution Exploring Operation: 99-19=80, Resulting Numbers: [80] 80,29 unequal: No Solution Exploring Operation: 99*19=1881, Resulting Numbers: [1881] 1881,29 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 #0,1,1 Current State: 29:[5, 85], Operations: ['83-69=14', '99-14=85'] Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 5+85=90, Resulting Numbers: [90] 90,29 unequal: No Solution Exploring Operation: 85-5=80, Resulting Numbers: [80] 80,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 29:[14, 94], Operations: ['83-69=14', '99-5=94'] Exploring Operation: 14+94=108, Resulting Numbers: [108] 108,29 unequal: No Solution Exploring Operation: 14*94=1316, Resulting Numbers: [1316] 1316,29 unequal: No Solution Exploring Operation: 94-14=80, Resulting Numbers: [80] 80,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 6, 23, 86, 8 ]
65
[ "6+23=29", "86+8=94", "94-29=65" ]
Current State: 65:[6, 23, 86, 8], Operations: [] Exploring Operation: 6+23=29, Resulting Numbers: [86, 8, 29] Generated Node #2: [86, 8, 29] from Operation: 6+23=29 Current State: 65:[86, 8, 29], Operations: ['6+23=29'] Exploring Operation: 86+8=94, Resulting Numbers: [29, 94] Generated Node #3: [29, 94] from Operation: 86+8=94 Current State: 65:[29, 94], Operations: ['6+23=29', '86+8=94'] Exploring Operation: 94-29=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[6, 23, 86, 8], Operations: [] Exploring Operation: 23-8=15, Resulting Numbers: [6, 86, 15] Generated Node #0,0: 65:[6, 86, 15] Operation: 23-8=15 Exploring Operation: 86-23=63, Resulting Numbers: [6, 8, 63] Generated Node #0,1: 65:[6, 8, 63] Operation: 86-23=63 Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[6, 8, 63], Operations: ['86-23=63'] Exploring Operation: 6+8=14, Resulting Numbers: [63, 14] Generated Node #0,1,0: 65:[63, 14] Operation: 6+8=14 Exploring Operation: 8-6=2, Resulting Numbers: [63, 2] Generated Node #0,1,1: 65:[63, 2] Operation: 8-6=2 Moving to Node #0,1,0 Current State: 65:[63, 14], Operations: ['86-23=63', '6+8=14'] Exploring Operation: 63+14=77, Resulting Numbers: [77] 77,65 unequal: No Solution Exploring Operation: 63-14=49, Resulting Numbers: [49] 49,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[63, 2], Operations: ['86-23=63', '8-6=2'] Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[6, 23, 86, 8], Operations: [] Exploring Operation: 86-23=63, Resulting Numbers: [6, 8, 63] Generated Node #0,1: 65:[6, 8, 63] Operation: 86-23=63 Moving to Node #0,1 Current State: 65:[6, 8, 63], Operations: ['86-23=63'] Exploring Operation: 8-6=2, Resulting Numbers: [63, 2] Generated Node #0,1,1: 65:[63, 2] Operation: 8-6=2 Moving to Node #0,1,1 Current State: 65:[63, 2], Operations: ['86-23=63', '8-6=2'] Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 12, 69, 47, 27 ]
55
[ "69+27=96", "96/12=8", "47+8=55" ]
Current State: 55:[12, 69, 47, 27], Operations: [] Exploring Operation: 69+27=96, Resulting Numbers: [12, 47, 96] Generated Node #2: [12, 47, 96] from Operation: 69+27=96 Current State: 55:[12, 47, 96], Operations: ['69+27=96'] Exploring Operation: 96/12=8, Resulting Numbers: [47, 8] Generated Node #3: [47, 8] from Operation: 96/12=8 Current State: 55:[47, 8], Operations: ['69+27=96', '96/12=8'] Exploring Operation: 47+8=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[12, 69, 47, 27], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [12, 69, 20] Generated Node #0,0: 55:[12, 69, 20] Operation: 47-27=20 Exploring Operation: 27-12=15, Resulting Numbers: [69, 47, 15] Generated Node #0,1: 55:[69, 47, 15] Operation: 27-12=15 Exploring Operation: 69-12=57, Resulting Numbers: [47, 27, 57] Generated Node #0,2: 55:[47, 27, 57] Operation: 69-12=57 Exploring Operation: 69-27=42, Resulting Numbers: [12, 47, 42] Generated Node #0,3: 55:[12, 47, 42] Operation: 69-27=42 Start Sub Search at level 1: Moving to Node #0,3 Current State: 55:[12, 47, 42], Operations: ['69-27=42'] Exploring Operation: 42-12=30, Resulting Numbers: [47, 30] Generated Node #0,3,0: 55:[47, 30] Operation: 42-12=30 Exploring Operation: 47-42=5, Resulting Numbers: [12, 5] Generated Node #0,3,1: 55:[12, 5] Operation: 47-42=5 Exploring Operation: 12+47=59, Resulting Numbers: [42, 59] Generated Node #0,3,2: 55:[42, 59] Operation: 12+47=59 Exploring Operation: 12+42=54, Resulting Numbers: [47, 54] Generated Node #0,3,3: 55:[47, 54] Operation: 12+42=54 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 55:[12, 5], Operations: ['69-27=42', '47-42=5'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,55 unequal: No Solution Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 55:[47, 54], Operations: ['69-27=42', '12+42=54'] Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 47*54=2538, Resulting Numbers: [2538] 2538,55 unequal: No Solution Exploring Operation: 47+54=101, Resulting Numbers: [101] 101,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 55:[42, 59], Operations: ['69-27=42', '12+47=59'] Exploring Operation: 42*59=2478, Resulting Numbers: [2478] 2478,55 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,55 unequal: No Solution Exploring Operation: 42+59=101, Resulting Numbers: [101] 101,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 55:[47, 30], Operations: ['69-27=42', '42-12=30'] Exploring Operation: 47+30=77, Resulting Numbers: [77] 77,55 unequal: No Solution Exploring Operation: 47*30=1410, Resulting Numbers: [1410] 1410,55 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[12, 69, 20], Operations: ['47-27=20'] Exploring Operation: 69-20=49, Resulting Numbers: [12, 49] Generated Node #0,0,0: 55:[12, 49] Operation: 69-20=49 Exploring Operation: 20-12=8, Resulting Numbers: [69, 8] Generated Node #0,0,1: 55:[69, 8] Operation: 20-12=8 Exploring Operation: 69-12=57, Resulting Numbers: [20, 57] Generated Node #0,0,2: 55:[20, 57] Operation: 69-12=57 Exploring Operation: 12+69=81, Resulting Numbers: [20, 81] Generated Node #0,0,3: 55:[20, 81] Operation: 12+69=81 Moving to Node #0,0,0 Current State: 55:[12, 49], Operations: ['47-27=20', '69-20=49'] Exploring Operation: 49-12=37, Resulting Numbers: [37] 37,55 unequal: No Solution Exploring Operation: 12+49=61, Resulting Numbers: [61] 61,55 unequal: No Solution Exploring Operation: 12*49=588, Resulting Numbers: [588] 588,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[20, 57], Operations: ['47-27=20', '69-12=57'] Exploring Operation: 20+57=77, Resulting Numbers: [77] 77,55 unequal: No Solution Exploring Operation: 20*57=1140, Resulting Numbers: [1140] 1140,55 unequal: No Solution Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[69, 8], Operations: ['47-27=20', '20-12=8'] Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,55 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,55 unequal: No Solution Exploring Operation: 69*8=552, Resulting Numbers: [552] 552,55 unequal: No Solution Moving to Node #0,0,3 Current State: 55:[20, 81], Operations: ['47-27=20', '12+69=81'] Exploring Operation: 20*81=1620, Resulting Numbers: [1620] 1620,55 unequal: No Solution Exploring Operation: 20+81=101, Resulting Numbers: [101] 101,55 unequal: No Solution Exploring Operation: 81-20=61, Resulting Numbers: [61] 61,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[69, 47, 15], Operations: ['27-12=15'] Exploring Operation: 69-15=54, Resulting Numbers: [47, 54] Generated Node #0,1,0: 55:[47, 54] Operation: 69-15=54 Exploring Operation: 47-15=32, Resulting Numbers: [69, 32] Generated Node #0,1,1: 55:[69, 32] Operation: 47-15=32 Exploring Operation: 47+15=62, Resulting Numbers: [69, 62] Generated Node #0,1,2: 55:[69, 62] Operation: 47+15=62 Exploring Operation: 69-47=22, Resulting Numbers: [15, 22] Generated Node #0,1,3: 55:[15, 22] Operation: 69-47=22 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[47, 54], Operations: ['27-12=15', '69-15=54'] Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 47*54=2538, Resulting Numbers: [2538] 2538,55 unequal: No Solution Exploring Operation: 47+54=101, Resulting Numbers: [101] 101,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 55:[15, 22], Operations: ['27-12=15', '69-47=22'] Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,55 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 55:[69, 62], Operations: ['27-12=15', '47+15=62'] Exploring Operation: 69-62=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 69+62=131, Resulting Numbers: [131] 131,55 unequal: No Solution Exploring Operation: 69*62=4278, Resulting Numbers: [4278] 4278,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 55:[69, 32], Operations: ['27-12=15', '47-15=32'] Exploring Operation: 69+32=101, Resulting Numbers: [101] 101,55 unequal: No Solution Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,55 unequal: No Solution Exploring Operation: 69*32=2208, Resulting Numbers: [2208] 2208,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[47, 27, 57], Operations: ['69-12=57'] Exploring Operation: 47-27=20, Resulting Numbers: [57, 20] Generated Node #0,2,0: 55:[57, 20] Operation: 47-27=20 Exploring Operation: 57-27=30, Resulting Numbers: [47, 30] Generated Node #0,2,1: 55:[47, 30] Operation: 57-27=30 Exploring Operation: 47+27=74, Resulting Numbers: [57, 74] Generated Node #0,2,2: 55:[57, 74] Operation: 47+27=74 Exploring Operation: 57-47=10, Resulting Numbers: [27, 10] Generated Node #0,2,3: 55:[27, 10] Operation: 57-47=10 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 55:[57, 20], Operations: ['69-12=57', '47-27=20'] Exploring Operation: 57+20=77, Resulting Numbers: [77] 77,55 unequal: No Solution Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,55 unequal: No Solution Exploring Operation: 57*20=1140, Resulting Numbers: [1140] 1140,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 55:[27, 10], Operations: ['69-12=57', '57-47=10'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,55 unequal: No Solution Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,55 unequal: No Solution Exploring Operation: 27*10=270, Resulting Numbers: [270] 270,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 55:[57, 74], Operations: ['69-12=57', '47+27=74'] Exploring Operation: 57+74=131, Resulting Numbers: [131] 131,55 unequal: No Solution Exploring Operation: 57*74=4218, Resulting Numbers: [4218] 4218,55 unequal: No Solution Exploring Operation: 74-57=17, Resulting Numbers: [17] 17,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 55:[47, 30], Operations: ['69-12=57', '57-27=30'] Exploring Operation: 47+30=77, Resulting Numbers: [77] 77,55 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,55 unequal: No Solution Exploring Operation: 47*30=1410, Resulting Numbers: [1410] 1410,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 41, 6, 48, 92 ]
93
[ "41+6=47", "48+92=140", "140-47=93" ]
Current State: 93:[41, 6, 48, 92], Operations: [] Exploring Operation: 41+6=47, Resulting Numbers: [48, 92, 47] Generated Node #2: [48, 92, 47] from Operation: 41+6=47 Current State: 93:[48, 92, 47], Operations: ['41+6=47'] Exploring Operation: 48+92=140, Resulting Numbers: [47, 140] Generated Node #3: [47, 140] from Operation: 48+92=140 Current State: 93:[47, 140], Operations: ['41+6=47', '48+92=140'] Exploring Operation: 140-47=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[41, 6, 48, 92], Operations: [] Exploring Operation: 41+48=89, Resulting Numbers: [6, 92, 89] Generated Node #0,0: 93:[6, 92, 89] Operation: 41+48=89 Exploring Operation: 48/6=8, Resulting Numbers: [41, 92, 8] Generated Node #0,1: 93:[41, 92, 8] Operation: 48/6=8 Exploring Operation: 48-41=7, Resulting Numbers: [6, 92, 7] Generated Node #0,2: 93:[6, 92, 7] Operation: 48-41=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[6, 92, 89], Operations: ['41+48=89'] Exploring Operation: 6+92=98, Resulting Numbers: [89, 98] Generated Node #0,0,0: 93:[89, 98] Operation: 6+92=98 Exploring Operation: 92-89=3, Resulting Numbers: [6, 3] Generated Node #0,0,1: 93:[6, 3] Operation: 92-89=3 Exploring Operation: 6+89=95, Resulting Numbers: [92, 95] Generated Node #0,0,2: 93:[92, 95] Operation: 6+89=95 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 93:[6, 3], Operations: ['41+48=89', '92-89=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,93 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,93 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 93:[92, 95], Operations: ['41+48=89', '6+89=95'] Exploring Operation: 92*95=8740, Resulting Numbers: [8740] 8740,93 unequal: No Solution Exploring Operation: 95-92=3, Resulting Numbers: [3] 3,93 unequal: No Solution Exploring Operation: 92+95=187, Resulting Numbers: [187] 187,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 93:[89, 98], Operations: ['41+48=89', '6+92=98'] Exploring Operation: 98-89=9, Resulting Numbers: [9] 9,93 unequal: No Solution Exploring Operation: 89*98=8722, Resulting Numbers: [8722] 8722,93 unequal: No Solution Exploring Operation: 89+98=187, Resulting Numbers: [187] 187,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[6, 92, 7], Operations: ['48-41=7'] Exploring Operation: 92+7=99, Resulting Numbers: [6, 99] Generated Node #0,2,0: 93:[6, 99] Operation: 92+7=99 Exploring Operation: 6+92=98, Resulting Numbers: [7, 98] Generated Node #0,2,1: 93:[7, 98] Operation: 6+92=98 Exploring Operation: 7-6=1, Resulting Numbers: [92, 1] Generated Node #0,2,2: 93:[92, 1] Operation: 7-6=1 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 93:[92, 1], Operations: ['48-41=7', '7-6=1'] Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 92*1=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[41, 6, 48, 92], Operations: [] Exploring Operation: 48-41=7, Resulting Numbers: [6, 92, 7] Generated Node #0,2: 93:[6, 92, 7] Operation: 48-41=7 Moving to Node #0,2 Current State: 93:[6, 92, 7], Operations: ['48-41=7'] Exploring Operation: 7-6=1, Resulting Numbers: [92, 1] Generated Node #0,2,2: 93:[92, 1] Operation: 7-6=1 Moving to Node #0,2,2 Current State: 93:[92, 1], Operations: ['48-41=7', '7-6=1'] Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_3
sum_heuristic
[ 75, 47, 19, 50 ]
44
[ "47+19=66", "50*66=3300", "3300/75=44" ]
Current State: 44:[75, 47, 19, 50], Operations: [] Exploring Operation: 47+19=66, Resulting Numbers: [75, 50, 66] Generated Node #2: [75, 50, 66] from Operation: 47+19=66 Current State: 44:[75, 50, 66], Operations: ['47+19=66'] Exploring Operation: 50*66=3300, Resulting Numbers: [75, 3300] Generated Node #3: [75, 3300] from Operation: 50*66=3300 Current State: 44:[75, 3300], Operations: ['47+19=66', '50*66=3300'] Exploring Operation: 3300/75=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[75, 47, 19, 50], Operations: [] Exploring Operation: 75-50=25, Resulting Numbers: [47, 19, 25] Generated Node #0,0: 44:[47, 19, 25] Operation: 75-50=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[47, 19, 25], Operations: ['75-50=25'] Exploring Operation: 47-25=22, Resulting Numbers: [19, 22] Generated Node #0,0,0: 44:[19, 22] Operation: 47-25=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[19, 22], Operations: ['75-50=25', '47-25=22'] Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,44 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
[ 19, 46, 87, 75 ]
15
[ "46-19=27", "87-75=12", "27-12=15" ]
Current State: 15:[19, 46, 87, 75], Operations: [] Exploring Operation: 46-19=27, Resulting Numbers: [87, 75, 27] Generated Node #2: [87, 75, 27] from Operation: 46-19=27 Current State: 15:[87, 75, 27], Operations: ['46-19=27'] Exploring Operation: 87-75=12, Resulting Numbers: [27, 12] Generated Node #3: [27, 12] from Operation: 87-75=12 Current State: 15:[27, 12], Operations: ['46-19=27', '87-75=12'] Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[19, 46, 87, 75], Operations: [] Exploring Operation: 87-75=12, Resulting Numbers: [19, 46, 12] Generated Node #0,0: 15:[19, 46, 12] Operation: 87-75=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[19, 46, 12], Operations: ['87-75=12'] Exploring Operation: 46-19=27, Resulting Numbers: [12, 27] Generated Node #0,0,0: 15:[12, 27] Operation: 46-19=27 Moving to Node #0,0,0 Current State: 15:[12, 27], Operations: ['87-75=12', '46-19=27'] Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[19, 46, 87, 75], Operations: [] Exploring Operation: 87-75=12, Resulting Numbers: [19, 46, 12] Generated Node #0,0: 15:[19, 46, 12] Operation: 87-75=12 Moving to Node #0,0 Current State: 15:[19, 46, 12], Operations: ['87-75=12'] Exploring Operation: 46-19=27, Resulting Numbers: [12, 27] Generated Node #0,0,0: 15:[12, 27] Operation: 46-19=27 Moving to Node #0,0,0 Current State: 15:[12, 27], Operations: ['87-75=12', '46-19=27'] Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 86, 33, 84, 14 ]
21
[ "86+33=119", "84+14=98", "119-98=21" ]
Current State: 21:[86, 33, 84, 14], Operations: [] Exploring Operation: 86+33=119, Resulting Numbers: [84, 14, 119] Generated Node #2: [84, 14, 119] from Operation: 86+33=119 Current State: 21:[84, 14, 119], Operations: ['86+33=119'] Exploring Operation: 84+14=98, Resulting Numbers: [119, 98] Generated Node #3: [119, 98] from Operation: 84+14=98 Current State: 21:[119, 98], Operations: ['86+33=119', '84+14=98'] Exploring Operation: 119-98=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[86, 33, 84, 14], Operations: [] Exploring Operation: 86-14=72, Resulting Numbers: [33, 84, 72] Generated Node #0,0: 21:[33, 84, 72] Operation: 86-14=72 Exploring Operation: 84-33=51, Resulting Numbers: [86, 14, 51] Generated Node #0,1: 21:[86, 14, 51] Operation: 84-33=51 Exploring Operation: 84/14=6, Resulting Numbers: [86, 33, 6] Generated Node #0,2: 21:[86, 33, 6] Operation: 84/14=6 Exploring Operation: 86-33=53, Resulting Numbers: [84, 14, 53] Generated Node #0,3: 21:[84, 14, 53] Operation: 86-33=53 Exploring Operation: 86-84=2, Resulting Numbers: [33, 14, 2] Generated Node #0,4: 21:[33, 14, 2] Operation: 86-84=2 Start Sub Search at level 1: Moving to Node #0,4 Current State: 21:[33, 14, 2], Operations: ['86-84=2'] Exploring Operation: 33-14=19, Resulting Numbers: [2, 19] Generated Node #0,4,0: 21:[2, 19] Operation: 33-14=19 Exploring Operation: 14+2=16, Resulting Numbers: [33, 16] Generated Node #0,4,1: 21:[33, 16] Operation: 14+2=16 Exploring Operation: 14-2=12, Resulting Numbers: [33, 12] Generated Node #0,4,2: 21:[33, 12] Operation: 14-2=12 Exploring Operation: 33-2=31, Resulting Numbers: [14, 31] Generated Node #0,4,3: 21:[14, 31] Operation: 33-2=31 Exploring Operation: 14/2=7, Resulting Numbers: [33, 7] Generated Node #0,4,4: 21:[33, 7] Operation: 14/2=7 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 21:[2, 19], Operations: ['86-84=2', '33-14=19'] Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,21 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,21 unequal: No Solution Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[86, 33, 84, 14], Operations: [] Exploring Operation: 86-84=2, Resulting Numbers: [33, 14, 2] Generated Node #0,4: 21:[33, 14, 2] Operation: 86-84=2 Moving to Node #0,4 Current State: 21:[33, 14, 2], Operations: ['86-84=2'] Exploring Operation: 33-14=19, Resulting Numbers: [2, 19] Generated Node #0,4,0: 21:[2, 19] Operation: 33-14=19 Moving to Node #0,4,0 Current State: 21:[2, 19], Operations: ['86-84=2', '33-14=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 44, 46, 23, 10 ]
32
[ "44+46=90", "90/10=9", "23+9=32" ]
Current State: 32:[44, 46, 23, 10], Operations: [] Exploring Operation: 44+46=90, Resulting Numbers: [23, 10, 90] Generated Node #2: [23, 10, 90] from Operation: 44+46=90 Current State: 32:[23, 10, 90], Operations: ['44+46=90'] Exploring Operation: 90/10=9, Resulting Numbers: [23, 9] Generated Node #3: [23, 9] from Operation: 90/10=9 Current State: 32:[23, 9], Operations: ['44+46=90', '90/10=9'] Exploring Operation: 23+9=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[44, 46, 23, 10], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [23, 10, 2] Generated Node #0,0: 32:[23, 10, 2] Operation: 46-44=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[23, 10, 2], Operations: ['46-44=2'] Exploring Operation: 23+10=33, Resulting Numbers: [2, 33] Generated Node #0,0,0: 32:[2, 33] Operation: 23+10=33 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[2, 33], Operations: ['46-44=2', '23+10=33'] Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 3, 21, 29, 30 ]
80
[ "30/3=10", "29-21=8", "10*8=80" ]
Current State: 80:[3, 21, 29, 30], Operations: [] Exploring Operation: 30/3=10, Resulting Numbers: [21, 29, 10] Generated Node #2: [21, 29, 10] from Operation: 30/3=10 Current State: 80:[21, 29, 10], Operations: ['30/3=10'] Exploring Operation: 29-21=8, Resulting Numbers: [10, 8] Generated Node #3: [10, 8] from Operation: 29-21=8 Current State: 80:[10, 8], Operations: ['30/3=10', '29-21=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[3, 21, 29, 30], Operations: [] Exploring Operation: 30/3=10, Resulting Numbers: [21, 29, 10] Generated Node #0,0: 80:[21, 29, 10] Operation: 30/3=10 Exploring Operation: 30-21=9, Resulting Numbers: [3, 29, 9] Generated Node #0,1: 80:[3, 29, 9] Operation: 30-21=9 Exploring Operation: 29-21=8, Resulting Numbers: [3, 30, 8] Generated Node #0,2: 80:[3, 30, 8] Operation: 29-21=8 Exploring Operation: 30-29=1, Resulting Numbers: [3, 21, 1] Generated Node #0,3: 80:[3, 21, 1] Operation: 30-29=1 Moving to Node #0,3 Current State: 80:[3, 21, 1], Operations: ['30-29=1'] Exploring Operation: 21-1=20, Resulting Numbers: [3, 20] Generated Node #0,3,0: 80:[3, 20] Operation: 21-1=20 Exploring Operation: 3-1=2, Resulting Numbers: [21, 2] Generated Node #0,3,1: 80:[21, 2] Operation: 3-1=2 Exploring Operation: 21/3=7, Resulting Numbers: [1, 7] Generated Node #0,3,2: 80:[1, 7] Operation: 21/3=7 Exploring Operation: 3+1=4, Resulting Numbers: [21, 4] Generated Node #0,3,3: 80:[21, 4] Operation: 3+1=4 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 80:[3, 20], Operations: ['30-29=1', '21-1=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,80 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 80:[21, 2], Operations: ['30-29=1', '3-1=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,80 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 80:[21, 4], Operations: ['30-29=1', '3+1=4'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,80 unequal: No Solution Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,80 unequal: No Solution Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 80:[1, 7], Operations: ['30-29=1', '21/3=7'] Exploring Operation: 1+7=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,80 unequal: No Solution Exploring Operation: 1*7=7, Resulting Numbers: [7] 7,80 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 80:[21, 29, 10], Operations: ['30/3=10'] Exploring Operation: 21+29=50, Resulting Numbers: [10, 50] Generated Node #0,0,0: 80:[10, 50] Operation: 21+29=50 Exploring Operation: 29-10=19, Resulting Numbers: [21, 19] Generated Node #0,0,1: 80:[21, 19] Operation: 29-10=19 Exploring Operation: 29-21=8, Resulting Numbers: [10, 8] Generated Node #0,0,2: 80:[10, 8] Operation: 29-21=8 Exploring Operation: 29+10=39, Resulting Numbers: [21, 39] Generated Node #0,0,3: 80:[21, 39] Operation: 29+10=39 Moving to Node #0,2 Current State: 80:[3, 30, 8], Operations: ['29-21=8'] Exploring Operation: 30/3=10, Resulting Numbers: [8, 10] Generated Node #0,2,0: 80:[8, 10] Operation: 30/3=10 Exploring Operation: 30-8=22, Resulting Numbers: [3, 22] Generated Node #0,2,1: 80:[3, 22] Operation: 30-8=22 Exploring Operation: 30+8=38, Resulting Numbers: [3, 38] Generated Node #0,2,2: 80:[3, 38] Operation: 30+8=38 Exploring Operation: 3+30=33, Resulting Numbers: [8, 33] Generated Node #0,2,3: 80:[8, 33] Operation: 3+30=33 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[8, 10], Operations: ['29-21=8', '30/3=10'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[3, 21, 29, 30], Operations: [] Exploring Operation: 29-21=8, Resulting Numbers: [3, 30, 8] Generated Node #0,2: 80:[3, 30, 8] Operation: 29-21=8 Moving to Node #0,2 Current State: 80:[3, 30, 8], Operations: ['29-21=8'] Exploring Operation: 30/3=10, Resulting Numbers: [8, 10] Generated Node #0,2,0: 80:[8, 10] Operation: 30/3=10 Moving to Node #0,2,0 Current State: 80:[8, 10], Operations: ['29-21=8', '30/3=10'] Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_4
mult_heuristic
[ 99, 8, 83, 92 ]
84
[ "99-8=91", "83+92=175", "175-91=84" ]
Current State: 84:[99, 8, 83, 92], Operations: [] Exploring Operation: 99-8=91, Resulting Numbers: [83, 92, 91] Generated Node #2: [83, 92, 91] from Operation: 99-8=91 Current State: 84:[83, 92, 91], Operations: ['99-8=91'] Exploring Operation: 83+92=175, Resulting Numbers: [91, 175] Generated Node #3: [91, 175] from Operation: 83+92=175 Current State: 84:[91, 175], Operations: ['99-8=91', '83+92=175'] Exploring Operation: 175-91=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[99, 8, 83, 92], Operations: [] Exploring Operation: 99-92=7, Resulting Numbers: [8, 83, 7] Generated Node #0,0: 84:[8, 83, 7] Operation: 99-92=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[8, 83, 7], Operations: ['99-92=7'] Exploring Operation: 8+7=15, Resulting Numbers: [83, 15] Generated Node #0,0,0: 84:[83, 15] Operation: 8+7=15 Moving to Node #0,0,0 Current State: 84:[83, 15], Operations: ['99-92=7', '8+7=15'] Exploring Operation: 83+15=98, Resulting Numbers: [98] 98,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 40, 74, 69, 36 ]
96
[ "40*69=2760", "74*36=2664", "2760-2664=96" ]
Current State: 96:[40, 74, 69, 36], Operations: [] Exploring Operation: 40*69=2760, Resulting Numbers: [74, 36, 2760] Generated Node #2: [74, 36, 2760] from Operation: 40*69=2760 Current State: 96:[74, 36, 2760], Operations: ['40*69=2760'] Exploring Operation: 74*36=2664, Resulting Numbers: [2760, 2664] Generated Node #3: [2760, 2664] from Operation: 74*36=2664 Current State: 96:[2760, 2664], Operations: ['40*69=2760', '74*36=2664'] Exploring Operation: 2760-2664=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[40, 74, 69, 36], Operations: [] Exploring Operation: 74-40=34, Resulting Numbers: [69, 36, 34] Generated Node #0,0: 96:[69, 36, 34] Operation: 74-40=34 Exploring Operation: 74-69=5, Resulting Numbers: [40, 36, 5] Generated Node #0,1: 96:[40, 36, 5] Operation: 74-69=5 Moving to Node #0,1 Current State: 96:[40, 36, 5], Operations: ['74-69=5'] Exploring Operation: 40-36=4, Resulting Numbers: [5, 4] Generated Node #0,1,0: 96:[5, 4] Operation: 40-36=4 Exploring Operation: 40/5=8, Resulting Numbers: [36, 8] Generated Node #0,1,1: 96:[36, 8] Operation: 40/5=8 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 96:[5, 4], Operations: ['74-69=5', '40-36=4'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 96:[36, 8], Operations: ['74-69=5', '40/5=8'] Exploring Operation: 36+8=44, Resulting Numbers: [44] 44,96 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,96 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: 96:[69, 36, 34], Operations: ['74-40=34'] Exploring Operation: 69-36=33, Resulting Numbers: [34, 33] Generated Node #0,0,0: 96:[34, 33] Operation: 69-36=33 Exploring Operation: 69-34=35, Resulting Numbers: [36, 35] Generated Node #0,0,1: 96:[36, 35] Operation: 69-34=35 Moving to Node #0,0,0 Current State: 96:[34, 33], Operations: ['74-40=34', '69-36=33'] Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,96 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[36, 35], Operations: ['74-40=34', '69-34=35'] Exploring Operation: 36+35=71, Resulting Numbers: [71] 71,96 unequal: No Solution Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,96 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 19, 45, 12, 31 ]
99
[ "31-19=12", "12*12=144", "144-45=99" ]
Current State: 99:[19, 45, 12, 31], Operations: [] Exploring Operation: 31-19=12, Resulting Numbers: [45, 12, 12] Generated Node #2: [45, 12, 12] from Operation: 31-19=12 Current State: 99:[45, 12, 12], Operations: ['31-19=12'] Exploring Operation: 12*12=144, Resulting Numbers: [45, 144] Generated Node #3: [45, 144] from Operation: 12*12=144 Current State: 99:[45, 144], Operations: ['31-19=12', '12*12=144'] Exploring Operation: 144-45=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[19, 45, 12, 31], Operations: [] Exploring Operation: 45-12=33, Resulting Numbers: [19, 31, 33] Generated Node #0,0: 99:[19, 31, 33] Operation: 45-12=33 Exploring Operation: 45-19=26, Resulting Numbers: [12, 31, 26] Generated Node #0,1: 99:[12, 31, 26] Operation: 45-19=26 Exploring Operation: 31-19=12, Resulting Numbers: [45, 12, 12] Generated Node #0,2: 99:[45, 12, 12] Operation: 31-19=12 Exploring Operation: 45-31=14, Resulting Numbers: [19, 12, 14] Generated Node #0,3: 99:[19, 12, 14] Operation: 45-31=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[19, 31, 33], Operations: ['45-12=33'] Exploring Operation: 33-19=14, Resulting Numbers: [31, 14] Generated Node #0,0,0: 99:[31, 14] Operation: 33-19=14 Exploring Operation: 31-19=12, Resulting Numbers: [33, 12] Generated Node #0,0,1: 99:[33, 12] Operation: 31-19=12 Exploring Operation: 33-31=2, Resulting Numbers: [19, 2] Generated Node #0,0,2: 99:[19, 2] Operation: 33-31=2 Exploring Operation: 19+31=50, Resulting Numbers: [33, 50] Generated Node #0,0,3: 99:[33, 50] Operation: 19+31=50 Moving to Node #0,0,1 Current State: 99:[33, 12], Operations: ['45-12=33', '31-19=12'] Exploring Operation: 33*12=396, Resulting Numbers: [396] 396,99 unequal: No Solution Exploring Operation: 33+12=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[31, 14], Operations: ['45-12=33', '33-19=14'] Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 31+14=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 31*14=434, Resulting Numbers: [434] 434,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[19, 2], Operations: ['45-12=33', '33-31=2'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 19+2=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,99 unequal: No Solution Moving to Node #0,0,3 Current State: 99:[33, 50], Operations: ['45-12=33', '19+31=50'] Exploring Operation: 50-33=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 33+50=83, Resulting Numbers: [83] 83,99 unequal: No Solution Exploring Operation: 33*50=1650, Resulting Numbers: [1650] 1650,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[12, 31, 26], Operations: ['45-19=26'] Exploring Operation: 12+26=38, Resulting Numbers: [31, 38] Generated Node #0,1,0: 99:[31, 38] Operation: 12+26=38 Exploring Operation: 26-12=14, Resulting Numbers: [31, 14] Generated Node #0,1,1: 99:[31, 14] Operation: 26-12=14 Exploring Operation: 31-12=19, Resulting Numbers: [26, 19] Generated Node #0,1,2: 99:[26, 19] Operation: 31-12=19 Exploring Operation: 31-26=5, Resulting Numbers: [12, 5] Generated Node #0,1,3: 99:[12, 5] Operation: 31-26=5 Moving to Node #0,1,3 Current State: 99:[12, 5], Operations: ['45-19=26', '31-26=5'] Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,99 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[31, 14], Operations: ['45-19=26', '26-12=14'] Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 31*14=434, Resulting Numbers: [434] 434,99 unequal: No Solution Exploring Operation: 31+14=45, Resulting Numbers: [45] 45,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[31, 38], Operations: ['45-19=26', '12+26=38'] Exploring Operation: 31+38=69, Resulting Numbers: [69] 69,99 unequal: No Solution Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,99 unequal: No Solution Exploring Operation: 31*38=1178, Resulting Numbers: [1178] 1178,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[26, 19], Operations: ['45-19=26', '31-12=19'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,99 unequal: No Solution Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 99:[19, 12, 14], Operations: ['45-31=14'] Exploring Operation: 19+12=31, Resulting Numbers: [14, 31] Generated Node #0,3,0: 99:[14, 31] Operation: 19+12=31 Exploring Operation: 19+14=33, Resulting Numbers: [12, 33] Generated Node #0,3,1: 99:[12, 33] Operation: 19+14=33 Exploring Operation: 19-14=5, Resulting Numbers: [12, 5] Generated Node #0,3,2: 99:[12, 5] Operation: 19-14=5 Exploring Operation: 19-12=7, Resulting Numbers: [14, 7] Generated Node #0,3,3: 99:[14, 7] Operation: 19-12=7 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 99:[12, 33], Operations: ['45-31=14', '19+14=33'] Exploring Operation: 12*33=396, Resulting Numbers: [396] 396,99 unequal: No Solution Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,99 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 #0,3,2 Current State: 99:[12, 5], Operations: ['45-31=14', '19-14=5'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,99 unequal: No Solution Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,99 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,99 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 #0,3,0 Current State: 99:[14, 31], Operations: ['45-31=14', '19+12=31'] Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 14*31=434, Resulting Numbers: [434] 434,99 unequal: No Solution Exploring Operation: 14+31=45, Resulting Numbers: [45] 45,99 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 #0,3,3 Current State: 99:[14, 7], Operations: ['45-31=14', '19-12=7'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,99 unequal: No Solution Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,99 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: 99:[45, 12, 12], Operations: ['31-19=12'] Exploring Operation: 12/12=1, Resulting Numbers: [45, 1] Generated Node #0,2,0: 99:[45, 1] Operation: 12/12=1 Exploring Operation: 45-12=33, Resulting Numbers: [12, 33] Generated Node #0,2,1: 99:[12, 33] Operation: 45-12=33 Exploring Operation: 12-12=0, Resulting Numbers: [45, 0] Generated Node #0,2,2: 99:[45, 0] Operation: 12-12=0 Exploring Operation: 45-12=33, Resulting Numbers: [12, 33] Generated Node #0,2,3: 99:[12, 33] Operation: 45-12=33 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 99:[12, 33], Operations: ['31-19=12', '45-12=33'] Exploring Operation: 12*33=396, Resulting Numbers: [396] 396,99 unequal: No Solution Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,99 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 #0,2,3 Current State: 99:[12, 33], Operations: ['31-19=12', '45-12=33'] Exploring Operation: 12*33=396, Resulting Numbers: [396] 396,99 unequal: No Solution Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,99 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 #0,2,0 Current State: 99:[45, 1], Operations: ['31-19=12', '12/12=1'] Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 45+1=46, Resulting Numbers: [46] 46,99 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,99 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 #0,2,2 Current State: 99:[45, 0], Operations: ['31-19=12', '12-12=0'] Exploring Operation: 45+0=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 45-0=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 45*0=0, Resulting Numbers: [0] 0,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 14, 74, 7, 21 ]
88
[ "74-14=60", "7+21=28", "60+28=88" ]
Current State: 88:[14, 74, 7, 21], Operations: [] Exploring Operation: 74-14=60, Resulting Numbers: [7, 21, 60] Generated Node #2: [7, 21, 60] from Operation: 74-14=60 Current State: 88:[7, 21, 60], Operations: ['74-14=60'] Exploring Operation: 7+21=28, Resulting Numbers: [60, 28] Generated Node #3: [60, 28] from Operation: 7+21=28 Current State: 88:[60, 28], Operations: ['74-14=60', '7+21=28'] Exploring Operation: 60+28=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[14, 74, 7, 21], Operations: [] Exploring Operation: 74+7=81, Resulting Numbers: [14, 21, 81] Generated Node #0,0: 88:[14, 21, 81] Operation: 74+7=81 Exploring Operation: 74-21=53, Resulting Numbers: [14, 7, 53] Generated Node #0,1: 88:[14, 7, 53] Operation: 74-21=53 Exploring Operation: 74+21=95, Resulting Numbers: [14, 7, 95] Generated Node #0,2: 88:[14, 7, 95] Operation: 74+21=95 Exploring Operation: 14+74=88, Resulting Numbers: [7, 21, 88] Generated Node #0,3: 88:[7, 21, 88] Operation: 14+74=88 Moving to Node #0,3 Current State: 88:[7, 21, 88], Operations: ['14+74=88'] Exploring Operation: 21-7=14, Resulting Numbers: [88, 14] Generated Node #0,3,0: 88:[88, 14] Operation: 21-7=14 Exploring Operation: 21/7=3, Resulting Numbers: [88, 3] Generated Node #0,3,1: 88:[88, 3] Operation: 21/7=3 Exploring Operation: 7+21=28, Resulting Numbers: [88, 28] Generated Node #0,3,2: 88:[88, 28] Operation: 7+21=28 Exploring Operation: 7+88=95, Resulting Numbers: [21, 95] Generated Node #0,3,3: 88:[21, 95] Operation: 7+88=95 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 88:[88, 3], Operations: ['14+74=88', '21/7=3'] Exploring Operation: 88+3=91, Resulting Numbers: [91] 91,88 unequal: No Solution Exploring Operation: 88*3=264, Resulting Numbers: [264] 264,88 unequal: No Solution Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,88 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 #0,3,0 Current State: 88:[88, 14], Operations: ['14+74=88', '21-7=14'] Exploring Operation: 88-14=74, Resulting Numbers: [74] 74,88 unequal: No Solution Exploring Operation: 88*14=1232, Resulting Numbers: [1232] 1232,88 unequal: No Solution Exploring Operation: 88+14=102, Resulting Numbers: [102] 102,88 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 #0,3,2 Current State: 88:[88, 28], Operations: ['14+74=88', '7+21=28'] Exploring Operation: 88-28=60, Resulting Numbers: [60] 60,88 unequal: No Solution Exploring Operation: 88*28=2464, Resulting Numbers: [2464] 2464,88 unequal: No Solution Exploring Operation: 88+28=116, Resulting Numbers: [116] 116,88 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 #0,3,3 Current State: 88:[21, 95], Operations: ['14+74=88', '7+88=95'] Exploring Operation: 95-21=74, Resulting Numbers: [74] 74,88 unequal: No Solution Exploring Operation: 21*95=1995, Resulting Numbers: [1995] 1995,88 unequal: No Solution Exploring Operation: 21+95=116, Resulting Numbers: [116] 116,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 88:[14, 7, 95], Operations: ['74+21=95'] Exploring Operation: 14+7=21, Resulting Numbers: [95, 21] Generated Node #0,2,0: 88:[95, 21] Operation: 14+7=21 Exploring Operation: 14-7=7, Resulting Numbers: [95, 7] Generated Node #0,2,1: 88:[95, 7] Operation: 14-7=7 Exploring Operation: 95-7=88, Resulting Numbers: [14, 88] Generated Node #0,2,2: 88:[14, 88] Operation: 95-7=88 Exploring Operation: 14/7=2, Resulting Numbers: [95, 2] Generated Node #0,2,3: 88:[95, 2] Operation: 14/7=2 Moving to Node #0,0 Current State: 88:[14, 21, 81], Operations: ['74+7=81'] Exploring Operation: 21-14=7, Resulting Numbers: [81, 7] Generated Node #0,0,0: 88:[81, 7] Operation: 21-14=7 Exploring Operation: 14+21=35, Resulting Numbers: [81, 35] Generated Node #0,0,1: 88:[81, 35] Operation: 14+21=35 Exploring Operation: 14+81=95, Resulting Numbers: [21, 95] Generated Node #0,0,2: 88:[21, 95] Operation: 14+81=95 Exploring Operation: 21+81=102, Resulting Numbers: [14, 102] Generated Node #0,0,3: 88:[14, 102] Operation: 21+81=102 Moving to Node #0,1 Current State: 88:[14, 7, 53], Operations: ['74-21=53'] Exploring Operation: 53-14=39, Resulting Numbers: [7, 39] Generated Node #0,1,0: 88:[7, 39] Operation: 53-14=39 Exploring Operation: 53-7=46, Resulting Numbers: [14, 46] Generated Node #0,1,1: 88:[14, 46] Operation: 53-7=46 Exploring Operation: 14+7=21, Resulting Numbers: [53, 21] Generated Node #0,1,2: 88:[53, 21] Operation: 14+7=21 Exploring Operation: 14/7=2, Resulting Numbers: [53, 2] Generated Node #0,1,3: 88:[53, 2] Operation: 14/7=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 88:[14, 46], Operations: ['74-21=53', '53-7=46'] Exploring Operation: 14+46=60, Resulting Numbers: [60] 60,88 unequal: No Solution Exploring Operation: 14*46=644, Resulting Numbers: [644] 644,88 unequal: No Solution Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,88 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:[7, 39], Operations: ['74-21=53', '53-14=39'] Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,88 unequal: No Solution Exploring Operation: 7*39=273, Resulting Numbers: [273] 273,88 unequal: No Solution Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 88:[53, 2], Operations: ['74-21=53', '14/7=2'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,88 unequal: No Solution Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,88 unequal: No Solution Exploring Operation: 53*2=106, Resulting Numbers: [106] 106,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 88:[53, 21], Operations: ['74-21=53', '14+7=21'] Exploring Operation: 53-21=32, Resulting Numbers: [32] 32,88 unequal: No Solution Exploring Operation: 53+21=74, Resulting Numbers: [74] 74,88 unequal: No Solution Exploring Operation: 53*21=1113, Resulting Numbers: [1113] 1113,88 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: 88:[14, 88], Operations: ['74+21=95', '95-7=88'] Exploring Operation: 88-14=74, Resulting Numbers: [74] 74,88 unequal: No Solution Exploring Operation: 14*88=1232, Resulting Numbers: [1232] 1232,88 unequal: No Solution Exploring Operation: 14+88=102, Resulting Numbers: [102] 102,88 unequal: No Solution Moving to Node #0,2,3 Current State: 88:[95, 2], Operations: ['74+21=95', '14/7=2'] Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,88 unequal: No Solution Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,88 unequal: No Solution Exploring Operation: 95*2=190, Resulting Numbers: [190] 190,88 unequal: No Solution Moving to Node #0,2,0 Current State: 88:[95, 21], Operations: ['74+21=95', '14+7=21'] Exploring Operation: 95-21=74, Resulting Numbers: [74] 74,88 unequal: No Solution Exploring Operation: 95+21=116, Resulting Numbers: [116] 116,88 unequal: No Solution Exploring Operation: 95*21=1995, Resulting Numbers: [1995] 1995,88 unequal: No Solution Moving to Node #0,0,2 Current State: 88:[21, 95], Operations: ['74+7=81', '14+81=95'] Exploring Operation: 21*95=1995, Resulting Numbers: [1995] 1995,88 unequal: No Solution Exploring Operation: 95-21=74, Resulting Numbers: [74] 74,88 unequal: No Solution Exploring Operation: 21+95=116, Resulting Numbers: [116] 116,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[81, 7], Operations: ['74+7=81', '21-14=7'] Exploring Operation: 81-7=74, Resulting Numbers: [74] 74,88 unequal: No Solution Exploring Operation: 81*7=567, Resulting Numbers: [567] 567,88 unequal: No Solution Exploring Operation: 81+7=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[14, 74, 7, 21], Operations: [] Exploring Operation: 74+7=81, Resulting Numbers: [14, 21, 81] Generated Node #0,0: 88:[14, 21, 81] Operation: 74+7=81 Moving to Node #0,0 Current State: 88:[14, 21, 81], Operations: ['74+7=81'] Exploring Operation: 21-14=7, Resulting Numbers: [81, 7] Generated Node #0,0,0: 88:[81, 7] Operation: 21-14=7 Moving to Node #0,0,0 Current State: 88:[81, 7], Operations: ['74+7=81', '21-14=7'] Exploring Operation: 81+7=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.945313
hs_4
mult_heuristic
[ 48, 5, 55, 13 ]
72
[ "55-48=7", "5*13=65", "7+65=72" ]
Current State: 72:[48, 5, 55, 13], Operations: [] Exploring Operation: 55-48=7, Resulting Numbers: [5, 13, 7] Generated Node #2: [5, 13, 7] from Operation: 55-48=7 Current State: 72:[5, 13, 7], Operations: ['55-48=7'] Exploring Operation: 5*13=65, Resulting Numbers: [7, 65] Generated Node #3: [7, 65] from Operation: 5*13=65 Current State: 72:[7, 65], Operations: ['55-48=7', '5*13=65'] Exploring Operation: 7+65=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[48, 5, 55, 13], Operations: [] Exploring Operation: 55/5=11, Resulting Numbers: [48, 13, 11] Generated Node #0,0: 72:[48, 13, 11] Operation: 55/5=11 Exploring Operation: 55-48=7, Resulting Numbers: [5, 13, 7] Generated Node #0,1: 72:[5, 13, 7] Operation: 55-48=7 Exploring Operation: 55+13=68, Resulting Numbers: [48, 5, 68] Generated Node #0,2: 72:[48, 5, 68] Operation: 55+13=68 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[5, 13, 7], Operations: ['55-48=7'] Exploring Operation: 13-5=8, Resulting Numbers: [7, 8] Generated Node #0,1,0: 72:[7, 8] Operation: 13-5=8 Exploring Operation: 5+13=18, Resulting Numbers: [7, 18] Generated Node #0,1,1: 72:[7, 18] Operation: 5+13=18 Exploring Operation: 5+7=12, Resulting Numbers: [13, 12] Generated Node #0,1,2: 72:[13, 12] Operation: 5+7=12 Moving to Node #0,1,0 Current State: 72:[7, 8], Operations: ['55-48=7', '13-5=8'] Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,72 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,72 unequal: No Solution Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[7, 18], Operations: ['55-48=7', '5+13=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,72 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,72 unequal: No Solution Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[13, 12], Operations: ['55-48=7', '5+7=12'] Exploring Operation: 13+12=25, Resulting Numbers: [25] 25,72 unequal: No Solution Exploring Operation: 13*12=156, Resulting Numbers: [156] 156,72 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,72 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 #0,0 Current State: 72:[48, 13, 11], Operations: ['55/5=11'] Exploring Operation: 48-13=35, Resulting Numbers: [11, 35] Generated Node #0,0,0: 72:[11, 35] Operation: 48-13=35 Exploring Operation: 48+13=61, Resulting Numbers: [11, 61] Generated Node #0,0,1: 72:[11, 61] Operation: 48+13=61 Exploring Operation: 48-11=37, Resulting Numbers: [13, 37] Generated Node #0,0,2: 72:[13, 37] Operation: 48-11=37 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[11, 35], Operations: ['55/5=11', '48-13=35'] Exploring Operation: 11+35=46, Resulting Numbers: [46] 46,72 unequal: No Solution Exploring Operation: 35-11=24, Resulting Numbers: [24] 24,72 unequal: No Solution Exploring Operation: 11*35=385, Resulting Numbers: [385] 385,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 72:[13, 37], Operations: ['55/5=11', '48-11=37'] Exploring Operation: 13+37=50, Resulting Numbers: [50] 50,72 unequal: No Solution Exploring Operation: 37-13=24, Resulting Numbers: [24] 24,72 unequal: No Solution Exploring Operation: 13*37=481, Resulting Numbers: [481] 481,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 72:[11, 61], Operations: ['55/5=11', '48+13=61'] Exploring Operation: 61-11=50, Resulting Numbers: [50] 50,72 unequal: No Solution Exploring Operation: 11+61=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[48, 5, 55, 13], Operations: [] Exploring Operation: 55/5=11, Resulting Numbers: [48, 13, 11] Generated Node #0,0: 72:[48, 13, 11] Operation: 55/5=11 Moving to Node #0,0 Current State: 72:[48, 13, 11], Operations: ['55/5=11'] Exploring Operation: 48+13=61, Resulting Numbers: [11, 61] Generated Node #0,0,1: 72:[11, 61] Operation: 48+13=61 Moving to Node #0,0,1 Current State: 72:[11, 61], Operations: ['55/5=11', '48+13=61'] Exploring Operation: 11+61=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_3
sum_heuristic
[ 16, 2, 9, 46 ]
51
[ "16-2=14", "46-9=37", "14+37=51" ]
Current State: 51:[16, 2, 9, 46], Operations: [] Exploring Operation: 16-2=14, Resulting Numbers: [9, 46, 14] Generated Node #2: [9, 46, 14] from Operation: 16-2=14 Current State: 51:[9, 46, 14], Operations: ['16-2=14'] Exploring Operation: 46-9=37, Resulting Numbers: [14, 37] Generated Node #3: [14, 37] from Operation: 46-9=37 Current State: 51:[14, 37], Operations: ['16-2=14', '46-9=37'] Exploring Operation: 14+37=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[16, 2, 9, 46], Operations: [] Exploring Operation: 9-2=7, Resulting Numbers: [16, 46, 7] Generated Node #0,0: 51:[16, 46, 7] Operation: 9-2=7 Exploring Operation: 9+46=55, Resulting Numbers: [16, 2, 55] Generated Node #0,1: 51:[16, 2, 55] Operation: 9+46=55 Exploring Operation: 2*9=18, Resulting Numbers: [16, 46, 18] Generated Node #0,2: 51:[16, 46, 18] Operation: 2*9=18 Exploring Operation: 16-9=7, Resulting Numbers: [2, 46, 7] Generated Node #0,3: 51:[2, 46, 7] Operation: 16-9=7 Moving to Node #0,1 Current State: 51:[16, 2, 55], Operations: ['9+46=55'] Exploring Operation: 16-2=14, Resulting Numbers: [55, 14] Generated Node #0,1,0: 51:[55, 14] Operation: 16-2=14 Exploring Operation: 2+55=57, Resulting Numbers: [16, 57] Generated Node #0,1,1: 51:[16, 57] Operation: 2+55=57 Exploring Operation: 16+2=18, Resulting Numbers: [55, 18] Generated Node #0,1,2: 51:[55, 18] Operation: 16+2=18 Exploring Operation: 55-2=53, Resulting Numbers: [16, 53] Generated Node #0,1,3: 51:[16, 53] Operation: 55-2=53 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 51:[16, 53], Operations: ['9+46=55', '55-2=53'] Exploring Operation: 16+53=69, Resulting Numbers: [69] 69,51 unequal: No Solution Exploring Operation: 16*53=848, Resulting Numbers: [848] 848,51 unequal: No Solution Exploring Operation: 53-16=37, Resulting Numbers: [37] 37,51 unequal: No Solution No 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: 51:[55, 18], Operations: ['9+46=55', '16+2=18'] Exploring Operation: 55-18=37, Resulting Numbers: [37] 37,51 unequal: No Solution Exploring Operation: 55*18=990, Resulting Numbers: [990] 990,51 unequal: No Solution Exploring Operation: 55+18=73, Resulting Numbers: [73] 73,51 unequal: No Solution No 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: 51:[55, 14], Operations: ['9+46=55', '16-2=14'] Exploring Operation: 55-14=41, Resulting Numbers: [41] 41,51 unequal: No Solution Exploring Operation: 55+14=69, Resulting Numbers: [69] 69,51 unequal: No Solution Exploring Operation: 55*14=770, Resulting Numbers: [770] 770,51 unequal: No Solution No 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: 51:[16, 57], Operations: ['9+46=55', '2+55=57'] Exploring Operation: 16+57=73, Resulting Numbers: [73] 73,51 unequal: No Solution Exploring Operation: 57-16=41, Resulting Numbers: [41] 41,51 unequal: No Solution Exploring Operation: 16*57=912, Resulting Numbers: [912] 912,51 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: 51:[16, 46, 18], Operations: ['2*9=18'] Exploring Operation: 46-18=28, Resulting Numbers: [16, 28] Generated Node #0,2,0: 51:[16, 28] Operation: 46-18=28 Exploring Operation: 18-16=2, Resulting Numbers: [46, 2] Generated Node #0,2,1: 51:[46, 2] Operation: 18-16=2 Exploring Operation: 46-16=30, Resulting Numbers: [18, 30] Generated Node #0,2,2: 51:[18, 30] Operation: 46-16=30 Exploring Operation: 16+46=62, Resulting Numbers: [18, 62] Generated Node #0,2,3: 51:[18, 62] Operation: 16+46=62 Moving to Node #0,3 Current State: 51:[2, 46, 7], Operations: ['16-9=7'] Exploring Operation: 46+7=53, Resulting Numbers: [2, 53] Generated Node #0,3,0: 51:[2, 53] Operation: 46+7=53 Exploring Operation: 7-2=5, Resulting Numbers: [46, 5] Generated Node #0,3,1: 51:[46, 5] Operation: 7-2=5 Exploring Operation: 2*7=14, Resulting Numbers: [46, 14] Generated Node #0,3,2: 51:[46, 14] Operation: 2*7=14 Exploring Operation: 2+46=48, Resulting Numbers: [7, 48] Generated Node #0,3,3: 51:[7, 48] Operation: 2+46=48 Moving to Node #0,0 Current State: 51:[16, 46, 7], Operations: ['9-2=7'] Exploring Operation: 16+7=23, Resulting Numbers: [46, 23] Generated Node #0,0,0: 51:[46, 23] Operation: 16+7=23 Exploring Operation: 46+7=53, Resulting Numbers: [16, 53] Generated Node #0,0,1: 51:[16, 53] Operation: 46+7=53 Exploring Operation: 16-7=9, Resulting Numbers: [46, 9] Generated Node #0,0,2: 51:[46, 9] Operation: 16-7=9 Exploring Operation: 46-7=39, Resulting Numbers: [16, 39] Generated Node #0,0,3: 51:[16, 39] Operation: 46-7=39 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 51:[16, 53], Operations: ['9-2=7', '46+7=53'] Exploring Operation: 16*53=848, Resulting Numbers: [848] 848,51 unequal: No Solution Exploring Operation: 53-16=37, Resulting Numbers: [37] 37,51 unequal: No Solution Exploring Operation: 16+53=69, Resulting Numbers: [69] 69,51 unequal: No Solution No 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: 51:[46, 23], Operations: ['9-2=7', '16+7=23'] Exploring Operation: 46*23=1058, Resulting Numbers: [1058] 1058,51 unequal: No Solution Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 46+23=69, Resulting Numbers: [69] 69,51 unequal: No Solution Exploring Operation: 46/23=2, Resulting Numbers: [2] 2,51 unequal: No Solution No 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: 51:[46, 9], Operations: ['9-2=7', '16-7=9'] Exploring Operation: 46*9=414, Resulting Numbers: [414] 414,51 unequal: No Solution Exploring Operation: 46+9=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,51 unequal: No Solution No 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: 51:[16, 39], Operations: ['9-2=7', '46-7=39'] Exploring Operation: 16+39=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 16*39=624, Resulting Numbers: [624] 624,51 unequal: No Solution Exploring Operation: 39-16=23, Resulting Numbers: [23] 23,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 51:[2, 53], Operations: ['16-9=7', '46+7=53'] Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,51 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[16, 2, 9, 46], Operations: [] Exploring Operation: 16-9=7, Resulting Numbers: [2, 46, 7] Generated Node #0,3: 51:[2, 46, 7] Operation: 16-9=7 Moving to Node #0,3 Current State: 51:[2, 46, 7], Operations: ['16-9=7'] Exploring Operation: 46+7=53, Resulting Numbers: [2, 53] Generated Node #0,3,0: 51:[2, 53] Operation: 46+7=53 Moving to Node #0,3,0 Current State: 51:[2, 53], Operations: ['16-9=7', '46+7=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
0.955729
hs_4
sum_heuristic
[ 31, 10, 15, 84 ]
23
[ "31+84=115", "15-10=5", "115/5=23" ]
Current State: 23:[31, 10, 15, 84], Operations: [] Exploring Operation: 31+84=115, Resulting Numbers: [10, 15, 115] Generated Node #2: [10, 15, 115] from Operation: 31+84=115 Current State: 23:[10, 15, 115], Operations: ['31+84=115'] Exploring Operation: 15-10=5, Resulting Numbers: [115, 5] Generated Node #3: [115, 5] from Operation: 15-10=5 Current State: 23:[115, 5], Operations: ['31+84=115', '15-10=5'] Exploring Operation: 115/5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[31, 10, 15, 84], Operations: [] Exploring Operation: 84-31=53, Resulting Numbers: [10, 15, 53] Generated Node #0,0: 23:[10, 15, 53] Operation: 84-31=53 Exploring Operation: 84-10=74, Resulting Numbers: [31, 15, 74] Generated Node #0,1: 23:[31, 15, 74] Operation: 84-10=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[10, 15, 53], Operations: ['84-31=53'] Exploring Operation: 53-10=43, Resulting Numbers: [15, 43] Generated Node #0,0,0: 23:[15, 43] Operation: 53-10=43 Exploring Operation: 53-15=38, Resulting Numbers: [10, 38] Generated Node #0,0,1: 23:[10, 38] Operation: 53-15=38 Moving to Node #0,0,0 Current State: 23:[15, 43], Operations: ['84-31=53', '53-10=43'] Exploring Operation: 43-15=28, Resulting Numbers: [28] 28,23 unequal: No Solution Exploring Operation: 15+43=58, Resulting Numbers: [58] 58,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[10, 38], Operations: ['84-31=53', '53-15=38'] Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,23 unequal: No Solution Exploring Operation: 10+38=48, Resulting Numbers: [48] 48,23 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 Current State: 23:[31, 15, 74], Operations: ['84-10=74'] Exploring Operation: 74-15=59, Resulting Numbers: [31, 59] Generated Node #0,1,0: 23:[31, 59] Operation: 74-15=59 Exploring Operation: 74-31=43, Resulting Numbers: [15, 43] Generated Node #0,1,1: 23:[15, 43] Operation: 74-31=43 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 23:[15, 43], Operations: ['84-10=74', '74-31=43'] Exploring Operation: 15+43=58, Resulting Numbers: [58] 58,23 unequal: No Solution Exploring Operation: 43-15=28, Resulting Numbers: [28] 28,23 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 #0,1,0 Current State: 23:[31, 59], Operations: ['84-10=74', '74-15=59'] Exploring Operation: 59-31=28, Resulting Numbers: [28] 28,23 unequal: No Solution Exploring Operation: 31+59=90, Resulting Numbers: [90] 90,23 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
[ 45, 11, 63, 72 ]
90
[ "11+63=74", "74-72=2", "45*2=90" ]
Current State: 90:[45, 11, 63, 72], Operations: [] Exploring Operation: 11+63=74, Resulting Numbers: [45, 72, 74] Generated Node #2: [45, 72, 74] from Operation: 11+63=74 Current State: 90:[45, 72, 74], Operations: ['11+63=74'] Exploring Operation: 74-72=2, Resulting Numbers: [45, 2] Generated Node #3: [45, 2] from Operation: 74-72=2 Current State: 90:[45, 2], Operations: ['11+63=74', '74-72=2'] Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[45, 11, 63, 72], Operations: [] Exploring Operation: 72-63=9, Resulting Numbers: [45, 11, 9] Generated Node #0,0: 90:[45, 11, 9] Operation: 72-63=9 Exploring Operation: 63-45=18, Resulting Numbers: [11, 72, 18] Generated Node #0,1: 90:[11, 72, 18] Operation: 63-45=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[45, 11, 9], Operations: ['72-63=9'] Exploring Operation: 11-9=2, Resulting Numbers: [45, 2] Generated Node #0,0,0: 90:[45, 2] Operation: 11-9=2 Exploring Operation: 45/9=5, Resulting Numbers: [11, 5] Generated Node #0,0,1: 90:[11, 5] Operation: 45/9=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[45, 2], Operations: ['72-63=9', '11-9=2'] Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,90 unequal: No Solution Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[45, 11, 63, 72], Operations: [] Exploring Operation: 72-63=9, Resulting Numbers: [45, 11, 9] Generated Node #0,0: 90:[45, 11, 9] Operation: 72-63=9 Moving to Node #0,0 Current State: 90:[45, 11, 9], Operations: ['72-63=9'] Exploring Operation: 11-9=2, Resulting Numbers: [45, 2] Generated Node #0,0,0: 90:[45, 2] Operation: 11-9=2 Moving to Node #0,0,0 Current State: 90:[45, 2], Operations: ['72-63=9', '11-9=2'] Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 75, 11, 96, 86 ]
54
[ "75-11=64", "96-86=10", "64-10=54" ]
Current State: 54:[75, 11, 96, 86], Operations: [] Exploring Operation: 75-11=64, Resulting Numbers: [96, 86, 64] Generated Node #2: [96, 86, 64] from Operation: 75-11=64 Current State: 54:[96, 86, 64], Operations: ['75-11=64'] Exploring Operation: 96-86=10, Resulting Numbers: [64, 10] Generated Node #3: [64, 10] from Operation: 96-86=10 Current State: 54:[64, 10], Operations: ['75-11=64', '96-86=10'] Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[75, 11, 96, 86], Operations: [] Exploring Operation: 75-11=64, Resulting Numbers: [96, 86, 64] Generated Node #0,0: 54:[96, 86, 64] Operation: 75-11=64 Exploring Operation: 86-75=11, Resulting Numbers: [11, 96, 11] Generated Node #0,1: 54:[11, 96, 11] Operation: 86-75=11 Exploring Operation: 96-86=10, Resulting Numbers: [75, 11, 10] Generated Node #0,2: 54:[75, 11, 10] Operation: 96-86=10 Exploring Operation: 96-75=21, Resulting Numbers: [11, 86, 21] Generated Node #0,3: 54:[11, 86, 21] Operation: 96-75=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[75, 11, 10], Operations: ['96-86=10'] Exploring Operation: 11+10=21, Resulting Numbers: [75, 21] Generated Node #0,2,0: 54:[75, 21] Operation: 11+10=21 Exploring Operation: 75-10=65, Resulting Numbers: [11, 65] Generated Node #0,2,1: 54:[11, 65] Operation: 75-10=65 Exploring Operation: 11-10=1, Resulting Numbers: [75, 1] Generated Node #0,2,2: 54:[75, 1] Operation: 11-10=1 Exploring Operation: 75-11=64, Resulting Numbers: [10, 64] Generated Node #0,2,3: 54:[10, 64] Operation: 75-11=64 Moving to Node #0,2,3 Current State: 54:[10, 64], Operations: ['96-86=10', '75-11=64'] Exploring Operation: 10+64=74, Resulting Numbers: [74] 74,54 unequal: No Solution Exploring Operation: 10*64=640, Resulting Numbers: [640] 640,54 unequal: No Solution Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[75, 11, 96, 86], Operations: [] Exploring Operation: 96-86=10, Resulting Numbers: [75, 11, 10] Generated Node #0,2: 54:[75, 11, 10] Operation: 96-86=10 Moving to Node #0,2 Current State: 54:[75, 11, 10], Operations: ['96-86=10'] Exploring Operation: 75-11=64, Resulting Numbers: [10, 64] Generated Node #0,2,3: 54:[10, 64] Operation: 75-11=64 Moving to Node #0,2,3 Current State: 54:[10, 64], Operations: ['96-86=10', '75-11=64'] Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 39, 19, 74, 70 ]
16
[ "39-19=20", "74-70=4", "20-4=16" ]
Current State: 16:[39, 19, 74, 70], Operations: [] Exploring Operation: 39-19=20, Resulting Numbers: [74, 70, 20] Generated Node #2: [74, 70, 20] from Operation: 39-19=20 Current State: 16:[74, 70, 20], Operations: ['39-19=20'] Exploring Operation: 74-70=4, Resulting Numbers: [20, 4] Generated Node #3: [20, 4] from Operation: 74-70=4 Current State: 16:[20, 4], Operations: ['39-19=20', '74-70=4'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[39, 19, 74, 70], Operations: [] Exploring Operation: 70-39=31, Resulting Numbers: [19, 74, 31] Generated Node #0,0: 16:[19, 74, 31] Operation: 70-39=31 Exploring Operation: 39-19=20, Resulting Numbers: [74, 70, 20] Generated Node #0,1: 16:[74, 70, 20] Operation: 39-19=20 Exploring Operation: 74-39=35, Resulting Numbers: [19, 70, 35] Generated Node #0,2: 16:[19, 70, 35] Operation: 74-39=35 Exploring Operation: 74-70=4, Resulting Numbers: [39, 19, 4] Generated Node #0,3: 16:[39, 19, 4] Operation: 74-70=4 Start Sub Search at level 1: Moving to Node #0,3 Current State: 16:[39, 19, 4], Operations: ['74-70=4'] Exploring Operation: 39-19=20, Resulting Numbers: [4, 20] Generated Node #0,3,0: 16:[4, 20] Operation: 39-19=20 Exploring Operation: 19-4=15, Resulting Numbers: [39, 15] Generated Node #0,3,1: 16:[39, 15] Operation: 19-4=15 Exploring Operation: 39+4=43, Resulting Numbers: [19, 43] Generated Node #0,3,2: 16:[19, 43] Operation: 39+4=43 Exploring Operation: 39-4=35, Resulting Numbers: [19, 35] Generated Node #0,3,3: 16:[19, 35] Operation: 39-4=35 Moving to Node #0,3,0 Current State: 16:[4, 20], Operations: ['74-70=4', '39-19=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[39, 19, 74, 70], Operations: [] Exploring Operation: 74-70=4, Resulting Numbers: [39, 19, 4] Generated Node #0,3: 16:[39, 19, 4] Operation: 74-70=4 Moving to Node #0,3 Current State: 16:[39, 19, 4], Operations: ['74-70=4'] Exploring Operation: 39-19=20, Resulting Numbers: [4, 20] Generated Node #0,3,0: 16:[4, 20] Operation: 39-19=20 Moving to Node #0,3,0 Current State: 16:[4, 20], Operations: ['74-70=4', '39-19=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 97, 60, 30, 32 ]
99
[ "97-60=37", "30+32=62", "37+62=99" ]
Current State: 99:[97, 60, 30, 32], Operations: [] Exploring Operation: 97-60=37, Resulting Numbers: [30, 32, 37] Generated Node #2: [30, 32, 37] from Operation: 97-60=37 Current State: 99:[30, 32, 37], Operations: ['97-60=37'] Exploring Operation: 30+32=62, Resulting Numbers: [37, 62] Generated Node #3: [37, 62] from Operation: 30+32=62 Current State: 99:[37, 62], Operations: ['97-60=37', '30+32=62'] Exploring Operation: 37+62=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[97, 60, 30, 32], Operations: [] Exploring Operation: 60/30=2, Resulting Numbers: [97, 32, 2] Generated Node #0,0: 99:[97, 32, 2] Operation: 60/30=2 Exploring Operation: 97-60=37, Resulting Numbers: [30, 32, 37] Generated Node #0,1: 99:[30, 32, 37] Operation: 97-60=37 Exploring Operation: 60-30=30, Resulting Numbers: [97, 32, 30] Generated Node #0,2: 99:[97, 32, 30] Operation: 60-30=30 Exploring Operation: 60+30=90, Resulting Numbers: [97, 32, 90] Generated Node #0,3: 99:[97, 32, 90] Operation: 60+30=90 Exploring Operation: 60-32=28, Resulting Numbers: [97, 30, 28] Generated Node #0,4: 99:[97, 30, 28] Operation: 60-32=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[97, 32, 2], Operations: ['60/30=2'] Exploring Operation: 97+2=99, Resulting Numbers: [32, 99] Generated Node #0,0,0: 99:[32, 99] Operation: 97+2=99 Exploring Operation: 32+2=34, Resulting Numbers: [97, 34] Generated Node #0,0,1: 99:[97, 34] Operation: 32+2=34 Exploring Operation: 97-2=95, Resulting Numbers: [32, 95] Generated Node #0,0,2: 99:[32, 95] Operation: 97-2=95 Exploring Operation: 32-2=30, Resulting Numbers: [97, 30] Generated Node #0,0,3: 99:[97, 30] Operation: 32-2=30 Exploring Operation: 32/2=16, Resulting Numbers: [97, 16] Generated Node #0,0,4: 99:[97, 16] Operation: 32/2=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[32, 99], Operations: ['60/30=2', '97+2=99'] Exploring Operation: 99-32=67, Resulting Numbers: [67] 67,99 unequal: No Solution Exploring Operation: 32+99=131, Resulting Numbers: [131] 131,99 unequal: No Solution Exploring Operation: 32*99=3168, Resulting Numbers: [3168] 3168,99 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 #0,0,1 Current State: 99:[97, 34], Operations: ['60/30=2', '32+2=34'] Exploring Operation: 97+34=131, Resulting Numbers: [131] 131,99 unequal: No Solution Exploring Operation: 97*34=3298, Resulting Numbers: [3298] 3298,99 unequal: No Solution Exploring Operation: 97-34=63, Resulting Numbers: [63] 63,99 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 #0,0,2 Current State: 99:[32, 95], Operations: ['60/30=2', '97-2=95'] Exploring Operation: 32+95=127, Resulting Numbers: [127] 127,99 unequal: No Solution Exploring Operation: 95-32=63, Resulting Numbers: [63] 63,99 unequal: No Solution Exploring Operation: 32*95=3040, Resulting Numbers: [3040] 3040,99 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 #0,0,3 Current State: 99:[97, 30], Operations: ['60/30=2', '32-2=30'] Exploring Operation: 97+30=127, Resulting Numbers: [127] 127,99 unequal: No Solution Exploring Operation: 97*30=2910, Resulting Numbers: [2910] 2910,99 unequal: No Solution Exploring Operation: 97-30=67, Resulting Numbers: [67] 67,99 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 #0,0,4 Current State: 99:[97, 16], Operations: ['60/30=2', '32/2=16'] Exploring Operation: 97-16=81, Resulting Numbers: [81] 81,99 unequal: No Solution Exploring Operation: 97+16=113, Resulting Numbers: [113] 113,99 unequal: No Solution Exploring Operation: 97*16=1552, Resulting Numbers: [1552] 1552,99 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: 99:[97, 32, 30], Operations: ['60-30=30'] Exploring Operation: 97+32=129, Resulting Numbers: [30, 129] Generated Node #0,2,0: 99:[30, 129] Operation: 97+32=129 Exploring Operation: 32+30=62, Resulting Numbers: [97, 62] Generated Node #0,2,1: 99:[97, 62] Operation: 32+30=62 Exploring Operation: 32-30=2, Resulting Numbers: [97, 2] Generated Node #0,2,2: 99:[97, 2] Operation: 32-30=2 Exploring Operation: 97+30=127, Resulting Numbers: [32, 127] Generated Node #0,2,3: 99:[32, 127] Operation: 97+30=127 Exploring Operation: 97-30=67, Resulting Numbers: [32, 67] Generated Node #0,2,4: 99:[32, 67] Operation: 97-30=67 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 99:[97, 2], Operations: ['60-30=30', '32-30=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[97, 60, 30, 32], Operations: [] Exploring Operation: 60-30=30, Resulting Numbers: [97, 32, 30] Generated Node #0,2: 99:[97, 32, 30] Operation: 60-30=30 Moving to Node #0,2 Current State: 99:[97, 32, 30], Operations: ['60-30=30'] Exploring Operation: 32-30=2, Resulting Numbers: [97, 2] Generated Node #0,2,2: 99:[97, 2] Operation: 32-30=2 Moving to Node #0,2,2 Current State: 99:[97, 2], Operations: ['60-30=30', '32-30=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_5
mult_heuristic
[ 73, 5, 8, 43 ]
56
[ "73-8=65", "65/5=13", "43+13=56" ]
Current State: 56:[73, 5, 8, 43], Operations: [] Exploring Operation: 73-8=65, Resulting Numbers: [5, 43, 65] Generated Node #2: [5, 43, 65] from Operation: 73-8=65 Current State: 56:[5, 43, 65], Operations: ['73-8=65'] Exploring Operation: 65/5=13, Resulting Numbers: [43, 13] Generated Node #3: [43, 13] from Operation: 65/5=13 Current State: 56:[43, 13], Operations: ['73-8=65', '65/5=13'] Exploring Operation: 43+13=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[73, 5, 8, 43], Operations: [] Exploring Operation: 73-43=30, Resulting Numbers: [5, 8, 30] Generated Node #0,0: 56:[5, 8, 30] Operation: 73-43=30 Moving to Node #0,0 Current State: 56:[5, 8, 30], Operations: ['73-43=30'] Exploring Operation: 30/5=6, Resulting Numbers: [8, 6] Generated Node #0,0,0: 56:[8, 6] Operation: 30/5=6 Moving to Node #0,0,0 Current State: 56:[8, 6], Operations: ['73-43=30', '30/5=6'] Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,56 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 39, 87, 14, 77 ]
86
[ "39+87=126", "126/14=9", "77+9=86" ]
Current State: 86:[39, 87, 14, 77], Operations: [] Exploring Operation: 39+87=126, Resulting Numbers: [14, 77, 126] Generated Node #2: [14, 77, 126] from Operation: 39+87=126 Current State: 86:[14, 77, 126], Operations: ['39+87=126'] Exploring Operation: 126/14=9, Resulting Numbers: [77, 9] Generated Node #3: [77, 9] from Operation: 126/14=9 Current State: 86:[77, 9], Operations: ['39+87=126', '126/14=9'] Exploring Operation: 77+9=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[39, 87, 14, 77], Operations: [] Exploring Operation: 77-39=38, Resulting Numbers: [87, 14, 38] Generated Node #0,0: 86:[87, 14, 38] Operation: 77-39=38 Exploring Operation: 39+14=53, Resulting Numbers: [87, 77, 53] Generated Node #0,1: 86:[87, 77, 53] Operation: 39+14=53 Exploring Operation: 14+77=91, Resulting Numbers: [39, 87, 91] Generated Node #0,2: 86:[39, 87, 91] Operation: 14+77=91 Exploring Operation: 87-77=10, Resulting Numbers: [39, 14, 10] Generated Node #0,3: 86:[39, 14, 10] Operation: 87-77=10 Moving to Node #0,2 Current State: 86:[39, 87, 91], Operations: ['14+77=91'] Exploring Operation: 87-39=48, Resulting Numbers: [91, 48] Generated Node #0,2,0: 86:[91, 48] Operation: 87-39=48 Exploring Operation: 91-39=52, Resulting Numbers: [87, 52] Generated Node #0,2,1: 86:[87, 52] Operation: 91-39=52 Exploring Operation: 39+87=126, Resulting Numbers: [91, 126] Generated Node #0,2,2: 86:[91, 126] Operation: 39+87=126 Exploring Operation: 91-87=4, Resulting Numbers: [39, 4] Generated Node #0,2,3: 86:[39, 4] Operation: 91-87=4 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 86:[39, 4], Operations: ['14+77=91', '91-87=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 39*4=156, Resulting Numbers: [156] 156,86 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 86:[91, 48], Operations: ['14+77=91', '87-39=48'] Exploring Operation: 91+48=139, Resulting Numbers: [139] 139,86 unequal: No Solution Exploring Operation: 91-48=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 91*48=4368, Resulting Numbers: [4368] 4368,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 86:[87, 52], Operations: ['14+77=91', '91-39=52'] Exploring Operation: 87+52=139, Resulting Numbers: [139] 139,86 unequal: No Solution Exploring Operation: 87*52=4524, Resulting Numbers: [4524] 4524,86 unequal: No Solution Exploring Operation: 87-52=35, Resulting Numbers: [35] 35,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 86:[91, 126], Operations: ['14+77=91', '39+87=126'] Exploring Operation: 126-91=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 91*126=11466, Resulting Numbers: [11466] 11466,86 unequal: No Solution Exploring Operation: 91+126=217, Resulting Numbers: [217] 217,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 86:[87, 14, 38], Operations: ['77-39=38'] Exploring Operation: 87-14=73, Resulting Numbers: [38, 73] Generated Node #0,0,0: 86:[38, 73] Operation: 87-14=73 Exploring Operation: 87+14=101, Resulting Numbers: [38, 101] Generated Node #0,0,1: 86:[38, 101] Operation: 87+14=101 Exploring Operation: 87-38=49, Resulting Numbers: [14, 49] Generated Node #0,0,2: 86:[14, 49] Operation: 87-38=49 Exploring Operation: 14+38=52, Resulting Numbers: [87, 52] Generated Node #0,0,3: 86:[87, 52] Operation: 14+38=52 Moving to Node #0,1 Current State: 86:[87, 77, 53], Operations: ['39+14=53'] Exploring Operation: 77+53=130, Resulting Numbers: [87, 130] Generated Node #0,1,0: 86:[87, 130] Operation: 77+53=130 Exploring Operation: 77-53=24, Resulting Numbers: [87, 24] Generated Node #0,1,1: 86:[87, 24] Operation: 77-53=24 Exploring Operation: 87-53=34, Resulting Numbers: [77, 34] Generated Node #0,1,2: 86:[77, 34] Operation: 87-53=34 Exploring Operation: 87-77=10, Resulting Numbers: [53, 10] Generated Node #0,1,3: 86:[53, 10] Operation: 87-77=10 Moving to Node #0,3 Current State: 86:[39, 14, 10], Operations: ['87-77=10'] Exploring Operation: 14+10=24, Resulting Numbers: [39, 24] Generated Node #0,3,0: 86:[39, 24] Operation: 14+10=24 Exploring Operation: 39+14=53, Resulting Numbers: [10, 53] Generated Node #0,3,1: 86:[10, 53] Operation: 39+14=53 Exploring Operation: 14-10=4, Resulting Numbers: [39, 4] Generated Node #0,3,2: 86:[39, 4] Operation: 14-10=4 Exploring Operation: 39+10=49, Resulting Numbers: [14, 49] Generated Node #0,3,3: 86:[14, 49] Operation: 39+10=49 Moving to Node #0,3,2 Current State: 86:[39, 4], Operations: ['87-77=10', '14-10=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 39*4=156, Resulting Numbers: [156] 156,86 unequal: No Solution Moving to Node #0,0,3 Current State: 86:[87, 52], Operations: ['77-39=38', '14+38=52'] Exploring Operation: 87*52=4524, Resulting Numbers: [4524] 4524,86 unequal: No Solution Exploring Operation: 87+52=139, Resulting Numbers: [139] 139,86 unequal: No Solution Exploring Operation: 87-52=35, Resulting Numbers: [35] 35,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[14, 49], Operations: ['77-39=38', '87-38=49'] Exploring Operation: 14*49=686, Resulting Numbers: [686] 686,86 unequal: No Solution Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 14+49=63, Resulting Numbers: [63] 63,86 unequal: No Solution Moving to Node #0,1,3 Current State: 86:[53, 10], Operations: ['39+14=53', '87-77=10'] Exploring Operation: 53+10=63, Resulting Numbers: [63] 63,86 unequal: No Solution Exploring Operation: 53*10=530, Resulting Numbers: [530] 530,86 unequal: No Solution Exploring Operation: 53-10=43, Resulting Numbers: [43] 43,86 unequal: No Solution Moving to Node #0,3,1 Current State: 86:[10, 53], Operations: ['87-77=10', '39+14=53'] Exploring Operation: 53-10=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 10+53=63, Resulting Numbers: [63] 63,86 unequal: No Solution Exploring Operation: 10*53=530, Resulting Numbers: [530] 530,86 unequal: No Solution Moving to Node #0,1,2 Current State: 86:[77, 34], Operations: ['39+14=53', '87-53=34'] Exploring Operation: 77-34=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 77*34=2618, Resulting Numbers: [2618] 2618,86 unequal: No Solution Exploring Operation: 77+34=111, Resulting Numbers: [111] 111,86 unequal: No Solution Moving to Node #0,3,3 Current State: 86:[14, 49], Operations: ['87-77=10', '39+10=49'] Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 14*49=686, Resulting Numbers: [686] 686,86 unequal: No Solution Exploring Operation: 14+49=63, Resulting Numbers: [63] 63,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[38, 73], Operations: ['77-39=38', '87-14=73'] Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 38+73=111, Resulting Numbers: [111] 111,86 unequal: No Solution Exploring Operation: 38*73=2774, Resulting Numbers: [2774] 2774,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[87, 24], Operations: ['39+14=53', '77-53=24'] Exploring Operation: 87-24=63, Resulting Numbers: [63] 63,86 unequal: No Solution Exploring Operation: 87*24=2088, Resulting Numbers: [2088] 2088,86 unequal: No Solution Exploring Operation: 87+24=111, Resulting Numbers: [111] 111,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[38, 101], Operations: ['77-39=38', '87+14=101'] Exploring Operation: 38+101=139, Resulting Numbers: [139] 139,86 unequal: No Solution Exploring Operation: 101-38=63, Resulting Numbers: [63] 63,86 unequal: No Solution Exploring Operation: 38*101=3838, Resulting Numbers: [3838] 3838,86 unequal: No Solution Moving to Node #0,3,0 Current State: 86:[39, 24], Operations: ['87-77=10', '14+10=24'] Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,86 unequal: No Solution Exploring Operation: 39+24=63, Resulting Numbers: [63] 63,86 unequal: No Solution Exploring Operation: 39*24=936, Resulting Numbers: [936] 936,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[87, 130], Operations: ['39+14=53', '77+53=130'] Exploring Operation: 130-87=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 87+130=217, Resulting Numbers: [217] 217,86 unequal: No Solution Exploring Operation: 87*130=11310, Resulting Numbers: [11310] 11310,86 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 17, 14, 43, 95 ]
55
[ "17-14=3", "95-43=52", "3+52=55" ]
Current State: 55:[17, 14, 43, 95], Operations: [] Exploring Operation: 17-14=3, Resulting Numbers: [43, 95, 3] Generated Node #2: [43, 95, 3] from Operation: 17-14=3 Current State: 55:[43, 95, 3], Operations: ['17-14=3'] Exploring Operation: 95-43=52, Resulting Numbers: [3, 52] Generated Node #3: [3, 52] from Operation: 95-43=52 Current State: 55:[3, 52], Operations: ['17-14=3', '95-43=52'] Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[17, 14, 43, 95], Operations: [] Exploring Operation: 95-17=78, Resulting Numbers: [14, 43, 78] Generated Node #0,0: 55:[14, 43, 78] Operation: 95-17=78 Exploring Operation: 17+43=60, Resulting Numbers: [14, 95, 60] Generated Node #0,1: 55:[14, 95, 60] Operation: 17+43=60 Exploring Operation: 95-43=52, Resulting Numbers: [17, 14, 52] Generated Node #0,2: 55:[17, 14, 52] Operation: 95-43=52 Exploring Operation: 95-14=81, Resulting Numbers: [17, 43, 81] Generated Node #0,3: 55:[17, 43, 81] Operation: 95-14=81 Moving to Node #0,2 Current State: 55:[17, 14, 52], Operations: ['95-43=52'] Exploring Operation: 14+52=66, Resulting Numbers: [17, 66] Generated Node #0,2,0: 55:[17, 66] Operation: 14+52=66 Exploring Operation: 17-14=3, Resulting Numbers: [52, 3] Generated Node #0,2,1: 55:[52, 3] Operation: 17-14=3 Exploring Operation: 17+14=31, Resulting Numbers: [52, 31] Generated Node #0,2,2: 55:[52, 31] Operation: 17+14=31 Exploring Operation: 17+52=69, Resulting Numbers: [14, 69] Generated Node #0,2,3: 55:[14, 69] Operation: 17+52=69 Moving to Node #0,0 Current State: 55:[14, 43, 78], Operations: ['95-17=78'] Exploring Operation: 78-43=35, Resulting Numbers: [14, 35] Generated Node #0,0,0: 55:[14, 35] Operation: 78-43=35 Exploring Operation: 43-14=29, Resulting Numbers: [78, 29] Generated Node #0,0,1: 55:[78, 29] Operation: 43-14=29 Exploring Operation: 78-14=64, Resulting Numbers: [43, 64] Generated Node #0,0,2: 55:[43, 64] Operation: 78-14=64 Exploring Operation: 14+43=57, Resulting Numbers: [78, 57] Generated Node #0,0,3: 55:[78, 57] Operation: 14+43=57 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 55:[43, 64], Operations: ['95-17=78', '78-14=64'] Exploring Operation: 64-43=21, Resulting Numbers: [21] 21,55 unequal: No Solution Exploring Operation: 43+64=107, Resulting Numbers: [107] 107,55 unequal: No Solution Exploring Operation: 43*64=2752, Resulting Numbers: [2752] 2752,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 55:[14, 35], Operations: ['95-17=78', '78-43=35'] Exploring Operation: 14*35=490, Resulting Numbers: [490] 490,55 unequal: No Solution Exploring Operation: 14+35=49, Resulting Numbers: [49] 49,55 unequal: No Solution Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 55:[78, 57], Operations: ['95-17=78', '14+43=57'] Exploring Operation: 78*57=4446, Resulting Numbers: [4446] 4446,55 unequal: No Solution Exploring Operation: 78-57=21, Resulting Numbers: [21] 21,55 unequal: No Solution Exploring Operation: 78+57=135, Resulting Numbers: [135] 135,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 55:[78, 29], Operations: ['95-17=78', '43-14=29'] Exploring Operation: 78*29=2262, Resulting Numbers: [2262] 2262,55 unequal: No Solution Exploring Operation: 78+29=107, Resulting Numbers: [107] 107,55 unequal: No Solution Exploring Operation: 78-29=49, Resulting Numbers: [49] 49,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 55:[17, 43, 81], Operations: ['95-14=81'] Exploring Operation: 81-43=38, Resulting Numbers: [17, 38] Generated Node #0,3,0: 55:[17, 38] Operation: 81-43=38 Exploring Operation: 81-17=64, Resulting Numbers: [43, 64] Generated Node #0,3,1: 55:[43, 64] Operation: 81-17=64 Exploring Operation: 43-17=26, Resulting Numbers: [81, 26] Generated Node #0,3,2: 55:[81, 26] Operation: 43-17=26 Exploring Operation: 17+43=60, Resulting Numbers: [81, 60] Generated Node #0,3,3: 55:[81, 60] Operation: 17+43=60 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 55:[43, 64], Operations: ['95-14=81', '81-17=64'] Exploring Operation: 43*64=2752, Resulting Numbers: [2752] 2752,55 unequal: No Solution Exploring Operation: 43+64=107, Resulting Numbers: [107] 107,55 unequal: No Solution Exploring Operation: 64-43=21, Resulting Numbers: [21] 21,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 55:[17, 38], Operations: ['95-14=81', '81-43=38'] Exploring Operation: 17*38=646, Resulting Numbers: [646] 646,55 unequal: No Solution Exploring Operation: 17+38=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[17, 14, 43, 95], Operations: [] Exploring Operation: 95-14=81, Resulting Numbers: [17, 43, 81] Generated Node #0,3: 55:[17, 43, 81] Operation: 95-14=81 Moving to Node #0,3 Current State: 55:[17, 43, 81], Operations: ['95-14=81'] Exploring Operation: 81-43=38, Resulting Numbers: [17, 38] Generated Node #0,3,0: 55:[17, 38] Operation: 81-43=38 Moving to Node #0,3,0 Current State: 55:[17, 38], Operations: ['95-14=81', '81-43=38'] Exploring Operation: 17+38=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_4
sum_heuristic
[ 22, 37, 9, 62 ]
33
[ "37+62=99", "99/9=11", "22+11=33" ]
Current State: 33:[22, 37, 9, 62], Operations: [] Exploring Operation: 37+62=99, Resulting Numbers: [22, 9, 99] Generated Node #2: [22, 9, 99] from Operation: 37+62=99 Current State: 33:[22, 9, 99], Operations: ['37+62=99'] Exploring Operation: 99/9=11, Resulting Numbers: [22, 11] Generated Node #3: [22, 11] from Operation: 99/9=11 Current State: 33:[22, 11], Operations: ['37+62=99', '99/9=11'] Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[22, 37, 9, 62], Operations: [] Exploring Operation: 62-22=40, Resulting Numbers: [37, 9, 40] Generated Node #0,0: 33:[37, 9, 40] Operation: 62-22=40 Moving to Node #0,0 Current State: 33:[37, 9, 40], Operations: ['62-22=40'] Exploring Operation: 40-37=3, Resulting Numbers: [9, 3] Generated Node #0,0,0: 33:[9, 3] Operation: 40-37=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[9, 3], Operations: ['62-22=40', '40-37=3'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 25, 53, 35, 8 ]
35
[ "25+53=78", "35+8=43", "78-43=35" ]
Current State: 35:[25, 53, 35, 8], Operations: [] Exploring Operation: 25+53=78, Resulting Numbers: [35, 8, 78] Generated Node #2: [35, 8, 78] from Operation: 25+53=78 Current State: 35:[35, 8, 78], Operations: ['25+53=78'] Exploring Operation: 35+8=43, Resulting Numbers: [78, 43] Generated Node #3: [78, 43] from Operation: 35+8=43 Current State: 35:[78, 43], Operations: ['25+53=78', '35+8=43'] Exploring Operation: 78-43=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[25, 53, 35, 8], Operations: [] Exploring Operation: 25+8=33, Resulting Numbers: [53, 35, 33] Generated Node #0,0: 35:[53, 35, 33] Operation: 25+8=33 Exploring Operation: 53-25=28, Resulting Numbers: [35, 8, 28] Generated Node #0,1: 35:[35, 8, 28] Operation: 53-25=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[35, 8, 28], Operations: ['53-25=28'] Exploring Operation: 35-28=7, Resulting Numbers: [8, 7] Generated Node #0,1,0: 35:[8, 7] Operation: 35-28=7 Exploring Operation: 8+28=36, Resulting Numbers: [35, 36] Generated Node #0,1,1: 35:[35, 36] Operation: 8+28=36 Moving to Node #0,1,0 Current State: 35:[8, 7], Operations: ['53-25=28', '35-28=7'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[35, 36], Operations: ['53-25=28', '8+28=36'] Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[53, 35, 33], Operations: ['25+8=33'] Exploring Operation: 53-33=20, Resulting Numbers: [35, 20] Generated Node #0,0,0: 35:[35, 20] Operation: 53-33=20 Exploring Operation: 53-35=18, Resulting Numbers: [33, 18] Generated Node #0,0,1: 35:[33, 18] Operation: 53-35=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[35, 20], Operations: ['25+8=33', '53-33=20'] Exploring Operation: 35+20=55, Resulting Numbers: [55] 55,35 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 35:[33, 18], Operations: ['25+8=33', '53-35=18'] Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,35 unequal: No Solution Exploring Operation: 33+18=51, Resulting Numbers: [51] 51,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 44, 82, 21, 49 ]
56
[ "44+82=126", "21+49=70", "126-70=56" ]
Current State: 56:[44, 82, 21, 49], Operations: [] Exploring Operation: 44+82=126, Resulting Numbers: [21, 49, 126] Generated Node #2: [21, 49, 126] from Operation: 44+82=126 Current State: 56:[21, 49, 126], Operations: ['44+82=126'] Exploring Operation: 21+49=70, Resulting Numbers: [126, 70] Generated Node #3: [126, 70] from Operation: 21+49=70 Current State: 56:[126, 70], Operations: ['44+82=126', '21+49=70'] Exploring Operation: 126-70=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[44, 82, 21, 49], Operations: [] Exploring Operation: 82-44=38, Resulting Numbers: [21, 49, 38] Generated Node #0,0: 56:[21, 49, 38] Operation: 82-44=38 Exploring Operation: 82-21=61, Resulting Numbers: [44, 49, 61] Generated Node #0,1: 56:[44, 49, 61] Operation: 82-21=61 Moving to Node #0,0 Current State: 56:[21, 49, 38], Operations: ['82-44=38'] Exploring Operation: 49-21=28, Resulting Numbers: [38, 28] Generated Node #0,0,0: 56:[38, 28] Operation: 49-21=28 Exploring Operation: 21+38=59, Resulting Numbers: [49, 59] Generated Node #0,0,1: 56:[49, 59] Operation: 21+38=59 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[38, 28], Operations: ['82-44=38', '49-21=28'] Exploring Operation: 38+28=66, Resulting Numbers: [66] 66,56 unequal: No Solution Exploring Operation: 38-28=10, Resulting Numbers: [10] 10,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 56:[49, 59], Operations: ['82-44=38', '21+38=59'] Exploring Operation: 59-49=10, Resulting Numbers: [10] 10,56 unequal: No Solution Exploring Operation: 49+59=108, Resulting Numbers: [108] 108,56 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: 56:[44, 49, 61], Operations: ['82-21=61'] Exploring Operation: 61-44=17, Resulting Numbers: [49, 17] Generated Node #0,1,0: 56:[49, 17] Operation: 61-44=17 Exploring Operation: 49-44=5, Resulting Numbers: [61, 5] Generated Node #0,1,1: 56:[61, 5] Operation: 49-44=5 Moving to Node #0,1,1 Current State: 56:[61, 5], Operations: ['82-21=61', '49-44=5'] Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[44, 82, 21, 49], Operations: [] Exploring Operation: 82-21=61, Resulting Numbers: [44, 49, 61] Generated Node #0,1: 56:[44, 49, 61] Operation: 82-21=61 Moving to Node #0,1 Current State: 56:[44, 49, 61], Operations: ['82-21=61'] Exploring Operation: 49-44=5, Resulting Numbers: [61, 5] Generated Node #0,1,1: 56:[61, 5] Operation: 49-44=5 Moving to Node #0,1,1 Current State: 56:[61, 5], Operations: ['82-21=61', '49-44=5'] Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 56, 92, 93, 11 ]
67
[ "56+11=67", "93-92=1", "67*1=67" ]
Current State: 67:[56, 92, 93, 11], Operations: [] Exploring Operation: 56+11=67, Resulting Numbers: [92, 93, 67] Generated Node #2: [92, 93, 67] from Operation: 56+11=67 Current State: 67:[92, 93, 67], Operations: ['56+11=67'] Exploring Operation: 93-92=1, Resulting Numbers: [67, 1] Generated Node #3: [67, 1] from Operation: 93-92=1 Current State: 67:[67, 1], Operations: ['56+11=67', '93-92=1'] Exploring Operation: 67*1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[56, 92, 93, 11], Operations: [] Exploring Operation: 56+11=67, Resulting Numbers: [92, 93, 67] Generated Node #0,0: 67:[92, 93, 67] Operation: 56+11=67 Exploring Operation: 92-11=81, Resulting Numbers: [56, 93, 81] Generated Node #0,1: 67:[56, 93, 81] Operation: 92-11=81 Moving to Node #0,0 Current State: 67:[92, 93, 67], Operations: ['56+11=67'] Exploring Operation: 93-92=1, Resulting Numbers: [67, 1] Generated Node #0,0,0: 67:[67, 1] Operation: 93-92=1 Exploring Operation: 93-67=26, Resulting Numbers: [92, 26] Generated Node #0,0,1: 67:[92, 26] Operation: 93-67=26 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[67, 1], Operations: ['56+11=67', '93-92=1'] Exploring Operation: 67/1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[56, 92, 93, 11], Operations: [] Exploring Operation: 56+11=67, Resulting Numbers: [92, 93, 67] Generated Node #0,0: 67:[92, 93, 67] Operation: 56+11=67 Moving to Node #0,0 Current State: 67:[92, 93, 67], Operations: ['56+11=67'] Exploring Operation: 93-92=1, Resulting Numbers: [67, 1] Generated Node #0,0,0: 67:[67, 1] Operation: 93-92=1 Moving to Node #0,0,0 Current State: 67:[67, 1], Operations: ['56+11=67', '93-92=1'] Exploring Operation: 67/1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 84, 37, 40, 39 ]
97
[ "40-37=3", "39/3=13", "84+13=97" ]
Current State: 97:[84, 37, 40, 39], Operations: [] Exploring Operation: 40-37=3, Resulting Numbers: [84, 39, 3] Generated Node #2: [84, 39, 3] from Operation: 40-37=3 Current State: 97:[84, 39, 3], Operations: ['40-37=3'] Exploring Operation: 39/3=13, Resulting Numbers: [84, 13] Generated Node #3: [84, 13] from Operation: 39/3=13 Current State: 97:[84, 13], Operations: ['40-37=3', '39/3=13'] Exploring Operation: 84+13=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[84, 37, 40, 39], Operations: [] Exploring Operation: 37+39=76, Resulting Numbers: [84, 40, 76] Generated Node #0,0: 97:[84, 40, 76] Operation: 37+39=76 Exploring Operation: 37+40=77, Resulting Numbers: [84, 39, 77] Generated Node #0,1: 97:[84, 39, 77] Operation: 37+40=77 Exploring Operation: 40+39=79, Resulting Numbers: [84, 37, 79] Generated Node #0,2: 97:[84, 37, 79] Operation: 40+39=79 Moving to Node #0,0 Current State: 97:[84, 40, 76], Operations: ['37+39=76'] Exploring Operation: 84-40=44, Resulting Numbers: [76, 44] Generated Node #0,0,0: 97:[76, 44] Operation: 84-40=44 Exploring Operation: 84+40=124, Resulting Numbers: [76, 124] Generated Node #0,0,1: 97:[76, 124] Operation: 84+40=124 Exploring Operation: 40+76=116, Resulting Numbers: [84, 116] Generated Node #0,0,2: 97:[84, 116] Operation: 40+76=116 Moving to Node #0,1 Current State: 97:[84, 39, 77], Operations: ['37+40=77'] Exploring Operation: 84+39=123, Resulting Numbers: [77, 123] Generated Node #0,1,0: 97:[77, 123] Operation: 84+39=123 Exploring Operation: 39+77=116, Resulting Numbers: [84, 116] Generated Node #0,1,1: 97:[84, 116] Operation: 39+77=116 Exploring Operation: 84-39=45, Resulting Numbers: [77, 45] Generated Node #0,1,2: 97:[77, 45] Operation: 84-39=45 Moving to Node #0,2 Current State: 97:[84, 37, 79], Operations: ['40+39=79'] Exploring Operation: 84-37=47, Resulting Numbers: [79, 47] Generated Node #0,2,0: 97:[79, 47] Operation: 84-37=47 Exploring Operation: 84+37=121, Resulting Numbers: [79, 121] Generated Node #0,2,1: 97:[79, 121] Operation: 84+37=121 Exploring Operation: 37+79=116, Resulting Numbers: [84, 116] Generated Node #0,2,2: 97:[84, 116] Operation: 37+79=116 Moving to Node #0,0,2 Current State: 97:[84, 116], Operations: ['37+39=76', '40+76=116'] Exploring Operation: 84+116=200, Resulting Numbers: [200] 200,97 unequal: No Solution Exploring Operation: 116-84=32, Resulting Numbers: [32] 32,97 unequal: No Solution Exploring Operation: 84*116=9744, Resulting Numbers: [9744] 9744,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[84, 116], Operations: ['40+39=79', '37+79=116'] Exploring Operation: 84+116=200, Resulting Numbers: [200] 200,97 unequal: No Solution Exploring Operation: 84*116=9744, Resulting Numbers: [9744] 9744,97 unequal: No Solution Exploring Operation: 116-84=32, Resulting Numbers: [32] 32,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[84, 116], Operations: ['37+40=77', '39+77=116'] Exploring Operation: 116-84=32, Resulting Numbers: [32] 32,97 unequal: No Solution Exploring Operation: 84*116=9744, Resulting Numbers: [9744] 9744,97 unequal: No Solution Exploring Operation: 84+116=200, Resulting Numbers: [200] 200,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[79, 121], Operations: ['40+39=79', '84+37=121'] Exploring Operation: 121-79=42, Resulting Numbers: [42] 42,97 unequal: No Solution Exploring Operation: 79*121=9559, Resulting Numbers: [9559] 9559,97 unequal: No Solution Exploring Operation: 79+121=200, Resulting Numbers: [200] 200,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[77, 123], Operations: ['37+40=77', '84+39=123'] Exploring Operation: 77*123=9471, Resulting Numbers: [9471] 9471,97 unequal: No Solution Exploring Operation: 123-77=46, Resulting Numbers: [46] 46,97 unequal: No Solution Exploring Operation: 77+123=200, Resulting Numbers: [200] 200,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[76, 124], Operations: ['37+39=76', '84+40=124'] Exploring Operation: 76*124=9424, Resulting Numbers: [9424] 9424,97 unequal: No Solution Exploring Operation: 76+124=200, Resulting Numbers: [200] 200,97 unequal: No Solution Exploring Operation: 124-76=48, Resulting Numbers: [48] 48,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[79, 47], Operations: ['40+39=79', '84-37=47'] Exploring Operation: 79-47=32, Resulting Numbers: [32] 32,97 unequal: No Solution Exploring Operation: 79+47=126, Resulting Numbers: [126] 126,97 unequal: No Solution Exploring Operation: 79*47=3713, Resulting Numbers: [3713] 3713,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[77, 45], Operations: ['37+40=77', '84-39=45'] Exploring Operation: 77-45=32, Resulting Numbers: [32] 32,97 unequal: No Solution Exploring Operation: 77+45=122, Resulting Numbers: [122] 122,97 unequal: No Solution Exploring Operation: 77*45=3465, Resulting Numbers: [3465] 3465,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[76, 44], Operations: ['37+39=76', '84-40=44'] Exploring Operation: 76-44=32, Resulting Numbers: [32] 32,97 unequal: No Solution Exploring Operation: 76+44=120, Resulting Numbers: [120] 120,97 unequal: No Solution Exploring Operation: 76*44=3344, Resulting Numbers: [3344] 3344,97 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 58, 44, 4, 27 ]
79
[ "58+44=102", "27-4=23", "102-23=79" ]
Current State: 79:[58, 44, 4, 27], Operations: [] Exploring Operation: 58+44=102, Resulting Numbers: [4, 27, 102] Generated Node #2: [4, 27, 102] from Operation: 58+44=102 Current State: 79:[4, 27, 102], Operations: ['58+44=102'] Exploring Operation: 27-4=23, Resulting Numbers: [102, 23] Generated Node #3: [102, 23] from Operation: 27-4=23 Current State: 79:[102, 23], Operations: ['58+44=102', '27-4=23'] Exploring Operation: 102-23=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[58, 44, 4, 27], Operations: [] Exploring Operation: 58+4=62, Resulting Numbers: [44, 27, 62] Generated Node #0,0: 79:[44, 27, 62] Operation: 58+4=62 Exploring Operation: 4*27=108, Resulting Numbers: [58, 44, 108] Generated Node #0,1: 79:[58, 44, 108] Operation: 4*27=108 Exploring Operation: 44+4=48, Resulting Numbers: [58, 27, 48] Generated Node #0,2: 79:[58, 27, 48] Operation: 44+4=48 Moving to Node #0,1 Current State: 79:[58, 44, 108], Operations: ['4*27=108'] Exploring Operation: 108-58=50, Resulting Numbers: [44, 50] Generated Node #0,1,0: 79:[44, 50] Operation: 108-58=50 Exploring Operation: 108-44=64, Resulting Numbers: [58, 64] Generated Node #0,1,1: 79:[58, 64] Operation: 108-44=64 Exploring Operation: 58+44=102, Resulting Numbers: [108, 102] Generated Node #0,1,2: 79:[108, 102] Operation: 58+44=102 Moving to Node #0,0 Current State: 79:[44, 27, 62], Operations: ['58+4=62'] Exploring Operation: 44+27=71, Resulting Numbers: [62, 71] Generated Node #0,0,0: 79:[62, 71] Operation: 44+27=71 Exploring Operation: 27+62=89, Resulting Numbers: [44, 89] Generated Node #0,0,1: 79:[44, 89] Operation: 27+62=89 Exploring Operation: 44-27=17, Resulting Numbers: [62, 17] Generated Node #0,0,2: 79:[62, 17] Operation: 44-27=17 Moving to Node #0,2 Current State: 79:[58, 27, 48], Operations: ['44+4=48'] Exploring Operation: 27+48=75, Resulting Numbers: [58, 75] Generated Node #0,2,0: 79:[58, 75] Operation: 27+48=75 Exploring Operation: 58-27=31, Resulting Numbers: [48, 31] Generated Node #0,2,1: 79:[48, 31] Operation: 58-27=31 Exploring Operation: 58+27=85, Resulting Numbers: [48, 85] Generated Node #0,2,2: 79:[48, 85] Operation: 58+27=85 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[58, 75], Operations: ['44+4=48', '27+48=75'] Exploring Operation: 58*75=4350, Resulting Numbers: [4350] 4350,79 unequal: No Solution Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,79 unequal: No Solution Exploring Operation: 58+75=133, Resulting Numbers: [133] 133,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[48, 85], Operations: ['44+4=48', '58+27=85'] Exploring Operation: 48*85=4080, Resulting Numbers: [4080] 4080,79 unequal: No Solution Exploring Operation: 85-48=37, Resulting Numbers: [37] 37,79 unequal: No Solution Exploring Operation: 48+85=133, Resulting Numbers: [133] 133,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[48, 31], Operations: ['44+4=48', '58-27=31'] Exploring Operation: 48+31=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[58, 44, 4, 27], Operations: [] Exploring Operation: 44+4=48, Resulting Numbers: [58, 27, 48] Generated Node #0,2: 79:[58, 27, 48] Operation: 44+4=48 Moving to Node #0,2 Current State: 79:[58, 27, 48], Operations: ['44+4=48'] Exploring Operation: 58-27=31, Resulting Numbers: [48, 31] Generated Node #0,2,1: 79:[48, 31] Operation: 58-27=31 Moving to Node #0,2,1 Current State: 79:[48, 31], Operations: ['44+4=48', '58-27=31'] Exploring Operation: 48+31=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 59, 2, 31, 92 ]
91
[ "59+31=90", "92+90=182", "182/2=91" ]
Current State: 91:[59, 2, 31, 92], Operations: [] Exploring Operation: 59+31=90, Resulting Numbers: [2, 92, 90] Generated Node #2: [2, 92, 90] from Operation: 59+31=90 Current State: 91:[2, 92, 90], Operations: ['59+31=90'] Exploring Operation: 92+90=182, Resulting Numbers: [2, 182] Generated Node #3: [2, 182] from Operation: 92+90=182 Current State: 91:[2, 182], Operations: ['59+31=90', '92+90=182'] Exploring Operation: 182/2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[59, 2, 31, 92], Operations: [] Exploring Operation: 59+31=90, Resulting Numbers: [2, 92, 90] Generated Node #0,0: 91:[2, 92, 90] Operation: 59+31=90 Exploring Operation: 92-59=33, Resulting Numbers: [2, 31, 33] Generated Node #0,1: 91:[2, 31, 33] Operation: 92-59=33 Exploring Operation: 59-31=28, Resulting Numbers: [2, 92, 28] Generated Node #0,2: 91:[2, 92, 28] Operation: 59-31=28 Moving to Node #0,0 Current State: 91:[2, 92, 90], Operations: ['59+31=90'] Exploring Operation: 92-2=90, Resulting Numbers: [90, 90] Generated Node #0,0,0: 91:[90, 90] Operation: 92-2=90 Exploring Operation: 2+92=94, Resulting Numbers: [90, 94] Generated Node #0,0,1: 91:[90, 94] Operation: 2+92=94 Exploring Operation: 2+90=92, Resulting Numbers: [92, 92] Generated Node #0,0,2: 91:[92, 92] Operation: 2+90=92 Moving to Node #0,2 Current State: 91:[2, 92, 28], Operations: ['59-31=28'] Exploring Operation: 28/2=14, Resulting Numbers: [92, 14] Generated Node #0,2,0: 91:[92, 14] Operation: 28/2=14 Exploring Operation: 92-2=90, Resulting Numbers: [28, 90] Generated Node #0,2,1: 91:[28, 90] Operation: 92-2=90 Exploring Operation: 28-2=26, Resulting Numbers: [92, 26] Generated Node #0,2,2: 91:[92, 26] Operation: 28-2=26 Moving to Node #0,1 Current State: 91:[2, 31, 33], Operations: ['92-59=33'] Exploring Operation: 31+33=64, Resulting Numbers: [2, 64] Generated Node #0,1,0: 91:[2, 64] Operation: 31+33=64 Exploring Operation: 33-31=2, Resulting Numbers: [2, 2] Generated Node #0,1,1: 91:[2, 2] Operation: 33-31=2 Exploring Operation: 31-2=29, Resulting Numbers: [33, 29] Generated Node #0,1,2: 91:[33, 29] Operation: 31-2=29 Moving to Node #0,0,0 Current State: 91:[90, 90], Operations: ['59+31=90', '92-2=90'] Exploring Operation: 90/90=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 90+90=180, Resulting Numbers: [180] 180,91 unequal: No Solution Exploring Operation: 90-90=0, Resulting Numbers: [0] 0,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[92, 92], Operations: ['59+31=90', '2+90=92'] Exploring Operation: 92/92=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 92-92=0, Resulting Numbers: [0] 0,91 unequal: No Solution Exploring Operation: 92+92=184, Resulting Numbers: [184] 184,91 unequal: No Solution Moving to Node #0,2,0 Current State: 91:[92, 14], Operations: ['59-31=28', '28/2=14'] Exploring Operation: 92*14=1288, Resulting Numbers: [1288] 1288,91 unequal: No Solution Exploring Operation: 92-14=78, Resulting Numbers: [78] 78,91 unequal: No Solution Exploring Operation: 92+14=106, Resulting Numbers: [106] 106,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[90, 94], Operations: ['59+31=90', '2+92=94'] Exploring Operation: 90+94=184, Resulting Numbers: [184] 184,91 unequal: No Solution Exploring Operation: 90*94=8460, Resulting Numbers: [8460] 8460,91 unequal: No Solution Exploring Operation: 94-90=4, Resulting Numbers: [4] 4,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[2, 2], Operations: ['92-59=33', '33-31=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,91 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,91 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[92, 26], Operations: ['59-31=28', '28-2=26'] Exploring Operation: 92+26=118, Resulting Numbers: [118] 118,91 unequal: No Solution Exploring Operation: 92-26=66, Resulting Numbers: [66] 66,91 unequal: No Solution Exploring Operation: 92*26=2392, Resulting Numbers: [2392] 2392,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[28, 90], Operations: ['59-31=28', '92-2=90'] Exploring Operation: 28*90=2520, Resulting Numbers: [2520] 2520,91 unequal: No Solution Exploring Operation: 90-28=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 28+90=118, Resulting Numbers: [118] 118,91 unequal: No Solution Moving to Node #0,1,0 Current State: 91:[2, 64], Operations: ['92-59=33', '31+33=64'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,91 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,91 unequal: No Solution Moving to Node #0,1,2 Current State: 91:[33, 29], Operations: ['92-59=33', '31-2=29'] Exploring Operation: 33-29=4, Resulting Numbers: [4] 4,91 unequal: No Solution Exploring Operation: 33+29=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 33*29=957, Resulting Numbers: [957] 957,91 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 16, 72, 18, 78 ]
14
[ "16*72=1152", "1152/18=64", "78-64=14" ]
Current State: 14:[16, 72, 18, 78], Operations: [] Exploring Operation: 16*72=1152, Resulting Numbers: [18, 78, 1152] Generated Node #2: [18, 78, 1152] from Operation: 16*72=1152 Current State: 14:[18, 78, 1152], Operations: ['16*72=1152'] Exploring Operation: 1152/18=64, Resulting Numbers: [78, 64] Generated Node #3: [78, 64] from Operation: 1152/18=64 Current State: 14:[78, 64], Operations: ['16*72=1152', '1152/18=64'] Exploring Operation: 78-64=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[16, 72, 18, 78], Operations: [] Exploring Operation: 78-72=6, Resulting Numbers: [16, 18, 6] Generated Node #0,0: 14:[16, 18, 6] Operation: 78-72=6 Moving to Node #0,0 Current State: 14:[16, 18, 6], Operations: ['78-72=6'] Exploring Operation: 18-16=2, Resulting Numbers: [6, 2] Generated Node #0,0,0: 14:[6, 2] Operation: 18-16=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[6, 2], Operations: ['78-72=6', '18-16=2'] Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,14 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
[ 95, 94, 67, 29 ]
96
[ "95-94=1", "67+29=96", "1*96=96" ]
Current State: 96:[95, 94, 67, 29], Operations: [] Exploring Operation: 95-94=1, Resulting Numbers: [67, 29, 1] Generated Node #2: [67, 29, 1] from Operation: 95-94=1 Current State: 96:[67, 29, 1], Operations: ['95-94=1'] Exploring Operation: 67+29=96, Resulting Numbers: [1, 96] Generated Node #3: [1, 96] from Operation: 67+29=96 Current State: 96:[1, 96], Operations: ['95-94=1', '67+29=96'] Exploring Operation: 1*96=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[95, 94, 67, 29], Operations: [] Exploring Operation: 67+29=96, Resulting Numbers: [95, 94, 96] Generated Node #0,0: 96:[95, 94, 96] Operation: 67+29=96 Exploring Operation: 94-67=27, Resulting Numbers: [95, 29, 27] Generated Node #0,1: 96:[95, 29, 27] Operation: 94-67=27 Exploring Operation: 95-67=28, Resulting Numbers: [94, 29, 28] Generated Node #0,2: 96:[94, 29, 28] Operation: 95-67=28 Exploring Operation: 95-94=1, Resulting Numbers: [67, 29, 1] Generated Node #0,3: 96:[67, 29, 1] Operation: 95-94=1 Exploring Operation: 67-29=38, Resulting Numbers: [95, 94, 38] Generated Node #0,4: 96:[95, 94, 38] Operation: 67-29=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[95, 94, 96], Operations: ['67+29=96'] Exploring Operation: 96-94=2, Resulting Numbers: [95, 2] Generated Node #0,0,0: 96:[95, 2] Operation: 96-94=2 Exploring Operation: 96-95=1, Resulting Numbers: [94, 1] Generated Node #0,0,1: 96:[94, 1] Operation: 96-95=1 Exploring Operation: 94+96=190, Resulting Numbers: [95, 190] Generated Node #0,0,2: 96:[95, 190] Operation: 94+96=190 Exploring Operation: 95-94=1, Resulting Numbers: [96, 1] Generated Node #0,0,3: 96:[96, 1] Operation: 95-94=1 Exploring Operation: 95+94=189, Resulting Numbers: [96, 189] Generated Node #0,0,4: 96:[96, 189] Operation: 95+94=189 Moving to Node #0,0,0 Current State: 96:[95, 2], Operations: ['67+29=96', '96-94=2'] Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,96 unequal: No Solution Exploring Operation: 95*2=190, Resulting Numbers: [190] 190,96 unequal: No Solution Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[96, 1], Operations: ['67+29=96', '95-94=1'] Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,96 unequal: No Solution Exploring Operation: 96+1=97, Resulting Numbers: [97] 97,96 unequal: No Solution Exploring Operation: 96*1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[95, 94, 67, 29], Operations: [] Exploring Operation: 67+29=96, Resulting Numbers: [95, 94, 96] Generated Node #0,0: 96:[95, 94, 96] Operation: 67+29=96 Moving to Node #0,0 Current State: 96:[95, 94, 96], Operations: ['67+29=96'] Exploring Operation: 95-94=1, Resulting Numbers: [96, 1] Generated Node #0,0,3: 96:[96, 1] Operation: 95-94=1 Moving to Node #0,0,3 Current State: 96:[96, 1], Operations: ['67+29=96', '95-94=1'] Exploring Operation: 96*1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 84, 64, 61, 65 ]
57
[ "84-65=19", "64-61=3", "19*3=57" ]
Current State: 57:[84, 64, 61, 65], Operations: [] Exploring Operation: 84-65=19, Resulting Numbers: [64, 61, 19] Generated Node #2: [64, 61, 19] from Operation: 84-65=19 Current State: 57:[64, 61, 19], Operations: ['84-65=19'] Exploring Operation: 64-61=3, Resulting Numbers: [19, 3] Generated Node #3: [19, 3] from Operation: 64-61=3 Current State: 57:[19, 3], Operations: ['84-65=19', '64-61=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[84, 64, 61, 65], Operations: [] Exploring Operation: 84-65=19, Resulting Numbers: [64, 61, 19] Generated Node #0,0: 57:[64, 61, 19] Operation: 84-65=19 Exploring Operation: 84-64=20, Resulting Numbers: [61, 65, 20] Generated Node #0,1: 57:[61, 65, 20] Operation: 84-64=20 Moving to Node #0,0 Current State: 57:[64, 61, 19], Operations: ['84-65=19'] Exploring Operation: 64-19=45, Resulting Numbers: [61, 45] Generated Node #0,0,0: 57:[61, 45] Operation: 64-19=45 Exploring Operation: 64-61=3, Resulting Numbers: [19, 3] Generated Node #0,0,1: 57:[19, 3] Operation: 64-61=3 Moving to Node #0,1 Current State: 57:[61, 65, 20], Operations: ['84-64=20'] Exploring Operation: 65-61=4, Resulting Numbers: [20, 4] Generated Node #0,1,0: 57:[20, 4] Operation: 65-61=4 Exploring Operation: 65-20=45, Resulting Numbers: [61, 45] Generated Node #0,1,1: 57:[61, 45] Operation: 65-20=45 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[20, 4], Operations: ['84-64=20', '65-61=4'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,57 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,57 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:[61, 45], Operations: ['84-64=20', '65-20=45'] Exploring Operation: 61+45=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 61-45=16, Resulting Numbers: [16] 16,57 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: 57:[19, 3], Operations: ['84-65=19', '64-61=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[84, 64, 61, 65], Operations: [] Exploring Operation: 84-65=19, Resulting Numbers: [64, 61, 19] Generated Node #0,0: 57:[64, 61, 19] Operation: 84-65=19 Moving to Node #0,0 Current State: 57:[64, 61, 19], Operations: ['84-65=19'] Exploring Operation: 64-61=3, Resulting Numbers: [19, 3] Generated Node #0,0,1: 57:[19, 3] Operation: 64-61=3 Moving to Node #0,0,1 Current State: 57:[19, 3], Operations: ['84-65=19', '64-61=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 10, 5, 96, 80 ]
31
[ "10+5=15", "96-80=16", "15+16=31" ]
Current State: 31:[10, 5, 96, 80], Operations: [] Exploring Operation: 10+5=15, Resulting Numbers: [96, 80, 15] Generated Node #2: [96, 80, 15] from Operation: 10+5=15 Current State: 31:[96, 80, 15], Operations: ['10+5=15'] Exploring Operation: 96-80=16, Resulting Numbers: [15, 16] Generated Node #3: [15, 16] from Operation: 96-80=16 Current State: 31:[15, 16], Operations: ['10+5=15', '96-80=16'] Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[10, 5, 96, 80], Operations: [] Exploring Operation: 80/10=8, Resulting Numbers: [5, 96, 8] Generated Node #0,0: 31:[5, 96, 8] Operation: 80/10=8 Exploring Operation: 10+5=15, Resulting Numbers: [96, 80, 15] Generated Node #0,1: 31:[96, 80, 15] Operation: 10+5=15 Exploring Operation: 80/5=16, Resulting Numbers: [10, 96, 16] Generated Node #0,2: 31:[10, 96, 16] Operation: 80/5=16 Exploring Operation: 96-80=16, Resulting Numbers: [10, 5, 16] Generated Node #0,3: 31:[10, 5, 16] Operation: 96-80=16 Moving to Node #0,3 Current State: 31:[10, 5, 16], Operations: ['96-80=16'] Exploring Operation: 5+16=21, Resulting Numbers: [10, 21] Generated Node #0,3,0: 31:[10, 21] Operation: 5+16=21 Exploring Operation: 10+16=26, Resulting Numbers: [5, 26] Generated Node #0,3,1: 31:[5, 26] Operation: 10+16=26 Exploring Operation: 10*5=50, Resulting Numbers: [16, 50] Generated Node #0,3,2: 31:[16, 50] Operation: 10*5=50 Exploring Operation: 10+5=15, Resulting Numbers: [16, 15] Generated Node #0,3,3: 31:[16, 15] Operation: 10+5=15 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 31:[10, 21], Operations: ['96-80=16', '5+16=21'] Exploring Operation: 10*21=210, Resulting Numbers: [210] 210,31 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,31 unequal: No Solution Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[10, 5, 96, 80], Operations: [] Exploring Operation: 96-80=16, Resulting Numbers: [10, 5, 16] Generated Node #0,3: 31:[10, 5, 16] Operation: 96-80=16 Moving to Node #0,3 Current State: 31:[10, 5, 16], Operations: ['96-80=16'] Exploring Operation: 5+16=21, Resulting Numbers: [10, 21] Generated Node #0,3,0: 31:[10, 21] Operation: 5+16=21 Moving to Node #0,3,0 Current State: 31:[10, 21], Operations: ['96-80=16', '5+16=21'] Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 30, 50, 48, 3 ]
63
[ "50-48=2", "30*2=60", "3+60=63" ]
Current State: 63:[30, 50, 48, 3], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [30, 3, 2] Generated Node #2: [30, 3, 2] from Operation: 50-48=2 Current State: 63:[30, 3, 2], Operations: ['50-48=2'] Exploring Operation: 30*2=60, Resulting Numbers: [3, 60] Generated Node #3: [3, 60] from Operation: 30*2=60 Current State: 63:[3, 60], Operations: ['50-48=2', '30*2=60'] Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[30, 50, 48, 3], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [30, 3, 2] Generated Node #0,0: 63:[30, 3, 2] Operation: 50-48=2 Exploring Operation: 50-30=20, Resulting Numbers: [48, 3, 20] Generated Node #0,1: 63:[48, 3, 20] Operation: 50-30=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[30, 3, 2], Operations: ['50-48=2'] Exploring Operation: 30*2=60, Resulting Numbers: [3, 60] Generated Node #0,0,0: 63:[3, 60] Operation: 30*2=60 Exploring Operation: 30/3=10, Resulting Numbers: [2, 10] Generated Node #0,0,1: 63:[2, 10] Operation: 30/3=10 Moving to Node #0,0,1 Current State: 63:[2, 10], Operations: ['50-48=2', '30/3=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,63 unequal: No Solution Moving to Node #0,0,0 Current State: 63:[3, 60], Operations: ['50-48=2', '30*2=60'] Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[30, 50, 48, 3], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [30, 3, 2] Generated Node #0,0: 63:[30, 3, 2] Operation: 50-48=2 Moving to Node #0,0 Current State: 63:[30, 3, 2], Operations: ['50-48=2'] Exploring Operation: 30*2=60, Resulting Numbers: [3, 60] Generated Node #0,0,0: 63:[3, 60] Operation: 30*2=60 Moving to Node #0,0,0 Current State: 63:[3, 60], Operations: ['50-48=2', '30*2=60'] Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 23, 10, 40, 84 ]
11
[ "23+10=33", "84-40=44", "44-33=11" ]
Current State: 11:[23, 10, 40, 84], Operations: [] Exploring Operation: 23+10=33, Resulting Numbers: [40, 84, 33] Generated Node #2: [40, 84, 33] from Operation: 23+10=33 Current State: 11:[40, 84, 33], Operations: ['23+10=33'] Exploring Operation: 84-40=44, Resulting Numbers: [33, 44] Generated Node #3: [33, 44] from Operation: 84-40=44 Current State: 11:[33, 44], Operations: ['23+10=33', '84-40=44'] Exploring Operation: 44-33=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[23, 10, 40, 84], Operations: [] Exploring Operation: 84-23=61, Resulting Numbers: [10, 40, 61] Generated Node #0,0: 11:[10, 40, 61] Operation: 84-23=61 Exploring Operation: 84-40=44, Resulting Numbers: [23, 10, 44] Generated Node #0,1: 11:[23, 10, 44] Operation: 84-40=44 Exploring Operation: 40-23=17, Resulting Numbers: [10, 84, 17] Generated Node #0,2: 11:[10, 84, 17] Operation: 40-23=17 Exploring Operation: 40/10=4, Resulting Numbers: [23, 84, 4] Generated Node #0,3: 11:[23, 84, 4] Operation: 40/10=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[23, 10, 44], Operations: ['84-40=44'] Exploring Operation: 44-23=21, Resulting Numbers: [10, 21] Generated Node #0,1,0: 11:[10, 21] Operation: 44-23=21 Exploring Operation: 23-10=13, Resulting Numbers: [44, 13] Generated Node #0,1,1: 11:[44, 13] Operation: 23-10=13 Exploring Operation: 23+10=33, Resulting Numbers: [44, 33] Generated Node #0,1,2: 11:[44, 33] Operation: 23+10=33 Exploring Operation: 44-10=34, Resulting Numbers: [23, 34] Generated Node #0,1,3: 11:[23, 34] Operation: 44-10=34 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 11:[10, 21], Operations: ['84-40=44', '44-23=21'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[23, 10, 40, 84], Operations: [] Exploring Operation: 84-40=44, Resulting Numbers: [23, 10, 44] Generated Node #0,1: 11:[23, 10, 44] Operation: 84-40=44 Moving to Node #0,1 Current State: 11:[23, 10, 44], Operations: ['84-40=44'] Exploring Operation: 44-23=21, Resulting Numbers: [10, 21] Generated Node #0,1,0: 11:[10, 21] Operation: 44-23=21 Moving to Node #0,1,0 Current State: 11:[10, 21], Operations: ['84-40=44', '44-23=21'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 30, 12, 27, 47 ]
32
[ "30+12=42", "27+47=74", "74-42=32" ]
Current State: 32:[30, 12, 27, 47], Operations: [] Exploring Operation: 30+12=42, Resulting Numbers: [27, 47, 42] Generated Node #2: [27, 47, 42] from Operation: 30+12=42 Current State: 32:[27, 47, 42], Operations: ['30+12=42'] Exploring Operation: 27+47=74, Resulting Numbers: [42, 74] Generated Node #3: [42, 74] from Operation: 27+47=74 Current State: 32:[42, 74], Operations: ['30+12=42', '27+47=74'] Exploring Operation: 74-42=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[30, 12, 27, 47], Operations: [] Exploring Operation: 47-12=35, Resulting Numbers: [30, 27, 35] Generated Node #0,0: 32:[30, 27, 35] Operation: 47-12=35 Exploring Operation: 47-30=17, Resulting Numbers: [12, 27, 17] Generated Node #0,1: 32:[12, 27, 17] Operation: 47-30=17 Exploring Operation: 47-27=20, Resulting Numbers: [30, 12, 20] Generated Node #0,2: 32:[30, 12, 20] Operation: 47-27=20 Moving to Node #0,0 Current State: 32:[30, 27, 35], Operations: ['47-12=35'] Exploring Operation: 30-27=3, Resulting Numbers: [35, 3] Generated Node #0,0,0: 32:[35, 3] Operation: 30-27=3 Exploring Operation: 35-30=5, Resulting Numbers: [27, 5] Generated Node #0,0,1: 32:[27, 5] Operation: 35-30=5 Exploring Operation: 35-27=8, Resulting Numbers: [30, 8] Generated Node #0,0,2: 32:[30, 8] Operation: 35-27=8 Moving to Node #0,1 Current State: 32:[12, 27, 17], Operations: ['47-30=17'] Exploring Operation: 27-12=15, Resulting Numbers: [17, 15] Generated Node #0,1,0: 32:[17, 15] Operation: 27-12=15 Exploring Operation: 27-17=10, Resulting Numbers: [12, 10] Generated Node #0,1,1: 32:[12, 10] Operation: 27-17=10 Exploring Operation: 17-12=5, Resulting Numbers: [27, 5] Generated Node #0,1,2: 32:[27, 5] Operation: 17-12=5 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[17, 15], Operations: ['47-30=17', '27-12=15'] Exploring Operation: 17*15=255, Resulting Numbers: [255] 255,32 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[30, 12, 27, 47], Operations: [] Exploring Operation: 47-30=17, Resulting Numbers: [12, 27, 17] Generated Node #0,1: 32:[12, 27, 17] Operation: 47-30=17 Moving to Node #0,1 Current State: 32:[12, 27, 17], Operations: ['47-30=17'] Exploring Operation: 27-12=15, Resulting Numbers: [17, 15] Generated Node #0,1,0: 32:[17, 15] Operation: 27-12=15 Moving to Node #0,1,0 Current State: 32:[17, 15], Operations: ['47-30=17', '27-12=15'] Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 12, 33, 14, 13 ]
59
[ "14-12=2", "13*2=26", "33+26=59" ]
Current State: 59:[12, 33, 14, 13], Operations: [] Exploring Operation: 14-12=2, Resulting Numbers: [33, 13, 2] Generated Node #2: [33, 13, 2] from Operation: 14-12=2 Current State: 59:[33, 13, 2], Operations: ['14-12=2'] Exploring Operation: 13*2=26, Resulting Numbers: [33, 26] Generated Node #3: [33, 26] from Operation: 13*2=26 Current State: 59:[33, 26], Operations: ['14-12=2', '13*2=26'] Exploring Operation: 33+26=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[12, 33, 14, 13], Operations: [] Exploring Operation: 12+33=45, Resulting Numbers: [14, 13, 45] Generated Node #0,0: 59:[14, 13, 45] Operation: 12+33=45 Exploring Operation: 33+14=47, Resulting Numbers: [12, 13, 47] Generated Node #0,1: 59:[12, 13, 47] Operation: 33+14=47 Exploring Operation: 12+13=25, Resulting Numbers: [33, 14, 25] Generated Node #0,2: 59:[33, 14, 25] Operation: 12+13=25 Exploring Operation: 12+14=26, Resulting Numbers: [33, 13, 26] Generated Node #0,3: 59:[33, 13, 26] Operation: 12+14=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[14, 13, 45], Operations: ['12+33=45'] Exploring Operation: 14+13=27, Resulting Numbers: [45, 27] Generated Node #0,0,0: 59:[45, 27] Operation: 14+13=27 Exploring Operation: 13+45=58, Resulting Numbers: [14, 58] Generated Node #0,0,1: 59:[14, 58] Operation: 13+45=58 Exploring Operation: 14-13=1, Resulting Numbers: [45, 1] Generated Node #0,0,2: 59:[45, 1] Operation: 14-13=1 Exploring Operation: 14+45=59, Resulting Numbers: [13, 59] Generated Node #0,0,3: 59:[13, 59] Operation: 14+45=59 Moving to Node #0,0,0 Current State: 59:[45, 27], Operations: ['12+33=45', '14+13=27'] Exploring Operation: 45+27=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,59 unequal: No Solution Exploring Operation: 45*27=1215, Resulting Numbers: [1215] 1215,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[13, 59], Operations: ['12+33=45', '14+45=59'] Exploring Operation: 13+59=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 13*59=767, Resulting Numbers: [767] 767,59 unequal: No Solution Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[14, 58], Operations: ['12+33=45', '13+45=58'] Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,59 unequal: No Solution Exploring Operation: 14*58=812, Resulting Numbers: [812] 812,59 unequal: No Solution Exploring Operation: 14+58=72, Resulting Numbers: [72] 72,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[45, 1], Operations: ['12+33=45', '14-13=1'] Exploring Operation: 45+1=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,59 unequal: No Solution Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,59 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 Current State: 59:[12, 13, 47], Operations: ['33+14=47'] Exploring Operation: 12+13=25, Resulting Numbers: [47, 25] Generated Node #0,1,0: 59:[47, 25] Operation: 12+13=25 Exploring Operation: 13-12=1, Resulting Numbers: [47, 1] Generated Node #0,1,1: 59:[47, 1] Operation: 13-12=1 Exploring Operation: 13+47=60, Resulting Numbers: [12, 60] Generated Node #0,1,2: 59:[12, 60] Operation: 13+47=60 Exploring Operation: 12+47=59, Resulting Numbers: [13, 59] Generated Node #0,1,3: 59:[13, 59] Operation: 12+47=59 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 59:[47, 25], Operations: ['33+14=47', '12+13=25'] Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 47+25=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 47*25=1175, Resulting Numbers: [1175] 1175,59 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:[13, 59], Operations: ['33+14=47', '12+47=59'] Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 13+59=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 13*59=767, Resulting Numbers: [767] 767,59 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:[12, 60], Operations: ['33+14=47', '13+47=60'] Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,59 unequal: No Solution Exploring Operation: 12*60=720, Resulting Numbers: [720] 720,59 unequal: No Solution Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,59 unequal: No Solution Exploring Operation: 12+60=72, Resulting Numbers: [72] 72,59 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 #0,1,1 Current State: 59:[47, 1], Operations: ['33+14=47', '13-12=1'] Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,59 unequal: No Solution Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,59 unequal: No Solution Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,59 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,59 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:[33, 14, 25], Operations: ['12+13=25'] Exploring Operation: 33+25=58, Resulting Numbers: [14, 58] Generated Node #0,2,0: 59:[14, 58] Operation: 33+25=58 Exploring Operation: 14+25=39, Resulting Numbers: [33, 39] Generated Node #0,2,1: 59:[33, 39] Operation: 14+25=39 Exploring Operation: 33+14=47, Resulting Numbers: [25, 47] Generated Node #0,2,2: 59:[25, 47] Operation: 33+14=47 Exploring Operation: 33-14=19, Resulting Numbers: [25, 19] Generated Node #0,2,3: 59:[25, 19] Operation: 33-14=19 Moving to Node #0,2,0 Current State: 59:[14, 58], Operations: ['12+13=25', '33+25=58'] Exploring Operation: 14+58=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,59 unequal: No Solution Exploring Operation: 14*58=812, Resulting Numbers: [812] 812,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[25, 47], Operations: ['12+13=25', '33+14=47'] Exploring Operation: 25*47=1175, Resulting Numbers: [1175] 1175,59 unequal: No Solution Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 25+47=72, Resulting Numbers: [72] 72,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[33, 39], Operations: ['12+13=25', '14+25=39'] Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,59 unequal: No Solution Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[25, 19], Operations: ['12+13=25', '33-14=19'] Exploring Operation: 25*19=475, Resulting Numbers: [475] 475,59 unequal: No Solution Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,59 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,59 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 Current State: 59:[33, 13, 26], Operations: ['12+14=26'] Exploring Operation: 33+13=46, Resulting Numbers: [26, 46] Generated Node #0,3,0: 59:[26, 46] Operation: 33+13=46 Exploring Operation: 33-13=20, Resulting Numbers: [26, 20] Generated Node #0,3,1: 59:[26, 20] Operation: 33-13=20 Exploring Operation: 13+26=39, Resulting Numbers: [33, 39] Generated Node #0,3,2: 59:[33, 39] Operation: 13+26=39 Exploring Operation: 33+26=59, Resulting Numbers: [13, 59] Generated Node #0,3,3: 59:[13, 59] Operation: 33+26=59 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 59:[26, 46], Operations: ['12+14=26', '33+13=46'] Exploring Operation: 26+46=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 26*46=1196, Resulting Numbers: [1196] 1196,59 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 #0,3,2 Current State: 59:[33, 39], Operations: ['12+14=26', '13+26=39'] Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,59 unequal: No Solution Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,59 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 #0,3,3 Current State: 59:[13, 59], Operations: ['12+14=26', '33+26=59'] Exploring Operation: 13+59=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 13*59=767, Resulting Numbers: [767] 767,59 unequal: No Solution Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,59 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 #0,3,1 Current State: 59:[26, 20], Operations: ['12+14=26', '33-13=20'] Exploring Operation: 26*20=520, Resulting Numbers: [520] 520,59 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,59 unequal: No Solution Exploring Operation: 26+20=46, Resulting Numbers: [46] 46,59 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 No solution found.
0
hs_4
mult_heuristic
[ 60, 68, 7, 34 ]
51
[ "60-7=53", "68/34=2", "53-2=51" ]
Current State: 51:[60, 68, 7, 34], Operations: [] Exploring Operation: 60-7=53, Resulting Numbers: [68, 34, 53] Generated Node #2: [68, 34, 53] from Operation: 60-7=53 Current State: 51:[68, 34, 53], Operations: ['60-7=53'] Exploring Operation: 68/34=2, Resulting Numbers: [53, 2] Generated Node #3: [53, 2] from Operation: 68/34=2 Current State: 51:[53, 2], Operations: ['60-7=53', '68/34=2'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[60, 68, 7, 34], Operations: [] Exploring Operation: 68-60=8, Resulting Numbers: [7, 34, 8] Generated Node #0,0: 51:[7, 34, 8] Operation: 68-60=8 Exploring Operation: 60-34=26, Resulting Numbers: [68, 7, 26] Generated Node #0,1: 51:[68, 7, 26] Operation: 60-34=26 Exploring Operation: 68/34=2, Resulting Numbers: [60, 7, 2] Generated Node #0,2: 51:[60, 7, 2] Operation: 68/34=2 Moving to Node #0,2 Current State: 51:[60, 7, 2], Operations: ['68/34=2'] Exploring Operation: 7-2=5, Resulting Numbers: [60, 5] Generated Node #0,2,0: 51:[60, 5] Operation: 7-2=5 Exploring Operation: 60-2=58, Resulting Numbers: [7, 58] Generated Node #0,2,1: 51:[7, 58] Operation: 60-2=58 Exploring Operation: 60-7=53, Resulting Numbers: [2, 53] Generated Node #0,2,2: 51:[2, 53] Operation: 60-7=53 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 51:[2, 53], Operations: ['68/34=2', '60-7=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[60, 68, 7, 34], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [60, 7, 2] Generated Node #0,2: 51:[60, 7, 2] Operation: 68/34=2 Moving to Node #0,2 Current State: 51:[60, 7, 2], Operations: ['68/34=2'] Exploring Operation: 60-7=53, Resulting Numbers: [2, 53] Generated Node #0,2,2: 51:[2, 53] Operation: 60-7=53 Moving to Node #0,2,2 Current State: 51:[2, 53], Operations: ['68/34=2', '60-7=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic