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
[ 2, 71, 3, 98 ]
86
[ "71+3=74", "98+74=172", "172/2=86" ]
Current State: 86:[2, 71, 3, 98], Operations: [] Exploring Operation: 71+3=74, Resulting Numbers: [2, 98, 74] Generated Node #2: [2, 98, 74] from Operation: 71+3=74 Current State: 86:[2, 98, 74], Operations: ['71+3=74'] Exploring Operation: 98+74=172, Resulting Numbers: [2, 172] Generated Node #3: [2, 172] from Operation: 98+74=172 Current State: 86:[2, 172], Operations: ['71+3=74', '98+74=172'] Exploring Operation: 172/2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[2, 71, 3, 98], Operations: [] Exploring Operation: 98/2=49, Resulting Numbers: [71, 3, 49] Generated Node #0,0: 86:[71, 3, 49] Operation: 98/2=49 Exploring Operation: 71+3=74, Resulting Numbers: [2, 98, 74] Generated Node #0,1: 86:[2, 98, 74] Operation: 71+3=74 Exploring Operation: 98-3=95, Resulting Numbers: [2, 71, 95] Generated Node #0,2: 86:[2, 71, 95] Operation: 98-3=95 Exploring Operation: 98-71=27, Resulting Numbers: [2, 3, 27] Generated Node #0,3: 86:[2, 3, 27] Operation: 98-71=27 Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[2, 3, 27], Operations: ['98-71=27'] Exploring Operation: 27/3=9, Resulting Numbers: [2, 9] Generated Node #0,3,0: 86:[2, 9] Operation: 27/3=9 Exploring Operation: 3+27=30, Resulting Numbers: [2, 30] Generated Node #0,3,1: 86:[2, 30] Operation: 3+27=30 Exploring Operation: 2*27=54, Resulting Numbers: [3, 54] Generated Node #0,3,2: 86:[3, 54] Operation: 2*27=54 Exploring Operation: 3*27=81, Resulting Numbers: [2, 81] Generated Node #0,3,3: 86:[2, 81] Operation: 3*27=81 Moving to Node #0,3,3 Current State: 86:[2, 81], Operations: ['98-71=27', '3*27=81'] Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 2*81=162, Resulting Numbers: [162] 162,86 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,86 unequal: No Solution Moving to Node #0,3,0 Current State: 86:[2, 9], Operations: ['98-71=27', '27/3=9'] Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,86 unequal: No Solution Moving to Node #0,3,2 Current State: 86:[3, 54], Operations: ['98-71=27', '2*27=54'] Exploring Operation: 3+54=57, Resulting Numbers: [57] 57,86 unequal: No Solution Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,86 unequal: No Solution Exploring Operation: 3*54=162, Resulting Numbers: [162] 162,86 unequal: No Solution Moving to Node #0,3,1 Current State: 86:[2, 30], Operations: ['98-71=27', '3+27=30'] Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,86 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,86 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[71, 3, 49], Operations: ['98/2=49'] Exploring Operation: 71-3=68, Resulting Numbers: [49, 68] Generated Node #0,0,0: 86:[49, 68] Operation: 71-3=68 Exploring Operation: 49-3=46, Resulting Numbers: [71, 46] Generated Node #0,0,1: 86:[71, 46] Operation: 49-3=46 Exploring Operation: 71+3=74, Resulting Numbers: [49, 74] Generated Node #0,0,2: 86:[49, 74] Operation: 71+3=74 Exploring Operation: 71-49=22, Resulting Numbers: [3, 22] Generated Node #0,0,3: 86:[3, 22] Operation: 71-49=22 Moving to Node #0,0,1 Current State: 86:[71, 46], Operations: ['98/2=49', '49-3=46'] Exploring Operation: 71*46=3266, Resulting Numbers: [3266] 3266,86 unequal: No Solution Exploring Operation: 71-46=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 71+46=117, Resulting Numbers: [117] 117,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[49, 74], Operations: ['98/2=49', '71+3=74'] Exploring Operation: 49*74=3626, Resulting Numbers: [3626] 3626,86 unequal: No Solution Exploring Operation: 49+74=123, Resulting Numbers: [123] 123,86 unequal: No Solution Exploring Operation: 74-49=25, Resulting Numbers: [25] 25,86 unequal: No Solution Moving to Node #0,0,3 Current State: 86:[3, 22], Operations: ['98/2=49', '71-49=22'] Exploring Operation: 3*22=66, Resulting Numbers: [66] 66,86 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,86 unequal: No Solution Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[49, 68], Operations: ['98/2=49', '71-3=68'] Exploring Operation: 49+68=117, Resulting Numbers: [117] 117,86 unequal: No Solution Exploring Operation: 68-49=19, Resulting Numbers: [19] 19,86 unequal: No Solution Exploring Operation: 49*68=3332, Resulting Numbers: [3332] 3332,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[2, 98, 74], Operations: ['71+3=74'] Exploring Operation: 98-74=24, Resulting Numbers: [2, 24] Generated Node #0,1,0: 86:[2, 24] Operation: 98-74=24 Exploring Operation: 74/2=37, Resulting Numbers: [98, 37] Generated Node #0,1,1: 86:[98, 37] Operation: 74/2=37 Exploring Operation: 98-2=96, Resulting Numbers: [74, 96] Generated Node #0,1,2: 86:[74, 96] Operation: 98-2=96 Exploring Operation: 98/2=49, Resulting Numbers: [74, 49] Generated Node #0,1,3: 86:[74, 49] Operation: 98/2=49 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 86:[98, 37], Operations: ['71+3=74', '74/2=37'] Exploring Operation: 98*37=3626, Resulting Numbers: [3626] 3626,86 unequal: No Solution Exploring Operation: 98+37=135, Resulting Numbers: [135] 135,86 unequal: No Solution Exploring Operation: 98-37=61, Resulting Numbers: [61] 61,86 unequal: No Solution No 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: 86:[74, 49], Operations: ['71+3=74', '98/2=49'] Exploring Operation: 74-49=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 74+49=123, Resulting Numbers: [123] 123,86 unequal: No Solution Exploring Operation: 74*49=3626, Resulting Numbers: [3626] 3626,86 unequal: No Solution No 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: 86:[2, 24], Operations: ['71+3=74', '98-74=24'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,86 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,86 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,86 unequal: No Solution No 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: 86:[74, 96], Operations: ['71+3=74', '98-2=96'] Exploring Operation: 74*96=7104, Resulting Numbers: [7104] 7104,86 unequal: No Solution Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,86 unequal: No Solution Exploring Operation: 74+96=170, Resulting Numbers: [170] 170,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[2, 71, 95], Operations: ['98-3=95'] Exploring Operation: 95-71=24, Resulting Numbers: [2, 24] Generated Node #0,2,0: 86:[2, 24] Operation: 95-71=24 Exploring Operation: 95-2=93, Resulting Numbers: [71, 93] Generated Node #0,2,1: 86:[71, 93] Operation: 95-2=93 Exploring Operation: 71-2=69, Resulting Numbers: [95, 69] Generated Node #0,2,2: 86:[95, 69] Operation: 71-2=69 Exploring Operation: 2+71=73, Resulting Numbers: [95, 73] Generated Node #0,2,3: 86:[95, 73] Operation: 2+71=73 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 86:[2, 24], Operations: ['98-3=95', '95-71=24'] Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,86 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,86 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,86 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,86 unequal: No Solution No 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: 86:[71, 93], Operations: ['98-3=95', '95-2=93'] Exploring Operation: 93-71=22, Resulting Numbers: [22] 22,86 unequal: No Solution Exploring Operation: 71*93=6603, Resulting Numbers: [6603] 6603,86 unequal: No Solution Exploring Operation: 71+93=164, Resulting Numbers: [164] 164,86 unequal: No Solution No 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: 86:[95, 73], Operations: ['98-3=95', '2+71=73'] Exploring Operation: 95+73=168, Resulting Numbers: [168] 168,86 unequal: No Solution Exploring Operation: 95*73=6935, Resulting Numbers: [6935] 6935,86 unequal: No Solution Exploring Operation: 95-73=22, Resulting Numbers: [22] 22,86 unequal: No Solution No 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: 86:[95, 69], Operations: ['98-3=95', '71-2=69'] Exploring Operation: 95-69=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 95+69=164, Resulting Numbers: [164] 164,86 unequal: No Solution Exploring Operation: 95*69=6555, Resulting Numbers: [6555] 6555,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 63, 30, 15, 23 ]
42
[ "63-23=40", "30/15=2", "40+2=42" ]
Current State: 42:[63, 30, 15, 23], Operations: [] Exploring Operation: 63-23=40, Resulting Numbers: [30, 15, 40] Generated Node #2: [30, 15, 40] from Operation: 63-23=40 Current State: 42:[30, 15, 40], Operations: ['63-23=40'] Exploring Operation: 30/15=2, Resulting Numbers: [40, 2] Generated Node #3: [40, 2] from Operation: 30/15=2 Current State: 42:[40, 2], Operations: ['63-23=40', '30/15=2'] Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[63, 30, 15, 23], Operations: [] Exploring Operation: 63-23=40, Resulting Numbers: [30, 15, 40] Generated Node #0,0: 42:[30, 15, 40] Operation: 63-23=40 Exploring Operation: 30-23=7, Resulting Numbers: [63, 15, 7] Generated Node #0,1: 42:[63, 15, 7] Operation: 30-23=7 Exploring Operation: 63-30=33, Resulting Numbers: [15, 23, 33] Generated Node #0,2: 42:[15, 23, 33] Operation: 63-30=33 Exploring Operation: 63-15=48, Resulting Numbers: [30, 23, 48] Generated Node #0,3: 42:[30, 23, 48] Operation: 63-15=48 Moving to Node #0,0 Current State: 42:[30, 15, 40], Operations: ['63-23=40'] Exploring Operation: 30-15=15, Resulting Numbers: [40, 15] Generated Node #0,0,0: 42:[40, 15] Operation: 30-15=15 Exploring Operation: 30+15=45, Resulting Numbers: [40, 45] Generated Node #0,0,1: 42:[40, 45] Operation: 30+15=45 Exploring Operation: 30/15=2, Resulting Numbers: [40, 2] Generated Node #0,0,2: 42:[40, 2] Operation: 30/15=2 Exploring Operation: 40-30=10, Resulting Numbers: [15, 10] Generated Node #0,0,3: 42:[15, 10] Operation: 40-30=10 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 42:[40, 2], Operations: ['63-23=40', '30/15=2'] Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[63, 30, 15, 23], Operations: [] Exploring Operation: 63-23=40, Resulting Numbers: [30, 15, 40] Generated Node #0,0: 42:[30, 15, 40] Operation: 63-23=40 Moving to Node #0,0 Current State: 42:[30, 15, 40], Operations: ['63-23=40'] Exploring Operation: 30/15=2, Resulting Numbers: [40, 2] Generated Node #0,0,2: 42:[40, 2] Operation: 30/15=2 Moving to Node #0,0,2 Current State: 42:[40, 2], Operations: ['63-23=40', '30/15=2'] Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 38, 6, 97, 95 ]
16
[ "38-6=32", "97-95=2", "32/2=16" ]
Current State: 16:[38, 6, 97, 95], Operations: [] Exploring Operation: 38-6=32, Resulting Numbers: [97, 95, 32] Generated Node #2: [97, 95, 32] from Operation: 38-6=32 Current State: 16:[97, 95, 32], Operations: ['38-6=32'] Exploring Operation: 97-95=2, Resulting Numbers: [32, 2] Generated Node #3: [32, 2] from Operation: 97-95=2 Current State: 16:[32, 2], Operations: ['38-6=32', '97-95=2'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[38, 6, 97, 95], Operations: [] Exploring Operation: 97-38=59, Resulting Numbers: [6, 95, 59] Generated Node #0,0: 16:[6, 95, 59] Operation: 97-38=59 Exploring Operation: 97-95=2, Resulting Numbers: [38, 6, 2] Generated Node #0,1: 16:[38, 6, 2] Operation: 97-95=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[38, 6, 2], Operations: ['97-95=2'] Exploring Operation: 38-6=32, Resulting Numbers: [2, 32] Generated Node #0,1,0: 16:[2, 32] Operation: 38-6=32 Exploring Operation: 38/2=19, Resulting Numbers: [6, 19] Generated Node #0,1,1: 16:[6, 19] Operation: 38/2=19 Moving to Node #0,1,1 Current State: 16:[6, 19], Operations: ['97-95=2', '38/2=19'] Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[2, 32], Operations: ['97-95=2', '38-6=32'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,16 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[38, 6, 97, 95], Operations: [] Exploring Operation: 97-95=2, Resulting Numbers: [38, 6, 2] Generated Node #0,1: 16:[38, 6, 2] Operation: 97-95=2 Moving to Node #0,1 Current State: 16:[38, 6, 2], Operations: ['97-95=2'] Exploring Operation: 38-6=32, Resulting Numbers: [2, 32] Generated Node #0,1,0: 16:[2, 32] Operation: 38-6=32 Moving to Node #0,1,0 Current State: 16:[2, 32], Operations: ['97-95=2', '38-6=32'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 23, 68, 50, 89 ]
94
[ "68-23=45", "50+89=139", "139-45=94" ]
Current State: 94:[23, 68, 50, 89], Operations: [] Exploring Operation: 68-23=45, Resulting Numbers: [50, 89, 45] Generated Node #2: [50, 89, 45] from Operation: 68-23=45 Current State: 94:[50, 89, 45], Operations: ['68-23=45'] Exploring Operation: 50+89=139, Resulting Numbers: [45, 139] Generated Node #3: [45, 139] from Operation: 50+89=139 Current State: 94:[45, 139], Operations: ['68-23=45', '50+89=139'] Exploring Operation: 139-45=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[23, 68, 50, 89], Operations: [] Exploring Operation: 68-23=45, Resulting Numbers: [50, 89, 45] Generated Node #0,0: 94:[50, 89, 45] Operation: 68-23=45 Exploring Operation: 89-23=66, Resulting Numbers: [68, 50, 66] Generated Node #0,1: 94:[68, 50, 66] Operation: 89-23=66 Exploring Operation: 23+89=112, Resulting Numbers: [68, 50, 112] Generated Node #0,2: 94:[68, 50, 112] Operation: 23+89=112 Exploring Operation: 23+68=91, Resulting Numbers: [50, 89, 91] Generated Node #0,3: 94:[50, 89, 91] Operation: 23+68=91 Exploring Operation: 68-50=18, Resulting Numbers: [23, 89, 18] Generated Node #0,4: 94:[23, 89, 18] Operation: 68-50=18 Moving to Node #0,0 Current State: 94:[50, 89, 45], Operations: ['68-23=45'] Exploring Operation: 50-45=5, Resulting Numbers: [89, 5] Generated Node #0,0,0: 94:[89, 5] Operation: 50-45=5 Exploring Operation: 89-45=44, Resulting Numbers: [50, 44] Generated Node #0,0,1: 94:[50, 44] Operation: 89-45=44 Exploring Operation: 89+45=134, Resulting Numbers: [50, 134] Generated Node #0,0,2: 94:[50, 134] Operation: 89+45=134 Exploring Operation: 50+45=95, Resulting Numbers: [89, 95] Generated Node #0,0,3: 94:[89, 95] Operation: 50+45=95 Exploring Operation: 89-50=39, Resulting Numbers: [45, 39] Generated Node #0,0,4: 94:[45, 39] Operation: 89-50=39 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 94:[50, 44], Operations: ['68-23=45', '89-45=44'] Exploring Operation: 50-44=6, Resulting Numbers: [6] 6,94 unequal: No Solution Exploring Operation: 50+44=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[23, 68, 50, 89], Operations: [] Exploring Operation: 68-23=45, Resulting Numbers: [50, 89, 45] Generated Node #0,0: 94:[50, 89, 45] Operation: 68-23=45 Moving to Node #0,0 Current State: 94:[50, 89, 45], Operations: ['68-23=45'] Exploring Operation: 89-45=44, Resulting Numbers: [50, 44] Generated Node #0,0,1: 94:[50, 44] Operation: 89-45=44 Moving to Node #0,0,1 Current State: 94:[50, 44], Operations: ['68-23=45', '89-45=44'] Exploring Operation: 50+44=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 34, 96, 17, 27 ]
52
[ "96-34=62", "27-17=10", "62-10=52" ]
Current State: 52:[34, 96, 17, 27], Operations: [] Exploring Operation: 96-34=62, Resulting Numbers: [17, 27, 62] Generated Node #2: [17, 27, 62] from Operation: 96-34=62 Current State: 52:[17, 27, 62], Operations: ['96-34=62'] Exploring Operation: 27-17=10, Resulting Numbers: [62, 10] Generated Node #3: [62, 10] from Operation: 27-17=10 Current State: 52:[62, 10], Operations: ['96-34=62', '27-17=10'] Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[34, 96, 17, 27], Operations: [] Exploring Operation: 96-34=62, Resulting Numbers: [17, 27, 62] Generated Node #0,0: 52:[17, 27, 62] Operation: 96-34=62 Exploring Operation: 34/17=2, Resulting Numbers: [96, 27, 2] Generated Node #0,1: 52:[96, 27, 2] Operation: 34/17=2 Exploring Operation: 96-27=69, Resulting Numbers: [34, 17, 69] Generated Node #0,2: 52:[34, 17, 69] Operation: 96-27=69 Exploring Operation: 96-17=79, Resulting Numbers: [34, 27, 79] Generated Node #0,3: 52:[34, 27, 79] Operation: 96-17=79 Moving to Node #0,0 Current State: 52:[17, 27, 62], Operations: ['96-34=62'] Exploring Operation: 27-17=10, Resulting Numbers: [62, 10] Generated Node #0,0,0: 52:[62, 10] Operation: 27-17=10 Exploring Operation: 62-27=35, Resulting Numbers: [17, 35] Generated Node #0,0,1: 52:[17, 35] Operation: 62-27=35 Exploring Operation: 17+27=44, Resulting Numbers: [62, 44] Generated Node #0,0,2: 52:[62, 44] Operation: 17+27=44 Exploring Operation: 62-17=45, Resulting Numbers: [27, 45] Generated Node #0,0,3: 52:[27, 45] Operation: 62-17=45 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 52:[27, 45], Operations: ['96-34=62', '62-17=45'] Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,52 unequal: No Solution Exploring Operation: 27+45=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 27*45=1215, Resulting Numbers: [1215] 1215,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[62, 10], Operations: ['96-34=62', '27-17=10'] Exploring Operation: 62+10=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[34, 96, 17, 27], Operations: [] Exploring Operation: 96-34=62, Resulting Numbers: [17, 27, 62] Generated Node #0,0: 52:[17, 27, 62] Operation: 96-34=62 Moving to Node #0,0 Current State: 52:[17, 27, 62], Operations: ['96-34=62'] Exploring Operation: 27-17=10, Resulting Numbers: [62, 10] Generated Node #0,0,0: 52:[62, 10] Operation: 27-17=10 Moving to Node #0,0,0 Current State: 52:[62, 10], Operations: ['96-34=62', '27-17=10'] Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 81, 86, 96, 80 ]
65
[ "86-80=6", "96/6=16", "81-16=65" ]
Current State: 65:[81, 86, 96, 80], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [81, 96, 6] Generated Node #2: [81, 96, 6] from Operation: 86-80=6 Current State: 65:[81, 96, 6], Operations: ['86-80=6'] Exploring Operation: 96/6=16, Resulting Numbers: [81, 16] Generated Node #3: [81, 16] from Operation: 96/6=16 Current State: 65:[81, 16], Operations: ['86-80=6', '96/6=16'] Exploring Operation: 81-16=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[81, 86, 96, 80], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [96, 80, 5] Generated Node #0,0: 65:[96, 80, 5] Operation: 86-81=5 Exploring Operation: 86-80=6, Resulting Numbers: [81, 96, 6] Generated Node #0,1: 65:[81, 96, 6] Operation: 86-80=6 Exploring Operation: 96-86=10, Resulting Numbers: [81, 80, 10] Generated Node #0,2: 65:[81, 80, 10] Operation: 96-86=10 Exploring Operation: 96-81=15, Resulting Numbers: [86, 80, 15] Generated Node #0,3: 65:[86, 80, 15] Operation: 96-81=15 Exploring Operation: 96-80=16, Resulting Numbers: [81, 86, 16] Generated Node #0,4: 65:[81, 86, 16] Operation: 96-80=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[81, 80, 10], Operations: ['96-86=10'] Exploring Operation: 81-10=71, Resulting Numbers: [80, 71] Generated Node #0,2,0: 65:[80, 71] Operation: 81-10=71 Exploring Operation: 81+10=91, Resulting Numbers: [80, 91] Generated Node #0,2,1: 65:[80, 91] Operation: 81+10=91 Exploring Operation: 80/10=8, Resulting Numbers: [81, 8] Generated Node #0,2,2: 65:[81, 8] Operation: 80/10=8 Exploring Operation: 81-80=1, Resulting Numbers: [10, 1] Generated Node #0,2,3: 65:[10, 1] Operation: 81-80=1 Exploring Operation: 80-10=70, Resulting Numbers: [81, 70] Generated Node #0,2,4: 65:[81, 70] Operation: 80-10=70 Moving to Node #0,2,3 Current State: 65:[10, 1], Operations: ['96-86=10', '81-80=1'] Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,65 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[81, 8], Operations: ['96-86=10', '80/10=8'] Exploring Operation: 81*8=648, Resulting Numbers: [648] 648,65 unequal: No Solution Exploring Operation: 81+8=89, Resulting Numbers: [89] 89,65 unequal: No Solution Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[80, 71], Operations: ['96-86=10', '81-10=71'] Exploring Operation: 80*71=5680, Resulting Numbers: [5680] 5680,65 unequal: No Solution Exploring Operation: 80-71=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 80+71=151, Resulting Numbers: [151] 151,65 unequal: No Solution Moving to Node #0,2,4 Current State: 65:[81, 70], Operations: ['96-86=10', '80-10=70'] Exploring Operation: 81+70=151, Resulting Numbers: [151] 151,65 unequal: No Solution Exploring Operation: 81*70=5670, Resulting Numbers: [5670] 5670,65 unequal: No Solution Exploring Operation: 81-70=11, Resulting Numbers: [11] 11,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[80, 91], Operations: ['96-86=10', '81+10=91'] Exploring Operation: 91-80=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 80+91=171, Resulting Numbers: [171] 171,65 unequal: No Solution Exploring Operation: 80*91=7280, Resulting Numbers: [7280] 7280,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 65:[86, 80, 15], Operations: ['96-81=15'] Exploring Operation: 80+15=95, Resulting Numbers: [86, 95] Generated Node #0,3,0: 65:[86, 95] Operation: 80+15=95 Exploring Operation: 80-15=65, Resulting Numbers: [86, 65] Generated Node #0,3,1: 65:[86, 65] Operation: 80-15=65 Exploring Operation: 86-15=71, Resulting Numbers: [80, 71] Generated Node #0,3,2: 65:[80, 71] Operation: 86-15=71 Exploring Operation: 86-80=6, Resulting Numbers: [15, 6] Generated Node #0,3,3: 65:[15, 6] Operation: 86-80=6 Exploring Operation: 86+15=101, Resulting Numbers: [80, 101] Generated Node #0,3,4: 65:[80, 101] Operation: 86+15=101 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 65:[15, 6], Operations: ['96-81=15', '86-80=6'] Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,65 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 65:[86, 65], Operations: ['96-81=15', '80-15=65'] Exploring Operation: 86-65=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 86*65=5590, Resulting Numbers: [5590] 5590,65 unequal: No Solution Exploring Operation: 86+65=151, Resulting Numbers: [151] 151,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 65:[80, 71], Operations: ['96-81=15', '86-15=71'] Exploring Operation: 80-71=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 80*71=5680, Resulting Numbers: [5680] 5680,65 unequal: No Solution Exploring Operation: 80+71=151, Resulting Numbers: [151] 151,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 65:[86, 95], Operations: ['96-81=15', '80+15=95'] Exploring Operation: 86+95=181, Resulting Numbers: [181] 181,65 unequal: No Solution Exploring Operation: 95-86=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 86*95=8170, Resulting Numbers: [8170] 8170,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 65:[80, 101], Operations: ['96-81=15', '86+15=101'] Exploring Operation: 80+101=181, Resulting Numbers: [181] 181,65 unequal: No Solution Exploring Operation: 101-80=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 80*101=8080, Resulting Numbers: [8080] 8080,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 65:[81, 86, 16], Operations: ['96-80=16'] Exploring Operation: 86+16=102, Resulting Numbers: [81, 102] Generated Node #0,4,0: 65:[81, 102] Operation: 86+16=102 Exploring Operation: 81+16=97, Resulting Numbers: [86, 97] Generated Node #0,4,1: 65:[86, 97] Operation: 81+16=97 Exploring Operation: 86-16=70, Resulting Numbers: [81, 70] Generated Node #0,4,2: 65:[81, 70] Operation: 86-16=70 Exploring Operation: 81-16=65, Resulting Numbers: [86, 65] Generated Node #0,4,3: 65:[86, 65] Operation: 81-16=65 Exploring Operation: 86-81=5, Resulting Numbers: [16, 5] Generated Node #0,4,4: 65:[16, 5] Operation: 86-81=5 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 65:[16, 5], Operations: ['96-80=16', '86-81=5'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 65:[81, 70], Operations: ['96-80=16', '86-16=70'] Exploring Operation: 81-70=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 81*70=5670, Resulting Numbers: [5670] 5670,65 unequal: No Solution Exploring Operation: 81+70=151, Resulting Numbers: [151] 151,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 65:[86, 65], Operations: ['96-80=16', '81-16=65'] Exploring Operation: 86-65=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 86*65=5590, Resulting Numbers: [5590] 5590,65 unequal: No Solution Exploring Operation: 86+65=151, Resulting Numbers: [151] 151,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 65:[81, 102], Operations: ['96-80=16', '86+16=102'] Exploring Operation: 81+102=183, Resulting Numbers: [183] 183,65 unequal: No Solution Exploring Operation: 102-81=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 81*102=8262, Resulting Numbers: [8262] 8262,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 65:[86, 97], Operations: ['96-80=16', '81+16=97'] Exploring Operation: 97-86=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 86*97=8342, Resulting Numbers: [8342] 8342,65 unequal: No Solution Exploring Operation: 86+97=183, Resulting Numbers: [183] 183,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[96, 80, 5], Operations: ['86-81=5'] Exploring Operation: 80/5=16, Resulting Numbers: [96, 16] Generated Node #0,0,0: 65:[96, 16] Operation: 80/5=16 Exploring Operation: 96-5=91, Resulting Numbers: [80, 91] Generated Node #0,0,1: 65:[80, 91] Operation: 96-5=91 Exploring Operation: 96-80=16, Resulting Numbers: [5, 16] Generated Node #0,0,2: 65:[5, 16] Operation: 96-80=16 Exploring Operation: 80-5=75, Resulting Numbers: [96, 75] Generated Node #0,0,3: 65:[96, 75] Operation: 80-5=75 Exploring Operation: 96+5=101, Resulting Numbers: [80, 101] Generated Node #0,0,4: 65:[80, 101] Operation: 96+5=101 Moving to Node #0,0,2 Current State: 65:[5, 16], Operations: ['86-81=5', '96-80=16'] Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[96, 16], Operations: ['86-81=5', '80/5=16'] Exploring Operation: 96-16=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 96*16=1536, Resulting Numbers: [1536] 1536,65 unequal: No Solution Exploring Operation: 96+16=112, Resulting Numbers: [112] 112,65 unequal: No Solution Exploring Operation: 96/16=6, Resulting Numbers: [6] 6,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[80, 91], Operations: ['86-81=5', '96-5=91'] Exploring Operation: 80*91=7280, Resulting Numbers: [7280] 7280,65 unequal: No Solution Exploring Operation: 91-80=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 80+91=171, Resulting Numbers: [171] 171,65 unequal: No Solution Moving to Node #0,0,3 Current State: 65:[96, 75], Operations: ['86-81=5', '80-5=75'] Exploring Operation: 96*75=7200, Resulting Numbers: [7200] 7200,65 unequal: No Solution Exploring Operation: 96+75=171, Resulting Numbers: [171] 171,65 unequal: No Solution Exploring Operation: 96-75=21, Resulting Numbers: [21] 21,65 unequal: No Solution Moving to Node #0,0,4 Current State: 65:[80, 101], Operations: ['86-81=5', '96+5=101'] Exploring Operation: 80+101=181, Resulting Numbers: [181] 181,65 unequal: No Solution Exploring Operation: 80*101=8080, Resulting Numbers: [8080] 8080,65 unequal: No Solution Exploring Operation: 101-80=21, Resulting Numbers: [21] 21,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[81, 96, 6], Operations: ['86-80=6'] Exploring Operation: 96-81=15, Resulting Numbers: [6, 15] Generated Node #0,1,0: 65:[6, 15] Operation: 96-81=15 Exploring Operation: 96/6=16, Resulting Numbers: [81, 16] Generated Node #0,1,1: 65:[81, 16] Operation: 96/6=16 Exploring Operation: 81+6=87, Resulting Numbers: [96, 87] Generated Node #0,1,2: 65:[96, 87] Operation: 81+6=87 Exploring Operation: 96-6=90, Resulting Numbers: [81, 90] Generated Node #0,1,3: 65:[81, 90] Operation: 96-6=90 Exploring Operation: 81-6=75, Resulting Numbers: [96, 75] Generated Node #0,1,4: 65:[96, 75] Operation: 81-6=75 Moving to Node #0,1,0 Current State: 65:[6, 15], Operations: ['86-80=6', '96-81=15'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[81, 16], Operations: ['86-80=6', '96/6=16'] Exploring Operation: 81-16=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[81, 86, 96, 80], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [81, 96, 6] Generated Node #0,1: 65:[81, 96, 6] Operation: 86-80=6 Moving to Node #0,1 Current State: 65:[81, 96, 6], Operations: ['86-80=6'] Exploring Operation: 96/6=16, Resulting Numbers: [81, 16] Generated Node #0,1,1: 65:[81, 16] Operation: 96/6=16 Moving to Node #0,1,1 Current State: 65:[81, 16], Operations: ['86-80=6', '96/6=16'] Exploring Operation: 81-16=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.913194
hs_5
mult_heuristic
[ 50, 34, 4, 30 ]
58
[ "50+34=84", "30-4=26", "84-26=58" ]
Current State: 58:[50, 34, 4, 30], Operations: [] Exploring Operation: 50+34=84, Resulting Numbers: [4, 30, 84] Generated Node #2: [4, 30, 84] from Operation: 50+34=84 Current State: 58:[4, 30, 84], Operations: ['50+34=84'] Exploring Operation: 30-4=26, Resulting Numbers: [84, 26] Generated Node #3: [84, 26] from Operation: 30-4=26 Current State: 58:[84, 26], Operations: ['50+34=84', '30-4=26'] Exploring Operation: 84-26=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[50, 34, 4, 30], Operations: [] Exploring Operation: 34-4=30, Resulting Numbers: [50, 30, 30] Generated Node #0,0: 58:[50, 30, 30] Operation: 34-4=30 Exploring Operation: 50-34=16, Resulting Numbers: [4, 30, 16] Generated Node #0,1: 58:[4, 30, 16] Operation: 50-34=16 Exploring Operation: 50-30=20, Resulting Numbers: [34, 4, 20] Generated Node #0,2: 58:[34, 4, 20] Operation: 50-30=20 Exploring Operation: 34-30=4, Resulting Numbers: [50, 4, 4] Generated Node #0,3: 58:[50, 4, 4] Operation: 34-30=4 Exploring Operation: 50+4=54, Resulting Numbers: [34, 30, 54] Generated Node #0,4: 58:[34, 30, 54] Operation: 50+4=54 Moving to Node #0,0 Current State: 58:[50, 30, 30], Operations: ['34-4=30'] Exploring Operation: 30+30=60, Resulting Numbers: [50, 60] Generated Node #0,0,0: 58:[50, 60] Operation: 30+30=60 Exploring Operation: 30/30=1, Resulting Numbers: [50, 1] Generated Node #0,0,1: 58:[50, 1] Operation: 30/30=1 Exploring Operation: 50-30=20, Resulting Numbers: [30, 20] Generated Node #0,0,2: 58:[30, 20] Operation: 50-30=20 Exploring Operation: 30-30=0, Resulting Numbers: [50, 0] Generated Node #0,0,3: 58:[50, 0] Operation: 30-30=0 Exploring Operation: 50-30=20, Resulting Numbers: [30, 20] Generated Node #0,0,4: 58:[30, 20] Operation: 50-30=20 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 58:[50, 1], Operations: ['34-4=30', '30/30=1'] Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,58 unequal: No Solution Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,58 unequal: No Solution Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,58 unequal: No Solution Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,58 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 #0,0,0 Current State: 58:[50, 60], Operations: ['34-4=30', '30+30=60'] Exploring Operation: 50+60=110, Resulting Numbers: [110] 110,58 unequal: No Solution Exploring Operation: 50*60=3000, Resulting Numbers: [3000] 3000,58 unequal: No Solution Exploring Operation: 60-50=10, Resulting Numbers: [10] 10,58 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:[30, 20], Operations: ['34-4=30', '50-30=20'] Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,58 unequal: No Solution Exploring Operation: 30*20=600, Resulting Numbers: [600] 600,58 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,58 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 #0,0,3 Current State: 58:[50, 0], Operations: ['34-4=30', '30-30=0'] Exploring Operation: 50-0=50, Resulting Numbers: [50] 50,58 unequal: No Solution Exploring Operation: 50+0=50, Resulting Numbers: [50] 50,58 unequal: No Solution Exploring Operation: 50*0=0, Resulting Numbers: [0] 0,58 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 #0,0,4 Current State: 58:[30, 20], Operations: ['34-4=30', '50-30=20'] Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,58 unequal: No Solution Exploring Operation: 30*20=600, Resulting Numbers: [600] 600,58 unequal: No Solution Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 58:[34, 30, 54], Operations: ['50+4=54'] Exploring Operation: 34-30=4, Resulting Numbers: [54, 4] Generated Node #0,4,0: 58:[54, 4] Operation: 34-30=4 Exploring Operation: 34+54=88, Resulting Numbers: [30, 88] Generated Node #0,4,1: 58:[30, 88] Operation: 34+54=88 Exploring Operation: 34+30=64, Resulting Numbers: [54, 64] Generated Node #0,4,2: 58:[54, 64] Operation: 34+30=64 Exploring Operation: 54-34=20, Resulting Numbers: [30, 20] Generated Node #0,4,3: 58:[30, 20] Operation: 54-34=20 Exploring Operation: 54-30=24, Resulting Numbers: [34, 24] Generated Node #0,4,4: 58:[34, 24] Operation: 54-30=24 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 58:[54, 4], Operations: ['50+4=54', '34-30=4'] Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[50, 34, 4, 30], Operations: [] Exploring Operation: 50+4=54, Resulting Numbers: [34, 30, 54] Generated Node #0,4: 58:[34, 30, 54] Operation: 50+4=54 Moving to Node #0,4 Current State: 58:[34, 30, 54], Operations: ['50+4=54'] Exploring Operation: 34-30=4, Resulting Numbers: [54, 4] Generated Node #0,4,0: 58:[54, 4] Operation: 34-30=4 Moving to Node #0,4,0 Current State: 58:[54, 4], Operations: ['50+4=54', '34-30=4'] Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 42, 77, 23, 92 ]
31
[ "77-42=35", "92/23=4", "35-4=31" ]
Current State: 31:[42, 77, 23, 92], Operations: [] Exploring Operation: 77-42=35, Resulting Numbers: [23, 92, 35] Generated Node #2: [23, 92, 35] from Operation: 77-42=35 Current State: 31:[23, 92, 35], Operations: ['77-42=35'] Exploring Operation: 92/23=4, Resulting Numbers: [35, 4] Generated Node #3: [35, 4] from Operation: 92/23=4 Current State: 31:[35, 4], Operations: ['77-42=35', '92/23=4'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[42, 77, 23, 92], Operations: [] Exploring Operation: 92-42=50, Resulting Numbers: [77, 23, 50] Generated Node #0,0: 31:[77, 23, 50] Operation: 92-42=50 Exploring Operation: 77-42=35, Resulting Numbers: [23, 92, 35] Generated Node #0,1: 31:[23, 92, 35] Operation: 77-42=35 Exploring Operation: 92-77=15, Resulting Numbers: [42, 23, 15] Generated Node #0,2: 31:[42, 23, 15] Operation: 92-77=15 Exploring Operation: 92/23=4, Resulting Numbers: [42, 77, 4] Generated Node #0,3: 31:[42, 77, 4] Operation: 92/23=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 31:[42, 23, 15], Operations: ['92-77=15'] Exploring Operation: 42-23=19, Resulting Numbers: [15, 19] Generated Node #0,2,0: 31:[15, 19] Operation: 42-23=19 Exploring Operation: 42+15=57, Resulting Numbers: [23, 57] Generated Node #0,2,1: 31:[23, 57] Operation: 42+15=57 Exploring Operation: 42-15=27, Resulting Numbers: [23, 27] Generated Node #0,2,2: 31:[23, 27] Operation: 42-15=27 Exploring Operation: 23+15=38, Resulting Numbers: [42, 38] Generated Node #0,2,3: 31:[42, 38] Operation: 23+15=38 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 31:[23, 27], Operations: ['92-77=15', '42-15=27'] Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 23+27=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 23*27=621, Resulting Numbers: [621] 621,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 31:[42, 38], Operations: ['92-77=15', '23+15=38'] Exploring Operation: 42-38=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 42+38=80, Resulting Numbers: [80] 80,31 unequal: No Solution Exploring Operation: 42*38=1596, Resulting Numbers: [1596] 1596,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 31:[15, 19], Operations: ['92-77=15', '42-23=19'] Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,31 unequal: No Solution Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,31 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 31:[23, 57], Operations: ['92-77=15', '42+15=57'] Exploring Operation: 23+57=80, Resulting Numbers: [80] 80,31 unequal: No Solution Exploring Operation: 23*57=1311, Resulting Numbers: [1311] 1311,31 unequal: No Solution Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[77, 23, 50], Operations: ['92-42=50'] Exploring Operation: 77-50=27, Resulting Numbers: [23, 27] Generated Node #0,0,0: 31:[23, 27] Operation: 77-50=27 Exploring Operation: 77+23=100, Resulting Numbers: [50, 100] Generated Node #0,0,1: 31:[50, 100] Operation: 77+23=100 Exploring Operation: 50-23=27, Resulting Numbers: [77, 27] Generated Node #0,0,2: 31:[77, 27] Operation: 50-23=27 Exploring Operation: 77-23=54, Resulting Numbers: [50, 54] Generated Node #0,0,3: 31:[50, 54] Operation: 77-23=54 Moving to Node #0,0,0 Current State: 31:[23, 27], Operations: ['92-42=50', '77-50=27'] Exploring Operation: 23+27=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 23*27=621, Resulting Numbers: [621] 621,31 unequal: No Solution Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[50, 54], Operations: ['92-42=50', '77-23=54'] Exploring Operation: 54-50=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 50*54=2700, Resulting Numbers: [2700] 2700,31 unequal: No Solution Exploring Operation: 50+54=104, Resulting Numbers: [104] 104,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[77, 27], Operations: ['92-42=50', '50-23=27'] Exploring Operation: 77*27=2079, Resulting Numbers: [2079] 2079,31 unequal: No Solution Exploring Operation: 77+27=104, Resulting Numbers: [104] 104,31 unequal: No Solution Exploring Operation: 77-27=50, Resulting Numbers: [50] 50,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[50, 100], Operations: ['92-42=50', '77+23=100'] Exploring Operation: 50+100=150, Resulting Numbers: [150] 150,31 unequal: No Solution Exploring Operation: 50*100=5000, Resulting Numbers: [5000] 5000,31 unequal: No Solution Exploring Operation: 100/50=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 100-50=50, Resulting Numbers: [50] 50,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[23, 92, 35], Operations: ['77-42=35'] Exploring Operation: 35-23=12, Resulting Numbers: [92, 12] Generated Node #0,1,0: 31:[92, 12] Operation: 35-23=12 Exploring Operation: 92-23=69, Resulting Numbers: [35, 69] Generated Node #0,1,1: 31:[35, 69] Operation: 92-23=69 Exploring Operation: 92-35=57, Resulting Numbers: [23, 57] Generated Node #0,1,2: 31:[23, 57] Operation: 92-35=57 Exploring Operation: 92/23=4, Resulting Numbers: [35, 4] Generated Node #0,1,3: 31:[35, 4] Operation: 92/23=4 Moving to Node #0,1,3 Current State: 31:[35, 4], Operations: ['77-42=35', '92/23=4'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[42, 77, 23, 92], Operations: [] Exploring Operation: 77-42=35, Resulting Numbers: [23, 92, 35] Generated Node #0,1: 31:[23, 92, 35] Operation: 77-42=35 Moving to Node #0,1 Current State: 31:[23, 92, 35], Operations: ['77-42=35'] Exploring Operation: 92/23=4, Resulting Numbers: [35, 4] Generated Node #0,1,3: 31:[35, 4] Operation: 92/23=4 Moving to Node #0,1,3 Current State: 31:[35, 4], Operations: ['77-42=35', '92/23=4'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.960069
hs_4
mult_heuristic
[ 29, 68, 1, 67 ]
27
[ "68-29=39", "67-1=66", "66-39=27" ]
Current State: 27:[29, 68, 1, 67], Operations: [] Exploring Operation: 68-29=39, Resulting Numbers: [1, 67, 39] Generated Node #2: [1, 67, 39] from Operation: 68-29=39 Current State: 27:[1, 67, 39], Operations: ['68-29=39'] Exploring Operation: 67-1=66, Resulting Numbers: [39, 66] Generated Node #3: [39, 66] from Operation: 67-1=66 Current State: 27:[39, 66], Operations: ['68-29=39', '67-1=66'] Exploring Operation: 66-39=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[29, 68, 1, 67], Operations: [] Exploring Operation: 68-67=1, Resulting Numbers: [29, 1, 1] Generated Node #0,0: 27:[29, 1, 1] Operation: 68-67=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[29, 1, 1], Operations: ['68-67=1'] Exploring Operation: 29-1=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 27:[1, 28] Operation: 29-1=28 Moving to Node #0,0,0 Current State: 27:[1, 28], Operations: ['68-67=1', '29-1=28'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[29, 68, 1, 67], Operations: [] Exploring Operation: 68-67=1, Resulting Numbers: [29, 1, 1] Generated Node #0,0: 27:[29, 1, 1] Operation: 68-67=1 Moving to Node #0,0 Current State: 27:[29, 1, 1], Operations: ['68-67=1'] Exploring Operation: 29-1=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 27:[1, 28] Operation: 29-1=28 Moving to Node #0,0,0 Current State: 27:[1, 28], Operations: ['68-67=1', '29-1=28'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 40, 52, 76, 33 ]
64
[ "76*33=2508", "52+2508=2560", "2560/40=64" ]
Current State: 64:[40, 52, 76, 33], Operations: [] Exploring Operation: 76*33=2508, Resulting Numbers: [40, 52, 2508] Generated Node #2: [40, 52, 2508] from Operation: 76*33=2508 Current State: 64:[40, 52, 2508], Operations: ['76*33=2508'] Exploring Operation: 52+2508=2560, Resulting Numbers: [40, 2560] Generated Node #3: [40, 2560] from Operation: 52+2508=2560 Current State: 64:[40, 2560], Operations: ['76*33=2508', '52+2508=2560'] Exploring Operation: 2560/40=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[40, 52, 76, 33], Operations: [] Exploring Operation: 76-40=36, Resulting Numbers: [52, 33, 36] Generated Node #0,0: 64:[52, 33, 36] Operation: 76-40=36 Exploring Operation: 52-40=12, Resulting Numbers: [76, 33, 12] Generated Node #0,1: 64:[76, 33, 12] Operation: 52-40=12 Moving to Node #0,0 Current State: 64:[52, 33, 36], Operations: ['76-40=36'] Exploring Operation: 52-33=19, Resulting Numbers: [36, 19] Generated Node #0,0,0: 64:[36, 19] Operation: 52-33=19 Exploring Operation: 52-36=16, Resulting Numbers: [33, 16] Generated Node #0,0,1: 64:[33, 16] Operation: 52-36=16 Moving to Node #0,1 Current State: 64:[76, 33, 12], Operations: ['52-40=12'] Exploring Operation: 76-33=43, Resulting Numbers: [12, 43] Generated Node #0,1,0: 64:[12, 43] Operation: 76-33=43 Exploring Operation: 76-12=64, Resulting Numbers: [33, 64] Generated Node #0,1,1: 64:[33, 64] Operation: 76-12=64 Moving to Node #0,0,1 Current State: 64:[33, 16], Operations: ['76-40=36', '52-36=16'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,64 unequal: No Solution Exploring Operation: 33+16=49, Resulting Numbers: [49] 49,64 unequal: No Solution Moving to Node #0,1,1 Current State: 64:[33, 64], Operations: ['52-40=12', '76-12=64'] Exploring Operation: 33+64=97, Resulting Numbers: [97] 97,64 unequal: No Solution Exploring Operation: 64-33=31, Resulting Numbers: [31] 31,64 unequal: No Solution Moving to Node #0,0,0 Current State: 64:[36, 19], Operations: ['76-40=36', '52-33=19'] Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,64 unequal: No Solution Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,64 unequal: No Solution Moving to Node #0,1,0 Current State: 64:[12, 43], Operations: ['52-40=12', '76-33=43'] Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,64 unequal: No Solution Exploring Operation: 12+43=55, Resulting Numbers: [55] 55,64 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 96, 87, 9, 79 ]
61
[ "96-87=9", "79-9=70", "70-9=61" ]
Current State: 61:[96, 87, 9, 79], Operations: [] Exploring Operation: 96-87=9, Resulting Numbers: [9, 79, 9] Generated Node #2: [9, 79, 9] from Operation: 96-87=9 Current State: 61:[9, 79, 9], Operations: ['96-87=9'] Exploring Operation: 79-9=70, Resulting Numbers: [70] 70,61 equal: Goal Reached Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[96, 87, 9, 79], Operations: [] Exploring Operation: 79-9=70, Resulting Numbers: [96, 87, 70] Generated Node #0,0: 61:[96, 87, 70] Operation: 79-9=70 Exploring Operation: 87-9=78, Resulting Numbers: [96, 79, 78] Generated Node #0,1: 61:[96, 79, 78] Operation: 87-9=78 Exploring Operation: 96-9=87, Resulting Numbers: [87, 79, 87] Generated Node #0,2: 61:[87, 79, 87] Operation: 96-9=87 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[96, 87, 70], Operations: ['79-9=70'] Exploring Operation: 96-87=9, Resulting Numbers: [70, 9] Generated Node #0,0,0: 61:[70, 9] Operation: 96-87=9 Exploring Operation: 96-70=26, Resulting Numbers: [87, 26] Generated Node #0,0,1: 61:[87, 26] Operation: 96-70=26 Exploring Operation: 87-70=17, Resulting Numbers: [96, 17] Generated Node #0,0,2: 61:[96, 17] Operation: 87-70=17 Moving to Node #0,0,0 Current State: 61:[70, 9], Operations: ['79-9=70', '96-87=9'] Exploring Operation: 70*9=630, Resulting Numbers: [630] 630,61 unequal: No Solution Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[96, 87, 9, 79], Operations: [] Exploring Operation: 79-9=70, Resulting Numbers: [96, 87, 70] Generated Node #0,0: 61:[96, 87, 70] Operation: 79-9=70 Moving to Node #0,0 Current State: 61:[96, 87, 70], Operations: ['79-9=70'] Exploring Operation: 96-87=9, Resulting Numbers: [70, 9] Generated Node #0,0,0: 61:[70, 9] Operation: 96-87=9 Moving to Node #0,0,0 Current State: 61:[70, 9], Operations: ['79-9=70', '96-87=9'] Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 81, 12, 32, 81 ]
45
[ "81/81=1", "12+32=44", "1+44=45" ]
Current State: 45:[81, 12, 32, 81], Operations: [] Exploring Operation: 81/81=1, Resulting Numbers: [12, 32, 1] Generated Node #2: [12, 32, 1] from Operation: 81/81=1 Current State: 45:[12, 32, 1], Operations: ['81/81=1'] Exploring Operation: 12+32=44, Resulting Numbers: [1, 44] Generated Node #3: [1, 44] from Operation: 12+32=44 Current State: 45:[1, 44], Operations: ['81/81=1', '12+32=44'] Exploring Operation: 1+44=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[81, 12, 32, 81], Operations: [] Exploring Operation: 81-81=0, Resulting Numbers: [12, 32, 0] Generated Node #0,0: 45:[12, 32, 0] Operation: 81-81=0 Exploring Operation: 81/81=1, Resulting Numbers: [12, 32, 1] Generated Node #0,1: 45:[12, 32, 1] Operation: 81/81=1 Moving to Node #0,1 Current State: 45:[12, 32, 1], Operations: ['81/81=1'] Exploring Operation: 12+32=44, Resulting Numbers: [1, 44] Generated Node #0,1,0: 45:[1, 44] Operation: 12+32=44 Exploring Operation: 32-12=20, Resulting Numbers: [1, 20] Generated Node #0,1,1: 45:[1, 20] Operation: 32-12=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[1, 44], Operations: ['81/81=1', '12+32=44'] Exploring Operation: 1+44=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[81, 12, 32, 81], Operations: [] Exploring Operation: 81/81=1, Resulting Numbers: [12, 32, 1] Generated Node #0,1: 45:[12, 32, 1] Operation: 81/81=1 Moving to Node #0,1 Current State: 45:[12, 32, 1], Operations: ['81/81=1'] Exploring Operation: 12+32=44, Resulting Numbers: [1, 44] Generated Node #0,1,0: 45:[1, 44] Operation: 12+32=44 Moving to Node #0,1,0 Current State: 45:[1, 44], Operations: ['81/81=1', '12+32=44'] Exploring Operation: 1+44=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 52, 52, 50, 7 ]
50
[ "52-52=0", "7*0=0", "50+0=50" ]
Current State: 50:[52, 52, 50, 7], Operations: [] Exploring Operation: 52-52=0, Resulting Numbers: [50, 7, 0] Generated Node #2: [50, 7, 0] from Operation: 52-52=0 Current State: 50:[50, 7, 0], Operations: ['52-52=0'] Exploring Operation: 7*0=0, Resulting Numbers: [50, 0] Generated Node #3: [50, 0] from Operation: 7*0=0 Current State: 50:[50, 0], Operations: ['52-52=0', '7*0=0'] Exploring Operation: 50+0=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[52, 52, 50, 7], Operations: [] Exploring Operation: 52-50=2, Resulting Numbers: [52, 7, 2] Generated Node #0,0: 50:[52, 7, 2] Operation: 52-50=2 Exploring Operation: 52-52=0, Resulting Numbers: [50, 7, 0] Generated Node #0,1: 50:[50, 7, 0] Operation: 52-52=0 Exploring Operation: 52/52=1, Resulting Numbers: [50, 7, 1] Generated Node #0,2: 50:[50, 7, 1] Operation: 52/52=1 Exploring Operation: 52-50=2, Resulting Numbers: [52, 7, 2] Generated Node #0,3: 50:[52, 7, 2] Operation: 52-50=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 50:[50, 7, 1], Operations: ['52/52=1'] Exploring Operation: 50*1=50, Resulting Numbers: [7, 50] Generated Node #0,2,0: 50:[7, 50] Operation: 50*1=50 Exploring Operation: 7+1=8, Resulting Numbers: [50, 8] Generated Node #0,2,1: 50:[50, 8] Operation: 7+1=8 Exploring Operation: 7-1=6, Resulting Numbers: [50, 6] Generated Node #0,2,2: 50:[50, 6] Operation: 7-1=6 Exploring Operation: 50/1=50, Resulting Numbers: [7, 50] Generated Node #0,2,3: 50:[7, 50] Operation: 50/1=50 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 50:[50, 6], Operations: ['52/52=1', '7-1=6'] Exploring Operation: 50+6=56, Resulting Numbers: [56] 56,50 unequal: No Solution Exploring Operation: 50*6=300, Resulting Numbers: [300] 300,50 unequal: No Solution Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,50 unequal: No Solution No 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: 50:[7, 50], Operations: ['52/52=1', '50*1=50'] Exploring Operation: 7*50=350, Resulting Numbers: [350] 350,50 unequal: No Solution Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,50 unequal: No Solution Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,50 unequal: No Solution No 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: 50:[50, 8], Operations: ['52/52=1', '7+1=8'] Exploring Operation: 50*8=400, Resulting Numbers: [400] 400,50 unequal: No Solution Exploring Operation: 50+8=58, Resulting Numbers: [58] 58,50 unequal: No Solution Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,50 unequal: No Solution No 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: 50:[7, 50], Operations: ['52/52=1', '50/1=50'] Exploring Operation: 7*50=350, Resulting Numbers: [350] 350,50 unequal: No Solution Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,50 unequal: No Solution Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,50 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: 50:[52, 7, 2], Operations: ['52-50=2'] Exploring Operation: 52-2=50, Resulting Numbers: [7, 50] Generated Node #0,0,0: 50:[7, 50] Operation: 52-2=50 Exploring Operation: 7-2=5, Resulting Numbers: [52, 5] Generated Node #0,0,1: 50:[52, 5] Operation: 7-2=5 Exploring Operation: 52/2=26, Resulting Numbers: [7, 26] Generated Node #0,0,2: 50:[7, 26] Operation: 52/2=26 Exploring Operation: 7+2=9, Resulting Numbers: [52, 9] Generated Node #0,0,3: 50:[52, 9] Operation: 7+2=9 Moving to Node #0,0,0 Current State: 50:[7, 50], Operations: ['52-50=2', '52-2=50'] Exploring Operation: 7*50=350, Resulting Numbers: [350] 350,50 unequal: No Solution Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,50 unequal: No Solution Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[52, 5], Operations: ['52-50=2', '7-2=5'] Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,50 unequal: No Solution Exploring Operation: 52+5=57, Resulting Numbers: [57] 57,50 unequal: No Solution Exploring Operation: 52*5=260, Resulting Numbers: [260] 260,50 unequal: No Solution Moving to Node #0,0,3 Current State: 50:[52, 9], Operations: ['52-50=2', '7+2=9'] Exploring Operation: 52*9=468, Resulting Numbers: [468] 468,50 unequal: No Solution Exploring Operation: 52+9=61, Resulting Numbers: [61] 61,50 unequal: No Solution Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,50 unequal: No Solution Moving to Node #0,0,2 Current State: 50:[7, 26], Operations: ['52-50=2', '52/2=26'] Exploring Operation: 7*26=182, Resulting Numbers: [182] 182,50 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,50 unequal: No Solution Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,50 unequal: No Solution No 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: 50:[50, 7, 0], Operations: ['52-52=0'] Exploring Operation: 7+0=7, Resulting Numbers: [50, 7] Generated Node #0,1,0: 50:[50, 7] Operation: 7+0=7 Exploring Operation: 50+0=50, Resulting Numbers: [7, 50] Generated Node #0,1,1: 50:[7, 50] Operation: 50+0=50 Exploring Operation: 7*0=0, Resulting Numbers: [50, 0] Generated Node #0,1,2: 50:[50, 0] Operation: 7*0=0 Exploring Operation: 50-0=50, Resulting Numbers: [7, 50] Generated Node #0,1,3: 50:[7, 50] Operation: 50-0=50 Moving to Node #0,1,0 Current State: 50:[50, 7], Operations: ['52-52=0', '7+0=7'] Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,50 unequal: No Solution Exploring Operation: 50*7=350, Resulting Numbers: [350] 350,50 unequal: No Solution Exploring Operation: 50+7=57, Resulting Numbers: [57] 57,50 unequal: No Solution Moving to Node #0,1,2 Current State: 50:[50, 0], Operations: ['52-52=0', '7*0=0'] Exploring Operation: 50*0=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 50+0=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[52, 52, 50, 7], Operations: [] Exploring Operation: 52-52=0, Resulting Numbers: [50, 7, 0] Generated Node #0,1: 50:[50, 7, 0] Operation: 52-52=0 Moving to Node #0,1 Current State: 50:[50, 7, 0], Operations: ['52-52=0'] Exploring Operation: 7*0=0, Resulting Numbers: [50, 0] Generated Node #0,1,2: 50:[50, 0] Operation: 7*0=0 Moving to Node #0,1,2 Current State: 50:[50, 0], Operations: ['52-52=0', '7*0=0'] Exploring Operation: 50+0=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.957465
hs_4
mult_heuristic
[ 52, 70, 2, 66 ]
30
[ "70-52=18", "2*18=36", "66-36=30" ]
Current State: 30:[52, 70, 2, 66], Operations: [] Exploring Operation: 70-52=18, Resulting Numbers: [2, 66, 18] Generated Node #2: [2, 66, 18] from Operation: 70-52=18 Current State: 30:[2, 66, 18], Operations: ['70-52=18'] Exploring Operation: 2*18=36, Resulting Numbers: [66, 36] Generated Node #3: [66, 36] from Operation: 2*18=36 Current State: 30:[66, 36], Operations: ['70-52=18', '2*18=36'] Exploring Operation: 66-36=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[52, 70, 2, 66], Operations: [] Exploring Operation: 70/2=35, Resulting Numbers: [52, 66, 35] Generated Node #0,0: 30:[52, 66, 35] Operation: 70/2=35 Exploring Operation: 70-52=18, Resulting Numbers: [2, 66, 18] Generated Node #0,1: 30:[2, 66, 18] Operation: 70-52=18 Exploring Operation: 66-52=14, Resulting Numbers: [70, 2, 14] Generated Node #0,2: 30:[70, 2, 14] Operation: 66-52=14 Exploring Operation: 70-66=4, Resulting Numbers: [52, 2, 4] Generated Node #0,3: 30:[52, 2, 4] Operation: 70-66=4 Exploring Operation: 66/2=33, Resulting Numbers: [52, 70, 33] Generated Node #0,4: 30:[52, 70, 33] Operation: 66/2=33 Moving to Node #0,3 Current State: 30:[52, 2, 4], Operations: ['70-66=4'] Exploring Operation: 2+4=6, Resulting Numbers: [52, 6] Generated Node #0,3,0: 30:[52, 6] Operation: 2+4=6 Exploring Operation: 52/2=26, Resulting Numbers: [4, 26] Generated Node #0,3,1: 30:[4, 26] Operation: 52/2=26 Exploring Operation: 52-4=48, Resulting Numbers: [2, 48] Generated Node #0,3,2: 30:[2, 48] Operation: 52-4=48 Exploring Operation: 52-2=50, Resulting Numbers: [4, 50] Generated Node #0,3,3: 30:[4, 50] Operation: 52-2=50 Exploring Operation: 52/4=13, Resulting Numbers: [2, 13] Generated Node #0,3,4: 30:[2, 13] Operation: 52/4=13 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 30:[2, 13], Operations: ['70-66=4', '52/4=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,30 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,30 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,30 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 #0,3,1 Current State: 30:[4, 26], Operations: ['70-66=4', '52/2=26'] Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[52, 70, 2, 66], Operations: [] Exploring Operation: 70-66=4, Resulting Numbers: [52, 2, 4] Generated Node #0,3: 30:[52, 2, 4] Operation: 70-66=4 Moving to Node #0,3 Current State: 30:[52, 2, 4], Operations: ['70-66=4'] Exploring Operation: 52/2=26, Resulting Numbers: [4, 26] Generated Node #0,3,1: 30:[4, 26] Operation: 52/2=26 Moving to Node #0,3,1 Current State: 30:[4, 26], Operations: ['70-66=4', '52/2=26'] Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 24, 42, 58, 92 ]
40
[ "24+92=116", "116/58=2", "42-2=40" ]
Current State: 40:[24, 42, 58, 92], Operations: [] Exploring Operation: 24+92=116, Resulting Numbers: [42, 58, 116] Generated Node #2: [42, 58, 116] from Operation: 24+92=116 Current State: 40:[42, 58, 116], Operations: ['24+92=116'] Exploring Operation: 116/58=2, Resulting Numbers: [42, 2] Generated Node #3: [42, 2] from Operation: 116/58=2 Current State: 40:[42, 2], Operations: ['24+92=116', '116/58=2'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[24, 42, 58, 92], Operations: [] Exploring Operation: 92-58=34, Resulting Numbers: [24, 42, 34] Generated Node #0,0: 40:[24, 42, 34] Operation: 92-58=34 Exploring Operation: 92-42=50, Resulting Numbers: [24, 58, 50] Generated Node #0,1: 40:[24, 58, 50] Operation: 92-42=50 Moving to Node #0,0 Current State: 40:[24, 42, 34], Operations: ['92-58=34'] Exploring Operation: 42-34=8, Resulting Numbers: [24, 8] Generated Node #0,0,0: 40:[24, 8] Operation: 42-34=8 Exploring Operation: 34-24=10, Resulting Numbers: [42, 10] Generated Node #0,0,1: 40:[42, 10] Operation: 34-24=10 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[42, 10], Operations: ['92-58=34', '34-24=10'] Exploring Operation: 42+10=52, Resulting Numbers: [52] 52,40 unequal: No Solution Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[24, 8], Operations: ['92-58=34', '42-34=8'] Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,40 unequal: No Solution Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,40 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: 40:[24, 58, 50], Operations: ['92-42=50'] Exploring Operation: 58-50=8, Resulting Numbers: [24, 8] Generated Node #0,1,0: 40:[24, 8] Operation: 58-50=8 Exploring Operation: 58-24=34, Resulting Numbers: [50, 34] Generated Node #0,1,1: 40:[50, 34] Operation: 58-24=34 Moving to Node #0,1,0 Current State: 40:[24, 8], Operations: ['92-42=50', '58-50=8'] Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,40 unequal: No Solution Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,40 unequal: No Solution Moving to Node #0,1,1 Current State: 40:[50, 34], Operations: ['92-42=50', '58-24=34'] Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,40 unequal: No Solution Exploring Operation: 50+34=84, Resulting Numbers: [84] 84,40 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 26, 54, 20, 28 ]
72
[ "26+54=80", "28-20=8", "80-8=72" ]
Current State: 72:[26, 54, 20, 28], Operations: [] Exploring Operation: 26+54=80, Resulting Numbers: [20, 28, 80] Generated Node #2: [20, 28, 80] from Operation: 26+54=80 Current State: 72:[20, 28, 80], Operations: ['26+54=80'] Exploring Operation: 28-20=8, Resulting Numbers: [80, 8] Generated Node #3: [80, 8] from Operation: 28-20=8 Current State: 72:[80, 8], Operations: ['26+54=80', '28-20=8'] Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[26, 54, 20, 28], Operations: [] Exploring Operation: 54+20=74, Resulting Numbers: [26, 28, 74] Generated Node #0,0: 72:[26, 28, 74] Operation: 54+20=74 Exploring Operation: 54-20=34, Resulting Numbers: [26, 28, 34] Generated Node #0,1: 72:[26, 28, 34] Operation: 54-20=34 Exploring Operation: 54-28=26, Resulting Numbers: [26, 20, 26] Generated Node #0,2: 72:[26, 20, 26] Operation: 54-28=26 Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[26, 20, 26], Operations: ['54-28=26'] Exploring Operation: 26/26=1, Resulting Numbers: [20, 1] Generated Node #0,2,0: 72:[20, 1] Operation: 26/26=1 Exploring Operation: 26-20=6, Resulting Numbers: [26, 6] Generated Node #0,2,1: 72:[26, 6] Operation: 26-20=6 Exploring Operation: 26-20=6, Resulting Numbers: [26, 6] Generated Node #0,2,2: 72:[26, 6] Operation: 26-20=6 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 72:[26, 6], Operations: ['54-28=26', '26-20=6'] Exploring Operation: 26*6=156, Resulting Numbers: [156] 156,72 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,72 unequal: No Solution Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 72:[26, 6], Operations: ['54-28=26', '26-20=6'] Exploring Operation: 26*6=156, Resulting Numbers: [156] 156,72 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,72 unequal: No Solution Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 72:[20, 1], Operations: ['54-28=26', '26/26=1'] Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,72 unequal: No Solution Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[26, 28, 74], Operations: ['54+20=74'] Exploring Operation: 74-26=48, Resulting Numbers: [28, 48] Generated Node #0,0,0: 72:[28, 48] Operation: 74-26=48 Exploring Operation: 28-26=2, Resulting Numbers: [74, 2] Generated Node #0,0,1: 72:[74, 2] Operation: 28-26=2 Exploring Operation: 74-28=46, Resulting Numbers: [26, 46] Generated Node #0,0,2: 72:[26, 46] Operation: 74-28=46 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 72:[74, 2], Operations: ['54+20=74', '28-26=2'] Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,72 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[26, 54, 20, 28], Operations: [] Exploring Operation: 54+20=74, Resulting Numbers: [26, 28, 74] Generated Node #0,0: 72:[26, 28, 74] Operation: 54+20=74 Moving to Node #0,0 Current State: 72:[26, 28, 74], Operations: ['54+20=74'] Exploring Operation: 28-26=2, Resulting Numbers: [74, 2] Generated Node #0,0,1: 72:[74, 2] Operation: 28-26=2 Moving to Node #0,0,1 Current State: 72:[74, 2], Operations: ['54+20=74', '28-26=2'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 10, 68, 13, 95 ]
89
[ "10+68=78", "78/13=6", "95-6=89" ]
Current State: 89:[10, 68, 13, 95], Operations: [] Exploring Operation: 10+68=78, Resulting Numbers: [13, 95, 78] Generated Node #2: [13, 95, 78] from Operation: 10+68=78 Current State: 89:[13, 95, 78], Operations: ['10+68=78'] Exploring Operation: 78/13=6, Resulting Numbers: [95, 6] Generated Node #3: [95, 6] from Operation: 78/13=6 Current State: 89:[95, 6], Operations: ['10+68=78', '78/13=6'] Exploring Operation: 95-6=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[10, 68, 13, 95], Operations: [] Exploring Operation: 10*13=130, Resulting Numbers: [68, 95, 130] Generated Node #0,0: 89:[68, 95, 130] Operation: 10*13=130 Moving to Node #0,0 Current State: 89:[68, 95, 130], Operations: ['10*13=130'] Exploring Operation: 130-68=62, Resulting Numbers: [95, 62] Generated Node #0,0,0: 89:[95, 62] Operation: 130-68=62 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[95, 62], Operations: ['10*13=130', '130-68=62'] Exploring Operation: 95-62=33, Resulting Numbers: [33] 33,89 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
[ 49, 44, 27, 64 ]
96
[ "49-44=5", "27+64=91", "5+91=96" ]
Current State: 96:[49, 44, 27, 64], Operations: [] Exploring Operation: 49-44=5, Resulting Numbers: [27, 64, 5] Generated Node #2: [27, 64, 5] from Operation: 49-44=5 Current State: 96:[27, 64, 5], Operations: ['49-44=5'] Exploring Operation: 27+64=91, Resulting Numbers: [5, 91] Generated Node #3: [5, 91] from Operation: 27+64=91 Current State: 96:[5, 91], Operations: ['49-44=5', '27+64=91'] Exploring Operation: 5+91=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[49, 44, 27, 64], Operations: [] Exploring Operation: 64-44=20, Resulting Numbers: [49, 27, 20] Generated Node #0,0: 96:[49, 27, 20] Operation: 64-44=20 Exploring Operation: 44+64=108, Resulting Numbers: [49, 27, 108] Generated Node #0,1: 96:[49, 27, 108] Operation: 44+64=108 Exploring Operation: 64-27=37, Resulting Numbers: [49, 44, 37] Generated Node #0,2: 96:[49, 44, 37] Operation: 64-27=37 Exploring Operation: 27+64=91, Resulting Numbers: [49, 44, 91] Generated Node #0,3: 96:[49, 44, 91] Operation: 27+64=91 Exploring Operation: 64-49=15, Resulting Numbers: [44, 27, 15] Generated Node #0,4: 96:[44, 27, 15] Operation: 64-49=15 Moving to Node #0,0 Current State: 96:[49, 27, 20], Operations: ['64-44=20'] Exploring Operation: 27+20=47, Resulting Numbers: [49, 47] Generated Node #0,0,0: 96:[49, 47] Operation: 27+20=47 Exploring Operation: 49+27=76, Resulting Numbers: [20, 76] Generated Node #0,0,1: 96:[20, 76] Operation: 49+27=76 Exploring Operation: 49-27=22, Resulting Numbers: [20, 22] Generated Node #0,0,2: 96:[20, 22] Operation: 49-27=22 Exploring Operation: 49-20=29, Resulting Numbers: [27, 29] Generated Node #0,0,3: 96:[27, 29] Operation: 49-20=29 Exploring Operation: 27-20=7, Resulting Numbers: [49, 7] Generated Node #0,0,4: 96:[49, 7] Operation: 27-20=7 Moving to Node #0,4 Current State: 96:[44, 27, 15], Operations: ['64-49=15'] Exploring Operation: 44+15=59, Resulting Numbers: [27, 59] Generated Node #0,4,0: 96:[27, 59] Operation: 44+15=59 Exploring Operation: 27-15=12, Resulting Numbers: [44, 12] Generated Node #0,4,1: 96:[44, 12] Operation: 27-15=12 Exploring Operation: 44-27=17, Resulting Numbers: [15, 17] Generated Node #0,4,2: 96:[15, 17] Operation: 44-27=17 Exploring Operation: 44-15=29, Resulting Numbers: [27, 29] Generated Node #0,4,3: 96:[27, 29] Operation: 44-15=29 Exploring Operation: 27+15=42, Resulting Numbers: [44, 42] Generated Node #0,4,4: 96:[44, 42] Operation: 27+15=42 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 96:[15, 17], Operations: ['64-49=15', '44-27=17'] Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,96 unequal: No Solution Exploring Operation: 15*17=255, Resulting Numbers: [255] 255,96 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 #0,4,1 Current State: 96:[44, 12], Operations: ['64-49=15', '27-15=12'] Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,96 unequal: No Solution Exploring Operation: 44*12=528, Resulting Numbers: [528] 528,96 unequal: No Solution Exploring Operation: 44+12=56, Resulting Numbers: [56] 56,96 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 #0,4,3 Current State: 96:[27, 29], Operations: ['64-49=15', '44-15=29'] Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,96 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 #0,4,4 Current State: 96:[44, 42], Operations: ['64-49=15', '27+15=42'] Exploring Operation: 44+42=86, Resulting Numbers: [86] 86,96 unequal: No Solution Exploring Operation: 44*42=1848, Resulting Numbers: [1848] 1848,96 unequal: No Solution Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,96 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 #0,4,0 Current State: 96:[27, 59], Operations: ['64-49=15', '44+15=59'] Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,96 unequal: No Solution Exploring Operation: 27*59=1593, Resulting Numbers: [1593] 1593,96 unequal: No Solution Exploring Operation: 27+59=86, Resulting Numbers: [86] 86,96 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: 96:[49, 44, 37], Operations: ['64-27=37'] Exploring Operation: 49-37=12, Resulting Numbers: [44, 12] Generated Node #0,2,0: 96:[44, 12] Operation: 49-37=12 Exploring Operation: 49+37=86, Resulting Numbers: [44, 86] Generated Node #0,2,1: 96:[44, 86] Operation: 49+37=86 Exploring Operation: 49+44=93, Resulting Numbers: [37, 93] Generated Node #0,2,2: 96:[37, 93] Operation: 49+44=93 Exploring Operation: 49-44=5, Resulting Numbers: [37, 5] Generated Node #0,2,3: 96:[37, 5] Operation: 49-44=5 Exploring Operation: 44-37=7, Resulting Numbers: [49, 7] Generated Node #0,2,4: 96:[49, 7] Operation: 44-37=7 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 96:[49, 7], Operations: ['64-27=37', '44-37=7'] Exploring Operation: 49*7=343, Resulting Numbers: [343] 343,96 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,96 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,96 unequal: No Solution Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 96:[44, 12], Operations: ['64-27=37', '49-37=12'] Exploring Operation: 44*12=528, Resulting Numbers: [528] 528,96 unequal: No Solution Exploring Operation: 44+12=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 96:[37, 5], Operations: ['64-27=37', '49-44=5'] Exploring Operation: 37*5=185, Resulting Numbers: [185] 185,96 unequal: No Solution Exploring Operation: 37+5=42, Resulting Numbers: [42] 42,96 unequal: No Solution Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 96:[37, 93], Operations: ['64-27=37', '49+44=93'] Exploring Operation: 37*93=3441, Resulting Numbers: [3441] 3441,96 unequal: No Solution Exploring Operation: 37+93=130, Resulting Numbers: [130] 130,96 unequal: No Solution Exploring Operation: 93-37=56, Resulting Numbers: [56] 56,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 96:[44, 86], Operations: ['64-27=37', '49+37=86'] Exploring Operation: 44+86=130, Resulting Numbers: [130] 130,96 unequal: No Solution Exploring Operation: 86-44=42, Resulting Numbers: [42] 42,96 unequal: No Solution Exploring Operation: 44*86=3784, Resulting Numbers: [3784] 3784,96 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: 96:[49, 44, 91], Operations: ['27+64=91'] Exploring Operation: 49+44=93, Resulting Numbers: [91, 93] Generated Node #0,3,0: 96:[91, 93] Operation: 49+44=93 Exploring Operation: 91-44=47, Resulting Numbers: [49, 47] Generated Node #0,3,1: 96:[49, 47] Operation: 91-44=47 Exploring Operation: 44+91=135, Resulting Numbers: [49, 135] Generated Node #0,3,2: 96:[49, 135] Operation: 44+91=135 Exploring Operation: 91-49=42, Resulting Numbers: [44, 42] Generated Node #0,3,3: 96:[44, 42] Operation: 91-49=42 Exploring Operation: 49-44=5, Resulting Numbers: [91, 5] Generated Node #0,3,4: 96:[91, 5] Operation: 49-44=5 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 96:[49, 47], Operations: ['27+64=91', '91-44=47'] Exploring Operation: 49*47=2303, Resulting Numbers: [2303] 2303,96 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[49, 44, 27, 64], Operations: [] Exploring Operation: 27+64=91, Resulting Numbers: [49, 44, 91] Generated Node #0,3: 96:[49, 44, 91] Operation: 27+64=91 Moving to Node #0,3 Current State: 96:[49, 44, 91], Operations: ['27+64=91'] Exploring Operation: 91-44=47, Resulting Numbers: [49, 47] Generated Node #0,3,1: 96:[49, 47] Operation: 91-44=47 Moving to Node #0,3,1 Current State: 96:[49, 47], Operations: ['27+64=91', '91-44=47'] Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.945313
hs_5
sum_heuristic
[ 87, 74, 49, 47 ]
26
[ "87-74=13", "49-47=2", "13*2=26" ]
Current State: 26:[87, 74, 49, 47], Operations: [] Exploring Operation: 87-74=13, Resulting Numbers: [49, 47, 13] Generated Node #2: [49, 47, 13] from Operation: 87-74=13 Current State: 26:[49, 47, 13], Operations: ['87-74=13'] Exploring Operation: 49-47=2, Resulting Numbers: [13, 2] Generated Node #3: [13, 2] from Operation: 49-47=2 Current State: 26:[13, 2], Operations: ['87-74=13', '49-47=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[87, 74, 49, 47], Operations: [] Exploring Operation: 87-49=38, Resulting Numbers: [74, 47, 38] Generated Node #0,0: 26:[74, 47, 38] Operation: 87-49=38 Exploring Operation: 87-74=13, Resulting Numbers: [49, 47, 13] Generated Node #0,1: 26:[49, 47, 13] Operation: 87-74=13 Exploring Operation: 74-49=25, Resulting Numbers: [87, 47, 25] Generated Node #0,2: 26:[87, 47, 25] Operation: 74-49=25 Moving to Node #0,1 Current State: 26:[49, 47, 13], Operations: ['87-74=13'] Exploring Operation: 49-47=2, Resulting Numbers: [13, 2] Generated Node #0,1,0: 26:[13, 2] Operation: 49-47=2 Exploring Operation: 49-13=36, Resulting Numbers: [47, 36] Generated Node #0,1,1: 26:[47, 36] Operation: 49-13=36 Exploring Operation: 47-13=34, Resulting Numbers: [49, 34] Generated Node #0,1,2: 26:[49, 34] Operation: 47-13=34 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 26:[13, 2], Operations: ['87-74=13', '49-47=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[87, 74, 49, 47], Operations: [] Exploring Operation: 87-74=13, Resulting Numbers: [49, 47, 13] Generated Node #0,1: 26:[49, 47, 13] Operation: 87-74=13 Moving to Node #0,1 Current State: 26:[49, 47, 13], Operations: ['87-74=13'] Exploring Operation: 49-47=2, Resulting Numbers: [13, 2] Generated Node #0,1,0: 26:[13, 2] Operation: 49-47=2 Moving to Node #0,1,0 Current State: 26:[13, 2], Operations: ['87-74=13', '49-47=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 70, 24, 49, 13 ]
10
[ "70-24=46", "49-13=36", "46-36=10" ]
Current State: 10:[70, 24, 49, 13], Operations: [] Exploring Operation: 70-24=46, Resulting Numbers: [49, 13, 46] Generated Node #2: [49, 13, 46] from Operation: 70-24=46 Current State: 10:[49, 13, 46], Operations: ['70-24=46'] Exploring Operation: 49-13=36, Resulting Numbers: [46, 36] Generated Node #3: [46, 36] from Operation: 49-13=36 Current State: 10:[46, 36], Operations: ['70-24=46', '49-13=36'] Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[70, 24, 49, 13], Operations: [] Exploring Operation: 70-49=21, Resulting Numbers: [24, 13, 21] Generated Node #0,0: 10:[24, 13, 21] Operation: 70-49=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[24, 13, 21], Operations: ['70-49=21'] Exploring Operation: 24-21=3, Resulting Numbers: [13, 3] Generated Node #0,0,0: 10:[13, 3] Operation: 24-21=3 Moving to Node #0,0,0 Current State: 10:[13, 3], Operations: ['70-49=21', '24-21=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[70, 24, 49, 13], Operations: [] Exploring Operation: 70-49=21, Resulting Numbers: [24, 13, 21] Generated Node #0,0: 10:[24, 13, 21] Operation: 70-49=21 Moving to Node #0,0 Current State: 10:[24, 13, 21], Operations: ['70-49=21'] Exploring Operation: 24-21=3, Resulting Numbers: [13, 3] Generated Node #0,0,0: 10:[13, 3] Operation: 24-21=3 Moving to Node #0,0,0 Current State: 10:[13, 3], Operations: ['70-49=21', '24-21=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 1, 28, 7, 5 ]
40
[ "1*28=28", "7+5=12", "28+12=40" ]
Current State: 40:[1, 28, 7, 5], Operations: [] Exploring Operation: 1*28=28, Resulting Numbers: [7, 5, 28] Generated Node #2: [7, 5, 28] from Operation: 1*28=28 Current State: 40:[7, 5, 28], Operations: ['1*28=28'] Exploring Operation: 7+5=12, Resulting Numbers: [28, 12] Generated Node #3: [28, 12] from Operation: 7+5=12 Current State: 40:[28, 12], Operations: ['1*28=28', '7+5=12'] Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[1, 28, 7, 5], Operations: [] Exploring Operation: 28/7=4, Resulting Numbers: [1, 5, 4] Generated Node #0,0: 40:[1, 5, 4] Operation: 28/7=4 Exploring Operation: 28-7=21, Resulting Numbers: [1, 5, 21] Generated Node #0,1: 40:[1, 5, 21] Operation: 28-7=21 Moving to Node #0,0 Current State: 40:[1, 5, 4], Operations: ['28/7=4'] Exploring Operation: 5-1=4, Resulting Numbers: [4, 4] Generated Node #0,0,0: 40:[4, 4] Operation: 5-1=4 Exploring Operation: 1*5=5, Resulting Numbers: [4, 5] Generated Node #0,0,1: 40:[4, 5] Operation: 1*5=5 Moving to Node #0,1 Current State: 40:[1, 5, 21], Operations: ['28-7=21'] Exploring Operation: 21-1=20, Resulting Numbers: [5, 20] Generated Node #0,1,0: 40:[5, 20] Operation: 21-1=20 Exploring Operation: 1*5=5, Resulting Numbers: [21, 5] Generated Node #0,1,1: 40:[21, 5] Operation: 1*5=5 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[5, 20], Operations: ['28-7=21', '21-1=20'] Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,40 unequal: No Solution Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 40:[21, 5], Operations: ['28-7=21', '1*5=5'] Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,40 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,40 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: 40:[4, 4], Operations: ['28/7=4', '5-1=4'] Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[4, 5], Operations: ['28/7=4', '1*5=5'] Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,40 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,40 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 19, 2, 80, 38 ]
65
[ "80-38=42", "2*42=84", "84-19=65" ]
Current State: 65:[19, 2, 80, 38], Operations: [] Exploring Operation: 80-38=42, Resulting Numbers: [19, 2, 42] Generated Node #2: [19, 2, 42] from Operation: 80-38=42 Current State: 65:[19, 2, 42], Operations: ['80-38=42'] Exploring Operation: 2*42=84, Resulting Numbers: [19, 84] Generated Node #3: [19, 84] from Operation: 2*42=84 Current State: 65:[19, 84], Operations: ['80-38=42', '2*42=84'] Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[19, 2, 80, 38], Operations: [] Exploring Operation: 38-19=19, Resulting Numbers: [2, 80, 19] Generated Node #0,0: 65:[2, 80, 19] Operation: 38-19=19 Exploring Operation: 19+38=57, Resulting Numbers: [2, 80, 57] Generated Node #0,1: 65:[2, 80, 57] Operation: 19+38=57 Exploring Operation: 80-19=61, Resulting Numbers: [2, 38, 61] Generated Node #0,2: 65:[2, 38, 61] Operation: 80-19=61 Exploring Operation: 38/19=2, Resulting Numbers: [2, 80, 2] Generated Node #0,3: 65:[2, 80, 2] Operation: 38/19=2 Exploring Operation: 38/2=19, Resulting Numbers: [19, 80, 19] Generated Node #0,4: 65:[19, 80, 19] Operation: 38/2=19 Moving to Node #0,3 Current State: 65:[2, 80, 2], Operations: ['38/19=2'] Exploring Operation: 2+2=4, Resulting Numbers: [80, 4] Generated Node #0,3,0: 65:[80, 4] Operation: 2+2=4 Exploring Operation: 80-2=78, Resulting Numbers: [2, 78] Generated Node #0,3,1: 65:[2, 78] Operation: 80-2=78 Exploring Operation: 80-2=78, Resulting Numbers: [2, 78] Generated Node #0,3,2: 65:[2, 78] Operation: 80-2=78 Exploring Operation: 2*2=4, Resulting Numbers: [80, 4] Generated Node #0,3,3: 65:[80, 4] Operation: 2*2=4 Exploring Operation: 2/2=1, Resulting Numbers: [80, 1] Generated Node #0,3,4: 65:[80, 1] Operation: 2/2=1 Moving to Node #0,0 Current State: 65:[2, 80, 19], Operations: ['38-19=19'] Exploring Operation: 80-2=78, Resulting Numbers: [19, 78] Generated Node #0,0,0: 65:[19, 78] Operation: 80-2=78 Exploring Operation: 19-2=17, Resulting Numbers: [80, 17] Generated Node #0,0,1: 65:[80, 17] Operation: 19-2=17 Exploring Operation: 80-19=61, Resulting Numbers: [2, 61] Generated Node #0,0,2: 65:[2, 61] Operation: 80-19=61 Exploring Operation: 2+19=21, Resulting Numbers: [80, 21] Generated Node #0,0,3: 65:[80, 21] Operation: 2+19=21 Exploring Operation: 2+80=82, Resulting Numbers: [19, 82] Generated Node #0,0,4: 65:[19, 82] Operation: 2+80=82 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 65:[2, 61], Operations: ['38-19=19', '80-19=61'] Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,65 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,65 unequal: No Solution Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[19, 78], Operations: ['38-19=19', '80-2=78'] Exploring Operation: 78-19=59, Resulting Numbers: [59] 59,65 unequal: No Solution Exploring Operation: 19+78=97, Resulting Numbers: [97] 97,65 unequal: No Solution Exploring Operation: 19*78=1482, Resulting Numbers: [1482] 1482,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 65:[80, 17], Operations: ['38-19=19', '19-2=17'] Exploring Operation: 80*17=1360, Resulting Numbers: [1360] 1360,65 unequal: No Solution Exploring Operation: 80+17=97, Resulting Numbers: [97] 97,65 unequal: No Solution Exploring Operation: 80-17=63, Resulting Numbers: [63] 63,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 65:[80, 21], Operations: ['38-19=19', '2+19=21'] Exploring Operation: 80+21=101, Resulting Numbers: [101] 101,65 unequal: No Solution Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,65 unequal: No Solution Exploring Operation: 80*21=1680, Resulting Numbers: [1680] 1680,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 65:[19, 82], Operations: ['38-19=19', '2+80=82'] Exploring Operation: 19+82=101, Resulting Numbers: [101] 101,65 unequal: No Solution Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,65 unequal: No Solution Exploring Operation: 19*82=1558, Resulting Numbers: [1558] 1558,65 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: 65:[2, 80, 57], Operations: ['19+38=57'] Exploring Operation: 80-57=23, Resulting Numbers: [2, 23] Generated Node #0,1,0: 65:[2, 23] Operation: 80-57=23 Exploring Operation: 2+57=59, Resulting Numbers: [80, 59] Generated Node #0,1,1: 65:[80, 59] Operation: 2+57=59 Exploring Operation: 2+80=82, Resulting Numbers: [57, 82] Generated Node #0,1,2: 65:[57, 82] Operation: 2+80=82 Exploring Operation: 57-2=55, Resulting Numbers: [80, 55] Generated Node #0,1,3: 65:[80, 55] Operation: 57-2=55 Exploring Operation: 80-2=78, Resulting Numbers: [57, 78] Generated Node #0,1,4: 65:[57, 78] Operation: 80-2=78 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[2, 23], Operations: ['19+38=57', '80-57=23'] Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,65 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,65 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:[80, 59], Operations: ['19+38=57', '2+57=59'] Exploring Operation: 80-59=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 80+59=139, Resulting Numbers: [139] 139,65 unequal: No Solution Exploring Operation: 80*59=4720, Resulting Numbers: [4720] 4720,65 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 #0,1,4 Current State: 65:[57, 78], Operations: ['19+38=57', '80-2=78'] Exploring Operation: 78-57=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 57*78=4446, Resulting Numbers: [4446] 4446,65 unequal: No Solution Exploring Operation: 57+78=135, Resulting Numbers: [135] 135,65 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 #0,1,2 Current State: 65:[57, 82], Operations: ['19+38=57', '2+80=82'] Exploring Operation: 57*82=4674, Resulting Numbers: [4674] 4674,65 unequal: No Solution Exploring Operation: 82-57=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 57+82=139, Resulting Numbers: [139] 139,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 65:[80, 55], Operations: ['19+38=57', '57-2=55'] Exploring Operation: 80+55=135, Resulting Numbers: [135] 135,65 unequal: No Solution Exploring Operation: 80-55=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 80*55=4400, Resulting Numbers: [4400] 4400,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 65:[19, 80, 19], Operations: ['38/2=19'] Exploring Operation: 80-19=61, Resulting Numbers: [19, 61] Generated Node #0,4,0: 65:[19, 61] Operation: 80-19=61 Exploring Operation: 19+80=99, Resulting Numbers: [19, 99] Generated Node #0,4,1: 65:[19, 99] Operation: 19+80=99 Exploring Operation: 19/19=1, Resulting Numbers: [80, 1] Generated Node #0,4,2: 65:[80, 1] Operation: 19/19=1 Exploring Operation: 19-19=0, Resulting Numbers: [80, 0] Generated Node #0,4,3: 65:[80, 0] Operation: 19-19=0 Exploring Operation: 80-19=61, Resulting Numbers: [19, 61] Generated Node #0,4,4: 65:[19, 61] Operation: 80-19=61 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 65:[19, 61], Operations: ['38/2=19', '80-19=61'] Exploring Operation: 61-19=42, Resulting Numbers: [42] 42,65 unequal: No Solution Exploring Operation: 19+61=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 19*61=1159, Resulting Numbers: [1159] 1159,65 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 #0,4,4 Current State: 65:[19, 61], Operations: ['38/2=19', '80-19=61'] Exploring Operation: 19*61=1159, Resulting Numbers: [1159] 1159,65 unequal: No Solution Exploring Operation: 19+61=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 61-19=42, Resulting Numbers: [42] 42,65 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 #0,4,2 Current State: 65:[80, 1], Operations: ['38/2=19', '19/19=1'] Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,65 unequal: No Solution Exploring Operation: 80*1=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 80/1=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,65 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 #0,4,3 Current State: 65:[80, 0], Operations: ['38/2=19', '19-19=0'] Exploring Operation: 80*0=0, Resulting Numbers: [0] 0,65 unequal: No Solution Exploring Operation: 80-0=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 80+0=80, Resulting Numbers: [80] 80,65 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 #0,4,1 Current State: 65:[19, 99], Operations: ['38/2=19', '19+80=99'] Exploring Operation: 19*99=1881, Resulting Numbers: [1881] 1881,65 unequal: No Solution Exploring Operation: 99-19=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 19+99=118, Resulting Numbers: [118] 118,65 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: 65:[2, 38, 61], Operations: ['80-19=61'] Exploring Operation: 38-2=36, Resulting Numbers: [61, 36] Generated Node #0,2,0: 65:[61, 36] Operation: 38-2=36 Exploring Operation: 38/2=19, Resulting Numbers: [61, 19] Generated Node #0,2,1: 65:[61, 19] Operation: 38/2=19 Exploring Operation: 61-38=23, Resulting Numbers: [2, 23] Generated Node #0,2,2: 65:[2, 23] Operation: 61-38=23 Exploring Operation: 2+61=63, Resulting Numbers: [38, 63] Generated Node #0,2,3: 65:[38, 63] Operation: 2+61=63 Exploring Operation: 2*38=76, Resulting Numbers: [61, 76] Generated Node #0,2,4: 65:[61, 76] Operation: 2*38=76 Moving to Node #0,2,1 Current State: 65:[61, 19], Operations: ['80-19=61', '38/2=19'] Exploring Operation: 61+19=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 61-19=42, Resulting Numbers: [42] 42,65 unequal: No Solution Exploring Operation: 61*19=1159, Resulting Numbers: [1159] 1159,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[2, 23], Operations: ['80-19=61', '61-38=23'] Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,65 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,65 unequal: No Solution Moving to Node #0,2,4 Current State: 65:[61, 76], Operations: ['80-19=61', '2*38=76'] Exploring Operation: 61*76=4636, Resulting Numbers: [4636] 4636,65 unequal: No Solution Exploring Operation: 76-61=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 61+76=137, Resulting Numbers: [137] 137,65 unequal: No Solution Moving to Node #0,3,0 Current State: 65:[80, 4], Operations: ['38/19=2', '2+2=4'] Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,65 unequal: No Solution Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,65 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,65 unequal: No Solution Exploring Operation: 80*4=320, Resulting Numbers: [320] 320,65 unequal: No Solution Moving to Node #0,3,2 Current State: 65:[2, 78], Operations: ['38/19=2', '80-2=78'] Exploring Operation: 2*78=156, Resulting Numbers: [156] 156,65 unequal: No Solution Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,65 unequal: No Solution Exploring Operation: 2+78=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,65 unequal: No Solution Moving to Node #0,3,1 Current State: 65:[2, 78], Operations: ['38/19=2', '80-2=78'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,65 unequal: No Solution Exploring Operation: 2*78=156, Resulting Numbers: [156] 156,65 unequal: No Solution Exploring Operation: 2+78=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,65 unequal: No Solution Moving to Node #0,3,3 Current State: 65:[80, 4], Operations: ['38/19=2', '2*2=4'] Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,65 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,65 unequal: No Solution Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,65 unequal: No Solution Exploring Operation: 80*4=320, Resulting Numbers: [320] 320,65 unequal: No Solution Moving to Node #0,3,4 Current State: 65:[80, 1], Operations: ['38/19=2', '2/2=1'] Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,65 unequal: No Solution Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,65 unequal: No Solution Exploring Operation: 80/1=80, Resulting Numbers: [80] 80,65 unequal: No Solution Exploring Operation: 80*1=80, Resulting Numbers: [80] 80,65 unequal: No Solution Moving to Node #0,2,3 Current State: 65:[38, 63], Operations: ['80-19=61', '2+61=63'] Exploring Operation: 38*63=2394, Resulting Numbers: [2394] 2394,65 unequal: No Solution Exploring Operation: 63-38=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 38+63=101, Resulting Numbers: [101] 101,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[61, 36], Operations: ['80-19=61', '38-2=36'] Exploring Operation: 61+36=97, Resulting Numbers: [97] 97,65 unequal: No Solution Exploring Operation: 61-36=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 61*36=2196, Resulting Numbers: [2196] 2196,65 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 63, 42, 33, 55 ]
62
[ "42-33=9", "63/9=7", "55+7=62" ]
Current State: 62:[63, 42, 33, 55], Operations: [] Exploring Operation: 42-33=9, Resulting Numbers: [63, 55, 9] Generated Node #2: [63, 55, 9] from Operation: 42-33=9 Current State: 62:[63, 55, 9], Operations: ['42-33=9'] Exploring Operation: 63/9=7, Resulting Numbers: [55, 7] Generated Node #3: [55, 7] from Operation: 63/9=7 Current State: 62:[55, 7], Operations: ['42-33=9', '63/9=7'] Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[63, 42, 33, 55], Operations: [] Exploring Operation: 55-42=13, Resulting Numbers: [63, 33, 13] Generated Node #0,0: 62:[63, 33, 13] Operation: 55-42=13 Exploring Operation: 42-33=9, Resulting Numbers: [63, 55, 9] Generated Node #0,1: 62:[63, 55, 9] Operation: 42-33=9 Moving to Node #0,0 Current State: 62:[63, 33, 13], Operations: ['55-42=13'] Exploring Operation: 33-13=20, Resulting Numbers: [63, 20] Generated Node #0,0,0: 62:[63, 20] Operation: 33-13=20 Exploring Operation: 63-33=30, Resulting Numbers: [13, 30] Generated Node #0,0,1: 62:[13, 30] Operation: 63-33=30 Moving to Node #0,1 Current State: 62:[63, 55, 9], Operations: ['42-33=9'] Exploring Operation: 63/9=7, Resulting Numbers: [55, 7] Generated Node #0,1,0: 62:[55, 7] Operation: 63/9=7 Exploring Operation: 55+9=64, Resulting Numbers: [63, 64] Generated Node #0,1,1: 62:[63, 64] Operation: 55+9=64 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 62:[63, 64], Operations: ['42-33=9', '55+9=64'] Exploring Operation: 64-63=1, Resulting Numbers: [1] 1,62 unequal: No Solution Exploring Operation: 63+64=127, Resulting Numbers: [127] 127,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[55, 7], Operations: ['42-33=9', '63/9=7'] Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[63, 42, 33, 55], Operations: [] Exploring Operation: 42-33=9, Resulting Numbers: [63, 55, 9] Generated Node #0,1: 62:[63, 55, 9] Operation: 42-33=9 Moving to Node #0,1 Current State: 62:[63, 55, 9], Operations: ['42-33=9'] Exploring Operation: 63/9=7, Resulting Numbers: [55, 7] Generated Node #0,1,0: 62:[55, 7] Operation: 63/9=7 Moving to Node #0,1,0 Current State: 62:[55, 7], Operations: ['42-33=9', '63/9=7'] Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_2
mult_heuristic
[ 14, 2, 81, 36 ]
36
[ "14+2=16", "81*16=1296", "1296/36=36" ]
Current State: 36:[14, 2, 81, 36], Operations: [] Exploring Operation: 14+2=16, Resulting Numbers: [81, 36, 16] Generated Node #2: [81, 36, 16] from Operation: 14+2=16 Current State: 36:[81, 36, 16], Operations: ['14+2=16'] Exploring Operation: 81*16=1296, Resulting Numbers: [36, 1296] Generated Node #3: [36, 1296] from Operation: 81*16=1296 Current State: 36:[36, 1296], Operations: ['14+2=16', '81*16=1296'] Exploring Operation: 1296/36=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[14, 2, 81, 36], Operations: [] Exploring Operation: 81-14=67, Resulting Numbers: [2, 36, 67] Generated Node #0,0: 36:[2, 36, 67] Operation: 81-14=67 Exploring Operation: 81-2=79, Resulting Numbers: [14, 36, 79] Generated Node #0,1: 36:[14, 36, 79] Operation: 81-2=79 Exploring Operation: 81-36=45, Resulting Numbers: [14, 2, 45] Generated Node #0,2: 36:[14, 2, 45] Operation: 81-36=45 Exploring Operation: 14-2=12, Resulting Numbers: [81, 36, 12] Generated Node #0,3: 36:[81, 36, 12] Operation: 14-2=12 Start Sub Search at level 1: Moving to Node #0,2 Current State: 36:[14, 2, 45], Operations: ['81-36=45'] Exploring Operation: 14/2=7, Resulting Numbers: [45, 7] Generated Node #0,2,0: 36:[45, 7] Operation: 14/2=7 Exploring Operation: 45-2=43, Resulting Numbers: [14, 43] Generated Node #0,2,1: 36:[14, 43] Operation: 45-2=43 Exploring Operation: 45-14=31, Resulting Numbers: [2, 31] Generated Node #0,2,2: 36:[2, 31] Operation: 45-14=31 Exploring Operation: 14-2=12, Resulting Numbers: [45, 12] Generated Node #0,2,3: 36:[45, 12] Operation: 14-2=12 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 36:[2, 31], Operations: ['81-36=45', '45-14=31'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,36 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,36 unequal: No Solution No 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: 36:[14, 43], Operations: ['81-36=45', '45-2=43'] Exploring Operation: 14*43=602, Resulting Numbers: [602] 602,36 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 14+43=57, Resulting Numbers: [57] 57,36 unequal: No Solution No 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: 36:[45, 12], Operations: ['81-36=45', '14-2=12'] Exploring Operation: 45*12=540, Resulting Numbers: [540] 540,36 unequal: No Solution Exploring Operation: 45+12=57, Resulting Numbers: [57] 57,36 unequal: No Solution Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,36 unequal: No Solution No 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: 36:[45, 7], Operations: ['81-36=45', '14/2=7'] Exploring Operation: 45*7=315, Resulting Numbers: [315] 315,36 unequal: No Solution Exploring Operation: 45+7=52, Resulting Numbers: [52] 52,36 unequal: No Solution Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,36 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: 36:[2, 36, 67], Operations: ['81-14=67'] Exploring Operation: 67-36=31, Resulting Numbers: [2, 31] Generated Node #0,0,0: 36:[2, 31] Operation: 67-36=31 Exploring Operation: 67-2=65, Resulting Numbers: [36, 65] Generated Node #0,0,1: 36:[36, 65] Operation: 67-2=65 Exploring Operation: 2+36=38, Resulting Numbers: [67, 38] Generated Node #0,0,2: 36:[67, 38] Operation: 2+36=38 Exploring Operation: 36/2=18, Resulting Numbers: [67, 18] Generated Node #0,0,3: 36:[67, 18] Operation: 36/2=18 Moving to Node #0,0,0 Current State: 36:[2, 31], Operations: ['81-14=67', '67-36=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,36 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,36 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,36 unequal: No Solution Moving to Node #0,0,1 Current State: 36:[36, 65], Operations: ['81-14=67', '67-2=65'] Exploring Operation: 36+65=101, Resulting Numbers: [101] 101,36 unequal: No Solution Exploring Operation: 36*65=2340, Resulting Numbers: [2340] 2340,36 unequal: No Solution Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,36 unequal: No Solution Moving to Node #0,0,3 Current State: 36:[67, 18], Operations: ['81-14=67', '36/2=18'] Exploring Operation: 67*18=1206, Resulting Numbers: [1206] 1206,36 unequal: No Solution Exploring Operation: 67+18=85, Resulting Numbers: [85] 85,36 unequal: No Solution Exploring Operation: 67-18=49, Resulting Numbers: [49] 49,36 unequal: No Solution Moving to Node #0,0,2 Current State: 36:[67, 38], Operations: ['81-14=67', '2+36=38'] Exploring Operation: 67+38=105, Resulting Numbers: [105] 105,36 unequal: No Solution Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 67*38=2546, Resulting Numbers: [2546] 2546,36 unequal: No Solution No 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: 36:[14, 36, 79], Operations: ['81-2=79'] Exploring Operation: 79-14=65, Resulting Numbers: [36, 65] Generated Node #0,1,0: 36:[36, 65] Operation: 79-14=65 Exploring Operation: 36-14=22, Resulting Numbers: [79, 22] Generated Node #0,1,1: 36:[79, 22] Operation: 36-14=22 Exploring Operation: 14+36=50, Resulting Numbers: [79, 50] Generated Node #0,1,2: 36:[79, 50] Operation: 14+36=50 Exploring Operation: 79-36=43, Resulting Numbers: [14, 43] Generated Node #0,1,3: 36:[14, 43] Operation: 79-36=43 Moving to Node #0,1,3 Current State: 36:[14, 43], Operations: ['81-2=79', '79-36=43'] Exploring Operation: 14*43=602, Resulting Numbers: [602] 602,36 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 14+43=57, Resulting Numbers: [57] 57,36 unequal: No Solution Moving to Node #0,1,0 Current State: 36:[36, 65], Operations: ['81-2=79', '79-14=65'] Exploring Operation: 36+65=101, Resulting Numbers: [101] 101,36 unequal: No Solution Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 36*65=2340, Resulting Numbers: [2340] 2340,36 unequal: No Solution Moving to Node #0,1,1 Current State: 36:[79, 22], Operations: ['81-2=79', '36-14=22'] Exploring Operation: 79*22=1738, Resulting Numbers: [1738] 1738,36 unequal: No Solution Exploring Operation: 79-22=57, Resulting Numbers: [57] 57,36 unequal: No Solution Exploring Operation: 79+22=101, Resulting Numbers: [101] 101,36 unequal: No Solution Moving to Node #0,1,2 Current State: 36:[79, 50], Operations: ['81-2=79', '14+36=50'] Exploring Operation: 79-50=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 79+50=129, Resulting Numbers: [129] 129,36 unequal: No Solution Exploring Operation: 79*50=3950, Resulting Numbers: [3950] 3950,36 unequal: No Solution No 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: 36:[81, 36, 12], Operations: ['14-2=12'] Exploring Operation: 81-36=45, Resulting Numbers: [12, 45] Generated Node #0,3,0: 36:[12, 45] Operation: 81-36=45 Exploring Operation: 36-12=24, Resulting Numbers: [81, 24] Generated Node #0,3,1: 36:[81, 24] Operation: 36-12=24 Exploring Operation: 36/12=3, Resulting Numbers: [81, 3] Generated Node #0,3,2: 36:[81, 3] Operation: 36/12=3 Exploring Operation: 81-12=69, Resulting Numbers: [36, 69] Generated Node #0,3,3: 36:[36, 69] Operation: 81-12=69 Moving to Node #0,3,0 Current State: 36:[12, 45], Operations: ['14-2=12', '81-36=45'] Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,36 unequal: No Solution Exploring Operation: 12*45=540, Resulting Numbers: [540] 540,36 unequal: No Solution Exploring Operation: 12+45=57, Resulting Numbers: [57] 57,36 unequal: No Solution Moving to Node #0,3,3 Current State: 36:[36, 69], Operations: ['14-2=12', '81-12=69'] Exploring Operation: 36+69=105, Resulting Numbers: [105] 105,36 unequal: No Solution Exploring Operation: 69-36=33, Resulting Numbers: [33] 33,36 unequal: No Solution Exploring Operation: 36*69=2484, Resulting Numbers: [2484] 2484,36 unequal: No Solution Moving to Node #0,3,2 Current State: 36:[81, 3], Operations: ['14-2=12', '36/12=3'] Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,36 unequal: No Solution Exploring Operation: 81+3=84, Resulting Numbers: [84] 84,36 unequal: No Solution Exploring Operation: 81/3=27, Resulting Numbers: [27] 27,36 unequal: No Solution Exploring Operation: 81*3=243, Resulting Numbers: [243] 243,36 unequal: No Solution Moving to Node #0,3,1 Current State: 36:[81, 24], Operations: ['14-2=12', '36-12=24'] Exploring Operation: 81+24=105, Resulting Numbers: [105] 105,36 unequal: No Solution Exploring Operation: 81-24=57, Resulting Numbers: [57] 57,36 unequal: No Solution Exploring Operation: 81*24=1944, Resulting Numbers: [1944] 1944,36 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
[ 5, 80, 32, 86 ]
62
[ "86-80=6", "5*6=30", "32+30=62" ]
Current State: 62:[5, 80, 32, 86], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [5, 32, 6] Generated Node #2: [5, 32, 6] from Operation: 86-80=6 Current State: 62:[5, 32, 6], Operations: ['86-80=6'] Exploring Operation: 5*6=30, Resulting Numbers: [32, 30] Generated Node #3: [32, 30] from Operation: 5*6=30 Current State: 62:[32, 30], Operations: ['86-80=6', '5*6=30'] Exploring Operation: 32+30=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[5, 80, 32, 86], Operations: [] Exploring Operation: 86-32=54, Resulting Numbers: [5, 80, 54] Generated Node #0,0: 62:[5, 80, 54] Operation: 86-32=54 Exploring Operation: 86-80=6, Resulting Numbers: [5, 32, 6] Generated Node #0,1: 62:[5, 32, 6] Operation: 86-80=6 Moving to Node #0,1 Current State: 62:[5, 32, 6], Operations: ['86-80=6'] Exploring Operation: 6-5=1, Resulting Numbers: [32, 1] Generated Node #0,1,0: 62:[32, 1] Operation: 6-5=1 Exploring Operation: 5*6=30, Resulting Numbers: [32, 30] Generated Node #0,1,1: 62:[32, 30] Operation: 5*6=30 Moving to Node #0,0 Current State: 62:[5, 80, 54], Operations: ['86-32=54'] Exploring Operation: 80-5=75, Resulting Numbers: [54, 75] Generated Node #0,0,0: 62:[54, 75] Operation: 80-5=75 Exploring Operation: 80-54=26, Resulting Numbers: [5, 26] Generated Node #0,0,1: 62:[5, 26] Operation: 80-54=26 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 62:[5, 26], Operations: ['86-32=54', '80-54=26'] Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[54, 75], Operations: ['86-32=54', '80-5=75'] Exploring Operation: 54+75=129, Resulting Numbers: [129] 129,62 unequal: No Solution Exploring Operation: 75-54=21, Resulting Numbers: [21] 21,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 62:[32, 1], Operations: ['86-80=6', '6-5=1'] Exploring Operation: 32*1=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,62 unequal: No Solution Moving to Node #0,1,1 Current State: 62:[32, 30], Operations: ['86-80=6', '5*6=30'] Exploring Operation: 32+30=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[5, 80, 32, 86], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [5, 32, 6] Generated Node #0,1: 62:[5, 32, 6] Operation: 86-80=6 Moving to Node #0,1 Current State: 62:[5, 32, 6], Operations: ['86-80=6'] Exploring Operation: 5*6=30, Resulting Numbers: [32, 30] Generated Node #0,1,1: 62:[32, 30] Operation: 5*6=30 Moving to Node #0,1,1 Current State: 62:[32, 30], Operations: ['86-80=6', '5*6=30'] Exploring Operation: 32+30=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.985243
hs_2
sum_heuristic
[ 6, 71, 94, 76 ]
59
[ "6+71=77", "94-76=18", "77-18=59" ]
Current State: 59:[6, 71, 94, 76], Operations: [] Exploring Operation: 6+71=77, Resulting Numbers: [94, 76, 77] Generated Node #2: [94, 76, 77] from Operation: 6+71=77 Current State: 59:[94, 76, 77], Operations: ['6+71=77'] Exploring Operation: 94-76=18, Resulting Numbers: [77, 18] Generated Node #3: [77, 18] from Operation: 94-76=18 Current State: 59:[77, 18], Operations: ['6+71=77', '94-76=18'] Exploring Operation: 77-18=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[6, 71, 94, 76], Operations: [] Exploring Operation: 71-6=65, Resulting Numbers: [94, 76, 65] Generated Node #0,0: 59:[94, 76, 65] Operation: 71-6=65 Moving to Node #0,0 Current State: 59:[94, 76, 65], Operations: ['71-6=65'] Exploring Operation: 94-76=18, Resulting Numbers: [65, 18] Generated Node #0,0,0: 59:[65, 18] Operation: 94-76=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[65, 18], Operations: ['71-6=65', '94-76=18'] Exploring Operation: 65-18=47, Resulting Numbers: [47] 47,59 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
[ 13, 3, 60, 94 ]
67
[ "94-3=91", "91/13=7", "60+7=67" ]
Current State: 67:[13, 3, 60, 94], Operations: [] Exploring Operation: 94-3=91, Resulting Numbers: [13, 60, 91] Generated Node #2: [13, 60, 91] from Operation: 94-3=91 Current State: 67:[13, 60, 91], Operations: ['94-3=91'] Exploring Operation: 91/13=7, Resulting Numbers: [60, 7] Generated Node #3: [60, 7] from Operation: 91/13=7 Current State: 67:[60, 7], Operations: ['94-3=91', '91/13=7'] Exploring Operation: 60+7=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[13, 3, 60, 94], Operations: [] Exploring Operation: 13*3=39, Resulting Numbers: [60, 94, 39] Generated Node #0,0: 67:[60, 94, 39] Operation: 13*3=39 Exploring Operation: 13+3=16, Resulting Numbers: [60, 94, 16] Generated Node #0,1: 67:[60, 94, 16] Operation: 13+3=16 Moving to Node #0,0 Current State: 67:[60, 94, 39], Operations: ['13*3=39'] Exploring Operation: 94-39=55, Resulting Numbers: [60, 55] Generated Node #0,0,0: 67:[60, 55] Operation: 94-39=55 Exploring Operation: 60+39=99, Resulting Numbers: [94, 99] Generated Node #0,0,1: 67:[94, 99] Operation: 60+39=99 Moving to Node #0,1 Current State: 67:[60, 94, 16], Operations: ['13+3=16'] Exploring Operation: 60+16=76, Resulting Numbers: [94, 76] Generated Node #0,1,0: 67:[94, 76] Operation: 60+16=76 Exploring Operation: 94-16=78, Resulting Numbers: [60, 78] Generated Node #0,1,1: 67:[60, 78] Operation: 94-16=78 Moving to Node #0,1,1 Current State: 67:[60, 78], Operations: ['13+3=16', '94-16=78'] Exploring Operation: 60+78=138, Resulting Numbers: [138] 138,67 unequal: No Solution Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[60, 55], Operations: ['13*3=39', '94-39=55'] Exploring Operation: 60+55=115, Resulting Numbers: [115] 115,67 unequal: No Solution Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[94, 76], Operations: ['13+3=16', '60+16=76'] Exploring Operation: 94-76=18, Resulting Numbers: [18] 18,67 unequal: No Solution Exploring Operation: 94+76=170, Resulting Numbers: [170] 170,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[94, 99], Operations: ['13*3=39', '60+39=99'] Exploring Operation: 94+99=193, Resulting Numbers: [193] 193,67 unequal: No Solution Exploring Operation: 99-94=5, Resulting Numbers: [5] 5,67 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 50, 1, 92, 52 ]
94
[ "50*1=50", "92+52=144", "144-50=94" ]
Current State: 94:[50, 1, 92, 52], Operations: [] Exploring Operation: 50*1=50, Resulting Numbers: [92, 52, 50] Generated Node #2: [92, 52, 50] from Operation: 50*1=50 Current State: 94:[92, 52, 50], Operations: ['50*1=50'] Exploring Operation: 92+52=144, Resulting Numbers: [50, 144] Generated Node #3: [50, 144] from Operation: 92+52=144 Current State: 94:[50, 144], Operations: ['50*1=50', '92+52=144'] Exploring Operation: 144-50=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[50, 1, 92, 52], Operations: [] Exploring Operation: 1+92=93, Resulting Numbers: [50, 52, 93] Generated Node #0,0: 94:[50, 52, 93] Operation: 1+92=93 Exploring Operation: 52-50=2, Resulting Numbers: [1, 92, 2] Generated Node #0,1: 94:[1, 92, 2] Operation: 52-50=2 Exploring Operation: 52-1=51, Resulting Numbers: [50, 92, 51] Generated Node #0,2: 94:[50, 92, 51] Operation: 52-1=51 Exploring Operation: 50-1=49, Resulting Numbers: [92, 52, 49] Generated Node #0,3: 94:[92, 52, 49] Operation: 50-1=49 Moving to Node #0,1 Current State: 94:[1, 92, 2], Operations: ['52-50=2'] Exploring Operation: 92+2=94, Resulting Numbers: [1, 94] Generated Node #0,1,0: 94:[1, 94] Operation: 92+2=94 Exploring Operation: 1+92=93, Resulting Numbers: [2, 93] Generated Node #0,1,1: 94:[2, 93] Operation: 1+92=93 Exploring Operation: 1*92=92, Resulting Numbers: [2, 92] Generated Node #0,1,2: 94:[2, 92] Operation: 1*92=92 Exploring Operation: 92/1=92, Resulting Numbers: [2, 92] Generated Node #0,1,3: 94:[2, 92] Operation: 92/1=92 Moving to Node #0,2 Current State: 94:[50, 92, 51], Operations: ['52-1=51'] Exploring Operation: 51-50=1, Resulting Numbers: [92, 1] Generated Node #0,2,0: 94:[92, 1] Operation: 51-50=1 Exploring Operation: 92-50=42, Resulting Numbers: [51, 42] Generated Node #0,2,1: 94:[51, 42] Operation: 92-50=42 Exploring Operation: 92-51=41, Resulting Numbers: [50, 41] Generated Node #0,2,2: 94:[50, 41] Operation: 92-51=41 Exploring Operation: 50+51=101, Resulting Numbers: [92, 101] Generated Node #0,2,3: 94:[92, 101] Operation: 50+51=101 Moving to Node #0,0 Current State: 94:[50, 52, 93], Operations: ['1+92=93'] Exploring Operation: 93-50=43, Resulting Numbers: [52, 43] Generated Node #0,0,0: 94:[52, 43] Operation: 93-50=43 Exploring Operation: 52-50=2, Resulting Numbers: [93, 2] Generated Node #0,0,1: 94:[93, 2] Operation: 52-50=2 Exploring Operation: 50+52=102, Resulting Numbers: [93, 102] Generated Node #0,0,2: 94:[93, 102] Operation: 50+52=102 Exploring Operation: 93-52=41, Resulting Numbers: [50, 41] Generated Node #0,0,3: 94:[50, 41] Operation: 93-52=41 Moving to Node #0,3 Current State: 94:[92, 52, 49], Operations: ['50-1=49'] Exploring Operation: 92-49=43, Resulting Numbers: [52, 43] Generated Node #0,3,0: 94:[52, 43] Operation: 92-49=43 Exploring Operation: 52-49=3, Resulting Numbers: [92, 3] Generated Node #0,3,1: 94:[92, 3] Operation: 52-49=3 Exploring Operation: 52+49=101, Resulting Numbers: [92, 101] Generated Node #0,3,2: 94:[92, 101] Operation: 52+49=101 Exploring Operation: 92-52=40, Resulting Numbers: [49, 40] Generated Node #0,3,3: 94:[49, 40] Operation: 92-52=40 Moving to Node #0,1,0 Current State: 94:[1, 94], Operations: ['52-50=2', '92+2=94'] Exploring Operation: 1+94=95, Resulting Numbers: [95] 95,94 unequal: No Solution Exploring Operation: 1*94=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[50, 1, 92, 52], Operations: [] Exploring Operation: 52-50=2, Resulting Numbers: [1, 92, 2] Generated Node #0,1: 94:[1, 92, 2] Operation: 52-50=2 Moving to Node #0,1 Current State: 94:[1, 92, 2], Operations: ['52-50=2'] Exploring Operation: 92+2=94, Resulting Numbers: [1, 94] Generated Node #0,1,0: 94:[1, 94] Operation: 92+2=94 Moving to Node #0,1,0 Current State: 94:[1, 94], Operations: ['52-50=2', '92+2=94'] Exploring Operation: 1*94=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.977431
hs_4
sum_heuristic
[ 2, 29, 24, 50 ]
30
[ "50/2=25", "29-24=5", "25+5=30" ]
Current State: 30:[2, 29, 24, 50], Operations: [] Exploring Operation: 50/2=25, Resulting Numbers: [29, 24, 25] Generated Node #2: [29, 24, 25] from Operation: 50/2=25 Current State: 30:[29, 24, 25], Operations: ['50/2=25'] Exploring Operation: 29-24=5, Resulting Numbers: [25, 5] Generated Node #3: [25, 5] from Operation: 29-24=5 Current State: 30:[25, 5], Operations: ['50/2=25', '29-24=5'] Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[2, 29, 24, 50], Operations: [] Exploring Operation: 50-24=26, Resulting Numbers: [2, 29, 26] Generated Node #0,0: 30:[2, 29, 26] Operation: 50-24=26 Exploring Operation: 50/2=25, Resulting Numbers: [29, 24, 25] Generated Node #0,1: 30:[29, 24, 25] Operation: 50/2=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[2, 29, 26], Operations: ['50-24=26'] Exploring Operation: 2+26=28, Resulting Numbers: [29, 28] Generated Node #0,0,0: 30:[29, 28] Operation: 2+26=28 Exploring Operation: 29-26=3, Resulting Numbers: [2, 3] Generated Node #0,0,1: 30:[2, 3] Operation: 29-26=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[2, 3], Operations: ['50-24=26', '29-26=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[29, 28], Operations: ['50-24=26', '2+26=28'] Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 29+28=57, Resulting Numbers: [57] 57,30 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:[29, 24, 25], Operations: ['50/2=25'] Exploring Operation: 25-24=1, Resulting Numbers: [29, 1] Generated Node #0,1,0: 30:[29, 1] Operation: 25-24=1 Exploring Operation: 29-24=5, Resulting Numbers: [25, 5] Generated Node #0,1,1: 30:[25, 5] Operation: 29-24=5 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[29, 1], Operations: ['50/2=25', '25-24=1'] Exploring Operation: 29*1=29, Resulting Numbers: [29] 29,30 unequal: No Solution Exploring Operation: 29+1=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[2, 29, 24, 50], Operations: [] Exploring Operation: 50/2=25, Resulting Numbers: [29, 24, 25] Generated Node #0,1: 30:[29, 24, 25] Operation: 50/2=25 Moving to Node #0,1 Current State: 30:[29, 24, 25], Operations: ['50/2=25'] Exploring Operation: 25-24=1, Resulting Numbers: [29, 1] Generated Node #0,1,0: 30:[29, 1] Operation: 25-24=1 Moving to Node #0,1,0 Current State: 30:[29, 1], Operations: ['50/2=25', '25-24=1'] Exploring Operation: 29+1=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 74, 25, 19, 92 ]
24
[ "74-25=49", "92-19=73", "73-49=24" ]
Current State: 24:[74, 25, 19, 92], Operations: [] Exploring Operation: 74-25=49, Resulting Numbers: [19, 92, 49] Generated Node #2: [19, 92, 49] from Operation: 74-25=49 Current State: 24:[19, 92, 49], Operations: ['74-25=49'] Exploring Operation: 92-19=73, Resulting Numbers: [49, 73] Generated Node #3: [49, 73] from Operation: 92-19=73 Current State: 24:[49, 73], Operations: ['74-25=49', '92-19=73'] Exploring Operation: 73-49=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[74, 25, 19, 92], Operations: [] Exploring Operation: 92-74=18, Resulting Numbers: [25, 19, 18] Generated Node #0,0: 24:[25, 19, 18] Operation: 92-74=18 Moving to Node #0,0 Current State: 24:[25, 19, 18], Operations: ['92-74=18'] Exploring Operation: 19-18=1, Resulting Numbers: [25, 1] Generated Node #0,0,0: 24:[25, 1] Operation: 19-18=1 Moving to Node #0,0,0 Current State: 24:[25, 1], Operations: ['92-74=18', '19-18=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[74, 25, 19, 92], Operations: [] Exploring Operation: 92-74=18, Resulting Numbers: [25, 19, 18] Generated Node #0,0: 24:[25, 19, 18] Operation: 92-74=18 Moving to Node #0,0 Current State: 24:[25, 19, 18], Operations: ['92-74=18'] Exploring Operation: 19-18=1, Resulting Numbers: [25, 1] Generated Node #0,0,0: 24:[25, 1] Operation: 19-18=1 Moving to Node #0,0,0 Current State: 24:[25, 1], Operations: ['92-74=18', '19-18=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 41, 36, 46, 94 ]
26
[ "46-41=5", "36+94=130", "130/5=26" ]
Current State: 26:[41, 36, 46, 94], Operations: [] Exploring Operation: 46-41=5, Resulting Numbers: [36, 94, 5] Generated Node #2: [36, 94, 5] from Operation: 46-41=5 Current State: 26:[36, 94, 5], Operations: ['46-41=5'] Exploring Operation: 36+94=130, Resulting Numbers: [5, 130] Generated Node #3: [5, 130] from Operation: 36+94=130 Current State: 26:[5, 130], Operations: ['46-41=5', '36+94=130'] Exploring Operation: 130/5=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[41, 36, 46, 94], Operations: [] Exploring Operation: 94-46=48, Resulting Numbers: [41, 36, 48] Generated Node #0,0: 26:[41, 36, 48] Operation: 94-46=48 Moving to Node #0,0 Current State: 26:[41, 36, 48], Operations: ['94-46=48'] Exploring Operation: 48-41=7, Resulting Numbers: [36, 7] Generated Node #0,0,0: 26:[36, 7] Operation: 48-41=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[36, 7], Operations: ['94-46=48', '48-41=7'] Exploring Operation: 36-7=29, Resulting Numbers: [29] 29,26 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
[ 26, 50, 25, 8 ]
36
[ "26+8=34", "50/25=2", "34+2=36" ]
Current State: 36:[26, 50, 25, 8], Operations: [] Exploring Operation: 26+8=34, Resulting Numbers: [50, 25, 34] Generated Node #2: [50, 25, 34] from Operation: 26+8=34 Current State: 36:[50, 25, 34], Operations: ['26+8=34'] Exploring Operation: 50/25=2, Resulting Numbers: [34, 2] Generated Node #3: [34, 2] from Operation: 50/25=2 Current State: 36:[34, 2], Operations: ['26+8=34', '50/25=2'] Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[26, 50, 25, 8], Operations: [] Exploring Operation: 50/25=2, Resulting Numbers: [26, 8, 2] Generated Node #0,0: 36:[26, 8, 2] Operation: 50/25=2 Exploring Operation: 26-25=1, Resulting Numbers: [50, 8, 1] Generated Node #0,1: 36:[50, 8, 1] Operation: 26-25=1 Exploring Operation: 50-26=24, Resulting Numbers: [25, 8, 24] Generated Node #0,2: 36:[25, 8, 24] Operation: 50-26=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[26, 8, 2], Operations: ['50/25=2'] Exploring Operation: 26+8=34, Resulting Numbers: [2, 34] Generated Node #0,0,0: 36:[2, 34] Operation: 26+8=34 Exploring Operation: 26/2=13, Resulting Numbers: [8, 13] Generated Node #0,0,1: 36:[8, 13] Operation: 26/2=13 Exploring Operation: 26-8=18, Resulting Numbers: [2, 18] Generated Node #0,0,2: 36:[2, 18] Operation: 26-8=18 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 36:[2, 18], Operations: ['50/25=2', '26-8=18'] Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,36 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[26, 50, 25, 8], Operations: [] Exploring Operation: 50/25=2, Resulting Numbers: [26, 8, 2] Generated Node #0,0: 36:[26, 8, 2] Operation: 50/25=2 Moving to Node #0,0 Current State: 36:[26, 8, 2], Operations: ['50/25=2'] Exploring Operation: 26-8=18, Resulting Numbers: [2, 18] Generated Node #0,0,2: 36:[2, 18] Operation: 26-8=18 Moving to Node #0,0,2 Current State: 36:[2, 18], Operations: ['50/25=2', '26-8=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 88, 75, 43, 10 ]
40
[ "88-75=13", "43+10=53", "53-13=40" ]
Current State: 40:[88, 75, 43, 10], Operations: [] Exploring Operation: 88-75=13, Resulting Numbers: [43, 10, 13] Generated Node #2: [43, 10, 13] from Operation: 88-75=13 Current State: 40:[43, 10, 13], Operations: ['88-75=13'] Exploring Operation: 43+10=53, Resulting Numbers: [13, 53] Generated Node #3: [13, 53] from Operation: 43+10=53 Current State: 40:[13, 53], Operations: ['88-75=13', '43+10=53'] Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[88, 75, 43, 10], Operations: [] Exploring Operation: 88-43=45, Resulting Numbers: [75, 10, 45] Generated Node #0,0: 40:[75, 10, 45] Operation: 88-43=45 Exploring Operation: 88-75=13, Resulting Numbers: [43, 10, 13] Generated Node #0,1: 40:[43, 10, 13] Operation: 88-75=13 Moving to Node #0,1 Current State: 40:[43, 10, 13], Operations: ['88-75=13'] Exploring Operation: 10+13=23, Resulting Numbers: [43, 23] Generated Node #0,1,0: 40:[43, 23] Operation: 10+13=23 Exploring Operation: 13-10=3, Resulting Numbers: [43, 3] Generated Node #0,1,1: 40:[43, 3] Operation: 13-10=3 Moving to Node #0,0 Current State: 40:[75, 10, 45], Operations: ['88-43=45'] Exploring Operation: 75-10=65, Resulting Numbers: [45, 65] Generated Node #0,0,0: 40:[45, 65] Operation: 75-10=65 Exploring Operation: 75-45=30, Resulting Numbers: [10, 30] Generated Node #0,0,1: 40:[10, 30] Operation: 75-45=30 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[10, 30], Operations: ['88-43=45', '75-45=30'] Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[88, 75, 43, 10], Operations: [] Exploring Operation: 88-43=45, Resulting Numbers: [75, 10, 45] Generated Node #0,0: 40:[75, 10, 45] Operation: 88-43=45 Moving to Node #0,0 Current State: 40:[75, 10, 45], Operations: ['88-43=45'] Exploring Operation: 75-45=30, Resulting Numbers: [10, 30] Generated Node #0,0,1: 40:[10, 30] Operation: 75-45=30 Moving to Node #0,0,1 Current State: 40:[10, 30], Operations: ['88-43=45', '75-45=30'] Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 9, 18, 3, 11 ]
56
[ "9*3=27", "18+11=29", "27+29=56" ]
Current State: 56:[9, 18, 3, 11], Operations: [] Exploring Operation: 9*3=27, Resulting Numbers: [18, 11, 27] Generated Node #2: [18, 11, 27] from Operation: 9*3=27 Current State: 56:[18, 11, 27], Operations: ['9*3=27'] Exploring Operation: 18+11=29, Resulting Numbers: [27, 29] Generated Node #3: [27, 29] from Operation: 18+11=29 Current State: 56:[27, 29], Operations: ['9*3=27', '18+11=29'] Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[9, 18, 3, 11], Operations: [] Exploring Operation: 18+11=29, Resulting Numbers: [9, 3, 29] Generated Node #0,0: 56:[9, 3, 29] Operation: 18+11=29 Exploring Operation: 18-9=9, Resulting Numbers: [3, 11, 9] Generated Node #0,1: 56:[3, 11, 9] Operation: 18-9=9 Exploring Operation: 18/9=2, Resulting Numbers: [3, 11, 2] Generated Node #0,2: 56:[3, 11, 2] Operation: 18/9=2 Exploring Operation: 9+18=27, Resulting Numbers: [3, 11, 27] Generated Node #0,3: 56:[3, 11, 27] Operation: 9+18=27 Exploring Operation: 18-11=7, Resulting Numbers: [9, 3, 7] Generated Node #0,4: 56:[9, 3, 7] Operation: 18-11=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 56:[9, 3, 7], Operations: ['18-11=7'] Exploring Operation: 9*3=27, Resulting Numbers: [7, 27] Generated Node #0,4,0: 56:[7, 27] Operation: 9*3=27 Exploring Operation: 9-3=6, Resulting Numbers: [7, 6] Generated Node #0,4,1: 56:[7, 6] Operation: 9-3=6 Exploring Operation: 9/3=3, Resulting Numbers: [7, 3] Generated Node #0,4,2: 56:[7, 3] Operation: 9/3=3 Exploring Operation: 7-3=4, Resulting Numbers: [9, 4] Generated Node #0,4,3: 56:[9, 4] Operation: 7-3=4 Exploring Operation: 9-7=2, Resulting Numbers: [3, 2] Generated Node #0,4,4: 56:[3, 2] Operation: 9-7=2 Moving to Node #0,4,0 Current State: 56:[7, 27], Operations: ['18-11=7', '9*3=27'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,56 unequal: No Solution Exploring Operation: 7*27=189, Resulting Numbers: [189] 189,56 unequal: No Solution Moving to Node #0,4,2 Current State: 56:[7, 3], Operations: ['18-11=7', '9/3=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,56 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,56 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,56 unequal: No Solution Moving to Node #0,4,4 Current State: 56:[3, 2], Operations: ['18-11=7', '9-7=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,56 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,56 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,56 unequal: No Solution Moving to Node #0,4,1 Current State: 56:[7, 6], Operations: ['18-11=7', '9-3=6'] Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,56 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,56 unequal: No Solution Moving to Node #0,4,3 Current State: 56:[9, 4], Operations: ['18-11=7', '7-3=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,56 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,56 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,56 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 Current State: 56:[9, 3, 29], Operations: ['18+11=29'] Exploring Operation: 29-3=26, Resulting Numbers: [9, 26] Generated Node #0,0,0: 56:[9, 26] Operation: 29-3=26 Exploring Operation: 9-3=6, Resulting Numbers: [29, 6] Generated Node #0,0,1: 56:[29, 6] Operation: 9-3=6 Exploring Operation: 9/3=3, Resulting Numbers: [29, 3] Generated Node #0,0,2: 56:[29, 3] Operation: 9/3=3 Exploring Operation: 9*3=27, Resulting Numbers: [29, 27] Generated Node #0,0,3: 56:[29, 27] Operation: 9*3=27 Exploring Operation: 9+3=12, Resulting Numbers: [29, 12] Generated Node #0,0,4: 56:[29, 12] Operation: 9+3=12 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 56:[29, 6], Operations: ['18+11=29', '9-3=6'] Exploring Operation: 29*6=174, Resulting Numbers: [174] 174,56 unequal: No Solution Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,56 unequal: No Solution No 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: 56:[29, 3], Operations: ['18+11=29', '9/3=3'] Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,56 unequal: No Solution Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,56 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,56 unequal: No Solution No 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: 56:[29, 27], Operations: ['18+11=29', '9*3=27'] Exploring Operation: 29*27=783, Resulting Numbers: [783] 783,56 unequal: No Solution Exploring Operation: 29+27=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[9, 18, 3, 11], Operations: [] Exploring Operation: 18+11=29, Resulting Numbers: [9, 3, 29] Generated Node #0,0: 56:[9, 3, 29] Operation: 18+11=29 Moving to Node #0,0 Current State: 56:[9, 3, 29], Operations: ['18+11=29'] Exploring Operation: 9*3=27, Resulting Numbers: [29, 27] Generated Node #0,0,3: 56:[29, 27] Operation: 9*3=27 Moving to Node #0,0,3 Current State: 56:[29, 27], Operations: ['18+11=29', '9*3=27'] Exploring Operation: 29+27=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.963542
hs_5
sum_heuristic
[ 66, 1, 83, 82 ]
66
[ "66+1=67", "83-82=1", "67-1=66" ]
Current State: 66:[66, 1, 83, 82], Operations: [] Exploring Operation: 66+1=67, Resulting Numbers: [83, 82, 67] Generated Node #2: [83, 82, 67] from Operation: 66+1=67 Current State: 66:[83, 82, 67], Operations: ['66+1=67'] Exploring Operation: 83-82=1, Resulting Numbers: [67, 1] Generated Node #3: [67, 1] from Operation: 83-82=1 Current State: 66:[67, 1], Operations: ['66+1=67', '83-82=1'] Exploring Operation: 67-1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[66, 1, 83, 82], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [66, 1, 1] Generated Node #0,0: 66:[66, 1, 1] Operation: 83-82=1 Exploring Operation: 82-1=81, Resulting Numbers: [66, 83, 81] Generated Node #0,1: 66:[66, 83, 81] Operation: 82-1=81 Exploring Operation: 83-1=82, Resulting Numbers: [66, 82, 82] Generated Node #0,2: 66:[66, 82, 82] Operation: 83-1=82 Exploring Operation: 82-66=16, Resulting Numbers: [1, 83, 16] Generated Node #0,3: 66:[1, 83, 16] Operation: 82-66=16 Exploring Operation: 83-66=17, Resulting Numbers: [1, 82, 17] Generated Node #0,4: 66:[1, 82, 17] Operation: 83-66=17 Moving to Node #0,0 Current State: 66:[66, 1, 1], Operations: ['83-82=1'] Exploring Operation: 66/1=66, Resulting Numbers: [1, 66] Generated Node #0,0,0: 66:[1, 66] Operation: 66/1=66 Exploring Operation: 66/1=66, Resulting Numbers: [1, 66] Generated Node #0,0,1: 66:[1, 66] Operation: 66/1=66 Exploring Operation: 1+1=2, Resulting Numbers: [66, 2] Generated Node #0,0,2: 66:[66, 2] Operation: 1+1=2 Exploring Operation: 66*1=66, Resulting Numbers: [1, 66] Generated Node #0,0,3: 66:[1, 66] Operation: 66*1=66 Exploring Operation: 66*1=66, Resulting Numbers: [1, 66] Generated Node #0,0,4: 66:[1, 66] Operation: 66*1=66 Moving to Node #0,4 Current State: 66:[1, 82, 17], Operations: ['83-66=17'] Exploring Operation: 1*82=82, Resulting Numbers: [17, 82] Generated Node #0,4,0: 66:[17, 82] Operation: 1*82=82 Exploring Operation: 1+17=18, Resulting Numbers: [82, 18] Generated Node #0,4,1: 66:[82, 18] Operation: 1+17=18 Exploring Operation: 82-1=81, Resulting Numbers: [17, 81] Generated Node #0,4,2: 66:[17, 81] Operation: 82-1=81 Exploring Operation: 82/1=82, Resulting Numbers: [17, 82] Generated Node #0,4,3: 66:[17, 82] Operation: 82/1=82 Exploring Operation: 82-17=65, Resulting Numbers: [1, 65] Generated Node #0,4,4: 66:[1, 65] Operation: 82-17=65 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 66:[1, 65], Operations: ['83-66=17', '82-17=65'] Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,66 unequal: No Solution Exploring Operation: 1*65=65, Resulting Numbers: [65] 65,66 unequal: No Solution Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,66 unequal: No Solution Exploring Operation: 1+65=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[66, 1, 83, 82], Operations: [] Exploring Operation: 83-66=17, Resulting Numbers: [1, 82, 17] Generated Node #0,4: 66:[1, 82, 17] Operation: 83-66=17 Moving to Node #0,4 Current State: 66:[1, 82, 17], Operations: ['83-66=17'] Exploring Operation: 82-17=65, Resulting Numbers: [1, 65] Generated Node #0,4,4: 66:[1, 65] Operation: 82-17=65 Moving to Node #0,4,4 Current State: 66:[1, 65], Operations: ['83-66=17', '82-17=65'] Exploring Operation: 1+65=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 72, 59, 65, 91 ]
12
[ "72-59=13", "65+91=156", "156/13=12" ]
Current State: 12:[72, 59, 65, 91], Operations: [] Exploring Operation: 72-59=13, Resulting Numbers: [65, 91, 13] Generated Node #2: [65, 91, 13] from Operation: 72-59=13 Current State: 12:[65, 91, 13], Operations: ['72-59=13'] Exploring Operation: 65+91=156, Resulting Numbers: [13, 156] Generated Node #3: [13, 156] from Operation: 65+91=156 Current State: 12:[13, 156], Operations: ['72-59=13', '65+91=156'] Exploring Operation: 156/13=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[72, 59, 65, 91], Operations: [] Exploring Operation: 91-65=26, Resulting Numbers: [72, 59, 26] Generated Node #0,0: 12:[72, 59, 26] Operation: 91-65=26 Exploring Operation: 91-72=19, Resulting Numbers: [59, 65, 19] Generated Node #0,1: 12:[59, 65, 19] Operation: 91-72=19 Exploring Operation: 72-65=7, Resulting Numbers: [59, 91, 7] Generated Node #0,2: 12:[59, 91, 7] Operation: 72-65=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[59, 65, 19], Operations: ['91-72=19'] Exploring Operation: 65-19=46, Resulting Numbers: [59, 46] Generated Node #0,1,0: 12:[59, 46] Operation: 65-19=46 Exploring Operation: 59-19=40, Resulting Numbers: [65, 40] Generated Node #0,1,1: 12:[65, 40] Operation: 59-19=40 Exploring Operation: 65-59=6, Resulting Numbers: [19, 6] Generated Node #0,1,2: 12:[19, 6] Operation: 65-59=6 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 12:[19, 6], Operations: ['91-72=19', '65-59=6'] Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,12 unequal: No Solution Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,12 unequal: No Solution No 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: 12:[59, 46], Operations: ['91-72=19', '65-19=46'] Exploring Operation: 59+46=105, Resulting Numbers: [105] 105,12 unequal: No Solution Exploring Operation: 59*46=2714, Resulting Numbers: [2714] 2714,12 unequal: No Solution Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,12 unequal: No Solution No 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: 12:[65, 40], Operations: ['91-72=19', '59-19=40'] Exploring Operation: 65+40=105, Resulting Numbers: [105] 105,12 unequal: No Solution Exploring Operation: 65-40=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 65*40=2600, Resulting Numbers: [2600] 2600,12 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: 12:[72, 59, 26], Operations: ['91-65=26'] Exploring Operation: 59-26=33, Resulting Numbers: [72, 33] Generated Node #0,0,0: 12:[72, 33] Operation: 59-26=33 Exploring Operation: 72-26=46, Resulting Numbers: [59, 46] Generated Node #0,0,1: 12:[59, 46] Operation: 72-26=46 Exploring Operation: 72-59=13, Resulting Numbers: [26, 13] Generated Node #0,0,2: 12:[26, 13] Operation: 72-59=13 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 12:[26, 13], Operations: ['91-65=26', '72-59=13'] Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,12 unequal: No Solution Exploring Operation: 26+13=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,12 unequal: No Solution No 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: 12:[72, 33], Operations: ['91-65=26', '59-26=33'] Exploring Operation: 72-33=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 72*33=2376, Resulting Numbers: [2376] 2376,12 unequal: No Solution Exploring Operation: 72+33=105, Resulting Numbers: [105] 105,12 unequal: No Solution No 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: 12:[59, 46], Operations: ['91-65=26', '72-26=46'] Exploring Operation: 59+46=105, Resulting Numbers: [105] 105,12 unequal: No Solution Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,12 unequal: No Solution Exploring Operation: 59*46=2714, Resulting Numbers: [2714] 2714,12 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: 12:[59, 91, 7], Operations: ['72-65=7'] Exploring Operation: 91/7=13, Resulting Numbers: [59, 13] Generated Node #0,2,0: 12:[59, 13] Operation: 91/7=13 Exploring Operation: 59-7=52, Resulting Numbers: [91, 52] Generated Node #0,2,1: 12:[91, 52] Operation: 59-7=52 Exploring Operation: 91-59=32, Resulting Numbers: [7, 32] Generated Node #0,2,2: 12:[7, 32] Operation: 91-59=32 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 12:[7, 32], Operations: ['72-65=7', '91-59=32'] Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,12 unequal: No Solution No 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: 12:[59, 13], Operations: ['72-65=7', '91/7=13'] Exploring Operation: 59*13=767, Resulting Numbers: [767] 767,12 unequal: No Solution Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,12 unequal: No Solution Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,12 unequal: No Solution No 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: 12:[91, 52], Operations: ['72-65=7', '59-7=52'] Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 91+52=143, Resulting Numbers: [143] 143,12 unequal: No Solution Exploring Operation: 91*52=4732, Resulting Numbers: [4732] 4732,12 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
[ 9, 5, 56, 99 ]
86
[ "9+56=65", "65/5=13", "99-13=86" ]
Current State: 86:[9, 5, 56, 99], Operations: [] Exploring Operation: 9+56=65, Resulting Numbers: [5, 99, 65] Generated Node #2: [5, 99, 65] from Operation: 9+56=65 Current State: 86:[5, 99, 65], Operations: ['9+56=65'] Exploring Operation: 65/5=13, Resulting Numbers: [99, 13] Generated Node #3: [99, 13] from Operation: 65/5=13 Current State: 86:[99, 13], Operations: ['9+56=65', '65/5=13'] Exploring Operation: 99-13=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[9, 5, 56, 99], Operations: [] Exploring Operation: 99-9=90, Resulting Numbers: [5, 56, 90] Generated Node #0,0: 86:[5, 56, 90] Operation: 99-9=90 Exploring Operation: 56-9=47, Resulting Numbers: [5, 99, 47] Generated Node #0,1: 86:[5, 99, 47] Operation: 56-9=47 Exploring Operation: 99-56=43, Resulting Numbers: [9, 5, 43] Generated Node #0,2: 86:[9, 5, 43] Operation: 99-56=43 Exploring Operation: 99/9=11, Resulting Numbers: [5, 56, 11] Generated Node #0,3: 86:[5, 56, 11] Operation: 99/9=11 Moving to Node #0,2 Current State: 86:[9, 5, 43], Operations: ['99-56=43'] Exploring Operation: 9*5=45, Resulting Numbers: [43, 45] Generated Node #0,2,0: 86:[43, 45] Operation: 9*5=45 Exploring Operation: 9-5=4, Resulting Numbers: [43, 4] Generated Node #0,2,1: 86:[43, 4] Operation: 9-5=4 Exploring Operation: 9+5=14, Resulting Numbers: [43, 14] Generated Node #0,2,2: 86:[43, 14] Operation: 9+5=14 Exploring Operation: 9+43=52, Resulting Numbers: [5, 52] Generated Node #0,2,3: 86:[5, 52] Operation: 9+43=52 Moving to Node #0,1 Current State: 86:[5, 99, 47], Operations: ['56-9=47'] Exploring Operation: 99-5=94, Resulting Numbers: [47, 94] Generated Node #0,1,0: 86:[47, 94] Operation: 99-5=94 Exploring Operation: 5+99=104, Resulting Numbers: [47, 104] Generated Node #0,1,1: 86:[47, 104] Operation: 5+99=104 Exploring Operation: 99-47=52, Resulting Numbers: [5, 52] Generated Node #0,1,2: 86:[5, 52] Operation: 99-47=52 Exploring Operation: 47-5=42, Resulting Numbers: [99, 42] Generated Node #0,1,3: 86:[99, 42] Operation: 47-5=42 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[47, 94], Operations: ['56-9=47', '99-5=94'] Exploring Operation: 94/47=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 47*94=4418, Resulting Numbers: [4418] 4418,86 unequal: No Solution Exploring Operation: 47+94=141, Resulting Numbers: [141] 141,86 unequal: No Solution Exploring Operation: 94-47=47, Resulting Numbers: [47] 47,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[5, 52], Operations: ['56-9=47', '99-47=52'] Exploring Operation: 5+52=57, Resulting Numbers: [57] 57,86 unequal: No Solution Exploring Operation: 5*52=260, Resulting Numbers: [260] 260,86 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 86:[99, 42], Operations: ['56-9=47', '47-5=42'] Exploring Operation: 99+42=141, Resulting Numbers: [141] 141,86 unequal: No Solution Exploring Operation: 99*42=4158, Resulting Numbers: [4158] 4158,86 unequal: No Solution Exploring Operation: 99-42=57, Resulting Numbers: [57] 57,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[47, 104], Operations: ['56-9=47', '5+99=104'] Exploring Operation: 47+104=151, Resulting Numbers: [151] 151,86 unequal: No Solution Exploring Operation: 104-47=57, Resulting Numbers: [57] 57,86 unequal: No Solution Exploring Operation: 47*104=4888, Resulting Numbers: [4888] 4888,86 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:[5, 56, 90], Operations: ['99-9=90'] Exploring Operation: 5+56=61, Resulting Numbers: [90, 61] Generated Node #0,0,0: 86:[90, 61] Operation: 5+56=61 Exploring Operation: 90-56=34, Resulting Numbers: [5, 34] Generated Node #0,0,1: 86:[5, 34] Operation: 90-56=34 Exploring Operation: 90-5=85, Resulting Numbers: [56, 85] Generated Node #0,0,2: 86:[56, 85] Operation: 90-5=85 Exploring Operation: 56-5=51, Resulting Numbers: [90, 51] Generated Node #0,0,3: 86:[90, 51] Operation: 56-5=51 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 86:[5, 34], Operations: ['99-9=90', '90-56=34'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,86 unequal: No Solution Exploring Operation: 5+34=39, Resulting Numbers: [39] 39,86 unequal: No Solution Exploring Operation: 5*34=170, Resulting Numbers: [170] 170,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 86:[90, 51], Operations: ['99-9=90', '56-5=51'] Exploring Operation: 90+51=141, Resulting Numbers: [141] 141,86 unequal: No Solution Exploring Operation: 90*51=4590, Resulting Numbers: [4590] 4590,86 unequal: No Solution Exploring Operation: 90-51=39, Resulting Numbers: [39] 39,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 86:[56, 85], Operations: ['99-9=90', '90-5=85'] Exploring Operation: 56*85=4760, Resulting Numbers: [4760] 4760,86 unequal: No Solution Exploring Operation: 56+85=141, Resulting Numbers: [141] 141,86 unequal: No Solution Exploring Operation: 85-56=29, Resulting Numbers: [29] 29,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[90, 61], Operations: ['99-9=90', '5+56=61'] Exploring Operation: 90-61=29, Resulting Numbers: [29] 29,86 unequal: No Solution Exploring Operation: 90*61=5490, Resulting Numbers: [5490] 5490,86 unequal: No Solution Exploring Operation: 90+61=151, Resulting Numbers: [151] 151,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 86:[5, 56, 11], Operations: ['99/9=11'] Exploring Operation: 56+11=67, Resulting Numbers: [5, 67] Generated Node #0,3,0: 86:[5, 67] Operation: 56+11=67 Exploring Operation: 11-5=6, Resulting Numbers: [56, 6] Generated Node #0,3,1: 86:[56, 6] Operation: 11-5=6 Exploring Operation: 56-11=45, Resulting Numbers: [5, 45] Generated Node #0,3,2: 86:[5, 45] Operation: 56-11=45 Exploring Operation: 56-5=51, Resulting Numbers: [11, 51] Generated Node #0,3,3: 86:[11, 51] Operation: 56-5=51 Moving to Node #0,2,0 Current State: 86:[43, 45], Operations: ['99-56=43', '9*5=45'] Exploring Operation: 43*45=1935, Resulting Numbers: [1935] 1935,86 unequal: No Solution Exploring Operation: 45-43=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 43+45=88, Resulting Numbers: [88] 88,86 unequal: No Solution Moving to Node #0,2,1 Current State: 86:[43, 4], Operations: ['99-56=43', '9-5=4'] Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,86 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,86 unequal: No Solution Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,86 unequal: No Solution Moving to Node #0,3,2 Current State: 86:[5, 45], Operations: ['99/9=11', '56-11=45'] Exploring Operation: 5*45=225, Resulting Numbers: [225] 225,86 unequal: No Solution Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 5+45=50, Resulting Numbers: [50] 50,86 unequal: No Solution Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,86 unequal: No Solution Moving to Node #0,2,2 Current State: 86:[43, 14], Operations: ['99-56=43', '9+5=14'] Exploring Operation: 43*14=602, Resulting Numbers: [602] 602,86 unequal: No Solution Exploring Operation: 43+14=57, Resulting Numbers: [57] 57,86 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,86 unequal: No Solution Moving to Node #0,2,3 Current State: 86:[5, 52], Operations: ['99-56=43', '9+43=52'] Exploring Operation: 5+52=57, Resulting Numbers: [57] 57,86 unequal: No Solution Exploring Operation: 5*52=260, Resulting Numbers: [260] 260,86 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,86 unequal: No Solution Moving to Node #0,3,1 Current State: 86:[56, 6], Operations: ['99/9=11', '11-5=6'] Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,86 unequal: No Solution Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,86 unequal: No Solution Moving to Node #0,3,3 Current State: 86:[11, 51], Operations: ['99/9=11', '56-5=51'] Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,86 unequal: No Solution Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,86 unequal: No Solution Moving to Node #0,3,0 Current State: 86:[5, 67], Operations: ['99/9=11', '56+11=67'] Exploring Operation: 5+67=72, Resulting Numbers: [72] 72,86 unequal: No Solution Exploring Operation: 5*67=335, Resulting Numbers: [335] 335,86 unequal: No Solution Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,86 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 12, 72, 36, 80 ]
89
[ "72+36=108", "108/12=9", "80+9=89" ]
Current State: 89:[12, 72, 36, 80], Operations: [] Exploring Operation: 72+36=108, Resulting Numbers: [12, 80, 108] Generated Node #2: [12, 80, 108] from Operation: 72+36=108 Current State: 89:[12, 80, 108], Operations: ['72+36=108'] Exploring Operation: 108/12=9, Resulting Numbers: [80, 9] Generated Node #3: [80, 9] from Operation: 108/12=9 Current State: 89:[80, 9], Operations: ['72+36=108', '108/12=9'] Exploring Operation: 80+9=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[12, 72, 36, 80], Operations: [] Exploring Operation: 12+36=48, Resulting Numbers: [72, 80, 48] Generated Node #0,0: 89:[72, 80, 48] Operation: 12+36=48 Exploring Operation: 12+72=84, Resulting Numbers: [36, 80, 84] Generated Node #0,1: 89:[36, 80, 84] Operation: 12+72=84 Moving to Node #0,0 Current State: 89:[72, 80, 48], Operations: ['12+36=48'] Exploring Operation: 80+48=128, Resulting Numbers: [72, 128] Generated Node #0,0,0: 89:[72, 128] Operation: 80+48=128 Exploring Operation: 72+48=120, Resulting Numbers: [80, 120] Generated Node #0,0,1: 89:[80, 120] Operation: 72+48=120 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[80, 120], Operations: ['12+36=48', '72+48=120'] Exploring Operation: 80+120=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 120-80=40, Resulting Numbers: [40] 40,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[72, 128], Operations: ['12+36=48', '80+48=128'] Exploring Operation: 72+128=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 128-72=56, Resulting Numbers: [56] 56,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 89:[36, 80, 84], Operations: ['12+72=84'] Exploring Operation: 36+80=116, Resulting Numbers: [84, 116] Generated Node #0,1,0: 89:[84, 116] Operation: 36+80=116 Exploring Operation: 36+84=120, Resulting Numbers: [80, 120] Generated Node #0,1,1: 89:[80, 120] Operation: 36+84=120 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[84, 116], Operations: ['12+72=84', '36+80=116'] Exploring Operation: 116-84=32, Resulting Numbers: [32] 32,89 unequal: No Solution Exploring Operation: 84+116=200, Resulting Numbers: [200] 200,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[80, 120], Operations: ['12+72=84', '36+84=120'] Exploring Operation: 80+120=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 120-80=40, Resulting Numbers: [40] 40,89 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
[ 3, 25, 29, 56 ]
68
[ "29-25=4", "3*4=12", "56+12=68" ]
Current State: 68:[3, 25, 29, 56], Operations: [] Exploring Operation: 29-25=4, Resulting Numbers: [3, 56, 4] Generated Node #2: [3, 56, 4] from Operation: 29-25=4 Current State: 68:[3, 56, 4], Operations: ['29-25=4'] Exploring Operation: 3*4=12, Resulting Numbers: [56, 12] Generated Node #3: [56, 12] from Operation: 3*4=12 Current State: 68:[56, 12], Operations: ['29-25=4', '3*4=12'] Exploring Operation: 56+12=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[3, 25, 29, 56], Operations: [] Exploring Operation: 25-3=22, Resulting Numbers: [29, 56, 22] Generated Node #0,0: 68:[29, 56, 22] Operation: 25-3=22 Exploring Operation: 56-25=31, Resulting Numbers: [3, 29, 31] Generated Node #0,1: 68:[3, 29, 31] Operation: 56-25=31 Exploring Operation: 56-29=27, Resulting Numbers: [3, 25, 27] Generated Node #0,2: 68:[3, 25, 27] Operation: 56-29=27 Exploring Operation: 25+56=81, Resulting Numbers: [3, 29, 81] Generated Node #0,3: 68:[3, 29, 81] Operation: 25+56=81 Exploring Operation: 29-25=4, Resulting Numbers: [3, 56, 4] Generated Node #0,4: 68:[3, 56, 4] Operation: 29-25=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[3, 29, 31], Operations: ['56-25=31'] Exploring Operation: 3+29=32, Resulting Numbers: [31, 32] Generated Node #0,1,0: 68:[31, 32] Operation: 3+29=32 Exploring Operation: 29-3=26, Resulting Numbers: [31, 26] Generated Node #0,1,1: 68:[31, 26] Operation: 29-3=26 Exploring Operation: 29+31=60, Resulting Numbers: [3, 60] Generated Node #0,1,2: 68:[3, 60] Operation: 29+31=60 Exploring Operation: 31-29=2, Resulting Numbers: [3, 2] Generated Node #0,1,3: 68:[3, 2] Operation: 31-29=2 Exploring Operation: 3+31=34, Resulting Numbers: [29, 34] Generated Node #0,1,4: 68:[29, 34] Operation: 3+31=34 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 68:[3, 2], Operations: ['56-25=31', '31-29=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,68 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,68 unequal: No Solution No 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: 68:[31, 32], Operations: ['56-25=31', '3+29=32'] Exploring Operation: 31*32=992, Resulting Numbers: [992] 992,68 unequal: No Solution Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,68 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 68:[29, 34], Operations: ['56-25=31', '3+31=34'] Exploring Operation: 29+34=63, Resulting Numbers: [63] 63,68 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 29*34=986, Resulting Numbers: [986] 986,68 unequal: No Solution No 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: 68:[3, 60], Operations: ['56-25=31', '29+31=60'] Exploring Operation: 3*60=180, Resulting Numbers: [180] 180,68 unequal: No Solution Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,68 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,68 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,68 unequal: No Solution No 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: 68:[31, 26], Operations: ['56-25=31', '29-3=26'] Exploring Operation: 31+26=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 31*26=806, Resulting Numbers: [806] 806,68 unequal: No Solution Exploring Operation: 31-26=5, Resulting Numbers: [5] 5,68 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: 68:[3, 56, 4], Operations: ['29-25=4'] Exploring Operation: 4-3=1, Resulting Numbers: [56, 1] Generated Node #0,4,0: 68:[56, 1] Operation: 4-3=1 Exploring Operation: 56+4=60, Resulting Numbers: [3, 60] Generated Node #0,4,1: 68:[3, 60] Operation: 56+4=60 Exploring Operation: 56-3=53, Resulting Numbers: [4, 53] Generated Node #0,4,2: 68:[4, 53] Operation: 56-3=53 Exploring Operation: 3+56=59, Resulting Numbers: [4, 59] Generated Node #0,4,3: 68:[4, 59] Operation: 3+56=59 Exploring Operation: 56/4=14, Resulting Numbers: [3, 14] Generated Node #0,4,4: 68:[3, 14] Operation: 56/4=14 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 68:[3, 14], Operations: ['29-25=4', '56/4=14'] Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,68 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,68 unequal: No Solution No 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: 68:[3, 60], Operations: ['29-25=4', '56+4=60'] Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,68 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,68 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 3*60=180, Resulting Numbers: [180] 180,68 unequal: No Solution No 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: 68:[4, 59], Operations: ['29-25=4', '3+56=59'] Exploring Operation: 4+59=63, Resulting Numbers: [63] 63,68 unequal: No Solution Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,68 unequal: No Solution Exploring Operation: 4*59=236, Resulting Numbers: [236] 236,68 unequal: No Solution No 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: 68:[56, 1], Operations: ['29-25=4', '4-3=1'] Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,68 unequal: No Solution Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,68 unequal: No Solution Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,68 unequal: No Solution No 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: 68:[4, 53], Operations: ['29-25=4', '56-3=53'] Exploring Operation: 4*53=212, Resulting Numbers: [212] 212,68 unequal: No Solution Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,68 unequal: No Solution Exploring Operation: 4+53=57, Resulting Numbers: [57] 57,68 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: 68:[3, 25, 27], Operations: ['56-29=27'] Exploring Operation: 25-3=22, Resulting Numbers: [27, 22] Generated Node #0,2,0: 68:[27, 22] Operation: 25-3=22 Exploring Operation: 27-25=2, Resulting Numbers: [3, 2] Generated Node #0,2,1: 68:[3, 2] Operation: 27-25=2 Exploring Operation: 3+25=28, Resulting Numbers: [27, 28] Generated Node #0,2,2: 68:[27, 28] Operation: 3+25=28 Exploring Operation: 27/3=9, Resulting Numbers: [25, 9] Generated Node #0,2,3: 68:[25, 9] Operation: 27/3=9 Exploring Operation: 3+27=30, Resulting Numbers: [25, 30] Generated Node #0,2,4: 68:[25, 30] Operation: 3+27=30 Moving to Node #0,2,1 Current State: 68:[3, 2], Operations: ['56-29=27', '27-25=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,68 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,68 unequal: No Solution Moving to Node #0,2,4 Current State: 68:[25, 30], Operations: ['56-29=27', '3+27=30'] Exploring Operation: 25+30=55, Resulting Numbers: [55] 55,68 unequal: No Solution Exploring Operation: 30-25=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 25*30=750, Resulting Numbers: [750] 750,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[27, 22], Operations: ['56-29=27', '25-3=22'] Exploring Operation: 27-22=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 27+22=49, Resulting Numbers: [49] 49,68 unequal: No Solution Exploring Operation: 27*22=594, Resulting Numbers: [594] 594,68 unequal: No Solution Moving to Node #0,2,2 Current State: 68:[27, 28], Operations: ['56-29=27', '3+25=28'] Exploring Operation: 27*28=756, Resulting Numbers: [756] 756,68 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,68 unequal: No Solution Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,68 unequal: No Solution Moving to Node #0,2,3 Current State: 68:[25, 9], Operations: ['56-29=27', '27/3=9'] Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,68 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,68 unequal: No Solution Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 68:[3, 29, 81], Operations: ['25+56=81'] Exploring Operation: 3+29=32, Resulting Numbers: [81, 32] Generated Node #0,3,0: 68:[81, 32] Operation: 3+29=32 Exploring Operation: 81-3=78, Resulting Numbers: [29, 78] Generated Node #0,3,1: 68:[29, 78] Operation: 81-3=78 Exploring Operation: 81-29=52, Resulting Numbers: [3, 52] Generated Node #0,3,2: 68:[3, 52] Operation: 81-29=52 Exploring Operation: 29-3=26, Resulting Numbers: [81, 26] Generated Node #0,3,3: 68:[81, 26] Operation: 29-3=26 Exploring Operation: 81/3=27, Resulting Numbers: [29, 27] Generated Node #0,3,4: 68:[29, 27] Operation: 81/3=27 Moving to Node #0,3,4 Current State: 68:[29, 27], Operations: ['25+56=81', '81/3=27'] Exploring Operation: 29+27=56, Resulting Numbers: [56] 56,68 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 29*27=783, Resulting Numbers: [783] 783,68 unequal: No Solution Moving to Node #0,3,1 Current State: 68:[29, 78], Operations: ['25+56=81', '81-3=78'] Exploring Operation: 29+78=107, Resulting Numbers: [107] 107,68 unequal: No Solution Exploring Operation: 29*78=2262, Resulting Numbers: [2262] 2262,68 unequal: No Solution Exploring Operation: 78-29=49, Resulting Numbers: [49] 49,68 unequal: No Solution Moving to Node #0,3,0 Current State: 68:[81, 32], Operations: ['25+56=81', '3+29=32'] Exploring Operation: 81*32=2592, Resulting Numbers: [2592] 2592,68 unequal: No Solution Exploring Operation: 81+32=113, Resulting Numbers: [113] 113,68 unequal: No Solution Exploring Operation: 81-32=49, Resulting Numbers: [49] 49,68 unequal: No Solution Moving to Node #0,3,2 Current State: 68:[3, 52], Operations: ['25+56=81', '81-29=52'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,68 unequal: No Solution Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,68 unequal: No Solution Exploring Operation: 3*52=156, Resulting Numbers: [156] 156,68 unequal: No Solution Moving to Node #0,3,3 Current State: 68:[81, 26], Operations: ['25+56=81', '29-3=26'] Exploring Operation: 81+26=107, Resulting Numbers: [107] 107,68 unequal: No Solution Exploring Operation: 81*26=2106, Resulting Numbers: [2106] 2106,68 unequal: No Solution Exploring Operation: 81-26=55, Resulting Numbers: [55] 55,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[29, 56, 22], Operations: ['25-3=22'] Exploring Operation: 29+56=85, Resulting Numbers: [22, 85] Generated Node #0,0,0: 68:[22, 85] Operation: 29+56=85 Exploring Operation: 29-22=7, Resulting Numbers: [56, 7] Generated Node #0,0,1: 68:[56, 7] Operation: 29-22=7 Exploring Operation: 56+22=78, Resulting Numbers: [29, 78] Generated Node #0,0,2: 68:[29, 78] Operation: 56+22=78 Exploring Operation: 56-29=27, Resulting Numbers: [22, 27] Generated Node #0,0,3: 68:[22, 27] Operation: 56-29=27 Exploring Operation: 56-22=34, Resulting Numbers: [29, 34] Generated Node #0,0,4: 68:[29, 34] Operation: 56-22=34 Moving to Node #0,0,4 Current State: 68:[29, 34], Operations: ['25-3=22', '56-22=34'] Exploring Operation: 29+34=63, Resulting Numbers: [63] 63,68 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 29*34=986, Resulting Numbers: [986] 986,68 unequal: No Solution Moving to Node #0,0,3 Current State: 68:[22, 27], Operations: ['25-3=22', '56-29=27'] Exploring Operation: 27-22=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 22+27=49, Resulting Numbers: [49] 49,68 unequal: No Solution Exploring Operation: 22*27=594, Resulting Numbers: [594] 594,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[56, 7], Operations: ['25-3=22', '29-22=7'] Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,68 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,68 unequal: No Solution Exploring Operation: 56*7=392, Resulting Numbers: [392] 392,68 unequal: No Solution Exploring Operation: 56+7=63, Resulting Numbers: [63] 63,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[29, 78], Operations: ['25-3=22', '56+22=78'] Exploring Operation: 29+78=107, Resulting Numbers: [107] 107,68 unequal: No Solution Exploring Operation: 29*78=2262, Resulting Numbers: [2262] 2262,68 unequal: No Solution Exploring Operation: 78-29=49, Resulting Numbers: [49] 49,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[22, 85], Operations: ['25-3=22', '29+56=85'] Exploring Operation: 22*85=1870, Resulting Numbers: [1870] 1870,68 unequal: No Solution Exploring Operation: 85-22=63, Resulting Numbers: [63] 63,68 unequal: No Solution Exploring Operation: 22+85=107, Resulting Numbers: [107] 107,68 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
[ 96, 95, 91, 78 ]
72
[ "96-78=18", "95-91=4", "18*4=72" ]
Current State: 72:[96, 95, 91, 78], Operations: [] Exploring Operation: 96-78=18, Resulting Numbers: [95, 91, 18] Generated Node #2: [95, 91, 18] from Operation: 96-78=18 Current State: 72:[95, 91, 18], Operations: ['96-78=18'] Exploring Operation: 95-91=4, Resulting Numbers: [18, 4] Generated Node #3: [18, 4] from Operation: 95-91=4 Current State: 72:[18, 4], Operations: ['96-78=18', '95-91=4'] Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[96, 95, 91, 78], Operations: [] Exploring Operation: 96-95=1, Resulting Numbers: [91, 78, 1] Generated Node #0,0: 72:[91, 78, 1] Operation: 96-95=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[91, 78, 1], Operations: ['96-95=1'] Exploring Operation: 91-78=13, Resulting Numbers: [1, 13] Generated Node #0,0,0: 72:[1, 13] Operation: 91-78=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[1, 13], Operations: ['96-95=1', '91-78=13'] Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 15, 14, 75, 11 ]
81
[ "75/15=5", "14*5=70", "11+70=81" ]
Current State: 81:[15, 14, 75, 11], Operations: [] Exploring Operation: 75/15=5, Resulting Numbers: [14, 11, 5] Generated Node #2: [14, 11, 5] from Operation: 75/15=5 Current State: 81:[14, 11, 5], Operations: ['75/15=5'] Exploring Operation: 14*5=70, Resulting Numbers: [11, 70] Generated Node #3: [11, 70] from Operation: 14*5=70 Current State: 81:[11, 70], Operations: ['75/15=5', '14*5=70'] Exploring Operation: 11+70=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[15, 14, 75, 11], Operations: [] Exploring Operation: 15+14=29, Resulting Numbers: [75, 11, 29] Generated Node #0,0: 81:[75, 11, 29] Operation: 15+14=29 Exploring Operation: 15-14=1, Resulting Numbers: [75, 11, 1] Generated Node #0,1: 81:[75, 11, 1] Operation: 15-14=1 Exploring Operation: 75/15=5, Resulting Numbers: [14, 11, 5] Generated Node #0,2: 81:[14, 11, 5] Operation: 75/15=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[14, 11, 5], Operations: ['75/15=5'] Exploring Operation: 14-11=3, Resulting Numbers: [5, 3] Generated Node #0,2,0: 81:[5, 3] Operation: 14-11=3 Exploring Operation: 14-5=9, Resulting Numbers: [11, 9] Generated Node #0,2,1: 81:[11, 9] Operation: 14-5=9 Exploring Operation: 14+11=25, Resulting Numbers: [5, 25] Generated Node #0,2,2: 81:[5, 25] Operation: 14+11=25 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 81:[5, 3], Operations: ['75/15=5', '14-11=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,81 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,81 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,81 unequal: No Solution No 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: 81:[11, 9], Operations: ['75/15=5', '14-5=9'] Exploring Operation: 11*9=99, Resulting Numbers: [99] 99,81 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,81 unequal: No Solution Exploring Operation: 11+9=20, Resulting Numbers: [20] 20,81 unequal: No Solution No 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: 81:[5, 25], Operations: ['75/15=5', '14+11=25'] Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,81 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,81 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: 81:[75, 11, 29], Operations: ['15+14=29'] Exploring Operation: 75+11=86, Resulting Numbers: [29, 86] Generated Node #0,0,0: 81:[29, 86] Operation: 75+11=86 Exploring Operation: 75-11=64, Resulting Numbers: [29, 64] Generated Node #0,0,1: 81:[29, 64] Operation: 75-11=64 Exploring Operation: 29-11=18, Resulting Numbers: [75, 18] Generated Node #0,0,2: 81:[75, 18] Operation: 29-11=18 Moving to Node #0,0,0 Current State: 81:[29, 86], Operations: ['15+14=29', '75+11=86'] Exploring Operation: 29+86=115, Resulting Numbers: [115] 115,81 unequal: No Solution Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,81 unequal: No Solution Exploring Operation: 29*86=2494, Resulting Numbers: [2494] 2494,81 unequal: No Solution Moving to Node #0,0,2 Current State: 81:[75, 18], Operations: ['15+14=29', '29-11=18'] Exploring Operation: 75*18=1350, Resulting Numbers: [1350] 1350,81 unequal: No Solution Exploring Operation: 75-18=57, Resulting Numbers: [57] 57,81 unequal: No Solution Exploring Operation: 75+18=93, Resulting Numbers: [93] 93,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[29, 64], Operations: ['15+14=29', '75-11=64'] Exploring Operation: 64-29=35, Resulting Numbers: [35] 35,81 unequal: No Solution Exploring Operation: 29+64=93, Resulting Numbers: [93] 93,81 unequal: No Solution Exploring Operation: 29*64=1856, Resulting Numbers: [1856] 1856,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[75, 11, 1], Operations: ['15-14=1'] Exploring Operation: 11-1=10, Resulting Numbers: [75, 10] Generated Node #0,1,0: 81:[75, 10] Operation: 11-1=10 Exploring Operation: 75+1=76, Resulting Numbers: [11, 76] Generated Node #0,1,1: 81:[11, 76] Operation: 75+1=76 Exploring Operation: 75+11=86, Resulting Numbers: [1, 86] Generated Node #0,1,2: 81:[1, 86] Operation: 75+11=86 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 81:[75, 10], Operations: ['15-14=1', '11-1=10'] Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 75+10=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 75*10=750, Resulting Numbers: [750] 750,81 unequal: No Solution No 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: 81:[11, 76], Operations: ['15-14=1', '75+1=76'] Exploring Operation: 11+76=87, Resulting Numbers: [87] 87,81 unequal: No Solution Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 11*76=836, Resulting Numbers: [836] 836,81 unequal: No Solution No 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: 81:[1, 86], Operations: ['15-14=1', '75+11=86'] Exploring Operation: 86/1=86, Resulting Numbers: [86] 86,81 unequal: No Solution Exploring Operation: 86-1=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 1*86=86, Resulting Numbers: [86] 86,81 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
[ 13, 31, 11, 74 ]
100
[ "13*11=143", "74-31=43", "143-43=100" ]
Current State: 100:[13, 31, 11, 74], Operations: [] Exploring Operation: 13*11=143, Resulting Numbers: [31, 74, 143] Generated Node #2: [31, 74, 143] from Operation: 13*11=143 Current State: 100:[31, 74, 143], Operations: ['13*11=143'] Exploring Operation: 74-31=43, Resulting Numbers: [143, 43] Generated Node #3: [143, 43] from Operation: 74-31=43 Current State: 100:[143, 43], Operations: ['13*11=143', '74-31=43'] Exploring Operation: 143-43=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[13, 31, 11, 74], Operations: [] Exploring Operation: 31+74=105, Resulting Numbers: [13, 11, 105] Generated Node #0,0: 100:[13, 11, 105] Operation: 31+74=105 Exploring Operation: 74-31=43, Resulting Numbers: [13, 11, 43] Generated Node #0,1: 100:[13, 11, 43] Operation: 74-31=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[13, 11, 105], Operations: ['31+74=105'] Exploring Operation: 13+11=24, Resulting Numbers: [105, 24] Generated Node #0,0,0: 100:[105, 24] Operation: 13+11=24 Exploring Operation: 13-11=2, Resulting Numbers: [105, 2] Generated Node #0,0,1: 100:[105, 2] Operation: 13-11=2 Moving to Node #0,0,1 Current State: 100:[105, 2], Operations: ['31+74=105', '13-11=2'] Exploring Operation: 105-2=103, Resulting Numbers: [103] 103,100 unequal: No Solution Exploring Operation: 105+2=107, Resulting Numbers: [107] 107,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[105, 24], Operations: ['31+74=105', '13+11=24'] Exploring Operation: 105-24=81, Resulting Numbers: [81] 81,100 unequal: No Solution Exploring Operation: 105+24=129, Resulting Numbers: [129] 129,100 unequal: No Solution No 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: 100:[13, 11, 43], Operations: ['74-31=43'] Exploring Operation: 43-13=30, Resulting Numbers: [11, 30] Generated Node #0,1,0: 100:[11, 30] Operation: 43-13=30 Exploring Operation: 13-11=2, Resulting Numbers: [43, 2] Generated Node #0,1,1: 100:[43, 2] Operation: 13-11=2 Moving to Node #0,1,0 Current State: 100:[11, 30], Operations: ['74-31=43', '43-13=30'] Exploring Operation: 11+30=41, Resulting Numbers: [41] 41,100 unequal: No Solution Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[43, 2], Operations: ['74-31=43', '13-11=2'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,100 unequal: No Solution Exploring Operation: 43+2=45, Resulting Numbers: [45] 45,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 6, 97, 68, 83 ]
16
[ "97-83=14", "6*14=84", "84-68=16" ]
Current State: 16:[6, 97, 68, 83], Operations: [] Exploring Operation: 97-83=14, Resulting Numbers: [6, 68, 14] Generated Node #2: [6, 68, 14] from Operation: 97-83=14 Current State: 16:[6, 68, 14], Operations: ['97-83=14'] Exploring Operation: 6*14=84, Resulting Numbers: [68, 84] Generated Node #3: [68, 84] from Operation: 6*14=84 Current State: 16:[68, 84], Operations: ['97-83=14', '6*14=84'] Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[6, 97, 68, 83], Operations: [] Exploring Operation: 97-83=14, Resulting Numbers: [6, 68, 14] Generated Node #0,0: 16:[6, 68, 14] Operation: 97-83=14 Exploring Operation: 97-68=29, Resulting Numbers: [6, 83, 29] Generated Node #0,1: 16:[6, 83, 29] Operation: 97-68=29 Exploring Operation: 68-6=62, Resulting Numbers: [97, 83, 62] Generated Node #0,2: 16:[97, 83, 62] Operation: 68-6=62 Exploring Operation: 97-6=91, Resulting Numbers: [68, 83, 91] Generated Node #0,3: 16:[68, 83, 91] Operation: 97-6=91 Exploring Operation: 83-68=15, Resulting Numbers: [6, 97, 15] Generated Node #0,4: 16:[6, 97, 15] Operation: 83-68=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[6, 68, 14], Operations: ['97-83=14'] Exploring Operation: 68-14=54, Resulting Numbers: [6, 54] Generated Node #0,0,0: 16:[6, 54] Operation: 68-14=54 Exploring Operation: 6+68=74, Resulting Numbers: [14, 74] Generated Node #0,0,1: 16:[14, 74] Operation: 6+68=74 Exploring Operation: 6+14=20, Resulting Numbers: [68, 20] Generated Node #0,0,2: 16:[68, 20] Operation: 6+14=20 Exploring Operation: 14-6=8, Resulting Numbers: [68, 8] Generated Node #0,0,3: 16:[68, 8] Operation: 14-6=8 Exploring Operation: 68-6=62, Resulting Numbers: [14, 62] Generated Node #0,0,4: 16:[14, 62] Operation: 68-6=62 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 16:[6, 54], Operations: ['97-83=14', '68-14=54'] Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 6*54=324, Resulting Numbers: [324] 324,16 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 16:[14, 62], Operations: ['97-83=14', '68-6=62'] Exploring Operation: 14*62=868, Resulting Numbers: [868] 868,16 unequal: No Solution Exploring Operation: 62-14=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 14+62=76, Resulting Numbers: [76] 76,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 16:[68, 8], Operations: ['97-83=14', '14-6=8'] Exploring Operation: 68*8=544, Resulting Numbers: [544] 544,16 unequal: No Solution Exploring Operation: 68-8=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 68+8=76, Resulting Numbers: [76] 76,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 16:[68, 20], Operations: ['97-83=14', '6+14=20'] Exploring Operation: 68*20=1360, Resulting Numbers: [1360] 1360,16 unequal: No Solution Exploring Operation: 68+20=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 68-20=48, Resulting Numbers: [48] 48,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 16:[14, 74], Operations: ['97-83=14', '6+68=74'] Exploring Operation: 74-14=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 14*74=1036, Resulting Numbers: [1036] 1036,16 unequal: No Solution Exploring Operation: 14+74=88, Resulting Numbers: [88] 88,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[6, 83, 29], Operations: ['97-68=29'] Exploring Operation: 83-29=54, Resulting Numbers: [6, 54] Generated Node #0,1,0: 16:[6, 54] Operation: 83-29=54 Exploring Operation: 6+29=35, Resulting Numbers: [83, 35] Generated Node #0,1,1: 16:[83, 35] Operation: 6+29=35 Exploring Operation: 29-6=23, Resulting Numbers: [83, 23] Generated Node #0,1,2: 16:[83, 23] Operation: 29-6=23 Exploring Operation: 6+83=89, Resulting Numbers: [29, 89] Generated Node #0,1,3: 16:[29, 89] Operation: 6+83=89 Exploring Operation: 83-6=77, Resulting Numbers: [29, 77] Generated Node #0,1,4: 16:[29, 77] Operation: 83-6=77 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[6, 54], Operations: ['97-68=29', '83-29=54'] Exploring Operation: 6*54=324, Resulting Numbers: [324] 324,16 unequal: No Solution Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 16:[83, 23], Operations: ['97-68=29', '29-6=23'] Exploring Operation: 83-23=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 83+23=106, Resulting Numbers: [106] 106,16 unequal: No Solution Exploring Operation: 83*23=1909, Resulting Numbers: [1909] 1909,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 16:[29, 77], Operations: ['97-68=29', '83-6=77'] Exploring Operation: 29+77=106, Resulting Numbers: [106] 106,16 unequal: No Solution Exploring Operation: 77-29=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 29*77=2233, Resulting Numbers: [2233] 2233,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[83, 35], Operations: ['97-68=29', '6+29=35'] Exploring Operation: 83*35=2905, Resulting Numbers: [2905] 2905,16 unequal: No Solution Exploring Operation: 83+35=118, Resulting Numbers: [118] 118,16 unequal: No Solution Exploring Operation: 83-35=48, Resulting Numbers: [48] 48,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 16:[29, 89], Operations: ['97-68=29', '6+83=89'] Exploring Operation: 29*89=2581, Resulting Numbers: [2581] 2581,16 unequal: No Solution Exploring Operation: 29+89=118, Resulting Numbers: [118] 118,16 unequal: No Solution Exploring Operation: 89-29=60, Resulting Numbers: [60] 60,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 16:[6, 97, 15], Operations: ['83-68=15'] Exploring Operation: 15-6=9, Resulting Numbers: [97, 9] Generated Node #0,4,0: 16:[97, 9] Operation: 15-6=9 Exploring Operation: 6+97=103, Resulting Numbers: [15, 103] Generated Node #0,4,1: 16:[15, 103] Operation: 6+97=103 Exploring Operation: 97-6=91, Resulting Numbers: [15, 91] Generated Node #0,4,2: 16:[15, 91] Operation: 97-6=91 Exploring Operation: 6+15=21, Resulting Numbers: [97, 21] Generated Node #0,4,3: 16:[97, 21] Operation: 6+15=21 Exploring Operation: 97-15=82, Resulting Numbers: [6, 82] Generated Node #0,4,4: 16:[6, 82] Operation: 97-15=82 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 16:[6, 82], Operations: ['83-68=15', '97-15=82'] Exploring Operation: 6+82=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 82-6=76, Resulting Numbers: [76] 76,16 unequal: No Solution Exploring Operation: 6*82=492, Resulting Numbers: [492] 492,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 16:[15, 91], Operations: ['83-68=15', '97-6=91'] Exploring Operation: 15+91=106, Resulting Numbers: [106] 106,16 unequal: No Solution Exploring Operation: 91-15=76, Resulting Numbers: [76] 76,16 unequal: No Solution Exploring Operation: 15*91=1365, Resulting Numbers: [1365] 1365,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 16:[97, 9], Operations: ['83-68=15', '15-6=9'] Exploring Operation: 97*9=873, Resulting Numbers: [873] 873,16 unequal: No Solution Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 97+9=106, Resulting Numbers: [106] 106,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 16:[97, 21], Operations: ['83-68=15', '6+15=21'] Exploring Operation: 97-21=76, Resulting Numbers: [76] 76,16 unequal: No Solution Exploring Operation: 97*21=2037, Resulting Numbers: [2037] 2037,16 unequal: No Solution Exploring Operation: 97+21=118, Resulting Numbers: [118] 118,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 16:[15, 103], Operations: ['83-68=15', '6+97=103'] Exploring Operation: 15+103=118, Resulting Numbers: [118] 118,16 unequal: No Solution Exploring Operation: 15*103=1545, Resulting Numbers: [1545] 1545,16 unequal: No Solution Exploring Operation: 103-15=88, Resulting Numbers: [88] 88,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[97, 83, 62], Operations: ['68-6=62'] Exploring Operation: 83-62=21, Resulting Numbers: [97, 21] Generated Node #0,2,0: 16:[97, 21] Operation: 83-62=21 Exploring Operation: 97+83=180, Resulting Numbers: [62, 180] Generated Node #0,2,1: 16:[62, 180] Operation: 97+83=180 Exploring Operation: 97-62=35, Resulting Numbers: [83, 35] Generated Node #0,2,2: 16:[83, 35] Operation: 97-62=35 Exploring Operation: 97-83=14, Resulting Numbers: [62, 14] Generated Node #0,2,3: 16:[62, 14] Operation: 97-83=14 Exploring Operation: 97+62=159, Resulting Numbers: [83, 159] Generated Node #0,2,4: 16:[83, 159] Operation: 97+62=159 Moving to Node #0,2,3 Current State: 16:[62, 14], Operations: ['68-6=62', '97-83=14'] Exploring Operation: 62*14=868, Resulting Numbers: [868] 868,16 unequal: No Solution Exploring Operation: 62-14=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 62+14=76, Resulting Numbers: [76] 76,16 unequal: No Solution Moving to Node #0,2,2 Current State: 16:[83, 35], Operations: ['68-6=62', '97-62=35'] Exploring Operation: 83*35=2905, Resulting Numbers: [2905] 2905,16 unequal: No Solution Exploring Operation: 83+35=118, Resulting Numbers: [118] 118,16 unequal: No Solution Exploring Operation: 83-35=48, Resulting Numbers: [48] 48,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[97, 21], Operations: ['68-6=62', '83-62=21'] Exploring Operation: 97+21=118, Resulting Numbers: [118] 118,16 unequal: No Solution Exploring Operation: 97*21=2037, Resulting Numbers: [2037] 2037,16 unequal: No Solution Exploring Operation: 97-21=76, Resulting Numbers: [76] 76,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[62, 180], Operations: ['68-6=62', '97+83=180'] Exploring Operation: 180-62=118, Resulting Numbers: [118] 118,16 unequal: No Solution Exploring Operation: 62+180=242, Resulting Numbers: [242] 242,16 unequal: No Solution Exploring Operation: 62*180=11160, Resulting Numbers: [11160] 11160,16 unequal: No Solution Moving to Node #0,2,4 Current State: 16:[83, 159], Operations: ['68-6=62', '97+62=159'] Exploring Operation: 83*159=13197, Resulting Numbers: [13197] 13197,16 unequal: No Solution Exploring Operation: 159-83=76, Resulting Numbers: [76] 76,16 unequal: No Solution Exploring Operation: 83+159=242, Resulting Numbers: [242] 242,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 16:[68, 83, 91], Operations: ['97-6=91'] Exploring Operation: 68+91=159, Resulting Numbers: [83, 159] Generated Node #0,3,0: 16:[83, 159] Operation: 68+91=159 Exploring Operation: 68+83=151, Resulting Numbers: [91, 151] Generated Node #0,3,1: 16:[91, 151] Operation: 68+83=151 Exploring Operation: 83-68=15, Resulting Numbers: [91, 15] Generated Node #0,3,2: 16:[91, 15] Operation: 83-68=15 Exploring Operation: 91-68=23, Resulting Numbers: [83, 23] Generated Node #0,3,3: 16:[83, 23] Operation: 91-68=23 Exploring Operation: 91-83=8, Resulting Numbers: [68, 8] Generated Node #0,3,4: 16:[68, 8] Operation: 91-83=8 Moving to Node #0,3,4 Current State: 16:[68, 8], Operations: ['97-6=91', '91-83=8'] Exploring Operation: 68+8=76, Resulting Numbers: [76] 76,16 unequal: No Solution Exploring Operation: 68*8=544, Resulting Numbers: [544] 544,16 unequal: No Solution Exploring Operation: 68-8=60, Resulting Numbers: [60] 60,16 unequal: No Solution Moving to Node #0,3,3 Current State: 16:[83, 23], Operations: ['97-6=91', '91-68=23'] Exploring Operation: 83*23=1909, Resulting Numbers: [1909] 1909,16 unequal: No Solution Exploring Operation: 83+23=106, Resulting Numbers: [106] 106,16 unequal: No Solution Exploring Operation: 83-23=60, Resulting Numbers: [60] 60,16 unequal: No Solution Moving to Node #0,3,2 Current State: 16:[91, 15], Operations: ['97-6=91', '83-68=15'] Exploring Operation: 91-15=76, Resulting Numbers: [76] 76,16 unequal: No Solution Exploring Operation: 91*15=1365, Resulting Numbers: [1365] 1365,16 unequal: No Solution Exploring Operation: 91+15=106, Resulting Numbers: [106] 106,16 unequal: No Solution Moving to Node #0,3,0 Current State: 16:[83, 159], Operations: ['97-6=91', '68+91=159'] Exploring Operation: 159-83=76, Resulting Numbers: [76] 76,16 unequal: No Solution Exploring Operation: 83*159=13197, Resulting Numbers: [13197] 13197,16 unequal: No Solution Exploring Operation: 83+159=242, Resulting Numbers: [242] 242,16 unequal: No Solution Moving to Node #0,3,1 Current State: 16:[91, 151], Operations: ['97-6=91', '68+83=151'] Exploring Operation: 91*151=13741, Resulting Numbers: [13741] 13741,16 unequal: No Solution Exploring Operation: 91+151=242, Resulting Numbers: [242] 242,16 unequal: No Solution Exploring Operation: 151-91=60, Resulting Numbers: [60] 60,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 49, 7, 36, 70 ]
90
[ "49+7=56", "70-36=34", "56+34=90" ]
Current State: 90:[49, 7, 36, 70], Operations: [] Exploring Operation: 49+7=56, Resulting Numbers: [36, 70, 56] Generated Node #2: [36, 70, 56] from Operation: 49+7=56 Current State: 90:[36, 70, 56], Operations: ['49+7=56'] Exploring Operation: 70-36=34, Resulting Numbers: [56, 34] Generated Node #3: [56, 34] from Operation: 70-36=34 Current State: 90:[56, 34], Operations: ['49+7=56', '70-36=34'] Exploring Operation: 56+34=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[49, 7, 36, 70], Operations: [] Exploring Operation: 70-36=34, Resulting Numbers: [49, 7, 34] Generated Node #0,0: 90:[49, 7, 34] Operation: 70-36=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[49, 7, 34], Operations: ['70-36=34'] Exploring Operation: 49-34=15, Resulting Numbers: [7, 15] Generated Node #0,0,0: 90:[7, 15] Operation: 49-34=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[7, 15], Operations: ['70-36=34', '49-34=15'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 89, 25, 15, 92 ]
30
[ "92-89=3", "25-15=10", "3*10=30" ]
Current State: 30:[89, 25, 15, 92], Operations: [] Exploring Operation: 92-89=3, Resulting Numbers: [25, 15, 3] Generated Node #2: [25, 15, 3] from Operation: 92-89=3 Current State: 30:[25, 15, 3], Operations: ['92-89=3'] Exploring Operation: 25-15=10, Resulting Numbers: [3, 10] Generated Node #3: [3, 10] from Operation: 25-15=10 Current State: 30:[3, 10], Operations: ['92-89=3', '25-15=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[89, 25, 15, 92], Operations: [] Exploring Operation: 92-25=67, Resulting Numbers: [89, 15, 67] Generated Node #0,0: 30:[89, 15, 67] Operation: 92-25=67 Exploring Operation: 89-25=64, Resulting Numbers: [15, 92, 64] Generated Node #0,1: 30:[15, 92, 64] Operation: 89-25=64 Exploring Operation: 92-89=3, Resulting Numbers: [25, 15, 3] Generated Node #0,2: 30:[25, 15, 3] Operation: 92-89=3 Moving to Node #0,2 Current State: 30:[25, 15, 3], Operations: ['92-89=3'] Exploring Operation: 25+3=28, Resulting Numbers: [15, 28] Generated Node #0,2,0: 30:[15, 28] Operation: 25+3=28 Exploring Operation: 15/3=5, Resulting Numbers: [25, 5] Generated Node #0,2,1: 30:[25, 5] Operation: 15/3=5 Exploring Operation: 25-15=10, Resulting Numbers: [3, 10] Generated Node #0,2,2: 30:[3, 10] Operation: 25-15=10 Moving to Node #0,0 Current State: 30:[89, 15, 67], Operations: ['92-25=67'] Exploring Operation: 67-15=52, Resulting Numbers: [89, 52] Generated Node #0,0,0: 30:[89, 52] Operation: 67-15=52 Exploring Operation: 89-67=22, Resulting Numbers: [15, 22] Generated Node #0,0,1: 30:[15, 22] Operation: 89-67=22 Exploring Operation: 89-15=74, Resulting Numbers: [67, 74] Generated Node #0,0,2: 30:[67, 74] Operation: 89-15=74 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[15, 22], Operations: ['92-25=67', '89-67=22'] Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[89, 52], Operations: ['92-25=67', '67-15=52'] Exploring Operation: 89+52=141, Resulting Numbers: [141] 141,30 unequal: No Solution Exploring Operation: 89*52=4628, Resulting Numbers: [4628] 4628,30 unequal: No Solution Exploring Operation: 89-52=37, Resulting Numbers: [37] 37,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 30:[67, 74], Operations: ['92-25=67', '89-15=74'] Exploring Operation: 67*74=4958, Resulting Numbers: [4958] 4958,30 unequal: No Solution Exploring Operation: 67+74=141, Resulting Numbers: [141] 141,30 unequal: No Solution Exploring Operation: 74-67=7, Resulting Numbers: [7] 7,30 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: 30:[15, 92, 64], Operations: ['89-25=64'] Exploring Operation: 92-15=77, Resulting Numbers: [64, 77] Generated Node #0,1,0: 30:[64, 77] Operation: 92-15=77 Exploring Operation: 64-15=49, Resulting Numbers: [92, 49] Generated Node #0,1,1: 30:[92, 49] Operation: 64-15=49 Exploring Operation: 92-64=28, Resulting Numbers: [15, 28] Generated Node #0,1,2: 30:[15, 28] Operation: 92-64=28 Moving to Node #0,2,2 Current State: 30:[3, 10], Operations: ['92-89=3', '25-15=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[89, 25, 15, 92], Operations: [] Exploring Operation: 92-89=3, Resulting Numbers: [25, 15, 3] Generated Node #0,2: 30:[25, 15, 3] Operation: 92-89=3 Moving to Node #0,2 Current State: 30:[25, 15, 3], Operations: ['92-89=3'] Exploring Operation: 25-15=10, Resulting Numbers: [3, 10] Generated Node #0,2,2: 30:[3, 10] Operation: 25-15=10 Moving to Node #0,2,2 Current State: 30:[3, 10], Operations: ['92-89=3', '25-15=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
0.976563
hs_3
mult_heuristic
[ 17, 14, 69, 44 ]
63
[ "17-14=3", "44*3=132", "132-69=63" ]
Current State: 63:[17, 14, 69, 44], Operations: [] Exploring Operation: 17-14=3, Resulting Numbers: [69, 44, 3] Generated Node #2: [69, 44, 3] from Operation: 17-14=3 Current State: 63:[69, 44, 3], Operations: ['17-14=3'] Exploring Operation: 44*3=132, Resulting Numbers: [69, 132] Generated Node #3: [69, 132] from Operation: 44*3=132 Current State: 63:[69, 132], Operations: ['17-14=3', '44*3=132'] Exploring Operation: 132-69=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[17, 14, 69, 44], Operations: [] Exploring Operation: 69-44=25, Resulting Numbers: [17, 14, 25] Generated Node #0,0: 63:[17, 14, 25] Operation: 69-44=25 Exploring Operation: 44-17=27, Resulting Numbers: [14, 69, 27] Generated Node #0,1: 63:[14, 69, 27] Operation: 44-17=27 Exploring Operation: 14+44=58, Resulting Numbers: [17, 69, 58] Generated Node #0,2: 63:[17, 69, 58] Operation: 14+44=58 Exploring Operation: 17+44=61, Resulting Numbers: [14, 69, 61] Generated Node #0,3: 63:[14, 69, 61] Operation: 17+44=61 Moving to Node #0,0 Current State: 63:[17, 14, 25], Operations: ['69-44=25'] Exploring Operation: 17+14=31, Resulting Numbers: [25, 31] Generated Node #0,0,0: 63:[25, 31] Operation: 17+14=31 Exploring Operation: 25-14=11, Resulting Numbers: [17, 11] Generated Node #0,0,1: 63:[17, 11] Operation: 25-14=11 Exploring Operation: 25-17=8, Resulting Numbers: [14, 8] Generated Node #0,0,2: 63:[14, 8] Operation: 25-17=8 Exploring Operation: 17-14=3, Resulting Numbers: [25, 3] Generated Node #0,0,3: 63:[25, 3] Operation: 17-14=3 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 63:[25, 3], Operations: ['69-44=25', '17-14=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,63 unequal: No Solution Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,63 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,63 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 #0,0,1 Current State: 63:[17, 11], Operations: ['69-44=25', '25-14=11'] Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 17*11=187, Resulting Numbers: [187] 187,63 unequal: No Solution Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,63 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 #0,0,2 Current State: 63:[14, 8], Operations: ['69-44=25', '25-17=8'] Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,63 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 #0,0,0 Current State: 63:[25, 31], Operations: ['69-44=25', '17+14=31'] Exploring Operation: 25+31=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 25*31=775, Resulting Numbers: [775] 775,63 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: 63:[14, 69, 61], Operations: ['17+44=61'] Exploring Operation: 14+69=83, Resulting Numbers: [61, 83] Generated Node #0,3,0: 63:[61, 83] Operation: 14+69=83 Exploring Operation: 14+61=75, Resulting Numbers: [69, 75] Generated Node #0,3,1: 63:[69, 75] Operation: 14+61=75 Exploring Operation: 69-14=55, Resulting Numbers: [61, 55] Generated Node #0,3,2: 63:[61, 55] Operation: 69-14=55 Exploring Operation: 69-61=8, Resulting Numbers: [14, 8] Generated Node #0,3,3: 63:[14, 8] Operation: 69-61=8 Moving to Node #0,2 Current State: 63:[17, 69, 58], Operations: ['14+44=58'] Exploring Operation: 69-17=52, Resulting Numbers: [58, 52] Generated Node #0,2,0: 63:[58, 52] Operation: 69-17=52 Exploring Operation: 58-17=41, Resulting Numbers: [69, 41] Generated Node #0,2,1: 63:[69, 41] Operation: 58-17=41 Exploring Operation: 17+58=75, Resulting Numbers: [69, 75] Generated Node #0,2,2: 63:[69, 75] Operation: 17+58=75 Exploring Operation: 69-58=11, Resulting Numbers: [17, 11] Generated Node #0,2,3: 63:[17, 11] Operation: 69-58=11 Moving to Node #0,1 Current State: 63:[14, 69, 27], Operations: ['44-17=27'] Exploring Operation: 69-14=55, Resulting Numbers: [27, 55] Generated Node #0,1,0: 63:[27, 55] Operation: 69-14=55 Exploring Operation: 14+69=83, Resulting Numbers: [27, 83] Generated Node #0,1,1: 63:[27, 83] Operation: 14+69=83 Exploring Operation: 14+27=41, Resulting Numbers: [69, 41] Generated Node #0,1,2: 63:[69, 41] Operation: 14+27=41 Exploring Operation: 27-14=13, Resulting Numbers: [69, 13] Generated Node #0,1,3: 63:[69, 13] Operation: 27-14=13 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 63:[69, 13], Operations: ['44-17=27', '27-14=13'] Exploring Operation: 69*13=897, Resulting Numbers: [897] 897,63 unequal: No Solution Exploring Operation: 69+13=82, Resulting Numbers: [82] 82,63 unequal: No Solution Exploring Operation: 69-13=56, Resulting Numbers: [56] 56,63 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 #0,1,0 Current State: 63:[27, 55], Operations: ['44-17=27', '69-14=55'] Exploring Operation: 27*55=1485, Resulting Numbers: [1485] 1485,63 unequal: No Solution Exploring Operation: 55-27=28, Resulting Numbers: [28] 28,63 unequal: No Solution Exploring Operation: 27+55=82, Resulting Numbers: [82] 82,63 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 #0,1,1 Current State: 63:[27, 83], Operations: ['44-17=27', '14+69=83'] Exploring Operation: 27+83=110, Resulting Numbers: [110] 110,63 unequal: No Solution Exploring Operation: 83-27=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 27*83=2241, Resulting Numbers: [2241] 2241,63 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 #0,1,2 Current State: 63:[69, 41], Operations: ['44-17=27', '14+27=41'] Exploring Operation: 69-41=28, Resulting Numbers: [28] 28,63 unequal: No Solution Exploring Operation: 69*41=2829, Resulting Numbers: [2829] 2829,63 unequal: No Solution Exploring Operation: 69+41=110, Resulting Numbers: [110] 110,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,3 Current State: 63:[14, 8], Operations: ['17+44=61', '69-61=8'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,63 unequal: No Solution Moving to Node #0,2,3 Current State: 63:[17, 11], Operations: ['14+44=58', '69-58=11'] Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,63 unequal: No Solution Exploring Operation: 17*11=187, Resulting Numbers: [187] 187,63 unequal: No Solution Moving to Node #0,3,2 Current State: 63:[61, 55], Operations: ['17+44=61', '69-14=55'] Exploring Operation: 61*55=3355, Resulting Numbers: [3355] 3355,63 unequal: No Solution Exploring Operation: 61-55=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 61+55=116, Resulting Numbers: [116] 116,63 unequal: No Solution Moving to Node #0,2,0 Current State: 63:[58, 52], Operations: ['14+44=58', '69-17=52'] Exploring Operation: 58+52=110, Resulting Numbers: [110] 110,63 unequal: No Solution Exploring Operation: 58-52=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 58*52=3016, Resulting Numbers: [3016] 3016,63 unequal: No Solution Moving to Node #0,3,1 Current State: 63:[69, 75], Operations: ['17+44=61', '14+61=75'] Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 69*75=5175, Resulting Numbers: [5175] 5175,63 unequal: No Solution Exploring Operation: 69+75=144, Resulting Numbers: [144] 144,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[69, 75], Operations: ['14+44=58', '17+58=75'] Exploring Operation: 69*75=5175, Resulting Numbers: [5175] 5175,63 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 69+75=144, Resulting Numbers: [144] 144,63 unequal: No Solution Moving to Node #0,3,0 Current State: 63:[61, 83], Operations: ['17+44=61', '14+69=83'] Exploring Operation: 83-61=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 61+83=144, Resulting Numbers: [144] 144,63 unequal: No Solution Exploring Operation: 61*83=5063, Resulting Numbers: [5063] 5063,63 unequal: No Solution Moving to Node #0,2,1 Current State: 63:[69, 41], Operations: ['14+44=58', '58-17=41'] Exploring Operation: 69-41=28, Resulting Numbers: [28] 28,63 unequal: No Solution Exploring Operation: 69*41=2829, Resulting Numbers: [2829] 2829,63 unequal: No Solution Exploring Operation: 69+41=110, Resulting Numbers: [110] 110,63 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 7, 92, 4, 34 ]
22
[ "92+34=126", "126/7=18", "4+18=22" ]
Current State: 22:[7, 92, 4, 34], Operations: [] Exploring Operation: 92+34=126, Resulting Numbers: [7, 4, 126] Generated Node #2: [7, 4, 126] from Operation: 92+34=126 Current State: 22:[7, 4, 126], Operations: ['92+34=126'] Exploring Operation: 126/7=18, Resulting Numbers: [4, 18] Generated Node #3: [4, 18] from Operation: 126/7=18 Current State: 22:[4, 18], Operations: ['92+34=126', '126/7=18'] Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[7, 92, 4, 34], Operations: [] Exploring Operation: 92-34=58, Resulting Numbers: [7, 4, 58] Generated Node #0,0: 22:[7, 4, 58] Operation: 92-34=58 Exploring Operation: 92/4=23, Resulting Numbers: [7, 34, 23] Generated Node #0,1: 22:[7, 34, 23] Operation: 92/4=23 Moving to Node #0,1 Current State: 22:[7, 34, 23], Operations: ['92/4=23'] Exploring Operation: 34-23=11, Resulting Numbers: [7, 11] Generated Node #0,1,0: 22:[7, 11] Operation: 34-23=11 Exploring Operation: 34-7=27, Resulting Numbers: [23, 27] Generated Node #0,1,1: 22:[23, 27] Operation: 34-7=27 Moving to Node #0,0 Current State: 22:[7, 4, 58], Operations: ['92-34=58'] Exploring Operation: 58-7=51, Resulting Numbers: [4, 51] Generated Node #0,0,0: 22:[4, 51] Operation: 58-7=51 Exploring Operation: 7+4=11, Resulting Numbers: [58, 11] Generated Node #0,0,1: 22:[58, 11] Operation: 7+4=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[4, 51], Operations: ['92-34=58', '58-7=51'] Exploring Operation: 4+51=55, Resulting Numbers: [55] 55,22 unequal: No Solution Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 22:[58, 11], Operations: ['92-34=58', '7+4=11'] Exploring Operation: 58+11=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 22:[7, 11], Operations: ['92/4=23', '34-23=11'] Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[23, 27], Operations: ['92/4=23', '34-7=27'] Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 23+27=50, Resulting Numbers: [50] 50,22 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 48, 29, 35, 84 ]
30
[ "48-29=19", "84-35=49", "49-19=30" ]
Current State: 30:[48, 29, 35, 84], Operations: [] Exploring Operation: 48-29=19, Resulting Numbers: [35, 84, 19] Generated Node #2: [35, 84, 19] from Operation: 48-29=19 Current State: 30:[35, 84, 19], Operations: ['48-29=19'] Exploring Operation: 84-35=49, Resulting Numbers: [19, 49] Generated Node #3: [19, 49] from Operation: 84-35=49 Current State: 30:[19, 49], Operations: ['48-29=19', '84-35=49'] Exploring Operation: 49-19=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[48, 29, 35, 84], Operations: [] Exploring Operation: 84-48=36, Resulting Numbers: [29, 35, 36] Generated Node #0,0: 30:[29, 35, 36] Operation: 84-48=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[29, 35, 36], Operations: ['84-48=36'] Exploring Operation: 36-35=1, Resulting Numbers: [29, 1] Generated Node #0,0,0: 30:[29, 1] Operation: 36-35=1 Moving to Node #0,0,0 Current State: 30:[29, 1], Operations: ['84-48=36', '36-35=1'] Exploring Operation: 29+1=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[48, 29, 35, 84], Operations: [] Exploring Operation: 84-48=36, Resulting Numbers: [29, 35, 36] Generated Node #0,0: 30:[29, 35, 36] Operation: 84-48=36 Moving to Node #0,0 Current State: 30:[29, 35, 36], Operations: ['84-48=36'] Exploring Operation: 36-35=1, Resulting Numbers: [29, 1] Generated Node #0,0,0: 30:[29, 1] Operation: 36-35=1 Moving to Node #0,0,0 Current State: 30:[29, 1], Operations: ['84-48=36', '36-35=1'] Exploring Operation: 29+1=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 2, 16, 31, 83 ]
84
[ "2*16=32", "83-31=52", "32+52=84" ]
Current State: 84:[2, 16, 31, 83], Operations: [] Exploring Operation: 2*16=32, Resulting Numbers: [31, 83, 32] Generated Node #2: [31, 83, 32] from Operation: 2*16=32 Current State: 84:[31, 83, 32], Operations: ['2*16=32'] Exploring Operation: 83-31=52, Resulting Numbers: [32, 52] Generated Node #3: [32, 52] from Operation: 83-31=52 Current State: 84:[32, 52], Operations: ['2*16=32', '83-31=52'] Exploring Operation: 32+52=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[2, 16, 31, 83], Operations: [] Exploring Operation: 2+83=85, Resulting Numbers: [16, 31, 85] Generated Node #0,0: 84:[16, 31, 85] Operation: 2+83=85 Exploring Operation: 16-2=14, Resulting Numbers: [31, 83, 14] Generated Node #0,1: 84:[31, 83, 14] Operation: 16-2=14 Exploring Operation: 31-16=15, Resulting Numbers: [2, 83, 15] Generated Node #0,2: 84:[2, 83, 15] Operation: 31-16=15 Exploring Operation: 31-2=29, Resulting Numbers: [16, 83, 29] Generated Node #0,3: 84:[16, 83, 29] Operation: 31-2=29 Exploring Operation: 16/2=8, Resulting Numbers: [31, 83, 8] Generated Node #0,4: 84:[31, 83, 8] Operation: 16/2=8 Moving to Node #0,2 Current State: 84:[2, 83, 15], Operations: ['31-16=15'] Exploring Operation: 15-2=13, Resulting Numbers: [83, 13] Generated Node #0,2,0: 84:[83, 13] Operation: 15-2=13 Exploring Operation: 2*15=30, Resulting Numbers: [83, 30] Generated Node #0,2,1: 84:[83, 30] Operation: 2*15=30 Exploring Operation: 83-2=81, Resulting Numbers: [15, 81] Generated Node #0,2,2: 84:[15, 81] Operation: 83-2=81 Exploring Operation: 2+83=85, Resulting Numbers: [15, 85] Generated Node #0,2,3: 84:[15, 85] Operation: 2+83=85 Exploring Operation: 2+15=17, Resulting Numbers: [83, 17] Generated Node #0,2,4: 84:[83, 17] Operation: 2+15=17 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[83, 13], Operations: ['31-16=15', '15-2=13'] Exploring Operation: 83+13=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 83*13=1079, Resulting Numbers: [1079] 1079,84 unequal: No Solution Exploring Operation: 83-13=70, Resulting Numbers: [70] 70,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 84:[15, 85], Operations: ['31-16=15', '2+83=85'] Exploring Operation: 15+85=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 85-15=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 15*85=1275, Resulting Numbers: [1275] 1275,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 84:[83, 30], Operations: ['31-16=15', '2*15=30'] Exploring Operation: 83-30=53, Resulting Numbers: [53] 53,84 unequal: No Solution Exploring Operation: 83*30=2490, Resulting Numbers: [2490] 2490,84 unequal: No Solution Exploring Operation: 83+30=113, Resulting Numbers: [113] 113,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 84:[15, 81], Operations: ['31-16=15', '83-2=81'] Exploring Operation: 15*81=1215, Resulting Numbers: [1215] 1215,84 unequal: No Solution Exploring Operation: 15+81=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 81-15=66, Resulting Numbers: [66] 66,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 84:[83, 17], Operations: ['31-16=15', '2+15=17'] Exploring Operation: 83-17=66, Resulting Numbers: [66] 66,84 unequal: No Solution Exploring Operation: 83+17=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 83*17=1411, Resulting Numbers: [1411] 1411,84 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: 84:[16, 83, 29], Operations: ['31-2=29'] Exploring Operation: 16+83=99, Resulting Numbers: [29, 99] Generated Node #0,3,0: 84:[29, 99] Operation: 16+83=99 Exploring Operation: 83-29=54, Resulting Numbers: [16, 54] Generated Node #0,3,1: 84:[16, 54] Operation: 83-29=54 Exploring Operation: 83-16=67, Resulting Numbers: [29, 67] Generated Node #0,3,2: 84:[29, 67] Operation: 83-16=67 Exploring Operation: 29-16=13, Resulting Numbers: [83, 13] Generated Node #0,3,3: 84:[83, 13] Operation: 29-16=13 Exploring Operation: 16+29=45, Resulting Numbers: [83, 45] Generated Node #0,3,4: 84:[83, 45] Operation: 16+29=45 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 84:[83, 13], Operations: ['31-2=29', '29-16=13'] Exploring Operation: 83+13=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 83-13=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 83*13=1079, Resulting Numbers: [1079] 1079,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 84:[83, 45], Operations: ['31-2=29', '16+29=45'] Exploring Operation: 83+45=128, Resulting Numbers: [128] 128,84 unequal: No Solution Exploring Operation: 83-45=38, Resulting Numbers: [38] 38,84 unequal: No Solution Exploring Operation: 83*45=3735, Resulting Numbers: [3735] 3735,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 84:[16, 54], Operations: ['31-2=29', '83-29=54'] Exploring Operation: 16*54=864, Resulting Numbers: [864] 864,84 unequal: No Solution Exploring Operation: 54-16=38, Resulting Numbers: [38] 38,84 unequal: No Solution Exploring Operation: 16+54=70, Resulting Numbers: [70] 70,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 84:[29, 99], Operations: ['31-2=29', '16+83=99'] Exploring Operation: 99-29=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 29+99=128, Resulting Numbers: [128] 128,84 unequal: No Solution Exploring Operation: 29*99=2871, Resulting Numbers: [2871] 2871,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 84:[29, 67], Operations: ['31-2=29', '83-16=67'] Exploring Operation: 29+67=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 29*67=1943, Resulting Numbers: [1943] 1943,84 unequal: No Solution Exploring Operation: 67-29=38, Resulting Numbers: [38] 38,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 84:[31, 83, 14], Operations: ['16-2=14'] Exploring Operation: 83-14=69, Resulting Numbers: [31, 69] Generated Node #0,1,0: 84:[31, 69] Operation: 83-14=69 Exploring Operation: 83-31=52, Resulting Numbers: [14, 52] Generated Node #0,1,1: 84:[14, 52] Operation: 83-31=52 Exploring Operation: 31+14=45, Resulting Numbers: [83, 45] Generated Node #0,1,2: 84:[83, 45] Operation: 31+14=45 Exploring Operation: 31-14=17, Resulting Numbers: [83, 17] Generated Node #0,1,3: 84:[83, 17] Operation: 31-14=17 Exploring Operation: 83+14=97, Resulting Numbers: [31, 97] Generated Node #0,1,4: 84:[31, 97] Operation: 83+14=97 Moving to Node #0,4 Current State: 84:[31, 83, 8], Operations: ['16/2=8'] Exploring Operation: 83+8=91, Resulting Numbers: [31, 91] Generated Node #0,4,0: 84:[31, 91] Operation: 83+8=91 Exploring Operation: 83-31=52, Resulting Numbers: [8, 52] Generated Node #0,4,1: 84:[8, 52] Operation: 83-31=52 Exploring Operation: 31+8=39, Resulting Numbers: [83, 39] Generated Node #0,4,2: 84:[83, 39] Operation: 31+8=39 Exploring Operation: 31-8=23, Resulting Numbers: [83, 23] Generated Node #0,4,3: 84:[83, 23] Operation: 31-8=23 Exploring Operation: 83-8=75, Resulting Numbers: [31, 75] Generated Node #0,4,4: 84:[31, 75] Operation: 83-8=75 Moving to Node #0,0 Current State: 84:[16, 31, 85], Operations: ['2+83=85'] Exploring Operation: 31-16=15, Resulting Numbers: [85, 15] Generated Node #0,0,0: 84:[85, 15] Operation: 31-16=15 Exploring Operation: 16+31=47, Resulting Numbers: [85, 47] Generated Node #0,0,1: 84:[85, 47] Operation: 16+31=47 Exploring Operation: 85-31=54, Resulting Numbers: [16, 54] Generated Node #0,0,2: 84:[16, 54] Operation: 85-31=54 Exploring Operation: 85-16=69, Resulting Numbers: [31, 69] Generated Node #0,0,3: 84:[31, 69] Operation: 85-16=69 Exploring Operation: 16+85=101, Resulting Numbers: [31, 101] Generated Node #0,0,4: 84:[31, 101] Operation: 16+85=101 Moving to Node #0,0,0 Current State: 84:[85, 15], Operations: ['2+83=85', '31-16=15'] Exploring Operation: 85*15=1275, Resulting Numbers: [1275] 1275,84 unequal: No Solution Exploring Operation: 85+15=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 85-15=70, Resulting Numbers: [70] 70,84 unequal: No Solution Moving to Node #0,4,3 Current State: 84:[83, 23], Operations: ['16/2=8', '31-8=23'] Exploring Operation: 83+23=106, Resulting Numbers: [106] 106,84 unequal: No Solution Exploring Operation: 83*23=1909, Resulting Numbers: [1909] 1909,84 unequal: No Solution Exploring Operation: 83-23=60, Resulting Numbers: [60] 60,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[83, 45], Operations: ['16-2=14', '31+14=45'] Exploring Operation: 83*45=3735, Resulting Numbers: [3735] 3735,84 unequal: No Solution Exploring Operation: 83-45=38, Resulting Numbers: [38] 38,84 unequal: No Solution Exploring Operation: 83+45=128, Resulting Numbers: [128] 128,84 unequal: No Solution Moving to Node #0,4,2 Current State: 84:[83, 39], Operations: ['16/2=8', '31+8=39'] Exploring Operation: 83-39=44, Resulting Numbers: [44] 44,84 unequal: No Solution Exploring Operation: 83*39=3237, Resulting Numbers: [3237] 3237,84 unequal: No Solution Exploring Operation: 83+39=122, Resulting Numbers: [122] 122,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[83, 17], Operations: ['16-2=14', '31-14=17'] Exploring Operation: 83-17=66, Resulting Numbers: [66] 66,84 unequal: No Solution Exploring Operation: 83+17=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 83*17=1411, Resulting Numbers: [1411] 1411,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[85, 47], Operations: ['2+83=85', '16+31=47'] Exploring Operation: 85*47=3995, Resulting Numbers: [3995] 3995,84 unequal: No Solution Exploring Operation: 85+47=132, Resulting Numbers: [132] 132,84 unequal: No Solution Exploring Operation: 85-47=38, Resulting Numbers: [38] 38,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[14, 52], Operations: ['16-2=14', '83-31=52'] Exploring Operation: 14+52=66, Resulting Numbers: [66] 66,84 unequal: No Solution Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,84 unequal: No Solution Exploring Operation: 14*52=728, Resulting Numbers: [728] 728,84 unequal: No Solution Moving to Node #0,4,0 Current State: 84:[31, 91], Operations: ['16/2=8', '83+8=91'] Exploring Operation: 91-31=60, Resulting Numbers: [60] 60,84 unequal: No Solution Exploring Operation: 31+91=122, Resulting Numbers: [122] 122,84 unequal: No Solution Exploring Operation: 31*91=2821, Resulting Numbers: [2821] 2821,84 unequal: No Solution Moving to Node #0,4,1 Current State: 84:[8, 52], Operations: ['16/2=8', '83-31=52'] Exploring Operation: 8+52=60, Resulting Numbers: [60] 60,84 unequal: No Solution Exploring Operation: 8*52=416, Resulting Numbers: [416] 416,84 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,84 unequal: No Solution Moving to Node #0,4,4 Current State: 84:[31, 75], Operations: ['16/2=8', '83-8=75'] Exploring Operation: 31+75=106, Resulting Numbers: [106] 106,84 unequal: No Solution Exploring Operation: 31*75=2325, Resulting Numbers: [2325] 2325,84 unequal: No Solution Exploring Operation: 75-31=44, Resulting Numbers: [44] 44,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[16, 54], Operations: ['2+83=85', '85-31=54'] Exploring Operation: 54-16=38, Resulting Numbers: [38] 38,84 unequal: No Solution Exploring Operation: 16+54=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 16*54=864, Resulting Numbers: [864] 864,84 unequal: No Solution Moving to Node #0,1,4 Current State: 84:[31, 97], Operations: ['16-2=14', '83+14=97'] Exploring Operation: 31+97=128, Resulting Numbers: [128] 128,84 unequal: No Solution Exploring Operation: 31*97=3007, Resulting Numbers: [3007] 3007,84 unequal: No Solution Exploring Operation: 97-31=66, Resulting Numbers: [66] 66,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[31, 69], Operations: ['2+83=85', '85-16=69'] Exploring Operation: 69-31=38, Resulting Numbers: [38] 38,84 unequal: No Solution Exploring Operation: 31*69=2139, Resulting Numbers: [2139] 2139,84 unequal: No Solution Exploring Operation: 31+69=100, Resulting Numbers: [100] 100,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[31, 69], Operations: ['16-2=14', '83-14=69'] Exploring Operation: 31*69=2139, Resulting Numbers: [2139] 2139,84 unequal: No Solution Exploring Operation: 31+69=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 69-31=38, Resulting Numbers: [38] 38,84 unequal: No Solution Moving to Node #0,0,4 Current State: 84:[31, 101], Operations: ['2+83=85', '16+85=101'] Exploring Operation: 31+101=132, Resulting Numbers: [132] 132,84 unequal: No Solution Exploring Operation: 101-31=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 31*101=3131, Resulting Numbers: [3131] 3131,84 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 81, 36, 22, 9 ]
26
[ "81/9=9", "36/9=4", "22+4=26" ]
Current State: 26:[81, 36, 22, 9], Operations: [] Exploring Operation: 81/9=9, Resulting Numbers: [36, 22, 9] Generated Node #2: [36, 22, 9] from Operation: 81/9=9 Current State: 26:[36, 22, 9], Operations: ['81/9=9'] Exploring Operation: 36/9=4, Resulting Numbers: [22, 4] Generated Node #3: [22, 4] from Operation: 36/9=4 Current State: 26:[22, 4], Operations: ['81/9=9', '36/9=4'] Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[81, 36, 22, 9], Operations: [] Exploring Operation: 81/9=9, Resulting Numbers: [36, 22, 9] Generated Node #0,0: 26:[36, 22, 9] Operation: 81/9=9 Exploring Operation: 81-36=45, Resulting Numbers: [22, 9, 45] Generated Node #0,1: 26:[22, 9, 45] Operation: 81-36=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[36, 22, 9], Operations: ['81/9=9'] Exploring Operation: 36-9=27, Resulting Numbers: [22, 27] Generated Node #0,0,0: 26:[22, 27] Operation: 36-9=27 Exploring Operation: 36-22=14, Resulting Numbers: [9, 14] Generated Node #0,0,1: 26:[9, 14] Operation: 36-22=14 Moving to Node #0,0,0 Current State: 26:[22, 27], Operations: ['81/9=9', '36-9=27'] Exploring Operation: 27-22=5, Resulting Numbers: [5] 5,26 unequal: No Solution Exploring Operation: 22+27=49, Resulting Numbers: [49] 49,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[9, 14], Operations: ['81/9=9', '36-22=14'] Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,26 unequal: No Solution Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,26 unequal: No Solution No 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: 26:[22, 9, 45], Operations: ['81-36=45'] Exploring Operation: 45-22=23, Resulting Numbers: [9, 23] Generated Node #0,1,0: 26:[9, 23] Operation: 45-22=23 Exploring Operation: 45/9=5, Resulting Numbers: [22, 5] Generated Node #0,1,1: 26:[22, 5] Operation: 45/9=5 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 26:[9, 23], Operations: ['81-36=45', '45-22=23'] Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,26 unequal: No Solution Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,26 unequal: No Solution No 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: 26:[22, 5], Operations: ['81-36=45', '45/9=5'] Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,26 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
[ 43, 70, 39, 34 ]
46
[ "70-43=27", "39+34=73", "73-27=46" ]
Current State: 46:[43, 70, 39, 34], Operations: [] Exploring Operation: 70-43=27, Resulting Numbers: [39, 34, 27] Generated Node #2: [39, 34, 27] from Operation: 70-43=27 Current State: 46:[39, 34, 27], Operations: ['70-43=27'] Exploring Operation: 39+34=73, Resulting Numbers: [27, 73] Generated Node #3: [27, 73] from Operation: 39+34=73 Current State: 46:[27, 73], Operations: ['70-43=27', '39+34=73'] Exploring Operation: 73-27=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[43, 70, 39, 34], Operations: [] Exploring Operation: 70-34=36, Resulting Numbers: [43, 39, 36] Generated Node #0,0: 46:[43, 39, 36] Operation: 70-34=36 Exploring Operation: 70-39=31, Resulting Numbers: [43, 34, 31] Generated Node #0,1: 46:[43, 34, 31] Operation: 70-39=31 Exploring Operation: 70-43=27, Resulting Numbers: [39, 34, 27] Generated Node #0,2: 46:[39, 34, 27] Operation: 70-43=27 Moving to Node #0,0 Current State: 46:[43, 39, 36], Operations: ['70-34=36'] Exploring Operation: 43-39=4, Resulting Numbers: [36, 4] Generated Node #0,0,0: 46:[36, 4] Operation: 43-39=4 Exploring Operation: 43-36=7, Resulting Numbers: [39, 7] Generated Node #0,0,1: 46:[39, 7] Operation: 43-36=7 Exploring Operation: 39-36=3, Resulting Numbers: [43, 3] Generated Node #0,0,2: 46:[43, 3] Operation: 39-36=3 Moving to Node #0,1 Current State: 46:[43, 34, 31], Operations: ['70-39=31'] Exploring Operation: 43-31=12, Resulting Numbers: [34, 12] Generated Node #0,1,0: 46:[34, 12] Operation: 43-31=12 Exploring Operation: 43-34=9, Resulting Numbers: [31, 9] Generated Node #0,1,1: 46:[31, 9] Operation: 43-34=9 Exploring Operation: 34-31=3, Resulting Numbers: [43, 3] Generated Node #0,1,2: 46:[43, 3] Operation: 34-31=3 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 46:[43, 3], Operations: ['70-39=31', '34-31=3'] Exploring Operation: 43*3=129, Resulting Numbers: [129] 129,46 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,46 unequal: No Solution Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[43, 70, 39, 34], Operations: [] Exploring Operation: 70-39=31, Resulting Numbers: [43, 34, 31] Generated Node #0,1: 46:[43, 34, 31] Operation: 70-39=31 Moving to Node #0,1 Current State: 46:[43, 34, 31], Operations: ['70-39=31'] Exploring Operation: 34-31=3, Resulting Numbers: [43, 3] Generated Node #0,1,2: 46:[43, 3] Operation: 34-31=3 Moving to Node #0,1,2 Current State: 46:[43, 3], Operations: ['70-39=31', '34-31=3'] Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 14, 60, 33, 13 ]
94
[ "14+60=74", "33-13=20", "74+20=94" ]
Current State: 94:[14, 60, 33, 13], Operations: [] Exploring Operation: 14+60=74, Resulting Numbers: [33, 13, 74] Generated Node #2: [33, 13, 74] from Operation: 14+60=74 Current State: 94:[33, 13, 74], Operations: ['14+60=74'] Exploring Operation: 33-13=20, Resulting Numbers: [74, 20] Generated Node #3: [74, 20] from Operation: 33-13=20 Current State: 94:[74, 20], Operations: ['14+60=74', '33-13=20'] Exploring Operation: 74+20=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[14, 60, 33, 13], Operations: [] Exploring Operation: 60+33=93, Resulting Numbers: [14, 13, 93] Generated Node #0,0: 94:[14, 13, 93] Operation: 60+33=93 Exploring Operation: 33+13=46, Resulting Numbers: [14, 60, 46] Generated Node #0,1: 94:[14, 60, 46] Operation: 33+13=46 Exploring Operation: 60-14=46, Resulting Numbers: [33, 13, 46] Generated Node #0,2: 94:[33, 13, 46] Operation: 60-14=46 Exploring Operation: 60-13=47, Resulting Numbers: [14, 33, 47] Generated Node #0,3: 94:[14, 33, 47] Operation: 60-13=47 Exploring Operation: 14+33=47, Resulting Numbers: [60, 13, 47] Generated Node #0,4: 94:[60, 13, 47] Operation: 14+33=47 Moving to Node #0,0 Current State: 94:[14, 13, 93], Operations: ['60+33=93'] Exploring Operation: 14-13=1, Resulting Numbers: [93, 1] Generated Node #0,0,0: 94:[93, 1] Operation: 14-13=1 Exploring Operation: 14+93=107, Resulting Numbers: [13, 107] Generated Node #0,0,1: 94:[13, 107] Operation: 14+93=107 Exploring Operation: 14+13=27, Resulting Numbers: [93, 27] Generated Node #0,0,2: 94:[93, 27] Operation: 14+13=27 Exploring Operation: 13+93=106, Resulting Numbers: [14, 106] Generated Node #0,0,3: 94:[14, 106] Operation: 13+93=106 Exploring Operation: 93-14=79, Resulting Numbers: [13, 79] Generated Node #0,0,4: 94:[13, 79] Operation: 93-14=79 Moving to Node #0,4 Current State: 94:[60, 13, 47], Operations: ['14+33=47'] Exploring Operation: 60+13=73, Resulting Numbers: [47, 73] Generated Node #0,4,0: 94:[47, 73] Operation: 60+13=73 Exploring Operation: 60-13=47, Resulting Numbers: [47, 47] Generated Node #0,4,1: 94:[47, 47] Operation: 60-13=47 Exploring Operation: 60-47=13, Resulting Numbers: [13, 13] Generated Node #0,4,2: 94:[13, 13] Operation: 60-47=13 Exploring Operation: 13+47=60, Resulting Numbers: [60, 60] Generated Node #0,4,3: 94:[60, 60] Operation: 13+47=60 Exploring Operation: 60+47=107, Resulting Numbers: [13, 107] Generated Node #0,4,4: 94:[13, 107] Operation: 60+47=107 Moving to Node #0,1 Current State: 94:[14, 60, 46], Operations: ['33+13=46'] Exploring Operation: 60-46=14, Resulting Numbers: [14, 14] Generated Node #0,1,0: 94:[14, 14] Operation: 60-46=14 Exploring Operation: 60+46=106, Resulting Numbers: [14, 106] Generated Node #0,1,1: 94:[14, 106] Operation: 60+46=106 Exploring Operation: 60-14=46, Resulting Numbers: [46, 46] Generated Node #0,1,2: 94:[46, 46] Operation: 60-14=46 Exploring Operation: 14+60=74, Resulting Numbers: [46, 74] Generated Node #0,1,3: 94:[46, 74] Operation: 14+60=74 Exploring Operation: 14+46=60, Resulting Numbers: [60, 60] Generated Node #0,1,4: 94:[60, 60] Operation: 14+46=60 Moving to Node #0,2 Current State: 94:[33, 13, 46], Operations: ['60-14=46'] Exploring Operation: 46-33=13, Resulting Numbers: [13, 13] Generated Node #0,2,0: 94:[13, 13] Operation: 46-33=13 Exploring Operation: 33+46=79, Resulting Numbers: [13, 79] Generated Node #0,2,1: 94:[13, 79] Operation: 33+46=79 Exploring Operation: 13+46=59, Resulting Numbers: [33, 59] Generated Node #0,2,2: 94:[33, 59] Operation: 13+46=59 Exploring Operation: 33-13=20, Resulting Numbers: [46, 20] Generated Node #0,2,3: 94:[46, 20] Operation: 33-13=20 Exploring Operation: 33+13=46, Resulting Numbers: [46, 46] Generated Node #0,2,4: 94:[46, 46] Operation: 33+13=46 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 94:[46, 46], Operations: ['60-14=46', '33+13=46'] Exploring Operation: 46+46=92, Resulting Numbers: [92] 92,94 unequal: No Solution Exploring Operation: 46/46=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 46*46=2116, Resulting Numbers: [2116] 2116,94 unequal: No Solution Exploring Operation: 46-46=0, Resulting Numbers: [0] 0,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 94:[46, 20], Operations: ['60-14=46', '33-13=20'] Exploring Operation: 46+20=66, Resulting Numbers: [66] 66,94 unequal: No Solution Exploring Operation: 46-20=26, Resulting Numbers: [26] 26,94 unequal: No Solution Exploring Operation: 46*20=920, Resulting Numbers: [920] 920,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 94:[13, 13], Operations: ['60-14=46', '46-33=13'] Exploring Operation: 13/13=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 13+13=26, Resulting Numbers: [26] 26,94 unequal: No Solution Exploring Operation: 13*13=169, Resulting Numbers: [169] 169,94 unequal: No Solution Exploring Operation: 13-13=0, Resulting Numbers: [0] 0,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 94:[13, 79], Operations: ['60-14=46', '33+46=79'] Exploring Operation: 13*79=1027, Resulting Numbers: [1027] 1027,94 unequal: No Solution Exploring Operation: 79-13=66, Resulting Numbers: [66] 66,94 unequal: No Solution Exploring Operation: 13+79=92, Resulting Numbers: [92] 92,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 94:[33, 59], Operations: ['60-14=46', '13+46=59'] Exploring Operation: 33+59=92, Resulting Numbers: [92] 92,94 unequal: No Solution Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,94 unequal: No Solution Exploring Operation: 33*59=1947, Resulting Numbers: [1947] 1947,94 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: 94:[14, 33, 47], Operations: ['60-13=47'] Exploring Operation: 33-14=19, Resulting Numbers: [47, 19] Generated Node #0,3,0: 94:[47, 19] Operation: 33-14=19 Exploring Operation: 33+47=80, Resulting Numbers: [14, 80] Generated Node #0,3,1: 94:[14, 80] Operation: 33+47=80 Exploring Operation: 14+33=47, Resulting Numbers: [47, 47] Generated Node #0,3,2: 94:[47, 47] Operation: 14+33=47 Exploring Operation: 14+47=61, Resulting Numbers: [33, 61] Generated Node #0,3,3: 94:[33, 61] Operation: 14+47=61 Exploring Operation: 47-33=14, Resulting Numbers: [14, 14] Generated Node #0,3,4: 94:[14, 14] Operation: 47-33=14 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 94:[47, 47], Operations: ['60-13=47', '14+33=47'] Exploring Operation: 47/47=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[14, 60, 33, 13], Operations: [] Exploring Operation: 60-13=47, Resulting Numbers: [14, 33, 47] Generated Node #0,3: 94:[14, 33, 47] Operation: 60-13=47 Moving to Node #0,3 Current State: 94:[14, 33, 47], Operations: ['60-13=47'] Exploring Operation: 14+33=47, Resulting Numbers: [47, 47] Generated Node #0,3,2: 94:[47, 47] Operation: 14+33=47 Moving to Node #0,3,2 Current State: 94:[47, 47], Operations: ['60-13=47', '14+33=47'] Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.953993
hs_5
sum_heuristic
[ 29, 58, 25, 18 ]
86
[ "58/29=2", "25+18=43", "2*43=86" ]
Current State: 86:[29, 58, 25, 18], Operations: [] Exploring Operation: 58/29=2, Resulting Numbers: [25, 18, 2] Generated Node #2: [25, 18, 2] from Operation: 58/29=2 Current State: 86:[25, 18, 2], Operations: ['58/29=2'] Exploring Operation: 25+18=43, Resulting Numbers: [2, 43] Generated Node #3: [2, 43] from Operation: 25+18=43 Current State: 86:[2, 43], Operations: ['58/29=2', '25+18=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[29, 58, 25, 18], Operations: [] Exploring Operation: 29-25=4, Resulting Numbers: [58, 18, 4] Generated Node #0,0: 86:[58, 18, 4] Operation: 29-25=4 Exploring Operation: 25+18=43, Resulting Numbers: [29, 58, 43] Generated Node #0,1: 86:[29, 58, 43] Operation: 25+18=43 Exploring Operation: 58+25=83, Resulting Numbers: [29, 18, 83] Generated Node #0,2: 86:[29, 18, 83] Operation: 58+25=83 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[29, 58, 43], Operations: ['25+18=43'] Exploring Operation: 58-29=29, Resulting Numbers: [43, 29] Generated Node #0,1,0: 86:[43, 29] Operation: 58-29=29 Exploring Operation: 58/29=2, Resulting Numbers: [43, 2] Generated Node #0,1,1: 86:[43, 2] Operation: 58/29=2 Exploring Operation: 29+58=87, Resulting Numbers: [43, 87] Generated Node #0,1,2: 86:[43, 87] Operation: 29+58=87 Moving to Node #0,1,1 Current State: 86:[43, 2], Operations: ['25+18=43', '58/29=2'] Exploring Operation: 43*2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[29, 58, 25, 18], Operations: [] Exploring Operation: 25+18=43, Resulting Numbers: [29, 58, 43] Generated Node #0,1: 86:[29, 58, 43] Operation: 25+18=43 Moving to Node #0,1 Current State: 86:[29, 58, 43], Operations: ['25+18=43'] Exploring Operation: 58/29=2, Resulting Numbers: [43, 2] Generated Node #0,1,1: 86:[43, 2] Operation: 58/29=2 Moving to Node #0,1,1 Current State: 86:[43, 2], Operations: ['25+18=43', '58/29=2'] Exploring Operation: 43*2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 75, 77, 56, 40 ]
94
[ "77-75=2", "56+40=96", "96-2=94" ]
Current State: 94:[75, 77, 56, 40], Operations: [] Exploring Operation: 77-75=2, Resulting Numbers: [56, 40, 2] Generated Node #2: [56, 40, 2] from Operation: 77-75=2 Current State: 94:[56, 40, 2], Operations: ['77-75=2'] Exploring Operation: 56+40=96, Resulting Numbers: [2, 96] Generated Node #3: [2, 96] from Operation: 56+40=96 Current State: 94:[2, 96], Operations: ['77-75=2', '56+40=96'] Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[75, 77, 56, 40], Operations: [] Exploring Operation: 77-75=2, Resulting Numbers: [56, 40, 2] Generated Node #0,0: 94:[56, 40, 2] Operation: 77-75=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[56, 40, 2], Operations: ['77-75=2'] Exploring Operation: 56+40=96, Resulting Numbers: [2, 96] Generated Node #0,0,0: 94:[2, 96] Operation: 56+40=96 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[2, 96], Operations: ['77-75=2', '56+40=96'] Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[75, 77, 56, 40], Operations: [] Exploring Operation: 77-75=2, Resulting Numbers: [56, 40, 2] Generated Node #0,0: 94:[56, 40, 2] Operation: 77-75=2 Moving to Node #0,0 Current State: 94:[56, 40, 2], Operations: ['77-75=2'] Exploring Operation: 56+40=96, Resulting Numbers: [2, 96] Generated Node #0,0,0: 94:[2, 96] Operation: 56+40=96 Moving to Node #0,0,0 Current State: 94:[2, 96], Operations: ['77-75=2', '56+40=96'] Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 5, 8, 2, 54 ]
60
[ "8-5=3", "2*3=6", "54+6=60" ]
Current State: 60:[5, 8, 2, 54], Operations: [] Exploring Operation: 8-5=3, Resulting Numbers: [2, 54, 3] Generated Node #2: [2, 54, 3] from Operation: 8-5=3 Current State: 60:[2, 54, 3], Operations: ['8-5=3'] Exploring Operation: 2*3=6, Resulting Numbers: [54, 6] Generated Node #3: [54, 6] from Operation: 2*3=6 Current State: 60:[54, 6], Operations: ['8-5=3', '2*3=6'] Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[5, 8, 2, 54], Operations: [] Exploring Operation: 5+54=59, Resulting Numbers: [8, 2, 59] Generated Node #0,0: 60:[8, 2, 59] Operation: 5+54=59 Exploring Operation: 54/2=27, Resulting Numbers: [5, 8, 27] Generated Node #0,1: 60:[5, 8, 27] Operation: 54/2=27 Exploring Operation: 8+54=62, Resulting Numbers: [5, 2, 62] Generated Node #0,2: 60:[5, 2, 62] Operation: 8+54=62 Moving to Node #0,2 Current State: 60:[5, 2, 62], Operations: ['8+54=62'] Exploring Operation: 5*2=10, Resulting Numbers: [62, 10] Generated Node #0,2,0: 60:[62, 10] Operation: 5*2=10 Exploring Operation: 62-2=60, Resulting Numbers: [5, 60] Generated Node #0,2,1: 60:[5, 60] Operation: 62-2=60 Exploring Operation: 62/2=31, Resulting Numbers: [5, 31] Generated Node #0,2,2: 60:[5, 31] Operation: 62/2=31 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 60:[5, 60], Operations: ['8+54=62', '62-2=60'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,60 unequal: No Solution Exploring Operation: 5+60=65, Resulting Numbers: [65] 65,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 60:[5, 31], Operations: ['8+54=62', '62/2=31'] Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,60 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,60 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 60:[62, 10], Operations: ['8+54=62', '5*2=10'] Exploring Operation: 62+10=72, Resulting Numbers: [72] 72,60 unequal: No Solution Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,60 unequal: No Solution Exploring Operation: 62*10=620, Resulting Numbers: [620] 620,60 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: 60:[8, 2, 59], Operations: ['5+54=59'] Exploring Operation: 8+2=10, Resulting Numbers: [59, 10] Generated Node #0,0,0: 60:[59, 10] Operation: 8+2=10 Exploring Operation: 8/2=4, Resulting Numbers: [59, 4] Generated Node #0,0,1: 60:[59, 4] Operation: 8/2=4 Exploring Operation: 8-2=6, Resulting Numbers: [59, 6] Generated Node #0,0,2: 60:[59, 6] Operation: 8-2=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[59, 10], Operations: ['5+54=59', '8+2=10'] Exploring Operation: 59-10=49, Resulting Numbers: [49] 49,60 unequal: No Solution Exploring Operation: 59+10=69, Resulting Numbers: [69] 69,60 unequal: No Solution Exploring Operation: 59*10=590, Resulting Numbers: [590] 590,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[59, 4], Operations: ['5+54=59', '8/2=4'] Exploring Operation: 59*4=236, Resulting Numbers: [236] 236,60 unequal: No Solution Exploring Operation: 59+4=63, Resulting Numbers: [63] 63,60 unequal: No Solution Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[59, 6], Operations: ['5+54=59', '8-2=6'] Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,60 unequal: No Solution Exploring Operation: 59+6=65, Resulting Numbers: [65] 65,60 unequal: No Solution Exploring Operation: 59*6=354, Resulting Numbers: [354] 354,60 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: 60:[5, 8, 27], Operations: ['54/2=27'] Exploring Operation: 27-8=19, Resulting Numbers: [5, 19] Generated Node #0,1,0: 60:[5, 19] Operation: 27-8=19 Exploring Operation: 5+8=13, Resulting Numbers: [27, 13] Generated Node #0,1,1: 60:[27, 13] Operation: 5+8=13 Exploring Operation: 8-5=3, Resulting Numbers: [27, 3] Generated Node #0,1,2: 60:[27, 3] Operation: 8-5=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[5, 19], Operations: ['54/2=27', '27-8=19'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,60 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,60 unequal: No Solution Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 60:[27, 3], Operations: ['54/2=27', '8-5=3'] Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,60 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,60 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[27, 13], Operations: ['54/2=27', '5+8=13'] Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,60 unequal: No Solution Exploring Operation: 27*13=351, Resulting Numbers: [351] 351,60 unequal: No Solution Exploring Operation: 27+13=40, Resulting Numbers: [40] 40,60 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
[ 67, 43, 86, 8 ]
71
[ "86/43=2", "8/2=4", "67+4=71" ]
Current State: 71:[67, 43, 86, 8], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [67, 8, 2] Generated Node #2: [67, 8, 2] from Operation: 86/43=2 Current State: 71:[67, 8, 2], Operations: ['86/43=2'] Exploring Operation: 8/2=4, Resulting Numbers: [67, 4] Generated Node #3: [67, 4] from Operation: 8/2=4 Current State: 71:[67, 4], Operations: ['86/43=2', '8/2=4'] Exploring Operation: 67+4=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[67, 43, 86, 8], Operations: [] Exploring Operation: 43+8=51, Resulting Numbers: [67, 86, 51] Generated Node #0,0: 71:[67, 86, 51] Operation: 43+8=51 Exploring Operation: 86-8=78, Resulting Numbers: [67, 43, 78] Generated Node #0,1: 71:[67, 43, 78] Operation: 86-8=78 Exploring Operation: 67-8=59, Resulting Numbers: [43, 86, 59] Generated Node #0,2: 71:[43, 86, 59] Operation: 67-8=59 Exploring Operation: 67+8=75, Resulting Numbers: [43, 86, 75] Generated Node #0,3: 71:[43, 86, 75] Operation: 67+8=75 Moving to Node #0,0 Current State: 71:[67, 86, 51], Operations: ['43+8=51'] Exploring Operation: 67+51=118, Resulting Numbers: [86, 118] Generated Node #0,0,0: 71:[86, 118] Operation: 67+51=118 Exploring Operation: 86+51=137, Resulting Numbers: [67, 137] Generated Node #0,0,1: 71:[67, 137] Operation: 86+51=137 Exploring Operation: 86-51=35, Resulting Numbers: [67, 35] Generated Node #0,0,2: 71:[67, 35] Operation: 86-51=35 Exploring Operation: 67-51=16, Resulting Numbers: [86, 16] Generated Node #0,0,3: 71:[86, 16] Operation: 67-51=16 Moving to Node #0,1 Current State: 71:[67, 43, 78], Operations: ['86-8=78'] Exploring Operation: 67+43=110, Resulting Numbers: [78, 110] Generated Node #0,1,0: 71:[78, 110] Operation: 67+43=110 Exploring Operation: 78-43=35, Resulting Numbers: [67, 35] Generated Node #0,1,1: 71:[67, 35] Operation: 78-43=35 Exploring Operation: 67-43=24, Resulting Numbers: [78, 24] Generated Node #0,1,2: 71:[78, 24] Operation: 67-43=24 Exploring Operation: 43+78=121, Resulting Numbers: [67, 121] Generated Node #0,1,3: 71:[67, 121] Operation: 43+78=121 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 71:[67, 35], Operations: ['86-8=78', '78-43=35'] Exploring Operation: 67-35=32, Resulting Numbers: [32] 32,71 unequal: No Solution Exploring Operation: 67+35=102, Resulting Numbers: [102] 102,71 unequal: No Solution Exploring Operation: 67*35=2345, Resulting Numbers: [2345] 2345,71 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 #0,1,0 Current State: 71:[78, 110], Operations: ['86-8=78', '67+43=110'] Exploring Operation: 110-78=32, Resulting Numbers: [32] 32,71 unequal: No Solution Exploring Operation: 78+110=188, Resulting Numbers: [188] 188,71 unequal: No Solution Exploring Operation: 78*110=8580, Resulting Numbers: [8580] 8580,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 71:[78, 24], Operations: ['86-8=78', '67-43=24'] Exploring Operation: 78+24=102, Resulting Numbers: [102] 102,71 unequal: No Solution Exploring Operation: 78*24=1872, Resulting Numbers: [1872] 1872,71 unequal: No Solution Exploring Operation: 78-24=54, Resulting Numbers: [54] 54,71 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 #0,1,3 Current State: 71:[67, 121], Operations: ['86-8=78', '43+78=121'] Exploring Operation: 67*121=8107, Resulting Numbers: [8107] 8107,71 unequal: No Solution Exploring Operation: 121-67=54, Resulting Numbers: [54] 54,71 unequal: No Solution Exploring Operation: 67+121=188, Resulting Numbers: [188] 188,71 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: 71:[43, 86, 75], Operations: ['67+8=75'] Exploring Operation: 43+75=118, Resulting Numbers: [86, 118] Generated Node #0,3,0: 71:[86, 118] Operation: 43+75=118 Exploring Operation: 43+86=129, Resulting Numbers: [75, 129] Generated Node #0,3,1: 71:[75, 129] Operation: 43+86=129 Exploring Operation: 75-43=32, Resulting Numbers: [86, 32] Generated Node #0,3,2: 71:[86, 32] Operation: 75-43=32 Exploring Operation: 86-43=43, Resulting Numbers: [75, 43] Generated Node #0,3,3: 71:[75, 43] Operation: 86-43=43 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 71:[75, 43], Operations: ['67+8=75', '86-43=43'] Exploring Operation: 75*43=3225, Resulting Numbers: [3225] 3225,71 unequal: No Solution Exploring Operation: 75-43=32, Resulting Numbers: [32] 32,71 unequal: No Solution Exploring Operation: 75+43=118, Resulting Numbers: [118] 118,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 71:[86, 32], Operations: ['67+8=75', '75-43=32'] Exploring Operation: 86*32=2752, Resulting Numbers: [2752] 2752,71 unequal: No Solution Exploring Operation: 86-32=54, Resulting Numbers: [54] 54,71 unequal: No Solution Exploring Operation: 86+32=118, Resulting Numbers: [118] 118,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 71:[86, 118], Operations: ['67+8=75', '43+75=118'] Exploring Operation: 118-86=32, Resulting Numbers: [32] 32,71 unequal: No Solution Exploring Operation: 86+118=204, Resulting Numbers: [204] 204,71 unequal: No Solution Exploring Operation: 86*118=10148, Resulting Numbers: [10148] 10148,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 71:[75, 129], Operations: ['67+8=75', '43+86=129'] Exploring Operation: 129-75=54, Resulting Numbers: [54] 54,71 unequal: No Solution Exploring Operation: 75*129=9675, Resulting Numbers: [9675] 9675,71 unequal: No Solution Exploring Operation: 75+129=204, Resulting Numbers: [204] 204,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 71:[43, 86, 59], Operations: ['67-8=59'] Exploring Operation: 43+86=129, Resulting Numbers: [59, 129] Generated Node #0,2,0: 71:[59, 129] Operation: 43+86=129 Exploring Operation: 43+59=102, Resulting Numbers: [86, 102] Generated Node #0,2,1: 71:[86, 102] Operation: 43+59=102 Exploring Operation: 59-43=16, Resulting Numbers: [86, 16] Generated Node #0,2,2: 71:[86, 16] Operation: 59-43=16 Exploring Operation: 86-43=43, Resulting Numbers: [59, 43] Generated Node #0,2,3: 71:[59, 43] Operation: 86-43=43 Moving to Node #0,0,2 Current State: 71:[67, 35], Operations: ['43+8=51', '86-51=35'] Exploring Operation: 67+35=102, Resulting Numbers: [102] 102,71 unequal: No Solution Exploring Operation: 67*35=2345, Resulting Numbers: [2345] 2345,71 unequal: No Solution Exploring Operation: 67-35=32, Resulting Numbers: [32] 32,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[59, 43], Operations: ['67-8=59', '86-43=43'] Exploring Operation: 59-43=16, Resulting Numbers: [16] 16,71 unequal: No Solution Exploring Operation: 59*43=2537, Resulting Numbers: [2537] 2537,71 unequal: No Solution Exploring Operation: 59+43=102, Resulting Numbers: [102] 102,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[86, 102], Operations: ['67-8=59', '43+59=102'] Exploring Operation: 86+102=188, Resulting Numbers: [188] 188,71 unequal: No Solution Exploring Operation: 86*102=8772, Resulting Numbers: [8772] 8772,71 unequal: No Solution Exploring Operation: 102-86=16, Resulting Numbers: [16] 16,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[86, 118], Operations: ['43+8=51', '67+51=118'] Exploring Operation: 86*118=10148, Resulting Numbers: [10148] 10148,71 unequal: No Solution Exploring Operation: 86+118=204, Resulting Numbers: [204] 204,71 unequal: No Solution Exploring Operation: 118-86=32, Resulting Numbers: [32] 32,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[67, 137], Operations: ['43+8=51', '86+51=137'] Exploring Operation: 137-67=70, Resulting Numbers: [70] 70,71 unequal: No Solution Exploring Operation: 67*137=9179, Resulting Numbers: [9179] 9179,71 unequal: No Solution Exploring Operation: 67+137=204, Resulting Numbers: [204] 204,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[59, 129], Operations: ['67-8=59', '43+86=129'] Exploring Operation: 129-59=70, Resulting Numbers: [70] 70,71 unequal: No Solution Exploring Operation: 59+129=188, Resulting Numbers: [188] 188,71 unequal: No Solution Exploring Operation: 59*129=7611, Resulting Numbers: [7611] 7611,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[86, 16], Operations: ['67-8=59', '59-43=16'] Exploring Operation: 86-16=70, Resulting Numbers: [70] 70,71 unequal: No Solution Exploring Operation: 86+16=102, Resulting Numbers: [102] 102,71 unequal: No Solution Exploring Operation: 86*16=1376, Resulting Numbers: [1376] 1376,71 unequal: No Solution Moving to Node #0,0,3 Current State: 71:[86, 16], Operations: ['43+8=51', '67-51=16'] Exploring Operation: 86-16=70, Resulting Numbers: [70] 70,71 unequal: No Solution Exploring Operation: 86*16=1376, Resulting Numbers: [1376] 1376,71 unequal: No Solution Exploring Operation: 86+16=102, Resulting Numbers: [102] 102,71 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 52, 47, 23, 23 ]
47
[ "23-23=0", "52*0=0", "47+0=47" ]
Current State: 47:[52, 47, 23, 23], Operations: [] Exploring Operation: 23-23=0, Resulting Numbers: [52, 47, 0] Generated Node #2: [52, 47, 0] from Operation: 23-23=0 Current State: 47:[52, 47, 0], Operations: ['23-23=0'] Exploring Operation: 52*0=0, Resulting Numbers: [47, 0] Generated Node #3: [47, 0] from Operation: 52*0=0 Current State: 47:[47, 0], Operations: ['23-23=0', '52*0=0'] Exploring Operation: 47+0=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[52, 47, 23, 23], Operations: [] Exploring Operation: 52-23=29, Resulting Numbers: [47, 23, 29] Generated Node #0,0: 47:[47, 23, 29] Operation: 52-23=29 Exploring Operation: 23+23=46, Resulting Numbers: [52, 47, 46] Generated Node #0,1: 47:[52, 47, 46] Operation: 23+23=46 Moving to Node #0,1 Current State: 47:[52, 47, 46], Operations: ['23+23=46'] Exploring Operation: 52-46=6, Resulting Numbers: [47, 6] Generated Node #0,1,0: 47:[47, 6] Operation: 52-46=6 Exploring Operation: 52-47=5, Resulting Numbers: [46, 5] Generated Node #0,1,1: 47:[46, 5] Operation: 52-47=5 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 47:[47, 6], Operations: ['23+23=46', '52-46=6'] Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,47 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 47:[46, 5], Operations: ['23+23=46', '52-47=5'] Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 46+5=51, Resulting Numbers: [51] 51,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 47:[47, 23, 29], Operations: ['52-23=29'] Exploring Operation: 23+29=52, Resulting Numbers: [47, 52] Generated Node #0,0,0: 47:[47, 52] Operation: 23+29=52 Exploring Operation: 47+23=70, Resulting Numbers: [29, 70] Generated Node #0,0,1: 47:[29, 70] Operation: 47+23=70 Moving to Node #0,0,0 Current State: 47:[47, 52], Operations: ['52-23=29', '23+29=52'] Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 47+52=99, Resulting Numbers: [99] 99,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[29, 70], Operations: ['52-23=29', '47+23=70'] Exploring Operation: 70-29=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 29+70=99, Resulting Numbers: [99] 99,47 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 68, 24, 80, 75 ]
49
[ "68-24=44", "80-75=5", "44+5=49" ]
Current State: 49:[68, 24, 80, 75], Operations: [] Exploring Operation: 68-24=44, Resulting Numbers: [80, 75, 44] Generated Node #2: [80, 75, 44] from Operation: 68-24=44 Current State: 49:[80, 75, 44], Operations: ['68-24=44'] Exploring Operation: 80-75=5, Resulting Numbers: [44, 5] Generated Node #3: [44, 5] from Operation: 80-75=5 Current State: 49:[44, 5], Operations: ['68-24=44', '80-75=5'] Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[68, 24, 80, 75], Operations: [] Exploring Operation: 80-68=12, Resulting Numbers: [24, 75, 12] Generated Node #0,0: 49:[24, 75, 12] Operation: 80-68=12 Exploring Operation: 80-75=5, Resulting Numbers: [68, 24, 5] Generated Node #0,1: 49:[68, 24, 5] Operation: 80-75=5 Exploring Operation: 75-68=7, Resulting Numbers: [24, 80, 7] Generated Node #0,2: 49:[24, 80, 7] Operation: 75-68=7 Moving to Node #0,1 Current State: 49:[68, 24, 5], Operations: ['80-75=5'] Exploring Operation: 24-5=19, Resulting Numbers: [68, 19] Generated Node #0,1,0: 49:[68, 19] Operation: 24-5=19 Exploring Operation: 68-5=63, Resulting Numbers: [24, 63] Generated Node #0,1,1: 49:[24, 63] Operation: 68-5=63 Exploring Operation: 68-24=44, Resulting Numbers: [5, 44] Generated Node #0,1,2: 49:[5, 44] Operation: 68-24=44 Moving to Node #0,0 Current State: 49:[24, 75, 12], Operations: ['80-68=12'] Exploring Operation: 24/12=2, Resulting Numbers: [75, 2] Generated Node #0,0,0: 49:[75, 2] Operation: 24/12=2 Exploring Operation: 75-24=51, Resulting Numbers: [12, 51] Generated Node #0,0,1: 49:[12, 51] Operation: 75-24=51 Exploring Operation: 24-12=12, Resulting Numbers: [75, 12] Generated Node #0,0,2: 49:[75, 12] Operation: 24-12=12 Moving to Node #0,2 Current State: 49:[24, 80, 7], Operations: ['75-68=7'] Exploring Operation: 80-7=73, Resulting Numbers: [24, 73] Generated Node #0,2,0: 49:[24, 73] Operation: 80-7=73 Exploring Operation: 24-7=17, Resulting Numbers: [80, 17] Generated Node #0,2,1: 49:[80, 17] Operation: 24-7=17 Exploring Operation: 80-24=56, Resulting Numbers: [7, 56] Generated Node #0,2,2: 49:[7, 56] Operation: 80-24=56 Moving to Node #0,1,2 Current State: 49:[5, 44], Operations: ['80-75=5', '68-24=44'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,49 unequal: No Solution Exploring Operation: 5*44=220, Resulting Numbers: [220] 220,49 unequal: No Solution Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[68, 24, 80, 75], Operations: [] Exploring Operation: 80-75=5, Resulting Numbers: [68, 24, 5] Generated Node #0,1: 49:[68, 24, 5] Operation: 80-75=5 Moving to Node #0,1 Current State: 49:[68, 24, 5], Operations: ['80-75=5'] Exploring Operation: 68-24=44, Resulting Numbers: [5, 44] Generated Node #0,1,2: 49:[5, 44] Operation: 68-24=44 Moving to Node #0,1,2 Current State: 49:[5, 44], Operations: ['80-75=5', '68-24=44'] Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
0.983507
hs_3
mult_heuristic
[ 47, 4, 77, 79 ]
98
[ "79-77=2", "47*2=94", "4+94=98" ]
Current State: 98:[47, 4, 77, 79], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [47, 4, 2] Generated Node #2: [47, 4, 2] from Operation: 79-77=2 Current State: 98:[47, 4, 2], Operations: ['79-77=2'] Exploring Operation: 47*2=94, Resulting Numbers: [4, 94] Generated Node #3: [4, 94] from Operation: 47*2=94 Current State: 98:[4, 94], Operations: ['79-77=2', '47*2=94'] Exploring Operation: 4+94=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[47, 4, 77, 79], Operations: [] Exploring Operation: 4+77=81, Resulting Numbers: [47, 79, 81] Generated Node #0,0: 98:[47, 79, 81] Operation: 4+77=81 Exploring Operation: 4+79=83, Resulting Numbers: [47, 77, 83] Generated Node #0,1: 98:[47, 77, 83] Operation: 4+79=83 Exploring Operation: 79-77=2, Resulting Numbers: [47, 4, 2] Generated Node #0,2: 98:[47, 4, 2] Operation: 79-77=2 Exploring Operation: 77-47=30, Resulting Numbers: [4, 79, 30] Generated Node #0,3: 98:[4, 79, 30] Operation: 77-47=30 Moving to Node #0,2 Current State: 98:[47, 4, 2], Operations: ['79-77=2'] Exploring Operation: 47+4=51, Resulting Numbers: [2, 51] Generated Node #0,2,0: 98:[2, 51] Operation: 47+4=51 Exploring Operation: 4/2=2, Resulting Numbers: [47, 2] Generated Node #0,2,1: 98:[47, 2] Operation: 4/2=2 Exploring Operation: 47+2=49, Resulting Numbers: [4, 49] Generated Node #0,2,2: 98:[4, 49] Operation: 47+2=49 Exploring Operation: 4-2=2, Resulting Numbers: [47, 2] Generated Node #0,2,3: 98:[47, 2] Operation: 4-2=2 Moving to Node #0,3 Current State: 98:[4, 79, 30], Operations: ['77-47=30'] Exploring Operation: 30-4=26, Resulting Numbers: [79, 26] Generated Node #0,3,0: 98:[79, 26] Operation: 30-4=26 Exploring Operation: 79+30=109, Resulting Numbers: [4, 109] Generated Node #0,3,1: 98:[4, 109] Operation: 79+30=109 Exploring Operation: 79-30=49, Resulting Numbers: [4, 49] Generated Node #0,3,2: 98:[4, 49] Operation: 79-30=49 Exploring Operation: 4+79=83, Resulting Numbers: [30, 83] Generated Node #0,3,3: 98:[30, 83] Operation: 4+79=83 Moving to Node #0,1 Current State: 98:[47, 77, 83], Operations: ['4+79=83'] Exploring Operation: 83-47=36, Resulting Numbers: [77, 36] Generated Node #0,1,0: 98:[77, 36] Operation: 83-47=36 Exploring Operation: 83-77=6, Resulting Numbers: [47, 6] Generated Node #0,1,1: 98:[47, 6] Operation: 83-77=6 Exploring Operation: 47+77=124, Resulting Numbers: [83, 124] Generated Node #0,1,2: 98:[83, 124] Operation: 47+77=124 Exploring Operation: 77-47=30, Resulting Numbers: [83, 30] Generated Node #0,1,3: 98:[83, 30] Operation: 77-47=30 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 98:[47, 6], Operations: ['4+79=83', '83-77=6'] Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,98 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,98 unequal: No Solution Exploring Operation: 47*6=282, Resulting Numbers: [282] 282,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 98:[83, 30], Operations: ['4+79=83', '77-47=30'] Exploring Operation: 83+30=113, Resulting Numbers: [113] 113,98 unequal: No Solution Exploring Operation: 83-30=53, Resulting Numbers: [53] 53,98 unequal: No Solution Exploring Operation: 83*30=2490, Resulting Numbers: [2490] 2490,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 98:[77, 36], Operations: ['4+79=83', '83-47=36'] Exploring Operation: 77+36=113, Resulting Numbers: [113] 113,98 unequal: No Solution Exploring Operation: 77-36=41, Resulting Numbers: [41] 41,98 unequal: No Solution Exploring Operation: 77*36=2772, Resulting Numbers: [2772] 2772,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 98:[83, 124], Operations: ['4+79=83', '47+77=124'] Exploring Operation: 83*124=10292, Resulting Numbers: [10292] 10292,98 unequal: No Solution Exploring Operation: 124-83=41, Resulting Numbers: [41] 41,98 unequal: No Solution Exploring Operation: 83+124=207, Resulting Numbers: [207] 207,98 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: 98:[47, 79, 81], Operations: ['4+77=81'] Exploring Operation: 81-79=2, Resulting Numbers: [47, 2] Generated Node #0,0,0: 98:[47, 2] Operation: 81-79=2 Exploring Operation: 47+79=126, Resulting Numbers: [81, 126] Generated Node #0,0,1: 98:[81, 126] Operation: 47+79=126 Exploring Operation: 79-47=32, Resulting Numbers: [81, 32] Generated Node #0,0,2: 98:[81, 32] Operation: 79-47=32 Exploring Operation: 81-47=34, Resulting Numbers: [79, 34] Generated Node #0,0,3: 98:[79, 34] Operation: 81-47=34 Moving to Node #0,2,0 Current State: 98:[2, 51], Operations: ['79-77=2', '47+4=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,98 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,98 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[4, 49], Operations: ['79-77=2', '47+2=49'] Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,98 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,98 unequal: No Solution Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[47, 2], Operations: ['79-77=2', '4/2=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,98 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,98 unequal: No Solution Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,98 unequal: No Solution Moving to Node #0,3,2 Current State: 98:[4, 49], Operations: ['77-47=30', '79-30=49'] Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,98 unequal: No Solution Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,98 unequal: No Solution Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,98 unequal: No Solution Moving to Node #0,2,3 Current State: 98:[47, 2], Operations: ['79-77=2', '4-2=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,98 unequal: No Solution Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,98 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[47, 2], Operations: ['4+77=81', '81-79=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,98 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,98 unequal: No Solution Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,98 unequal: No Solution Moving to Node #0,3,1 Current State: 98:[4, 109], Operations: ['77-47=30', '79+30=109'] Exploring Operation: 4*109=436, Resulting Numbers: [436] 436,98 unequal: No Solution Exploring Operation: 109-4=105, Resulting Numbers: [105] 105,98 unequal: No Solution Exploring Operation: 4+109=113, Resulting Numbers: [113] 113,98 unequal: No Solution Moving to Node #0,3,0 Current State: 98:[79, 26], Operations: ['77-47=30', '30-4=26'] Exploring Operation: 79*26=2054, Resulting Numbers: [2054] 2054,98 unequal: No Solution Exploring Operation: 79+26=105, Resulting Numbers: [105] 105,98 unequal: No Solution Exploring Operation: 79-26=53, Resulting Numbers: [53] 53,98 unequal: No Solution Moving to Node #0,3,3 Current State: 98:[30, 83], Operations: ['77-47=30', '4+79=83'] Exploring Operation: 30*83=2490, Resulting Numbers: [2490] 2490,98 unequal: No Solution Exploring Operation: 30+83=113, Resulting Numbers: [113] 113,98 unequal: No Solution Exploring Operation: 83-30=53, Resulting Numbers: [53] 53,98 unequal: No Solution Moving to Node #0,0,3 Current State: 98:[79, 34], Operations: ['4+77=81', '81-47=34'] Exploring Operation: 79+34=113, Resulting Numbers: [113] 113,98 unequal: No Solution Exploring Operation: 79-34=45, Resulting Numbers: [45] 45,98 unequal: No Solution Exploring Operation: 79*34=2686, Resulting Numbers: [2686] 2686,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[81, 32], Operations: ['4+77=81', '79-47=32'] Exploring Operation: 81-32=49, Resulting Numbers: [49] 49,98 unequal: No Solution Exploring Operation: 81+32=113, Resulting Numbers: [113] 113,98 unequal: No Solution Exploring Operation: 81*32=2592, Resulting Numbers: [2592] 2592,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[81, 126], Operations: ['4+77=81', '47+79=126'] Exploring Operation: 126-81=45, Resulting Numbers: [45] 45,98 unequal: No Solution Exploring Operation: 81+126=207, Resulting Numbers: [207] 207,98 unequal: No Solution Exploring Operation: 81*126=10206, Resulting Numbers: [10206] 10206,98 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 67, 12, 42, 6 ]
64
[ "42-6=36", "36/12=3", "67-3=64" ]
Current State: 64:[67, 12, 42, 6], Operations: [] Exploring Operation: 42-6=36, Resulting Numbers: [67, 12, 36] Generated Node #2: [67, 12, 36] from Operation: 42-6=36 Current State: 64:[67, 12, 36], Operations: ['42-6=36'] Exploring Operation: 36/12=3, Resulting Numbers: [67, 3] Generated Node #3: [67, 3] from Operation: 36/12=3 Current State: 64:[67, 3], Operations: ['42-6=36', '36/12=3'] Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[67, 12, 42, 6], Operations: [] Exploring Operation: 42-12=30, Resulting Numbers: [67, 6, 30] Generated Node #0,0: 64:[67, 6, 30] Operation: 42-12=30 Exploring Operation: 67-42=25, Resulting Numbers: [12, 6, 25] Generated Node #0,1: 64:[12, 6, 25] Operation: 67-42=25 Exploring Operation: 42-6=36, Resulting Numbers: [67, 12, 36] Generated Node #0,2: 64:[67, 12, 36] Operation: 42-6=36 Exploring Operation: 42/6=7, Resulting Numbers: [67, 12, 7] Generated Node #0,3: 64:[67, 12, 7] Operation: 42/6=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[67, 6, 30], Operations: ['42-12=30'] Exploring Operation: 67-6=61, Resulting Numbers: [30, 61] Generated Node #0,0,0: 64:[30, 61] Operation: 67-6=61 Exploring Operation: 6+30=36, Resulting Numbers: [67, 36] Generated Node #0,0,1: 64:[67, 36] Operation: 6+30=36 Exploring Operation: 30/6=5, Resulting Numbers: [67, 5] Generated Node #0,0,2: 64:[67, 5] Operation: 30/6=5 Exploring Operation: 67-30=37, Resulting Numbers: [6, 37] Generated Node #0,0,3: 64:[6, 37] Operation: 67-30=37 Moving to Node #0,0,2 Current State: 64:[67, 5], Operations: ['42-12=30', '30/6=5'] Exploring Operation: 67+5=72, Resulting Numbers: [72] 72,64 unequal: No Solution Exploring Operation: 67*5=335, Resulting Numbers: [335] 335,64 unequal: No Solution Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,64 unequal: No Solution Moving to Node #0,0,0 Current State: 64:[30, 61], Operations: ['42-12=30', '67-6=61'] Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,64 unequal: No Solution Exploring Operation: 30+61=91, Resulting Numbers: [91] 91,64 unequal: No Solution Exploring Operation: 30*61=1830, Resulting Numbers: [1830] 1830,64 unequal: No Solution Moving to Node #0,0,3 Current State: 64:[6, 37], Operations: ['42-12=30', '67-30=37'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,64 unequal: No Solution Exploring Operation: 6*37=222, Resulting Numbers: [222] 222,64 unequal: No Solution Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[67, 36], Operations: ['42-12=30', '6+30=36'] Exploring Operation: 67-36=31, Resulting Numbers: [31] 31,64 unequal: No Solution Exploring Operation: 67*36=2412, Resulting Numbers: [2412] 2412,64 unequal: No Solution Exploring Operation: 67+36=103, Resulting Numbers: [103] 103,64 unequal: No Solution No 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: 64:[67, 12, 7], Operations: ['42/6=7'] Exploring Operation: 12+7=19, Resulting Numbers: [67, 19] Generated Node #0,3,0: 64:[67, 19] Operation: 12+7=19 Exploring Operation: 67-12=55, Resulting Numbers: [7, 55] Generated Node #0,3,1: 64:[7, 55] Operation: 67-12=55 Exploring Operation: 12-7=5, Resulting Numbers: [67, 5] Generated Node #0,3,2: 64:[67, 5] Operation: 12-7=5 Exploring Operation: 67-7=60, Resulting Numbers: [12, 60] Generated Node #0,3,3: 64:[12, 60] Operation: 67-7=60 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 64:[67, 5], Operations: ['42/6=7', '12-7=5'] Exploring Operation: 67*5=335, Resulting Numbers: [335] 335,64 unequal: No Solution Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,64 unequal: No Solution Exploring Operation: 67+5=72, Resulting Numbers: [72] 72,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 64:[67, 19], Operations: ['42/6=7', '12+7=19'] Exploring Operation: 67+19=86, Resulting Numbers: [86] 86,64 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,64 unequal: No Solution Exploring Operation: 67*19=1273, Resulting Numbers: [1273] 1273,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 64:[12, 60], Operations: ['42/6=7', '67-7=60'] Exploring Operation: 12+60=72, Resulting Numbers: [72] 72,64 unequal: No Solution Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,64 unequal: No Solution Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,64 unequal: No Solution Exploring Operation: 12*60=720, Resulting Numbers: [720] 720,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 64:[7, 55], Operations: ['42/6=7', '67-12=55'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,64 unequal: No Solution Exploring Operation: 7*55=385, Resulting Numbers: [385] 385,64 unequal: No Solution Exploring Operation: 7+55=62, Resulting Numbers: [62] 62,64 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: 64:[67, 12, 36], Operations: ['42-6=36'] Exploring Operation: 67-36=31, Resulting Numbers: [12, 31] Generated Node #0,2,0: 64:[12, 31] Operation: 67-36=31 Exploring Operation: 67-12=55, Resulting Numbers: [36, 55] Generated Node #0,2,1: 64:[36, 55] Operation: 67-12=55 Exploring Operation: 36-12=24, Resulting Numbers: [67, 24] Generated Node #0,2,2: 64:[67, 24] Operation: 36-12=24 Exploring Operation: 36/12=3, Resulting Numbers: [67, 3] Generated Node #0,2,3: 64:[67, 3] Operation: 36/12=3 Moving to Node #0,2,3 Current State: 64:[67, 3], Operations: ['42-6=36', '36/12=3'] Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[67, 12, 42, 6], Operations: [] Exploring Operation: 42-6=36, Resulting Numbers: [67, 12, 36] Generated Node #0,2: 64:[67, 12, 36] Operation: 42-6=36 Moving to Node #0,2 Current State: 64:[67, 12, 36], Operations: ['42-6=36'] Exploring Operation: 36/12=3, Resulting Numbers: [67, 3] Generated Node #0,2,3: 64:[67, 3] Operation: 36/12=3 Moving to Node #0,2,3 Current State: 64:[67, 3], Operations: ['42-6=36', '36/12=3'] Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.960069
hs_4
mult_heuristic
[ 80, 94, 94, 53 ]
80
[ "94-94=0", "53*0=0", "80+0=80" ]
Current State: 80:[80, 94, 94, 53], Operations: [] Exploring Operation: 94-94=0, Resulting Numbers: [80, 53, 0] Generated Node #2: [80, 53, 0] from Operation: 94-94=0 Current State: 80:[80, 53, 0], Operations: ['94-94=0'] Exploring Operation: 53*0=0, Resulting Numbers: [80, 0] Generated Node #3: [80, 0] from Operation: 53*0=0 Current State: 80:[80, 0], Operations: ['94-94=0', '53*0=0'] Exploring Operation: 80+0=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[80, 94, 94, 53], Operations: [] Exploring Operation: 94-53=41, Resulting Numbers: [80, 94, 41] Generated Node #0,0: 80:[80, 94, 41] Operation: 94-53=41 Exploring Operation: 94-94=0, Resulting Numbers: [80, 53, 0] Generated Node #0,1: 80:[80, 53, 0] Operation: 94-94=0 Exploring Operation: 94-80=14, Resulting Numbers: [94, 53, 14] Generated Node #0,2: 80:[94, 53, 14] Operation: 94-80=14 Exploring Operation: 94-53=41, Resulting Numbers: [80, 94, 41] Generated Node #0,3: 80:[80, 94, 41] Operation: 94-53=41 Exploring Operation: 94/94=1, Resulting Numbers: [80, 53, 1] Generated Node #0,4: 80:[80, 53, 1] Operation: 94/94=1 Moving to Node #0,4 Current State: 80:[80, 53, 1], Operations: ['94/94=1'] Exploring Operation: 53-1=52, Resulting Numbers: [80, 52] Generated Node #0,4,0: 80:[80, 52] Operation: 53-1=52 Exploring Operation: 80/1=80, Resulting Numbers: [53, 80] Generated Node #0,4,1: 80:[53, 80] Operation: 80/1=80 Exploring Operation: 80*1=80, Resulting Numbers: [53, 80] Generated Node #0,4,2: 80:[53, 80] Operation: 80*1=80 Exploring Operation: 53*1=53, Resulting Numbers: [80, 53] Generated Node #0,4,3: 80:[80, 53] Operation: 53*1=53 Exploring Operation: 80-53=27, Resulting Numbers: [1, 27] Generated Node #0,4,4: 80:[1, 27] Operation: 80-53=27 Moving to Node #0,1 Current State: 80:[80, 53, 0], Operations: ['94-94=0'] Exploring Operation: 53+0=53, Resulting Numbers: [80, 53] Generated Node #0,1,0: 80:[80, 53] Operation: 53+0=53 Exploring Operation: 80-53=27, Resulting Numbers: [0, 27] Generated Node #0,1,1: 80:[0, 27] Operation: 80-53=27 Exploring Operation: 80+0=80, Resulting Numbers: [53, 80] Generated Node #0,1,2: 80:[53, 80] Operation: 80+0=80 Exploring Operation: 53*0=0, Resulting Numbers: [80, 0] Generated Node #0,1,3: 80:[80, 0] Operation: 53*0=0 Exploring Operation: 80-0=80, Resulting Numbers: [53, 80] Generated Node #0,1,4: 80:[53, 80] Operation: 80-0=80 Moving to Node #0,0 Current State: 80:[80, 94, 41], Operations: ['94-53=41'] Exploring Operation: 94+41=135, Resulting Numbers: [80, 135] Generated Node #0,0,0: 80:[80, 135] Operation: 94+41=135 Exploring Operation: 80-41=39, Resulting Numbers: [94, 39] Generated Node #0,0,1: 80:[94, 39] Operation: 80-41=39 Exploring Operation: 94-41=53, Resulting Numbers: [80, 53] Generated Node #0,0,2: 80:[80, 53] Operation: 94-41=53 Exploring Operation: 80+41=121, Resulting Numbers: [94, 121] Generated Node #0,0,3: 80:[94, 121] Operation: 80+41=121 Exploring Operation: 94-80=14, Resulting Numbers: [41, 14] Generated Node #0,0,4: 80:[41, 14] Operation: 94-80=14 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 80:[41, 14], Operations: ['94-53=41', '94-80=14'] Exploring Operation: 41*14=574, Resulting Numbers: [574] 574,80 unequal: No Solution Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 80:[80, 53], Operations: ['94-53=41', '94-41=53'] Exploring Operation: 80-53=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 80+53=133, Resulting Numbers: [133] 133,80 unequal: No Solution Exploring Operation: 80*53=4240, Resulting Numbers: [4240] 4240,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[94, 39], Operations: ['94-53=41', '80-41=39'] Exploring Operation: 94*39=3666, Resulting Numbers: [3666] 3666,80 unequal: No Solution Exploring Operation: 94-39=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 94+39=133, Resulting Numbers: [133] 133,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[80, 135], Operations: ['94-53=41', '94+41=135'] Exploring Operation: 135-80=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 80*135=10800, Resulting Numbers: [10800] 10800,80 unequal: No Solution Exploring Operation: 80+135=215, Resulting Numbers: [215] 215,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 80:[94, 121], Operations: ['94-53=41', '80+41=121'] Exploring Operation: 94+121=215, Resulting Numbers: [215] 215,80 unequal: No Solution Exploring Operation: 121-94=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 94*121=11374, Resulting Numbers: [11374] 11374,80 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: 80:[80, 94, 41], Operations: ['94-53=41'] Exploring Operation: 80+41=121, Resulting Numbers: [94, 121] Generated Node #0,3,0: 80:[94, 121] Operation: 80+41=121 Exploring Operation: 94-80=14, Resulting Numbers: [41, 14] Generated Node #0,3,1: 80:[41, 14] Operation: 94-80=14 Exploring Operation: 80-41=39, Resulting Numbers: [94, 39] Generated Node #0,3,2: 80:[94, 39] Operation: 80-41=39 Exploring Operation: 94+41=135, Resulting Numbers: [80, 135] Generated Node #0,3,3: 80:[80, 135] Operation: 94+41=135 Exploring Operation: 94-41=53, Resulting Numbers: [80, 53] Generated Node #0,3,4: 80:[80, 53] Operation: 94-41=53 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 80:[41, 14], Operations: ['94-53=41', '94-80=14'] Exploring Operation: 41*14=574, Resulting Numbers: [574] 574,80 unequal: No Solution Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,80 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 #0,3,4 Current State: 80:[80, 53], Operations: ['94-53=41', '94-41=53'] Exploring Operation: 80-53=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 80*53=4240, Resulting Numbers: [4240] 4240,80 unequal: No Solution Exploring Operation: 80+53=133, Resulting Numbers: [133] 133,80 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:[94, 39], Operations: ['94-53=41', '80-41=39'] Exploring Operation: 94+39=133, Resulting Numbers: [133] 133,80 unequal: No Solution Exploring Operation: 94-39=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 94*39=3666, Resulting Numbers: [3666] 3666,80 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 #0,3,0 Current State: 80:[94, 121], Operations: ['94-53=41', '80+41=121'] Exploring Operation: 121-94=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 94*121=11374, Resulting Numbers: [11374] 11374,80 unequal: No Solution Exploring Operation: 94+121=215, Resulting Numbers: [215] 215,80 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:[80, 135], Operations: ['94-53=41', '94+41=135'] Exploring Operation: 80+135=215, Resulting Numbers: [215] 215,80 unequal: No Solution Exploring Operation: 80*135=10800, Resulting Numbers: [10800] 10800,80 unequal: No Solution Exploring Operation: 135-80=55, Resulting Numbers: [55] 55,80 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: 80:[94, 53, 14], Operations: ['94-80=14'] Exploring Operation: 94-53=41, Resulting Numbers: [14, 41] Generated Node #0,2,0: 80:[14, 41] Operation: 94-53=41 Exploring Operation: 53-14=39, Resulting Numbers: [94, 39] Generated Node #0,2,1: 80:[94, 39] Operation: 53-14=39 Exploring Operation: 53+14=67, Resulting Numbers: [94, 67] Generated Node #0,2,2: 80:[94, 67] Operation: 53+14=67 Exploring Operation: 94+14=108, Resulting Numbers: [53, 108] Generated Node #0,2,3: 80:[53, 108] Operation: 94+14=108 Exploring Operation: 94-14=80, Resulting Numbers: [53, 80] Generated Node #0,2,4: 80:[53, 80] Operation: 94-14=80 Moving to Node #0,1,3 Current State: 80:[80, 0], Operations: ['94-94=0', '53*0=0'] Exploring Operation: 80+0=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[80, 94, 94, 53], Operations: [] Exploring Operation: 94-94=0, Resulting Numbers: [80, 53, 0] Generated Node #0,1: 80:[80, 53, 0] Operation: 94-94=0 Moving to Node #0,1 Current State: 80:[80, 53, 0], Operations: ['94-94=0'] Exploring Operation: 53*0=0, Resulting Numbers: [80, 0] Generated Node #0,1,3: 80:[80, 0] Operation: 53*0=0 Moving to Node #0,1,3 Current State: 80:[80, 0], Operations: ['94-94=0', '53*0=0'] Exploring Operation: 80+0=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
0.943576
hs_5
mult_heuristic
[ 81, 57, 9, 38 ]
91
[ "81+57=138", "9+38=47", "138-47=91" ]
Current State: 91:[81, 57, 9, 38], Operations: [] Exploring Operation: 81+57=138, Resulting Numbers: [9, 38, 138] Generated Node #2: [9, 38, 138] from Operation: 81+57=138 Current State: 91:[9, 38, 138], Operations: ['81+57=138'] Exploring Operation: 9+38=47, Resulting Numbers: [138, 47] Generated Node #3: [138, 47] from Operation: 9+38=47 Current State: 91:[138, 47], Operations: ['81+57=138', '9+38=47'] Exploring Operation: 138-47=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[81, 57, 9, 38], Operations: [] Exploring Operation: 81-57=24, Resulting Numbers: [9, 38, 24] Generated Node #0,0: 91:[9, 38, 24] Operation: 81-57=24 Exploring Operation: 57-38=19, Resulting Numbers: [81, 9, 19] Generated Node #0,1: 91:[81, 9, 19] Operation: 57-38=19 Exploring Operation: 57+38=95, Resulting Numbers: [81, 9, 95] Generated Node #0,2: 91:[81, 9, 95] Operation: 57+38=95 Exploring Operation: 81+9=90, Resulting Numbers: [57, 38, 90] Generated Node #0,3: 91:[57, 38, 90] Operation: 81+9=90 Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[81, 9, 95], Operations: ['57+38=95'] Exploring Operation: 81+9=90, Resulting Numbers: [95, 90] Generated Node #0,2,0: 91:[95, 90] Operation: 81+9=90 Exploring Operation: 95-9=86, Resulting Numbers: [81, 86] Generated Node #0,2,1: 91:[81, 86] Operation: 95-9=86 Exploring Operation: 81/9=9, Resulting Numbers: [95, 9] Generated Node #0,2,2: 91:[95, 9] Operation: 81/9=9 Exploring Operation: 95-81=14, Resulting Numbers: [9, 14] Generated Node #0,2,3: 91:[9, 14] Operation: 95-81=14 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 91:[9, 14], Operations: ['57+38=95', '95-81=14'] Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,91 unequal: No Solution Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,91 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,91 unequal: No Solution No 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: 91:[95, 90], Operations: ['57+38=95', '81+9=90'] Exploring Operation: 95+90=185, Resulting Numbers: [185] 185,91 unequal: No Solution Exploring Operation: 95*90=8550, Resulting Numbers: [8550] 8550,91 unequal: No Solution Exploring Operation: 95-90=5, Resulting Numbers: [5] 5,91 unequal: No Solution No 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: 91:[95, 9], Operations: ['57+38=95', '81/9=9'] Exploring Operation: 95-9=86, Resulting Numbers: [86] 86,91 unequal: No Solution Exploring Operation: 95+9=104, Resulting Numbers: [104] 104,91 unequal: No Solution Exploring Operation: 95*9=855, Resulting Numbers: [855] 855,91 unequal: No Solution No 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: 91:[81, 86], Operations: ['57+38=95', '95-9=86'] Exploring Operation: 81*86=6966, Resulting Numbers: [6966] 6966,91 unequal: No Solution Exploring Operation: 81+86=167, Resulting Numbers: [167] 167,91 unequal: No Solution Exploring Operation: 86-81=5, Resulting Numbers: [5] 5,91 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: 91:[81, 9, 19], Operations: ['57-38=19'] Exploring Operation: 81/9=9, Resulting Numbers: [19, 9] Generated Node #0,1,0: 91:[19, 9] Operation: 81/9=9 Exploring Operation: 81+9=90, Resulting Numbers: [19, 90] Generated Node #0,1,1: 91:[19, 90] Operation: 81+9=90 Exploring Operation: 19-9=10, Resulting Numbers: [81, 10] Generated Node #0,1,2: 91:[81, 10] Operation: 19-9=10 Exploring Operation: 81+19=100, Resulting Numbers: [9, 100] Generated Node #0,1,3: 91:[9, 100] Operation: 81+19=100 Moving to Node #0,1,1 Current State: 91:[19, 90], Operations: ['57-38=19', '81+9=90'] Exploring Operation: 19+90=109, Resulting Numbers: [109] 109,91 unequal: No Solution Exploring Operation: 90-19=71, Resulting Numbers: [71] 71,91 unequal: No Solution Exploring Operation: 19*90=1710, Resulting Numbers: [1710] 1710,91 unequal: No Solution Moving to Node #0,1,0 Current State: 91:[19, 9], Operations: ['57-38=19', '81/9=9'] Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,91 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,91 unequal: No Solution Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,91 unequal: No Solution Moving to Node #0,1,3 Current State: 91:[9, 100], Operations: ['57-38=19', '81+19=100'] Exploring Operation: 9+100=109, Resulting Numbers: [109] 109,91 unequal: No Solution Exploring Operation: 9*100=900, Resulting Numbers: [900] 900,91 unequal: No Solution Exploring Operation: 100-9=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[81, 57, 9, 38], Operations: [] Exploring Operation: 57-38=19, Resulting Numbers: [81, 9, 19] Generated Node #0,1: 91:[81, 9, 19] Operation: 57-38=19 Moving to Node #0,1 Current State: 91:[81, 9, 19], Operations: ['57-38=19'] Exploring Operation: 81+19=100, Resulting Numbers: [9, 100] Generated Node #0,1,3: 91:[9, 100] Operation: 81+19=100 Moving to Node #0,1,3 Current State: 91:[9, 100], Operations: ['57-38=19', '81+19=100'] Exploring Operation: 100-9=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_4
mult_heuristic
[ 7, 82, 93, 7 ]
60
[ "7*7=49", "93-82=11", "49+11=60" ]
Current State: 60:[7, 82, 93, 7], Operations: [] Exploring Operation: 7*7=49, Resulting Numbers: [82, 93, 49] Generated Node #2: [82, 93, 49] from Operation: 7*7=49 Current State: 60:[82, 93, 49], Operations: ['7*7=49'] Exploring Operation: 93-82=11, Resulting Numbers: [49, 11] Generated Node #3: [49, 11] from Operation: 93-82=11 Current State: 60:[49, 11], Operations: ['7*7=49', '93-82=11'] Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[7, 82, 93, 7], Operations: [] Exploring Operation: 82-7=75, Resulting Numbers: [93, 7, 75] Generated Node #0,0: 60:[93, 7, 75] Operation: 82-7=75 Exploring Operation: 93-82=11, Resulting Numbers: [7, 7, 11] Generated Node #0,1: 60:[7, 7, 11] Operation: 93-82=11 Exploring Operation: 93-7=86, Resulting Numbers: [82, 7, 86] Generated Node #0,2: 60:[82, 7, 86] Operation: 93-7=86 Exploring Operation: 82-7=75, Resulting Numbers: [7, 93, 75] Generated Node #0,3: 60:[7, 93, 75] Operation: 82-7=75 Moving to Node #0,1 Current State: 60:[7, 7, 11], Operations: ['93-82=11'] Exploring Operation: 11-7=4, Resulting Numbers: [7, 4] Generated Node #0,1,0: 60:[7, 4] Operation: 11-7=4 Exploring Operation: 7+7=14, Resulting Numbers: [11, 14] Generated Node #0,1,1: 60:[11, 14] Operation: 7+7=14 Exploring Operation: 7/7=1, Resulting Numbers: [11, 1] Generated Node #0,1,2: 60:[11, 1] Operation: 7/7=1 Exploring Operation: 11-7=4, Resulting Numbers: [7, 4] Generated Node #0,1,3: 60:[7, 4] Operation: 11-7=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[7, 4], Operations: ['93-82=11', '11-7=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 60:[7, 4], Operations: ['93-82=11', '11-7=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[11, 14], Operations: ['93-82=11', '7+7=14'] Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,60 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,60 unequal: No Solution Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 60:[11, 1], Operations: ['93-82=11', '7/7=1'] Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,60 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: 60:[82, 7, 86], Operations: ['93-7=86'] Exploring Operation: 86-7=79, Resulting Numbers: [82, 79] Generated Node #0,2,0: 60:[82, 79] Operation: 86-7=79 Exploring Operation: 86-82=4, Resulting Numbers: [7, 4] Generated Node #0,2,1: 60:[7, 4] Operation: 86-82=4 Exploring Operation: 82-7=75, Resulting Numbers: [86, 75] Generated Node #0,2,2: 60:[86, 75] Operation: 82-7=75 Exploring Operation: 82+7=89, Resulting Numbers: [86, 89] Generated Node #0,2,3: 60:[86, 89] Operation: 82+7=89 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 60:[7, 4], Operations: ['93-7=86', '86-82=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,60 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 60:[82, 79], Operations: ['93-7=86', '86-7=79'] Exploring Operation: 82*79=6478, Resulting Numbers: [6478] 6478,60 unequal: No Solution Exploring Operation: 82-79=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 82+79=161, Resulting Numbers: [161] 161,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 60:[86, 75], Operations: ['93-7=86', '82-7=75'] Exploring Operation: 86*75=6450, Resulting Numbers: [6450] 6450,60 unequal: No Solution Exploring Operation: 86+75=161, Resulting Numbers: [161] 161,60 unequal: No Solution Exploring Operation: 86-75=11, Resulting Numbers: [11] 11,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 60:[86, 89], Operations: ['93-7=86', '82+7=89'] Exploring Operation: 86+89=175, Resulting Numbers: [175] 175,60 unequal: No Solution Exploring Operation: 89-86=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 86*89=7654, Resulting Numbers: [7654] 7654,60 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: 60:[93, 7, 75], Operations: ['82-7=75'] Exploring Operation: 93+7=100, Resulting Numbers: [75, 100] Generated Node #0,0,0: 60:[75, 100] Operation: 93+7=100 Exploring Operation: 75-7=68, Resulting Numbers: [93, 68] Generated Node #0,0,1: 60:[93, 68] Operation: 75-7=68 Exploring Operation: 93-7=86, Resulting Numbers: [75, 86] Generated Node #0,0,2: 60:[75, 86] Operation: 93-7=86 Exploring Operation: 93-75=18, Resulting Numbers: [7, 18] Generated Node #0,0,3: 60:[7, 18] Operation: 93-75=18 Moving to Node #0,3 Current State: 60:[7, 93, 75], Operations: ['82-7=75'] Exploring Operation: 93-7=86, Resulting Numbers: [75, 86] Generated Node #0,3,0: 60:[75, 86] Operation: 93-7=86 Exploring Operation: 7+93=100, Resulting Numbers: [75, 100] Generated Node #0,3,1: 60:[75, 100] Operation: 7+93=100 Exploring Operation: 75-7=68, Resulting Numbers: [93, 68] Generated Node #0,3,2: 60:[93, 68] Operation: 75-7=68 Exploring Operation: 93-75=18, Resulting Numbers: [7, 18] Generated Node #0,3,3: 60:[7, 18] Operation: 93-75=18 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 60:[7, 18], Operations: ['82-7=75', '93-75=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,60 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 60:[75, 86], Operations: ['82-7=75', '93-7=86'] Exploring Operation: 75*86=6450, Resulting Numbers: [6450] 6450,60 unequal: No Solution Exploring Operation: 75+86=161, Resulting Numbers: [161] 161,60 unequal: No Solution Exploring Operation: 86-75=11, Resulting Numbers: [11] 11,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 60:[93, 68], Operations: ['82-7=75', '75-7=68'] Exploring Operation: 93*68=6324, Resulting Numbers: [6324] 6324,60 unequal: No Solution Exploring Operation: 93+68=161, Resulting Numbers: [161] 161,60 unequal: No Solution Exploring Operation: 93-68=25, Resulting Numbers: [25] 25,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 60:[75, 100], Operations: ['82-7=75', '7+93=100'] Exploring Operation: 75+100=175, Resulting Numbers: [175] 175,60 unequal: No Solution Exploring Operation: 75*100=7500, Resulting Numbers: [7500] 7500,60 unequal: No Solution Exploring Operation: 100-75=25, Resulting Numbers: [25] 25,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 60:[7, 18], Operations: ['82-7=75', '93-75=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,60 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,60 unequal: No Solution Moving to Node #0,0,2 Current State: 60:[75, 86], Operations: ['82-7=75', '93-7=86'] Exploring Operation: 75*86=6450, Resulting Numbers: [6450] 6450,60 unequal: No Solution Exploring Operation: 86-75=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 75+86=161, Resulting Numbers: [161] 161,60 unequal: No Solution Moving to Node #0,0,1 Current State: 60:[93, 68], Operations: ['82-7=75', '75-7=68'] Exploring Operation: 93-68=25, Resulting Numbers: [25] 25,60 unequal: No Solution Exploring Operation: 93+68=161, Resulting Numbers: [161] 161,60 unequal: No Solution Exploring Operation: 93*68=6324, Resulting Numbers: [6324] 6324,60 unequal: No Solution Moving to Node #0,0,0 Current State: 60:[75, 100], Operations: ['82-7=75', '93+7=100'] Exploring Operation: 75*100=7500, Resulting Numbers: [7500] 7500,60 unequal: No Solution Exploring Operation: 100-75=25, Resulting Numbers: [25] 25,60 unequal: No Solution Exploring Operation: 75+100=175, Resulting Numbers: [175] 175,60 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 66, 90, 30, 76 ]
95
[ "90-66=24", "30*76=2280", "2280/24=95" ]
Current State: 95:[66, 90, 30, 76], Operations: [] Exploring Operation: 90-66=24, Resulting Numbers: [30, 76, 24] Generated Node #2: [30, 76, 24] from Operation: 90-66=24 Current State: 95:[30, 76, 24], Operations: ['90-66=24'] Exploring Operation: 30*76=2280, Resulting Numbers: [24, 2280] Generated Node #3: [24, 2280] from Operation: 30*76=2280 Current State: 95:[24, 2280], Operations: ['90-66=24', '30*76=2280'] Exploring Operation: 2280/24=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[66, 90, 30, 76], Operations: [] Exploring Operation: 76-66=10, Resulting Numbers: [90, 30, 10] Generated Node #0,0: 95:[90, 30, 10] Operation: 76-66=10 Exploring Operation: 66+30=96, Resulting Numbers: [90, 76, 96] Generated Node #0,1: 95:[90, 76, 96] Operation: 66+30=96 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[90, 30, 10], Operations: ['76-66=10'] Exploring Operation: 90/30=3, Resulting Numbers: [10, 3] Generated Node #0,0,0: 95:[10, 3] Operation: 90/30=3 Exploring Operation: 30-10=20, Resulting Numbers: [90, 20] Generated Node #0,0,1: 95:[90, 20] Operation: 30-10=20 Moving to Node #0,0,1 Current State: 95:[90, 20], Operations: ['76-66=10', '30-10=20'] Exploring Operation: 90-20=70, Resulting Numbers: [70] 70,95 unequal: No Solution Exploring Operation: 90+20=110, Resulting Numbers: [110] 110,95 unequal: No Solution Moving to Node #0,0,0 Current State: 95:[10, 3], Operations: ['76-66=10', '90/30=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,95 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[90, 76, 96], Operations: ['66+30=96'] Exploring Operation: 96-76=20, Resulting Numbers: [90, 20] Generated Node #0,1,0: 95:[90, 20] Operation: 96-76=20 Exploring Operation: 90-76=14, Resulting Numbers: [96, 14] Generated Node #0,1,1: 95:[96, 14] Operation: 90-76=14 Moving to Node #0,1,0 Current State: 95:[90, 20], Operations: ['66+30=96', '96-76=20'] Exploring Operation: 90-20=70, Resulting Numbers: [70] 70,95 unequal: No Solution Exploring Operation: 90+20=110, Resulting Numbers: [110] 110,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[96, 14], Operations: ['66+30=96', '90-76=14'] Exploring Operation: 96+14=110, Resulting Numbers: [110] 110,95 unequal: No Solution Exploring Operation: 96-14=82, Resulting Numbers: [82] 82,95 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
[ 70, 53, 71, 9 ]
35
[ "70*9=630", "71-53=18", "630/18=35" ]
Current State: 35:[70, 53, 71, 9], Operations: [] Exploring Operation: 70*9=630, Resulting Numbers: [53, 71, 630] Generated Node #2: [53, 71, 630] from Operation: 70*9=630 Current State: 35:[53, 71, 630], Operations: ['70*9=630'] Exploring Operation: 71-53=18, Resulting Numbers: [630, 18] Generated Node #3: [630, 18] from Operation: 71-53=18 Current State: 35:[630, 18], Operations: ['70*9=630', '71-53=18'] Exploring Operation: 630/18=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[70, 53, 71, 9], Operations: [] Exploring Operation: 71-53=18, Resulting Numbers: [70, 9, 18] Generated Node #0,0: 35:[70, 9, 18] Operation: 71-53=18 Exploring Operation: 70-53=17, Resulting Numbers: [71, 9, 17] Generated Node #0,1: 35:[71, 9, 17] Operation: 70-53=17 Exploring Operation: 70-9=61, Resulting Numbers: [53, 71, 61] Generated Node #0,2: 35:[53, 71, 61] Operation: 70-9=61 Exploring Operation: 71-70=1, Resulting Numbers: [53, 9, 1] Generated Node #0,3: 35:[53, 9, 1] Operation: 71-70=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 35:[53, 9, 1], Operations: ['71-70=1'] Exploring Operation: 53*1=53, Resulting Numbers: [9, 53] Generated Node #0,3,0: 35:[9, 53] Operation: 53*1=53 Exploring Operation: 53-1=52, Resulting Numbers: [9, 52] Generated Node #0,3,1: 35:[9, 52] Operation: 53-1=52 Exploring Operation: 9-1=8, Resulting Numbers: [53, 8] Generated Node #0,3,2: 35:[53, 8] Operation: 9-1=8 Exploring Operation: 53-9=44, Resulting Numbers: [1, 44] Generated Node #0,3,3: 35:[1, 44] Operation: 53-9=44 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 35:[1, 44], Operations: ['71-70=1', '53-9=44'] Exploring Operation: 1+44=45, Resulting Numbers: [45] 45,35 unequal: No Solution Exploring Operation: 1*44=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 35:[9, 52], Operations: ['71-70=1', '53-1=52'] Exploring Operation: 9+52=61, Resulting Numbers: [61] 61,35 unequal: No Solution Exploring Operation: 9*52=468, Resulting Numbers: [468] 468,35 unequal: No Solution Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 35:[53, 8], Operations: ['71-70=1', '9-1=8'] Exploring Operation: 53*8=424, Resulting Numbers: [424] 424,35 unequal: No Solution Exploring Operation: 53+8=61, Resulting Numbers: [61] 61,35 unequal: No Solution Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 35:[9, 53], Operations: ['71-70=1', '53*1=53'] Exploring Operation: 53-9=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 9+53=62, Resulting Numbers: [62] 62,35 unequal: No Solution Exploring Operation: 9*53=477, Resulting Numbers: [477] 477,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[70, 9, 18], Operations: ['71-53=18'] Exploring Operation: 70-18=52, Resulting Numbers: [9, 52] Generated Node #0,0,0: 35:[9, 52] Operation: 70-18=52 Exploring Operation: 18-9=9, Resulting Numbers: [70, 9] Generated Node #0,0,1: 35:[70, 9] Operation: 18-9=9 Exploring Operation: 18/9=2, Resulting Numbers: [70, 2] Generated Node #0,0,2: 35:[70, 2] Operation: 18/9=2 Exploring Operation: 70-9=61, Resulting Numbers: [18, 61] Generated Node #0,0,3: 35:[18, 61] Operation: 70-9=61 Moving to Node #0,0,0 Current State: 35:[9, 52], Operations: ['71-53=18', '70-18=52'] Exploring Operation: 9*52=468, Resulting Numbers: [468] 468,35 unequal: No Solution Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,35 unequal: No Solution Exploring Operation: 9+52=61, Resulting Numbers: [61] 61,35 unequal: No Solution Moving to Node #0,0,3 Current State: 35:[18, 61], Operations: ['71-53=18', '70-9=61'] Exploring Operation: 18*61=1098, Resulting Numbers: [1098] 1098,35 unequal: No Solution Exploring Operation: 18+61=79, Resulting Numbers: [79] 79,35 unequal: No Solution Exploring Operation: 61-18=43, Resulting Numbers: [43] 43,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[70, 9], Operations: ['71-53=18', '18-9=9'] Exploring Operation: 70*9=630, Resulting Numbers: [630] 630,35 unequal: No Solution Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,35 unequal: No Solution Exploring Operation: 70+9=79, Resulting Numbers: [79] 79,35 unequal: No Solution Moving to Node #0,0,2 Current State: 35:[70, 2], Operations: ['71-53=18', '18/9=2'] Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[70, 53, 71, 9], Operations: [] Exploring Operation: 71-53=18, Resulting Numbers: [70, 9, 18] Generated Node #0,0: 35:[70, 9, 18] Operation: 71-53=18 Moving to Node #0,0 Current State: 35:[70, 9, 18], Operations: ['71-53=18'] Exploring Operation: 18/9=2, Resulting Numbers: [70, 2] Generated Node #0,0,2: 35:[70, 2] Operation: 18/9=2 Moving to Node #0,0,2 Current State: 35:[70, 2], Operations: ['71-53=18', '18/9=2'] Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_4
sum_heuristic
[ 33, 55, 84, 77 ]
27
[ "55*84=4620", "4620/77=60", "60-33=27" ]
Current State: 27:[33, 55, 84, 77], Operations: [] Exploring Operation: 55*84=4620, Resulting Numbers: [33, 77, 4620] Generated Node #2: [33, 77, 4620] from Operation: 55*84=4620 Current State: 27:[33, 77, 4620], Operations: ['55*84=4620'] Exploring Operation: 4620/77=60, Resulting Numbers: [33, 60] Generated Node #3: [33, 60] from Operation: 4620/77=60 Current State: 27:[33, 60], Operations: ['55*84=4620', '4620/77=60'] Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[33, 55, 84, 77], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [33, 55, 7] Generated Node #0,0: 27:[33, 55, 7] Operation: 84-77=7 Moving to Node #0,0 Current State: 27:[33, 55, 7], Operations: ['84-77=7'] Exploring Operation: 55-33=22, Resulting Numbers: [7, 22] Generated Node #0,0,0: 27:[7, 22] Operation: 55-33=22 Moving to Node #0,0,0 Current State: 27:[7, 22], Operations: ['84-77=7', '55-33=22'] Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,27 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 7, 87, 58, 28 ]
35
[ "87*28=2436", "2436/58=42", "42-7=35" ]
Current State: 35:[7, 87, 58, 28], Operations: [] Exploring Operation: 87*28=2436, Resulting Numbers: [7, 58, 2436] Generated Node #2: [7, 58, 2436] from Operation: 87*28=2436 Current State: 35:[7, 58, 2436], Operations: ['87*28=2436'] Exploring Operation: 2436/58=42, Resulting Numbers: [7, 42] Generated Node #3: [7, 42] from Operation: 2436/58=42 Current State: 35:[7, 42], Operations: ['87*28=2436', '2436/58=42'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[7, 87, 58, 28], Operations: [] Exploring Operation: 87-58=29, Resulting Numbers: [7, 28, 29] Generated Node #0,0: 35:[7, 28, 29] Operation: 87-58=29 Exploring Operation: 87-28=59, Resulting Numbers: [7, 58, 59] Generated Node #0,1: 35:[7, 58, 59] Operation: 87-28=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[7, 28, 29], Operations: ['87-58=29'] Exploring Operation: 7+28=35, Resulting Numbers: [29, 35] Generated Node #0,0,0: 35:[29, 35] Operation: 7+28=35 Exploring Operation: 29-28=1, Resulting Numbers: [7, 1] Generated Node #0,0,1: 35:[7, 1] Operation: 29-28=1 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 35:[7, 1], Operations: ['87-58=29', '29-28=1'] Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,35 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 #0,0,0 Current State: 35:[29, 35], Operations: ['87-58=29', '7+28=35'] Exploring Operation: 29+35=64, Resulting Numbers: [64] 64,35 unequal: No Solution Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[7, 58, 59], Operations: ['87-28=59'] Exploring Operation: 58-7=51, Resulting Numbers: [59, 51] Generated Node #0,1,0: 35:[59, 51] Operation: 58-7=51 Exploring Operation: 59-58=1, Resulting Numbers: [7, 1] Generated Node #0,1,1: 35:[7, 1] Operation: 59-58=1 Moving to Node #0,1,1 Current State: 35:[7, 1], Operations: ['87-28=59', '59-58=1'] Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[59, 51], Operations: ['87-28=59', '58-7=51'] Exploring Operation: 59+51=110, Resulting Numbers: [110] 110,35 unequal: No Solution Exploring Operation: 59-51=8, Resulting Numbers: [8] 8,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 2, 10, 72, 10 ]
64
[ "72/2=36", "10*10=100", "100-36=64" ]
Current State: 64:[2, 10, 72, 10], Operations: [] Exploring Operation: 72/2=36, Resulting Numbers: [10, 10, 36] Generated Node #2: [10, 10, 36] from Operation: 72/2=36 Current State: 64:[10, 10, 36], Operations: ['72/2=36'] Exploring Operation: 10*10=100, Resulting Numbers: [36, 100] Generated Node #3: [36, 100] from Operation: 10*10=100 Current State: 64:[36, 100], Operations: ['72/2=36', '10*10=100'] Exploring Operation: 100-36=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[2, 10, 72, 10], Operations: [] Exploring Operation: 72-10=62, Resulting Numbers: [2, 10, 62] Generated Node #0,0: 64:[2, 10, 62] Operation: 72-10=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[2, 10, 62], Operations: ['72-10=62'] Exploring Operation: 10-2=8, Resulting Numbers: [62, 8] Generated Node #0,0,0: 64:[62, 8] Operation: 10-2=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 64:[62, 8], Operations: ['72-10=62', '10-2=8'] Exploring Operation: 62+8=70, Resulting Numbers: [70] 70,64 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
[ 90, 5, 45, 58 ]
61
[ "90/45=2", "5+58=63", "63-2=61" ]
Current State: 61:[90, 5, 45, 58], Operations: [] Exploring Operation: 90/45=2, Resulting Numbers: [5, 58, 2] Generated Node #2: [5, 58, 2] from Operation: 90/45=2 Current State: 61:[5, 58, 2], Operations: ['90/45=2'] Exploring Operation: 5+58=63, Resulting Numbers: [2, 63] Generated Node #3: [2, 63] from Operation: 5+58=63 Current State: 61:[2, 63], Operations: ['90/45=2', '5+58=63'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[90, 5, 45, 58], Operations: [] Exploring Operation: 5+45=50, Resulting Numbers: [90, 58, 50] Generated Node #0,0: 61:[90, 58, 50] Operation: 5+45=50 Exploring Operation: 5+58=63, Resulting Numbers: [90, 45, 63] Generated Node #0,1: 61:[90, 45, 63] Operation: 5+58=63 Exploring Operation: 90-5=85, Resulting Numbers: [45, 58, 85] Generated Node #0,2: 61:[45, 58, 85] Operation: 90-5=85 Moving to Node #0,0 Current State: 61:[90, 58, 50], Operations: ['5+45=50'] Exploring Operation: 90-58=32, Resulting Numbers: [50, 32] Generated Node #0,0,0: 61:[50, 32] Operation: 90-58=32 Exploring Operation: 58+50=108, Resulting Numbers: [90, 108] Generated Node #0,0,1: 61:[90, 108] Operation: 58+50=108 Exploring Operation: 90-50=40, Resulting Numbers: [58, 40] Generated Node #0,0,2: 61:[58, 40] Operation: 90-50=40 Moving to Node #0,2 Current State: 61:[45, 58, 85], Operations: ['90-5=85'] Exploring Operation: 45+58=103, Resulting Numbers: [85, 103] Generated Node #0,2,0: 61:[85, 103] Operation: 45+58=103 Exploring Operation: 85-45=40, Resulting Numbers: [58, 40] Generated Node #0,2,1: 61:[58, 40] Operation: 85-45=40 Exploring Operation: 85-58=27, Resulting Numbers: [45, 27] Generated Node #0,2,2: 61:[45, 27] Operation: 85-58=27 Moving to Node #0,1 Current State: 61:[90, 45, 63], Operations: ['5+58=63'] Exploring Operation: 90/45=2, Resulting Numbers: [63, 2] Generated Node #0,1,0: 61:[63, 2] Operation: 90/45=2 Exploring Operation: 90-63=27, Resulting Numbers: [45, 27] Generated Node #0,1,1: 61:[45, 27] Operation: 90-63=27 Exploring Operation: 90-45=45, Resulting Numbers: [63, 45] Generated Node #0,1,2: 61:[63, 45] Operation: 90-45=45 Moving to Node #0,1,2 Current State: 61:[63, 45], Operations: ['5+58=63', '90-45=45'] Exploring Operation: 63-45=18, Resulting Numbers: [18] 18,61 unequal: No Solution Exploring Operation: 63+45=108, Resulting Numbers: [108] 108,61 unequal: No Solution Exploring Operation: 63*45=2835, Resulting Numbers: [2835] 2835,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[58, 40], Operations: ['5+45=50', '90-50=40'] Exploring Operation: 58+40=98, Resulting Numbers: [98] 98,61 unequal: No Solution Exploring Operation: 58*40=2320, Resulting Numbers: [2320] 2320,61 unequal: No Solution Exploring Operation: 58-40=18, Resulting Numbers: [18] 18,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[58, 40], Operations: ['90-5=85', '85-45=40'] Exploring Operation: 58+40=98, Resulting Numbers: [98] 98,61 unequal: No Solution Exploring Operation: 58-40=18, Resulting Numbers: [18] 18,61 unequal: No Solution Exploring Operation: 58*40=2320, Resulting Numbers: [2320] 2320,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[50, 32], Operations: ['5+45=50', '90-58=32'] Exploring Operation: 50*32=1600, Resulting Numbers: [1600] 1600,61 unequal: No Solution Exploring Operation: 50+32=82, Resulting Numbers: [82] 82,61 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[45, 27], Operations: ['90-5=85', '85-58=27'] Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,61 unequal: No Solution Exploring Operation: 45+27=72, Resulting Numbers: [72] 72,61 unequal: No Solution Exploring Operation: 45*27=1215, Resulting Numbers: [1215] 1215,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[45, 27], Operations: ['5+58=63', '90-63=27'] Exploring Operation: 45+27=72, Resulting Numbers: [72] 72,61 unequal: No Solution Exploring Operation: 45*27=1215, Resulting Numbers: [1215] 1215,61 unequal: No Solution Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[63, 2], Operations: ['5+58=63', '90/45=2'] Exploring Operation: 63*2=126, Resulting Numbers: [126] 126,61 unequal: No Solution Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,61 unequal: No Solution Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[90, 5, 45, 58], Operations: [] Exploring Operation: 5+58=63, Resulting Numbers: [90, 45, 63] Generated Node #0,1: 61:[90, 45, 63] Operation: 5+58=63 Moving to Node #0,1 Current State: 61:[90, 45, 63], Operations: ['5+58=63'] Exploring Operation: 90/45=2, Resulting Numbers: [63, 2] Generated Node #0,1,0: 61:[63, 2] Operation: 90/45=2 Moving to Node #0,1,0 Current State: 61:[63, 2], Operations: ['5+58=63', '90/45=2'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
0.967882
hs_3
mult_heuristic
[ 14, 90, 44, 4 ]
78
[ "14*4=56", "90+44=134", "134-56=78" ]
Current State: 78:[14, 90, 44, 4], Operations: [] Exploring Operation: 14*4=56, Resulting Numbers: [90, 44, 56] Generated Node #2: [90, 44, 56] from Operation: 14*4=56 Current State: 78:[90, 44, 56], Operations: ['14*4=56'] Exploring Operation: 90+44=134, Resulting Numbers: [56, 134] Generated Node #3: [56, 134] from Operation: 90+44=134 Current State: 78:[56, 134], Operations: ['14*4=56', '90+44=134'] Exploring Operation: 134-56=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[14, 90, 44, 4], Operations: [] Exploring Operation: 90-14=76, Resulting Numbers: [44, 4, 76] Generated Node #0,0: 78:[44, 4, 76] Operation: 90-14=76 Exploring Operation: 90-44=46, Resulting Numbers: [14, 4, 46] Generated Node #0,1: 78:[14, 4, 46] Operation: 90-44=46 Exploring Operation: 90-4=86, Resulting Numbers: [14, 44, 86] Generated Node #0,2: 78:[14, 44, 86] Operation: 90-4=86 Exploring Operation: 44-4=40, Resulting Numbers: [14, 90, 40] Generated Node #0,3: 78:[14, 90, 40] Operation: 44-4=40 Moving to Node #0,0 Current State: 78:[44, 4, 76], Operations: ['90-14=76'] Exploring Operation: 44-4=40, Resulting Numbers: [76, 40] Generated Node #0,0,0: 78:[76, 40] Operation: 44-4=40 Exploring Operation: 4+76=80, Resulting Numbers: [44, 80] Generated Node #0,0,1: 78:[44, 80] Operation: 4+76=80 Exploring Operation: 76-44=32, Resulting Numbers: [4, 32] Generated Node #0,0,2: 78:[4, 32] Operation: 76-44=32 Exploring Operation: 44/4=11, Resulting Numbers: [76, 11] Generated Node #0,0,3: 78:[76, 11] Operation: 44/4=11 Moving to Node #0,1 Current State: 78:[14, 4, 46], Operations: ['90-44=46'] Exploring Operation: 46-4=42, Resulting Numbers: [14, 42] Generated Node #0,1,0: 78:[14, 42] Operation: 46-4=42 Exploring Operation: 14-4=10, Resulting Numbers: [46, 10] Generated Node #0,1,1: 78:[46, 10] Operation: 14-4=10 Exploring Operation: 46-14=32, Resulting Numbers: [4, 32] Generated Node #0,1,2: 78:[4, 32] Operation: 46-14=32 Exploring Operation: 14+4=18, Resulting Numbers: [46, 18] Generated Node #0,1,3: 78:[46, 18] Operation: 14+4=18 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[14, 42], Operations: ['90-44=46', '46-4=42'] Exploring Operation: 14+42=56, Resulting Numbers: [56] 56,78 unequal: No Solution Exploring Operation: 42/14=3, Resulting Numbers: [3] 3,78 unequal: No Solution Exploring Operation: 42-14=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 14*42=588, Resulting Numbers: [588] 588,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 78:[4, 32], Operations: ['90-44=46', '46-14=32'] Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,78 unequal: No Solution Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[46, 10], Operations: ['90-44=46', '14-4=10'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 46+10=56, Resulting Numbers: [56] 56,78 unequal: No Solution Exploring Operation: 46*10=460, Resulting Numbers: [460] 460,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 78:[46, 18], Operations: ['90-44=46', '14+4=18'] Exploring Operation: 46+18=64, Resulting Numbers: [64] 64,78 unequal: No Solution Exploring Operation: 46-18=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 46*18=828, Resulting Numbers: [828] 828,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 78:[14, 90, 40], Operations: ['44-4=40'] Exploring Operation: 90-40=50, Resulting Numbers: [14, 50] Generated Node #0,3,0: 78:[14, 50] Operation: 90-40=50 Exploring Operation: 14+90=104, Resulting Numbers: [40, 104] Generated Node #0,3,1: 78:[40, 104] Operation: 14+90=104 Exploring Operation: 40-14=26, Resulting Numbers: [90, 26] Generated Node #0,3,2: 78:[90, 26] Operation: 40-14=26 Exploring Operation: 90-14=76, Resulting Numbers: [40, 76] Generated Node #0,3,3: 78:[40, 76] Operation: 90-14=76 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 78:[40, 76], Operations: ['44-4=40', '90-14=76'] Exploring Operation: 76-40=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 40*76=3040, Resulting Numbers: [3040] 3040,78 unequal: No Solution Exploring Operation: 40+76=116, Resulting Numbers: [116] 116,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 78:[14, 50], Operations: ['44-4=40', '90-40=50'] Exploring Operation: 14*50=700, Resulting Numbers: [700] 700,78 unequal: No Solution Exploring Operation: 14+50=64, Resulting Numbers: [64] 64,78 unequal: No Solution Exploring Operation: 50-14=36, Resulting Numbers: [36] 36,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 78:[90, 26], Operations: ['44-4=40', '40-14=26'] Exploring Operation: 90-26=64, Resulting Numbers: [64] 64,78 unequal: No Solution Exploring Operation: 90*26=2340, Resulting Numbers: [2340] 2340,78 unequal: No Solution Exploring Operation: 90+26=116, Resulting Numbers: [116] 116,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 78:[40, 104], Operations: ['44-4=40', '14+90=104'] Exploring Operation: 40*104=4160, Resulting Numbers: [4160] 4160,78 unequal: No Solution Exploring Operation: 104-40=64, Resulting Numbers: [64] 64,78 unequal: No Solution Exploring Operation: 40+104=144, Resulting Numbers: [144] 144,78 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: 78:[14, 44, 86], Operations: ['90-4=86'] Exploring Operation: 14+44=58, Resulting Numbers: [86, 58] Generated Node #0,2,0: 78:[86, 58] Operation: 14+44=58 Exploring Operation: 86-44=42, Resulting Numbers: [14, 42] Generated Node #0,2,1: 78:[14, 42] Operation: 86-44=42 Exploring Operation: 44-14=30, Resulting Numbers: [86, 30] Generated Node #0,2,2: 78:[86, 30] Operation: 44-14=30 Exploring Operation: 86-14=72, Resulting Numbers: [44, 72] Generated Node #0,2,3: 78:[44, 72] Operation: 86-14=72 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 78:[14, 42], Operations: ['90-4=86', '86-44=42'] Exploring Operation: 42/14=3, Resulting Numbers: [3] 3,78 unequal: No Solution Exploring Operation: 14+42=56, Resulting Numbers: [56] 56,78 unequal: No Solution Exploring Operation: 42-14=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 14*42=588, Resulting Numbers: [588] 588,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 78:[44, 72], Operations: ['90-4=86', '86-14=72'] Exploring Operation: 44+72=116, Resulting Numbers: [116] 116,78 unequal: No Solution Exploring Operation: 44*72=3168, Resulting Numbers: [3168] 3168,78 unequal: No Solution Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 78:[86, 30], Operations: ['90-4=86', '44-14=30'] Exploring Operation: 86+30=116, Resulting Numbers: [116] 116,78 unequal: No Solution Exploring Operation: 86-30=56, Resulting Numbers: [56] 56,78 unequal: No Solution Exploring Operation: 86*30=2580, Resulting Numbers: [2580] 2580,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 78:[86, 58], Operations: ['90-4=86', '14+44=58'] Exploring Operation: 86*58=4988, Resulting Numbers: [4988] 4988,78 unequal: No Solution Exploring Operation: 86-58=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 86+58=144, Resulting Numbers: [144] 144,78 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: 78:[76, 40], Operations: ['90-14=76', '44-4=40'] Exploring Operation: 76+40=116, Resulting Numbers: [116] 116,78 unequal: No Solution Exploring Operation: 76-40=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 76*40=3040, Resulting Numbers: [3040] 3040,78 unequal: No Solution Moving to Node #0,0,3 Current State: 78:[76, 11], Operations: ['90-14=76', '44/4=11'] Exploring Operation: 76+11=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,78 unequal: No Solution Exploring Operation: 76*11=836, Resulting Numbers: [836] 836,78 unequal: No Solution Moving to Node #0,0,2 Current State: 78:[4, 32], Operations: ['90-14=76', '76-44=32'] Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,78 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,78 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,78 unequal: No Solution Moving to Node #0,0,1 Current State: 78:[44, 80], Operations: ['90-14=76', '4+76=80'] Exploring Operation: 44+80=124, Resulting Numbers: [124] 124,78 unequal: No Solution Exploring Operation: 44*80=3520, Resulting Numbers: [3520] 3520,78 unequal: No Solution Exploring Operation: 80-44=36, Resulting Numbers: [36] 36,78 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 48, 59, 27, 2 ]
76
[ "59-48=11", "27+11=38", "2*38=76" ]
Current State: 76:[48, 59, 27, 2], Operations: [] Exploring Operation: 59-48=11, Resulting Numbers: [27, 2, 11] Generated Node #2: [27, 2, 11] from Operation: 59-48=11 Current State: 76:[27, 2, 11], Operations: ['59-48=11'] Exploring Operation: 27+11=38, Resulting Numbers: [2, 38] Generated Node #3: [2, 38] from Operation: 27+11=38 Current State: 76:[2, 38], Operations: ['59-48=11', '27+11=38'] Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[48, 59, 27, 2], Operations: [] Exploring Operation: 59-48=11, Resulting Numbers: [27, 2, 11] Generated Node #0,0: 76:[27, 2, 11] Operation: 59-48=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[27, 2, 11], Operations: ['59-48=11'] Exploring Operation: 27+11=38, Resulting Numbers: [2, 38] Generated Node #0,0,0: 76:[2, 38] Operation: 27+11=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 76:[2, 38], Operations: ['59-48=11', '27+11=38'] Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[48, 59, 27, 2], Operations: [] Exploring Operation: 59-48=11, Resulting Numbers: [27, 2, 11] Generated Node #0,0: 76:[27, 2, 11] Operation: 59-48=11 Moving to Node #0,0 Current State: 76:[27, 2, 11], Operations: ['59-48=11'] Exploring Operation: 27+11=38, Resulting Numbers: [2, 38] Generated Node #0,0,0: 76:[2, 38] Operation: 27+11=38 Moving to Node #0,0,0 Current State: 76:[2, 38], Operations: ['59-48=11', '27+11=38'] Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 8, 74, 2, 18 ]
37
[ "8*74=592", "18-2=16", "592/16=37" ]
Current State: 37:[8, 74, 2, 18], Operations: [] Exploring Operation: 8*74=592, Resulting Numbers: [2, 18, 592] Generated Node #2: [2, 18, 592] from Operation: 8*74=592 Current State: 37:[2, 18, 592], Operations: ['8*74=592'] Exploring Operation: 18-2=16, Resulting Numbers: [592, 16] Generated Node #3: [592, 16] from Operation: 18-2=16 Current State: 37:[592, 16], Operations: ['8*74=592', '18-2=16'] Exploring Operation: 592/16=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[8, 74, 2, 18], Operations: [] Exploring Operation: 2*18=36, Resulting Numbers: [8, 74, 36] Generated Node #0,0: 37:[8, 74, 36] Operation: 2*18=36 Exploring Operation: 74/2=37, Resulting Numbers: [8, 18, 37] Generated Node #0,1: 37:[8, 18, 37] Operation: 74/2=37 Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[8, 18, 37], Operations: ['74/2=37'] Exploring Operation: 18-8=10, Resulting Numbers: [37, 10] Generated Node #0,1,0: 37:[37, 10] Operation: 18-8=10 Exploring Operation: 8+18=26, Resulting Numbers: [37, 26] Generated Node #0,1,1: 37:[37, 26] Operation: 8+18=26 Moving to Node #0,1,1 Current State: 37:[37, 26], Operations: ['74/2=37', '8+18=26'] Exploring Operation: 37+26=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 37-26=11, Resulting Numbers: [11] 11,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[37, 10], Operations: ['74/2=37', '18-8=10'] Exploring Operation: 37-10=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 37+10=47, Resulting Numbers: [47] 47,37 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 Current State: 37:[8, 74, 36], Operations: ['2*18=36'] Exploring Operation: 74-8=66, Resulting Numbers: [36, 66] Generated Node #0,0,0: 37:[36, 66] Operation: 74-8=66 Exploring Operation: 74-36=38, Resulting Numbers: [8, 38] Generated Node #0,0,1: 37:[8, 38] Operation: 74-36=38 Moving to Node #0,0,0 Current State: 37:[36, 66], Operations: ['2*18=36', '74-8=66'] Exploring Operation: 36+66=102, Resulting Numbers: [102] 102,37 unequal: No Solution Exploring Operation: 66-36=30, Resulting Numbers: [30] 30,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[8, 38], Operations: ['2*18=36', '74-36=38'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,37 unequal: No Solution Exploring Operation: 8+38=46, Resulting Numbers: [46] 46,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 19, 91, 45, 44 ]
73
[ "91-19=72", "45-44=1", "72+1=73" ]
Current State: 73:[19, 91, 45, 44], Operations: [] Exploring Operation: 91-19=72, Resulting Numbers: [45, 44, 72] Generated Node #2: [45, 44, 72] from Operation: 91-19=72 Current State: 73:[45, 44, 72], Operations: ['91-19=72'] Exploring Operation: 45-44=1, Resulting Numbers: [72, 1] Generated Node #3: [72, 1] from Operation: 45-44=1 Current State: 73:[72, 1], Operations: ['91-19=72', '45-44=1'] Exploring Operation: 72+1=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[19, 91, 45, 44], Operations: [] Exploring Operation: 91-19=72, Resulting Numbers: [45, 44, 72] Generated Node #0,0: 73:[45, 44, 72] Operation: 91-19=72 Exploring Operation: 19+44=63, Resulting Numbers: [91, 45, 63] Generated Node #0,1: 73:[91, 45, 63] Operation: 19+44=63 Exploring Operation: 19+45=64, Resulting Numbers: [91, 44, 64] Generated Node #0,2: 73:[91, 44, 64] Operation: 19+45=64 Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[91, 45, 63], Operations: ['19+44=63'] Exploring Operation: 91+45=136, Resulting Numbers: [63, 136] Generated Node #0,1,0: 73:[63, 136] Operation: 91+45=136 Exploring Operation: 91-45=46, Resulting Numbers: [63, 46] Generated Node #0,1,1: 73:[63, 46] Operation: 91-45=46 Exploring Operation: 45+63=108, Resulting Numbers: [91, 108] Generated Node #0,1,2: 73:[91, 108] Operation: 45+63=108 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[63, 46], Operations: ['19+44=63', '91-45=46'] Exploring Operation: 63*46=2898, Resulting Numbers: [2898] 2898,73 unequal: No Solution Exploring Operation: 63-46=17, Resulting Numbers: [17] 17,73 unequal: No Solution Exploring Operation: 63+46=109, Resulting Numbers: [109] 109,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 73:[91, 108], Operations: ['19+44=63', '45+63=108'] Exploring Operation: 91+108=199, Resulting Numbers: [199] 199,73 unequal: No Solution Exploring Operation: 91*108=9828, Resulting Numbers: [9828] 9828,73 unequal: No Solution Exploring Operation: 108-91=17, Resulting Numbers: [17] 17,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[63, 136], Operations: ['19+44=63', '91+45=136'] Exploring Operation: 136-63=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[19, 91, 45, 44], Operations: [] Exploring Operation: 19+44=63, Resulting Numbers: [91, 45, 63] Generated Node #0,1: 73:[91, 45, 63] Operation: 19+44=63 Moving to Node #0,1 Current State: 73:[91, 45, 63], Operations: ['19+44=63'] Exploring Operation: 91+45=136, Resulting Numbers: [63, 136] Generated Node #0,1,0: 73:[63, 136] Operation: 91+45=136 Moving to Node #0,1,0 Current State: 73:[63, 136], Operations: ['19+44=63', '91+45=136'] Exploring Operation: 136-63=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 32, 60, 48, 50 ]
76
[ "50-48=2", "32/2=16", "60+16=76" ]
Current State: 76:[32, 60, 48, 50], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [32, 60, 2] Generated Node #2: [32, 60, 2] from Operation: 50-48=2 Current State: 76:[32, 60, 2], Operations: ['50-48=2'] Exploring Operation: 32/2=16, Resulting Numbers: [60, 16] Generated Node #3: [60, 16] from Operation: 32/2=16 Current State: 76:[60, 16], Operations: ['50-48=2', '32/2=16'] Exploring Operation: 60+16=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[32, 60, 48, 50], Operations: [] Exploring Operation: 50-32=18, Resulting Numbers: [60, 48, 18] Generated Node #0,0: 76:[60, 48, 18] Operation: 50-32=18 Exploring Operation: 50-48=2, Resulting Numbers: [32, 60, 2] Generated Node #0,1: 76:[32, 60, 2] Operation: 50-48=2 Exploring Operation: 60-48=12, Resulting Numbers: [32, 50, 12] Generated Node #0,2: 76:[32, 50, 12] Operation: 60-48=12 Exploring Operation: 60-50=10, Resulting Numbers: [32, 48, 10] Generated Node #0,3: 76:[32, 48, 10] Operation: 60-50=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[32, 60, 2], Operations: ['50-48=2'] Exploring Operation: 60/2=30, Resulting Numbers: [32, 30] Generated Node #0,1,0: 76:[32, 30] Operation: 60/2=30 Exploring Operation: 60-32=28, Resulting Numbers: [2, 28] Generated Node #0,1,1: 76:[2, 28] Operation: 60-32=28 Exploring Operation: 32/2=16, Resulting Numbers: [60, 16] Generated Node #0,1,2: 76:[60, 16] Operation: 32/2=16 Exploring Operation: 32+60=92, Resulting Numbers: [2, 92] Generated Node #0,1,3: 76:[2, 92] Operation: 32+60=92 Moving to Node #0,1,1 Current State: 76:[2, 28], Operations: ['50-48=2', '60-32=28'] Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,76 unequal: No Solution Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,76 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[32, 30], Operations: ['50-48=2', '60/2=30'] Exploring Operation: 32*30=960, Resulting Numbers: [960] 960,76 unequal: No Solution Exploring Operation: 32+30=62, Resulting Numbers: [62] 62,76 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,76 unequal: No Solution Moving to Node #0,1,3 Current State: 76:[2, 92], Operations: ['50-48=2', '32+60=92'] Exploring Operation: 2*92=184, Resulting Numbers: [184] 184,76 unequal: No Solution Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,76 unequal: No Solution Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,76 unequal: No Solution Exploring Operation: 2+92=94, Resulting Numbers: [94] 94,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[60, 16], Operations: ['50-48=2', '32/2=16'] Exploring Operation: 60-16=44, Resulting Numbers: [44] 44,76 unequal: No Solution Exploring Operation: 60*16=960, Resulting Numbers: [960] 960,76 unequal: No Solution Exploring Operation: 60+16=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[32, 60, 48, 50], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [32, 60, 2] Generated Node #0,1: 76:[32, 60, 2] Operation: 50-48=2 Moving to Node #0,1 Current State: 76:[32, 60, 2], Operations: ['50-48=2'] Exploring Operation: 32/2=16, Resulting Numbers: [60, 16] Generated Node #0,1,2: 76:[60, 16] Operation: 32/2=16 Moving to Node #0,1,2 Current State: 76:[60, 16], Operations: ['50-48=2', '32/2=16'] Exploring Operation: 60+16=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_4
sum_heuristic
[ 67, 53, 38, 50 ]
26
[ "67-53=14", "50-38=12", "14+12=26" ]
Current State: 26:[67, 53, 38, 50], Operations: [] Exploring Operation: 67-53=14, Resulting Numbers: [38, 50, 14] Generated Node #2: [38, 50, 14] from Operation: 67-53=14 Current State: 26:[38, 50, 14], Operations: ['67-53=14'] Exploring Operation: 50-38=12, Resulting Numbers: [14, 12] Generated Node #3: [14, 12] from Operation: 50-38=12 Current State: 26:[14, 12], Operations: ['67-53=14', '50-38=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[67, 53, 38, 50], Operations: [] Exploring Operation: 67-50=17, Resulting Numbers: [53, 38, 17] Generated Node #0,0: 26:[53, 38, 17] Operation: 67-50=17 Exploring Operation: 67-53=14, Resulting Numbers: [38, 50, 14] Generated Node #0,1: 26:[38, 50, 14] Operation: 67-53=14 Moving to Node #0,1 Current State: 26:[38, 50, 14], Operations: ['67-53=14'] Exploring Operation: 50-14=36, Resulting Numbers: [38, 36] Generated Node #0,1,0: 26:[38, 36] Operation: 50-14=36 Exploring Operation: 50-38=12, Resulting Numbers: [14, 12] Generated Node #0,1,1: 26:[14, 12] Operation: 50-38=12 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[14, 12], Operations: ['67-53=14', '50-38=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[67, 53, 38, 50], Operations: [] Exploring Operation: 67-53=14, Resulting Numbers: [38, 50, 14] Generated Node #0,1: 26:[38, 50, 14] Operation: 67-53=14 Moving to Node #0,1 Current State: 26:[38, 50, 14], Operations: ['67-53=14'] Exploring Operation: 50-38=12, Resulting Numbers: [14, 12] Generated Node #0,1,1: 26:[14, 12] Operation: 50-38=12 Moving to Node #0,1,1 Current State: 26:[14, 12], Operations: ['67-53=14', '50-38=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 97, 6, 8, 45 ]
39
[ "97-45=52", "6*52=312", "312/8=39" ]
Current State: 39:[97, 6, 8, 45], Operations: [] Exploring Operation: 97-45=52, Resulting Numbers: [6, 8, 52] Generated Node #2: [6, 8, 52] from Operation: 97-45=52 Current State: 39:[6, 8, 52], Operations: ['97-45=52'] Exploring Operation: 6*52=312, Resulting Numbers: [8, 312] Generated Node #3: [8, 312] from Operation: 6*52=312 Current State: 39:[8, 312], Operations: ['97-45=52', '6*52=312'] Exploring Operation: 312/8=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[97, 6, 8, 45], Operations: [] Exploring Operation: 97-6=91, Resulting Numbers: [8, 45, 91] Generated Node #0,0: 39:[8, 45, 91] Operation: 97-6=91 Exploring Operation: 97-8=89, Resulting Numbers: [6, 45, 89] Generated Node #0,1: 39:[6, 45, 89] Operation: 97-8=89 Exploring Operation: 97-45=52, Resulting Numbers: [6, 8, 52] Generated Node #0,2: 39:[6, 8, 52] Operation: 97-45=52 Moving to Node #0,2 Current State: 39:[6, 8, 52], Operations: ['97-45=52'] Exploring Operation: 52-6=46, Resulting Numbers: [8, 46] Generated Node #0,2,0: 39:[8, 46] Operation: 52-6=46 Exploring Operation: 6+8=14, Resulting Numbers: [52, 14] Generated Node #0,2,1: 39:[52, 14] Operation: 6+8=14 Exploring Operation: 52-8=44, Resulting Numbers: [6, 44] Generated Node #0,2,2: 39:[6, 44] Operation: 52-8=44 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 39:[6, 44], Operations: ['97-45=52', '52-8=44'] Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 6*44=264, Resulting Numbers: [264] 264,39 unequal: No Solution Exploring Operation: 6+44=50, Resulting Numbers: [50] 50,39 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 #0,2,0 Current State: 39:[8, 46], Operations: ['97-45=52', '52-6=46'] Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 8*46=368, Resulting Numbers: [368] 368,39 unequal: No Solution Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 39:[52, 14], Operations: ['97-45=52', '6+8=14'] Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 52+14=66, Resulting Numbers: [66] 66,39 unequal: No Solution Exploring Operation: 52*14=728, Resulting Numbers: [728] 728,39 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: 39:[6, 45, 89], Operations: ['97-8=89'] Exploring Operation: 89-6=83, Resulting Numbers: [45, 83] Generated Node #0,1,0: 39:[45, 83] Operation: 89-6=83 Exploring Operation: 89-45=44, Resulting Numbers: [6, 44] Generated Node #0,1,1: 39:[6, 44] Operation: 89-45=44 Exploring Operation: 45-6=39, Resulting Numbers: [89, 39] Generated Node #0,1,2: 39:[89, 39] Operation: 45-6=39 Moving to Node #0,0 Current State: 39:[8, 45, 91], Operations: ['97-6=91'] Exploring Operation: 45-8=37, Resulting Numbers: [91, 37] Generated Node #0,0,0: 39:[91, 37] Operation: 45-8=37 Exploring Operation: 91-45=46, Resulting Numbers: [8, 46] Generated Node #0,0,1: 39:[8, 46] Operation: 91-45=46 Exploring Operation: 91-8=83, Resulting Numbers: [45, 83] Generated Node #0,0,2: 39:[45, 83] Operation: 91-8=83 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 39:[8, 46], Operations: ['97-6=91', '91-45=46'] Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,39 unequal: No Solution Exploring Operation: 8*46=368, Resulting Numbers: [368] 368,39 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 39:[45, 83], Operations: ['97-6=91', '91-8=83'] Exploring Operation: 45+83=128, Resulting Numbers: [128] 128,39 unequal: No Solution Exploring Operation: 83-45=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 45*83=3735, Resulting Numbers: [3735] 3735,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[91, 37], Operations: ['97-6=91', '45-8=37'] Exploring Operation: 91-37=54, Resulting Numbers: [54] 54,39 unequal: No Solution Exploring Operation: 91+37=128, Resulting Numbers: [128] 128,39 unequal: No Solution Exploring Operation: 91*37=3367, Resulting Numbers: [3367] 3367,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 39:[6, 44], Operations: ['97-8=89', '89-45=44'] Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 6*44=264, Resulting Numbers: [264] 264,39 unequal: No Solution Exploring Operation: 6+44=50, Resulting Numbers: [50] 50,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[45, 83], Operations: ['97-8=89', '89-6=83'] Exploring Operation: 45+83=128, Resulting Numbers: [128] 128,39 unequal: No Solution Exploring Operation: 45*83=3735, Resulting Numbers: [3735] 3735,39 unequal: No Solution Exploring Operation: 83-45=38, Resulting Numbers: [38] 38,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[89, 39], Operations: ['97-8=89', '45-6=39'] Exploring Operation: 89+39=128, Resulting Numbers: [128] 128,39 unequal: No Solution Exploring Operation: 89*39=3471, Resulting Numbers: [3471] 3471,39 unequal: No Solution Exploring Operation: 89-39=50, Resulting Numbers: [50] 50,39 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 61, 69, 67, 60 ]
59
[ "67-61=6", "60/6=10", "69-10=59" ]
Current State: 59:[61, 69, 67, 60], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [69, 60, 6] Generated Node #2: [69, 60, 6] from Operation: 67-61=6 Current State: 59:[69, 60, 6], Operations: ['67-61=6'] Exploring Operation: 60/6=10, Resulting Numbers: [69, 10] Generated Node #3: [69, 10] from Operation: 60/6=10 Current State: 59:[69, 10], Operations: ['67-61=6', '60/6=10'] Exploring Operation: 69-10=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[61, 69, 67, 60], Operations: [] Exploring Operation: 69-61=8, Resulting Numbers: [67, 60, 8] Generated Node #0,0: 59:[67, 60, 8] Operation: 69-61=8 Exploring Operation: 69-67=2, Resulting Numbers: [61, 60, 2] Generated Node #0,1: 59:[61, 60, 2] Operation: 69-67=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[67, 60, 8], Operations: ['69-61=8'] Exploring Operation: 60-8=52, Resulting Numbers: [67, 52] Generated Node #0,0,0: 59:[67, 52] Operation: 60-8=52 Exploring Operation: 67-8=59, Resulting Numbers: [60, 59] Generated Node #0,0,1: 59:[60, 59] Operation: 67-8=59 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 59:[60, 59], Operations: ['69-61=8', '67-8=59'] Exploring Operation: 60+59=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[67, 52], Operations: ['69-61=8', '60-8=52'] Exploring Operation: 67-52=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 67+52=119, Resulting Numbers: [119] 119,59 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 #0,1 Current State: 59:[61, 60, 2], Operations: ['69-67=2'] Exploring Operation: 60-2=58, Resulting Numbers: [61, 58] Generated Node #0,1,0: 59:[61, 58] Operation: 60-2=58 Exploring Operation: 61-2=59, Resulting Numbers: [60, 59] Generated Node #0,1,1: 59:[60, 59] Operation: 61-2=59 Moving to Node #0,1,1 Current State: 59:[60, 59], Operations: ['69-67=2', '61-2=59'] Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 60+59=119, Resulting Numbers: [119] 119,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[61, 58], Operations: ['69-67=2', '60-2=58'] Exploring Operation: 61+58=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 69, 39, 96, 99 ]
87
[ "69+39=108", "96+99=195", "195-108=87" ]
Current State: 87:[69, 39, 96, 99], Operations: [] Exploring Operation: 69+39=108, Resulting Numbers: [96, 99, 108] Generated Node #2: [96, 99, 108] from Operation: 69+39=108 Current State: 87:[96, 99, 108], Operations: ['69+39=108'] Exploring Operation: 96+99=195, Resulting Numbers: [108, 195] Generated Node #3: [108, 195] from Operation: 96+99=195 Current State: 87:[108, 195], Operations: ['69+39=108', '96+99=195'] Exploring Operation: 195-108=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[69, 39, 96, 99], Operations: [] Exploring Operation: 99-96=3, Resulting Numbers: [69, 39, 3] Generated Node #0,0: 87:[69, 39, 3] Operation: 99-96=3 Exploring Operation: 96-69=27, Resulting Numbers: [39, 99, 27] Generated Node #0,1: 87:[39, 99, 27] Operation: 96-69=27 Exploring Operation: 69+39=108, Resulting Numbers: [96, 99, 108] Generated Node #0,2: 87:[96, 99, 108] Operation: 69+39=108 Exploring Operation: 99-69=30, Resulting Numbers: [39, 96, 30] Generated Node #0,3: 87:[39, 96, 30] Operation: 99-69=30 Exploring Operation: 69-39=30, Resulting Numbers: [96, 99, 30] Generated Node #0,4: 87:[96, 99, 30] Operation: 69-39=30 Moving to Node #0,3 Current State: 87:[39, 96, 30], Operations: ['99-69=30'] Exploring Operation: 39-30=9, Resulting Numbers: [96, 9] Generated Node #0,3,0: 87:[96, 9] Operation: 39-30=9 Exploring Operation: 39+96=135, Resulting Numbers: [30, 135] Generated Node #0,3,1: 87:[30, 135] Operation: 39+96=135 Exploring Operation: 39+30=69, Resulting Numbers: [96, 69] Generated Node #0,3,2: 87:[96, 69] Operation: 39+30=69 Exploring Operation: 96-39=57, Resulting Numbers: [30, 57] Generated Node #0,3,3: 87:[30, 57] Operation: 96-39=57 Exploring Operation: 96-30=66, Resulting Numbers: [39, 66] Generated Node #0,3,4: 87:[39, 66] Operation: 96-30=66 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 87:[96, 9], Operations: ['99-69=30', '39-30=9'] Exploring Operation: 96-9=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[69, 39, 96, 99], Operations: [] Exploring Operation: 99-69=30, Resulting Numbers: [39, 96, 30] Generated Node #0,3: 87:[39, 96, 30] Operation: 99-69=30 Moving to Node #0,3 Current State: 87:[39, 96, 30], Operations: ['99-69=30'] Exploring Operation: 39-30=9, Resulting Numbers: [96, 9] Generated Node #0,3,0: 87:[96, 9] Operation: 39-30=9 Moving to Node #0,3,0 Current State: 87:[96, 9], Operations: ['99-69=30', '39-30=9'] Exploring Operation: 96-9=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 26, 25, 6, 14 ]
23
[ "26-14=12", "12/6=2", "25-2=23" ]
Current State: 23:[26, 25, 6, 14], Operations: [] Exploring Operation: 26-14=12, Resulting Numbers: [25, 6, 12] Generated Node #2: [25, 6, 12] from Operation: 26-14=12 Current State: 23:[25, 6, 12], Operations: ['26-14=12'] Exploring Operation: 12/6=2, Resulting Numbers: [25, 2] Generated Node #3: [25, 2] from Operation: 12/6=2 Current State: 23:[25, 2], Operations: ['26-14=12', '12/6=2'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[26, 25, 6, 14], Operations: [] Exploring Operation: 25-6=19, Resulting Numbers: [26, 14, 19] Generated Node #0,0: 23:[26, 14, 19] Operation: 25-6=19 Exploring Operation: 26+6=32, Resulting Numbers: [25, 14, 32] Generated Node #0,1: 23:[25, 14, 32] Operation: 26+6=32 Exploring Operation: 25+6=31, Resulting Numbers: [26, 14, 31] Generated Node #0,2: 23:[26, 14, 31] Operation: 25+6=31 Exploring Operation: 6+14=20, Resulting Numbers: [26, 25, 20] Generated Node #0,3: 23:[26, 25, 20] Operation: 6+14=20 Exploring Operation: 26-6=20, Resulting Numbers: [25, 14, 20] Generated Node #0,4: 23:[25, 14, 20] Operation: 26-6=20 Start Sub Search at level 1: Moving to Node #0,3 Current State: 23:[26, 25, 20], Operations: ['6+14=20'] Exploring Operation: 25-20=5, Resulting Numbers: [26, 5] Generated Node #0,3,0: 23:[26, 5] Operation: 25-20=5 Exploring Operation: 26-20=6, Resulting Numbers: [25, 6] Generated Node #0,3,1: 23:[25, 6] Operation: 26-20=6 Exploring Operation: 26-25=1, Resulting Numbers: [20, 1] Generated Node #0,3,2: 23:[20, 1] Operation: 26-25=1 Exploring Operation: 26+20=46, Resulting Numbers: [25, 46] Generated Node #0,3,3: 23:[25, 46] Operation: 26+20=46 Exploring Operation: 25+20=45, Resulting Numbers: [26, 45] Generated Node #0,3,4: 23:[26, 45] Operation: 25+20=45 Moving to Node #0,3,1 Current State: 23:[25, 6], Operations: ['6+14=20', '26-20=6'] Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,23 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[26, 5], Operations: ['6+14=20', '25-20=5'] Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,23 unequal: No Solution Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,23 unequal: No Solution Moving to Node #0,3,2 Current State: 23:[20, 1], Operations: ['6+14=20', '26-25=1'] Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[25, 46], Operations: ['6+14=20', '26+20=46'] Exploring Operation: 25*46=1150, Resulting Numbers: [1150] 1150,23 unequal: No Solution Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 25+46=71, Resulting Numbers: [71] 71,23 unequal: No Solution Moving to Node #0,3,4 Current State: 23:[26, 45], Operations: ['6+14=20', '25+20=45'] Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 26*45=1170, Resulting Numbers: [1170] 1170,23 unequal: No Solution Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 23:[25, 14, 20], Operations: ['26-6=20'] Exploring Operation: 20-14=6, Resulting Numbers: [25, 6] Generated Node #0,4,0: 23:[25, 6] Operation: 20-14=6 Exploring Operation: 14+20=34, Resulting Numbers: [25, 34] Generated Node #0,4,1: 23:[25, 34] Operation: 14+20=34 Exploring Operation: 25+14=39, Resulting Numbers: [20, 39] Generated Node #0,4,2: 23:[20, 39] Operation: 25+14=39 Exploring Operation: 25-14=11, Resulting Numbers: [20, 11] Generated Node #0,4,3: 23:[20, 11] Operation: 25-14=11 Exploring Operation: 25-20=5, Resulting Numbers: [14, 5] Generated Node #0,4,4: 23:[14, 5] Operation: 25-20=5 Moving to Node #0,4,1 Current State: 23:[25, 34], Operations: ['26-6=20', '14+20=34'] Exploring Operation: 25+34=59, Resulting Numbers: [59] 59,23 unequal: No Solution Exploring Operation: 25*34=850, Resulting Numbers: [850] 850,23 unequal: No Solution Exploring Operation: 34-25=9, Resulting Numbers: [9] 9,23 unequal: No Solution Moving to Node #0,4,3 Current State: 23:[20, 11], Operations: ['26-6=20', '25-14=11'] Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 20*11=220, Resulting Numbers: [220] 220,23 unequal: No Solution Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,23 unequal: No Solution Moving to Node #0,4,0 Current State: 23:[25, 6], Operations: ['26-6=20', '20-14=6'] Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,23 unequal: No Solution Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,23 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,23 unequal: No Solution Moving to Node #0,4,2 Current State: 23:[20, 39], Operations: ['26-6=20', '25+14=39'] Exploring Operation: 20*39=780, Resulting Numbers: [780] 780,23 unequal: No Solution Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 20+39=59, Resulting Numbers: [59] 59,23 unequal: No Solution Moving to Node #0,4,4 Current State: 23:[14, 5], Operations: ['26-6=20', '25-20=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[26, 14, 19], Operations: ['25-6=19'] Exploring Operation: 26-19=7, Resulting Numbers: [14, 7] Generated Node #0,0,0: 23:[14, 7] Operation: 26-19=7 Exploring Operation: 26-14=12, Resulting Numbers: [19, 12] Generated Node #0,0,1: 23:[19, 12] Operation: 26-14=12 Exploring Operation: 26+14=40, Resulting Numbers: [19, 40] Generated Node #0,0,2: 23:[19, 40] Operation: 26+14=40 Exploring Operation: 14+19=33, Resulting Numbers: [26, 33] Generated Node #0,0,3: 23:[26, 33] Operation: 14+19=33 Exploring Operation: 19-14=5, Resulting Numbers: [26, 5] Generated Node #0,0,4: 23:[26, 5] Operation: 19-14=5 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 23:[26, 33], Operations: ['25-6=19', '14+19=33'] Exploring Operation: 26*33=858, Resulting Numbers: [858] 858,23 unequal: No Solution Exploring Operation: 26+33=59, Resulting Numbers: [59] 59,23 unequal: No Solution Exploring Operation: 33-26=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 #0,0,1 Current State: 23:[19, 12], Operations: ['25-6=19', '26-14=12'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,23 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 23:[19, 40], Operations: ['25-6=19', '26+14=40'] Exploring Operation: 19*40=760, Resulting Numbers: [760] 760,23 unequal: No Solution Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 19+40=59, Resulting Numbers: [59] 59,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 23:[26, 5], Operations: ['25-6=19', '19-14=5'] Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,23 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[14, 7], Operations: ['25-6=19', '26-19=7'] Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,23 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[25, 14, 32], Operations: ['26+6=32'] Exploring Operation: 25-14=11, Resulting Numbers: [32, 11] Generated Node #0,1,0: 23:[32, 11] Operation: 25-14=11 Exploring Operation: 32-14=18, Resulting Numbers: [25, 18] Generated Node #0,1,1: 23:[25, 18] Operation: 32-14=18 Exploring Operation: 14+32=46, Resulting Numbers: [25, 46] Generated Node #0,1,2: 23:[25, 46] Operation: 14+32=46 Exploring Operation: 25+14=39, Resulting Numbers: [32, 39] Generated Node #0,1,3: 23:[32, 39] Operation: 25+14=39 Exploring Operation: 32-25=7, Resulting Numbers: [14, 7] Generated Node #0,1,4: 23:[14, 7] Operation: 32-25=7 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 23:[25, 18], Operations: ['26+6=32', '32-14=18'] Exploring Operation: 25*18=450, Resulting Numbers: [450] 450,23 unequal: No Solution Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 25+18=43, Resulting Numbers: [43] 43,23 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:[32, 11], Operations: ['26+6=32', '25-14=11'] Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 32+11=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 32*11=352, Resulting Numbers: [352] 352,23 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 #0,1,2 Current State: 23:[25, 46], Operations: ['26+6=32', '14+32=46'] Exploring Operation: 25+46=71, Resulting Numbers: [71] 71,23 unequal: No Solution Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 25*46=1150, Resulting Numbers: [1150] 1150,23 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 #0,1,3 Current State: 23:[32, 39], Operations: ['26+6=32', '25+14=39'] Exploring Operation: 32+39=71, Resulting Numbers: [71] 71,23 unequal: No Solution Exploring Operation: 32*39=1248, Resulting Numbers: [1248] 1248,23 unequal: No Solution Exploring Operation: 39-32=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 #0,1,4 Current State: 23:[14, 7], Operations: ['26+6=32', '32-25=7'] Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,23 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[26, 14, 31], Operations: ['25+6=31'] Exploring Operation: 26-14=12, Resulting Numbers: [31, 12] Generated Node #0,2,0: 23:[31, 12] Operation: 26-14=12 Exploring Operation: 31-26=5, Resulting Numbers: [14, 5] Generated Node #0,2,1: 23:[14, 5] Operation: 31-26=5 Exploring Operation: 26+14=40, Resulting Numbers: [31, 40] Generated Node #0,2,2: 23:[31, 40] Operation: 26+14=40 Exploring Operation: 31-14=17, Resulting Numbers: [26, 17] Generated Node #0,2,3: 23:[26, 17] Operation: 31-14=17 Exploring Operation: 14+31=45, Resulting Numbers: [26, 45] Generated Node #0,2,4: 23:[26, 45] Operation: 14+31=45 Moving to Node #0,2,3 Current State: 23:[26, 17], Operations: ['25+6=31', '31-14=17'] Exploring Operation: 26+17=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 26*17=442, Resulting Numbers: [442] 442,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[31, 12], Operations: ['25+6=31', '26-14=12'] Exploring Operation: 31+12=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 31*12=372, Resulting Numbers: [372] 372,23 unequal: No Solution Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[31, 40], Operations: ['25+6=31', '26+14=40'] Exploring Operation: 31*40=1240, Resulting Numbers: [1240] 1240,23 unequal: No Solution Exploring Operation: 31+40=71, Resulting Numbers: [71] 71,23 unequal: No Solution Exploring Operation: 40-31=9, Resulting Numbers: [9] 9,23 unequal: No Solution Moving to Node #0,2,4 Current State: 23:[26, 45], Operations: ['25+6=31', '14+31=45'] Exploring Operation: 26*45=1170, Resulting Numbers: [1170] 1170,23 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[14, 5], Operations: ['25+6=31', '31-26=5'] Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,23 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
[ 74, 6, 64, 37 ]
88
[ "64-37=27", "6*27=162", "162-74=88" ]
Current State: 88:[74, 6, 64, 37], Operations: [] Exploring Operation: 64-37=27, Resulting Numbers: [74, 6, 27] Generated Node #2: [74, 6, 27] from Operation: 64-37=27 Current State: 88:[74, 6, 27], Operations: ['64-37=27'] Exploring Operation: 6*27=162, Resulting Numbers: [74, 162] Generated Node #3: [74, 162] from Operation: 6*27=162 Current State: 88:[74, 162], Operations: ['64-37=27', '6*27=162'] Exploring Operation: 162-74=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[74, 6, 64, 37], Operations: [] Exploring Operation: 74-64=10, Resulting Numbers: [6, 37, 10] Generated Node #0,0: 88:[6, 37, 10] Operation: 74-64=10 Exploring Operation: 64-37=27, Resulting Numbers: [74, 6, 27] Generated Node #0,1: 88:[74, 6, 27] Operation: 64-37=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[6, 37, 10], Operations: ['74-64=10'] Exploring Operation: 37+10=47, Resulting Numbers: [6, 47] Generated Node #0,0,0: 88:[6, 47] Operation: 37+10=47 Exploring Operation: 6+37=43, Resulting Numbers: [10, 43] Generated Node #0,0,1: 88:[10, 43] Operation: 6+37=43 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[10, 43], Operations: ['74-64=10', '6+37=43'] Exploring Operation: 10+43=53, Resulting Numbers: [53] 53,88 unequal: No Solution Exploring Operation: 43-10=33, Resulting Numbers: [33] 33,88 unequal: No Solution No 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: 88:[6, 47], Operations: ['74-64=10', '37+10=47'] Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,88 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,88 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: 88:[74, 6, 27], Operations: ['64-37=27'] Exploring Operation: 74+6=80, Resulting Numbers: [27, 80] Generated Node #0,1,0: 88:[27, 80] Operation: 74+6=80 Exploring Operation: 74-27=47, Resulting Numbers: [6, 47] Generated Node #0,1,1: 88:[6, 47] Operation: 74-27=47 Moving to Node #0,1,1 Current State: 88:[6, 47], Operations: ['64-37=27', '74-27=47'] Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,88 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[27, 80], Operations: ['64-37=27', '74+6=80'] Exploring Operation: 27+80=107, Resulting Numbers: [107] 107,88 unequal: No Solution Exploring Operation: 80-27=53, Resulting Numbers: [53] 53,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 24, 56, 56, 10 ]
10
[ "56-56=0", "24*0=0", "10+0=10" ]
Current State: 10:[24, 56, 56, 10], Operations: [] Exploring Operation: 56-56=0, Resulting Numbers: [24, 10, 0] Generated Node #2: [24, 10, 0] from Operation: 56-56=0 Current State: 10:[24, 10, 0], Operations: ['56-56=0'] Exploring Operation: 24*0=0, Resulting Numbers: [10, 0] Generated Node #3: [10, 0] from Operation: 24*0=0 Current State: 10:[10, 0], Operations: ['56-56=0', '24*0=0'] Exploring Operation: 10+0=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[24, 56, 56, 10], Operations: [] Exploring Operation: 56/56=1, Resulting Numbers: [24, 10, 1] Generated Node #0,0: 10:[24, 10, 1] Operation: 56/56=1 Moving to Node #0,0 Current State: 10:[24, 10, 1], Operations: ['56/56=1'] Exploring Operation: 24-10=14, Resulting Numbers: [1, 14] Generated Node #0,0,0: 10:[1, 14] Operation: 24-10=14 Moving to Node #0,0,0 Current State: 10:[1, 14], Operations: ['56/56=1', '24-10=14'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,10 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 5, 62, 16, 21 ]
52
[ "62-5=57", "21-16=5", "57-5=52" ]
Current State: 52:[5, 62, 16, 21], Operations: [] Exploring Operation: 62-5=57, Resulting Numbers: [16, 21, 57] Generated Node #2: [16, 21, 57] from Operation: 62-5=57 Current State: 52:[16, 21, 57], Operations: ['62-5=57'] Exploring Operation: 21-16=5, Resulting Numbers: [57, 5] Generated Node #3: [57, 5] from Operation: 21-16=5 Current State: 52:[57, 5], Operations: ['62-5=57', '21-16=5'] Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[5, 62, 16, 21], Operations: [] Exploring Operation: 21-16=5, Resulting Numbers: [5, 62, 5] Generated Node #0,0: 52:[5, 62, 5] Operation: 21-16=5 Exploring Operation: 62-5=57, Resulting Numbers: [16, 21, 57] Generated Node #0,1: 52:[16, 21, 57] Operation: 62-5=57 Exploring Operation: 62-16=46, Resulting Numbers: [5, 21, 46] Generated Node #0,2: 52:[5, 21, 46] Operation: 62-16=46 Moving to Node #0,0 Current State: 52:[5, 62, 5], Operations: ['21-16=5'] Exploring Operation: 62-5=57, Resulting Numbers: [5, 57] Generated Node #0,0,0: 52:[5, 57] Operation: 62-5=57 Exploring Operation: 62-5=57, Resulting Numbers: [5, 57] Generated Node #0,0,1: 52:[5, 57] Operation: 62-5=57 Exploring Operation: 5*5=25, Resulting Numbers: [62, 25] Generated Node #0,0,2: 52:[62, 25] Operation: 5*5=25 Moving to Node #0,2 Current State: 52:[5, 21, 46], Operations: ['62-16=46'] Exploring Operation: 46-21=25, Resulting Numbers: [5, 25] Generated Node #0,2,0: 52:[5, 25] Operation: 46-21=25 Exploring Operation: 5+46=51, Resulting Numbers: [21, 51] Generated Node #0,2,1: 52:[21, 51] Operation: 5+46=51 Exploring Operation: 5+21=26, Resulting Numbers: [46, 26] Generated Node #0,2,2: 52:[46, 26] Operation: 5+21=26 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 52:[5, 25], Operations: ['62-16=46', '46-21=25'] Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 52:[21, 51], Operations: ['62-16=46', '5+46=51'] Exploring Operation: 21*51=1071, Resulting Numbers: [1071] 1071,52 unequal: No Solution Exploring Operation: 21+51=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 51-21=30, Resulting Numbers: [30] 30,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 52:[46, 26], Operations: ['62-16=46', '5+21=26'] Exploring Operation: 46+26=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 46*26=1196, Resulting Numbers: [1196] 1196,52 unequal: No Solution Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 52:[16, 21, 57], Operations: ['62-5=57'] Exploring Operation: 57-21=36, Resulting Numbers: [16, 36] Generated Node #0,1,0: 52:[16, 36] Operation: 57-21=36 Exploring Operation: 16+21=37, Resulting Numbers: [57, 37] Generated Node #0,1,1: 52:[57, 37] Operation: 16+21=37 Exploring Operation: 21-16=5, Resulting Numbers: [57, 5] Generated Node #0,1,2: 52:[57, 5] Operation: 21-16=5 Moving to Node #0,0,0 Current State: 52:[5, 57], Operations: ['21-16=5', '62-5=57'] Exploring Operation: 5*57=285, Resulting Numbers: [285] 285,52 unequal: No Solution Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[5, 62, 16, 21], Operations: [] Exploring Operation: 21-16=5, Resulting Numbers: [5, 62, 5] Generated Node #0,0: 52:[5, 62, 5] Operation: 21-16=5 Moving to Node #0,0 Current State: 52:[5, 62, 5], Operations: ['21-16=5'] Exploring Operation: 62-5=57, Resulting Numbers: [5, 57] Generated Node #0,0,0: 52:[5, 57] Operation: 62-5=57 Moving to Node #0,0,0 Current State: 52:[5, 57], Operations: ['21-16=5', '62-5=57'] Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
0.976563
hs_3
mult_heuristic
[ 73, 17, 28, 88 ]
81
[ "28-17=11", "88/11=8", "73+8=81" ]
Current State: 81:[73, 17, 28, 88], Operations: [] Exploring Operation: 28-17=11, Resulting Numbers: [73, 88, 11] Generated Node #2: [73, 88, 11] from Operation: 28-17=11 Current State: 81:[73, 88, 11], Operations: ['28-17=11'] Exploring Operation: 88/11=8, Resulting Numbers: [73, 8] Generated Node #3: [73, 8] from Operation: 88/11=8 Current State: 81:[73, 8], Operations: ['28-17=11', '88/11=8'] Exploring Operation: 73+8=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[73, 17, 28, 88], Operations: [] Exploring Operation: 88-73=15, Resulting Numbers: [17, 28, 15] Generated Node #0,0: 81:[17, 28, 15] Operation: 88-73=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[17, 28, 15], Operations: ['88-73=15'] Exploring Operation: 17-15=2, Resulting Numbers: [28, 2] Generated Node #0,0,0: 81:[28, 2] Operation: 17-15=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[28, 2], Operations: ['88-73=15', '17-15=2'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,81 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
[ 23, 36, 21, 92 ]
60
[ "92/23=4", "36-21=15", "4*15=60" ]
Current State: 60:[23, 36, 21, 92], Operations: [] Exploring Operation: 92/23=4, Resulting Numbers: [36, 21, 4] Generated Node #2: [36, 21, 4] from Operation: 92/23=4 Current State: 60:[36, 21, 4], Operations: ['92/23=4'] Exploring Operation: 36-21=15, Resulting Numbers: [4, 15] Generated Node #3: [4, 15] from Operation: 36-21=15 Current State: 60:[4, 15], Operations: ['92/23=4', '36-21=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[23, 36, 21, 92], Operations: [] Exploring Operation: 92/23=4, Resulting Numbers: [36, 21, 4] Generated Node #0,0: 60:[36, 21, 4] Operation: 92/23=4 Exploring Operation: 92-36=56, Resulting Numbers: [23, 21, 56] Generated Node #0,1: 60:[23, 21, 56] Operation: 92-36=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[36, 21, 4], Operations: ['92/23=4'] Exploring Operation: 36/4=9, Resulting Numbers: [21, 9] Generated Node #0,0,0: 60:[21, 9] Operation: 36/4=9 Exploring Operation: 36-21=15, Resulting Numbers: [4, 15] Generated Node #0,0,1: 60:[4, 15] Operation: 36-21=15 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 60:[4, 15], Operations: ['92/23=4', '36-21=15'] Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,60 unequal: No Solution Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[23, 36, 21, 92], Operations: [] Exploring Operation: 92/23=4, Resulting Numbers: [36, 21, 4] Generated Node #0,0: 60:[36, 21, 4] Operation: 92/23=4 Moving to Node #0,0 Current State: 60:[36, 21, 4], Operations: ['92/23=4'] Exploring Operation: 36-21=15, Resulting Numbers: [4, 15] Generated Node #0,0,1: 60:[4, 15] Operation: 36-21=15 Moving to Node #0,0,1 Current State: 60:[4, 15], Operations: ['92/23=4', '36-21=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 60, 45, 13, 15 ]
54
[ "60/15=4", "45+13=58", "58-4=54" ]
Current State: 54:[60, 45, 13, 15], Operations: [] Exploring Operation: 60/15=4, Resulting Numbers: [45, 13, 4] Generated Node #2: [45, 13, 4] from Operation: 60/15=4 Current State: 54:[45, 13, 4], Operations: ['60/15=4'] Exploring Operation: 45+13=58, Resulting Numbers: [4, 58] Generated Node #3: [4, 58] from Operation: 45+13=58 Current State: 54:[4, 58], Operations: ['60/15=4', '45+13=58'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[60, 45, 13, 15], Operations: [] Exploring Operation: 60/15=4, Resulting Numbers: [45, 13, 4] Generated Node #0,0: 54:[45, 13, 4] Operation: 60/15=4 Exploring Operation: 45+13=58, Resulting Numbers: [60, 15, 58] Generated Node #0,1: 54:[60, 15, 58] Operation: 45+13=58 Exploring Operation: 45-15=30, Resulting Numbers: [60, 13, 30] Generated Node #0,2: 54:[60, 13, 30] Operation: 45-15=30 Exploring Operation: 60-45=15, Resulting Numbers: [13, 15, 15] Generated Node #0,3: 54:[13, 15, 15] Operation: 60-45=15 Exploring Operation: 45/15=3, Resulting Numbers: [60, 13, 3] Generated Node #0,4: 54:[60, 13, 3] Operation: 45/15=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 54:[13, 15, 15], Operations: ['60-45=15'] Exploring Operation: 15/15=1, Resulting Numbers: [13, 1] Generated Node #0,3,0: 54:[13, 1] Operation: 15/15=1 Exploring Operation: 13+15=28, Resulting Numbers: [15, 28] Generated Node #0,3,1: 54:[15, 28] Operation: 13+15=28 Exploring Operation: 13+15=28, Resulting Numbers: [15, 28] Generated Node #0,3,2: 54:[15, 28] Operation: 13+15=28 Exploring Operation: 15-13=2, Resulting Numbers: [15, 2] Generated Node #0,3,3: 54:[15, 2] Operation: 15-13=2 Exploring Operation: 15-13=2, Resulting Numbers: [15, 2] Generated Node #0,3,4: 54:[15, 2] Operation: 15-13=2 Moving to Node #0,3,3 Current State: 54:[15, 2], Operations: ['60-45=15', '15-13=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,54 unequal: No Solution Moving to Node #0,3,4 Current State: 54:[15, 2], Operations: ['60-45=15', '15-13=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,54 unequal: No Solution Moving to Node #0,3,1 Current State: 54:[15, 28], Operations: ['60-45=15', '13+15=28'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,54 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,54 unequal: No Solution Moving to Node #0,3,2 Current State: 54:[15, 28], Operations: ['60-45=15', '13+15=28'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,54 unequal: No Solution Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,54 unequal: No Solution Moving to Node #0,3,0 Current State: 54:[13, 1], Operations: ['60-45=15', '15/15=1'] Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 54:[60, 13, 3], Operations: ['45/15=3'] Exploring Operation: 60-13=47, Resulting Numbers: [3, 47] Generated Node #0,4,0: 54:[3, 47] Operation: 60-13=47 Exploring Operation: 60-3=57, Resulting Numbers: [13, 57] Generated Node #0,4,1: 54:[13, 57] Operation: 60-3=57 Exploring Operation: 60/3=20, Resulting Numbers: [13, 20] Generated Node #0,4,2: 54:[13, 20] Operation: 60/3=20 Exploring Operation: 13+3=16, Resulting Numbers: [60, 16] Generated Node #0,4,3: 54:[60, 16] Operation: 13+3=16 Exploring Operation: 13-3=10, Resulting Numbers: [60, 10] Generated Node #0,4,4: 54:[60, 10] Operation: 13-3=10 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 54:[13, 20], Operations: ['45/15=3', '60/3=20'] Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 13+20=33, Resulting Numbers: [33] 33,54 unequal: No Solution Exploring Operation: 13*20=260, Resulting Numbers: [260] 260,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 54:[3, 47], Operations: ['45/15=3', '60-13=47'] Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 3*47=141, Resulting Numbers: [141] 141,54 unequal: No Solution Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 54:[13, 57], Operations: ['45/15=3', '60-3=57'] Exploring Operation: 13*57=741, Resulting Numbers: [741] 741,54 unequal: No Solution Exploring Operation: 13+57=70, Resulting Numbers: [70] 70,54 unequal: No Solution Exploring Operation: 57-13=44, Resulting Numbers: [44] 44,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 54:[60, 10], Operations: ['45/15=3', '13-3=10'] Exploring Operation: 60+10=70, Resulting Numbers: [70] 70,54 unequal: No Solution Exploring Operation: 60*10=600, Resulting Numbers: [600] 600,54 unequal: No Solution Exploring Operation: 60-10=50, Resulting Numbers: [50] 50,54 unequal: No Solution Exploring Operation: 60/10=6, Resulting Numbers: [6] 6,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 54:[60, 16], Operations: ['45/15=3', '13+3=16'] Exploring Operation: 60-16=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 60+16=76, Resulting Numbers: [76] 76,54 unequal: No Solution Exploring Operation: 60*16=960, Resulting Numbers: [960] 960,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[60, 15, 58], Operations: ['45+13=58'] Exploring Operation: 58-15=43, Resulting Numbers: [60, 43] Generated Node #0,1,0: 54:[60, 43] Operation: 58-15=43 Exploring Operation: 60-58=2, Resulting Numbers: [15, 2] Generated Node #0,1,1: 54:[15, 2] Operation: 60-58=2 Exploring Operation: 60-15=45, Resulting Numbers: [58, 45] Generated Node #0,1,2: 54:[58, 45] Operation: 60-15=45 Exploring Operation: 60/15=4, Resulting Numbers: [58, 4] Generated Node #0,1,3: 54:[58, 4] Operation: 60/15=4 Exploring Operation: 60+15=75, Resulting Numbers: [58, 75] Generated Node #0,1,4: 54:[58, 75] Operation: 60+15=75 Moving to Node #0,1,1 Current State: 54:[15, 2], Operations: ['45+13=58', '60-58=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,54 unequal: No Solution Moving to Node #0,1,3 Current State: 54:[58, 4], Operations: ['45+13=58', '60/15=4'] Exploring Operation: 58*4=232, Resulting Numbers: [232] 232,54 unequal: No Solution Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,54 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[60, 45, 13, 15], Operations: [] Exploring Operation: 45+13=58, Resulting Numbers: [60, 15, 58] Generated Node #0,1: 54:[60, 15, 58] Operation: 45+13=58 Moving to Node #0,1 Current State: 54:[60, 15, 58], Operations: ['45+13=58'] Exploring Operation: 60/15=4, Resulting Numbers: [58, 4] Generated Node #0,1,3: 54:[58, 4] Operation: 60/15=4 Moving to Node #0,1,3 Current State: 54:[58, 4], Operations: ['45+13=58', '60/15=4'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.946181
hs_5
sum_heuristic
[ 82, 70, 7, 77 ]
58
[ "82-70=12", "77-7=70", "70-12=58" ]
Current State: 58:[82, 70, 7, 77], Operations: [] Exploring Operation: 82-70=12, Resulting Numbers: [7, 77, 12] Generated Node #2: [7, 77, 12] from Operation: 82-70=12 Current State: 58:[7, 77, 12], Operations: ['82-70=12'] Exploring Operation: 77-7=70, Resulting Numbers: [12, 70] Generated Node #3: [12, 70] from Operation: 77-7=70 Current State: 58:[12, 70], Operations: ['82-70=12', '77-7=70'] Exploring Operation: 70-12=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[82, 70, 7, 77], Operations: [] Exploring Operation: 77/7=11, Resulting Numbers: [82, 70, 11] Generated Node #0,0: 58:[82, 70, 11] Operation: 77/7=11 Exploring Operation: 82-70=12, Resulting Numbers: [7, 77, 12] Generated Node #0,1: 58:[7, 77, 12] Operation: 82-70=12 Exploring Operation: 82-77=5, Resulting Numbers: [70, 7, 5] Generated Node #0,2: 58:[70, 7, 5] Operation: 82-77=5 Exploring Operation: 77-70=7, Resulting Numbers: [82, 7, 7] Generated Node #0,3: 58:[82, 7, 7] Operation: 77-70=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[70, 7, 5], Operations: ['82-77=5'] Exploring Operation: 70-7=63, Resulting Numbers: [5, 63] Generated Node #0,2,0: 58:[5, 63] Operation: 70-7=63 Exploring Operation: 70/7=10, Resulting Numbers: [5, 10] Generated Node #0,2,1: 58:[5, 10] Operation: 70/7=10 Exploring Operation: 70-5=65, Resulting Numbers: [7, 65] Generated Node #0,2,2: 58:[7, 65] Operation: 70-5=65 Exploring Operation: 7-5=2, Resulting Numbers: [70, 2] Generated Node #0,2,3: 58:[70, 2] Operation: 7-5=2 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 58:[5, 63], Operations: ['82-77=5', '70-7=63'] Exploring Operation: 5*63=315, Resulting Numbers: [315] 315,58 unequal: No Solution Exploring Operation: 5+63=68, Resulting Numbers: [68] 68,58 unequal: No Solution Exploring Operation: 63-5=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[82, 70, 7, 77], Operations: [] Exploring Operation: 82-77=5, Resulting Numbers: [70, 7, 5] Generated Node #0,2: 58:[70, 7, 5] Operation: 82-77=5 Moving to Node #0,2 Current State: 58:[70, 7, 5], Operations: ['82-77=5'] Exploring Operation: 70-7=63, Resulting Numbers: [5, 63] Generated Node #0,2,0: 58:[5, 63] Operation: 70-7=63 Moving to Node #0,2,0 Current State: 58:[5, 63], Operations: ['82-77=5', '70-7=63'] Exploring Operation: 63-5=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 35, 83, 86, 63 ]
71
[ "83-35=48", "86-63=23", "48+23=71" ]
Current State: 71:[35, 83, 86, 63], Operations: [] Exploring Operation: 83-35=48, Resulting Numbers: [86, 63, 48] Generated Node #2: [86, 63, 48] from Operation: 83-35=48 Current State: 71:[86, 63, 48], Operations: ['83-35=48'] Exploring Operation: 86-63=23, Resulting Numbers: [48, 23] Generated Node #3: [48, 23] from Operation: 86-63=23 Current State: 71:[48, 23], Operations: ['83-35=48', '86-63=23'] Exploring Operation: 48+23=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[35, 83, 86, 63], Operations: [] Exploring Operation: 83-35=48, Resulting Numbers: [86, 63, 48] Generated Node #0,0: 71:[86, 63, 48] Operation: 83-35=48 Exploring Operation: 86-35=51, Resulting Numbers: [83, 63, 51] Generated Node #0,1: 71:[83, 63, 51] Operation: 86-35=51 Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[83, 63, 51], Operations: ['86-35=51'] Exploring Operation: 83-51=32, Resulting Numbers: [63, 32] Generated Node #0,1,0: 71:[63, 32] Operation: 83-51=32 Exploring Operation: 63+51=114, Resulting Numbers: [83, 114] Generated Node #0,1,1: 71:[83, 114] Operation: 63+51=114 Moving to Node #0,1,0 Current State: 71:[63, 32], Operations: ['86-35=51', '83-51=32'] Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,71 unequal: No Solution Exploring Operation: 63+32=95, Resulting Numbers: [95] 95,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[83, 114], Operations: ['86-35=51', '63+51=114'] Exploring Operation: 114-83=31, Resulting Numbers: [31] 31,71 unequal: No Solution Exploring Operation: 83+114=197, Resulting Numbers: [197] 197,71 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 Current State: 71:[86, 63, 48], Operations: ['83-35=48'] Exploring Operation: 63+48=111, Resulting Numbers: [86, 111] Generated Node #0,0,0: 71:[86, 111] Operation: 63+48=111 Exploring Operation: 86-48=38, Resulting Numbers: [63, 38] Generated Node #0,0,1: 71:[63, 38] Operation: 86-48=38 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 71:[63, 38], Operations: ['83-35=48', '86-48=38'] Exploring Operation: 63+38=101, Resulting Numbers: [101] 101,71 unequal: No Solution Exploring Operation: 63-38=25, Resulting Numbers: [25] 25,71 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 #0,0,0 Current State: 71:[86, 111], Operations: ['83-35=48', '63+48=111'] Exploring Operation: 111-86=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 86+111=197, Resulting Numbers: [197] 197,71 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_2
mult_heuristic
[ 91, 30, 72, 17 ]
60
[ "91-72=19", "19-17=2", "30*2=60" ]
Current State: 60:[91, 30, 72, 17], Operations: [] Exploring Operation: 91-72=19, Resulting Numbers: [30, 17, 19] Generated Node #2: [30, 17, 19] from Operation: 91-72=19 Current State: 60:[30, 17, 19], Operations: ['91-72=19'] Exploring Operation: 19-17=2, Resulting Numbers: [30, 2] Generated Node #3: [30, 2] from Operation: 19-17=2 Current State: 60:[30, 2], Operations: ['91-72=19', '19-17=2'] Exploring Operation: 30*2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[91, 30, 72, 17], Operations: [] Exploring Operation: 91-30=61, Resulting Numbers: [72, 17, 61] Generated Node #0,0: 60:[72, 17, 61] Operation: 91-30=61 Exploring Operation: 91-72=19, Resulting Numbers: [30, 17, 19] Generated Node #0,1: 60:[30, 17, 19] Operation: 91-72=19 Moving to Node #0,1 Current State: 60:[30, 17, 19], Operations: ['91-72=19'] Exploring Operation: 19-17=2, Resulting Numbers: [30, 2] Generated Node #0,1,0: 60:[30, 2] Operation: 19-17=2 Exploring Operation: 30-17=13, Resulting Numbers: [19, 13] Generated Node #0,1,1: 60:[19, 13] Operation: 30-17=13 Moving to Node #0,0 Current State: 60:[72, 17, 61], Operations: ['91-30=61'] Exploring Operation: 72-17=55, Resulting Numbers: [61, 55] Generated Node #0,0,0: 60:[61, 55] Operation: 72-17=55 Exploring Operation: 72-61=11, Resulting Numbers: [17, 11] Generated Node #0,0,1: 60:[17, 11] Operation: 72-61=11 Moving to Node #0,1,0 Current State: 60:[30, 2], Operations: ['91-72=19', '19-17=2'] Exploring Operation: 30*2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[91, 30, 72, 17], Operations: [] Exploring Operation: 91-72=19, Resulting Numbers: [30, 17, 19] Generated Node #0,1: 60:[30, 17, 19] Operation: 91-72=19 Moving to Node #0,1 Current State: 60:[30, 17, 19], Operations: ['91-72=19'] Exploring Operation: 19-17=2, Resulting Numbers: [30, 2] Generated Node #0,1,0: 60:[30, 2] Operation: 19-17=2 Moving to Node #0,1,0 Current State: 60:[30, 2], Operations: ['91-72=19', '19-17=2'] Exploring Operation: 30*2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
0.990451
hs_2
mult_heuristic
[ 93, 88, 60, 38 ]
97
[ "60-38=22", "88/22=4", "93+4=97" ]
Current State: 97:[93, 88, 60, 38], Operations: [] Exploring Operation: 60-38=22, Resulting Numbers: [93, 88, 22] Generated Node #2: [93, 88, 22] from Operation: 60-38=22 Current State: 97:[93, 88, 22], Operations: ['60-38=22'] Exploring Operation: 88/22=4, Resulting Numbers: [93, 4] Generated Node #3: [93, 4] from Operation: 88/22=4 Current State: 97:[93, 4], Operations: ['60-38=22', '88/22=4'] Exploring Operation: 93+4=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[93, 88, 60, 38], Operations: [] Exploring Operation: 93+38=131, Resulting Numbers: [88, 60, 131] Generated Node #0,0: 97:[88, 60, 131] Operation: 93+38=131 Exploring Operation: 88+38=126, Resulting Numbers: [93, 60, 126] Generated Node #0,1: 97:[93, 60, 126] Operation: 88+38=126 Exploring Operation: 60+38=98, Resulting Numbers: [93, 88, 98] Generated Node #0,2: 97:[93, 88, 98] Operation: 60+38=98 Exploring Operation: 93-38=55, Resulting Numbers: [88, 60, 55] Generated Node #0,3: 97:[88, 60, 55] Operation: 93-38=55 Moving to Node #0,2 Current State: 97:[93, 88, 98], Operations: ['60+38=98'] Exploring Operation: 93-88=5, Resulting Numbers: [98, 5] Generated Node #0,2,0: 97:[98, 5] Operation: 93-88=5 Exploring Operation: 88+98=186, Resulting Numbers: [93, 186] Generated Node #0,2,1: 97:[93, 186] Operation: 88+98=186 Exploring Operation: 93+88=181, Resulting Numbers: [98, 181] Generated Node #0,2,2: 97:[98, 181] Operation: 93+88=181 Exploring Operation: 98-88=10, Resulting Numbers: [93, 10] Generated Node #0,2,3: 97:[93, 10] Operation: 98-88=10 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 97:[98, 181], Operations: ['60+38=98', '93+88=181'] Exploring Operation: 181-98=83, Resulting Numbers: [83] 83,97 unequal: No Solution Exploring Operation: 98*181=17738, Resulting Numbers: [17738] 17738,97 unequal: No Solution Exploring Operation: 98+181=279, Resulting Numbers: [279] 279,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 97:[93, 10], Operations: ['60+38=98', '98-88=10'] Exploring Operation: 93+10=103, Resulting Numbers: [103] 103,97 unequal: No Solution Exploring Operation: 93-10=83, Resulting Numbers: [83] 83,97 unequal: No Solution Exploring Operation: 93*10=930, Resulting Numbers: [930] 930,97 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 #0,2,0 Current State: 97:[98, 5], Operations: ['60+38=98', '93-88=5'] Exploring Operation: 98*5=490, Resulting Numbers: [490] 490,97 unequal: No Solution Exploring Operation: 98-5=93, Resulting Numbers: [93] 93,97 unequal: No Solution Exploring Operation: 98+5=103, Resulting Numbers: [103] 103,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[93, 186], Operations: ['60+38=98', '88+98=186'] Exploring Operation: 186/93=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 186-93=93, Resulting Numbers: [93] 93,97 unequal: No Solution Exploring Operation: 93+186=279, Resulting Numbers: [279] 279,97 unequal: No Solution Exploring Operation: 93*186=17298, Resulting Numbers: [17298] 17298,97 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:[93, 60, 126], Operations: ['88+38=126'] Exploring Operation: 60+126=186, Resulting Numbers: [93, 186] Generated Node #0,1,0: 97:[93, 186] Operation: 60+126=186 Exploring Operation: 93+60=153, Resulting Numbers: [126, 153] Generated Node #0,1,1: 97:[126, 153] Operation: 93+60=153 Exploring Operation: 93-60=33, Resulting Numbers: [126, 33] Generated Node #0,1,2: 97:[126, 33] Operation: 93-60=33 Exploring Operation: 126-60=66, Resulting Numbers: [93, 66] Generated Node #0,1,3: 97:[93, 66] Operation: 126-60=66 Moving to Node #0,0 Current State: 97:[88, 60, 131], Operations: ['93+38=131'] Exploring Operation: 131-88=43, Resulting Numbers: [60, 43] Generated Node #0,0,0: 97:[60, 43] Operation: 131-88=43 Exploring Operation: 88+60=148, Resulting Numbers: [131, 148] Generated Node #0,0,1: 97:[131, 148] Operation: 88+60=148 Exploring Operation: 131-60=71, Resulting Numbers: [88, 71] Generated Node #0,0,2: 97:[88, 71] Operation: 131-60=71 Exploring Operation: 88-60=28, Resulting Numbers: [131, 28] Generated Node #0,0,3: 97:[131, 28] Operation: 88-60=28 Moving to Node #0,3 Current State: 97:[88, 60, 55], Operations: ['93-38=55'] Exploring Operation: 60+55=115, Resulting Numbers: [88, 115] Generated Node #0,3,0: 97:[88, 115] Operation: 60+55=115 Exploring Operation: 88+60=148, Resulting Numbers: [55, 148] Generated Node #0,3,1: 97:[55, 148] Operation: 88+60=148 Exploring Operation: 88+55=143, Resulting Numbers: [60, 143] Generated Node #0,3,2: 97:[60, 143] Operation: 88+55=143 Exploring Operation: 88-55=33, Resulting Numbers: [60, 33] Generated Node #0,3,3: 97:[60, 33] Operation: 88-55=33 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 97:[88, 115], Operations: ['93-38=55', '60+55=115'] Exploring Operation: 88*115=10120, Resulting Numbers: [10120] 10120,97 unequal: No Solution Exploring Operation: 115-88=27, Resulting Numbers: [27] 27,97 unequal: No Solution Exploring Operation: 88+115=203, Resulting Numbers: [203] 203,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 97:[60, 143], Operations: ['93-38=55', '88+55=143'] Exploring Operation: 143-60=83, Resulting Numbers: [83] 83,97 unequal: No Solution Exploring Operation: 60+143=203, Resulting Numbers: [203] 203,97 unequal: No Solution Exploring Operation: 60*143=8580, Resulting Numbers: [8580] 8580,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 97:[55, 148], Operations: ['93-38=55', '88+60=148'] Exploring Operation: 55*148=8140, Resulting Numbers: [8140] 8140,97 unequal: No Solution Exploring Operation: 148-55=93, Resulting Numbers: [93] 93,97 unequal: No Solution Exploring Operation: 55+148=203, Resulting Numbers: [203] 203,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 97:[60, 33], Operations: ['93-38=55', '88-55=33'] Exploring Operation: 60*33=1980, Resulting Numbers: [1980] 1980,97 unequal: No Solution Exploring Operation: 60+33=93, Resulting Numbers: [93] 93,97 unequal: No Solution Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 97:[93, 66], Operations: ['88+38=126', '126-60=66'] Exploring Operation: 93*66=6138, Resulting Numbers: [6138] 6138,97 unequal: No Solution Exploring Operation: 93-66=27, Resulting Numbers: [27] 27,97 unequal: No Solution Exploring Operation: 93+66=159, Resulting Numbers: [159] 159,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[88, 71], Operations: ['93+38=131', '131-60=71'] Exploring Operation: 88-71=17, Resulting Numbers: [17] 17,97 unequal: No Solution Exploring Operation: 88+71=159, Resulting Numbers: [159] 159,97 unequal: No Solution Exploring Operation: 88*71=6248, Resulting Numbers: [6248] 6248,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[131, 148], Operations: ['93+38=131', '88+60=148'] Exploring Operation: 131*148=19388, Resulting Numbers: [19388] 19388,97 unequal: No Solution Exploring Operation: 131+148=279, Resulting Numbers: [279] 279,97 unequal: No Solution Exploring Operation: 148-131=17, Resulting Numbers: [17] 17,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[126, 153], Operations: ['88+38=126', '93+60=153'] Exploring Operation: 126*153=19278, Resulting Numbers: [19278] 19278,97 unequal: No Solution Exploring Operation: 126+153=279, Resulting Numbers: [279] 279,97 unequal: No Solution Exploring Operation: 153-126=27, Resulting Numbers: [27] 27,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[60, 43], Operations: ['93+38=131', '131-88=43'] Exploring Operation: 60+43=103, Resulting Numbers: [103] 103,97 unequal: No Solution Exploring Operation: 60*43=2580, Resulting Numbers: [2580] 2580,97 unequal: No Solution Exploring Operation: 60-43=17, Resulting Numbers: [17] 17,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[126, 33], Operations: ['88+38=126', '93-60=33'] Exploring Operation: 126+33=159, Resulting Numbers: [159] 159,97 unequal: No Solution Exploring Operation: 126*33=4158, Resulting Numbers: [4158] 4158,97 unequal: No Solution Exploring Operation: 126-33=93, Resulting Numbers: [93] 93,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[93, 186], Operations: ['88+38=126', '60+126=186'] Exploring Operation: 93+186=279, Resulting Numbers: [279] 279,97 unequal: No Solution Exploring Operation: 93*186=17298, Resulting Numbers: [17298] 17298,97 unequal: No Solution Exploring Operation: 186/93=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 186-93=93, Resulting Numbers: [93] 93,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[131, 28], Operations: ['93+38=131', '88-60=28'] Exploring Operation: 131*28=3668, Resulting Numbers: [3668] 3668,97 unequal: No Solution Exploring Operation: 131-28=103, Resulting Numbers: [103] 103,97 unequal: No Solution Exploring Operation: 131+28=159, Resulting Numbers: [159] 159,97 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 4, 99, 93, 7 ]
17
[ "4+99=103", "93-7=86", "103-86=17" ]
Current State: 17:[4, 99, 93, 7], Operations: [] Exploring Operation: 4+99=103, Resulting Numbers: [93, 7, 103] Generated Node #2: [93, 7, 103] from Operation: 4+99=103 Current State: 17:[93, 7, 103], Operations: ['4+99=103'] Exploring Operation: 93-7=86, Resulting Numbers: [103, 86] Generated Node #3: [103, 86] from Operation: 93-7=86 Current State: 17:[103, 86], Operations: ['4+99=103', '93-7=86'] Exploring Operation: 103-86=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[4, 99, 93, 7], Operations: [] Exploring Operation: 99-4=95, Resulting Numbers: [93, 7, 95] Generated Node #0,0: 17:[93, 7, 95] Operation: 99-4=95 Exploring Operation: 93-4=89, Resulting Numbers: [99, 7, 89] Generated Node #0,1: 17:[99, 7, 89] Operation: 93-4=89 Exploring Operation: 99-93=6, Resulting Numbers: [4, 7, 6] Generated Node #0,2: 17:[4, 7, 6] Operation: 99-93=6 Exploring Operation: 4+7=11, Resulting Numbers: [99, 93, 11] Generated Node #0,3: 17:[99, 93, 11] Operation: 4+7=11 Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[4, 7, 6], Operations: ['99-93=6'] Exploring Operation: 4+6=10, Resulting Numbers: [7, 10] Generated Node #0,2,0: 17:[7, 10] Operation: 4+6=10 Exploring Operation: 7+6=13, Resulting Numbers: [4, 13] Generated Node #0,2,1: 17:[4, 13] Operation: 7+6=13 Exploring Operation: 4+7=11, Resulting Numbers: [6, 11] Generated Node #0,2,2: 17:[6, 11] Operation: 4+7=11 Exploring Operation: 4*6=24, Resulting Numbers: [7, 24] Generated Node #0,2,3: 17:[7, 24] Operation: 4*6=24 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 17:[7, 10], Operations: ['99-93=6', '4+6=10'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,17 unequal: No Solution Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,17 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[4, 99, 93, 7], Operations: [] Exploring Operation: 99-93=6, Resulting Numbers: [4, 7, 6] Generated Node #0,2: 17:[4, 7, 6] Operation: 99-93=6 Moving to Node #0,2 Current State: 17:[4, 7, 6], Operations: ['99-93=6'] Exploring Operation: 4+6=10, Resulting Numbers: [7, 10] Generated Node #0,2,0: 17:[7, 10] Operation: 4+6=10 Moving to Node #0,2,0 Current State: 17:[7, 10], Operations: ['99-93=6', '4+6=10'] Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 19, 44, 24, 1 ]
50
[ "44-19=25", "24+1=25", "25+25=50" ]
Current State: 50:[19, 44, 24, 1], Operations: [] Exploring Operation: 44-19=25, Resulting Numbers: [24, 1, 25] Generated Node #2: [24, 1, 25] from Operation: 44-19=25 Current State: 50:[24, 1, 25], Operations: ['44-19=25'] Exploring Operation: 24+1=25, Resulting Numbers: [25, 25] Generated Node #3: [25, 25] from Operation: 24+1=25 Current State: 50:[25, 25], Operations: ['44-19=25', '24+1=25'] Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[19, 44, 24, 1], Operations: [] Exploring Operation: 44-19=25, Resulting Numbers: [24, 1, 25] Generated Node #0,0: 50:[24, 1, 25] Operation: 44-19=25 Exploring Operation: 24-19=5, Resulting Numbers: [44, 1, 5] Generated Node #0,1: 50:[44, 1, 5] Operation: 24-19=5 Exploring Operation: 19+1=20, Resulting Numbers: [44, 24, 20] Generated Node #0,2: 50:[44, 24, 20] Operation: 19+1=20 Exploring Operation: 44+1=45, Resulting Numbers: [19, 24, 45] Generated Node #0,3: 50:[19, 24, 45] Operation: 44+1=45 Exploring Operation: 44-24=20, Resulting Numbers: [19, 1, 20] Generated Node #0,4: 50:[19, 1, 20] Operation: 44-24=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[24, 1, 25], Operations: ['44-19=25'] Exploring Operation: 24*1=24, Resulting Numbers: [25, 24] Generated Node #0,0,0: 50:[25, 24] Operation: 24*1=24 Exploring Operation: 24+1=25, Resulting Numbers: [25, 25] Generated Node #0,0,1: 50:[25, 25] Operation: 24+1=25 Exploring Operation: 24/1=24, Resulting Numbers: [25, 24] Generated Node #0,0,2: 50:[25, 24] Operation: 24/1=24 Exploring Operation: 1*25=25, Resulting Numbers: [24, 25] Generated Node #0,0,3: 50:[24, 25] Operation: 1*25=25 Exploring Operation: 25/1=25, Resulting Numbers: [24, 25] Generated Node #0,0,4: 50:[24, 25] Operation: 25/1=25 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 50:[25, 25], Operations: ['44-19=25', '24+1=25'] Exploring Operation: 25*25=625, Resulting Numbers: [625] 625,50 unequal: No Solution Exploring Operation: 25-25=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[19, 44, 24, 1], Operations: [] Exploring Operation: 44-19=25, Resulting Numbers: [24, 1, 25] Generated Node #0,0: 50:[24, 1, 25] Operation: 44-19=25 Moving to Node #0,0 Current State: 50:[24, 1, 25], Operations: ['44-19=25'] Exploring Operation: 24+1=25, Resulting Numbers: [25, 25] Generated Node #0,0,1: 50:[25, 25] Operation: 24+1=25 Moving to Node #0,0,1 Current State: 50:[25, 25], Operations: ['44-19=25', '24+1=25'] Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 21, 68, 9, 58 ]
22
[ "21+68=89", "9+58=67", "89-67=22" ]
Current State: 22:[21, 68, 9, 58], Operations: [] Exploring Operation: 21+68=89, Resulting Numbers: [9, 58, 89] Generated Node #2: [9, 58, 89] from Operation: 21+68=89 Current State: 22:[9, 58, 89], Operations: ['21+68=89'] Exploring Operation: 9+58=67, Resulting Numbers: [89, 67] Generated Node #3: [89, 67] from Operation: 9+58=67 Current State: 22:[89, 67], Operations: ['21+68=89', '9+58=67'] Exploring Operation: 89-67=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[21, 68, 9, 58], Operations: [] Exploring Operation: 68-9=59, Resulting Numbers: [21, 58, 59] Generated Node #0,0: 22:[21, 58, 59] Operation: 68-9=59 Exploring Operation: 68-58=10, Resulting Numbers: [21, 9, 10] Generated Node #0,1: 22:[21, 9, 10] Operation: 68-58=10 Exploring Operation: 58-21=37, Resulting Numbers: [68, 9, 37] Generated Node #0,2: 22:[68, 9, 37] Operation: 58-21=37 Exploring Operation: 68-21=47, Resulting Numbers: [9, 58, 47] Generated Node #0,3: 22:[9, 58, 47] Operation: 68-21=47 Moving to Node #0,1 Current State: 22:[21, 9, 10], Operations: ['68-58=10'] Exploring Operation: 21-9=12, Resulting Numbers: [10, 12] Generated Node #0,1,0: 22:[10, 12] Operation: 21-9=12 Exploring Operation: 21-10=11, Resulting Numbers: [9, 11] Generated Node #0,1,1: 22:[9, 11] Operation: 21-10=11 Exploring Operation: 10-9=1, Resulting Numbers: [21, 1] Generated Node #0,1,2: 22:[21, 1] Operation: 10-9=1 Exploring Operation: 9+10=19, Resulting Numbers: [21, 19] Generated Node #0,1,3: 22:[21, 19] Operation: 9+10=19 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[10, 12], Operations: ['68-58=10', '21-9=12'] Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 10*12=120, Resulting Numbers: [120] 120,22 unequal: No Solution Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[21, 68, 9, 58], Operations: [] Exploring Operation: 68-58=10, Resulting Numbers: [21, 9, 10] Generated Node #0,1: 22:[21, 9, 10] Operation: 68-58=10 Moving to Node #0,1 Current State: 22:[21, 9, 10], Operations: ['68-58=10'] Exploring Operation: 21-9=12, Resulting Numbers: [10, 12] Generated Node #0,1,0: 22:[10, 12] Operation: 21-9=12 Moving to Node #0,1,0 Current State: 22:[10, 12], Operations: ['68-58=10', '21-9=12'] Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 11, 93, 91, 34 ]
56
[ "93-91=2", "11*2=22", "34+22=56" ]
Current State: 56:[11, 93, 91, 34], Operations: [] Exploring Operation: 93-91=2, Resulting Numbers: [11, 34, 2] Generated Node #2: [11, 34, 2] from Operation: 93-91=2 Current State: 56:[11, 34, 2], Operations: ['93-91=2'] Exploring Operation: 11*2=22, Resulting Numbers: [34, 22] Generated Node #3: [34, 22] from Operation: 11*2=22 Current State: 56:[34, 22], Operations: ['93-91=2', '11*2=22'] Exploring Operation: 34+22=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[11, 93, 91, 34], Operations: [] Exploring Operation: 93-34=59, Resulting Numbers: [11, 91, 59] Generated Node #0,0: 56:[11, 91, 59] Operation: 93-34=59 Exploring Operation: 93-91=2, Resulting Numbers: [11, 34, 2] Generated Node #0,1: 56:[11, 34, 2] Operation: 93-91=2 Exploring Operation: 91-34=57, Resulting Numbers: [11, 93, 57] Generated Node #0,2: 56:[11, 93, 57] Operation: 91-34=57 Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[11, 34, 2], Operations: ['93-91=2'] Exploring Operation: 11+2=13, Resulting Numbers: [34, 13] Generated Node #0,1,0: 56:[34, 13] Operation: 11+2=13 Exploring Operation: 34-11=23, Resulting Numbers: [2, 23] Generated Node #0,1,1: 56:[2, 23] Operation: 34-11=23 Exploring Operation: 34/2=17, Resulting Numbers: [11, 17] Generated Node #0,1,2: 56:[11, 17] Operation: 34/2=17 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 56:[2, 23], Operations: ['93-91=2', '34-11=23'] Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,56 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,56 unequal: No Solution No 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: 56:[11, 17], Operations: ['93-91=2', '34/2=17'] Exploring Operation: 11*17=187, Resulting Numbers: [187] 187,56 unequal: No Solution Exploring Operation: 11+17=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,56 unequal: No Solution No 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: 56:[34, 13], Operations: ['93-91=2', '11+2=13'] Exploring Operation: 34-13=21, Resulting Numbers: [21] 21,56 unequal: No Solution Exploring Operation: 34*13=442, Resulting Numbers: [442] 442,56 unequal: No Solution Exploring Operation: 34+13=47, Resulting Numbers: [47] 47,56 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: 56:[11, 91, 59], Operations: ['93-34=59'] Exploring Operation: 59-11=48, Resulting Numbers: [91, 48] Generated Node #0,0,0: 56:[91, 48] Operation: 59-11=48 Exploring Operation: 91-59=32, Resulting Numbers: [11, 32] Generated Node #0,0,1: 56:[11, 32] Operation: 91-59=32 Exploring Operation: 91-11=80, Resulting Numbers: [59, 80] Generated Node #0,0,2: 56:[59, 80] Operation: 91-11=80 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 56:[11, 32], Operations: ['93-34=59', '91-59=32'] Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,56 unequal: No Solution Exploring Operation: 11+32=43, Resulting Numbers: [43] 43,56 unequal: No Solution Exploring Operation: 11*32=352, Resulting Numbers: [352] 352,56 unequal: No Solution No 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: 56:[59, 80], Operations: ['93-34=59', '91-11=80'] Exploring Operation: 80-59=21, Resulting Numbers: [21] 21,56 unequal: No Solution Exploring Operation: 59+80=139, Resulting Numbers: [139] 139,56 unequal: No Solution Exploring Operation: 59*80=4720, Resulting Numbers: [4720] 4720,56 unequal: No Solution No 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: 56:[91, 48], Operations: ['93-34=59', '59-11=48'] Exploring Operation: 91+48=139, Resulting Numbers: [139] 139,56 unequal: No Solution Exploring Operation: 91*48=4368, Resulting Numbers: [4368] 4368,56 unequal: No Solution Exploring Operation: 91-48=43, Resulting Numbers: [43] 43,56 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: 56:[11, 93, 57], Operations: ['91-34=57'] Exploring Operation: 93-57=36, Resulting Numbers: [11, 36] Generated Node #0,2,0: 56:[11, 36] Operation: 93-57=36 Exploring Operation: 57-11=46, Resulting Numbers: [93, 46] Generated Node #0,2,1: 56:[93, 46] Operation: 57-11=46 Exploring Operation: 93-11=82, Resulting Numbers: [57, 82] Generated Node #0,2,2: 56:[57, 82] Operation: 93-11=82 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 56:[11, 36], Operations: ['91-34=57', '93-57=36'] Exploring Operation: 11*36=396, Resulting Numbers: [396] 396,56 unequal: No Solution Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 11+36=47, Resulting Numbers: [47] 47,56 unequal: No Solution No 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: 56:[57, 82], Operations: ['91-34=57', '93-11=82'] Exploring Operation: 82-57=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 57+82=139, Resulting Numbers: [139] 139,56 unequal: No Solution Exploring Operation: 57*82=4674, Resulting Numbers: [4674] 4674,56 unequal: No Solution No 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: 56:[93, 46], Operations: ['91-34=57', '57-11=46'] Exploring Operation: 93+46=139, Resulting Numbers: [139] 139,56 unequal: No Solution Exploring Operation: 93*46=4278, Resulting Numbers: [4278] 4278,56 unequal: No Solution Exploring Operation: 93-46=47, Resulting Numbers: [47] 47,56 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
[ 42, 96, 32, 64 ]
22
[ "96-42=54", "64-32=32", "54-32=22" ]
Current State: 22:[42, 96, 32, 64], Operations: [] Exploring Operation: 96-42=54, Resulting Numbers: [32, 64, 54] Generated Node #2: [32, 64, 54] from Operation: 96-42=54 Current State: 22:[32, 64, 54], Operations: ['96-42=54'] Exploring Operation: 64-32=32, Resulting Numbers: [54, 32] Generated Node #3: [54, 32] from Operation: 64-32=32 Current State: 22:[54, 32], Operations: ['96-42=54', '64-32=32'] Exploring Operation: 54-32=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[42, 96, 32, 64], Operations: [] Exploring Operation: 96-64=32, Resulting Numbers: [42, 32, 32] Generated Node #0,0: 22:[42, 32, 32] Operation: 96-64=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[42, 32, 32], Operations: ['96-64=32'] Exploring Operation: 42-32=10, Resulting Numbers: [32, 10] Generated Node #0,0,0: 22:[32, 10] Operation: 42-32=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 22:[32, 10], Operations: ['96-64=32', '42-32=10'] Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[42, 96, 32, 64], Operations: [] Exploring Operation: 96-64=32, Resulting Numbers: [42, 32, 32] Generated Node #0,0: 22:[42, 32, 32] Operation: 96-64=32 Moving to Node #0,0 Current State: 22:[42, 32, 32], Operations: ['96-64=32'] Exploring Operation: 42-32=10, Resulting Numbers: [32, 10] Generated Node #0,0,0: 22:[32, 10] Operation: 42-32=10 Moving to Node #0,0,0 Current State: 22:[32, 10], Operations: ['96-64=32', '42-32=10'] Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 82, 65, 28, 64 ]
19
[ "82-65=17", "64-28=36", "36-17=19" ]
Current State: 19:[82, 65, 28, 64], Operations: [] Exploring Operation: 82-65=17, Resulting Numbers: [28, 64, 17] Generated Node #2: [28, 64, 17] from Operation: 82-65=17 Current State: 19:[28, 64, 17], Operations: ['82-65=17'] Exploring Operation: 64-28=36, Resulting Numbers: [17, 36] Generated Node #3: [17, 36] from Operation: 64-28=36 Current State: 19:[17, 36], Operations: ['82-65=17', '64-28=36'] Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[82, 65, 28, 64], Operations: [] Exploring Operation: 82-64=18, Resulting Numbers: [65, 28, 18] Generated Node #0,0: 19:[65, 28, 18] Operation: 82-64=18 Exploring Operation: 82-65=17, Resulting Numbers: [28, 64, 17] Generated Node #0,1: 19:[28, 64, 17] Operation: 82-65=17 Exploring Operation: 65-64=1, Resulting Numbers: [82, 28, 1] Generated Node #0,2: 19:[82, 28, 1] Operation: 65-64=1 Moving to Node #0,0 Current State: 19:[65, 28, 18], Operations: ['82-64=18'] Exploring Operation: 65-18=47, Resulting Numbers: [28, 47] Generated Node #0,0,0: 19:[28, 47] Operation: 65-18=47 Exploring Operation: 65-28=37, Resulting Numbers: [18, 37] Generated Node #0,0,1: 19:[18, 37] Operation: 65-28=37 Exploring Operation: 28-18=10, Resulting Numbers: [65, 10] Generated Node #0,0,2: 19:[65, 10] Operation: 28-18=10 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 19:[18, 37], Operations: ['82-64=18', '65-28=37'] Exploring Operation: 18+37=55, Resulting Numbers: [55] 55,19 unequal: No Solution Exploring Operation: 18*37=666, Resulting Numbers: [666] 666,19 unequal: No Solution Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[82, 65, 28, 64], Operations: [] Exploring Operation: 82-64=18, Resulting Numbers: [65, 28, 18] Generated Node #0,0: 19:[65, 28, 18] Operation: 82-64=18 Moving to Node #0,0 Current State: 19:[65, 28, 18], Operations: ['82-64=18'] Exploring Operation: 65-28=37, Resulting Numbers: [18, 37] Generated Node #0,0,1: 19:[18, 37] Operation: 65-28=37 Moving to Node #0,0,1 Current State: 19:[18, 37], Operations: ['82-64=18', '65-28=37'] Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 18, 75, 38, 12 ]
27
[ "18*75=1350", "38+12=50", "1350/50=27" ]
Current State: 27:[18, 75, 38, 12], Operations: [] Exploring Operation: 18*75=1350, Resulting Numbers: [38, 12, 1350] Generated Node #2: [38, 12, 1350] from Operation: 18*75=1350 Current State: 27:[38, 12, 1350], Operations: ['18*75=1350'] Exploring Operation: 38+12=50, Resulting Numbers: [1350, 50] Generated Node #3: [1350, 50] from Operation: 38+12=50 Current State: 27:[1350, 50], Operations: ['18*75=1350', '38+12=50'] Exploring Operation: 1350/50=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[18, 75, 38, 12], Operations: [] Exploring Operation: 75-38=37, Resulting Numbers: [18, 12, 37] Generated Node #0,0: 27:[18, 12, 37] Operation: 75-38=37 Exploring Operation: 75-18=57, Resulting Numbers: [38, 12, 57] Generated Node #0,1: 27:[38, 12, 57] Operation: 75-18=57 Exploring Operation: 75-12=63, Resulting Numbers: [18, 38, 63] Generated Node #0,2: 27:[18, 38, 63] Operation: 75-12=63 Exploring Operation: 38-18=20, Resulting Numbers: [75, 12, 20] Generated Node #0,3: 27:[75, 12, 20] Operation: 38-18=20 Moving to Node #0,0 Current State: 27:[18, 12, 37], Operations: ['75-38=37'] Exploring Operation: 37-18=19, Resulting Numbers: [12, 19] Generated Node #0,0,0: 27:[12, 19] Operation: 37-18=19 Exploring Operation: 18+12=30, Resulting Numbers: [37, 30] Generated Node #0,0,1: 27:[37, 30] Operation: 18+12=30 Exploring Operation: 37-12=25, Resulting Numbers: [18, 25] Generated Node #0,0,2: 27:[18, 25] Operation: 37-12=25 Exploring Operation: 18-12=6, Resulting Numbers: [37, 6] Generated Node #0,0,3: 27:[37, 6] Operation: 18-12=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[12, 19], Operations: ['75-38=37', '37-18=19'] Exploring Operation: 12*19=228, Resulting Numbers: [228] 228,27 unequal: No Solution Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,27 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 27:[18, 25], Operations: ['75-38=37', '37-12=25'] Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,27 unequal: No Solution Exploring Operation: 18+25=43, Resulting Numbers: [43] 43,27 unequal: No Solution Exploring Operation: 18*25=450, Resulting Numbers: [450] 450,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 27:[37, 30], Operations: ['75-38=37', '18+12=30'] Exploring Operation: 37-30=7, Resulting Numbers: [7] 7,27 unequal: No Solution Exploring Operation: 37+30=67, Resulting Numbers: [67] 67,27 unequal: No Solution Exploring Operation: 37*30=1110, Resulting Numbers: [1110] 1110,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 27:[37, 6], Operations: ['75-38=37', '18-12=6'] Exploring Operation: 37*6=222, Resulting Numbers: [222] 222,27 unequal: No Solution Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,27 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,27 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: 27:[38, 12, 57], Operations: ['75-18=57'] Exploring Operation: 57-38=19, Resulting Numbers: [12, 19] Generated Node #0,1,0: 27:[12, 19] Operation: 57-38=19 Exploring Operation: 38-12=26, Resulting Numbers: [57, 26] Generated Node #0,1,1: 27:[57, 26] Operation: 38-12=26 Exploring Operation: 38+12=50, Resulting Numbers: [57, 50] Generated Node #0,1,2: 27:[57, 50] Operation: 38+12=50 Exploring Operation: 57-12=45, Resulting Numbers: [38, 45] Generated Node #0,1,3: 27:[38, 45] Operation: 57-12=45 Moving to Node #0,2 Current State: 27:[18, 38, 63], Operations: ['75-12=63'] Exploring Operation: 63-18=45, Resulting Numbers: [38, 45] Generated Node #0,2,0: 27:[38, 45] Operation: 63-18=45 Exploring Operation: 38-18=20, Resulting Numbers: [63, 20] Generated Node #0,2,1: 27:[63, 20] Operation: 38-18=20 Exploring Operation: 18+38=56, Resulting Numbers: [63, 56] Generated Node #0,2,2: 27:[63, 56] Operation: 18+38=56 Exploring Operation: 63-38=25, Resulting Numbers: [18, 25] Generated Node #0,2,3: 27:[18, 25] Operation: 63-38=25 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 27:[18, 25], Operations: ['75-12=63', '63-38=25'] Exploring Operation: 18+25=43, Resulting Numbers: [43] 43,27 unequal: No Solution Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,27 unequal: No Solution Exploring Operation: 18*25=450, Resulting Numbers: [450] 450,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 27:[38, 45], Operations: ['75-12=63', '63-18=45'] Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,27 unequal: No Solution Exploring Operation: 38*45=1710, Resulting Numbers: [1710] 1710,27 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 27:[63, 20], Operations: ['75-12=63', '38-18=20'] Exploring Operation: 63+20=83, Resulting Numbers: [83] 83,27 unequal: No Solution Exploring Operation: 63*20=1260, Resulting Numbers: [1260] 1260,27 unequal: No Solution Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 27:[63, 56], Operations: ['75-12=63', '18+38=56'] Exploring Operation: 63*56=3528, Resulting Numbers: [3528] 3528,27 unequal: No Solution Exploring Operation: 63+56=119, Resulting Numbers: [119] 119,27 unequal: No Solution Exploring Operation: 63-56=7, Resulting Numbers: [7] 7,27 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: 27:[75, 12, 20], Operations: ['38-18=20'] Exploring Operation: 12+20=32, Resulting Numbers: [75, 32] Generated Node #0,3,0: 27:[75, 32] Operation: 12+20=32 Exploring Operation: 20-12=8, Resulting Numbers: [75, 8] Generated Node #0,3,1: 27:[75, 8] Operation: 20-12=8 Exploring Operation: 75-20=55, Resulting Numbers: [12, 55] Generated Node #0,3,2: 27:[12, 55] Operation: 75-20=55 Exploring Operation: 75-12=63, Resulting Numbers: [20, 63] Generated Node #0,3,3: 27:[20, 63] Operation: 75-12=63 Moving to Node #0,1,0 Current State: 27:[12, 19], Operations: ['75-18=57', '57-38=19'] Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,27 unequal: No Solution Exploring Operation: 12*19=228, Resulting Numbers: [228] 228,27 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,27 unequal: No Solution Moving to Node #0,1,3 Current State: 27:[38, 45], Operations: ['75-18=57', '57-12=45'] Exploring Operation: 38*45=1710, Resulting Numbers: [1710] 1710,27 unequal: No Solution Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,27 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[57, 26], Operations: ['75-18=57', '38-12=26'] Exploring Operation: 57+26=83, Resulting Numbers: [83] 83,27 unequal: No Solution Exploring Operation: 57*26=1482, Resulting Numbers: [1482] 1482,27 unequal: No Solution Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,27 unequal: No Solution Moving to Node #0,3,2 Current State: 27:[12, 55], Operations: ['38-18=20', '75-20=55'] Exploring Operation: 12+55=67, Resulting Numbers: [67] 67,27 unequal: No Solution Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,27 unequal: No Solution Exploring Operation: 12*55=660, Resulting Numbers: [660] 660,27 unequal: No Solution Moving to Node #0,3,3 Current State: 27:[20, 63], Operations: ['38-18=20', '75-12=63'] Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,27 unequal: No Solution Exploring Operation: 20*63=1260, Resulting Numbers: [1260] 1260,27 unequal: No Solution Exploring Operation: 20+63=83, Resulting Numbers: [83] 83,27 unequal: No Solution Moving to Node #0,3,1 Current State: 27:[75, 8], Operations: ['38-18=20', '20-12=8'] Exploring Operation: 75+8=83, Resulting Numbers: [83] 83,27 unequal: No Solution Exploring Operation: 75*8=600, Resulting Numbers: [600] 600,27 unequal: No Solution Exploring Operation: 75-8=67, Resulting Numbers: [67] 67,27 unequal: No Solution Moving to Node #0,1,2 Current State: 27:[57, 50], Operations: ['75-18=57', '38+12=50'] Exploring Operation: 57+50=107, Resulting Numbers: [107] 107,27 unequal: No Solution Exploring Operation: 57*50=2850, Resulting Numbers: [2850] 2850,27 unequal: No Solution Exploring Operation: 57-50=7, Resulting Numbers: [7] 7,27 unequal: No Solution Moving to Node #0,3,0 Current State: 27:[75, 32], Operations: ['38-18=20', '12+20=32'] Exploring Operation: 75*32=2400, Resulting Numbers: [2400] 2400,27 unequal: No Solution Exploring Operation: 75-32=43, Resulting Numbers: [43] 43,27 unequal: No Solution Exploring Operation: 75+32=107, Resulting Numbers: [107] 107,27 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 18, 67, 2, 25 ]
55
[ "18+67=85", "25+85=110", "110/2=55" ]
Current State: 55:[18, 67, 2, 25], Operations: [] Exploring Operation: 18+67=85, Resulting Numbers: [2, 25, 85] Generated Node #2: [2, 25, 85] from Operation: 18+67=85 Current State: 55:[2, 25, 85], Operations: ['18+67=85'] Exploring Operation: 25+85=110, Resulting Numbers: [2, 110] Generated Node #3: [2, 110] from Operation: 25+85=110 Current State: 55:[2, 110], Operations: ['18+67=85', '25+85=110'] Exploring Operation: 110/2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[18, 67, 2, 25], Operations: [] Exploring Operation: 67-18=49, Resulting Numbers: [2, 25, 49] Generated Node #0,0: 55:[2, 25, 49] Operation: 67-18=49 Exploring Operation: 67-25=42, Resulting Numbers: [18, 2, 42] Generated Node #0,1: 55:[18, 2, 42] Operation: 67-25=42 Exploring Operation: 25-18=7, Resulting Numbers: [67, 2, 7] Generated Node #0,2: 55:[67, 2, 7] Operation: 25-18=7 Moving to Node #0,2 Current State: 55:[67, 2, 7], Operations: ['25-18=7'] Exploring Operation: 67-7=60, Resulting Numbers: [2, 60] Generated Node #0,2,0: 55:[2, 60] Operation: 67-7=60 Exploring Operation: 7-2=5, Resulting Numbers: [67, 5] Generated Node #0,2,1: 55:[67, 5] Operation: 7-2=5 Exploring Operation: 67-2=65, Resulting Numbers: [7, 65] Generated Node #0,2,2: 55:[7, 65] Operation: 67-2=65 Moving to Node #0,0 Current State: 55:[2, 25, 49], Operations: ['67-18=49'] Exploring Operation: 2*25=50, Resulting Numbers: [49, 50] Generated Node #0,0,0: 55:[49, 50] Operation: 2*25=50 Exploring Operation: 25-2=23, Resulting Numbers: [49, 23] Generated Node #0,0,1: 55:[49, 23] Operation: 25-2=23 Exploring Operation: 49-25=24, Resulting Numbers: [2, 24] Generated Node #0,0,2: 55:[2, 24] Operation: 49-25=24 Moving to Node #0,1 Current State: 55:[18, 2, 42], Operations: ['67-25=42'] Exploring Operation: 18+42=60, Resulting Numbers: [2, 60] Generated Node #0,1,0: 55:[2, 60] Operation: 18+42=60 Exploring Operation: 42-18=24, Resulting Numbers: [2, 24] Generated Node #0,1,1: 55:[2, 24] Operation: 42-18=24 Exploring Operation: 18/2=9, Resulting Numbers: [42, 9] Generated Node #0,1,2: 55:[42, 9] Operation: 18/2=9 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[2, 60], Operations: ['67-25=42', '18+42=60'] Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,55 unequal: No Solution Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,55 unequal: No Solution Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 55:[42, 9], Operations: ['67-25=42', '18/2=9'] Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,55 unequal: No Solution Exploring Operation: 42*9=378, Resulting Numbers: [378] 378,55 unequal: No Solution Exploring Operation: 42+9=51, Resulting Numbers: [51] 51,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 55:[2, 24], Operations: ['67-25=42', '42-18=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,55 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 55:[2, 60], Operations: ['25-18=7', '67-7=60'] Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,55 unequal: No Solution Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,55 unequal: No Solution Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[49, 50], Operations: ['67-18=49', '2*25=50'] Exploring Operation: 50-49=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 49+50=99, Resulting Numbers: [99] 99,55 unequal: No Solution Exploring Operation: 49*50=2450, Resulting Numbers: [2450] 2450,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[7, 65], Operations: ['25-18=7', '67-2=65'] Exploring Operation: 65-7=58, Resulting Numbers: [58] 58,55 unequal: No Solution Exploring Operation: 7+65=72, Resulting Numbers: [72] 72,55 unequal: No Solution Exploring Operation: 7*65=455, Resulting Numbers: [455] 455,55 unequal: No Solution Moving to Node #0,2,1 Current State: 55:[67, 5], Operations: ['25-18=7', '7-2=5'] Exploring Operation: 67*5=335, Resulting Numbers: [335] 335,55 unequal: No Solution Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,55 unequal: No Solution Exploring Operation: 67+5=72, Resulting Numbers: [72] 72,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[2, 24], Operations: ['67-18=49', '49-25=24'] Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,55 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[49, 23], Operations: ['67-18=49', '25-2=23'] Exploring Operation: 49-23=26, Resulting Numbers: [26] 26,55 unequal: No Solution Exploring Operation: 49*23=1127, Resulting Numbers: [1127] 1127,55 unequal: No Solution Exploring Operation: 49+23=72, Resulting Numbers: [72] 72,55 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 16, 25, 42, 24 ]
57
[ "25-16=9", "42+24=66", "66-9=57" ]
Current State: 57:[16, 25, 42, 24], Operations: [] Exploring Operation: 25-16=9, Resulting Numbers: [42, 24, 9] Generated Node #2: [42, 24, 9] from Operation: 25-16=9 Current State: 57:[42, 24, 9], Operations: ['25-16=9'] Exploring Operation: 42+24=66, Resulting Numbers: [9, 66] Generated Node #3: [9, 66] from Operation: 42+24=66 Current State: 57:[9, 66], Operations: ['25-16=9', '42+24=66'] Exploring Operation: 66-9=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[16, 25, 42, 24], Operations: [] Exploring Operation: 42-25=17, Resulting Numbers: [16, 24, 17] Generated Node #0,0: 57:[16, 24, 17] Operation: 42-25=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[16, 24, 17], Operations: ['42-25=17'] Exploring Operation: 24-16=8, Resulting Numbers: [17, 8] Generated Node #0,0,0: 57:[17, 8] Operation: 24-16=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[17, 8], Operations: ['42-25=17', '24-16=8'] Exploring Operation: 17+8=25, Resulting Numbers: [25] 25,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 39, 72, 3, 32 ]
64
[ "39-3=36", "72*32=2304", "2304/36=64" ]
Current State: 64:[39, 72, 3, 32], Operations: [] Exploring Operation: 39-3=36, Resulting Numbers: [72, 32, 36] Generated Node #2: [72, 32, 36] from Operation: 39-3=36 Current State: 64:[72, 32, 36], Operations: ['39-3=36'] Exploring Operation: 72*32=2304, Resulting Numbers: [36, 2304] Generated Node #3: [36, 2304] from Operation: 72*32=2304 Current State: 64:[36, 2304], Operations: ['39-3=36', '72*32=2304'] Exploring Operation: 2304/36=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[39, 72, 3, 32], Operations: [] Exploring Operation: 39/3=13, Resulting Numbers: [72, 32, 13] Generated Node #0,0: 64:[72, 32, 13] Operation: 39/3=13 Exploring Operation: 72-39=33, Resulting Numbers: [3, 32, 33] Generated Node #0,1: 64:[3, 32, 33] Operation: 72-39=33 Exploring Operation: 39-3=36, Resulting Numbers: [72, 32, 36] Generated Node #0,2: 64:[72, 32, 36] Operation: 39-3=36 Exploring Operation: 39-32=7, Resulting Numbers: [72, 3, 7] Generated Node #0,3: 64:[72, 3, 7] Operation: 39-32=7 Moving to Node #0,1 Current State: 64:[3, 32, 33], Operations: ['72-39=33'] Exploring Operation: 33/3=11, Resulting Numbers: [32, 11] Generated Node #0,1,0: 64:[32, 11] Operation: 33/3=11 Exploring Operation: 33-3=30, Resulting Numbers: [32, 30] Generated Node #0,1,1: 64:[32, 30] Operation: 33-3=30 Exploring Operation: 33-32=1, Resulting Numbers: [3, 1] Generated Node #0,1,2: 64:[3, 1] Operation: 33-32=1 Exploring Operation: 32+33=65, Resulting Numbers: [3, 65] Generated Node #0,1,3: 64:[3, 65] Operation: 32+33=65 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 64:[32, 30], Operations: ['72-39=33', '33-3=30'] Exploring Operation: 32+30=62, Resulting Numbers: [62] 62,64 unequal: No Solution Exploring Operation: 32*30=960, Resulting Numbers: [960] 960,64 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,64 unequal: No Solution No 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: 64:[3, 1], Operations: ['72-39=33', '33-32=1'] Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,64 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,64 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,64 unequal: No Solution No 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: 64:[3, 65], Operations: ['72-39=33', '32+33=65'] Exploring Operation: 3+65=68, Resulting Numbers: [68] 68,64 unequal: No Solution Exploring Operation: 3*65=195, Resulting Numbers: [195] 195,64 unequal: No Solution Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,64 unequal: No Solution No 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: 64:[32, 11], Operations: ['72-39=33', '33/3=11'] Exploring Operation: 32*11=352, Resulting Numbers: [352] 352,64 unequal: No Solution Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,64 unequal: No Solution Exploring Operation: 32+11=43, Resulting Numbers: [43] 43,64 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: 64:[72, 3, 7], Operations: ['39-32=7'] Exploring Operation: 72-7=65, Resulting Numbers: [3, 65] Generated Node #0,3,0: 64:[3, 65] Operation: 72-7=65 Exploring Operation: 7-3=4, Resulting Numbers: [72, 4] Generated Node #0,3,1: 64:[72, 4] Operation: 7-3=4 Exploring Operation: 72/3=24, Resulting Numbers: [7, 24] Generated Node #0,3,2: 64:[7, 24] Operation: 72/3=24 Exploring Operation: 72-3=69, Resulting Numbers: [7, 69] Generated Node #0,3,3: 64:[7, 69] Operation: 72-3=69 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 64:[3, 65], Operations: ['39-32=7', '72-7=65'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,64 unequal: No Solution Exploring Operation: 3*65=195, Resulting Numbers: [195] 195,64 unequal: No Solution Exploring Operation: 3+65=68, Resulting Numbers: [68] 68,64 unequal: No Solution No 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: 64:[7, 69], Operations: ['39-32=7', '72-3=69'] Exploring Operation: 7+69=76, Resulting Numbers: [76] 76,64 unequal: No Solution Exploring Operation: 7*69=483, Resulting Numbers: [483] 483,64 unequal: No Solution Exploring Operation: 69-7=62, Resulting Numbers: [62] 62,64 unequal: No Solution No 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: 64:[72, 4], Operations: ['39-32=7', '7-3=4'] Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,64 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,64 unequal: No Solution Exploring Operation: 72*4=288, Resulting Numbers: [288] 288,64 unequal: No Solution Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,64 unequal: No Solution No 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: 64:[7, 24], Operations: ['39-32=7', '72/3=24'] Exploring Operation: 7*24=168, Resulting Numbers: [168] 168,64 unequal: No Solution Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,64 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,64 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: 64:[72, 32, 13], Operations: ['39/3=13'] Exploring Operation: 72-13=59, Resulting Numbers: [32, 59] Generated Node #0,0,0: 64:[32, 59] Operation: 72-13=59 Exploring Operation: 72+13=85, Resulting Numbers: [32, 85] Generated Node #0,0,1: 64:[32, 85] Operation: 72+13=85 Exploring Operation: 32-13=19, Resulting Numbers: [72, 19] Generated Node #0,0,2: 64:[72, 19] Operation: 32-13=19 Exploring Operation: 72-32=40, Resulting Numbers: [13, 40] Generated Node #0,0,3: 64:[13, 40] Operation: 72-32=40 Moving to Node #0,2 Current State: 64:[72, 32, 36], Operations: ['39-3=36'] Exploring Operation: 36-32=4, Resulting Numbers: [72, 4] Generated Node #0,2,0: 64:[72, 4] Operation: 36-32=4 Exploring Operation: 72-32=40, Resulting Numbers: [36, 40] Generated Node #0,2,1: 64:[36, 40] Operation: 72-32=40 Exploring Operation: 72-36=36, Resulting Numbers: [32, 36] Generated Node #0,2,2: 64:[32, 36] Operation: 72-36=36 Exploring Operation: 72/36=2, Resulting Numbers: [32, 2] Generated Node #0,2,3: 64:[32, 2] Operation: 72/36=2 Moving to Node #0,2,3 Current State: 64:[32, 2], Operations: ['39-3=36', '72/36=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[39, 72, 3, 32], Operations: [] Exploring Operation: 39-3=36, Resulting Numbers: [72, 32, 36] Generated Node #0,2: 64:[72, 32, 36] Operation: 39-3=36 Moving to Node #0,2 Current State: 64:[72, 32, 36], Operations: ['39-3=36'] Exploring Operation: 72/36=2, Resulting Numbers: [32, 2] Generated Node #0,2,3: 64:[32, 2] Operation: 72/36=2 Moving to Node #0,2,3 Current State: 64:[32, 2], Operations: ['39-3=36', '72/36=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
0.955729
hs_4
mult_heuristic
[ 47, 3, 40, 1 ]
21
[ "47-40=7", "3*1=3", "7*3=21" ]
Current State: 21:[47, 3, 40, 1], Operations: [] Exploring Operation: 47-40=7, Resulting Numbers: [3, 1, 7] Generated Node #2: [3, 1, 7] from Operation: 47-40=7 Current State: 21:[3, 1, 7], Operations: ['47-40=7'] Exploring Operation: 3*1=3, Resulting Numbers: [7, 3] Generated Node #3: [7, 3] from Operation: 3*1=3 Current State: 21:[7, 3], Operations: ['47-40=7', '3*1=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[47, 3, 40, 1], Operations: [] Exploring Operation: 47-1=46, Resulting Numbers: [3, 40, 46] Generated Node #0,0: 21:[3, 40, 46] Operation: 47-1=46 Exploring Operation: 40-1=39, Resulting Numbers: [47, 3, 39] Generated Node #0,1: 21:[47, 3, 39] Operation: 40-1=39 Exploring Operation: 47-40=7, Resulting Numbers: [3, 1, 7] Generated Node #0,2: 21:[3, 1, 7] Operation: 47-40=7 Exploring Operation: 40-3=37, Resulting Numbers: [47, 1, 37] Generated Node #0,3: 21:[47, 1, 37] Operation: 40-3=37 Exploring Operation: 47-3=44, Resulting Numbers: [40, 1, 44] Generated Node #0,4: 21:[40, 1, 44] Operation: 47-3=44 Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[3, 1, 7], Operations: ['47-40=7'] Exploring Operation: 1*7=7, Resulting Numbers: [3, 7] Generated Node #0,2,0: 21:[3, 7] Operation: 1*7=7 Exploring Operation: 3*1=3, Resulting Numbers: [7, 3] Generated Node #0,2,1: 21:[7, 3] Operation: 3*1=3 Exploring Operation: 7/1=7, Resulting Numbers: [3, 7] Generated Node #0,2,2: 21:[3, 7] Operation: 7/1=7 Exploring Operation: 3+1=4, Resulting Numbers: [7, 4] Generated Node #0,2,3: 21:[7, 4] Operation: 3+1=4 Exploring Operation: 3/1=3, Resulting Numbers: [7, 3] Generated Node #0,2,4: 21:[7, 3] Operation: 3/1=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 21:[3, 7], Operations: ['47-40=7', '1*7=7'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[47, 3, 40, 1], Operations: [] Exploring Operation: 47-40=7, Resulting Numbers: [3, 1, 7] Generated Node #0,2: 21:[3, 1, 7] Operation: 47-40=7 Moving to Node #0,2 Current State: 21:[3, 1, 7], Operations: ['47-40=7'] Exploring Operation: 1*7=7, Resulting Numbers: [3, 7] Generated Node #0,2,0: 21:[3, 7] Operation: 1*7=7 Moving to Node #0,2,0 Current State: 21:[3, 7], Operations: ['47-40=7', '1*7=7'] Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic