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
[ 58, 55, 42, 23 ]
16
[ "58-55=3", "42-23=19", "19-3=16" ]
Current State: 16:[58, 55, 42, 23], Operations: [] Exploring Operation: 58-55=3, Resulting Numbers: [42, 23, 3] Generated Node #2: [42, 23, 3] from Operation: 58-55=3 Current State: 16:[42, 23, 3], Operations: ['58-55=3'] Exploring Operation: 42-23=19, Resulting Numbers: [3, 19] Generated Node #3: [3, 19] from Operation: 42-23=19 Current State: 16:[3, 19], Operations: ['58-55=3', '42-23=19'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[58, 55, 42, 23], Operations: [] Exploring Operation: 58-55=3, Resulting Numbers: [42, 23, 3] Generated Node #0,0: 16:[42, 23, 3] Operation: 58-55=3 Moving to Node #0,0 Current State: 16:[42, 23, 3], Operations: ['58-55=3'] Exploring Operation: 42-23=19, Resulting Numbers: [3, 19] Generated Node #0,0,0: 16:[3, 19] Operation: 42-23=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[3, 19], Operations: ['58-55=3', '42-23=19'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[58, 55, 42, 23], Operations: [] Exploring Operation: 58-55=3, Resulting Numbers: [42, 23, 3] Generated Node #0,0: 16:[42, 23, 3] Operation: 58-55=3 Moving to Node #0,0 Current State: 16:[42, 23, 3], Operations: ['58-55=3'] Exploring Operation: 42-23=19, Resulting Numbers: [3, 19] Generated Node #0,0,0: 16:[3, 19] Operation: 42-23=19 Moving to Node #0,0,0 Current State: 16:[3, 19], Operations: ['58-55=3', '42-23=19'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 69, 19, 72, 15 ]
26
[ "72-69=3", "15*3=45", "45-19=26" ]
Current State: 26:[69, 19, 72, 15], Operations: [] Exploring Operation: 72-69=3, Resulting Numbers: [19, 15, 3] Generated Node #2: [19, 15, 3] from Operation: 72-69=3 Current State: 26:[19, 15, 3], Operations: ['72-69=3'] Exploring Operation: 15*3=45, Resulting Numbers: [19, 45] Generated Node #3: [19, 45] from Operation: 15*3=45 Current State: 26:[19, 45], Operations: ['72-69=3', '15*3=45'] Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[69, 19, 72, 15], Operations: [] Exploring Operation: 72-69=3, Resulting Numbers: [19, 15, 3] Generated Node #0,0: 26:[19, 15, 3] Operation: 72-69=3 Exploring Operation: 69-19=50, Resulting Numbers: [72, 15, 50] Generated Node #0,1: 26:[72, 15, 50] Operation: 69-19=50 Exploring Operation: 72-19=53, Resulting Numbers: [69, 15, 53] Generated Node #0,2: 26:[69, 15, 53] Operation: 72-19=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[19, 15, 3], Operations: ['72-69=3'] Exploring Operation: 19-15=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 26:[3, 4] Operation: 19-15=4 Exploring Operation: 19+3=22, Resulting Numbers: [15, 22] Generated Node #0,0,1: 26:[15, 22] Operation: 19+3=22 Exploring Operation: 19-3=16, Resulting Numbers: [15, 16] Generated Node #0,0,2: 26:[15, 16] Operation: 19-3=16 Moving to Node #0,0,0 Current State: 26:[3, 4], Operations: ['72-69=3', '19-15=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,26 unequal: No Solution Moving to Node #0,0,2 Current State: 26:[15, 16], Operations: ['72-69=3', '19-3=16'] Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,26 unequal: No Solution Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,26 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[15, 22], Operations: ['72-69=3', '19+3=22'] Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,26 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,26 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:[72, 15, 50], Operations: ['69-19=50'] Exploring Operation: 50-15=35, Resulting Numbers: [72, 35] Generated Node #0,1,0: 26:[72, 35] Operation: 50-15=35 Exploring Operation: 72-50=22, Resulting Numbers: [15, 22] Generated Node #0,1,1: 26:[15, 22] Operation: 72-50=22 Exploring Operation: 72-15=57, Resulting Numbers: [50, 57] Generated Node #0,1,2: 26:[50, 57] Operation: 72-15=57 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 26:[15, 22], Operations: ['69-19=50', '72-50=22'] Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,26 unequal: No Solution Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,26 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 #0,1,0 Current State: 26:[72, 35], Operations: ['69-19=50', '50-15=35'] Exploring Operation: 72-35=37, Resulting Numbers: [37] 37,26 unequal: No Solution Exploring Operation: 72*35=2520, Resulting Numbers: [2520] 2520,26 unequal: No Solution Exploring Operation: 72+35=107, Resulting Numbers: [107] 107,26 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 #0,1,2 Current State: 26:[50, 57], Operations: ['69-19=50', '72-15=57'] Exploring Operation: 57-50=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 50*57=2850, Resulting Numbers: [2850] 2850,26 unequal: No Solution Exploring Operation: 50+57=107, Resulting Numbers: [107] 107,26 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 26:[69, 15, 53], Operations: ['72-19=53'] Exploring Operation: 69-15=54, Resulting Numbers: [53, 54] Generated Node #0,2,0: 26:[53, 54] Operation: 69-15=54 Exploring Operation: 69-53=16, Resulting Numbers: [15, 16] Generated Node #0,2,1: 26:[15, 16] Operation: 69-53=16 Exploring Operation: 53-15=38, Resulting Numbers: [69, 38] Generated Node #0,2,2: 26:[69, 38] Operation: 53-15=38 Moving to Node #0,2,1 Current State: 26:[15, 16], Operations: ['72-19=53', '69-53=16'] Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,26 unequal: No Solution Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,26 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[53, 54], Operations: ['72-19=53', '69-15=54'] Exploring Operation: 53+54=107, Resulting Numbers: [107] 107,26 unequal: No Solution Exploring Operation: 54-53=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 53*54=2862, Resulting Numbers: [2862] 2862,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[69, 38], Operations: ['72-19=53', '53-15=38'] Exploring Operation: 69+38=107, Resulting Numbers: [107] 107,26 unequal: No Solution Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,26 unequal: No Solution Exploring Operation: 69*38=2622, Resulting Numbers: [2622] 2622,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 29, 22, 20, 22 ]
29
[ "22-22=0", "20*0=0", "29+0=29" ]
Current State: 29:[29, 22, 20, 22], Operations: [] Exploring Operation: 22-22=0, Resulting Numbers: [29, 20, 0] Generated Node #2: [29, 20, 0] from Operation: 22-22=0 Current State: 29:[29, 20, 0], Operations: ['22-22=0'] Exploring Operation: 20*0=0, Resulting Numbers: [29, 0] Generated Node #3: [29, 0] from Operation: 20*0=0 Current State: 29:[29, 0], Operations: ['22-22=0', '20*0=0'] Exploring Operation: 29+0=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[29, 22, 20, 22], Operations: [] Exploring Operation: 22+20=42, Resulting Numbers: [29, 22, 42] Generated Node #0,0: 29:[29, 22, 42] Operation: 22+20=42 Exploring Operation: 20+22=42, Resulting Numbers: [29, 22, 42] Generated Node #0,1: 29:[29, 22, 42] Operation: 20+22=42 Exploring Operation: 22+22=44, Resulting Numbers: [29, 20, 44] Generated Node #0,2: 29:[29, 20, 44] Operation: 22+22=44 Moving to Node #0,0 Current State: 29:[29, 22, 42], Operations: ['22+20=42'] Exploring Operation: 42-22=20, Resulting Numbers: [29, 20] Generated Node #0,0,0: 29:[29, 20] Operation: 42-22=20 Exploring Operation: 29+22=51, Resulting Numbers: [42, 51] Generated Node #0,0,1: 29:[42, 51] Operation: 29+22=51 Exploring Operation: 42-29=13, Resulting Numbers: [22, 13] Generated Node #0,0,2: 29:[22, 13] Operation: 42-29=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[29, 20], Operations: ['22+20=42', '42-22=20'] Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,29 unequal: No Solution Exploring Operation: 29+20=49, Resulting Numbers: [49] 49,29 unequal: No Solution Exploring Operation: 29*20=580, Resulting Numbers: [580] 580,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 29:[22, 13], Operations: ['22+20=42', '42-29=13'] Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,29 unequal: No Solution Exploring Operation: 22+13=35, Resulting Numbers: [35] 35,29 unequal: No Solution Exploring Operation: 22*13=286, Resulting Numbers: [286] 286,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 29:[42, 51], Operations: ['22+20=42', '29+22=51'] Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,29 unequal: No Solution Exploring Operation: 42*51=2142, Resulting Numbers: [2142] 2142,29 unequal: No Solution Exploring Operation: 42+51=93, Resulting Numbers: [93] 93,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 29:[29, 22, 42], Operations: ['20+22=42'] Exploring Operation: 42-29=13, Resulting Numbers: [22, 13] Generated Node #0,1,0: 29:[22, 13] Operation: 42-29=13 Exploring Operation: 42-22=20, Resulting Numbers: [29, 20] Generated Node #0,1,1: 29:[29, 20] Operation: 42-22=20 Exploring Operation: 29+22=51, Resulting Numbers: [42, 51] Generated Node #0,1,2: 29:[42, 51] Operation: 29+22=51 Moving to Node #0,2 Current State: 29:[29, 20, 44], Operations: ['22+22=44'] Exploring Operation: 44-20=24, Resulting Numbers: [29, 24] Generated Node #0,2,0: 29:[29, 24] Operation: 44-20=24 Exploring Operation: 29+20=49, Resulting Numbers: [44, 49] Generated Node #0,2,1: 29:[44, 49] Operation: 29+20=49 Exploring Operation: 44-29=15, Resulting Numbers: [20, 15] Generated Node #0,2,2: 29:[20, 15] Operation: 44-29=15 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[29, 24], Operations: ['22+22=44', '44-20=24'] Exploring Operation: 29*24=696, Resulting Numbers: [696] 696,29 unequal: No Solution Exploring Operation: 29+24=53, Resulting Numbers: [53] 53,29 unequal: No Solution Exploring Operation: 29-24=5, Resulting Numbers: [5] 5,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 29:[20, 15], Operations: ['22+22=44', '44-29=15'] Exploring Operation: 20*15=300, Resulting Numbers: [300] 300,29 unequal: No Solution Exploring Operation: 20+15=35, Resulting Numbers: [35] 35,29 unequal: No Solution Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 29:[44, 49], Operations: ['22+22=44', '29+20=49'] Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,29 unequal: No Solution Exploring Operation: 44*49=2156, Resulting Numbers: [2156] 2156,29 unequal: No Solution Exploring Operation: 44+49=93, Resulting Numbers: [93] 93,29 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: 29:[29, 20], Operations: ['20+22=42', '42-22=20'] Exploring Operation: 29*20=580, Resulting Numbers: [580] 580,29 unequal: No Solution Exploring Operation: 29+20=49, Resulting Numbers: [49] 49,29 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[22, 13], Operations: ['20+22=42', '42-29=13'] Exploring Operation: 22+13=35, Resulting Numbers: [35] 35,29 unequal: No Solution Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,29 unequal: No Solution Exploring Operation: 22*13=286, Resulting Numbers: [286] 286,29 unequal: No Solution Moving to Node #0,1,2 Current State: 29:[42, 51], Operations: ['20+22=42', '29+22=51'] Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,29 unequal: No Solution Exploring Operation: 42+51=93, Resulting Numbers: [93] 93,29 unequal: No Solution Exploring Operation: 42*51=2142, Resulting Numbers: [2142] 2142,29 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 78, 37, 85, 14 ]
35
[ "85-78=7", "14/7=2", "37-2=35" ]
Current State: 35:[78, 37, 85, 14], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [37, 14, 7] Generated Node #2: [37, 14, 7] from Operation: 85-78=7 Current State: 35:[37, 14, 7], Operations: ['85-78=7'] Exploring Operation: 14/7=2, Resulting Numbers: [37, 2] Generated Node #3: [37, 2] from Operation: 14/7=2 Current State: 35:[37, 2], Operations: ['85-78=7', '14/7=2'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[78, 37, 85, 14], Operations: [] Exploring Operation: 85-14=71, Resulting Numbers: [78, 37, 71] Generated Node #0,0: 35:[78, 37, 71] Operation: 85-14=71 Exploring Operation: 78-14=64, Resulting Numbers: [37, 85, 64] Generated Node #0,1: 35:[37, 85, 64] Operation: 78-14=64 Exploring Operation: 78-37=41, Resulting Numbers: [85, 14, 41] Generated Node #0,2: 35:[85, 14, 41] Operation: 78-37=41 Exploring Operation: 85-37=48, Resulting Numbers: [78, 14, 48] Generated Node #0,3: 35:[78, 14, 48] Operation: 85-37=48 Exploring Operation: 85-78=7, Resulting Numbers: [37, 14, 7] Generated Node #0,4: 35:[37, 14, 7] Operation: 85-78=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 35:[37, 14, 7], Operations: ['85-78=7'] Exploring Operation: 14/7=2, Resulting Numbers: [37, 2] Generated Node #0,4,0: 35:[37, 2] Operation: 14/7=2 Exploring Operation: 37-7=30, Resulting Numbers: [14, 30] Generated Node #0,4,1: 35:[14, 30] Operation: 37-7=30 Exploring Operation: 37-14=23, Resulting Numbers: [7, 23] Generated Node #0,4,2: 35:[7, 23] Operation: 37-14=23 Exploring Operation: 14-7=7, Resulting Numbers: [37, 7] Generated Node #0,4,3: 35:[37, 7] Operation: 14-7=7 Exploring Operation: 37+14=51, Resulting Numbers: [7, 51] Generated Node #0,4,4: 35:[7, 51] Operation: 37+14=51 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 35:[37, 7], Operations: ['85-78=7', '14-7=7'] Exploring Operation: 37+7=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 37*7=259, Resulting Numbers: [259] 259,35 unequal: No Solution Exploring Operation: 37-7=30, Resulting Numbers: [30] 30,35 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 #0,4,0 Current State: 35:[37, 2], Operations: ['85-78=7', '14/7=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,35 unequal: No Solution Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,35 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[78, 37, 85, 14], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [37, 14, 7] Generated Node #0,4: 35:[37, 14, 7] Operation: 85-78=7 Moving to Node #0,4 Current State: 35:[37, 14, 7], Operations: ['85-78=7'] Exploring Operation: 14/7=2, Resulting Numbers: [37, 2] Generated Node #0,4,0: 35:[37, 2] Operation: 14/7=2 Moving to Node #0,4,0 Current State: 35:[37, 2], Operations: ['85-78=7', '14/7=2'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 98, 17, 4, 43 ]
68
[ "98+17=115", "4+43=47", "115-47=68" ]
Current State: 68:[98, 17, 4, 43], Operations: [] Exploring Operation: 98+17=115, Resulting Numbers: [4, 43, 115] Generated Node #2: [4, 43, 115] from Operation: 98+17=115 Current State: 68:[4, 43, 115], Operations: ['98+17=115'] Exploring Operation: 4+43=47, Resulting Numbers: [115, 47] Generated Node #3: [115, 47] from Operation: 4+43=47 Current State: 68:[115, 47], Operations: ['98+17=115', '4+43=47'] Exploring Operation: 115-47=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[98, 17, 4, 43], Operations: [] Exploring Operation: 98-4=94, Resulting Numbers: [17, 43, 94] Generated Node #0,0: 68:[17, 43, 94] Operation: 98-4=94 Exploring Operation: 98-17=81, Resulting Numbers: [4, 43, 81] Generated Node #0,1: 68:[4, 43, 81] Operation: 98-17=81 Exploring Operation: 98-43=55, Resulting Numbers: [17, 4, 55] Generated Node #0,2: 68:[17, 4, 55] Operation: 98-43=55 Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[17, 4, 55], Operations: ['98-43=55'] Exploring Operation: 17+55=72, Resulting Numbers: [4, 72] Generated Node #0,2,0: 68:[4, 72] Operation: 17+55=72 Exploring Operation: 4+55=59, Resulting Numbers: [17, 59] Generated Node #0,2,1: 68:[17, 59] Operation: 4+55=59 Exploring Operation: 55-17=38, Resulting Numbers: [4, 38] Generated Node #0,2,2: 68:[4, 38] Operation: 55-17=38 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 68:[4, 72], Operations: ['98-43=55', '17+55=72'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,68 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[98, 17, 4, 43], Operations: [] Exploring Operation: 98-43=55, Resulting Numbers: [17, 4, 55] Generated Node #0,2: 68:[17, 4, 55] Operation: 98-43=55 Moving to Node #0,2 Current State: 68:[17, 4, 55], Operations: ['98-43=55'] Exploring Operation: 17+55=72, Resulting Numbers: [4, 72] Generated Node #0,2,0: 68:[4, 72] Operation: 17+55=72 Moving to Node #0,2,0 Current State: 68:[4, 72], Operations: ['98-43=55', '17+55=72'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 13, 54, 45, 94 ]
72
[ "13+54=67", "45+94=139", "139-67=72" ]
Current State: 72:[13, 54, 45, 94], Operations: [] Exploring Operation: 13+54=67, Resulting Numbers: [45, 94, 67] Generated Node #2: [45, 94, 67] from Operation: 13+54=67 Current State: 72:[45, 94, 67], Operations: ['13+54=67'] Exploring Operation: 45+94=139, Resulting Numbers: [67, 139] Generated Node #3: [67, 139] from Operation: 45+94=139 Current State: 72:[67, 139], Operations: ['13+54=67', '45+94=139'] Exploring Operation: 139-67=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[13, 54, 45, 94], Operations: [] Exploring Operation: 54-45=9, Resulting Numbers: [13, 94, 9] Generated Node #0,0: 72:[13, 94, 9] Operation: 54-45=9 Exploring Operation: 94-54=40, Resulting Numbers: [13, 45, 40] Generated Node #0,1: 72:[13, 45, 40] Operation: 94-54=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[13, 45, 40], Operations: ['94-54=40'] Exploring Operation: 45-13=32, Resulting Numbers: [40, 32] Generated Node #0,1,0: 72:[40, 32] Operation: 45-13=32 Exploring Operation: 45-40=5, Resulting Numbers: [13, 5] Generated Node #0,1,1: 72:[13, 5] Operation: 45-40=5 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 72:[13, 5], Operations: ['94-54=40', '45-40=5'] Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 72:[40, 32], Operations: ['94-54=40', '45-13=32'] Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 40+32=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[13, 54, 45, 94], Operations: [] Exploring Operation: 94-54=40, Resulting Numbers: [13, 45, 40] Generated Node #0,1: 72:[13, 45, 40] Operation: 94-54=40 Moving to Node #0,1 Current State: 72:[13, 45, 40], Operations: ['94-54=40'] Exploring Operation: 45-13=32, Resulting Numbers: [40, 32] Generated Node #0,1,0: 72:[40, 32] Operation: 45-13=32 Moving to Node #0,1,0 Current State: 72:[40, 32], Operations: ['94-54=40', '45-13=32'] Exploring Operation: 40+32=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 90, 18, 62, 57 ]
48
[ "90+62=152", "18*152=2736", "2736/57=48" ]
Current State: 48:[90, 18, 62, 57], Operations: [] Exploring Operation: 90+62=152, Resulting Numbers: [18, 57, 152] Generated Node #2: [18, 57, 152] from Operation: 90+62=152 Current State: 48:[18, 57, 152], Operations: ['90+62=152'] Exploring Operation: 18*152=2736, Resulting Numbers: [57, 2736] Generated Node #3: [57, 2736] from Operation: 18*152=2736 Current State: 48:[57, 2736], Operations: ['90+62=152', '18*152=2736'] Exploring Operation: 2736/57=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[90, 18, 62, 57], Operations: [] Exploring Operation: 62-57=5, Resulting Numbers: [90, 18, 5] Generated Node #0,0: 48:[90, 18, 5] Operation: 62-57=5 Exploring Operation: 90-57=33, Resulting Numbers: [18, 62, 33] Generated Node #0,1: 48:[18, 62, 33] Operation: 90-57=33 Exploring Operation: 90-18=72, Resulting Numbers: [62, 57, 72] Generated Node #0,2: 48:[62, 57, 72] Operation: 90-18=72 Exploring Operation: 90-62=28, Resulting Numbers: [18, 57, 28] Generated Node #0,3: 48:[18, 57, 28] Operation: 90-62=28 Exploring Operation: 90/18=5, Resulting Numbers: [62, 57, 5] Generated Node #0,4: 48:[62, 57, 5] Operation: 90/18=5 Moving to Node #0,3 Current State: 48:[18, 57, 28], Operations: ['90-62=28'] Exploring Operation: 57-28=29, Resulting Numbers: [18, 29] Generated Node #0,3,0: 48:[18, 29] Operation: 57-28=29 Exploring Operation: 57-18=39, Resulting Numbers: [28, 39] Generated Node #0,3,1: 48:[28, 39] Operation: 57-18=39 Exploring Operation: 18+28=46, Resulting Numbers: [57, 46] Generated Node #0,3,2: 48:[57, 46] Operation: 18+28=46 Exploring Operation: 28-18=10, Resulting Numbers: [57, 10] Generated Node #0,3,3: 48:[57, 10] Operation: 28-18=10 Exploring Operation: 18+57=75, Resulting Numbers: [28, 75] Generated Node #0,3,4: 48:[28, 75] Operation: 18+57=75 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 48:[18, 29], Operations: ['90-62=28', '57-28=29'] Exploring Operation: 18*29=522, Resulting Numbers: [522] 522,48 unequal: No Solution Exploring Operation: 18+29=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,48 unequal: No Solution No 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: 48:[57, 46], Operations: ['90-62=28', '18+28=46'] Exploring Operation: 57+46=103, Resulting Numbers: [103] 103,48 unequal: No Solution Exploring Operation: 57*46=2622, Resulting Numbers: [2622] 2622,48 unequal: No Solution Exploring Operation: 57-46=11, Resulting Numbers: [11] 11,48 unequal: No Solution No 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: 48:[57, 10], Operations: ['90-62=28', '28-18=10'] Exploring Operation: 57+10=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 57-10=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 57*10=570, Resulting Numbers: [570] 570,48 unequal: No Solution No 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: 48:[28, 39], Operations: ['90-62=28', '57-18=39'] Exploring Operation: 39-28=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 28+39=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 28*39=1092, Resulting Numbers: [1092] 1092,48 unequal: No Solution No 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: 48:[28, 75], Operations: ['90-62=28', '18+57=75'] Exploring Operation: 28*75=2100, Resulting Numbers: [2100] 2100,48 unequal: No Solution Exploring Operation: 28+75=103, Resulting Numbers: [103] 103,48 unequal: No Solution Exploring Operation: 75-28=47, Resulting Numbers: [47] 47,48 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: 48:[62, 57, 5], Operations: ['90/18=5'] Exploring Operation: 57-5=52, Resulting Numbers: [62, 52] Generated Node #0,4,0: 48:[62, 52] Operation: 57-5=52 Exploring Operation: 62-57=5, Resulting Numbers: [5, 5] Generated Node #0,4,1: 48:[5, 5] Operation: 62-57=5 Exploring Operation: 62-5=57, Resulting Numbers: [57, 57] Generated Node #0,4,2: 48:[57, 57] Operation: 62-5=57 Exploring Operation: 62+5=67, Resulting Numbers: [57, 67] Generated Node #0,4,3: 48:[57, 67] Operation: 62+5=67 Exploring Operation: 57+5=62, Resulting Numbers: [62, 62] Generated Node #0,4,4: 48:[62, 62] Operation: 57+5=62 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 48:[5, 5], Operations: ['90/18=5', '62-57=5'] Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,48 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,48 unequal: No Solution Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,48 unequal: No Solution No 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: 48:[62, 52], Operations: ['90/18=5', '57-5=52'] Exploring Operation: 62-52=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 62*52=3224, Resulting Numbers: [3224] 3224,48 unequal: No Solution Exploring Operation: 62+52=114, Resulting Numbers: [114] 114,48 unequal: No Solution No 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: 48:[57, 57], Operations: ['90/18=5', '62-5=57'] Exploring Operation: 57/57=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 57+57=114, Resulting Numbers: [114] 114,48 unequal: No Solution Exploring Operation: 57-57=0, Resulting Numbers: [0] 0,48 unequal: No Solution Exploring Operation: 57*57=3249, Resulting Numbers: [3249] 3249,48 unequal: No Solution No 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: 48:[57, 67], Operations: ['90/18=5', '62+5=67'] Exploring Operation: 57+67=124, Resulting Numbers: [124] 124,48 unequal: No Solution Exploring Operation: 67-57=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 57*67=3819, Resulting Numbers: [3819] 3819,48 unequal: No Solution No 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: 48:[62, 62], Operations: ['90/18=5', '57+5=62'] Exploring Operation: 62+62=124, Resulting Numbers: [124] 124,48 unequal: No Solution Exploring Operation: 62/62=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 62*62=3844, Resulting Numbers: [3844] 3844,48 unequal: No Solution Exploring Operation: 62-62=0, Resulting Numbers: [0] 0,48 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: 48:[18, 62, 33], Operations: ['90-57=33'] Exploring Operation: 62-18=44, Resulting Numbers: [33, 44] Generated Node #0,1,0: 48:[33, 44] Operation: 62-18=44 Exploring Operation: 33-18=15, Resulting Numbers: [62, 15] Generated Node #0,1,1: 48:[62, 15] Operation: 33-18=15 Exploring Operation: 18+62=80, Resulting Numbers: [33, 80] Generated Node #0,1,2: 48:[33, 80] Operation: 18+62=80 Exploring Operation: 18+33=51, Resulting Numbers: [62, 51] Generated Node #0,1,3: 48:[62, 51] Operation: 18+33=51 Exploring Operation: 62-33=29, Resulting Numbers: [18, 29] Generated Node #0,1,4: 48:[18, 29] Operation: 62-33=29 Moving to Node #0,0 Current State: 48:[90, 18, 5], Operations: ['62-57=5'] Exploring Operation: 90/5=18, Resulting Numbers: [18, 18] Generated Node #0,0,0: 48:[18, 18] Operation: 90/5=18 Exploring Operation: 18+5=23, Resulting Numbers: [90, 23] Generated Node #0,0,1: 48:[90, 23] Operation: 18+5=23 Exploring Operation: 90/18=5, Resulting Numbers: [5, 5] Generated Node #0,0,2: 48:[5, 5] Operation: 90/18=5 Exploring Operation: 90-18=72, Resulting Numbers: [5, 72] Generated Node #0,0,3: 48:[5, 72] Operation: 90-18=72 Exploring Operation: 90-5=85, Resulting Numbers: [18, 85] Generated Node #0,0,4: 48:[18, 85] Operation: 90-5=85 Moving to Node #0,2 Current State: 48:[62, 57, 72], Operations: ['90-18=72'] Exploring Operation: 62+72=134, Resulting Numbers: [57, 134] Generated Node #0,2,0: 48:[57, 134] Operation: 62+72=134 Exploring Operation: 72-62=10, Resulting Numbers: [57, 10] Generated Node #0,2,1: 48:[57, 10] Operation: 72-62=10 Exploring Operation: 62+57=119, Resulting Numbers: [72, 119] Generated Node #0,2,2: 48:[72, 119] Operation: 62+57=119 Exploring Operation: 72-57=15, Resulting Numbers: [62, 15] Generated Node #0,2,3: 48:[62, 15] Operation: 72-57=15 Exploring Operation: 62-57=5, Resulting Numbers: [72, 5] Generated Node #0,2,4: 48:[72, 5] Operation: 62-57=5 Moving to Node #0,0,2 Current State: 48:[5, 5], Operations: ['62-57=5', '90/18=5'] Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,48 unequal: No Solution Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,48 unequal: No Solution Moving to Node #0,0,0 Current State: 48:[18, 18], Operations: ['62-57=5', '90/5=18'] Exploring Operation: 18-18=0, Resulting Numbers: [0] 0,48 unequal: No Solution Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,48 unequal: No Solution Exploring Operation: 18*18=324, Resulting Numbers: [324] 324,48 unequal: No Solution Moving to Node #0,1,4 Current State: 48:[18, 29], Operations: ['90-57=33', '62-33=29'] Exploring Operation: 18+29=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 18*29=522, Resulting Numbers: [522] 522,48 unequal: No Solution Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,48 unequal: No Solution Moving to Node #0,2,1 Current State: 48:[57, 10], Operations: ['90-18=72', '72-62=10'] Exploring Operation: 57*10=570, Resulting Numbers: [570] 570,48 unequal: No Solution Exploring Operation: 57+10=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 57-10=47, Resulting Numbers: [47] 47,48 unequal: No Solution Moving to Node #0,1,0 Current State: 48:[33, 44], Operations: ['90-57=33', '62-18=44'] Exploring Operation: 33*44=1452, Resulting Numbers: [1452] 1452,48 unequal: No Solution Exploring Operation: 44-33=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 33+44=77, Resulting Numbers: [77] 77,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[62, 15], Operations: ['90-57=33', '33-18=15'] Exploring Operation: 62*15=930, Resulting Numbers: [930] 930,48 unequal: No Solution Exploring Operation: 62+15=77, Resulting Numbers: [77] 77,48 unequal: No Solution Exploring Operation: 62-15=47, Resulting Numbers: [47] 47,48 unequal: No Solution Moving to Node #0,2,3 Current State: 48:[62, 15], Operations: ['90-18=72', '72-57=15'] Exploring Operation: 62*15=930, Resulting Numbers: [930] 930,48 unequal: No Solution Exploring Operation: 62+15=77, Resulting Numbers: [77] 77,48 unequal: No Solution Exploring Operation: 62-15=47, Resulting Numbers: [47] 47,48 unequal: No Solution Moving to Node #0,1,3 Current State: 48:[62, 51], Operations: ['90-57=33', '18+33=51'] Exploring Operation: 62*51=3162, Resulting Numbers: [3162] 3162,48 unequal: No Solution Exploring Operation: 62-51=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 62+51=113, Resulting Numbers: [113] 113,48 unequal: No Solution Moving to Node #0,2,4 Current State: 48:[72, 5], Operations: ['90-18=72', '62-57=5'] Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 72*5=360, Resulting Numbers: [360] 360,48 unequal: No Solution Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,48 unequal: No Solution Moving to Node #0,0,3 Current State: 48:[5, 72], Operations: ['62-57=5', '90-18=72'] Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,48 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,48 unequal: No Solution Moving to Node #0,0,4 Current State: 48:[18, 85], Operations: ['62-57=5', '90-5=85'] Exploring Operation: 18+85=103, Resulting Numbers: [103] 103,48 unequal: No Solution Exploring Operation: 18*85=1530, Resulting Numbers: [1530] 1530,48 unequal: No Solution Exploring Operation: 85-18=67, Resulting Numbers: [67] 67,48 unequal: No Solution Moving to Node #0,1,2 Current State: 48:[33, 80], Operations: ['90-57=33', '18+62=80'] Exploring Operation: 33*80=2640, Resulting Numbers: [2640] 2640,48 unequal: No Solution Exploring Operation: 33+80=113, Resulting Numbers: [113] 113,48 unequal: No Solution Exploring Operation: 80-33=47, Resulting Numbers: [47] 47,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[90, 23], Operations: ['62-57=5', '18+5=23'] Exploring Operation: 90*23=2070, Resulting Numbers: [2070] 2070,48 unequal: No Solution Exploring Operation: 90+23=113, Resulting Numbers: [113] 113,48 unequal: No Solution Exploring Operation: 90-23=67, Resulting Numbers: [67] 67,48 unequal: No Solution Moving to Node #0,2,2 Current State: 48:[72, 119], Operations: ['90-18=72', '62+57=119'] Exploring Operation: 72*119=8568, Resulting Numbers: [8568] 8568,48 unequal: No Solution Exploring Operation: 119-72=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 72+119=191, Resulting Numbers: [191] 191,48 unequal: No Solution Moving to Node #0,2,0 Current State: 48:[57, 134], Operations: ['90-18=72', '62+72=134'] Exploring Operation: 134-57=77, Resulting Numbers: [77] 77,48 unequal: No Solution Exploring Operation: 57+134=191, Resulting Numbers: [191] 191,48 unequal: No Solution Exploring Operation: 57*134=7638, Resulting Numbers: [7638] 7638,48 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 23, 92, 51, 23 ]
87
[ "23+92=115", "51-23=28", "115-28=87" ]
Current State: 87:[23, 92, 51, 23], Operations: [] Exploring Operation: 23+92=115, Resulting Numbers: [51, 115] Generated Node #2: [51, 115] from Operation: 23+92=115 Current State: 87:[51, 115], Operations: ['23+92=115'] Exploring Operation: 51-23=28, Resulting Numbers: [115, 28] Generated Node #3: [115, 28] from Operation: 51-23=28 Current State: 87:[115, 28], Operations: ['23+92=115', '51-23=28'] Exploring Operation: 115-28=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[23, 92, 51, 23], Operations: [] Exploring Operation: 51-23=28, Resulting Numbers: [92, 23, 28] Generated Node #0,0: 87:[92, 23, 28] Operation: 51-23=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[92, 23, 28], Operations: ['51-23=28'] Exploring Operation: 92/23=4, Resulting Numbers: [28, 4] Generated Node #0,0,0: 87:[28, 4] Operation: 92/23=4 Moving to Node #0,0,0 Current State: 87:[28, 4], Operations: ['51-23=28', '92/23=4'] Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,87 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
[ 89, 26, 5, 9 ]
14
[ "89+26=115", "115/5=23", "23-9=14" ]
Current State: 14:[89, 26, 5, 9], Operations: [] Exploring Operation: 89+26=115, Resulting Numbers: [5, 9, 115] Generated Node #2: [5, 9, 115] from Operation: 89+26=115 Current State: 14:[5, 9, 115], Operations: ['89+26=115'] Exploring Operation: 115/5=23, Resulting Numbers: [9, 23] Generated Node #3: [9, 23] from Operation: 115/5=23 Current State: 14:[9, 23], Operations: ['89+26=115', '115/5=23'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[89, 26, 5, 9], Operations: [] Exploring Operation: 89-26=63, Resulting Numbers: [5, 9, 63] Generated Node #0,0: 14:[5, 9, 63] Operation: 89-26=63 Exploring Operation: 89-9=80, Resulting Numbers: [26, 5, 80] Generated Node #0,1: 14:[26, 5, 80] Operation: 89-9=80 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[5, 9, 63], Operations: ['89-26=63'] Exploring Operation: 63/9=7, Resulting Numbers: [5, 7] Generated Node #0,0,0: 14:[5, 7] Operation: 63/9=7 Exploring Operation: 63-9=54, Resulting Numbers: [5, 54] Generated Node #0,0,1: 14:[5, 54] Operation: 63-9=54 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 14:[5, 7], Operations: ['89-26=63', '63/9=7'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,14 unequal: No Solution No 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: 14:[5, 54], Operations: ['89-26=63', '63-9=54'] Exploring Operation: 5+54=59, Resulting Numbers: [59] 59,14 unequal: No Solution Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,14 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: 14:[26, 5, 80], Operations: ['89-9=80'] Exploring Operation: 80/5=16, Resulting Numbers: [26, 16] Generated Node #0,1,0: 14:[26, 16] Operation: 80/5=16 Exploring Operation: 80-26=54, Resulting Numbers: [5, 54] Generated Node #0,1,1: 14:[5, 54] Operation: 80-26=54 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 14:[26, 16], Operations: ['89-9=80', '80/5=16'] Exploring Operation: 26+16=42, Resulting Numbers: [42] 42,14 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,14 unequal: No Solution No 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: 14:[5, 54], Operations: ['89-9=80', '80-26=54'] Exploring Operation: 5+54=59, Resulting Numbers: [59] 59,14 unequal: No Solution Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,14 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
[ 95, 82, 3, 75 ]
48
[ "95+82=177", "3*75=225", "225-177=48" ]
Current State: 48:[95, 82, 3, 75], Operations: [] Exploring Operation: 95+82=177, Resulting Numbers: [3, 75, 177] Generated Node #2: [3, 75, 177] from Operation: 95+82=177 Current State: 48:[3, 75, 177], Operations: ['95+82=177'] Exploring Operation: 3*75=225, Resulting Numbers: [177, 225] Generated Node #3: [177, 225] from Operation: 3*75=225 Current State: 48:[177, 225], Operations: ['95+82=177', '3*75=225'] Exploring Operation: 225-177=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[95, 82, 3, 75], Operations: [] Exploring Operation: 95-75=20, Resulting Numbers: [82, 3, 20] Generated Node #0,0: 48:[82, 3, 20] Operation: 95-75=20 Exploring Operation: 95-82=13, Resulting Numbers: [3, 75, 13] Generated Node #0,1: 48:[3, 75, 13] Operation: 95-82=13 Moving to Node #0,1 Current State: 48:[3, 75, 13], Operations: ['95-82=13'] Exploring Operation: 75/3=25, Resulting Numbers: [13, 25] Generated Node #0,1,0: 48:[13, 25] Operation: 75/3=25 Exploring Operation: 75-13=62, Resulting Numbers: [3, 62] Generated Node #0,1,1: 48:[3, 62] Operation: 75-13=62 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[13, 25], Operations: ['95-82=13', '75/3=25'] Exploring Operation: 13+25=38, Resulting Numbers: [38] 38,48 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,48 unequal: No Solution No 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: 48:[3, 62], Operations: ['95-82=13', '75-13=62'] Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,48 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,48 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: 48:[82, 3, 20], Operations: ['95-75=20'] Exploring Operation: 82-20=62, Resulting Numbers: [3, 62] Generated Node #0,0,0: 48:[3, 62] Operation: 82-20=62 Exploring Operation: 82-3=79, Resulting Numbers: [20, 79] Generated Node #0,0,1: 48:[20, 79] Operation: 82-3=79 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[3, 62], Operations: ['95-75=20', '82-20=62'] Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,48 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,48 unequal: No Solution No 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: 48:[20, 79], Operations: ['95-75=20', '82-3=79'] Exploring Operation: 20+79=99, Resulting Numbers: [99] 99,48 unequal: No Solution Exploring Operation: 79-20=59, Resulting Numbers: [59] 59,48 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
[ 17, 18, 87, 13 ]
65
[ "17+18=35", "87+13=100", "100-35=65" ]
Current State: 65:[17, 18, 87, 13], Operations: [] Exploring Operation: 17+18=35, Resulting Numbers: [87, 13, 35] Generated Node #2: [87, 13, 35] from Operation: 17+18=35 Current State: 65:[87, 13, 35], Operations: ['17+18=35'] Exploring Operation: 87+13=100, Resulting Numbers: [35, 100] Generated Node #3: [35, 100] from Operation: 87+13=100 Current State: 65:[35, 100], Operations: ['17+18=35', '87+13=100'] Exploring Operation: 100-35=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[17, 18, 87, 13], Operations: [] Exploring Operation: 87-18=69, Resulting Numbers: [17, 13, 69] Generated Node #0,0: 65:[17, 13, 69] Operation: 87-18=69 Exploring Operation: 87-17=70, Resulting Numbers: [18, 13, 70] Generated Node #0,1: 65:[18, 13, 70] Operation: 87-17=70 Moving to Node #0,0 Current State: 65:[17, 13, 69], Operations: ['87-18=69'] Exploring Operation: 17-13=4, Resulting Numbers: [69, 4] Generated Node #0,0,0: 65:[69, 4] Operation: 17-13=4 Exploring Operation: 69-17=52, Resulting Numbers: [13, 52] Generated Node #0,0,1: 65:[13, 52] Operation: 69-17=52 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[69, 4], Operations: ['87-18=69', '17-13=4'] Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,65 unequal: No Solution Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[17, 18, 87, 13], Operations: [] Exploring Operation: 87-18=69, Resulting Numbers: [17, 13, 69] Generated Node #0,0: 65:[17, 13, 69] Operation: 87-18=69 Moving to Node #0,0 Current State: 65:[17, 13, 69], Operations: ['87-18=69'] Exploring Operation: 17-13=4, Resulting Numbers: [69, 4] Generated Node #0,0,0: 65:[69, 4] Operation: 17-13=4 Moving to Node #0,0,0 Current State: 65:[69, 4], Operations: ['87-18=69', '17-13=4'] Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 49, 7, 90, 84 ]
91
[ "90-84=6", "7*6=42", "49+42=91" ]
Current State: 91:[49, 7, 90, 84], Operations: [] Exploring Operation: 90-84=6, Resulting Numbers: [49, 7, 6] Generated Node #2: [49, 7, 6] from Operation: 90-84=6 Current State: 91:[49, 7, 6], Operations: ['90-84=6'] Exploring Operation: 7*6=42, Resulting Numbers: [49, 42] Generated Node #3: [49, 42] from Operation: 7*6=42 Current State: 91:[49, 42], Operations: ['90-84=6', '7*6=42'] Exploring Operation: 49+42=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[49, 7, 90, 84], Operations: [] Exploring Operation: 49/7=7, Resulting Numbers: [90, 84, 7] Generated Node #0,0: 91:[90, 84, 7] Operation: 49/7=7 Moving to Node #0,0 Current State: 91:[90, 84, 7], Operations: ['49/7=7'] Exploring Operation: 90-84=6, Resulting Numbers: [7, 6] Generated Node #0,0,0: 91:[7, 6] Operation: 90-84=6 Moving to Node #0,0,0 Current State: 91:[7, 6], Operations: ['49/7=7', '90-84=6'] Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,91 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 13, 43, 94, 47 ]
99
[ "43*94=4042", "4042/47=86", "13+86=99" ]
Current State: 99:[13, 43, 94, 47], Operations: [] Exploring Operation: 43*94=4042, Resulting Numbers: [13, 47, 4042] Generated Node #2: [13, 47, 4042] from Operation: 43*94=4042 Current State: 99:[13, 47, 4042], Operations: ['43*94=4042'] Exploring Operation: 4042/47=86, Resulting Numbers: [13, 86] Generated Node #3: [13, 86] from Operation: 4042/47=86 Current State: 99:[13, 86], Operations: ['43*94=4042', '4042/47=86'] Exploring Operation: 13+86=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[13, 43, 94, 47], Operations: [] Exploring Operation: 47-43=4, Resulting Numbers: [13, 94, 4] Generated Node #0,0: 99:[13, 94, 4] Operation: 47-43=4 Exploring Operation: 94/47=2, Resulting Numbers: [13, 43, 2] Generated Node #0,1: 99:[13, 43, 2] Operation: 94/47=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[13, 94, 4], Operations: ['47-43=4'] Exploring Operation: 13-4=9, Resulting Numbers: [94, 9] Generated Node #0,0,0: 99:[94, 9] Operation: 13-4=9 Exploring Operation: 94+4=98, Resulting Numbers: [13, 98] Generated Node #0,0,1: 99:[13, 98] Operation: 94+4=98 Moving to Node #0,0,1 Current State: 99:[13, 98], Operations: ['47-43=4', '94+4=98'] Exploring Operation: 98-13=85, Resulting Numbers: [85] 85,99 unequal: No Solution Exploring Operation: 13+98=111, Resulting Numbers: [111] 111,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[94, 9], Operations: ['47-43=4', '13-4=9'] Exploring Operation: 94+9=103, Resulting Numbers: [103] 103,99 unequal: No Solution Exploring Operation: 94-9=85, Resulting Numbers: [85] 85,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[13, 43, 2], Operations: ['94/47=2'] Exploring Operation: 13-2=11, Resulting Numbers: [43, 11] Generated Node #0,1,0: 99:[43, 11] Operation: 13-2=11 Exploring Operation: 43-13=30, Resulting Numbers: [2, 30] Generated Node #0,1,1: 99:[2, 30] Operation: 43-13=30 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 99:[2, 30], Operations: ['94/47=2', '43-13=30'] Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 99:[43, 11], Operations: ['94/47=2', '13-2=11'] Exploring Operation: 43+11=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 47, 27, 43, 65 ]
42
[ "47-27=20", "65-43=22", "20+22=42" ]
Current State: 42:[47, 27, 43, 65], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [43, 65, 20] Generated Node #2: [43, 65, 20] from Operation: 47-27=20 Current State: 42:[43, 65, 20], Operations: ['47-27=20'] Exploring Operation: 65-43=22, Resulting Numbers: [20, 22] Generated Node #3: [20, 22] from Operation: 65-43=22 Current State: 42:[20, 22], Operations: ['47-27=20', '65-43=22'] Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[47, 27, 43, 65], Operations: [] Exploring Operation: 65-43=22, Resulting Numbers: [47, 27, 22] Generated Node #0,0: 42:[47, 27, 22] Operation: 65-43=22 Exploring Operation: 47-27=20, Resulting Numbers: [43, 65, 20] Generated Node #0,1: 42:[43, 65, 20] Operation: 47-27=20 Exploring Operation: 65-27=38, Resulting Numbers: [47, 43, 38] Generated Node #0,2: 42:[47, 43, 38] Operation: 65-27=38 Exploring Operation: 65-47=18, Resulting Numbers: [27, 43, 18] Generated Node #0,3: 42:[27, 43, 18] Operation: 65-47=18 Moving to Node #0,2 Current State: 42:[47, 43, 38], Operations: ['65-27=38'] Exploring Operation: 47+38=85, Resulting Numbers: [43, 85] Generated Node #0,2,0: 42:[43, 85] Operation: 47+38=85 Exploring Operation: 47-38=9, Resulting Numbers: [43, 9] Generated Node #0,2,1: 42:[43, 9] Operation: 47-38=9 Exploring Operation: 47-43=4, Resulting Numbers: [38, 4] Generated Node #0,2,2: 42:[38, 4] Operation: 47-43=4 Exploring Operation: 43-38=5, Resulting Numbers: [47, 5] Generated Node #0,2,3: 42:[47, 5] Operation: 43-38=5 Moving to Node #0,3 Current State: 42:[27, 43, 18], Operations: ['65-47=18'] Exploring Operation: 27-18=9, Resulting Numbers: [43, 9] Generated Node #0,3,0: 42:[43, 9] Operation: 27-18=9 Exploring Operation: 43-18=25, Resulting Numbers: [27, 25] Generated Node #0,3,1: 42:[27, 25] Operation: 43-18=25 Exploring Operation: 43-27=16, Resulting Numbers: [18, 16] Generated Node #0,3,2: 42:[18, 16] Operation: 43-27=16 Exploring Operation: 27+18=45, Resulting Numbers: [43, 45] Generated Node #0,3,3: 42:[43, 45] Operation: 27+18=45 Moving to Node #0,0 Current State: 42:[47, 27, 22], Operations: ['65-43=22'] Exploring Operation: 27+22=49, Resulting Numbers: [47, 49] Generated Node #0,0,0: 42:[47, 49] Operation: 27+22=49 Exploring Operation: 27-22=5, Resulting Numbers: [47, 5] Generated Node #0,0,1: 42:[47, 5] Operation: 27-22=5 Exploring Operation: 47-27=20, Resulting Numbers: [22, 20] Generated Node #0,0,2: 42:[22, 20] Operation: 47-27=20 Exploring Operation: 47-22=25, Resulting Numbers: [27, 25] Generated Node #0,0,3: 42:[27, 25] Operation: 47-22=25 Moving to Node #0,1 Current State: 42:[43, 65, 20], Operations: ['47-27=20'] Exploring Operation: 65-43=22, Resulting Numbers: [20, 22] Generated Node #0,1,0: 42:[20, 22] Operation: 65-43=22 Exploring Operation: 65-20=45, Resulting Numbers: [43, 45] Generated Node #0,1,1: 42:[43, 45] Operation: 65-20=45 Exploring Operation: 43+20=63, Resulting Numbers: [65, 63] Generated Node #0,1,2: 42:[65, 63] Operation: 43+20=63 Exploring Operation: 43-20=23, Resulting Numbers: [65, 23] Generated Node #0,1,3: 42:[65, 23] Operation: 43-20=23 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 42:[20, 22], Operations: ['47-27=20', '65-43=22'] Exploring Operation: 20*22=440, Resulting Numbers: [440] 440,42 unequal: No Solution Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[47, 27, 43, 65], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [43, 65, 20] Generated Node #0,1: 42:[43, 65, 20] Operation: 47-27=20 Moving to Node #0,1 Current State: 42:[43, 65, 20], Operations: ['47-27=20'] Exploring Operation: 65-43=22, Resulting Numbers: [20, 22] Generated Node #0,1,0: 42:[20, 22] Operation: 65-43=22 Moving to Node #0,1,0 Current State: 42:[20, 22], Operations: ['47-27=20', '65-43=22'] Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_4
mult_heuristic
[ 67, 59, 90, 6 ]
88
[ "67-59=8", "90+6=96", "96-8=88" ]
Current State: 88:[67, 59, 90, 6], Operations: [] Exploring Operation: 67-59=8, Resulting Numbers: [90, 6, 8] Generated Node #2: [90, 6, 8] from Operation: 67-59=8 Current State: 88:[90, 6, 8], Operations: ['67-59=8'] Exploring Operation: 90+6=96, Resulting Numbers: [8, 96] Generated Node #3: [8, 96] from Operation: 90+6=96 Current State: 88:[8, 96], Operations: ['67-59=8', '90+6=96'] Exploring Operation: 96-8=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[67, 59, 90, 6], Operations: [] Exploring Operation: 67-59=8, Resulting Numbers: [90, 6, 8] Generated Node #0,0: 88:[90, 6, 8] Operation: 67-59=8 Moving to Node #0,0 Current State: 88:[90, 6, 8], Operations: ['67-59=8'] Exploring Operation: 8-6=2, Resulting Numbers: [90, 2] Generated Node #0,0,0: 88:[90, 2] Operation: 8-6=2 Moving to Node #0,0,0 Current State: 88:[90, 2], Operations: ['67-59=8', '8-6=2'] Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[67, 59, 90, 6], Operations: [] Exploring Operation: 67-59=8, Resulting Numbers: [90, 6, 8] Generated Node #0,0: 88:[90, 6, 8] Operation: 67-59=8 Moving to Node #0,0 Current State: 88:[90, 6, 8], Operations: ['67-59=8'] Exploring Operation: 8-6=2, Resulting Numbers: [90, 2] Generated Node #0,0,0: 88:[90, 2] Operation: 8-6=2 Moving to Node #0,0,0 Current State: 88:[90, 2], Operations: ['67-59=8', '8-6=2'] Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 26, 91, 99, 70 ]
94
[ "91-26=65", "99-70=29", "65+29=94" ]
Current State: 94:[26, 91, 99, 70], Operations: [] Exploring Operation: 91-26=65, Resulting Numbers: [99, 70, 65] Generated Node #2: [99, 70, 65] from Operation: 91-26=65 Current State: 94:[99, 70, 65], Operations: ['91-26=65'] Exploring Operation: 99-70=29, Resulting Numbers: [65, 29] Generated Node #3: [65, 29] from Operation: 99-70=29 Current State: 94:[65, 29], Operations: ['91-26=65', '99-70=29'] Exploring Operation: 65+29=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[26, 91, 99, 70], Operations: [] Exploring Operation: 26+70=96, Resulting Numbers: [91, 99, 96] Generated Node #0,0: 94:[91, 99, 96] Operation: 26+70=96 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[91, 99, 96], Operations: ['26+70=96'] Exploring Operation: 99-96=3, Resulting Numbers: [91, 3] Generated Node #0,0,0: 94:[91, 3] Operation: 99-96=3 Moving to Node #0,0,0 Current State: 94:[91, 3], Operations: ['26+70=96', '99-96=3'] Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[26, 91, 99, 70], Operations: [] Exploring Operation: 26+70=96, Resulting Numbers: [91, 99, 96] Generated Node #0,0: 94:[91, 99, 96] Operation: 26+70=96 Moving to Node #0,0 Current State: 94:[91, 99, 96], Operations: ['26+70=96'] Exploring Operation: 99-96=3, Resulting Numbers: [91, 3] Generated Node #0,0,0: 94:[91, 3] Operation: 99-96=3 Moving to Node #0,0,0 Current State: 94:[91, 3], Operations: ['26+70=96', '99-96=3'] Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 22, 67, 83, 68 ]
74
[ "22+67=89", "83-68=15", "89-15=74" ]
Current State: 74:[22, 67, 83, 68], Operations: [] Exploring Operation: 22+67=89, Resulting Numbers: [83, 68, 89] Generated Node #2: [83, 68, 89] from Operation: 22+67=89 Current State: 74:[83, 68, 89], Operations: ['22+67=89'] Exploring Operation: 83-68=15, Resulting Numbers: [89, 15] Generated Node #3: [89, 15] from Operation: 83-68=15 Current State: 74:[89, 15], Operations: ['22+67=89', '83-68=15'] Exploring Operation: 89-15=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[22, 67, 83, 68], Operations: [] Exploring Operation: 68-22=46, Resulting Numbers: [67, 83, 46] Generated Node #0,0: 74:[67, 83, 46] Operation: 68-22=46 Exploring Operation: 83-22=61, Resulting Numbers: [67, 68, 61] Generated Node #0,1: 74:[67, 68, 61] Operation: 83-22=61 Exploring Operation: 68-67=1, Resulting Numbers: [22, 83, 1] Generated Node #0,2: 74:[22, 83, 1] Operation: 68-67=1 Exploring Operation: 22+67=89, Resulting Numbers: [83, 68, 89] Generated Node #0,3: 74:[83, 68, 89] Operation: 22+67=89 Exploring Operation: 67-22=45, Resulting Numbers: [83, 68, 45] Generated Node #0,4: 74:[83, 68, 45] Operation: 67-22=45 Moving to Node #0,4 Current State: 74:[83, 68, 45], Operations: ['67-22=45'] Exploring Operation: 83+45=128, Resulting Numbers: [68, 128] Generated Node #0,4,0: 74:[68, 128] Operation: 83+45=128 Exploring Operation: 68+45=113, Resulting Numbers: [83, 113] Generated Node #0,4,1: 74:[83, 113] Operation: 68+45=113 Exploring Operation: 83-68=15, Resulting Numbers: [45, 15] Generated Node #0,4,2: 74:[45, 15] Operation: 83-68=15 Exploring Operation: 83-45=38, Resulting Numbers: [68, 38] Generated Node #0,4,3: 74:[68, 38] Operation: 83-45=38 Exploring Operation: 68-45=23, Resulting Numbers: [83, 23] Generated Node #0,4,4: 74:[83, 23] Operation: 68-45=23 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 74:[68, 38], Operations: ['67-22=45', '83-45=38'] Exploring Operation: 68-38=30, Resulting Numbers: [30] 30,74 unequal: No Solution Exploring Operation: 68+38=106, Resulting Numbers: [106] 106,74 unequal: No Solution Exploring Operation: 68*38=2584, Resulting Numbers: [2584] 2584,74 unequal: No Solution No 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: 74:[45, 15], Operations: ['67-22=45', '83-68=15'] Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,74 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,74 unequal: No Solution Exploring Operation: 45+15=60, Resulting Numbers: [60] 60,74 unequal: No Solution Exploring Operation: 45*15=675, Resulting Numbers: [675] 675,74 unequal: No Solution No 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: 74:[83, 23], Operations: ['67-22=45', '68-45=23'] Exploring Operation: 83-23=60, Resulting Numbers: [60] 60,74 unequal: No Solution Exploring Operation: 83+23=106, Resulting Numbers: [106] 106,74 unequal: No Solution Exploring Operation: 83*23=1909, Resulting Numbers: [1909] 1909,74 unequal: No Solution No 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: 74:[83, 113], Operations: ['67-22=45', '68+45=113'] Exploring Operation: 83+113=196, Resulting Numbers: [196] 196,74 unequal: No Solution Exploring Operation: 113-83=30, Resulting Numbers: [30] 30,74 unequal: No Solution Exploring Operation: 83*113=9379, Resulting Numbers: [9379] 9379,74 unequal: No Solution No 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: 74:[68, 128], Operations: ['67-22=45', '83+45=128'] Exploring Operation: 68*128=8704, Resulting Numbers: [8704] 8704,74 unequal: No Solution Exploring Operation: 68+128=196, Resulting Numbers: [196] 196,74 unequal: No Solution Exploring Operation: 128-68=60, Resulting Numbers: [60] 60,74 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: 74:[22, 83, 1], Operations: ['68-67=1'] Exploring Operation: 22*1=22, Resulting Numbers: [83, 22] Generated Node #0,2,0: 74:[83, 22] Operation: 22*1=22 Exploring Operation: 22+1=23, Resulting Numbers: [83, 23] Generated Node #0,2,1: 74:[83, 23] Operation: 22+1=23 Exploring Operation: 83-22=61, Resulting Numbers: [1, 61] Generated Node #0,2,2: 74:[1, 61] Operation: 83-22=61 Exploring Operation: 83-1=82, Resulting Numbers: [22, 82] Generated Node #0,2,3: 74:[22, 82] Operation: 83-1=82 Exploring Operation: 22/1=22, Resulting Numbers: [83, 22] Generated Node #0,2,4: 74:[83, 22] Operation: 22/1=22 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 74:[1, 61], Operations: ['68-67=1', '83-22=61'] Exploring Operation: 1*61=61, Resulting Numbers: [61] 61,74 unequal: No Solution Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,74 unequal: No Solution Exploring Operation: 1+61=62, Resulting Numbers: [62] 62,74 unequal: No Solution Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,74 unequal: No Solution No 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: 74:[83, 23], Operations: ['68-67=1', '22+1=23'] Exploring Operation: 83+23=106, Resulting Numbers: [106] 106,74 unequal: No Solution Exploring Operation: 83-23=60, Resulting Numbers: [60] 60,74 unequal: No Solution Exploring Operation: 83*23=1909, Resulting Numbers: [1909] 1909,74 unequal: No Solution No 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: 74:[22, 82], Operations: ['68-67=1', '83-1=82'] Exploring Operation: 22*82=1804, Resulting Numbers: [1804] 1804,74 unequal: No Solution Exploring Operation: 22+82=104, Resulting Numbers: [104] 104,74 unequal: No Solution Exploring Operation: 82-22=60, Resulting Numbers: [60] 60,74 unequal: No Solution No 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: 74:[83, 22], Operations: ['68-67=1', '22*1=22'] Exploring Operation: 83+22=105, Resulting Numbers: [105] 105,74 unequal: No Solution Exploring Operation: 83-22=61, Resulting Numbers: [61] 61,74 unequal: No Solution Exploring Operation: 83*22=1826, Resulting Numbers: [1826] 1826,74 unequal: No Solution No 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: 74:[83, 22], Operations: ['68-67=1', '22/1=22'] Exploring Operation: 83-22=61, Resulting Numbers: [61] 61,74 unequal: No Solution Exploring Operation: 83+22=105, Resulting Numbers: [105] 105,74 unequal: No Solution Exploring Operation: 83*22=1826, Resulting Numbers: [1826] 1826,74 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: 74:[67, 83, 46], Operations: ['68-22=46'] Exploring Operation: 83-67=16, Resulting Numbers: [46, 16] Generated Node #0,0,0: 74:[46, 16] Operation: 83-67=16 Exploring Operation: 83+46=129, Resulting Numbers: [67, 129] Generated Node #0,0,1: 74:[67, 129] Operation: 83+46=129 Exploring Operation: 83-46=37, Resulting Numbers: [67, 37] Generated Node #0,0,2: 74:[67, 37] Operation: 83-46=37 Exploring Operation: 67-46=21, Resulting Numbers: [83, 21] Generated Node #0,0,3: 74:[83, 21] Operation: 67-46=21 Exploring Operation: 67+46=113, Resulting Numbers: [83, 113] Generated Node #0,0,4: 74:[83, 113] Operation: 67+46=113 Moving to Node #0,1 Current State: 74:[67, 68, 61], Operations: ['83-22=61'] Exploring Operation: 68-67=1, Resulting Numbers: [61, 1] Generated Node #0,1,0: 74:[61, 1] Operation: 68-67=1 Exploring Operation: 68+61=129, Resulting Numbers: [67, 129] Generated Node #0,1,1: 74:[67, 129] Operation: 68+61=129 Exploring Operation: 67-61=6, Resulting Numbers: [68, 6] Generated Node #0,1,2: 74:[68, 6] Operation: 67-61=6 Exploring Operation: 67+61=128, Resulting Numbers: [68, 128] Generated Node #0,1,3: 74:[68, 128] Operation: 67+61=128 Exploring Operation: 68-61=7, Resulting Numbers: [67, 7] Generated Node #0,1,4: 74:[67, 7] Operation: 68-61=7 Moving to Node #0,3 Current State: 74:[83, 68, 89], Operations: ['22+67=89'] Exploring Operation: 89-68=21, Resulting Numbers: [83, 21] Generated Node #0,3,0: 74:[83, 21] Operation: 89-68=21 Exploring Operation: 83-68=15, Resulting Numbers: [89, 15] Generated Node #0,3,1: 74:[89, 15] Operation: 83-68=15 Exploring Operation: 89-83=6, Resulting Numbers: [68, 6] Generated Node #0,3,2: 74:[68, 6] Operation: 89-83=6 Exploring Operation: 68+89=157, Resulting Numbers: [83, 157] Generated Node #0,3,3: 74:[83, 157] Operation: 68+89=157 Exploring Operation: 83+68=151, Resulting Numbers: [89, 151] Generated Node #0,3,4: 74:[89, 151] Operation: 83+68=151 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 74:[68, 6], Operations: ['22+67=89', '89-83=6'] Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,74 unequal: No Solution Exploring Operation: 68*6=408, Resulting Numbers: [408] 408,74 unequal: No Solution Exploring Operation: 68+6=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[22, 67, 83, 68], Operations: [] Exploring Operation: 22+67=89, Resulting Numbers: [83, 68, 89] Generated Node #0,3: 74:[83, 68, 89] Operation: 22+67=89 Moving to Node #0,3 Current State: 74:[83, 68, 89], Operations: ['22+67=89'] Exploring Operation: 89-83=6, Resulting Numbers: [68, 6] Generated Node #0,3,2: 74:[68, 6] Operation: 89-83=6 Moving to Node #0,3,2 Current State: 74:[68, 6], Operations: ['22+67=89', '89-83=6'] Exploring Operation: 68+6=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.940104
hs_5
mult_heuristic
[ 74, 88, 11, 88 ]
74
[ "88-88=0", "11*0=0", "74+0=74" ]
Current State: 74:[74, 88, 11, 88], Operations: [] Exploring Operation: 88-88=0, Resulting Numbers: [74, 11, 0] Generated Node #2: [74, 11, 0] from Operation: 88-88=0 Current State: 74:[74, 11, 0], Operations: ['88-88=0'] Exploring Operation: 11*0=0, Resulting Numbers: [74, 0] Generated Node #3: [74, 0] from Operation: 11*0=0 Current State: 74:[74, 0], Operations: ['88-88=0', '11*0=0'] Exploring Operation: 74+0=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[74, 88, 11, 88], Operations: [] Exploring Operation: 88-88=0, Resulting Numbers: [74, 11, 0] Generated Node #0,0: 74:[74, 11, 0] Operation: 88-88=0 Exploring Operation: 88-11=77, Resulting Numbers: [74, 88, 77] Generated Node #0,1: 74:[74, 88, 77] Operation: 88-11=77 Exploring Operation: 88/88=1, Resulting Numbers: [74, 11, 1] Generated Node #0,2: 74:[74, 11, 1] Operation: 88/88=1 Exploring Operation: 88-11=77, Resulting Numbers: [74, 88, 77] Generated Node #0,3: 74:[74, 88, 77] Operation: 88-11=77 Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[74, 11, 1], Operations: ['88/88=1'] Exploring Operation: 74/1=74, Resulting Numbers: [11, 74] Generated Node #0,2,0: 74:[11, 74] Operation: 74/1=74 Exploring Operation: 74*1=74, Resulting Numbers: [11, 74] Generated Node #0,2,1: 74:[11, 74] Operation: 74*1=74 Exploring Operation: 11-1=10, Resulting Numbers: [74, 10] Generated Node #0,2,2: 74:[74, 10] Operation: 11-1=10 Exploring Operation: 11*1=11, Resulting Numbers: [74, 11] Generated Node #0,2,3: 74:[74, 11] Operation: 11*1=11 Moving to Node #0,2,2 Current State: 74:[74, 10], Operations: ['88/88=1', '11-1=10'] Exploring Operation: 74+10=84, Resulting Numbers: [84] 84,74 unequal: No Solution Exploring Operation: 74*10=740, Resulting Numbers: [740] 740,74 unequal: No Solution Exploring Operation: 74-10=64, Resulting Numbers: [64] 64,74 unequal: No Solution Moving to Node #0,2,1 Current State: 74:[11, 74], Operations: ['88/88=1', '74*1=74'] Exploring Operation: 11+74=85, Resulting Numbers: [85] 85,74 unequal: No Solution Exploring Operation: 11*74=814, Resulting Numbers: [814] 814,74 unequal: No Solution Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,74 unequal: No Solution Moving to Node #0,2,0 Current State: 74:[11, 74], Operations: ['88/88=1', '74/1=74'] Exploring Operation: 11*74=814, Resulting Numbers: [814] 814,74 unequal: No Solution Exploring Operation: 11+74=85, Resulting Numbers: [85] 85,74 unequal: No Solution Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,74 unequal: No Solution Moving to Node #0,2,3 Current State: 74:[74, 11], Operations: ['88/88=1', '11*1=11'] Exploring Operation: 74+11=85, Resulting Numbers: [85] 85,74 unequal: No Solution Exploring Operation: 74*11=814, Resulting Numbers: [814] 814,74 unequal: No Solution Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,74 unequal: No Solution No 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: 74:[74, 11, 0], Operations: ['88-88=0'] Exploring Operation: 74-0=74, Resulting Numbers: [11, 74] Generated Node #0,0,0: 74:[11, 74] Operation: 74-0=74 Exploring Operation: 11*0=0, Resulting Numbers: [74, 0] Generated Node #0,0,1: 74:[74, 0] Operation: 11*0=0 Exploring Operation: 74+0=74, Resulting Numbers: [11, 74] Generated Node #0,0,2: 74:[11, 74] Operation: 74+0=74 Exploring Operation: 11+0=11, Resulting Numbers: [74, 11] Generated Node #0,0,3: 74:[74, 11] Operation: 11+0=11 Moving to Node #0,0,1 Current State: 74:[74, 0], Operations: ['88-88=0', '11*0=0'] Exploring Operation: 74*0=0, Resulting Numbers: [0] 0,74 unequal: No Solution Exploring Operation: 74-0=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[74, 88, 11, 88], Operations: [] Exploring Operation: 88-88=0, Resulting Numbers: [74, 11, 0] Generated Node #0,0: 74:[74, 11, 0] Operation: 88-88=0 Moving to Node #0,0 Current State: 74:[74, 11, 0], Operations: ['88-88=0'] Exploring Operation: 11*0=0, Resulting Numbers: [74, 0] Generated Node #0,0,1: 74:[74, 0] Operation: 11*0=0 Moving to Node #0,0,1 Current State: 74:[74, 0], Operations: ['88-88=0', '11*0=0'] Exploring Operation: 74-0=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 55, 24, 44, 18 ]
22
[ "44*18=792", "792/24=33", "55-33=22" ]
Current State: 22:[55, 24, 44, 18], Operations: [] Exploring Operation: 44*18=792, Resulting Numbers: [55, 24, 792] Generated Node #2: [55, 24, 792] from Operation: 44*18=792 Current State: 22:[55, 24, 792], Operations: ['44*18=792'] Exploring Operation: 792/24=33, Resulting Numbers: [55, 33] Generated Node #3: [55, 33] from Operation: 792/24=33 Current State: 22:[55, 33], Operations: ['44*18=792', '792/24=33'] Exploring Operation: 55-33=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[55, 24, 44, 18], Operations: [] Exploring Operation: 55-24=31, Resulting Numbers: [44, 18, 31] Generated Node #0,0: 22:[44, 18, 31] Operation: 55-24=31 Exploring Operation: 55-44=11, Resulting Numbers: [24, 18, 11] Generated Node #0,1: 22:[24, 18, 11] Operation: 55-44=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[24, 18, 11], Operations: ['55-44=11'] Exploring Operation: 24-18=6, Resulting Numbers: [11, 6] Generated Node #0,1,0: 22:[11, 6] Operation: 24-18=6 Exploring Operation: 24-11=13, Resulting Numbers: [18, 13] Generated Node #0,1,1: 22:[18, 13] Operation: 24-11=13 Moving to Node #0,1,0 Current State: 22:[11, 6], Operations: ['55-44=11', '24-18=6'] Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,22 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[18, 13], Operations: ['55-44=11', '24-11=13'] Exploring Operation: 18+13=31, Resulting Numbers: [31] 31,22 unequal: No Solution Exploring Operation: 18-13=5, Resulting Numbers: [5] 5,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[44, 18, 31], Operations: ['55-24=31'] Exploring Operation: 44-18=26, Resulting Numbers: [31, 26] Generated Node #0,0,0: 22:[31, 26] Operation: 44-18=26 Exploring Operation: 44-31=13, Resulting Numbers: [18, 13] Generated Node #0,0,1: 22:[18, 13] Operation: 44-31=13 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 22:[18, 13], Operations: ['55-24=31', '44-31=13'] Exploring Operation: 18+13=31, Resulting Numbers: [31] 31,22 unequal: No Solution Exploring Operation: 18-13=5, Resulting Numbers: [5] 5,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 22:[31, 26], Operations: ['55-24=31', '44-18=26'] Exploring Operation: 31-26=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 31+26=57, Resulting Numbers: [57] 57,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 2, 2, 79, 70 ]
90
[ "2*79=158", "70-2=68", "158-68=90" ]
Current State: 90:[2, 2, 79, 70], Operations: [] Exploring Operation: 2*79=158, Resulting Numbers: [70, 158] Generated Node #2: [70, 158] from Operation: 2*79=158 Current State: 90:[70, 158], Operations: ['2*79=158'] Exploring Operation: 70-2=68, Resulting Numbers: [158, 68] Generated Node #3: [158, 68] from Operation: 70-2=68 Current State: 90:[158, 68], Operations: ['2*79=158', '70-2=68'] Exploring Operation: 158-68=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[2, 2, 79, 70], Operations: [] Exploring Operation: 79-70=9, Resulting Numbers: [2, 2, 9] Generated Node #0,0: 90:[2, 2, 9] Operation: 79-70=9 Exploring Operation: 70/2=35, Resulting Numbers: [2, 79, 35] Generated Node #0,1: 90:[2, 79, 35] Operation: 70/2=35 Moving to Node #0,0 Current State: 90:[2, 2, 9], Operations: ['79-70=9'] Exploring Operation: 2*9=18, Resulting Numbers: [2, 18] Generated Node #0,0,0: 90:[2, 18] Operation: 2*9=18 Exploring Operation: 2*9=18, Resulting Numbers: [2, 18] Generated Node #0,0,1: 90:[2, 18] Operation: 2*9=18 Moving to Node #0,1 Current State: 90:[2, 79, 35], Operations: ['70/2=35'] Exploring Operation: 79-35=44, Resulting Numbers: [2, 44] Generated Node #0,1,0: 90:[2, 44] Operation: 79-35=44 Exploring Operation: 2+79=81, Resulting Numbers: [35, 81] Generated Node #0,1,1: 90:[35, 81] Operation: 2+79=81 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[2, 44], Operations: ['70/2=35', '79-35=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,90 unequal: No Solution Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[35, 81], Operations: ['70/2=35', '2+79=81'] Exploring Operation: 35+81=116, Resulting Numbers: [116] 116,90 unequal: No Solution Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,90 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: 90:[2, 18], Operations: ['79-70=9', '2*9=18'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[2, 18], Operations: ['79-70=9', '2*9=18'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,90 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,90 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 38, 48, 91, 98 ]
79
[ "38+48=86", "98-91=7", "86-7=79" ]
Current State: 79:[38, 48, 91, 98], Operations: [] Exploring Operation: 38+48=86, Resulting Numbers: [91, 98, 86] Generated Node #2: [91, 98, 86] from Operation: 38+48=86 Current State: 79:[91, 98, 86], Operations: ['38+48=86'] Exploring Operation: 98-91=7, Resulting Numbers: [86, 7] Generated Node #3: [86, 7] from Operation: 98-91=7 Current State: 79:[86, 7], Operations: ['38+48=86', '98-91=7'] Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[38, 48, 91, 98], Operations: [] Exploring Operation: 38+48=86, Resulting Numbers: [91, 98, 86] Generated Node #0,0: 79:[91, 98, 86] Operation: 38+48=86 Exploring Operation: 91-38=53, Resulting Numbers: [48, 98, 53] Generated Node #0,1: 79:[48, 98, 53] Operation: 91-38=53 Exploring Operation: 98-38=60, Resulting Numbers: [48, 91, 60] Generated Node #0,2: 79:[48, 91, 60] Operation: 98-38=60 Moving to Node #0,0 Current State: 79:[91, 98, 86], Operations: ['38+48=86'] Exploring Operation: 98-91=7, Resulting Numbers: [86, 7] Generated Node #0,0,0: 79:[86, 7] Operation: 98-91=7 Exploring Operation: 91-86=5, Resulting Numbers: [98, 5] Generated Node #0,0,1: 79:[98, 5] Operation: 91-86=5 Exploring Operation: 98-86=12, Resulting Numbers: [91, 12] Generated Node #0,0,2: 79:[91, 12] Operation: 98-86=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[86, 7], Operations: ['38+48=86', '98-91=7'] Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[38, 48, 91, 98], Operations: [] Exploring Operation: 38+48=86, Resulting Numbers: [91, 98, 86] Generated Node #0,0: 79:[91, 98, 86] Operation: 38+48=86 Moving to Node #0,0 Current State: 79:[91, 98, 86], Operations: ['38+48=86'] Exploring Operation: 98-91=7, Resulting Numbers: [86, 7] Generated Node #0,0,0: 79:[86, 7] Operation: 98-91=7 Moving to Node #0,0,0 Current State: 79:[86, 7], Operations: ['38+48=86', '98-91=7'] Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 70, 67, 21, 72 ]
31
[ "70-67=3", "21+72=93", "93/3=31" ]
Current State: 31:[70, 67, 21, 72], Operations: [] Exploring Operation: 70-67=3, Resulting Numbers: [21, 72, 3] Generated Node #2: [21, 72, 3] from Operation: 70-67=3 Current State: 31:[21, 72, 3], Operations: ['70-67=3'] Exploring Operation: 21+72=93, Resulting Numbers: [3, 93] Generated Node #3: [3, 93] from Operation: 21+72=93 Current State: 31:[3, 93], Operations: ['70-67=3', '21+72=93'] Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[70, 67, 21, 72], Operations: [] Exploring Operation: 72-67=5, Resulting Numbers: [70, 21, 5] Generated Node #0,0: 31:[70, 21, 5] Operation: 72-67=5 Exploring Operation: 72-70=2, Resulting Numbers: [67, 21, 2] Generated Node #0,1: 31:[67, 21, 2] Operation: 72-70=2 Moving to Node #0,0 Current State: 31:[70, 21, 5], Operations: ['72-67=5'] Exploring Operation: 70-21=49, Resulting Numbers: [5, 49] Generated Node #0,0,0: 31:[5, 49] Operation: 70-21=49 Exploring Operation: 70/5=14, Resulting Numbers: [21, 14] Generated Node #0,0,1: 31:[21, 14] Operation: 70/5=14 Moving to Node #0,1 Current State: 31:[67, 21, 2], Operations: ['72-70=2'] Exploring Operation: 67-2=65, Resulting Numbers: [21, 65] Generated Node #0,1,0: 31:[21, 65] Operation: 67-2=65 Exploring Operation: 67-21=46, Resulting Numbers: [2, 46] Generated Node #0,1,1: 31:[2, 46] Operation: 67-21=46 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[21, 65], Operations: ['72-70=2', '67-2=65'] Exploring Operation: 65-21=44, Resulting Numbers: [44] 44,31 unequal: No Solution Exploring Operation: 21+65=86, Resulting Numbers: [86] 86,31 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 #0,1,1 Current State: 31:[2, 46], Operations: ['72-70=2', '67-21=46'] Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,31 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 31:[21, 14], Operations: ['72-67=5', '70/5=14'] Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[5, 49], Operations: ['72-67=5', '70-21=49'] Exploring Operation: 49-5=44, Resulting Numbers: [44] 44,31 unequal: No Solution Exploring Operation: 5+49=54, Resulting Numbers: [54] 54,31 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 11, 36, 46, 44 ]
78
[ "44/11=4", "36+46=82", "82-4=78" ]
Current State: 78:[11, 36, 46, 44], Operations: [] Exploring Operation: 44/11=4, Resulting Numbers: [36, 46, 4] Generated Node #2: [36, 46, 4] from Operation: 44/11=4 Current State: 78:[36, 46, 4], Operations: ['44/11=4'] Exploring Operation: 36+46=82, Resulting Numbers: [4, 82] Generated Node #3: [4, 82] from Operation: 36+46=82 Current State: 78:[4, 82], Operations: ['44/11=4', '36+46=82'] Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[11, 36, 46, 44], Operations: [] Exploring Operation: 44/11=4, Resulting Numbers: [36, 46, 4] Generated Node #0,0: 78:[36, 46, 4] Operation: 44/11=4 Exploring Operation: 46-36=10, Resulting Numbers: [11, 44, 10] Generated Node #0,1: 78:[11, 44, 10] Operation: 46-36=10 Exploring Operation: 46-44=2, Resulting Numbers: [11, 36, 2] Generated Node #0,2: 78:[11, 36, 2] Operation: 46-44=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 78:[11, 36, 2], Operations: ['46-44=2'] Exploring Operation: 36+2=38, Resulting Numbers: [11, 38] Generated Node #0,2,0: 78:[11, 38] Operation: 36+2=38 Exploring Operation: 11+2=13, Resulting Numbers: [36, 13] Generated Node #0,2,1: 78:[36, 13] Operation: 11+2=13 Exploring Operation: 36-11=25, Resulting Numbers: [2, 25] Generated Node #0,2,2: 78:[2, 25] Operation: 36-11=25 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 78:[2, 25], Operations: ['46-44=2', '36-11=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,78 unequal: No Solution No 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: 78:[11, 38], Operations: ['46-44=2', '36+2=38'] Exploring Operation: 38-11=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 11*38=418, Resulting Numbers: [418] 418,78 unequal: No Solution Exploring Operation: 11+38=49, Resulting Numbers: [49] 49,78 unequal: No Solution No 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: 78:[36, 13], Operations: ['46-44=2', '11+2=13'] Exploring Operation: 36*13=468, Resulting Numbers: [468] 468,78 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 36+13=49, Resulting Numbers: [49] 49,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[11, 44, 10], Operations: ['46-36=10'] Exploring Operation: 44-10=34, Resulting Numbers: [11, 34] Generated Node #0,1,0: 78:[11, 34] Operation: 44-10=34 Exploring Operation: 11-10=1, Resulting Numbers: [44, 1] Generated Node #0,1,1: 78:[44, 1] Operation: 11-10=1 Exploring Operation: 44/11=4, Resulting Numbers: [10, 4] Generated Node #0,1,2: 78:[10, 4] Operation: 44/11=4 Moving to Node #0,1,2 Current State: 78:[10, 4], Operations: ['46-36=10', '44/11=4'] Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,78 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,78 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[44, 1], Operations: ['46-36=10', '11-10=1'] Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,78 unequal: No Solution Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,78 unequal: No Solution Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[11, 34], Operations: ['46-36=10', '44-10=34'] Exploring Operation: 11+34=45, Resulting Numbers: [45] 45,78 unequal: No Solution Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 11*34=374, Resulting Numbers: [374] 374,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[36, 46, 4], Operations: ['44/11=4'] Exploring Operation: 36+46=82, Resulting Numbers: [4, 82] Generated Node #0,0,0: 78:[4, 82] Operation: 36+46=82 Exploring Operation: 46-4=42, Resulting Numbers: [36, 42] Generated Node #0,0,1: 78:[36, 42] Operation: 46-4=42 Exploring Operation: 46-36=10, Resulting Numbers: [4, 10] Generated Node #0,0,2: 78:[4, 10] Operation: 46-36=10 Moving to Node #0,0,2 Current State: 78:[4, 10], Operations: ['44/11=4', '46-36=10'] Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,78 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,78 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[4, 82], Operations: ['44/11=4', '36+46=82'] Exploring Operation: 4*82=328, Resulting Numbers: [328] 328,78 unequal: No Solution Exploring Operation: 4+82=86, Resulting Numbers: [86] 86,78 unequal: No Solution Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[11, 36, 46, 44], Operations: [] Exploring Operation: 44/11=4, Resulting Numbers: [36, 46, 4] Generated Node #0,0: 78:[36, 46, 4] Operation: 44/11=4 Moving to Node #0,0 Current State: 78:[36, 46, 4], Operations: ['44/11=4'] Exploring Operation: 36+46=82, Resulting Numbers: [4, 82] Generated Node #0,0,0: 78:[4, 82] Operation: 36+46=82 Moving to Node #0,0,0 Current State: 78:[4, 82], Operations: ['44/11=4', '36+46=82'] Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_3
mult_heuristic
[ 36, 1, 26, 77 ]
67
[ "36*1=36", "26+77=103", "103-36=67" ]
Current State: 67:[36, 1, 26, 77], Operations: [] Exploring Operation: 36*1=36, Resulting Numbers: [26, 77, 36] Generated Node #2: [26, 77, 36] from Operation: 36*1=36 Current State: 67:[26, 77, 36], Operations: ['36*1=36'] Exploring Operation: 26+77=103, Resulting Numbers: [36, 103] Generated Node #3: [36, 103] from Operation: 26+77=103 Current State: 67:[36, 103], Operations: ['36*1=36', '26+77=103'] Exploring Operation: 103-36=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[36, 1, 26, 77], Operations: [] Exploring Operation: 36+26=62, Resulting Numbers: [1, 77, 62] Generated Node #0,0: 67:[1, 77, 62] Operation: 36+26=62 Exploring Operation: 36+1=37, Resulting Numbers: [26, 77, 37] Generated Node #0,1: 67:[26, 77, 37] Operation: 36+1=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[1, 77, 62], Operations: ['36+26=62'] Exploring Operation: 77-1=76, Resulting Numbers: [62, 76] Generated Node #0,0,0: 67:[62, 76] Operation: 77-1=76 Exploring Operation: 1+62=63, Resulting Numbers: [77, 63] Generated Node #0,0,1: 67:[77, 63] Operation: 1+62=63 Moving to Node #0,0,0 Current State: 67:[62, 76], Operations: ['36+26=62', '77-1=76'] Exploring Operation: 76-62=14, Resulting Numbers: [14] 14,67 unequal: No Solution Exploring Operation: 62+76=138, Resulting Numbers: [138] 138,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[77, 63], Operations: ['36+26=62', '1+62=63'] Exploring Operation: 77-63=14, Resulting Numbers: [14] 14,67 unequal: No Solution Exploring Operation: 77+63=140, Resulting Numbers: [140] 140,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[26, 77, 37], Operations: ['36+1=37'] Exploring Operation: 26+37=63, Resulting Numbers: [77, 63] Generated Node #0,1,0: 67:[77, 63] Operation: 26+37=63 Exploring Operation: 77-26=51, Resulting Numbers: [37, 51] Generated Node #0,1,1: 67:[37, 51] Operation: 77-26=51 Moving to Node #0,1,0 Current State: 67:[77, 63], Operations: ['36+1=37', '26+37=63'] Exploring Operation: 77-63=14, Resulting Numbers: [14] 14,67 unequal: No Solution Exploring Operation: 77+63=140, Resulting Numbers: [140] 140,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[37, 51], Operations: ['36+1=37', '77-26=51'] Exploring Operation: 37+51=88, Resulting Numbers: [88] 88,67 unequal: No Solution Exploring Operation: 51-37=14, Resulting Numbers: [14] 14,67 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
[ 35, 75, 47, 42 ]
49
[ "75-35=40", "47+42=89", "89-40=49" ]
Current State: 49:[35, 75, 47, 42], Operations: [] Exploring Operation: 75-35=40, Resulting Numbers: [47, 42, 40] Generated Node #2: [47, 42, 40] from Operation: 75-35=40 Current State: 49:[47, 42, 40], Operations: ['75-35=40'] Exploring Operation: 47+42=89, Resulting Numbers: [40, 89] Generated Node #3: [40, 89] from Operation: 47+42=89 Current State: 49:[40, 89], Operations: ['75-35=40', '47+42=89'] Exploring Operation: 89-40=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[35, 75, 47, 42], Operations: [] Exploring Operation: 42-35=7, Resulting Numbers: [75, 47, 7] Generated Node #0,0: 49:[75, 47, 7] Operation: 42-35=7 Exploring Operation: 75-35=40, Resulting Numbers: [47, 42, 40] Generated Node #0,1: 49:[47, 42, 40] Operation: 75-35=40 Moving to Node #0,1 Current State: 49:[47, 42, 40], Operations: ['75-35=40'] Exploring Operation: 47-40=7, Resulting Numbers: [42, 7] Generated Node #0,1,0: 49:[42, 7] Operation: 47-40=7 Exploring Operation: 42-40=2, Resulting Numbers: [47, 2] Generated Node #0,1,1: 49:[47, 2] Operation: 42-40=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 49:[42, 7], Operations: ['75-35=40', '47-40=7'] Exploring Operation: 42+7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[35, 75, 47, 42], Operations: [] Exploring Operation: 75-35=40, Resulting Numbers: [47, 42, 40] Generated Node #0,1: 49:[47, 42, 40] Operation: 75-35=40 Moving to Node #0,1 Current State: 49:[47, 42, 40], Operations: ['75-35=40'] Exploring Operation: 47-40=7, Resulting Numbers: [42, 7] Generated Node #0,1,0: 49:[42, 7] Operation: 47-40=7 Moving to Node #0,1,0 Current State: 49:[42, 7], Operations: ['75-35=40', '47-40=7'] Exploring Operation: 42+7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 80, 77, 62, 81 ]
89
[ "80-77=3", "81/3=27", "62+27=89" ]
Current State: 89:[80, 77, 62, 81], Operations: [] Exploring Operation: 80-77=3, Resulting Numbers: [62, 81, 3] Generated Node #2: [62, 81, 3] from Operation: 80-77=3 Current State: 89:[62, 81, 3], Operations: ['80-77=3'] Exploring Operation: 81/3=27, Resulting Numbers: [62, 27] Generated Node #3: [62, 27] from Operation: 81/3=27 Current State: 89:[62, 27], Operations: ['80-77=3', '81/3=27'] Exploring Operation: 62+27=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[80, 77, 62, 81], Operations: [] Exploring Operation: 77+62=139, Resulting Numbers: [80, 81, 139] Generated Node #0,0: 89:[80, 81, 139] Operation: 77+62=139 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[80, 81, 139], Operations: ['77+62=139'] Exploring Operation: 139-80=59, Resulting Numbers: [81, 59] Generated Node #0,0,0: 89:[81, 59] Operation: 139-80=59 Moving to Node #0,0,0 Current State: 89:[81, 59], Operations: ['77+62=139', '139-80=59'] Exploring Operation: 81+59=140, Resulting Numbers: [140] 140,89 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
[ 51, 36, 99, 41 ]
43
[ "51-36=15", "99-41=58", "58-15=43" ]
Current State: 43:[51, 36, 99, 41], Operations: [] Exploring Operation: 51-36=15, Resulting Numbers: [99, 41, 15] Generated Node #2: [99, 41, 15] from Operation: 51-36=15 Current State: 43:[99, 41, 15], Operations: ['51-36=15'] Exploring Operation: 99-41=58, Resulting Numbers: [15, 58] Generated Node #3: [15, 58] from Operation: 99-41=58 Current State: 43:[15, 58], Operations: ['51-36=15', '99-41=58'] Exploring Operation: 58-15=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[51, 36, 99, 41], Operations: [] Exploring Operation: 99-51=48, Resulting Numbers: [36, 41, 48] Generated Node #0,0: 43:[36, 41, 48] Operation: 99-51=48 Exploring Operation: 99-41=58, Resulting Numbers: [51, 36, 58] Generated Node #0,1: 43:[51, 36, 58] Operation: 99-41=58 Exploring Operation: 99-36=63, Resulting Numbers: [51, 41, 63] Generated Node #0,2: 43:[51, 41, 63] Operation: 99-36=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[36, 41, 48], Operations: ['99-51=48'] Exploring Operation: 36+41=77, Resulting Numbers: [48, 77] Generated Node #0,0,0: 43:[48, 77] Operation: 36+41=77 Exploring Operation: 48-36=12, Resulting Numbers: [41, 12] Generated Node #0,0,1: 43:[41, 12] Operation: 48-36=12 Exploring Operation: 41-36=5, Resulting Numbers: [48, 5] Generated Node #0,0,2: 43:[48, 5] Operation: 41-36=5 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 43:[41, 12], Operations: ['99-51=48', '48-36=12'] Exploring Operation: 41-12=29, Resulting Numbers: [29] 29,43 unequal: No Solution Exploring Operation: 41*12=492, Resulting Numbers: [492] 492,43 unequal: No Solution Exploring Operation: 41+12=53, Resulting Numbers: [53] 53,43 unequal: No Solution No 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: 43:[48, 77], Operations: ['99-51=48', '36+41=77'] Exploring Operation: 48*77=3696, Resulting Numbers: [3696] 3696,43 unequal: No Solution Exploring Operation: 48+77=125, Resulting Numbers: [125] 125,43 unequal: No Solution Exploring Operation: 77-48=29, Resulting Numbers: [29] 29,43 unequal: No Solution No 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: 43:[48, 5], Operations: ['99-51=48', '41-36=5'] Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[51, 36, 99, 41], Operations: [] Exploring Operation: 99-51=48, Resulting Numbers: [36, 41, 48] Generated Node #0,0: 43:[36, 41, 48] Operation: 99-51=48 Moving to Node #0,0 Current State: 43:[36, 41, 48], Operations: ['99-51=48'] Exploring Operation: 41-36=5, Resulting Numbers: [48, 5] Generated Node #0,0,2: 43:[48, 5] Operation: 41-36=5 Moving to Node #0,0,2 Current State: 43:[48, 5], Operations: ['99-51=48', '41-36=5'] Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 29, 34, 11, 37 ]
37
[ "29+34=63", "37-11=26", "63-26=37" ]
Current State: 37:[29, 34, 11, 37], Operations: [] Exploring Operation: 29+34=63, Resulting Numbers: [11, 37, 63] Generated Node #2: [11, 37, 63] from Operation: 29+34=63 Current State: 37:[11, 37, 63], Operations: ['29+34=63'] Exploring Operation: 37-11=26, Resulting Numbers: [63, 26] Generated Node #3: [63, 26] from Operation: 37-11=26 Current State: 37:[63, 26], Operations: ['29+34=63', '37-11=26'] Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[29, 34, 11, 37], Operations: [] Exploring Operation: 29+11=40, Resulting Numbers: [34, 37, 40] Generated Node #0,0: 37:[34, 37, 40] Operation: 29+11=40 Moving to Node #0,0 Current State: 37:[34, 37, 40], Operations: ['29+11=40'] Exploring Operation: 40-34=6, Resulting Numbers: [37, 6] Generated Node #0,0,0: 37:[37, 6] Operation: 40-34=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[37, 6], Operations: ['29+11=40', '40-34=6'] Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 19, 77, 22, 54 ]
88
[ "77-19=58", "58-54=4", "22*4=88" ]
Current State: 88:[19, 77, 22, 54], Operations: [] Exploring Operation: 77-19=58, Resulting Numbers: [22, 54, 58] Generated Node #2: [22, 54, 58] from Operation: 77-19=58 Current State: 88:[22, 54, 58], Operations: ['77-19=58'] Exploring Operation: 58-54=4, Resulting Numbers: [22, 4] Generated Node #3: [22, 4] from Operation: 58-54=4 Current State: 88:[22, 4], Operations: ['77-19=58', '58-54=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[19, 77, 22, 54], Operations: [] Exploring Operation: 77-54=23, Resulting Numbers: [19, 22, 23] Generated Node #0,0: 88:[19, 22, 23] Operation: 77-54=23 Moving to Node #0,0 Current State: 88:[19, 22, 23], Operations: ['77-54=23'] Exploring Operation: 23-19=4, Resulting Numbers: [22, 4] Generated Node #0,0,0: 88:[22, 4] Operation: 23-19=4 Moving to Node #0,0,0 Current State: 88:[22, 4], Operations: ['77-54=23', '23-19=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[19, 77, 22, 54], Operations: [] Exploring Operation: 77-54=23, Resulting Numbers: [19, 22, 23] Generated Node #0,0: 88:[19, 22, 23] Operation: 77-54=23 Moving to Node #0,0 Current State: 88:[19, 22, 23], Operations: ['77-54=23'] Exploring Operation: 23-19=4, Resulting Numbers: [22, 4] Generated Node #0,0,0: 88:[22, 4] Operation: 23-19=4 Moving to Node #0,0,0 Current State: 88:[22, 4], Operations: ['77-54=23', '23-19=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 76, 3, 64, 70 ]
78
[ "70-64=6", "6/3=2", "76+2=78" ]
Current State: 78:[76, 3, 64, 70], Operations: [] Exploring Operation: 70-64=6, Resulting Numbers: [76, 3, 6] Generated Node #2: [76, 3, 6] from Operation: 70-64=6 Current State: 78:[76, 3, 6], Operations: ['70-64=6'] Exploring Operation: 6/3=2, Resulting Numbers: [76, 2] Generated Node #3: [76, 2] from Operation: 6/3=2 Current State: 78:[76, 2], Operations: ['70-64=6', '6/3=2'] Exploring Operation: 76+2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[76, 3, 64, 70], Operations: [] Exploring Operation: 76-70=6, Resulting Numbers: [3, 64, 6] Generated Node #0,0: 78:[3, 64, 6] Operation: 76-70=6 Exploring Operation: 76-64=12, Resulting Numbers: [3, 70, 12] Generated Node #0,1: 78:[3, 70, 12] Operation: 76-64=12 Exploring Operation: 3+64=67, Resulting Numbers: [76, 70, 67] Generated Node #0,2: 78:[76, 70, 67] Operation: 3+64=67 Exploring Operation: 3+70=73, Resulting Numbers: [76, 64, 73] Generated Node #0,3: 78:[76, 64, 73] Operation: 3+70=73 Exploring Operation: 70-64=6, Resulting Numbers: [76, 3, 6] Generated Node #0,4: 78:[76, 3, 6] Operation: 70-64=6 Start Sub Search at level 1: Moving to Node #0,4 Current State: 78:[76, 3, 6], Operations: ['70-64=6'] Exploring Operation: 76-3=73, Resulting Numbers: [6, 73] Generated Node #0,4,0: 78:[6, 73] Operation: 76-3=73 Exploring Operation: 76+3=79, Resulting Numbers: [6, 79] Generated Node #0,4,1: 78:[6, 79] Operation: 76+3=79 Exploring Operation: 6-3=3, Resulting Numbers: [76, 3] Generated Node #0,4,2: 78:[76, 3] Operation: 6-3=3 Exploring Operation: 76+6=82, Resulting Numbers: [3, 82] Generated Node #0,4,3: 78:[3, 82] Operation: 76+6=82 Exploring Operation: 6/3=2, Resulting Numbers: [76, 2] Generated Node #0,4,4: 78:[76, 2] Operation: 6/3=2 Moving to Node #0,4,1 Current State: 78:[6, 79], Operations: ['70-64=6', '76+3=79'] Exploring Operation: 6+79=85, Resulting Numbers: [85] 85,78 unequal: No Solution Exploring Operation: 6*79=474, Resulting Numbers: [474] 474,78 unequal: No Solution Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,78 unequal: No Solution Moving to Node #0,4,4 Current State: 78:[76, 2], Operations: ['70-64=6', '6/3=2'] Exploring Operation: 76*2=152, Resulting Numbers: [152] 152,78 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,78 unequal: No Solution Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,78 unequal: No Solution Exploring Operation: 76+2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[76, 3, 64, 70], Operations: [] Exploring Operation: 70-64=6, Resulting Numbers: [76, 3, 6] Generated Node #0,4: 78:[76, 3, 6] Operation: 70-64=6 Moving to Node #0,4 Current State: 78:[76, 3, 6], Operations: ['70-64=6'] Exploring Operation: 6/3=2, Resulting Numbers: [76, 2] Generated Node #0,4,4: 78:[76, 2] Operation: 6/3=2 Moving to Node #0,4,4 Current State: 78:[76, 2], Operations: ['70-64=6', '6/3=2'] Exploring Operation: 76+2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 7, 45, 11, 18 ]
10
[ "11-7=4", "45*4=180", "180/18=10" ]
Current State: 10:[7, 45, 11, 18], Operations: [] Exploring Operation: 11-7=4, Resulting Numbers: [45, 18, 4] Generated Node #2: [45, 18, 4] from Operation: 11-7=4 Current State: 10:[45, 18, 4], Operations: ['11-7=4'] Exploring Operation: 45*4=180, Resulting Numbers: [18, 180] Generated Node #3: [18, 180] from Operation: 45*4=180 Current State: 10:[18, 180], Operations: ['11-7=4', '45*4=180'] Exploring Operation: 180/18=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[7, 45, 11, 18], Operations: [] Exploring Operation: 45-18=27, Resulting Numbers: [7, 11, 27] Generated Node #0,0: 10:[7, 11, 27] Operation: 45-18=27 Exploring Operation: 45-7=38, Resulting Numbers: [11, 18, 38] Generated Node #0,1: 10:[11, 18, 38] Operation: 45-7=38 Exploring Operation: 45-11=34, Resulting Numbers: [7, 18, 34] Generated Node #0,2: 10:[7, 18, 34] Operation: 45-11=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[7, 11, 27], Operations: ['45-18=27'] Exploring Operation: 27-7=20, Resulting Numbers: [11, 20] Generated Node #0,0,0: 10:[11, 20] Operation: 27-7=20 Exploring Operation: 27-11=16, Resulting Numbers: [7, 16] Generated Node #0,0,1: 10:[7, 16] Operation: 27-11=16 Exploring Operation: 11-7=4, Resulting Numbers: [27, 4] Generated Node #0,0,2: 10:[27, 4] Operation: 11-7=4 Moving to Node #0,0,1 Current State: 10:[7, 16], Operations: ['45-18=27', '27-11=16'] Exploring Operation: 7*16=112, Resulting Numbers: [112] 112,10 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,10 unequal: No Solution Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,10 unequal: No Solution Moving to Node #0,0,0 Current State: 10:[11, 20], Operations: ['45-18=27', '27-7=20'] Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,10 unequal: No Solution Exploring Operation: 11+20=31, Resulting Numbers: [31] 31,10 unequal: No Solution Exploring Operation: 11*20=220, Resulting Numbers: [220] 220,10 unequal: No Solution Moving to Node #0,0,2 Current State: 10:[27, 4], Operations: ['45-18=27', '11-7=4'] Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,10 unequal: No Solution Exploring Operation: 27*4=108, Resulting Numbers: [108] 108,10 unequal: No Solution Exploring Operation: 27+4=31, Resulting Numbers: [31] 31,10 unequal: No Solution No 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: 10:[7, 18, 34], Operations: ['45-11=34'] Exploring Operation: 18-7=11, Resulting Numbers: [34, 11] Generated Node #0,2,0: 10:[34, 11] Operation: 18-7=11 Exploring Operation: 34-18=16, Resulting Numbers: [7, 16] Generated Node #0,2,1: 10:[7, 16] Operation: 34-18=16 Exploring Operation: 34-7=27, Resulting Numbers: [18, 27] Generated Node #0,2,2: 10:[18, 27] Operation: 34-7=27 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 10:[7, 16], Operations: ['45-11=34', '34-18=16'] Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,10 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,10 unequal: No Solution Exploring Operation: 7*16=112, Resulting Numbers: [112] 112,10 unequal: No Solution No 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: 10:[34, 11], Operations: ['45-11=34', '18-7=11'] Exploring Operation: 34*11=374, Resulting Numbers: [374] 374,10 unequal: No Solution Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,10 unequal: No Solution Exploring Operation: 34+11=45, Resulting Numbers: [45] 45,10 unequal: No Solution No 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: 10:[18, 27], Operations: ['45-11=34', '34-7=27'] Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,10 unequal: No Solution Exploring Operation: 18*27=486, Resulting Numbers: [486] 486,10 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,10 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: 10:[11, 18, 38], Operations: ['45-7=38'] Exploring Operation: 38-18=20, Resulting Numbers: [11, 20] Generated Node #0,1,0: 10:[11, 20] Operation: 38-18=20 Exploring Operation: 38-11=27, Resulting Numbers: [18, 27] Generated Node #0,1,1: 10:[18, 27] Operation: 38-11=27 Exploring Operation: 18-11=7, Resulting Numbers: [38, 7] Generated Node #0,1,2: 10:[38, 7] Operation: 18-11=7 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 10:[11, 20], Operations: ['45-7=38', '38-18=20'] Exploring Operation: 11*20=220, Resulting Numbers: [220] 220,10 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,10 unequal: No Solution Exploring Operation: 11+20=31, Resulting Numbers: [31] 31,10 unequal: No Solution No 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: 10:[18, 27], Operations: ['45-7=38', '38-11=27'] Exploring Operation: 18*27=486, Resulting Numbers: [486] 486,10 unequal: No Solution Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,10 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,10 unequal: No Solution No 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: 10:[38, 7], Operations: ['45-7=38', '18-11=7'] Exploring Operation: 38*7=266, Resulting Numbers: [266] 266,10 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,10 unequal: No Solution Exploring Operation: 38+7=45, Resulting Numbers: [45] 45,10 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
[ 91, 47, 39, 87 ]
90
[ "91+47=138", "87-39=48", "138-48=90" ]
Current State: 90:[91, 47, 39, 87], Operations: [] Exploring Operation: 91+47=138, Resulting Numbers: [39, 87, 138] Generated Node #2: [39, 87, 138] from Operation: 91+47=138 Current State: 90:[39, 87, 138], Operations: ['91+47=138'] Exploring Operation: 87-39=48, Resulting Numbers: [138, 48] Generated Node #3: [138, 48] from Operation: 87-39=48 Current State: 90:[138, 48], Operations: ['91+47=138', '87-39=48'] Exploring Operation: 138-48=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[91, 47, 39, 87], Operations: [] Exploring Operation: 47+39=86, Resulting Numbers: [91, 87, 86] Generated Node #0,0: 90:[91, 87, 86] Operation: 47+39=86 Exploring Operation: 47-39=8, Resulting Numbers: [91, 87, 8] Generated Node #0,1: 90:[91, 87, 8] Operation: 47-39=8 Exploring Operation: 87-39=48, Resulting Numbers: [91, 47, 48] Generated Node #0,2: 90:[91, 47, 48] Operation: 87-39=48 Exploring Operation: 91-87=4, Resulting Numbers: [47, 39, 4] Generated Node #0,3: 90:[47, 39, 4] Operation: 91-87=4 Moving to Node #0,1 Current State: 90:[91, 87, 8], Operations: ['47-39=8'] Exploring Operation: 91+8=99, Resulting Numbers: [87, 99] Generated Node #0,1,0: 90:[87, 99] Operation: 91+8=99 Exploring Operation: 91-8=83, Resulting Numbers: [87, 83] Generated Node #0,1,1: 90:[87, 83] Operation: 91-8=83 Exploring Operation: 87+8=95, Resulting Numbers: [91, 95] Generated Node #0,1,2: 90:[91, 95] Operation: 87+8=95 Exploring Operation: 91-87=4, Resulting Numbers: [8, 4] Generated Node #0,1,3: 90:[8, 4] Operation: 91-87=4 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 90:[8, 4], Operations: ['47-39=8', '91-87=4'] Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,90 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,90 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 90:[91, 95], Operations: ['47-39=8', '87+8=95'] Exploring Operation: 91*95=8645, Resulting Numbers: [8645] 8645,90 unequal: No Solution Exploring Operation: 91+95=186, Resulting Numbers: [186] 186,90 unequal: No Solution Exploring Operation: 95-91=4, Resulting Numbers: [4] 4,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[87, 83], Operations: ['47-39=8', '91-8=83'] Exploring Operation: 87*83=7221, Resulting Numbers: [7221] 7221,90 unequal: No Solution Exploring Operation: 87+83=170, Resulting Numbers: [170] 170,90 unequal: No Solution Exploring Operation: 87-83=4, Resulting Numbers: [4] 4,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[87, 99], Operations: ['47-39=8', '91+8=99'] Exploring Operation: 87*99=8613, Resulting Numbers: [8613] 8613,90 unequal: No Solution Exploring Operation: 99-87=12, Resulting Numbers: [12] 12,90 unequal: No Solution Exploring Operation: 87+99=186, Resulting Numbers: [186] 186,90 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: 90:[91, 47, 48], Operations: ['87-39=48'] Exploring Operation: 91-47=44, Resulting Numbers: [48, 44] Generated Node #0,2,0: 90:[48, 44] Operation: 91-47=44 Exploring Operation: 47+48=95, Resulting Numbers: [91, 95] Generated Node #0,2,1: 90:[91, 95] Operation: 47+48=95 Exploring Operation: 91-48=43, Resulting Numbers: [47, 43] Generated Node #0,2,2: 90:[47, 43] Operation: 91-48=43 Exploring Operation: 48-47=1, Resulting Numbers: [91, 1] Generated Node #0,2,3: 90:[91, 1] Operation: 48-47=1 Moving to Node #0,0 Current State: 90:[91, 87, 86], Operations: ['47+39=86'] Exploring Operation: 87+86=173, Resulting Numbers: [91, 173] Generated Node #0,0,0: 90:[91, 173] Operation: 87+86=173 Exploring Operation: 91-87=4, Resulting Numbers: [86, 4] Generated Node #0,0,1: 90:[86, 4] Operation: 91-87=4 Exploring Operation: 91-86=5, Resulting Numbers: [87, 5] Generated Node #0,0,2: 90:[87, 5] Operation: 91-86=5 Exploring Operation: 87-86=1, Resulting Numbers: [91, 1] Generated Node #0,0,3: 90:[91, 1] Operation: 87-86=1 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 90:[91, 1], Operations: ['47+39=86', '87-86=1'] Exploring Operation: 91/1=91, Resulting Numbers: [91] 91,90 unequal: No Solution Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[91, 47, 39, 87], Operations: [] Exploring Operation: 47+39=86, Resulting Numbers: [91, 87, 86] Generated Node #0,0: 90:[91, 87, 86] Operation: 47+39=86 Moving to Node #0,0 Current State: 90:[91, 87, 86], Operations: ['47+39=86'] Exploring Operation: 87-86=1, Resulting Numbers: [91, 1] Generated Node #0,0,3: 90:[91, 1] Operation: 87-86=1 Moving to Node #0,0,3 Current State: 90:[91, 1], Operations: ['47+39=86', '87-86=1'] Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_4
sum_heuristic
[ 16, 41, 82, 92 ]
67
[ "16+41=57", "92-82=10", "57+10=67" ]
Current State: 67:[16, 41, 82, 92], Operations: [] Exploring Operation: 16+41=57, Resulting Numbers: [82, 92, 57] Generated Node #2: [82, 92, 57] from Operation: 16+41=57 Current State: 67:[82, 92, 57], Operations: ['16+41=57'] Exploring Operation: 92-82=10, Resulting Numbers: [57, 10] Generated Node #3: [57, 10] from Operation: 92-82=10 Current State: 67:[57, 10], Operations: ['16+41=57', '92-82=10'] Exploring Operation: 57+10=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[16, 41, 82, 92], Operations: [] Exploring Operation: 92-16=76, Resulting Numbers: [41, 82, 76] Generated Node #0,0: 67:[41, 82, 76] Operation: 92-16=76 Exploring Operation: 16+41=57, Resulting Numbers: [82, 92, 57] Generated Node #0,1: 67:[82, 92, 57] Operation: 16+41=57 Exploring Operation: 82-16=66, Resulting Numbers: [41, 92, 66] Generated Node #0,2: 67:[41, 92, 66] Operation: 82-16=66 Exploring Operation: 41-16=25, Resulting Numbers: [82, 92, 25] Generated Node #0,3: 67:[82, 92, 25] Operation: 41-16=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[41, 82, 76], Operations: ['92-16=76'] Exploring Operation: 41+76=117, Resulting Numbers: [82, 117] Generated Node #0,0,0: 67:[82, 117] Operation: 41+76=117 Exploring Operation: 76-41=35, Resulting Numbers: [82, 35] Generated Node #0,0,1: 67:[82, 35] Operation: 76-41=35 Exploring Operation: 41+82=123, Resulting Numbers: [76, 123] Generated Node #0,0,2: 67:[76, 123] Operation: 41+82=123 Exploring Operation: 82-41=41, Resulting Numbers: [76, 41] Generated Node #0,0,3: 67:[76, 41] Operation: 82-41=41 Moving to Node #0,0,3 Current State: 67:[76, 41], Operations: ['92-16=76', '82-41=41'] Exploring Operation: 76+41=117, Resulting Numbers: [117] 117,67 unequal: No Solution Exploring Operation: 76*41=3116, Resulting Numbers: [3116] 3116,67 unequal: No Solution Exploring Operation: 76-41=35, Resulting Numbers: [35] 35,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[82, 35], Operations: ['92-16=76', '76-41=35'] Exploring Operation: 82-35=47, Resulting Numbers: [47] 47,67 unequal: No Solution Exploring Operation: 82+35=117, Resulting Numbers: [117] 117,67 unequal: No Solution Exploring Operation: 82*35=2870, Resulting Numbers: [2870] 2870,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[76, 123], Operations: ['92-16=76', '41+82=123'] Exploring Operation: 123-76=47, Resulting Numbers: [47] 47,67 unequal: No Solution Exploring Operation: 76+123=199, Resulting Numbers: [199] 199,67 unequal: No Solution Exploring Operation: 76*123=9348, Resulting Numbers: [9348] 9348,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[82, 117], Operations: ['92-16=76', '41+76=117'] Exploring Operation: 82*117=9594, Resulting Numbers: [9594] 9594,67 unequal: No Solution Exploring Operation: 82+117=199, Resulting Numbers: [199] 199,67 unequal: No Solution Exploring Operation: 117-82=35, Resulting Numbers: [35] 35,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[82, 92, 57], Operations: ['16+41=57'] Exploring Operation: 82+57=139, Resulting Numbers: [92, 139] Generated Node #0,1,0: 67:[92, 139] Operation: 82+57=139 Exploring Operation: 92-57=35, Resulting Numbers: [82, 35] Generated Node #0,1,1: 67:[82, 35] Operation: 92-57=35 Exploring Operation: 92-82=10, Resulting Numbers: [57, 10] Generated Node #0,1,2: 67:[57, 10] Operation: 92-82=10 Exploring Operation: 82-57=25, Resulting Numbers: [92, 25] Generated Node #0,1,3: 67:[92, 25] Operation: 82-57=25 Moving to Node #0,1,1 Current State: 67:[82, 35], Operations: ['16+41=57', '92-57=35'] Exploring Operation: 82+35=117, Resulting Numbers: [117] 117,67 unequal: No Solution Exploring Operation: 82-35=47, Resulting Numbers: [47] 47,67 unequal: No Solution Exploring Operation: 82*35=2870, Resulting Numbers: [2870] 2870,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[92, 25], Operations: ['16+41=57', '82-57=25'] Exploring Operation: 92-25=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[16, 41, 82, 92], Operations: [] Exploring Operation: 16+41=57, Resulting Numbers: [82, 92, 57] Generated Node #0,1: 67:[82, 92, 57] Operation: 16+41=57 Moving to Node #0,1 Current State: 67:[82, 92, 57], Operations: ['16+41=57'] Exploring Operation: 82-57=25, Resulting Numbers: [92, 25] Generated Node #0,1,3: 67:[92, 25] Operation: 82-57=25 Moving to Node #0,1,3 Current State: 67:[92, 25], Operations: ['16+41=57', '82-57=25'] Exploring Operation: 92-25=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 12, 37, 20, 30 ]
19
[ "12*30=360", "360/20=18", "37-18=19" ]
Current State: 19:[12, 37, 20, 30], Operations: [] Exploring Operation: 12*30=360, Resulting Numbers: [37, 20, 360] Generated Node #2: [37, 20, 360] from Operation: 12*30=360 Current State: 19:[37, 20, 360], Operations: ['12*30=360'] Exploring Operation: 360/20=18, Resulting Numbers: [37, 18] Generated Node #3: [37, 18] from Operation: 360/20=18 Current State: 19:[37, 18], Operations: ['12*30=360', '360/20=18'] Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[12, 37, 20, 30], Operations: [] Exploring Operation: 30-12=18, Resulting Numbers: [37, 20, 18] Generated Node #0,0: 19:[37, 20, 18] Operation: 30-12=18 Exploring Operation: 37-30=7, Resulting Numbers: [12, 20, 7] Generated Node #0,1: 19:[12, 20, 7] Operation: 37-30=7 Exploring Operation: 37-12=25, Resulting Numbers: [20, 30, 25] Generated Node #0,2: 19:[20, 30, 25] Operation: 37-12=25 Exploring Operation: 37-20=17, Resulting Numbers: [12, 30, 17] Generated Node #0,3: 19:[12, 30, 17] Operation: 37-20=17 Exploring Operation: 30-20=10, Resulting Numbers: [12, 37, 10] Generated Node #0,4: 19:[12, 37, 10] Operation: 30-20=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[20, 30, 25], Operations: ['37-12=25'] Exploring Operation: 30-25=5, Resulting Numbers: [20, 5] Generated Node #0,2,0: 19:[20, 5] Operation: 30-25=5 Exploring Operation: 20+25=45, Resulting Numbers: [30, 45] Generated Node #0,2,1: 19:[30, 45] Operation: 20+25=45 Exploring Operation: 30-20=10, Resulting Numbers: [25, 10] Generated Node #0,2,2: 19:[25, 10] Operation: 30-20=10 Exploring Operation: 20+30=50, Resulting Numbers: [25, 50] Generated Node #0,2,3: 19:[25, 50] Operation: 20+30=50 Exploring Operation: 25-20=5, Resulting Numbers: [30, 5] Generated Node #0,2,4: 19:[30, 5] Operation: 25-20=5 Moving to Node #0,2,0 Current State: 19:[20, 5], Operations: ['37-12=25', '30-25=5'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,19 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,19 unequal: No Solution Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,19 unequal: No Solution Moving to Node #0,2,2 Current State: 19:[25, 10], Operations: ['37-12=25', '30-20=10'] Exploring Operation: 25*10=250, Resulting Numbers: [250] 250,19 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,19 unequal: No Solution Exploring Operation: 25+10=35, Resulting Numbers: [35] 35,19 unequal: No Solution Moving to Node #0,2,4 Current State: 19:[30, 5], Operations: ['37-12=25', '25-20=5'] Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,19 unequal: No Solution Exploring Operation: 30*5=150, Resulting Numbers: [150] 150,19 unequal: No Solution Moving to Node #0,2,1 Current State: 19:[30, 45], Operations: ['37-12=25', '20+25=45'] Exploring Operation: 30*45=1350, Resulting Numbers: [1350] 1350,19 unequal: No Solution Exploring Operation: 45-30=15, Resulting Numbers: [15] 15,19 unequal: No Solution Exploring Operation: 30+45=75, Resulting Numbers: [75] 75,19 unequal: No Solution Moving to Node #0,2,3 Current State: 19:[25, 50], Operations: ['37-12=25', '20+30=50'] Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 25+50=75, Resulting Numbers: [75] 75,19 unequal: No Solution Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 25*50=1250, Resulting Numbers: [1250] 1250,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[37, 20, 18], Operations: ['30-12=18'] Exploring Operation: 37-18=19, Resulting Numbers: [20, 19] Generated Node #0,0,0: 19:[20, 19] Operation: 37-18=19 Exploring Operation: 20+18=38, Resulting Numbers: [37, 38] Generated Node #0,0,1: 19:[37, 38] Operation: 20+18=38 Exploring Operation: 37-20=17, Resulting Numbers: [18, 17] Generated Node #0,0,2: 19:[18, 17] Operation: 37-20=17 Exploring Operation: 37+18=55, Resulting Numbers: [20, 55] Generated Node #0,0,3: 19:[20, 55] Operation: 37+18=55 Exploring Operation: 20-18=2, Resulting Numbers: [37, 2] Generated Node #0,0,4: 19:[37, 2] Operation: 20-18=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[20, 19], Operations: ['30-12=18', '37-18=19'] Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 20*19=380, Resulting Numbers: [380] 380,19 unequal: No Solution Exploring Operation: 20+19=39, Resulting Numbers: [39] 39,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 19:[18, 17], Operations: ['30-12=18', '37-20=17'] Exploring Operation: 18*17=306, Resulting Numbers: [306] 306,19 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 19:[37, 2], Operations: ['30-12=18', '20-18=2'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,19 unequal: No Solution Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 19:[37, 38], Operations: ['30-12=18', '20+18=38'] Exploring Operation: 38-37=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 37*38=1406, Resulting Numbers: [1406] 1406,19 unequal: No Solution Exploring Operation: 37+38=75, Resulting Numbers: [75] 75,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 19:[20, 55], Operations: ['30-12=18', '37+18=55'] Exploring Operation: 20+55=75, Resulting Numbers: [75] 75,19 unequal: No Solution Exploring Operation: 20*55=1100, Resulting Numbers: [1100] 1100,19 unequal: No Solution Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[12, 20, 7], Operations: ['37-30=7'] Exploring Operation: 12+7=19, Resulting Numbers: [20, 19] Generated Node #0,1,0: 19:[20, 19] Operation: 12+7=19 Exploring Operation: 20-7=13, Resulting Numbers: [12, 13] Generated Node #0,1,1: 19:[12, 13] Operation: 20-7=13 Exploring Operation: 12-7=5, Resulting Numbers: [20, 5] Generated Node #0,1,2: 19:[20, 5] Operation: 12-7=5 Exploring Operation: 20+7=27, Resulting Numbers: [12, 27] Generated Node #0,1,3: 19:[12, 27] Operation: 20+7=27 Exploring Operation: 20-12=8, Resulting Numbers: [7, 8] Generated Node #0,1,4: 19:[7, 8] Operation: 20-12=8 Moving to Node #0,1,0 Current State: 19:[20, 19], Operations: ['37-30=7', '12+7=19'] Exploring Operation: 20*19=380, Resulting Numbers: [380] 380,19 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 20+19=39, Resulting Numbers: [39] 39,19 unequal: No Solution Moving to Node #0,1,1 Current State: 19:[12, 13], Operations: ['37-30=7', '20-7=13'] Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,19 unequal: No Solution Moving to Node #0,1,2 Current State: 19:[20, 5], Operations: ['37-30=7', '12-7=5'] Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,19 unequal: No Solution Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,19 unequal: No Solution Moving to Node #0,1,3 Current State: 19:[12, 27], Operations: ['37-30=7', '20+7=27'] Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,19 unequal: No Solution Exploring Operation: 12*27=324, Resulting Numbers: [324] 324,19 unequal: No Solution Exploring Operation: 12+27=39, Resulting Numbers: [39] 39,19 unequal: No Solution Moving to Node #0,1,4 Current State: 19:[7, 8], Operations: ['37-30=7', '20-12=8'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,19 unequal: No Solution Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 19:[12, 30, 17], Operations: ['37-20=17'] Exploring Operation: 12+30=42, Resulting Numbers: [17, 42] Generated Node #0,3,0: 19:[17, 42] Operation: 12+30=42 Exploring Operation: 30-17=13, Resulting Numbers: [12, 13] Generated Node #0,3,1: 19:[12, 13] Operation: 30-17=13 Exploring Operation: 17-12=5, Resulting Numbers: [30, 5] Generated Node #0,3,2: 19:[30, 5] Operation: 17-12=5 Exploring Operation: 30-12=18, Resulting Numbers: [17, 18] Generated Node #0,3,3: 19:[17, 18] Operation: 30-12=18 Exploring Operation: 12+17=29, Resulting Numbers: [30, 29] Generated Node #0,3,4: 19:[30, 29] Operation: 12+17=29 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 19:[17, 18], Operations: ['37-20=17', '30-12=18'] Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 17*18=306, Resulting Numbers: [306] 306,19 unequal: No Solution Exploring Operation: 17+18=35, Resulting Numbers: [35] 35,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 19:[12, 13], Operations: ['37-20=17', '30-17=13'] Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,19 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 19:[30, 29], Operations: ['37-20=17', '12+17=29'] Exploring Operation: 30*29=870, Resulting Numbers: [870] 870,19 unequal: No Solution Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 30+29=59, Resulting Numbers: [59] 59,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 19:[17, 42], Operations: ['37-20=17', '12+30=42'] Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 17*42=714, Resulting Numbers: [714] 714,19 unequal: No Solution Exploring Operation: 17+42=59, Resulting Numbers: [59] 59,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 19:[30, 5], Operations: ['37-20=17', '17-12=5'] Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,19 unequal: No Solution Exploring Operation: 30*5=150, Resulting Numbers: [150] 150,19 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 19:[12, 37, 10], Operations: ['30-20=10'] Exploring Operation: 12+10=22, Resulting Numbers: [37, 22] Generated Node #0,4,0: 19:[37, 22] Operation: 12+10=22 Exploring Operation: 37+10=47, Resulting Numbers: [12, 47] Generated Node #0,4,1: 19:[12, 47] Operation: 37+10=47 Exploring Operation: 37-12=25, Resulting Numbers: [10, 25] Generated Node #0,4,2: 19:[10, 25] Operation: 37-12=25 Exploring Operation: 12-10=2, Resulting Numbers: [37, 2] Generated Node #0,4,3: 19:[37, 2] Operation: 12-10=2 Exploring Operation: 37-10=27, Resulting Numbers: [12, 27] Generated Node #0,4,4: 19:[12, 27] Operation: 37-10=27 Moving to Node #0,4,2 Current State: 19:[10, 25], Operations: ['30-20=10', '37-12=25'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,19 unequal: No Solution Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,19 unequal: No Solution Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,19 unequal: No Solution Moving to Node #0,4,4 Current State: 19:[12, 27], Operations: ['30-20=10', '37-10=27'] Exploring Operation: 12+27=39, Resulting Numbers: [39] 39,19 unequal: No Solution Exploring Operation: 12*27=324, Resulting Numbers: [324] 324,19 unequal: No Solution Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,19 unequal: No Solution Moving to Node #0,4,0 Current State: 19:[37, 22], Operations: ['30-20=10', '12+10=22'] Exploring Operation: 37*22=814, Resulting Numbers: [814] 814,19 unequal: No Solution Exploring Operation: 37+22=59, Resulting Numbers: [59] 59,19 unequal: No Solution Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,19 unequal: No Solution Moving to Node #0,4,1 Current State: 19:[12, 47], Operations: ['30-20=10', '37+10=47'] Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 12+47=59, Resulting Numbers: [59] 59,19 unequal: No Solution Exploring Operation: 12*47=564, Resulting Numbers: [564] 564,19 unequal: No Solution Moving to Node #0,4,3 Current State: 19:[37, 2], Operations: ['30-20=10', '12-10=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,19 unequal: No Solution Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,19 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,19 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
[ 23, 34, 37, 2 ]
50
[ "34-23=11", "37+2=39", "11+39=50" ]
Current State: 50:[23, 34, 37, 2], Operations: [] Exploring Operation: 34-23=11, Resulting Numbers: [37, 2, 11] Generated Node #2: [37, 2, 11] from Operation: 34-23=11 Current State: 50:[37, 2, 11], Operations: ['34-23=11'] Exploring Operation: 37+2=39, Resulting Numbers: [11, 39] Generated Node #3: [11, 39] from Operation: 37+2=39 Current State: 50:[11, 39], Operations: ['34-23=11', '37+2=39'] Exploring Operation: 11+39=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[23, 34, 37, 2], Operations: [] Exploring Operation: 37-23=14, Resulting Numbers: [34, 2, 14] Generated Node #0,0: 50:[34, 2, 14] Operation: 37-23=14 Exploring Operation: 37-34=3, Resulting Numbers: [23, 2, 3] Generated Node #0,1: 50:[23, 2, 3] Operation: 37-34=3 Exploring Operation: 34-23=11, Resulting Numbers: [37, 2, 11] Generated Node #0,2: 50:[37, 2, 11] Operation: 34-23=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[23, 2, 3], Operations: ['37-34=3'] Exploring Operation: 2+3=5, Resulting Numbers: [23, 5] Generated Node #0,1,0: 50:[23, 5] Operation: 2+3=5 Exploring Operation: 23+2=25, Resulting Numbers: [3, 25] Generated Node #0,1,1: 50:[3, 25] Operation: 23+2=25 Exploring Operation: 23+3=26, Resulting Numbers: [2, 26] Generated Node #0,1,2: 50:[2, 26] Operation: 23+3=26 Moving to Node #0,1,1 Current State: 50:[3, 25], Operations: ['37-34=3', '23+2=25'] Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,50 unequal: No Solution Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,50 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,50 unequal: No Solution Moving to Node #0,1,2 Current State: 50:[2, 26], Operations: ['37-34=3', '23+3=26'] Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,50 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,50 unequal: No Solution Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,50 unequal: No Solution Moving to Node #0,1,0 Current State: 50:[23, 5], Operations: ['37-34=3', '2+3=5'] Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,50 unequal: No Solution Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,50 unequal: No Solution Exploring Operation: 23*5=115, Resulting Numbers: [115] 115,50 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 #0,0 Current State: 50:[34, 2, 14], Operations: ['37-23=14'] Exploring Operation: 34+14=48, Resulting Numbers: [2, 48] Generated Node #0,0,0: 50:[2, 48] Operation: 34+14=48 Exploring Operation: 34-2=32, Resulting Numbers: [14, 32] Generated Node #0,0,1: 50:[14, 32] Operation: 34-2=32 Exploring Operation: 34-14=20, Resulting Numbers: [2, 20] Generated Node #0,0,2: 50:[2, 20] Operation: 34-14=20 Moving to Node #0,0,0 Current State: 50:[2, 48], Operations: ['37-23=14', '34+14=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[23, 34, 37, 2], Operations: [] Exploring Operation: 37-23=14, Resulting Numbers: [34, 2, 14] Generated Node #0,0: 50:[34, 2, 14] Operation: 37-23=14 Moving to Node #0,0 Current State: 50:[34, 2, 14], Operations: ['37-23=14'] Exploring Operation: 34+14=48, Resulting Numbers: [2, 48] Generated Node #0,0,0: 50:[2, 48] Operation: 34+14=48 Moving to Node #0,0,0 Current State: 50:[2, 48], Operations: ['37-23=14', '34+14=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 46, 54, 72, 44 ]
13
[ "54*44=2376", "2376/72=33", "46-33=13" ]
Current State: 13:[46, 54, 72, 44], Operations: [] Exploring Operation: 54*44=2376, Resulting Numbers: [46, 72, 2376] Generated Node #2: [46, 72, 2376] from Operation: 54*44=2376 Current State: 13:[46, 72, 2376], Operations: ['54*44=2376'] Exploring Operation: 2376/72=33, Resulting Numbers: [46, 33] Generated Node #3: [46, 33] from Operation: 2376/72=33 Current State: 13:[46, 33], Operations: ['54*44=2376', '2376/72=33'] Exploring Operation: 46-33=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[46, 54, 72, 44], Operations: [] Exploring Operation: 72-54=18, Resulting Numbers: [46, 44, 18] Generated Node #0,0: 13:[46, 44, 18] Operation: 72-54=18 Exploring Operation: 72-46=26, Resulting Numbers: [54, 44, 26] Generated Node #0,1: 13:[54, 44, 26] Operation: 72-46=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[46, 44, 18], Operations: ['72-54=18'] Exploring Operation: 46-44=2, Resulting Numbers: [18, 2] Generated Node #0,0,0: 13:[18, 2] Operation: 46-44=2 Exploring Operation: 46-18=28, Resulting Numbers: [44, 28] Generated Node #0,0,1: 13:[44, 28] Operation: 46-18=28 Moving to Node #0,0,0 Current State: 13:[18, 2], Operations: ['72-54=18', '46-44=2'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[44, 28], Operations: ['72-54=18', '46-18=28'] Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 44+28=72, Resulting Numbers: [72] 72,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[54, 44, 26], Operations: ['72-46=26'] Exploring Operation: 54-44=10, Resulting Numbers: [26, 10] Generated Node #0,1,0: 13:[26, 10] Operation: 54-44=10 Exploring Operation: 54-26=28, Resulting Numbers: [44, 28] Generated Node #0,1,1: 13:[44, 28] Operation: 54-26=28 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 13:[26, 10], Operations: ['72-46=26', '54-44=10'] Exploring Operation: 26+10=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[44, 28], Operations: ['72-46=26', '54-26=28'] Exploring Operation: 44+28=72, Resulting Numbers: [72] 72,13 unequal: No Solution Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 18, 36, 36, 6 ]
15
[ "18+36=54", "36+54=90", "90/6=15" ]
Current State: 15:[18, 36, 36, 6], Operations: [] Exploring Operation: 18+36=54, Resulting Numbers: [6, 54] Generated Node #2: [6, 54] from Operation: 18+36=54 Current State: 15:[6, 54], Operations: ['18+36=54'] Exploring Operation: 36+54=90, Resulting Numbers: [6, 90] Generated Node #3: [6, 90] from Operation: 36+54=90 Current State: 15:[6, 90], Operations: ['18+36=54', '36+54=90'] Exploring Operation: 90/6=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[18, 36, 36, 6], Operations: [] Exploring Operation: 36/36=1, Resulting Numbers: [18, 6, 1] Generated Node #0,0: 15:[18, 6, 1] Operation: 36/36=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[18, 6, 1], Operations: ['36/36=1'] Exploring Operation: 18/6=3, Resulting Numbers: [1, 3] Generated Node #0,0,0: 15:[1, 3] Operation: 18/6=3 Moving to Node #0,0,0 Current State: 15:[1, 3], Operations: ['36/36=1', '18/6=3'] Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 75, 8, 11, 21 ]
23
[ "75+21=96", "96/8=12", "11+12=23" ]
Current State: 23:[75, 8, 11, 21], Operations: [] Exploring Operation: 75+21=96, Resulting Numbers: [8, 11, 96] Generated Node #2: [8, 11, 96] from Operation: 75+21=96 Current State: 23:[8, 11, 96], Operations: ['75+21=96'] Exploring Operation: 96/8=12, Resulting Numbers: [11, 12] Generated Node #3: [11, 12] from Operation: 96/8=12 Current State: 23:[11, 12], Operations: ['75+21=96', '96/8=12'] Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[75, 8, 11, 21], Operations: [] Exploring Operation: 75-21=54, Resulting Numbers: [8, 11, 54] Generated Node #0,0: 23:[8, 11, 54] Operation: 75-21=54 Exploring Operation: 8+21=29, Resulting Numbers: [75, 11, 29] Generated Node #0,1: 23:[75, 11, 29] Operation: 8+21=29 Exploring Operation: 8+11=19, Resulting Numbers: [75, 21, 19] Generated Node #0,2: 23:[75, 21, 19] Operation: 8+11=19 Exploring Operation: 75-11=64, Resulting Numbers: [8, 21, 64] Generated Node #0,3: 23:[8, 21, 64] Operation: 75-11=64 Exploring Operation: 75-8=67, Resulting Numbers: [11, 21, 67] Generated Node #0,4: 23:[11, 21, 67] Operation: 75-8=67 Moving to Node #0,0 Current State: 23:[8, 11, 54], Operations: ['75-21=54'] Exploring Operation: 8+11=19, Resulting Numbers: [54, 19] Generated Node #0,0,0: 23:[54, 19] Operation: 8+11=19 Exploring Operation: 11-8=3, Resulting Numbers: [54, 3] Generated Node #0,0,1: 23:[54, 3] Operation: 11-8=3 Exploring Operation: 8+54=62, Resulting Numbers: [11, 62] Generated Node #0,0,2: 23:[11, 62] Operation: 8+54=62 Exploring Operation: 54-11=43, Resulting Numbers: [8, 43] Generated Node #0,0,3: 23:[8, 43] Operation: 54-11=43 Exploring Operation: 54-8=46, Resulting Numbers: [11, 46] Generated Node #0,0,4: 23:[11, 46] Operation: 54-8=46 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 23:[54, 19], Operations: ['75-21=54', '8+11=19'] Exploring Operation: 54-19=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 54*19=1026, Resulting Numbers: [1026] 1026,23 unequal: No Solution Exploring Operation: 54+19=73, Resulting Numbers: [73] 73,23 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 #0,0,3 Current State: 23:[8, 43], Operations: ['75-21=54', '54-11=43'] Exploring Operation: 8*43=344, Resulting Numbers: [344] 344,23 unequal: No Solution Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,23 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 #0,0,4 Current State: 23:[11, 46], Operations: ['75-21=54', '54-8=46'] Exploring Operation: 11*46=506, Resulting Numbers: [506] 506,23 unequal: No Solution Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 11+46=57, Resulting Numbers: [57] 57,23 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 #0,0,1 Current State: 23:[54, 3], Operations: ['75-21=54', '11-8=3'] Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,23 unequal: No Solution Exploring Operation: 54*3=162, Resulting Numbers: [162] 162,23 unequal: No Solution Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,23 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 #0,0,2 Current State: 23:[11, 62], Operations: ['75-21=54', '8+54=62'] Exploring Operation: 11+62=73, Resulting Numbers: [73] 73,23 unequal: No Solution Exploring Operation: 62-11=51, Resulting Numbers: [51] 51,23 unequal: No Solution Exploring Operation: 11*62=682, Resulting Numbers: [682] 682,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 23:[8, 21, 64], Operations: ['75-11=64'] Exploring Operation: 21-8=13, Resulting Numbers: [64, 13] Generated Node #0,3,0: 23:[64, 13] Operation: 21-8=13 Exploring Operation: 64/8=8, Resulting Numbers: [21, 8] Generated Node #0,3,1: 23:[21, 8] Operation: 64/8=8 Exploring Operation: 8+21=29, Resulting Numbers: [64, 29] Generated Node #0,3,2: 23:[64, 29] Operation: 8+21=29 Exploring Operation: 64-21=43, Resulting Numbers: [8, 43] Generated Node #0,3,3: 23:[8, 43] Operation: 64-21=43 Exploring Operation: 64-8=56, Resulting Numbers: [21, 56] Generated Node #0,3,4: 23:[21, 56] Operation: 64-8=56 Moving to Node #0,2 Current State: 23:[75, 21, 19], Operations: ['8+11=19'] Exploring Operation: 75-21=54, Resulting Numbers: [19, 54] Generated Node #0,2,0: 23:[19, 54] Operation: 75-21=54 Exploring Operation: 75-19=56, Resulting Numbers: [21, 56] Generated Node #0,2,1: 23:[21, 56] Operation: 75-19=56 Exploring Operation: 75+19=94, Resulting Numbers: [21, 94] Generated Node #0,2,2: 23:[21, 94] Operation: 75+19=94 Exploring Operation: 21-19=2, Resulting Numbers: [75, 2] Generated Node #0,2,3: 23:[75, 2] Operation: 21-19=2 Exploring Operation: 21+19=40, Resulting Numbers: [75, 40] Generated Node #0,2,4: 23:[75, 40] Operation: 21+19=40 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 23:[19, 54], Operations: ['8+11=19', '75-21=54'] Exploring Operation: 19+54=73, Resulting Numbers: [73] 73,23 unequal: No Solution Exploring Operation: 19*54=1026, Resulting Numbers: [1026] 1026,23 unequal: No Solution Exploring Operation: 54-19=35, Resulting Numbers: [35] 35,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[21, 56], Operations: ['8+11=19', '75-19=56'] Exploring Operation: 56-21=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 21*56=1176, Resulting Numbers: [1176] 1176,23 unequal: No Solution Exploring Operation: 21+56=77, Resulting Numbers: [77] 77,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 23:[75, 40], Operations: ['8+11=19', '21+19=40'] Exploring Operation: 75*40=3000, Resulting Numbers: [3000] 3000,23 unequal: No Solution Exploring Operation: 75-40=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 75+40=115, Resulting Numbers: [115] 115,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 23:[21, 94], Operations: ['8+11=19', '75+19=94'] Exploring Operation: 94-21=73, Resulting Numbers: [73] 73,23 unequal: No Solution Exploring Operation: 21+94=115, Resulting Numbers: [115] 115,23 unequal: No Solution Exploring Operation: 21*94=1974, Resulting Numbers: [1974] 1974,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 23:[75, 2], Operations: ['8+11=19', '21-19=2'] Exploring Operation: 75+2=77, Resulting Numbers: [77] 77,23 unequal: No Solution Exploring Operation: 75*2=150, Resulting Numbers: [150] 150,23 unequal: No Solution Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,23 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: 23:[11, 21, 67], Operations: ['75-8=67'] Exploring Operation: 67-21=46, Resulting Numbers: [11, 46] Generated Node #0,4,0: 23:[11, 46] Operation: 67-21=46 Exploring Operation: 11+67=78, Resulting Numbers: [21, 78] Generated Node #0,4,1: 23:[21, 78] Operation: 11+67=78 Exploring Operation: 11+21=32, Resulting Numbers: [67, 32] Generated Node #0,4,2: 23:[67, 32] Operation: 11+21=32 Exploring Operation: 21-11=10, Resulting Numbers: [67, 10] Generated Node #0,4,3: 23:[67, 10] Operation: 21-11=10 Exploring Operation: 67-11=56, Resulting Numbers: [21, 56] Generated Node #0,4,4: 23:[21, 56] Operation: 67-11=56 Moving to Node #0,1 Current State: 23:[75, 11, 29], Operations: ['8+21=29'] Exploring Operation: 11+29=40, Resulting Numbers: [75, 40] Generated Node #0,1,0: 23:[75, 40] Operation: 11+29=40 Exploring Operation: 75+11=86, Resulting Numbers: [29, 86] Generated Node #0,1,1: 23:[29, 86] Operation: 75+11=86 Exploring Operation: 75-29=46, Resulting Numbers: [11, 46] Generated Node #0,1,2: 23:[11, 46] Operation: 75-29=46 Exploring Operation: 29-11=18, Resulting Numbers: [75, 18] Generated Node #0,1,3: 23:[75, 18] Operation: 29-11=18 Exploring Operation: 75-11=64, Resulting Numbers: [29, 64] Generated Node #0,1,4: 23:[29, 64] Operation: 75-11=64 Moving to Node #0,3,1 Current State: 23:[21, 8], Operations: ['75-11=64', '64/8=8'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,23 unequal: No Solution Exploring Operation: 21*8=168, Resulting Numbers: [168] 168,23 unequal: No Solution Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,23 unequal: No Solution Moving to Node #0,3,4 Current State: 23:[21, 56], Operations: ['75-11=64', '64-8=56'] Exploring Operation: 21+56=77, Resulting Numbers: [77] 77,23 unequal: No Solution Exploring Operation: 21*56=1176, Resulting Numbers: [1176] 1176,23 unequal: No Solution Exploring Operation: 56-21=35, Resulting Numbers: [35] 35,23 unequal: No Solution Moving to Node #0,4,4 Current State: 23:[21, 56], Operations: ['75-8=67', '67-11=56'] Exploring Operation: 56-21=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 21+56=77, Resulting Numbers: [77] 77,23 unequal: No Solution Exploring Operation: 21*56=1176, Resulting Numbers: [1176] 1176,23 unequal: No Solution Moving to Node #0,4,0 Current State: 23:[11, 46], Operations: ['75-8=67', '67-21=46'] Exploring Operation: 11+46=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 11*46=506, Resulting Numbers: [506] 506,23 unequal: No Solution Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[8, 43], Operations: ['75-11=64', '64-21=43'] Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,23 unequal: No Solution Exploring Operation: 8*43=344, Resulting Numbers: [344] 344,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[11, 46], Operations: ['8+21=29', '75-29=46'] Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 11*46=506, Resulting Numbers: [506] 506,23 unequal: No Solution Exploring Operation: 11+46=57, Resulting Numbers: [57] 57,23 unequal: No Solution Moving to Node #0,1,4 Current State: 23:[29, 64], Operations: ['8+21=29', '75-11=64'] Exploring Operation: 64-29=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 29+64=93, Resulting Numbers: [93] 93,23 unequal: No Solution Exploring Operation: 29*64=1856, Resulting Numbers: [1856] 1856,23 unequal: No Solution Moving to Node #0,3,2 Current State: 23:[64, 29], Operations: ['75-11=64', '8+21=29'] Exploring Operation: 64+29=93, Resulting Numbers: [93] 93,23 unequal: No Solution Exploring Operation: 64*29=1856, Resulting Numbers: [1856] 1856,23 unequal: No Solution Exploring Operation: 64-29=35, Resulting Numbers: [35] 35,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[64, 13], Operations: ['75-11=64', '21-8=13'] Exploring Operation: 64+13=77, Resulting Numbers: [77] 77,23 unequal: No Solution Exploring Operation: 64-13=51, Resulting Numbers: [51] 51,23 unequal: No Solution Exploring Operation: 64*13=832, Resulting Numbers: [832] 832,23 unequal: No Solution Moving to Node #0,4,2 Current State: 23:[67, 32], Operations: ['75-8=67', '11+21=32'] Exploring Operation: 67*32=2144, Resulting Numbers: [2144] 2144,23 unequal: No Solution Exploring Operation: 67-32=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 67+32=99, Resulting Numbers: [99] 99,23 unequal: No Solution Moving to Node #0,1,3 Current State: 23:[75, 18], Operations: ['8+21=29', '29-11=18'] Exploring Operation: 75-18=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 75*18=1350, Resulting Numbers: [1350] 1350,23 unequal: No Solution Exploring Operation: 75+18=93, Resulting Numbers: [93] 93,23 unequal: No Solution Moving to Node #0,4,3 Current State: 23:[67, 10], Operations: ['75-8=67', '21-11=10'] Exploring Operation: 67-10=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 67+10=77, Resulting Numbers: [77] 77,23 unequal: No Solution Exploring Operation: 67*10=670, Resulting Numbers: [670] 670,23 unequal: No Solution Moving to Node #0,4,1 Current State: 23:[21, 78], Operations: ['75-8=67', '11+67=78'] Exploring Operation: 78-21=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 21*78=1638, Resulting Numbers: [1638] 1638,23 unequal: No Solution Exploring Operation: 21+78=99, Resulting Numbers: [99] 99,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[29, 86], Operations: ['8+21=29', '75+11=86'] Exploring Operation: 29*86=2494, Resulting Numbers: [2494] 2494,23 unequal: No Solution Exploring Operation: 29+86=115, Resulting Numbers: [115] 115,23 unequal: No Solution Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[75, 40], Operations: ['8+21=29', '11+29=40'] Exploring Operation: 75*40=3000, Resulting Numbers: [3000] 3000,23 unequal: No Solution Exploring Operation: 75-40=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 75+40=115, Resulting Numbers: [115] 115,23 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 29, 56, 88, 15 ]
100
[ "56-29=27", "88-15=73", "27+73=100" ]
Current State: 100:[29, 56, 88, 15], Operations: [] Exploring Operation: 56-29=27, Resulting Numbers: [88, 15, 27] Generated Node #2: [88, 15, 27] from Operation: 56-29=27 Current State: 100:[88, 15, 27], Operations: ['56-29=27'] Exploring Operation: 88-15=73, Resulting Numbers: [27, 73] Generated Node #3: [27, 73] from Operation: 88-15=73 Current State: 100:[27, 73], Operations: ['56-29=27', '88-15=73'] Exploring Operation: 27+73=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[29, 56, 88, 15], Operations: [] Exploring Operation: 88+15=103, Resulting Numbers: [29, 56, 103] Generated Node #0,0: 100:[29, 56, 103] Operation: 88+15=103 Exploring Operation: 88-29=59, Resulting Numbers: [56, 15, 59] Generated Node #0,1: 100:[56, 15, 59] Operation: 88-29=59 Exploring Operation: 88-56=32, Resulting Numbers: [29, 15, 32] Generated Node #0,2: 100:[29, 15, 32] Operation: 88-56=32 Exploring Operation: 56-29=27, Resulting Numbers: [88, 15, 27] Generated Node #0,3: 100:[88, 15, 27] Operation: 56-29=27 Moving to Node #0,0 Current State: 100:[29, 56, 103], Operations: ['88+15=103'] Exploring Operation: 103-29=74, Resulting Numbers: [56, 74] Generated Node #0,0,0: 100:[56, 74] Operation: 103-29=74 Exploring Operation: 56-29=27, Resulting Numbers: [103, 27] Generated Node #0,0,1: 100:[103, 27] Operation: 56-29=27 Exploring Operation: 103-56=47, Resulting Numbers: [29, 47] Generated Node #0,0,2: 100:[29, 47] Operation: 103-56=47 Exploring Operation: 29+56=85, Resulting Numbers: [103, 85] Generated Node #0,0,3: 100:[103, 85] Operation: 29+56=85 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[103, 27], Operations: ['88+15=103', '56-29=27'] Exploring Operation: 103-27=76, Resulting Numbers: [76] 76,100 unequal: No Solution Exploring Operation: 103+27=130, Resulting Numbers: [130] 130,100 unequal: No Solution Exploring Operation: 103*27=2781, Resulting Numbers: [2781] 2781,100 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 #0,0,2 Current State: 100:[29, 47], Operations: ['88+15=103', '103-56=47'] Exploring Operation: 29+47=76, Resulting Numbers: [76] 76,100 unequal: No Solution Exploring Operation: 29*47=1363, Resulting Numbers: [1363] 1363,100 unequal: No Solution Exploring Operation: 47-29=18, Resulting Numbers: [18] 18,100 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 #0,0,3 Current State: 100:[103, 85], Operations: ['88+15=103', '29+56=85'] Exploring Operation: 103-85=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 103+85=188, Resulting Numbers: [188] 188,100 unequal: No Solution Exploring Operation: 103*85=8755, Resulting Numbers: [8755] 8755,100 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 #0,0,0 Current State: 100:[56, 74], Operations: ['88+15=103', '103-29=74'] Exploring Operation: 56+74=130, Resulting Numbers: [130] 130,100 unequal: No Solution Exploring Operation: 74-56=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 56*74=4144, Resulting Numbers: [4144] 4144,100 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: 100:[29, 15, 32], Operations: ['88-56=32'] Exploring Operation: 32-15=17, Resulting Numbers: [29, 17] Generated Node #0,2,0: 100:[29, 17] Operation: 32-15=17 Exploring Operation: 32-29=3, Resulting Numbers: [15, 3] Generated Node #0,2,1: 100:[15, 3] Operation: 32-29=3 Exploring Operation: 15+32=47, Resulting Numbers: [29, 47] Generated Node #0,2,2: 100:[29, 47] Operation: 15+32=47 Exploring Operation: 29-15=14, Resulting Numbers: [32, 14] Generated Node #0,2,3: 100:[32, 14] Operation: 29-15=14 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 100:[15, 3], Operations: ['88-56=32', '32-29=3'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,100 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,100 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 #0,2,0 Current State: 100:[29, 17], Operations: ['88-56=32', '32-15=17'] Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 29+17=46, Resulting Numbers: [46] 46,100 unequal: No Solution Exploring Operation: 29*17=493, Resulting Numbers: [493] 493,100 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 #0,2,2 Current State: 100:[29, 47], Operations: ['88-56=32', '15+32=47'] Exploring Operation: 29*47=1363, Resulting Numbers: [1363] 1363,100 unequal: No Solution Exploring Operation: 47-29=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 29+47=76, Resulting Numbers: [76] 76,100 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 #0,2,3 Current State: 100:[32, 14], Operations: ['88-56=32', '29-15=14'] Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 32+14=46, Resulting Numbers: [46] 46,100 unequal: No Solution Exploring Operation: 32*14=448, Resulting Numbers: [448] 448,100 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: 100:[88, 15, 27], Operations: ['56-29=27'] Exploring Operation: 88-27=61, Resulting Numbers: [15, 61] Generated Node #0,3,0: 100:[15, 61] Operation: 88-27=61 Exploring Operation: 88+27=115, Resulting Numbers: [15, 115] Generated Node #0,3,1: 100:[15, 115] Operation: 88+27=115 Exploring Operation: 88+15=103, Resulting Numbers: [27, 103] Generated Node #0,3,2: 100:[27, 103] Operation: 88+15=103 Exploring Operation: 27-15=12, Resulting Numbers: [88, 12] Generated Node #0,3,3: 100:[88, 12] Operation: 27-15=12 Moving to Node #0,1 Current State: 100:[56, 15, 59], Operations: ['88-29=59'] Exploring Operation: 59-56=3, Resulting Numbers: [15, 3] Generated Node #0,1,0: 100:[15, 3] Operation: 59-56=3 Exploring Operation: 59-15=44, Resulting Numbers: [56, 44] Generated Node #0,1,1: 100:[56, 44] Operation: 59-15=44 Exploring Operation: 56-15=41, Resulting Numbers: [59, 41] Generated Node #0,1,2: 100:[59, 41] Operation: 56-15=41 Exploring Operation: 56+59=115, Resulting Numbers: [15, 115] Generated Node #0,1,3: 100:[15, 115] Operation: 56+59=115 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 100:[15, 3], Operations: ['88-29=59', '59-56=3'] Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,100 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,100 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 #0,1,1 Current State: 100:[56, 44], Operations: ['88-29=59', '59-15=44'] Exploring Operation: 56-44=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 56+44=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[29, 56, 88, 15], Operations: [] Exploring Operation: 88-29=59, Resulting Numbers: [56, 15, 59] Generated Node #0,1: 100:[56, 15, 59] Operation: 88-29=59 Moving to Node #0,1 Current State: 100:[56, 15, 59], Operations: ['88-29=59'] Exploring Operation: 59-15=44, Resulting Numbers: [56, 44] Generated Node #0,1,1: 100:[56, 44] Operation: 59-15=44 Moving to Node #0,1,1 Current State: 100:[56, 44], Operations: ['88-29=59', '59-15=44'] Exploring Operation: 56+44=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.952257
hs_4
sum_heuristic
[ 23, 73, 75, 63 ]
42
[ "23+73=96", "75+63=138", "138-96=42" ]
Current State: 42:[23, 73, 75, 63], Operations: [] Exploring Operation: 23+73=96, Resulting Numbers: [75, 63, 96] Generated Node #2: [75, 63, 96] from Operation: 23+73=96 Current State: 42:[75, 63, 96], Operations: ['23+73=96'] Exploring Operation: 75+63=138, Resulting Numbers: [96, 138] Generated Node #3: [96, 138] from Operation: 75+63=138 Current State: 42:[96, 138], Operations: ['23+73=96', '75+63=138'] Exploring Operation: 138-96=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[23, 73, 75, 63], Operations: [] Exploring Operation: 75-63=12, Resulting Numbers: [23, 73, 12] Generated Node #0,0: 42:[23, 73, 12] Operation: 75-63=12 Exploring Operation: 75-73=2, Resulting Numbers: [23, 63, 2] Generated Node #0,1: 42:[23, 63, 2] Operation: 75-73=2 Moving to Node #0,1 Current State: 42:[23, 63, 2], Operations: ['75-73=2'] Exploring Operation: 63-23=40, Resulting Numbers: [2, 40] Generated Node #0,1,0: 42:[2, 40] Operation: 63-23=40 Exploring Operation: 23-2=21, Resulting Numbers: [63, 21] Generated Node #0,1,1: 42:[63, 21] Operation: 23-2=21 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 42:[2, 40], Operations: ['75-73=2', '63-23=40'] Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[23, 73, 75, 63], Operations: [] Exploring Operation: 75-73=2, Resulting Numbers: [23, 63, 2] Generated Node #0,1: 42:[23, 63, 2] Operation: 75-73=2 Moving to Node #0,1 Current State: 42:[23, 63, 2], Operations: ['75-73=2'] Exploring Operation: 63-23=40, Resulting Numbers: [2, 40] Generated Node #0,1,0: 42:[2, 40] Operation: 63-23=40 Moving to Node #0,1,0 Current State: 42:[2, 40], Operations: ['75-73=2', '63-23=40'] Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 91, 66, 56, 13 ]
39
[ "66-56=10", "13*10=130", "130-91=39" ]
Current State: 39:[91, 66, 56, 13], Operations: [] Exploring Operation: 66-56=10, Resulting Numbers: [91, 13, 10] Generated Node #2: [91, 13, 10] from Operation: 66-56=10 Current State: 39:[91, 13, 10], Operations: ['66-56=10'] Exploring Operation: 13*10=130, Resulting Numbers: [91, 130] Generated Node #3: [91, 130] from Operation: 13*10=130 Current State: 39:[91, 130], Operations: ['66-56=10', '13*10=130'] Exploring Operation: 130-91=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[91, 66, 56, 13], Operations: [] Exploring Operation: 91-66=25, Resulting Numbers: [56, 13, 25] Generated Node #0,0: 39:[56, 13, 25] Operation: 91-66=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[56, 13, 25], Operations: ['91-66=25'] Exploring Operation: 56-25=31, Resulting Numbers: [13, 31] Generated Node #0,0,0: 39:[13, 31] Operation: 56-25=31 Moving to Node #0,0,0 Current State: 39:[13, 31], Operations: ['91-66=25', '56-25=31'] Exploring Operation: 13+31=44, Resulting Numbers: [44] 44,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 36, 30, 89, 74 ]
34
[ "89-74=15", "30/15=2", "36-2=34" ]
Current State: 34:[36, 30, 89, 74], Operations: [] Exploring Operation: 89-74=15, Resulting Numbers: [36, 30, 15] Generated Node #2: [36, 30, 15] from Operation: 89-74=15 Current State: 34:[36, 30, 15], Operations: ['89-74=15'] Exploring Operation: 30/15=2, Resulting Numbers: [36, 2] Generated Node #3: [36, 2] from Operation: 30/15=2 Current State: 34:[36, 2], Operations: ['89-74=15', '30/15=2'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[36, 30, 89, 74], Operations: [] Exploring Operation: 89-74=15, Resulting Numbers: [36, 30, 15] Generated Node #0,0: 34:[36, 30, 15] Operation: 89-74=15 Moving to Node #0,0 Current State: 34:[36, 30, 15], Operations: ['89-74=15'] Exploring Operation: 30/15=2, Resulting Numbers: [36, 2] Generated Node #0,0,0: 34:[36, 2] Operation: 30/15=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 34:[36, 2], Operations: ['89-74=15', '30/15=2'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[36, 30, 89, 74], Operations: [] Exploring Operation: 89-74=15, Resulting Numbers: [36, 30, 15] Generated Node #0,0: 34:[36, 30, 15] Operation: 89-74=15 Moving to Node #0,0 Current State: 34:[36, 30, 15], Operations: ['89-74=15'] Exploring Operation: 30/15=2, Resulting Numbers: [36, 2] Generated Node #0,0,0: 34:[36, 2] Operation: 30/15=2 Moving to Node #0,0,0 Current State: 34:[36, 2], Operations: ['89-74=15', '30/15=2'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 82, 33, 36, 69 ]
82
[ "82+33=115", "69-36=33", "115-33=82" ]
Current State: 82:[82, 33, 36, 69], Operations: [] Exploring Operation: 82+33=115, Resulting Numbers: [36, 69, 115] Generated Node #2: [36, 69, 115] from Operation: 82+33=115 Current State: 82:[36, 69, 115], Operations: ['82+33=115'] Exploring Operation: 69-36=33, Resulting Numbers: [115, 33] Generated Node #3: [115, 33] from Operation: 69-36=33 Current State: 82:[115, 33], Operations: ['82+33=115', '69-36=33'] Exploring Operation: 115-33=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[82, 33, 36, 69], Operations: [] Exploring Operation: 69-36=33, Resulting Numbers: [82, 33, 33] Generated Node #0,0: 82:[82, 33, 33] Operation: 69-36=33 Exploring Operation: 69-33=36, Resulting Numbers: [82, 36, 36] Generated Node #0,1: 82:[82, 36, 36] Operation: 69-33=36 Exploring Operation: 36-33=3, Resulting Numbers: [82, 69, 3] Generated Node #0,2: 82:[82, 69, 3] Operation: 36-33=3 Moving to Node #0,1 Current State: 82:[82, 36, 36], Operations: ['69-33=36'] Exploring Operation: 36-36=0, Resulting Numbers: [82, 0] Generated Node #0,1,0: 82:[82, 0] Operation: 36-36=0 Exploring Operation: 36/36=1, Resulting Numbers: [82, 1] Generated Node #0,1,1: 82:[82, 1] Operation: 36/36=1 Exploring Operation: 82-36=46, Resulting Numbers: [36, 46] Generated Node #0,1,2: 82:[36, 46] Operation: 82-36=46 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 82:[82, 1], Operations: ['69-33=36', '36/36=1'] Exploring Operation: 82+1=83, Resulting Numbers: [83] 83,82 unequal: No Solution Exploring Operation: 82*1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[82, 33, 36, 69], Operations: [] Exploring Operation: 69-33=36, Resulting Numbers: [82, 36, 36] Generated Node #0,1: 82:[82, 36, 36] Operation: 69-33=36 Moving to Node #0,1 Current State: 82:[82, 36, 36], Operations: ['69-33=36'] Exploring Operation: 36/36=1, Resulting Numbers: [82, 1] Generated Node #0,1,1: 82:[82, 1] Operation: 36/36=1 Moving to Node #0,1,1 Current State: 82:[82, 1], Operations: ['69-33=36', '36/36=1'] Exploring Operation: 82*1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 74, 36, 83, 40 ]
67
[ "74+36=110", "83-40=43", "110-43=67" ]
Current State: 67:[74, 36, 83, 40], Operations: [] Exploring Operation: 74+36=110, Resulting Numbers: [83, 40, 110] Generated Node #2: [83, 40, 110] from Operation: 74+36=110 Current State: 67:[83, 40, 110], Operations: ['74+36=110'] Exploring Operation: 83-40=43, Resulting Numbers: [110, 43] Generated Node #3: [110, 43] from Operation: 83-40=43 Current State: 67:[110, 43], Operations: ['74+36=110', '83-40=43'] Exploring Operation: 110-43=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[74, 36, 83, 40], Operations: [] Exploring Operation: 36+40=76, Resulting Numbers: [74, 83, 76] Generated Node #0,0: 67:[74, 83, 76] Operation: 36+40=76 Moving to Node #0,0 Current State: 67:[74, 83, 76], Operations: ['36+40=76'] Exploring Operation: 83-74=9, Resulting Numbers: [76, 9] Generated Node #0,0,0: 67:[76, 9] Operation: 83-74=9 Moving to Node #0,0,0 Current State: 67:[76, 9], Operations: ['36+40=76', '83-74=9'] Exploring Operation: 76-9=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[74, 36, 83, 40], Operations: [] Exploring Operation: 36+40=76, Resulting Numbers: [74, 83, 76] Generated Node #0,0: 67:[74, 83, 76] Operation: 36+40=76 Moving to Node #0,0 Current State: 67:[74, 83, 76], Operations: ['36+40=76'] Exploring Operation: 83-74=9, Resulting Numbers: [76, 9] Generated Node #0,0,0: 67:[76, 9] Operation: 83-74=9 Moving to Node #0,0,0 Current State: 67:[76, 9], Operations: ['36+40=76', '83-74=9'] Exploring Operation: 76-9=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 5, 22, 14, 91 ]
12
[ "5+91=96", "22-14=8", "96/8=12" ]
Current State: 12:[5, 22, 14, 91], Operations: [] Exploring Operation: 5+91=96, Resulting Numbers: [22, 14, 96] Generated Node #2: [22, 14, 96] from Operation: 5+91=96 Current State: 12:[22, 14, 96], Operations: ['5+91=96'] Exploring Operation: 22-14=8, Resulting Numbers: [96, 8] Generated Node #3: [96, 8] from Operation: 22-14=8 Current State: 12:[96, 8], Operations: ['5+91=96', '22-14=8'] Exploring Operation: 96/8=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[5, 22, 14, 91], Operations: [] Exploring Operation: 22-14=8, Resulting Numbers: [5, 91, 8] Generated Node #0,0: 12:[5, 91, 8] Operation: 22-14=8 Exploring Operation: 91-14=77, Resulting Numbers: [5, 22, 77] Generated Node #0,1: 12:[5, 22, 77] Operation: 91-14=77 Exploring Operation: 22-5=17, Resulting Numbers: [14, 91, 17] Generated Node #0,2: 12:[14, 91, 17] Operation: 22-5=17 Exploring Operation: 91-22=69, Resulting Numbers: [5, 14, 69] Generated Node #0,3: 12:[5, 14, 69] Operation: 91-22=69 Moving to Node #0,3 Current State: 12:[5, 14, 69], Operations: ['91-22=69'] Exploring Operation: 69-14=55, Resulting Numbers: [5, 55] Generated Node #0,3,0: 12:[5, 55] Operation: 69-14=55 Exploring Operation: 69-5=64, Resulting Numbers: [14, 64] Generated Node #0,3,1: 12:[14, 64] Operation: 69-5=64 Exploring Operation: 14-5=9, Resulting Numbers: [69, 9] Generated Node #0,3,2: 12:[69, 9] Operation: 14-5=9 Exploring Operation: 5+14=19, Resulting Numbers: [69, 19] Generated Node #0,3,3: 12:[69, 19] Operation: 5+14=19 Moving to Node #0,1 Current State: 12:[5, 22, 77], Operations: ['91-14=77'] Exploring Operation: 22-5=17, Resulting Numbers: [77, 17] Generated Node #0,1,0: 12:[77, 17] Operation: 22-5=17 Exploring Operation: 77-5=72, Resulting Numbers: [22, 72] Generated Node #0,1,1: 12:[22, 72] Operation: 77-5=72 Exploring Operation: 5+22=27, Resulting Numbers: [77, 27] Generated Node #0,1,2: 12:[77, 27] Operation: 5+22=27 Exploring Operation: 77-22=55, Resulting Numbers: [5, 55] Generated Node #0,1,3: 12:[5, 55] Operation: 77-22=55 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 12:[5, 55], Operations: ['91-14=77', '77-22=55'] Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,12 unequal: No Solution Exploring Operation: 5*55=275, Resulting Numbers: [275] 275,12 unequal: No Solution Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 12:[77, 17], Operations: ['91-14=77', '22-5=17'] Exploring Operation: 77-17=60, Resulting Numbers: [60] 60,12 unequal: No Solution Exploring Operation: 77*17=1309, Resulting Numbers: [1309] 1309,12 unequal: No Solution Exploring Operation: 77+17=94, Resulting Numbers: [94] 94,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 12:[22, 72], Operations: ['91-14=77', '77-5=72'] Exploring Operation: 72-22=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 22+72=94, Resulting Numbers: [94] 94,12 unequal: No Solution Exploring Operation: 22*72=1584, Resulting Numbers: [1584] 1584,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 12:[77, 27], Operations: ['91-14=77', '5+22=27'] Exploring Operation: 77+27=104, Resulting Numbers: [104] 104,12 unequal: No Solution Exploring Operation: 77-27=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 77*27=2079, Resulting Numbers: [2079] 2079,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 12:[5, 91, 8], Operations: ['22-14=8'] Exploring Operation: 91-5=86, Resulting Numbers: [8, 86] Generated Node #0,0,0: 12:[8, 86] Operation: 91-5=86 Exploring Operation: 5+8=13, Resulting Numbers: [91, 13] Generated Node #0,0,1: 12:[91, 13] Operation: 5+8=13 Exploring Operation: 91-8=83, Resulting Numbers: [5, 83] Generated Node #0,0,2: 12:[5, 83] Operation: 91-8=83 Exploring Operation: 8-5=3, Resulting Numbers: [91, 3] Generated Node #0,0,3: 12:[91, 3] Operation: 8-5=3 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 12:[5, 83], Operations: ['22-14=8', '91-8=83'] Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,12 unequal: No Solution Exploring Operation: 5+83=88, Resulting Numbers: [88] 88,12 unequal: No Solution Exploring Operation: 5*83=415, Resulting Numbers: [415] 415,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[8, 86], Operations: ['22-14=8', '91-5=86'] Exploring Operation: 86-8=78, Resulting Numbers: [78] 78,12 unequal: No Solution Exploring Operation: 8*86=688, Resulting Numbers: [688] 688,12 unequal: No Solution Exploring Operation: 8+86=94, Resulting Numbers: [94] 94,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 12:[91, 3], Operations: ['22-14=8', '8-5=3'] Exploring Operation: 91*3=273, Resulting Numbers: [273] 273,12 unequal: No Solution Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,12 unequal: No Solution Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[91, 13], Operations: ['22-14=8', '5+8=13'] Exploring Operation: 91*13=1183, Resulting Numbers: [1183] 1183,12 unequal: No Solution Exploring Operation: 91-13=78, Resulting Numbers: [78] 78,12 unequal: No Solution Exploring Operation: 91/13=7, Resulting Numbers: [7] 7,12 unequal: No Solution Exploring Operation: 91+13=104, Resulting Numbers: [104] 104,12 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: 12:[14, 91, 17], Operations: ['22-5=17'] Exploring Operation: 91-17=74, Resulting Numbers: [14, 74] Generated Node #0,2,0: 12:[14, 74] Operation: 91-17=74 Exploring Operation: 14+91=105, Resulting Numbers: [17, 105] Generated Node #0,2,1: 12:[17, 105] Operation: 14+91=105 Exploring Operation: 91-14=77, Resulting Numbers: [17, 77] Generated Node #0,2,2: 12:[17, 77] Operation: 91-14=77 Exploring Operation: 17-14=3, Resulting Numbers: [91, 3] Generated Node #0,2,3: 12:[91, 3] Operation: 17-14=3 Moving to Node #0,3,0 Current State: 12:[5, 55], Operations: ['91-22=69', '69-14=55'] Exploring Operation: 5*55=275, Resulting Numbers: [275] 275,12 unequal: No Solution Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,12 unequal: No Solution Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,12 unequal: No Solution Moving to Node #0,3,1 Current State: 12:[14, 64], Operations: ['91-22=69', '69-5=64'] Exploring Operation: 64-14=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 14+64=78, Resulting Numbers: [78] 78,12 unequal: No Solution Exploring Operation: 14*64=896, Resulting Numbers: [896] 896,12 unequal: No Solution Moving to Node #0,3,2 Current State: 12:[69, 9], Operations: ['91-22=69', '14-5=9'] Exploring Operation: 69*9=621, Resulting Numbers: [621] 621,12 unequal: No Solution Exploring Operation: 69-9=60, Resulting Numbers: [60] 60,12 unequal: No Solution Exploring Operation: 69+9=78, Resulting Numbers: [78] 78,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[14, 74], Operations: ['22-5=17', '91-17=74'] Exploring Operation: 74-14=60, Resulting Numbers: [60] 60,12 unequal: No Solution Exploring Operation: 14*74=1036, Resulting Numbers: [1036] 1036,12 unequal: No Solution Exploring Operation: 14+74=88, Resulting Numbers: [88] 88,12 unequal: No Solution Moving to Node #0,3,3 Current State: 12:[69, 19], Operations: ['91-22=69', '5+14=19'] Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 69*19=1311, Resulting Numbers: [1311] 1311,12 unequal: No Solution Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[17, 77], Operations: ['22-5=17', '91-14=77'] Exploring Operation: 77-17=60, Resulting Numbers: [60] 60,12 unequal: No Solution Exploring Operation: 17+77=94, Resulting Numbers: [94] 94,12 unequal: No Solution Exploring Operation: 17*77=1309, Resulting Numbers: [1309] 1309,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[91, 3], Operations: ['22-5=17', '17-14=3'] Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,12 unequal: No Solution Exploring Operation: 91*3=273, Resulting Numbers: [273] 273,12 unequal: No Solution Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[17, 105], Operations: ['22-5=17', '14+91=105'] Exploring Operation: 17*105=1785, Resulting Numbers: [1785] 1785,12 unequal: No Solution Exploring Operation: 105-17=88, Resulting Numbers: [88] 88,12 unequal: No Solution Exploring Operation: 17+105=122, Resulting Numbers: [122] 122,12 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 92, 55, 55, 19 ]
92
[ "55-55=0", "19*0=0", "92+0=92" ]
Current State: 92:[92, 55, 55, 19], Operations: [] Exploring Operation: 55-55=0, Resulting Numbers: [92, 19, 0] Generated Node #2: [92, 19, 0] from Operation: 55-55=0 Current State: 92:[92, 19, 0], Operations: ['55-55=0'] Exploring Operation: 19*0=0, Resulting Numbers: [92, 0] Generated Node #3: [92, 0] from Operation: 19*0=0 Current State: 92:[92, 0], Operations: ['55-55=0', '19*0=0'] Exploring Operation: 92+0=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[92, 55, 55, 19], Operations: [] Exploring Operation: 55-19=36, Resulting Numbers: [92, 55, 36] Generated Node #0,0: 92:[92, 55, 36] Operation: 55-19=36 Exploring Operation: 55/55=1, Resulting Numbers: [92, 19, 1] Generated Node #0,1: 92:[92, 19, 1] Operation: 55/55=1 Exploring Operation: 55-19=36, Resulting Numbers: [92, 55, 36] Generated Node #0,2: 92:[92, 55, 36] Operation: 55-19=36 Exploring Operation: 55-55=0, Resulting Numbers: [92, 19, 0] Generated Node #0,3: 92:[92, 19, 0] Operation: 55-55=0 Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[92, 19, 1], Operations: ['55/55=1'] Exploring Operation: 92/1=92, Resulting Numbers: [19, 92] Generated Node #0,1,0: 92:[19, 92] Operation: 92/1=92 Exploring Operation: 19+1=20, Resulting Numbers: [92, 20] Generated Node #0,1,1: 92:[92, 20] Operation: 19+1=20 Exploring Operation: 92*1=92, Resulting Numbers: [19, 92] Generated Node #0,1,2: 92:[19, 92] Operation: 92*1=92 Exploring Operation: 19*1=19, Resulting Numbers: [92, 19] Generated Node #0,1,3: 92:[92, 19] Operation: 19*1=19 Moving to Node #0,1,1 Current State: 92:[92, 20], Operations: ['55/55=1', '19+1=20'] Exploring Operation: 92+20=112, Resulting Numbers: [112] 112,92 unequal: No Solution Exploring Operation: 92*20=1840, Resulting Numbers: [1840] 1840,92 unequal: No Solution Exploring Operation: 92-20=72, Resulting Numbers: [72] 72,92 unequal: No Solution Moving to Node #0,1,2 Current State: 92:[19, 92], Operations: ['55/55=1', '92*1=92'] Exploring Operation: 19*92=1748, Resulting Numbers: [1748] 1748,92 unequal: No Solution Exploring Operation: 19+92=111, Resulting Numbers: [111] 111,92 unequal: No Solution Exploring Operation: 92-19=73, Resulting Numbers: [73] 73,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[19, 92], Operations: ['55/55=1', '92/1=92'] Exploring Operation: 19+92=111, Resulting Numbers: [111] 111,92 unequal: No Solution Exploring Operation: 19*92=1748, Resulting Numbers: [1748] 1748,92 unequal: No Solution Exploring Operation: 92-19=73, Resulting Numbers: [73] 73,92 unequal: No Solution Moving to Node #0,1,3 Current State: 92:[92, 19], Operations: ['55/55=1', '19*1=19'] Exploring Operation: 92+19=111, Resulting Numbers: [111] 111,92 unequal: No Solution Exploring Operation: 92-19=73, Resulting Numbers: [73] 73,92 unequal: No Solution Exploring Operation: 92*19=1748, Resulting Numbers: [1748] 1748,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 92:[92, 19, 0], Operations: ['55-55=0'] Exploring Operation: 92+0=92, Resulting Numbers: [19, 92] Generated Node #0,3,0: 92:[19, 92] Operation: 92+0=92 Exploring Operation: 19+0=19, Resulting Numbers: [92, 19] Generated Node #0,3,1: 92:[92, 19] Operation: 19+0=19 Exploring Operation: 92-0=92, Resulting Numbers: [19, 92] Generated Node #0,3,2: 92:[19, 92] Operation: 92-0=92 Exploring Operation: 19*0=0, Resulting Numbers: [92, 0] Generated Node #0,3,3: 92:[92, 0] Operation: 19*0=0 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 92:[92, 0], Operations: ['55-55=0', '19*0=0'] Exploring Operation: 92+0=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[92, 55, 55, 19], Operations: [] Exploring Operation: 55-55=0, Resulting Numbers: [92, 19, 0] Generated Node #0,3: 92:[92, 19, 0] Operation: 55-55=0 Moving to Node #0,3 Current State: 92:[92, 19, 0], Operations: ['55-55=0'] Exploring Operation: 19*0=0, Resulting Numbers: [92, 0] Generated Node #0,3,3: 92:[92, 0] Operation: 19*0=0 Moving to Node #0,3,3 Current State: 92:[92, 0], Operations: ['55-55=0', '19*0=0'] Exploring Operation: 92+0=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 48, 15, 8, 64 ]
25
[ "48-15=33", "64/8=8", "33-8=25" ]
Current State: 25:[48, 15, 8, 64], Operations: [] Exploring Operation: 48-15=33, Resulting Numbers: [8, 64, 33] Generated Node #2: [8, 64, 33] from Operation: 48-15=33 Current State: 25:[8, 64, 33], Operations: ['48-15=33'] Exploring Operation: 64/8=8, Resulting Numbers: [33, 8] Generated Node #3: [33, 8] from Operation: 64/8=8 Current State: 25:[33, 8], Operations: ['48-15=33', '64/8=8'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[48, 15, 8, 64], Operations: [] Exploring Operation: 48-15=33, Resulting Numbers: [8, 64, 33] Generated Node #0,0: 25:[8, 64, 33] Operation: 48-15=33 Exploring Operation: 64-48=16, Resulting Numbers: [15, 8, 16] Generated Node #0,1: 25:[15, 8, 16] Operation: 64-48=16 Exploring Operation: 64/8=8, Resulting Numbers: [48, 15, 8] Generated Node #0,2: 25:[48, 15, 8] Operation: 64/8=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[15, 8, 16], Operations: ['64-48=16'] Exploring Operation: 15+8=23, Resulting Numbers: [16, 23] Generated Node #0,1,0: 25:[16, 23] Operation: 15+8=23 Exploring Operation: 15+16=31, Resulting Numbers: [8, 31] Generated Node #0,1,1: 25:[8, 31] Operation: 15+16=31 Exploring Operation: 16-15=1, Resulting Numbers: [8, 1] Generated Node #0,1,2: 25:[8, 1] Operation: 16-15=1 Moving to Node #0,1,2 Current State: 25:[8, 1], Operations: ['64-48=16', '16-15=1'] Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,25 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,25 unequal: No Solution Moving to Node #0,1,1 Current State: 25:[8, 31], Operations: ['64-48=16', '15+16=31'] Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,25 unequal: No Solution Exploring Operation: 8*31=248, Resulting Numbers: [248] 248,25 unequal: No Solution Exploring Operation: 8+31=39, Resulting Numbers: [39] 39,25 unequal: No Solution Moving to Node #0,1,0 Current State: 25:[16, 23], Operations: ['64-48=16', '15+8=23'] Exploring Operation: 16*23=368, Resulting Numbers: [368] 368,25 unequal: No Solution Exploring Operation: 16+23=39, Resulting Numbers: [39] 39,25 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[48, 15, 8], Operations: ['64/8=8'] Exploring Operation: 48/8=6, Resulting Numbers: [15, 6] Generated Node #0,2,0: 25:[15, 6] Operation: 48/8=6 Exploring Operation: 48-8=40, Resulting Numbers: [15, 40] Generated Node #0,2,1: 25:[15, 40] Operation: 48-8=40 Exploring Operation: 48-15=33, Resulting Numbers: [8, 33] Generated Node #0,2,2: 25:[8, 33] Operation: 48-15=33 Moving to Node #0,2,0 Current State: 25:[15, 6], Operations: ['64/8=8', '48/8=6'] Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,25 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,25 unequal: No Solution Moving to Node #0,2,2 Current State: 25:[8, 33], Operations: ['64/8=8', '48-15=33'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[48, 15, 8, 64], Operations: [] Exploring Operation: 64/8=8, Resulting Numbers: [48, 15, 8] Generated Node #0,2: 25:[48, 15, 8] Operation: 64/8=8 Moving to Node #0,2 Current State: 25:[48, 15, 8], Operations: ['64/8=8'] Exploring Operation: 48-15=33, Resulting Numbers: [8, 33] Generated Node #0,2,2: 25:[8, 33] Operation: 48-15=33 Moving to Node #0,2,2 Current State: 25:[8, 33], Operations: ['64/8=8', '48-15=33'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_3
sum_heuristic
[ 42, 21, 3, 54 ]
39
[ "42+21=63", "54+63=117", "117/3=39" ]
Current State: 39:[42, 21, 3, 54], Operations: [] Exploring Operation: 42+21=63, Resulting Numbers: [3, 54, 63] Generated Node #2: [3, 54, 63] from Operation: 42+21=63 Current State: 39:[3, 54, 63], Operations: ['42+21=63'] Exploring Operation: 54+63=117, Resulting Numbers: [3, 117] Generated Node #3: [3, 117] from Operation: 54+63=117 Current State: 39:[3, 117], Operations: ['42+21=63', '54+63=117'] Exploring Operation: 117/3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[42, 21, 3, 54], Operations: [] Exploring Operation: 42/21=2, Resulting Numbers: [3, 54, 2] Generated Node #0,0: 39:[3, 54, 2] Operation: 42/21=2 Exploring Operation: 54-21=33, Resulting Numbers: [42, 3, 33] Generated Node #0,1: 39:[42, 3, 33] Operation: 54-21=33 Exploring Operation: 54-42=12, Resulting Numbers: [21, 3, 12] Generated Node #0,2: 39:[21, 3, 12] Operation: 54-42=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[42, 3, 33], Operations: ['54-21=33'] Exploring Operation: 42-33=9, Resulting Numbers: [3, 9] Generated Node #0,1,0: 39:[3, 9] Operation: 42-33=9 Exploring Operation: 33/3=11, Resulting Numbers: [42, 11] Generated Node #0,1,1: 39:[42, 11] Operation: 33/3=11 Exploring Operation: 42-3=39, Resulting Numbers: [33, 39] Generated Node #0,1,2: 39:[33, 39] Operation: 42-3=39 Moving to Node #0,1,0 Current State: 39:[3, 9], Operations: ['54-21=33', '42-33=9'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[42, 11], Operations: ['54-21=33', '33/3=11'] Exploring Operation: 42-11=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 42*11=462, Resulting Numbers: [462] 462,39 unequal: No Solution Exploring Operation: 42+11=53, Resulting Numbers: [53] 53,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[33, 39], Operations: ['54-21=33', '42-3=39'] Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,39 unequal: No Solution Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[21, 3, 12], Operations: ['54-42=12'] Exploring Operation: 21-3=18, Resulting Numbers: [12, 18] Generated Node #0,2,0: 39:[12, 18] Operation: 21-3=18 Exploring Operation: 21-12=9, Resulting Numbers: [3, 9] Generated Node #0,2,1: 39:[3, 9] Operation: 21-12=9 Exploring Operation: 21/3=7, Resulting Numbers: [12, 7] Generated Node #0,2,2: 39:[12, 7] Operation: 21/3=7 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 39:[3, 9], Operations: ['54-42=12', '21-12=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 39:[12, 7], Operations: ['54-42=12', '21/3=7'] Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,39 unequal: No Solution Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,39 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 39:[12, 18], Operations: ['54-42=12', '21-3=18'] Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,39 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[3, 54, 2], Operations: ['42/21=2'] Exploring Operation: 54-3=51, Resulting Numbers: [2, 51] Generated Node #0,0,0: 39:[2, 51] Operation: 54-3=51 Exploring Operation: 54/3=18, Resulting Numbers: [2, 18] Generated Node #0,0,1: 39:[2, 18] Operation: 54/3=18 Exploring Operation: 54/2=27, Resulting Numbers: [3, 27] Generated Node #0,0,2: 39:[3, 27] Operation: 54/2=27 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 39:[2, 18], Operations: ['42/21=2', '54/3=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,39 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 39:[3, 27], Operations: ['42/21=2', '54/2=27'] Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,39 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,39 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[2, 51], Operations: ['42/21=2', '54-3=51'] Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,39 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,39 unequal: No Solution Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 55, 98, 12, 36 ]
51
[ "55+98=153", "36/12=3", "153/3=51" ]
Current State: 51:[55, 98, 12, 36], Operations: [] Exploring Operation: 55+98=153, Resulting Numbers: [12, 36, 153] Generated Node #2: [12, 36, 153] from Operation: 55+98=153 Current State: 51:[12, 36, 153], Operations: ['55+98=153'] Exploring Operation: 36/12=3, Resulting Numbers: [153, 3] Generated Node #3: [153, 3] from Operation: 36/12=3 Current State: 51:[153, 3], Operations: ['55+98=153', '36/12=3'] Exploring Operation: 153/3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[55, 98, 12, 36], Operations: [] Exploring Operation: 36/12=3, Resulting Numbers: [55, 98, 3] Generated Node #0,0: 51:[55, 98, 3] Operation: 36/12=3 Exploring Operation: 98-55=43, Resulting Numbers: [12, 36, 43] Generated Node #0,1: 51:[12, 36, 43] Operation: 98-55=43 Exploring Operation: 55-36=19, Resulting Numbers: [98, 12, 19] Generated Node #0,2: 51:[98, 12, 19] Operation: 55-36=19 Exploring Operation: 98-36=62, Resulting Numbers: [55, 12, 62] Generated Node #0,3: 51:[55, 12, 62] Operation: 98-36=62 Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[55, 12, 62], Operations: ['98-36=62'] Exploring Operation: 62-12=50, Resulting Numbers: [55, 50] Generated Node #0,3,0: 51:[55, 50] Operation: 62-12=50 Exploring Operation: 55+12=67, Resulting Numbers: [62, 67] Generated Node #0,3,1: 51:[62, 67] Operation: 55+12=67 Exploring Operation: 55-12=43, Resulting Numbers: [62, 43] Generated Node #0,3,2: 51:[62, 43] Operation: 55-12=43 Exploring Operation: 62-55=7, Resulting Numbers: [12, 7] Generated Node #0,3,3: 51:[12, 7] Operation: 62-55=7 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 51:[55, 50], Operations: ['98-36=62', '62-12=50'] Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 55*50=2750, Resulting Numbers: [2750] 2750,51 unequal: No Solution Exploring Operation: 55+50=105, Resulting Numbers: [105] 105,51 unequal: No Solution No 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: 51:[12, 7], Operations: ['98-36=62', '62-55=7'] Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,51 unequal: No Solution Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,51 unequal: No Solution No 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: 51:[62, 43], Operations: ['98-36=62', '55-12=43'] Exploring Operation: 62*43=2666, Resulting Numbers: [2666] 2666,51 unequal: No Solution Exploring Operation: 62-43=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 62+43=105, Resulting Numbers: [105] 105,51 unequal: No Solution No 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: 51:[62, 67], Operations: ['98-36=62', '55+12=67'] Exploring Operation: 67-62=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 62+67=129, Resulting Numbers: [129] 129,51 unequal: No Solution Exploring Operation: 62*67=4154, Resulting Numbers: [4154] 4154,51 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: 51:[12, 36, 43], Operations: ['98-55=43'] Exploring Operation: 36-12=24, Resulting Numbers: [43, 24] Generated Node #0,1,0: 51:[43, 24] Operation: 36-12=24 Exploring Operation: 43-36=7, Resulting Numbers: [12, 7] Generated Node #0,1,1: 51:[12, 7] Operation: 43-36=7 Exploring Operation: 12+36=48, Resulting Numbers: [43, 48] Generated Node #0,1,2: 51:[43, 48] Operation: 12+36=48 Exploring Operation: 36/12=3, Resulting Numbers: [43, 3] Generated Node #0,1,3: 51:[43, 3] Operation: 36/12=3 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 51:[43, 3], Operations: ['98-55=43', '36/12=3'] Exploring Operation: 43*3=129, Resulting Numbers: [129] 129,51 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,51 unequal: No Solution Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,51 unequal: No Solution No 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: 51:[12, 7], Operations: ['98-55=43', '43-36=7'] Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,51 unequal: No Solution Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,51 unequal: No Solution No 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: 51:[43, 48], Operations: ['98-55=43', '12+36=48'] Exploring Operation: 43+48=91, Resulting Numbers: [91] 91,51 unequal: No Solution Exploring Operation: 48-43=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 43*48=2064, Resulting Numbers: [2064] 2064,51 unequal: No Solution No 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: 51:[43, 24], Operations: ['98-55=43', '36-12=24'] Exploring Operation: 43*24=1032, Resulting Numbers: [1032] 1032,51 unequal: No Solution Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,51 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,51 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: 51:[55, 98, 3], Operations: ['36/12=3'] Exploring Operation: 55-3=52, Resulting Numbers: [98, 52] Generated Node #0,0,0: 51:[98, 52] Operation: 55-3=52 Exploring Operation: 98-3=95, Resulting Numbers: [55, 95] Generated Node #0,0,1: 51:[55, 95] Operation: 98-3=95 Exploring Operation: 98-55=43, Resulting Numbers: [3, 43] Generated Node #0,0,2: 51:[3, 43] Operation: 98-55=43 Exploring Operation: 55+3=58, Resulting Numbers: [98, 58] Generated Node #0,0,3: 51:[98, 58] Operation: 55+3=58 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 51:[3, 43], Operations: ['36/12=3', '98-55=43'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,51 unequal: No Solution Exploring Operation: 3*43=129, Resulting Numbers: [129] 129,51 unequal: No Solution Exploring Operation: 3+43=46, Resulting Numbers: [46] 46,51 unequal: No Solution No 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: 51:[98, 52], Operations: ['36/12=3', '55-3=52'] Exploring Operation: 98*52=5096, Resulting Numbers: [5096] 5096,51 unequal: No Solution Exploring Operation: 98-52=46, Resulting Numbers: [46] 46,51 unequal: No Solution Exploring Operation: 98+52=150, Resulting Numbers: [150] 150,51 unequal: No Solution No 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: 51:[55, 95], Operations: ['36/12=3', '98-3=95'] Exploring Operation: 55*95=5225, Resulting Numbers: [5225] 5225,51 unequal: No Solution Exploring Operation: 55+95=150, Resulting Numbers: [150] 150,51 unequal: No Solution Exploring Operation: 95-55=40, Resulting Numbers: [40] 40,51 unequal: No Solution No 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: 51:[98, 58], Operations: ['36/12=3', '55+3=58'] Exploring Operation: 98-58=40, Resulting Numbers: [40] 40,51 unequal: No Solution Exploring Operation: 98+58=156, Resulting Numbers: [156] 156,51 unequal: No Solution Exploring Operation: 98*58=5684, Resulting Numbers: [5684] 5684,51 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: 51:[98, 12, 19], Operations: ['55-36=19'] Exploring Operation: 98-12=86, Resulting Numbers: [19, 86] Generated Node #0,2,0: 51:[19, 86] Operation: 98-12=86 Exploring Operation: 19-12=7, Resulting Numbers: [98, 7] Generated Node #0,2,1: 51:[98, 7] Operation: 19-12=7 Exploring Operation: 98+12=110, Resulting Numbers: [19, 110] Generated Node #0,2,2: 51:[19, 110] Operation: 98+12=110 Exploring Operation: 98-19=79, Resulting Numbers: [12, 79] Generated Node #0,2,3: 51:[12, 79] Operation: 98-19=79 Moving to Node #0,2,3 Current State: 51:[12, 79], Operations: ['55-36=19', '98-19=79'] Exploring Operation: 12*79=948, Resulting Numbers: [948] 948,51 unequal: No Solution Exploring Operation: 79-12=67, Resulting Numbers: [67] 67,51 unequal: No Solution Exploring Operation: 12+79=91, Resulting Numbers: [91] 91,51 unequal: No Solution Moving to Node #0,2,0 Current State: 51:[19, 86], Operations: ['55-36=19', '98-12=86'] Exploring Operation: 19+86=105, Resulting Numbers: [105] 105,51 unequal: No Solution Exploring Operation: 19*86=1634, Resulting Numbers: [1634] 1634,51 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[98, 7], Operations: ['55-36=19', '19-12=7'] Exploring Operation: 98/7=14, Resulting Numbers: [14] 14,51 unequal: No Solution Exploring Operation: 98*7=686, Resulting Numbers: [686] 686,51 unequal: No Solution Exploring Operation: 98+7=105, Resulting Numbers: [105] 105,51 unequal: No Solution Exploring Operation: 98-7=91, Resulting Numbers: [91] 91,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[19, 110], Operations: ['55-36=19', '98+12=110'] Exploring Operation: 19+110=129, Resulting Numbers: [129] 129,51 unequal: No Solution Exploring Operation: 110-19=91, Resulting Numbers: [91] 91,51 unequal: No Solution Exploring Operation: 19*110=2090, Resulting Numbers: [2090] 2090,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 87, 3, 14, 31 ]
74
[ "87/3=29", "14+31=45", "29+45=74" ]
Current State: 74:[87, 3, 14, 31], Operations: [] Exploring Operation: 87/3=29, Resulting Numbers: [14, 31, 29] Generated Node #2: [14, 31, 29] from Operation: 87/3=29 Current State: 74:[14, 31, 29], Operations: ['87/3=29'] Exploring Operation: 14+31=45, Resulting Numbers: [29, 45] Generated Node #3: [29, 45] from Operation: 14+31=45 Current State: 74:[29, 45], Operations: ['87/3=29', '14+31=45'] Exploring Operation: 29+45=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[87, 3, 14, 31], Operations: [] Exploring Operation: 3*14=42, Resulting Numbers: [87, 31, 42] Generated Node #0,0: 74:[87, 31, 42] Operation: 3*14=42 Exploring Operation: 14+31=45, Resulting Numbers: [87, 3, 45] Generated Node #0,1: 74:[87, 3, 45] Operation: 14+31=45 Exploring Operation: 87-3=84, Resulting Numbers: [14, 31, 84] Generated Node #0,2: 74:[14, 31, 84] Operation: 87-3=84 Exploring Operation: 87-14=73, Resulting Numbers: [3, 31, 73] Generated Node #0,3: 74:[3, 31, 73] Operation: 87-14=73 Exploring Operation: 87/3=29, Resulting Numbers: [14, 31, 29] Generated Node #0,4: 74:[14, 31, 29] Operation: 87/3=29 Start Sub Search at level 1: Moving to Node #0,3 Current State: 74:[3, 31, 73], Operations: ['87-14=73'] Exploring Operation: 31-3=28, Resulting Numbers: [73, 28] Generated Node #0,3,0: 74:[73, 28] Operation: 31-3=28 Exploring Operation: 73-3=70, Resulting Numbers: [31, 70] Generated Node #0,3,1: 74:[31, 70] Operation: 73-3=70 Exploring Operation: 3+73=76, Resulting Numbers: [31, 76] Generated Node #0,3,2: 74:[31, 76] Operation: 3+73=76 Exploring Operation: 3+31=34, Resulting Numbers: [73, 34] Generated Node #0,3,3: 74:[73, 34] Operation: 3+31=34 Exploring Operation: 73-31=42, Resulting Numbers: [3, 42] Generated Node #0,3,4: 74:[3, 42] Operation: 73-31=42 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 74:[73, 34], Operations: ['87-14=73', '3+31=34'] Exploring Operation: 73-34=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 73*34=2482, Resulting Numbers: [2482] 2482,74 unequal: No Solution Exploring Operation: 73+34=107, Resulting Numbers: [107] 107,74 unequal: No Solution No 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: 74:[3, 42], Operations: ['87-14=73', '73-31=42'] Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,74 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,74 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,74 unequal: No Solution No 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: 74:[31, 76], Operations: ['87-14=73', '3+73=76'] Exploring Operation: 31*76=2356, Resulting Numbers: [2356] 2356,74 unequal: No Solution Exploring Operation: 76-31=45, Resulting Numbers: [45] 45,74 unequal: No Solution Exploring Operation: 31+76=107, Resulting Numbers: [107] 107,74 unequal: No Solution No 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: 74:[73, 28], Operations: ['87-14=73', '31-3=28'] Exploring Operation: 73*28=2044, Resulting Numbers: [2044] 2044,74 unequal: No Solution Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,74 unequal: No Solution Exploring Operation: 73+28=101, Resulting Numbers: [101] 101,74 unequal: No Solution No 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: 74:[31, 70], Operations: ['87-14=73', '73-3=70'] Exploring Operation: 70-31=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 31+70=101, Resulting Numbers: [101] 101,74 unequal: No Solution Exploring Operation: 31*70=2170, Resulting Numbers: [2170] 2170,74 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: 74:[87, 3, 45], Operations: ['14+31=45'] Exploring Operation: 87-45=42, Resulting Numbers: [3, 42] Generated Node #0,1,0: 74:[3, 42] Operation: 87-45=42 Exploring Operation: 45-3=42, Resulting Numbers: [87, 42] Generated Node #0,1,1: 74:[87, 42] Operation: 45-3=42 Exploring Operation: 87+3=90, Resulting Numbers: [45, 90] Generated Node #0,1,2: 74:[45, 90] Operation: 87+3=90 Exploring Operation: 87-3=84, Resulting Numbers: [45, 84] Generated Node #0,1,3: 74:[45, 84] Operation: 87-3=84 Exploring Operation: 87/3=29, Resulting Numbers: [45, 29] Generated Node #0,1,4: 74:[45, 29] Operation: 87/3=29 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 74:[3, 42], Operations: ['14+31=45', '87-45=42'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,74 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,74 unequal: No Solution Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,74 unequal: No Solution No 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: 74:[45, 29], Operations: ['14+31=45', '87/3=29'] Exploring Operation: 45*29=1305, Resulting Numbers: [1305] 1305,74 unequal: No Solution Exploring Operation: 45+29=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[87, 3, 14, 31], Operations: [] Exploring Operation: 14+31=45, Resulting Numbers: [87, 3, 45] Generated Node #0,1: 74:[87, 3, 45] Operation: 14+31=45 Moving to Node #0,1 Current State: 74:[87, 3, 45], Operations: ['14+31=45'] Exploring Operation: 87/3=29, Resulting Numbers: [45, 29] Generated Node #0,1,4: 74:[45, 29] Operation: 87/3=29 Moving to Node #0,1,4 Current State: 74:[45, 29], Operations: ['14+31=45', '87/3=29'] Exploring Operation: 45+29=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_5
sum_heuristic
[ 56, 82, 24, 48 ]
97
[ "82*24=1968", "1968/48=41", "56+41=97" ]
Current State: 97:[56, 82, 24, 48], Operations: [] Exploring Operation: 82*24=1968, Resulting Numbers: [56, 48, 1968] Generated Node #2: [56, 48, 1968] from Operation: 82*24=1968 Current State: 97:[56, 48, 1968], Operations: ['82*24=1968'] Exploring Operation: 1968/48=41, Resulting Numbers: [56, 41] Generated Node #3: [56, 41] from Operation: 1968/48=41 Current State: 97:[56, 41], Operations: ['82*24=1968', '1968/48=41'] Exploring Operation: 56+41=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[56, 82, 24, 48], Operations: [] Exploring Operation: 56+24=80, Resulting Numbers: [82, 48, 80] Generated Node #0,0: 97:[82, 48, 80] Operation: 56+24=80 Exploring Operation: 24+48=72, Resulting Numbers: [56, 82, 72] Generated Node #0,1: 97:[56, 82, 72] Operation: 24+48=72 Moving to Node #0,0 Current State: 97:[82, 48, 80], Operations: ['56+24=80'] Exploring Operation: 48+80=128, Resulting Numbers: [82, 128] Generated Node #0,0,0: 97:[82, 128] Operation: 48+80=128 Exploring Operation: 82+48=130, Resulting Numbers: [80, 130] Generated Node #0,0,1: 97:[80, 130] Operation: 82+48=130 Moving to Node #0,1 Current State: 97:[56, 82, 72], Operations: ['24+48=72'] Exploring Operation: 56+72=128, Resulting Numbers: [82, 128] Generated Node #0,1,0: 97:[82, 128] Operation: 56+72=128 Exploring Operation: 56+82=138, Resulting Numbers: [72, 138] Generated Node #0,1,1: 97:[72, 138] Operation: 56+82=138 Moving to Node #0,0,0 Current State: 97:[82, 128], Operations: ['56+24=80', '48+80=128'] Exploring Operation: 128-82=46, Resulting Numbers: [46] 46,97 unequal: No Solution Exploring Operation: 82+128=210, Resulting Numbers: [210] 210,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[82, 128], Operations: ['24+48=72', '56+72=128'] Exploring Operation: 82+128=210, Resulting Numbers: [210] 210,97 unequal: No Solution Exploring Operation: 128-82=46, Resulting Numbers: [46] 46,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[80, 130], Operations: ['56+24=80', '82+48=130'] Exploring Operation: 80+130=210, Resulting Numbers: [210] 210,97 unequal: No Solution Exploring Operation: 130-80=50, Resulting Numbers: [50] 50,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[72, 138], Operations: ['24+48=72', '56+82=138'] Exploring Operation: 72+138=210, Resulting Numbers: [210] 210,97 unequal: No Solution Exploring Operation: 138-72=66, Resulting Numbers: [66] 66,97 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 22, 98, 78, 10 ]
52
[ "22+98=120", "78-10=68", "120-68=52" ]
Current State: 52:[22, 98, 78, 10], Operations: [] Exploring Operation: 22+98=120, Resulting Numbers: [78, 10, 120] Generated Node #2: [78, 10, 120] from Operation: 22+98=120 Current State: 52:[78, 10, 120], Operations: ['22+98=120'] Exploring Operation: 78-10=68, Resulting Numbers: [120, 68] Generated Node #3: [120, 68] from Operation: 78-10=68 Current State: 52:[120, 68], Operations: ['22+98=120', '78-10=68'] Exploring Operation: 120-68=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[22, 98, 78, 10], Operations: [] Exploring Operation: 98-78=20, Resulting Numbers: [22, 10, 20] Generated Node #0,0: 52:[22, 10, 20] Operation: 98-78=20 Exploring Operation: 98-22=76, Resulting Numbers: [78, 10, 76] Generated Node #0,1: 52:[78, 10, 76] Operation: 98-22=76 Exploring Operation: 78-22=56, Resulting Numbers: [98, 10, 56] Generated Node #0,2: 52:[98, 10, 56] Operation: 78-22=56 Moving to Node #0,0 Current State: 52:[22, 10, 20], Operations: ['98-78=20'] Exploring Operation: 22-10=12, Resulting Numbers: [20, 12] Generated Node #0,0,0: 52:[20, 12] Operation: 22-10=12 Exploring Operation: 20/10=2, Resulting Numbers: [22, 2] Generated Node #0,0,1: 52:[22, 2] Operation: 20/10=2 Exploring Operation: 22-20=2, Resulting Numbers: [10, 2] Generated Node #0,0,2: 52:[10, 2] Operation: 22-20=2 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 52:[10, 2], Operations: ['98-78=20', '22-20=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,52 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 #0,0,1 Current State: 52:[22, 2], Operations: ['98-78=20', '20/10=2'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,52 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,52 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:[20, 12], Operations: ['98-78=20', '22-10=12'] Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 20*12=240, Resulting Numbers: [240] 240,52 unequal: No Solution Exploring Operation: 20+12=32, Resulting Numbers: [32] 32,52 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:[78, 10, 76], Operations: ['98-22=76'] Exploring Operation: 78-10=68, Resulting Numbers: [76, 68] Generated Node #0,1,0: 52:[76, 68] Operation: 78-10=68 Exploring Operation: 78-76=2, Resulting Numbers: [10, 2] Generated Node #0,1,1: 52:[10, 2] Operation: 78-76=2 Exploring Operation: 76-10=66, Resulting Numbers: [78, 66] Generated Node #0,1,2: 52:[78, 66] Operation: 76-10=66 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 52:[10, 2], Operations: ['98-22=76', '78-76=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,52 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 #0,1,0 Current State: 52:[76, 68], Operations: ['98-22=76', '78-10=68'] Exploring Operation: 76*68=5168, Resulting Numbers: [5168] 5168,52 unequal: No Solution Exploring Operation: 76-68=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 76+68=144, Resulting Numbers: [144] 144,52 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 #0,1,2 Current State: 52:[78, 66], Operations: ['98-22=76', '76-10=66'] Exploring Operation: 78*66=5148, Resulting Numbers: [5148] 5148,52 unequal: No Solution Exploring Operation: 78-66=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 78+66=144, Resulting Numbers: [144] 144,52 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: 52:[98, 10, 56], Operations: ['78-22=56'] Exploring Operation: 98-56=42, Resulting Numbers: [10, 42] Generated Node #0,2,0: 52:[10, 42] Operation: 98-56=42 Exploring Operation: 56-10=46, Resulting Numbers: [98, 46] Generated Node #0,2,1: 52:[98, 46] Operation: 56-10=46 Exploring Operation: 98-10=88, Resulting Numbers: [56, 88] Generated Node #0,2,2: 52:[56, 88] Operation: 98-10=88 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 52:[10, 42], Operations: ['78-22=56', '98-56=42'] Exploring Operation: 10*42=420, Resulting Numbers: [420] 420,52 unequal: No Solution Exploring Operation: 10+42=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[22, 98, 78, 10], Operations: [] Exploring Operation: 78-22=56, Resulting Numbers: [98, 10, 56] Generated Node #0,2: 52:[98, 10, 56] Operation: 78-22=56 Moving to Node #0,2 Current State: 52:[98, 10, 56], Operations: ['78-22=56'] Exploring Operation: 98-56=42, Resulting Numbers: [10, 42] Generated Node #0,2,0: 52:[10, 42] Operation: 98-56=42 Moving to Node #0,2,0 Current State: 52:[10, 42], Operations: ['78-22=56', '98-56=42'] Exploring Operation: 10+42=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 61, 48, 44, 72 ]
44
[ "72-61=11", "48-44=4", "11*4=44" ]
Current State: 44:[61, 48, 44, 72], Operations: [] Exploring Operation: 72-61=11, Resulting Numbers: [48, 44, 11] Generated Node #2: [48, 44, 11] from Operation: 72-61=11 Current State: 44:[48, 44, 11], Operations: ['72-61=11'] Exploring Operation: 48-44=4, Resulting Numbers: [11, 4] Generated Node #3: [11, 4] from Operation: 48-44=4 Current State: 44:[11, 4], Operations: ['72-61=11', '48-44=4'] Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[61, 48, 44, 72], Operations: [] Exploring Operation: 72-48=24, Resulting Numbers: [61, 44, 24] Generated Node #0,0: 44:[61, 44, 24] Operation: 72-48=24 Exploring Operation: 72-44=28, Resulting Numbers: [61, 48, 28] Generated Node #0,1: 44:[61, 48, 28] Operation: 72-44=28 Exploring Operation: 72-61=11, Resulting Numbers: [48, 44, 11] Generated Node #0,2: 44:[48, 44, 11] Operation: 72-61=11 Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[48, 44, 11], Operations: ['72-61=11'] Exploring Operation: 44/11=4, Resulting Numbers: [48, 4] Generated Node #0,2,0: 44:[48, 4] Operation: 44/11=4 Exploring Operation: 48-44=4, Resulting Numbers: [11, 4] Generated Node #0,2,1: 44:[11, 4] Operation: 48-44=4 Exploring Operation: 48-11=37, Resulting Numbers: [44, 37] Generated Node #0,2,2: 44:[44, 37] Operation: 48-11=37 Moving to Node #0,2,1 Current State: 44:[11, 4], Operations: ['72-61=11', '48-44=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,44 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,44 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[61, 48, 44, 72], Operations: [] Exploring Operation: 72-61=11, Resulting Numbers: [48, 44, 11] Generated Node #0,2: 44:[48, 44, 11] Operation: 72-61=11 Moving to Node #0,2 Current State: 44:[48, 44, 11], Operations: ['72-61=11'] Exploring Operation: 48-44=4, Resulting Numbers: [11, 4] Generated Node #0,2,1: 44:[11, 4] Operation: 48-44=4 Moving to Node #0,2,1 Current State: 44:[11, 4], Operations: ['72-61=11', '48-44=4'] Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 34, 37, 19, 21 ]
31
[ "34+37=71", "19+21=40", "71-40=31" ]
Current State: 31:[34, 37, 19, 21], Operations: [] Exploring Operation: 34+37=71, Resulting Numbers: [19, 21, 71] Generated Node #2: [19, 21, 71] from Operation: 34+37=71 Current State: 31:[19, 21, 71], Operations: ['34+37=71'] Exploring Operation: 19+21=40, Resulting Numbers: [71, 40] Generated Node #3: [71, 40] from Operation: 19+21=40 Current State: 31:[71, 40], Operations: ['34+37=71', '19+21=40'] Exploring Operation: 71-40=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[34, 37, 19, 21], Operations: [] Exploring Operation: 19+21=40, Resulting Numbers: [34, 37, 40] Generated Node #0,0: 31:[34, 37, 40] Operation: 19+21=40 Exploring Operation: 34-19=15, Resulting Numbers: [37, 21, 15] Generated Node #0,1: 31:[37, 21, 15] Operation: 34-19=15 Exploring Operation: 34-21=13, Resulting Numbers: [37, 19, 13] Generated Node #0,2: 31:[37, 19, 13] Operation: 34-21=13 Exploring Operation: 37-19=18, Resulting Numbers: [34, 21, 18] Generated Node #0,3: 31:[34, 21, 18] Operation: 37-19=18 Exploring Operation: 37-21=16, Resulting Numbers: [34, 19, 16] Generated Node #0,4: 31:[34, 19, 16] Operation: 37-21=16 Moving to Node #0,0 Current State: 31:[34, 37, 40], Operations: ['19+21=40'] Exploring Operation: 34+40=74, Resulting Numbers: [37, 74] Generated Node #0,0,0: 31:[37, 74] Operation: 34+40=74 Exploring Operation: 34+37=71, Resulting Numbers: [40, 71] Generated Node #0,0,1: 31:[40, 71] Operation: 34+37=71 Exploring Operation: 40-34=6, Resulting Numbers: [37, 6] Generated Node #0,0,2: 31:[37, 6] Operation: 40-34=6 Exploring Operation: 40-37=3, Resulting Numbers: [34, 3] Generated Node #0,0,3: 31:[34, 3] Operation: 40-37=3 Exploring Operation: 37-34=3, Resulting Numbers: [40, 3] Generated Node #0,0,4: 31:[40, 3] Operation: 37-34=3 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 31:[37, 6], Operations: ['19+21=40', '40-34=6'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[34, 37, 19, 21], Operations: [] Exploring Operation: 19+21=40, Resulting Numbers: [34, 37, 40] Generated Node #0,0: 31:[34, 37, 40] Operation: 19+21=40 Moving to Node #0,0 Current State: 31:[34, 37, 40], Operations: ['19+21=40'] Exploring Operation: 40-34=6, Resulting Numbers: [37, 6] Generated Node #0,0,2: 31:[37, 6] Operation: 40-34=6 Moving to Node #0,0,2 Current State: 31:[37, 6], Operations: ['19+21=40', '40-34=6'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 29, 67, 94, 38 ]
93
[ "67-29=38", "38/38=1", "94-1=93" ]
Current State: 93:[29, 67, 94, 38], Operations: [] Exploring Operation: 67-29=38, Resulting Numbers: [94, 38, 38] Generated Node #2: [94, 38, 38] from Operation: 67-29=38 Current State: 93:[94, 38, 38], Operations: ['67-29=38'] Exploring Operation: 38/38=1, Resulting Numbers: [94, 1] Generated Node #3: [94, 1] from Operation: 38/38=1 Current State: 93:[94, 1], Operations: ['67-29=38', '38/38=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[29, 67, 94, 38], Operations: [] Exploring Operation: 67-38=29, Resulting Numbers: [29, 94, 29] Generated Node #0,0: 93:[29, 94, 29] Operation: 67-38=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[29, 94, 29], Operations: ['67-38=29'] Exploring Operation: 29/29=1, Resulting Numbers: [94, 1] Generated Node #0,0,0: 93:[94, 1] Operation: 29/29=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 93:[94, 1], Operations: ['67-38=29', '29/29=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[29, 67, 94, 38], Operations: [] Exploring Operation: 67-38=29, Resulting Numbers: [29, 94, 29] Generated Node #0,0: 93:[29, 94, 29] Operation: 67-38=29 Moving to Node #0,0 Current State: 93:[29, 94, 29], Operations: ['67-38=29'] Exploring Operation: 29/29=1, Resulting Numbers: [94, 1] Generated Node #0,0,0: 93:[94, 1] Operation: 29/29=1 Moving to Node #0,0,0 Current State: 93:[94, 1], Operations: ['67-38=29', '29/29=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 88, 71, 30, 78 ]
91
[ "88-71=17", "30+78=108", "108-17=91" ]
Current State: 91:[88, 71, 30, 78], Operations: [] Exploring Operation: 88-71=17, Resulting Numbers: [30, 78, 17] Generated Node #2: [30, 78, 17] from Operation: 88-71=17 Current State: 91:[30, 78, 17], Operations: ['88-71=17'] Exploring Operation: 30+78=108, Resulting Numbers: [17, 108] Generated Node #3: [17, 108] from Operation: 30+78=108 Current State: 91:[17, 108], Operations: ['88-71=17', '30+78=108'] Exploring Operation: 108-17=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[88, 71, 30, 78], Operations: [] Exploring Operation: 88-78=10, Resulting Numbers: [71, 30, 10] Generated Node #0,0: 91:[71, 30, 10] Operation: 88-78=10 Exploring Operation: 71+30=101, Resulting Numbers: [88, 78, 101] Generated Node #0,1: 91:[88, 78, 101] Operation: 71+30=101 Exploring Operation: 78-71=7, Resulting Numbers: [88, 30, 7] Generated Node #0,2: 91:[88, 30, 7] Operation: 78-71=7 Exploring Operation: 88-71=17, Resulting Numbers: [30, 78, 17] Generated Node #0,3: 91:[30, 78, 17] Operation: 88-71=17 Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[88, 30, 7], Operations: ['78-71=7'] Exploring Operation: 30-7=23, Resulting Numbers: [88, 23] Generated Node #0,2,0: 91:[88, 23] Operation: 30-7=23 Exploring Operation: 88+30=118, Resulting Numbers: [7, 118] Generated Node #0,2,1: 91:[7, 118] Operation: 88+30=118 Exploring Operation: 88+7=95, Resulting Numbers: [30, 95] Generated Node #0,2,2: 91:[30, 95] Operation: 88+7=95 Exploring Operation: 88-7=81, Resulting Numbers: [30, 81] Generated Node #0,2,3: 91:[30, 81] Operation: 88-7=81 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 91:[88, 23], Operations: ['78-71=7', '30-7=23'] Exploring Operation: 88+23=111, Resulting Numbers: [111] 111,91 unequal: No Solution Exploring Operation: 88*23=2024, Resulting Numbers: [2024] 2024,91 unequal: No Solution Exploring Operation: 88-23=65, Resulting Numbers: [65] 65,91 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:[30, 95], Operations: ['78-71=7', '88+7=95'] Exploring Operation: 30*95=2850, Resulting Numbers: [2850] 2850,91 unequal: No Solution Exploring Operation: 95-30=65, Resulting Numbers: [65] 65,91 unequal: No Solution Exploring Operation: 30+95=125, Resulting Numbers: [125] 125,91 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:[7, 118], Operations: ['78-71=7', '88+30=118'] Exploring Operation: 118-7=111, Resulting Numbers: [111] 111,91 unequal: No Solution Exploring Operation: 7+118=125, Resulting Numbers: [125] 125,91 unequal: No Solution Exploring Operation: 7*118=826, Resulting Numbers: [826] 826,91 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 #0,2,3 Current State: 91:[30, 81], Operations: ['78-71=7', '88-7=81'] Exploring Operation: 81-30=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 30+81=111, Resulting Numbers: [111] 111,91 unequal: No Solution Exploring Operation: 30*81=2430, Resulting Numbers: [2430] 2430,91 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:[88, 78, 101], Operations: ['71+30=101'] Exploring Operation: 101-78=23, Resulting Numbers: [88, 23] Generated Node #0,1,0: 91:[88, 23] Operation: 101-78=23 Exploring Operation: 88+78=166, Resulting Numbers: [101, 166] Generated Node #0,1,1: 91:[101, 166] Operation: 88+78=166 Exploring Operation: 88-78=10, Resulting Numbers: [101, 10] Generated Node #0,1,2: 91:[101, 10] Operation: 88-78=10 Exploring Operation: 101-88=13, Resulting Numbers: [78, 13] Generated Node #0,1,3: 91:[78, 13] Operation: 101-88=13 Moving to Node #0,1,0 Current State: 91:[88, 23], Operations: ['71+30=101', '101-78=23'] Exploring Operation: 88+23=111, Resulting Numbers: [111] 111,91 unequal: No Solution Exploring Operation: 88*23=2024, Resulting Numbers: [2024] 2024,91 unequal: No Solution Exploring Operation: 88-23=65, Resulting Numbers: [65] 65,91 unequal: No Solution Moving to Node #0,1,3 Current State: 91:[78, 13], Operations: ['71+30=101', '101-88=13'] Exploring Operation: 78+13=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[88, 71, 30, 78], Operations: [] Exploring Operation: 71+30=101, Resulting Numbers: [88, 78, 101] Generated Node #0,1: 91:[88, 78, 101] Operation: 71+30=101 Moving to Node #0,1 Current State: 91:[88, 78, 101], Operations: ['71+30=101'] Exploring Operation: 101-88=13, Resulting Numbers: [78, 13] Generated Node #0,1,3: 91:[78, 13] Operation: 101-88=13 Moving to Node #0,1,3 Current State: 91:[78, 13], Operations: ['71+30=101', '101-88=13'] Exploring Operation: 78+13=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 16, 63, 8, 75 ]
64
[ "63+8=71", "75-71=4", "16*4=64" ]
Current State: 64:[16, 63, 8, 75], Operations: [] Exploring Operation: 63+8=71, Resulting Numbers: [16, 75, 71] Generated Node #2: [16, 75, 71] from Operation: 63+8=71 Current State: 64:[16, 75, 71], Operations: ['63+8=71'] Exploring Operation: 75-71=4, Resulting Numbers: [16, 4] Generated Node #3: [16, 4] from Operation: 75-71=4 Current State: 64:[16, 4], Operations: ['63+8=71', '75-71=4'] Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[16, 63, 8, 75], Operations: [] Exploring Operation: 75-8=67, Resulting Numbers: [16, 63, 67] Generated Node #0,0: 64:[16, 63, 67] Operation: 75-8=67 Exploring Operation: 75-16=59, Resulting Numbers: [63, 8, 59] Generated Node #0,1: 64:[63, 8, 59] Operation: 75-16=59 Exploring Operation: 75-63=12, Resulting Numbers: [16, 8, 12] Generated Node #0,2: 64:[16, 8, 12] Operation: 75-63=12 Exploring Operation: 16-8=8, Resulting Numbers: [63, 75, 8] Generated Node #0,3: 64:[63, 75, 8] Operation: 16-8=8 Exploring Operation: 16/8=2, Resulting Numbers: [63, 75, 2] Generated Node #0,4: 64:[63, 75, 2] Operation: 16/8=2 Moving to Node #0,0 Current State: 64:[16, 63, 67], Operations: ['75-8=67'] Exploring Operation: 67-63=4, Resulting Numbers: [16, 4] Generated Node #0,0,0: 64:[16, 4] Operation: 67-63=4 Exploring Operation: 63-16=47, Resulting Numbers: [67, 47] Generated Node #0,0,1: 64:[67, 47] Operation: 63-16=47 Exploring Operation: 16+67=83, Resulting Numbers: [63, 83] Generated Node #0,0,2: 64:[63, 83] Operation: 16+67=83 Exploring Operation: 16+63=79, Resulting Numbers: [67, 79] Generated Node #0,0,3: 64:[67, 79] Operation: 16+63=79 Exploring Operation: 67-16=51, Resulting Numbers: [63, 51] Generated Node #0,0,4: 64:[63, 51] Operation: 67-16=51 Moving to Node #0,2 Current State: 64:[16, 8, 12], Operations: ['75-63=12'] Exploring Operation: 16/8=2, Resulting Numbers: [12, 2] Generated Node #0,2,0: 64:[12, 2] Operation: 16/8=2 Exploring Operation: 16-12=4, Resulting Numbers: [8, 4] Generated Node #0,2,1: 64:[8, 4] Operation: 16-12=4 Exploring Operation: 16+12=28, Resulting Numbers: [8, 28] Generated Node #0,2,2: 64:[8, 28] Operation: 16+12=28 Exploring Operation: 12-8=4, Resulting Numbers: [16, 4] Generated Node #0,2,3: 64:[16, 4] Operation: 12-8=4 Exploring Operation: 16-8=8, Resulting Numbers: [12, 8] Generated Node #0,2,4: 64:[12, 8] Operation: 16-8=8 Moving to Node #0,1 Current State: 64:[63, 8, 59], Operations: ['75-16=59'] Exploring Operation: 8+59=67, Resulting Numbers: [63, 67] Generated Node #0,1,0: 64:[63, 67] Operation: 8+59=67 Exploring Operation: 59-8=51, Resulting Numbers: [63, 51] Generated Node #0,1,1: 64:[63, 51] Operation: 59-8=51 Exploring Operation: 63-59=4, Resulting Numbers: [8, 4] Generated Node #0,1,2: 64:[8, 4] Operation: 63-59=4 Exploring Operation: 63-8=55, Resulting Numbers: [59, 55] Generated Node #0,1,3: 64:[59, 55] Operation: 63-8=55 Exploring Operation: 63+8=71, Resulting Numbers: [59, 71] Generated Node #0,1,4: 64:[59, 71] Operation: 63+8=71 Moving to Node #0,3 Current State: 64:[63, 75, 8], Operations: ['16-8=8'] Exploring Operation: 63+8=71, Resulting Numbers: [75, 71] Generated Node #0,3,0: 64:[75, 71] Operation: 63+8=71 Exploring Operation: 63-8=55, Resulting Numbers: [75, 55] Generated Node #0,3,1: 64:[75, 55] Operation: 63-8=55 Exploring Operation: 75-8=67, Resulting Numbers: [63, 67] Generated Node #0,3,2: 64:[63, 67] Operation: 75-8=67 Exploring Operation: 75+8=83, Resulting Numbers: [63, 83] Generated Node #0,3,3: 64:[63, 83] Operation: 75+8=83 Exploring Operation: 75-63=12, Resulting Numbers: [8, 12] Generated Node #0,3,4: 64:[8, 12] Operation: 75-63=12 Moving to Node #0,4 Current State: 64:[63, 75, 2], Operations: ['16/8=2'] Exploring Operation: 75-63=12, Resulting Numbers: [2, 12] Generated Node #0,4,0: 64:[2, 12] Operation: 75-63=12 Exploring Operation: 63+2=65, Resulting Numbers: [75, 65] Generated Node #0,4,1: 64:[75, 65] Operation: 63+2=65 Exploring Operation: 75-2=73, Resulting Numbers: [63, 73] Generated Node #0,4,2: 64:[63, 73] Operation: 75-2=73 Exploring Operation: 75+2=77, Resulting Numbers: [63, 77] Generated Node #0,4,3: 64:[63, 77] Operation: 75+2=77 Exploring Operation: 63-2=61, Resulting Numbers: [75, 61] Generated Node #0,4,4: 64:[75, 61] Operation: 63-2=61 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 64:[2, 12], Operations: ['16/8=2', '75-63=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,64 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,64 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,64 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,64 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 #0,4,2 Current State: 64:[63, 73], Operations: ['16/8=2', '75-2=73'] Exploring Operation: 63*73=4599, Resulting Numbers: [4599] 4599,64 unequal: No Solution Exploring Operation: 73-63=10, Resulting Numbers: [10] 10,64 unequal: No Solution Exploring Operation: 63+73=136, Resulting Numbers: [136] 136,64 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 #0,4,1 Current State: 64:[75, 65], Operations: ['16/8=2', '63+2=65'] Exploring Operation: 75-65=10, Resulting Numbers: [10] 10,64 unequal: No Solution Exploring Operation: 75*65=4875, Resulting Numbers: [4875] 4875,64 unequal: No Solution Exploring Operation: 75+65=140, Resulting Numbers: [140] 140,64 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 #0,4,3 Current State: 64:[63, 77], Operations: ['16/8=2', '75+2=77'] Exploring Operation: 63*77=4851, Resulting Numbers: [4851] 4851,64 unequal: No Solution Exploring Operation: 63+77=140, Resulting Numbers: [140] 140,64 unequal: No Solution Exploring Operation: 77-63=14, Resulting Numbers: [14] 14,64 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 #0,4,4 Current State: 64:[75, 61], Operations: ['16/8=2', '63-2=61'] Exploring Operation: 75+61=136, Resulting Numbers: [136] 136,64 unequal: No Solution Exploring Operation: 75-61=14, Resulting Numbers: [14] 14,64 unequal: No Solution Exploring Operation: 75*61=4575, Resulting Numbers: [4575] 4575,64 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: 64:[16, 4], Operations: ['75-8=67', '67-63=4'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,64 unequal: No Solution Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[16, 63, 8, 75], Operations: [] Exploring Operation: 75-8=67, Resulting Numbers: [16, 63, 67] Generated Node #0,0: 64:[16, 63, 67] Operation: 75-8=67 Moving to Node #0,0 Current State: 64:[16, 63, 67], Operations: ['75-8=67'] Exploring Operation: 67-63=4, Resulting Numbers: [16, 4] Generated Node #0,0,0: 64:[16, 4] Operation: 67-63=4 Moving to Node #0,0,0 Current State: 64:[16, 4], Operations: ['75-8=67', '67-63=4'] Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
0.954861
hs_5
sum_heuristic
[ 11, 18, 73, 5 ]
10
[ "73-18=55", "55/11=5", "5+5=10" ]
Current State: 10:[11, 18, 73, 5], Operations: [] Exploring Operation: 73-18=55, Resulting Numbers: [11, 5, 55] Generated Node #2: [11, 5, 55] from Operation: 73-18=55 Current State: 10:[11, 5, 55], Operations: ['73-18=55'] Exploring Operation: 55/11=5, Resulting Numbers: [5, 5] Generated Node #3: [5, 5] from Operation: 55/11=5 Current State: 10:[5, 5], Operations: ['73-18=55', '55/11=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[11, 18, 73, 5], Operations: [] Exploring Operation: 73-18=55, Resulting Numbers: [11, 5, 55] Generated Node #0,0: 10:[11, 5, 55] Operation: 73-18=55 Moving to Node #0,0 Current State: 10:[11, 5, 55], Operations: ['73-18=55'] Exploring Operation: 55/11=5, Resulting Numbers: [5, 5] Generated Node #0,0,0: 10:[5, 5] Operation: 55/11=5 Moving to Node #0,0,0 Current State: 10:[5, 5], Operations: ['73-18=55', '55/11=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[11, 18, 73, 5], Operations: [] Exploring Operation: 73-18=55, Resulting Numbers: [11, 5, 55] Generated Node #0,0: 10:[11, 5, 55] Operation: 73-18=55 Moving to Node #0,0 Current State: 10:[11, 5, 55], Operations: ['73-18=55'] Exploring Operation: 55/11=5, Resulting Numbers: [5, 5] Generated Node #0,0,0: 10:[5, 5] Operation: 55/11=5 Moving to Node #0,0,0 Current State: 10:[5, 5], Operations: ['73-18=55', '55/11=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 2, 84, 79, 35 ]
62
[ "79-35=44", "44/2=22", "84-22=62" ]
Current State: 62:[2, 84, 79, 35], Operations: [] Exploring Operation: 79-35=44, Resulting Numbers: [2, 84, 44] Generated Node #2: [2, 84, 44] from Operation: 79-35=44 Current State: 62:[2, 84, 44], Operations: ['79-35=44'] Exploring Operation: 44/2=22, Resulting Numbers: [84, 22] Generated Node #3: [84, 22] from Operation: 44/2=22 Current State: 62:[84, 22], Operations: ['79-35=44', '44/2=22'] Exploring Operation: 84-22=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[2, 84, 79, 35], Operations: [] Exploring Operation: 79-35=44, Resulting Numbers: [2, 84, 44] Generated Node #0,0: 62:[2, 84, 44] Operation: 79-35=44 Exploring Operation: 84-35=49, Resulting Numbers: [2, 79, 49] Generated Node #0,1: 62:[2, 79, 49] Operation: 84-35=49 Exploring Operation: 84-2=82, Resulting Numbers: [79, 35, 82] Generated Node #0,2: 62:[79, 35, 82] Operation: 84-2=82 Exploring Operation: 84-79=5, Resulting Numbers: [2, 35, 5] Generated Node #0,3: 62:[2, 35, 5] Operation: 84-79=5 Exploring Operation: 84/2=42, Resulting Numbers: [79, 35, 42] Generated Node #0,4: 62:[79, 35, 42] Operation: 84/2=42 Moving to Node #0,3 Current State: 62:[2, 35, 5], Operations: ['84-79=5'] Exploring Operation: 35/5=7, Resulting Numbers: [2, 7] Generated Node #0,3,0: 62:[2, 7] Operation: 35/5=7 Exploring Operation: 35-5=30, Resulting Numbers: [2, 30] Generated Node #0,3,1: 62:[2, 30] Operation: 35-5=30 Exploring Operation: 2+35=37, Resulting Numbers: [5, 37] Generated Node #0,3,2: 62:[5, 37] Operation: 2+35=37 Exploring Operation: 35-2=33, Resulting Numbers: [5, 33] Generated Node #0,3,3: 62:[5, 33] Operation: 35-2=33 Exploring Operation: 5-2=3, Resulting Numbers: [35, 3] Generated Node #0,3,4: 62:[35, 3] Operation: 5-2=3 Moving to Node #0,1 Current State: 62:[2, 79, 49], Operations: ['84-35=49'] Exploring Operation: 2+79=81, Resulting Numbers: [49, 81] Generated Node #0,1,0: 62:[49, 81] Operation: 2+79=81 Exploring Operation: 79-2=77, Resulting Numbers: [49, 77] Generated Node #0,1,1: 62:[49, 77] Operation: 79-2=77 Exploring Operation: 49-2=47, Resulting Numbers: [79, 47] Generated Node #0,1,2: 62:[79, 47] Operation: 49-2=47 Exploring Operation: 2+49=51, Resulting Numbers: [79, 51] Generated Node #0,1,3: 62:[79, 51] Operation: 2+49=51 Exploring Operation: 79-49=30, Resulting Numbers: [2, 30] Generated Node #0,1,4: 62:[2, 30] Operation: 79-49=30 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 62:[2, 30], Operations: ['84-35=49', '79-49=30'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,62 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 62:[49, 77], Operations: ['84-35=49', '79-2=77'] Exploring Operation: 49+77=126, Resulting Numbers: [126] 126,62 unequal: No Solution Exploring Operation: 49*77=3773, Resulting Numbers: [3773] 3773,62 unequal: No Solution Exploring Operation: 77-49=28, Resulting Numbers: [28] 28,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 62:[79, 51], Operations: ['84-35=49', '2+49=51'] Exploring Operation: 79*51=4029, Resulting Numbers: [4029] 4029,62 unequal: No Solution Exploring Operation: 79+51=130, Resulting Numbers: [130] 130,62 unequal: No Solution Exploring Operation: 79-51=28, Resulting Numbers: [28] 28,62 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:[49, 81], Operations: ['84-35=49', '2+79=81'] Exploring Operation: 81-49=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 49+81=130, Resulting Numbers: [130] 130,62 unequal: No Solution Exploring Operation: 49*81=3969, Resulting Numbers: [3969] 3969,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 62:[79, 47], Operations: ['84-35=49', '49-2=47'] Exploring Operation: 79*47=3713, Resulting Numbers: [3713] 3713,62 unequal: No Solution Exploring Operation: 79-47=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 79+47=126, Resulting Numbers: [126] 126,62 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: 62:[79, 35, 42], Operations: ['84/2=42'] Exploring Operation: 79+35=114, Resulting Numbers: [42, 114] Generated Node #0,4,0: 62:[42, 114] Operation: 79+35=114 Exploring Operation: 79-42=37, Resulting Numbers: [35, 37] Generated Node #0,4,1: 62:[35, 37] Operation: 79-42=37 Exploring Operation: 35+42=77, Resulting Numbers: [79, 77] Generated Node #0,4,2: 62:[79, 77] Operation: 35+42=77 Exploring Operation: 42-35=7, Resulting Numbers: [79, 7] Generated Node #0,4,3: 62:[79, 7] Operation: 42-35=7 Exploring Operation: 79-35=44, Resulting Numbers: [42, 44] Generated Node #0,4,4: 62:[42, 44] Operation: 79-35=44 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 62:[35, 37], Operations: ['84/2=42', '79-42=37'] Exploring Operation: 37-35=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 35*37=1295, Resulting Numbers: [1295] 1295,62 unequal: No Solution Exploring Operation: 35+37=72, Resulting Numbers: [72] 72,62 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 #0,4,3 Current State: 62:[79, 7], Operations: ['84/2=42', '42-35=7'] Exploring Operation: 79-7=72, Resulting Numbers: [72] 72,62 unequal: No Solution Exploring Operation: 79+7=86, Resulting Numbers: [86] 86,62 unequal: No Solution Exploring Operation: 79*7=553, Resulting Numbers: [553] 553,62 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 #0,4,4 Current State: 62:[42, 44], Operations: ['84/2=42', '79-35=44'] Exploring Operation: 42+44=86, Resulting Numbers: [86] 86,62 unequal: No Solution Exploring Operation: 42*44=1848, Resulting Numbers: [1848] 1848,62 unequal: No Solution Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,62 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 #0,4,2 Current State: 62:[79, 77], Operations: ['84/2=42', '35+42=77'] Exploring Operation: 79-77=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 79+77=156, Resulting Numbers: [156] 156,62 unequal: No Solution Exploring Operation: 79*77=6083, Resulting Numbers: [6083] 6083,62 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 #0,4,0 Current State: 62:[42, 114], Operations: ['84/2=42', '79+35=114'] Exploring Operation: 114-42=72, Resulting Numbers: [72] 72,62 unequal: No Solution Exploring Operation: 42*114=4788, Resulting Numbers: [4788] 4788,62 unequal: No Solution Exploring Operation: 42+114=156, Resulting Numbers: [156] 156,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 62:[2, 84, 44], Operations: ['79-35=44'] Exploring Operation: 84-2=82, Resulting Numbers: [44, 82] Generated Node #0,0,0: 62:[44, 82] Operation: 84-2=82 Exploring Operation: 84/2=42, Resulting Numbers: [44, 42] Generated Node #0,0,1: 62:[44, 42] Operation: 84/2=42 Exploring Operation: 44-2=42, Resulting Numbers: [84, 42] Generated Node #0,0,2: 62:[84, 42] Operation: 44-2=42 Exploring Operation: 84-44=40, Resulting Numbers: [2, 40] Generated Node #0,0,3: 62:[2, 40] Operation: 84-44=40 Exploring Operation: 44/2=22, Resulting Numbers: [84, 22] Generated Node #0,0,4: 62:[84, 22] Operation: 44/2=22 Moving to Node #0,2 Current State: 62:[79, 35, 82], Operations: ['84-2=82'] Exploring Operation: 35+82=117, Resulting Numbers: [79, 117] Generated Node #0,2,0: 62:[79, 117] Operation: 35+82=117 Exploring Operation: 79+35=114, Resulting Numbers: [82, 114] Generated Node #0,2,1: 62:[82, 114] Operation: 79+35=114 Exploring Operation: 82-79=3, Resulting Numbers: [35, 3] Generated Node #0,2,2: 62:[35, 3] Operation: 82-79=3 Exploring Operation: 79-35=44, Resulting Numbers: [82, 44] Generated Node #0,2,3: 62:[82, 44] Operation: 79-35=44 Exploring Operation: 82-35=47, Resulting Numbers: [79, 47] Generated Node #0,2,4: 62:[79, 47] Operation: 82-35=47 Moving to Node #0,3,1 Current State: 62:[2, 30], Operations: ['84-79=5', '35-5=30'] Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,62 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,62 unequal: No Solution Moving to Node #0,3,3 Current State: 62:[5, 33], Operations: ['84-79=5', '35-2=33'] Exploring Operation: 5*33=165, Resulting Numbers: [165] 165,62 unequal: No Solution Exploring Operation: 5+33=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,62 unequal: No Solution Moving to Node #0,3,0 Current State: 62:[2, 7], Operations: ['84-79=5', '35/5=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,62 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[35, 3], Operations: ['84-2=82', '82-79=3'] Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,62 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,62 unequal: No Solution Moving to Node #0,3,4 Current State: 62:[35, 3], Operations: ['84-79=5', '5-2=3'] Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,62 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,62 unequal: No Solution Moving to Node #0,0,3 Current State: 62:[2, 40], Operations: ['79-35=44', '84-44=40'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,62 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,62 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,62 unequal: No Solution Moving to Node #0,3,2 Current State: 62:[5, 37], Operations: ['84-79=5', '2+35=37'] Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 5*37=185, Resulting Numbers: [185] 185,62 unequal: No Solution Exploring Operation: 5+37=42, Resulting Numbers: [42] 42,62 unequal: No Solution Moving to Node #0,0,1 Current State: 62:[44, 42], Operations: ['79-35=44', '84/2=42'] Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 44*42=1848, Resulting Numbers: [1848] 1848,62 unequal: No Solution Exploring Operation: 44+42=86, Resulting Numbers: [86] 86,62 unequal: No Solution Moving to Node #0,0,4 Current State: 62:[84, 22], Operations: ['79-35=44', '44/2=22'] Exploring Operation: 84*22=1848, Resulting Numbers: [1848] 1848,62 unequal: No Solution Exploring Operation: 84-22=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[2, 84, 79, 35], Operations: [] Exploring Operation: 79-35=44, Resulting Numbers: [2, 84, 44] Generated Node #0,0: 62:[2, 84, 44] Operation: 79-35=44 Moving to Node #0,0 Current State: 62:[2, 84, 44], Operations: ['79-35=44'] Exploring Operation: 44/2=22, Resulting Numbers: [84, 22] Generated Node #0,0,4: 62:[84, 22] Operation: 44/2=22 Moving to Node #0,0,4 Current State: 62:[84, 22], Operations: ['79-35=44', '44/2=22'] Exploring Operation: 84-22=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.919271
hs_5
sum_heuristic
[ 10, 58, 35, 77 ]
64
[ "58-10=48", "35+77=112", "112-48=64" ]
Current State: 64:[10, 58, 35, 77], Operations: [] Exploring Operation: 58-10=48, Resulting Numbers: [35, 77, 48] Generated Node #2: [35, 77, 48] from Operation: 58-10=48 Current State: 64:[35, 77, 48], Operations: ['58-10=48'] Exploring Operation: 35+77=112, Resulting Numbers: [48, 112] Generated Node #3: [48, 112] from Operation: 35+77=112 Current State: 64:[48, 112], Operations: ['58-10=48', '35+77=112'] Exploring Operation: 112-48=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[10, 58, 35, 77], Operations: [] Exploring Operation: 10+58=68, Resulting Numbers: [35, 77, 68] Generated Node #0,0: 64:[35, 77, 68] Operation: 10+58=68 Exploring Operation: 77-58=19, Resulting Numbers: [10, 35, 19] Generated Node #0,1: 64:[10, 35, 19] Operation: 77-58=19 Exploring Operation: 77-10=67, Resulting Numbers: [58, 35, 67] Generated Node #0,2: 64:[58, 35, 67] Operation: 77-10=67 Exploring Operation: 77-35=42, Resulting Numbers: [10, 58, 42] Generated Node #0,3: 64:[10, 58, 42] Operation: 77-35=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[10, 35, 19], Operations: ['77-58=19'] Exploring Operation: 35-19=16, Resulting Numbers: [10, 16] Generated Node #0,1,0: 64:[10, 16] Operation: 35-19=16 Exploring Operation: 19-10=9, Resulting Numbers: [35, 9] Generated Node #0,1,1: 64:[35, 9] Operation: 19-10=9 Exploring Operation: 35-10=25, Resulting Numbers: [19, 25] Generated Node #0,1,2: 64:[19, 25] Operation: 35-10=25 Exploring Operation: 10+19=29, Resulting Numbers: [35, 29] Generated Node #0,1,3: 64:[35, 29] Operation: 10+19=29 Moving to Node #0,1,0 Current State: 64:[10, 16], Operations: ['77-58=19', '35-19=16'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,64 unequal: No Solution Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,64 unequal: No Solution Moving to Node #0,1,1 Current State: 64:[35, 9], Operations: ['77-58=19', '19-10=9'] Exploring Operation: 35*9=315, Resulting Numbers: [315] 315,64 unequal: No Solution Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,64 unequal: No Solution Moving to Node #0,1,3 Current State: 64:[35, 29], Operations: ['77-58=19', '10+19=29'] Exploring Operation: 35*29=1015, Resulting Numbers: [1015] 1015,64 unequal: No Solution Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,64 unequal: No Solution Exploring Operation: 35+29=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[10, 58, 35, 77], Operations: [] Exploring Operation: 77-58=19, Resulting Numbers: [10, 35, 19] Generated Node #0,1: 64:[10, 35, 19] Operation: 77-58=19 Moving to Node #0,1 Current State: 64:[10, 35, 19], Operations: ['77-58=19'] Exploring Operation: 10+19=29, Resulting Numbers: [35, 29] Generated Node #0,1,3: 64:[35, 29] Operation: 10+19=29 Moving to Node #0,1,3 Current State: 64:[35, 29], Operations: ['77-58=19', '10+19=29'] Exploring Operation: 35+29=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 78, 30, 60, 37 ]
43
[ "78-37=41", "60/30=2", "41+2=43" ]
Current State: 43:[78, 30, 60, 37], Operations: [] Exploring Operation: 78-37=41, Resulting Numbers: [30, 60, 41] Generated Node #2: [30, 60, 41] from Operation: 78-37=41 Current State: 43:[30, 60, 41], Operations: ['78-37=41'] Exploring Operation: 60/30=2, Resulting Numbers: [41, 2] Generated Node #3: [41, 2] from Operation: 60/30=2 Current State: 43:[41, 2], Operations: ['78-37=41', '60/30=2'] Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[78, 30, 60, 37], Operations: [] Exploring Operation: 78-30=48, Resulting Numbers: [60, 37, 48] Generated Node #0,0: 43:[60, 37, 48] Operation: 78-30=48 Exploring Operation: 78-37=41, Resulting Numbers: [30, 60, 41] Generated Node #0,1: 43:[30, 60, 41] Operation: 78-37=41 Moving to Node #0,0 Current State: 43:[60, 37, 48], Operations: ['78-30=48'] Exploring Operation: 60-48=12, Resulting Numbers: [37, 12] Generated Node #0,0,0: 43:[37, 12] Operation: 60-48=12 Exploring Operation: 60-37=23, Resulting Numbers: [48, 23] Generated Node #0,0,1: 43:[48, 23] Operation: 60-37=23 Moving to Node #0,1 Current State: 43:[30, 60, 41], Operations: ['78-37=41'] Exploring Operation: 60-41=19, Resulting Numbers: [30, 19] Generated Node #0,1,0: 43:[30, 19] Operation: 60-41=19 Exploring Operation: 60-30=30, Resulting Numbers: [41, 30] Generated Node #0,1,1: 43:[41, 30] Operation: 60-30=30 Moving to Node #0,1,1 Current State: 43:[41, 30], Operations: ['78-37=41', '60-30=30'] Exploring Operation: 41+30=71, Resulting Numbers: [71] 71,43 unequal: No Solution Exploring Operation: 41-30=11, Resulting Numbers: [11] 11,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[48, 23], Operations: ['78-30=48', '60-37=23'] Exploring Operation: 48-23=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 48+23=71, Resulting Numbers: [71] 71,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[37, 12], Operations: ['78-30=48', '60-48=12'] Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 37+12=49, Resulting Numbers: [49] 49,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[30, 19], Operations: ['78-37=41', '60-41=19'] Exploring Operation: 30-19=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 30+19=49, Resulting Numbers: [49] 49,43 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 35, 33, 72, 22 ]
96
[ "35-33=2", "72+22=94", "2+94=96" ]
Current State: 96:[35, 33, 72, 22], Operations: [] Exploring Operation: 35-33=2, Resulting Numbers: [72, 22, 2] Generated Node #2: [72, 22, 2] from Operation: 35-33=2 Current State: 96:[72, 22, 2], Operations: ['35-33=2'] Exploring Operation: 72+22=94, Resulting Numbers: [2, 94] Generated Node #3: [2, 94] from Operation: 72+22=94 Current State: 96:[2, 94], Operations: ['35-33=2', '72+22=94'] Exploring Operation: 2+94=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[35, 33, 72, 22], Operations: [] Exploring Operation: 72+22=94, Resulting Numbers: [35, 33, 94] Generated Node #0,0: 96:[35, 33, 94] Operation: 72+22=94 Exploring Operation: 35+72=107, Resulting Numbers: [33, 22, 107] Generated Node #0,1: 96:[33, 22, 107] Operation: 35+72=107 Exploring Operation: 72-33=39, Resulting Numbers: [35, 22, 39] Generated Node #0,2: 96:[35, 22, 39] Operation: 72-33=39 Exploring Operation: 72-35=37, Resulting Numbers: [33, 22, 37] Generated Node #0,3: 96:[33, 22, 37] Operation: 72-35=37 Exploring Operation: 72-22=50, Resulting Numbers: [35, 33, 50] Generated Node #0,4: 96:[35, 33, 50] Operation: 72-22=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[35, 33, 94], Operations: ['72+22=94'] Exploring Operation: 35+33=68, Resulting Numbers: [94, 68] Generated Node #0,0,0: 96:[94, 68] Operation: 35+33=68 Exploring Operation: 35+94=129, Resulting Numbers: [33, 129] Generated Node #0,0,1: 96:[33, 129] Operation: 35+94=129 Exploring Operation: 94-35=59, Resulting Numbers: [33, 59] Generated Node #0,0,2: 96:[33, 59] Operation: 94-35=59 Exploring Operation: 35-33=2, Resulting Numbers: [94, 2] Generated Node #0,0,3: 96:[94, 2] Operation: 35-33=2 Exploring Operation: 94-33=61, Resulting Numbers: [35, 61] Generated Node #0,0,4: 96:[35, 61] Operation: 94-33=61 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 96:[94, 2], Operations: ['72+22=94', '35-33=2'] Exploring Operation: 94*2=188, Resulting Numbers: [188] 188,96 unequal: No Solution Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,96 unequal: No Solution Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,96 unequal: No Solution Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[35, 33, 72, 22], Operations: [] Exploring Operation: 72+22=94, Resulting Numbers: [35, 33, 94] Generated Node #0,0: 96:[35, 33, 94] Operation: 72+22=94 Moving to Node #0,0 Current State: 96:[35, 33, 94], Operations: ['72+22=94'] Exploring Operation: 35-33=2, Resulting Numbers: [94, 2] Generated Node #0,0,3: 96:[94, 2] Operation: 35-33=2 Moving to Node #0,0,3 Current State: 96:[94, 2], Operations: ['72+22=94', '35-33=2'] Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 9, 4, 63, 15 ]
39
[ "15-9=6", "4*6=24", "63-24=39" ]
Current State: 39:[9, 4, 63, 15], Operations: [] Exploring Operation: 15-9=6, Resulting Numbers: [4, 63, 6] Generated Node #2: [4, 63, 6] from Operation: 15-9=6 Current State: 39:[4, 63, 6], Operations: ['15-9=6'] Exploring Operation: 4*6=24, Resulting Numbers: [63, 24] Generated Node #3: [63, 24] from Operation: 4*6=24 Current State: 39:[63, 24], Operations: ['15-9=6', '4*6=24'] Exploring Operation: 63-24=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[9, 4, 63, 15], Operations: [] Exploring Operation: 63/9=7, Resulting Numbers: [4, 15, 7] Generated Node #0,0: 39:[4, 15, 7] Operation: 63/9=7 Exploring Operation: 63-15=48, Resulting Numbers: [9, 4, 48] Generated Node #0,1: 39:[9, 4, 48] Operation: 63-15=48 Moving to Node #0,0 Current State: 39:[4, 15, 7], Operations: ['63/9=7'] Exploring Operation: 4+7=11, Resulting Numbers: [15, 11] Generated Node #0,0,0: 39:[15, 11] Operation: 4+7=11 Exploring Operation: 7-4=3, Resulting Numbers: [15, 3] Generated Node #0,0,1: 39:[15, 3] Operation: 7-4=3 Moving to Node #0,1 Current State: 39:[9, 4, 48], Operations: ['63-15=48'] Exploring Operation: 48/4=12, Resulting Numbers: [9, 12] Generated Node #0,1,0: 39:[9, 12] Operation: 48/4=12 Exploring Operation: 48-9=39, Resulting Numbers: [4, 39] Generated Node #0,1,1: 39:[4, 39] Operation: 48-9=39 Moving to Node #0,1,1 Current State: 39:[4, 39], Operations: ['63-15=48', '48-9=39'] Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 4+39=43, Resulting Numbers: [43] 43,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[15, 3], Operations: ['63/9=7', '7-4=3'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[15, 11], Operations: ['63/9=7', '4+7=11'] Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,39 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[9, 12], Operations: ['63-15=48', '48/4=12'] Exploring Operation: 9+12=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,39 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 59, 2, 14, 54 ]
63
[ "59-14=45", "2*54=108", "108-45=63" ]
Current State: 63:[59, 2, 14, 54], Operations: [] Exploring Operation: 59-14=45, Resulting Numbers: [2, 54, 45] Generated Node #2: [2, 54, 45] from Operation: 59-14=45 Current State: 63:[2, 54, 45], Operations: ['59-14=45'] Exploring Operation: 2*54=108, Resulting Numbers: [45, 108] Generated Node #3: [45, 108] from Operation: 2*54=108 Current State: 63:[45, 108], Operations: ['59-14=45', '2*54=108'] Exploring Operation: 108-45=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[59, 2, 14, 54], Operations: [] Exploring Operation: 14/2=7, Resulting Numbers: [59, 54, 7] Generated Node #0,0: 63:[59, 54, 7] Operation: 14/2=7 Exploring Operation: 54/2=27, Resulting Numbers: [59, 14, 27] Generated Node #0,1: 63:[59, 14, 27] Operation: 54/2=27 Exploring Operation: 14+54=68, Resulting Numbers: [59, 2, 68] Generated Node #0,2: 63:[59, 2, 68] Operation: 14+54=68 Exploring Operation: 59-54=5, Resulting Numbers: [2, 14, 5] Generated Node #0,3: 63:[2, 14, 5] Operation: 59-54=5 Exploring Operation: 59+2=61, Resulting Numbers: [14, 54, 61] Generated Node #0,4: 63:[14, 54, 61] Operation: 59+2=61 Moving to Node #0,3 Current State: 63:[2, 14, 5], Operations: ['59-54=5'] Exploring Operation: 14+5=19, Resulting Numbers: [2, 19] Generated Node #0,3,0: 63:[2, 19] Operation: 14+5=19 Exploring Operation: 2+5=7, Resulting Numbers: [14, 7] Generated Node #0,3,1: 63:[14, 7] Operation: 2+5=7 Exploring Operation: 14/2=7, Resulting Numbers: [5, 7] Generated Node #0,3,2: 63:[5, 7] Operation: 14/2=7 Exploring Operation: 14-2=12, Resulting Numbers: [5, 12] Generated Node #0,3,3: 63:[5, 12] Operation: 14-2=12 Exploring Operation: 14-5=9, Resulting Numbers: [2, 9] Generated Node #0,3,4: 63:[2, 9] Operation: 14-5=9 Moving to Node #0,2 Current State: 63:[59, 2, 68], Operations: ['14+54=68'] Exploring Operation: 68-2=66, Resulting Numbers: [59, 66] Generated Node #0,2,0: 63:[59, 66] Operation: 68-2=66 Exploring Operation: 2+68=70, Resulting Numbers: [59, 70] Generated Node #0,2,1: 63:[59, 70] Operation: 2+68=70 Exploring Operation: 59+2=61, Resulting Numbers: [68, 61] Generated Node #0,2,2: 63:[68, 61] Operation: 59+2=61 Exploring Operation: 59-2=57, Resulting Numbers: [68, 57] Generated Node #0,2,3: 63:[68, 57] Operation: 59-2=57 Exploring Operation: 68-59=9, Resulting Numbers: [2, 9] Generated Node #0,2,4: 63:[2, 9] Operation: 68-59=9 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 63:[2, 9], Operations: ['14+54=68', '68-59=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,63 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 63:[59, 66], Operations: ['14+54=68', '68-2=66'] Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 59+66=125, Resulting Numbers: [125] 125,63 unequal: No Solution Exploring Operation: 59*66=3894, Resulting Numbers: [3894] 3894,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 63:[68, 61], Operations: ['14+54=68', '59+2=61'] Exploring Operation: 68*61=4148, Resulting Numbers: [4148] 4148,63 unequal: No Solution Exploring Operation: 68+61=129, Resulting Numbers: [129] 129,63 unequal: No Solution Exploring Operation: 68-61=7, Resulting Numbers: [7] 7,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 63:[59, 70], Operations: ['14+54=68', '2+68=70'] Exploring Operation: 59*70=4130, Resulting Numbers: [4130] 4130,63 unequal: No Solution Exploring Operation: 70-59=11, Resulting Numbers: [11] 11,63 unequal: No Solution Exploring Operation: 59+70=129, Resulting Numbers: [129] 129,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 63:[68, 57], Operations: ['14+54=68', '59-2=57'] Exploring Operation: 68-57=11, Resulting Numbers: [11] 11,63 unequal: No Solution Exploring Operation: 68+57=125, Resulting Numbers: [125] 125,63 unequal: No Solution Exploring Operation: 68*57=3876, Resulting Numbers: [3876] 3876,63 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: 63:[59, 54, 7], Operations: ['14/2=7'] Exploring Operation: 54-7=47, Resulting Numbers: [59, 47] Generated Node #0,0,0: 63:[59, 47] Operation: 54-7=47 Exploring Operation: 54+7=61, Resulting Numbers: [59, 61] Generated Node #0,0,1: 63:[59, 61] Operation: 54+7=61 Exploring Operation: 59-7=52, Resulting Numbers: [54, 52] Generated Node #0,0,2: 63:[54, 52] Operation: 59-7=52 Exploring Operation: 59-54=5, Resulting Numbers: [7, 5] Generated Node #0,0,3: 63:[7, 5] Operation: 59-54=5 Exploring Operation: 59+7=66, Resulting Numbers: [54, 66] Generated Node #0,0,4: 63:[54, 66] Operation: 59+7=66 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 63:[7, 5], Operations: ['14/2=7', '59-54=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,63 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,63 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:[59, 61], Operations: ['14/2=7', '54+7=61'] Exploring Operation: 61-59=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 59+61=120, Resulting Numbers: [120] 120,63 unequal: No Solution Exploring Operation: 59*61=3599, Resulting Numbers: [3599] 3599,63 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 #0,0,4 Current State: 63:[54, 66], Operations: ['14/2=7', '59+7=66'] Exploring Operation: 54+66=120, Resulting Numbers: [120] 120,63 unequal: No Solution Exploring Operation: 54*66=3564, Resulting Numbers: [3564] 3564,63 unequal: No Solution Exploring Operation: 66-54=12, Resulting Numbers: [12] 12,63 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:[59, 47], Operations: ['14/2=7', '54-7=47'] Exploring Operation: 59*47=2773, Resulting Numbers: [2773] 2773,63 unequal: No Solution Exploring Operation: 59-47=12, Resulting Numbers: [12] 12,63 unequal: No Solution Exploring Operation: 59+47=106, Resulting Numbers: [106] 106,63 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:[54, 52], Operations: ['14/2=7', '59-7=52'] Exploring Operation: 54+52=106, Resulting Numbers: [106] 106,63 unequal: No Solution Exploring Operation: 54*52=2808, Resulting Numbers: [2808] 2808,63 unequal: No Solution Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,63 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: 63:[59, 14, 27], Operations: ['54/2=27'] Exploring Operation: 59-27=32, Resulting Numbers: [14, 32] Generated Node #0,1,0: 63:[14, 32] Operation: 59-27=32 Exploring Operation: 59-14=45, Resulting Numbers: [27, 45] Generated Node #0,1,1: 63:[27, 45] Operation: 59-14=45 Exploring Operation: 14+27=41, Resulting Numbers: [59, 41] Generated Node #0,1,2: 63:[59, 41] Operation: 14+27=41 Exploring Operation: 27-14=13, Resulting Numbers: [59, 13] Generated Node #0,1,3: 63:[59, 13] Operation: 27-14=13 Exploring Operation: 59+14=73, Resulting Numbers: [27, 73] Generated Node #0,1,4: 63:[27, 73] Operation: 59+14=73 Moving to Node #0,4 Current State: 63:[14, 54, 61], Operations: ['59+2=61'] Exploring Operation: 54-14=40, Resulting Numbers: [61, 40] Generated Node #0,4,0: 63:[61, 40] Operation: 54-14=40 Exploring Operation: 61-54=7, Resulting Numbers: [14, 7] Generated Node #0,4,1: 63:[14, 7] Operation: 61-54=7 Exploring Operation: 61-14=47, Resulting Numbers: [54, 47] Generated Node #0,4,2: 63:[54, 47] Operation: 61-14=47 Exploring Operation: 14+54=68, Resulting Numbers: [61, 68] Generated Node #0,4,3: 63:[61, 68] Operation: 14+54=68 Exploring Operation: 14+61=75, Resulting Numbers: [54, 75] Generated Node #0,4,4: 63:[54, 75] Operation: 14+61=75 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 63:[14, 7], Operations: ['59+2=61', '61-54=7'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,63 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,63 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 #0,4,3 Current State: 63:[61, 68], Operations: ['59+2=61', '14+54=68'] Exploring Operation: 61+68=129, Resulting Numbers: [129] 129,63 unequal: No Solution Exploring Operation: 68-61=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 61*68=4148, Resulting Numbers: [4148] 4148,63 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 #0,4,0 Current State: 63:[61, 40], Operations: ['59+2=61', '54-14=40'] Exploring Operation: 61+40=101, Resulting Numbers: [101] 101,63 unequal: No Solution Exploring Operation: 61*40=2440, Resulting Numbers: [2440] 2440,63 unequal: No Solution Exploring Operation: 61-40=21, Resulting Numbers: [21] 21,63 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 #0,4,4 Current State: 63:[54, 75], Operations: ['59+2=61', '14+61=75'] Exploring Operation: 54+75=129, Resulting Numbers: [129] 129,63 unequal: No Solution Exploring Operation: 75-54=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 54*75=4050, Resulting Numbers: [4050] 4050,63 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 #0,4,2 Current State: 63:[54, 47], Operations: ['59+2=61', '61-14=47'] Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 54*47=2538, Resulting Numbers: [2538] 2538,63 unequal: No Solution Exploring Operation: 54+47=101, Resulting Numbers: [101] 101,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,4 Current State: 63:[2, 9], Operations: ['59-54=5', '14-5=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,63 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,63 unequal: No Solution Moving to Node #0,3,2 Current State: 63:[5, 7], Operations: ['59-54=5', '14/2=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,63 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,63 unequal: No Solution Moving to Node #0,3,0 Current State: 63:[2, 19], Operations: ['59-54=5', '14+5=19'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,63 unequal: No Solution Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,63 unequal: No Solution Moving to Node #0,3,3 Current State: 63:[5, 12], Operations: ['59-54=5', '14-2=12'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,63 unequal: No Solution Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,63 unequal: No Solution Moving to Node #0,3,1 Current State: 63:[14, 7], Operations: ['59-54=5', '2+5=7'] Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,63 unequal: No Solution Moving to Node #0,1,3 Current State: 63:[59, 13], Operations: ['54/2=27', '27-14=13'] Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,63 unequal: No Solution Exploring Operation: 59*13=767, Resulting Numbers: [767] 767,63 unequal: No Solution Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,63 unequal: No Solution Moving to Node #0,1,4 Current State: 63:[27, 73], Operations: ['54/2=27', '59+14=73'] Exploring Operation: 73-27=46, Resulting Numbers: [46] 46,63 unequal: No Solution Exploring Operation: 27*73=1971, Resulting Numbers: [1971] 1971,63 unequal: No Solution Exploring Operation: 27+73=100, Resulting Numbers: [100] 100,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[14, 32], Operations: ['54/2=27', '59-27=32'] Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,63 unequal: No Solution Exploring Operation: 14+32=46, Resulting Numbers: [46] 46,63 unequal: No Solution Exploring Operation: 14*32=448, Resulting Numbers: [448] 448,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[59, 41], Operations: ['54/2=27', '14+27=41'] Exploring Operation: 59+41=100, Resulting Numbers: [100] 100,63 unequal: No Solution Exploring Operation: 59-41=18, Resulting Numbers: [18] 18,63 unequal: No Solution Exploring Operation: 59*41=2419, Resulting Numbers: [2419] 2419,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[27, 45], Operations: ['54/2=27', '59-14=45'] Exploring Operation: 27+45=72, Resulting Numbers: [72] 72,63 unequal: No Solution Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,63 unequal: No Solution Exploring Operation: 27*45=1215, Resulting Numbers: [1215] 1215,63 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 51, 54, 2, 34 ]
37
[ "51+54=105", "2*34=68", "105-68=37" ]
Current State: 37:[51, 54, 2, 34], Operations: [] Exploring Operation: 51+54=105, Resulting Numbers: [2, 34, 105] Generated Node #2: [2, 34, 105] from Operation: 51+54=105 Current State: 37:[2, 34, 105], Operations: ['51+54=105'] Exploring Operation: 2*34=68, Resulting Numbers: [105, 68] Generated Node #3: [105, 68] from Operation: 2*34=68 Current State: 37:[105, 68], Operations: ['51+54=105', '2*34=68'] Exploring Operation: 105-68=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[51, 54, 2, 34], Operations: [] Exploring Operation: 54/2=27, Resulting Numbers: [51, 34, 27] Generated Node #0,0: 37:[51, 34, 27] Operation: 54/2=27 Moving to Node #0,0 Current State: 37:[51, 34, 27], Operations: ['54/2=27'] Exploring Operation: 51-27=24, Resulting Numbers: [34, 24] Generated Node #0,0,0: 37:[34, 24] Operation: 51-27=24 Moving to Node #0,0,0 Current State: 37:[34, 24], Operations: ['54/2=27', '51-27=24'] Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,37 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 17, 2, 5, 78 ]
98
[ "17-2=15", "5+78=83", "15+83=98" ]
Current State: 98:[17, 2, 5, 78], Operations: [] Exploring Operation: 17-2=15, Resulting Numbers: [5, 78, 15] Generated Node #2: [5, 78, 15] from Operation: 17-2=15 Current State: 98:[5, 78, 15], Operations: ['17-2=15'] Exploring Operation: 5+78=83, Resulting Numbers: [15, 83] Generated Node #3: [15, 83] from Operation: 5+78=83 Current State: 98:[15, 83], Operations: ['17-2=15', '5+78=83'] Exploring Operation: 15+83=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[17, 2, 5, 78], Operations: [] Exploring Operation: 17+78=95, Resulting Numbers: [2, 5, 95] Generated Node #0,0: 98:[2, 5, 95] Operation: 17+78=95 Exploring Operation: 78-17=61, Resulting Numbers: [2, 5, 61] Generated Node #0,1: 98:[2, 5, 61] Operation: 78-17=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[2, 5, 95], Operations: ['17+78=95'] Exploring Operation: 2+5=7, Resulting Numbers: [95, 7] Generated Node #0,0,0: 98:[95, 7] Operation: 2+5=7 Exploring Operation: 5+95=100, Resulting Numbers: [2, 100] Generated Node #0,0,1: 98:[2, 100] Operation: 5+95=100 Moving to Node #0,0,1 Current State: 98:[2, 100], Operations: ['17+78=95', '5+95=100'] Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[17, 2, 5, 78], Operations: [] Exploring Operation: 17+78=95, Resulting Numbers: [2, 5, 95] Generated Node #0,0: 98:[2, 5, 95] Operation: 17+78=95 Moving to Node #0,0 Current State: 98:[2, 5, 95], Operations: ['17+78=95'] Exploring Operation: 5+95=100, Resulting Numbers: [2, 100] Generated Node #0,0,1: 98:[2, 100] Operation: 5+95=100 Moving to Node #0,0,1 Current State: 98:[2, 100], Operations: ['17+78=95', '5+95=100'] Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 80, 98, 89, 69 ]
38
[ "98-80=18", "89-69=20", "18+20=38" ]
Current State: 38:[80, 98, 89, 69], Operations: [] Exploring Operation: 98-80=18, Resulting Numbers: [89, 69, 18] Generated Node #2: [89, 69, 18] from Operation: 98-80=18 Current State: 38:[89, 69, 18], Operations: ['98-80=18'] Exploring Operation: 89-69=20, Resulting Numbers: [18, 20] Generated Node #3: [18, 20] from Operation: 89-69=20 Current State: 38:[18, 20], Operations: ['98-80=18', '89-69=20'] Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[80, 98, 89, 69], Operations: [] Exploring Operation: 98-80=18, Resulting Numbers: [89, 69, 18] Generated Node #0,0: 38:[89, 69, 18] Operation: 98-80=18 Exploring Operation: 98-69=29, Resulting Numbers: [80, 89, 29] Generated Node #0,1: 38:[80, 89, 29] Operation: 98-69=29 Exploring Operation: 89-80=9, Resulting Numbers: [98, 69, 9] Generated Node #0,2: 38:[98, 69, 9] Operation: 89-80=9 Exploring Operation: 98-89=9, Resulting Numbers: [80, 69, 9] Generated Node #0,3: 38:[80, 69, 9] Operation: 98-89=9 Moving to Node #0,3 Current State: 38:[80, 69, 9], Operations: ['98-89=9'] Exploring Operation: 80+9=89, Resulting Numbers: [69, 89] Generated Node #0,3,0: 38:[69, 89] Operation: 80+9=89 Exploring Operation: 80-9=71, Resulting Numbers: [69, 71] Generated Node #0,3,1: 38:[69, 71] Operation: 80-9=71 Exploring Operation: 69-9=60, Resulting Numbers: [80, 60] Generated Node #0,3,2: 38:[80, 60] Operation: 69-9=60 Exploring Operation: 80-69=11, Resulting Numbers: [9, 11] Generated Node #0,3,3: 38:[9, 11] Operation: 80-69=11 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 38:[9, 11], Operations: ['98-89=9', '80-69=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,38 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 38:[69, 71], Operations: ['98-89=9', '80-9=71'] Exploring Operation: 71-69=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 69+71=140, Resulting Numbers: [140] 140,38 unequal: No Solution Exploring Operation: 69*71=4899, Resulting Numbers: [4899] 4899,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 38:[80, 60], Operations: ['98-89=9', '69-9=60'] Exploring Operation: 80*60=4800, Resulting Numbers: [4800] 4800,38 unequal: No Solution Exploring Operation: 80+60=140, Resulting Numbers: [140] 140,38 unequal: No Solution Exploring Operation: 80-60=20, Resulting Numbers: [20] 20,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 38:[69, 89], Operations: ['98-89=9', '80+9=89'] Exploring Operation: 69+89=158, Resulting Numbers: [158] 158,38 unequal: No Solution Exploring Operation: 89-69=20, Resulting Numbers: [20] 20,38 unequal: No Solution Exploring Operation: 69*89=6141, Resulting Numbers: [6141] 6141,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 38:[89, 69, 18], Operations: ['98-80=18'] Exploring Operation: 69-18=51, Resulting Numbers: [89, 51] Generated Node #0,0,0: 38:[89, 51] Operation: 69-18=51 Exploring Operation: 89-18=71, Resulting Numbers: [69, 71] Generated Node #0,0,1: 38:[69, 71] Operation: 89-18=71 Exploring Operation: 89-69=20, Resulting Numbers: [18, 20] Generated Node #0,0,2: 38:[18, 20] Operation: 89-69=20 Exploring Operation: 89+18=107, Resulting Numbers: [69, 107] Generated Node #0,0,3: 38:[69, 107] Operation: 89+18=107 Moving to Node #0,2 Current State: 38:[98, 69, 9], Operations: ['89-80=9'] Exploring Operation: 69-9=60, Resulting Numbers: [98, 60] Generated Node #0,2,0: 38:[98, 60] Operation: 69-9=60 Exploring Operation: 98-9=89, Resulting Numbers: [69, 89] Generated Node #0,2,1: 38:[69, 89] Operation: 98-9=89 Exploring Operation: 98+9=107, Resulting Numbers: [69, 107] Generated Node #0,2,2: 38:[69, 107] Operation: 98+9=107 Exploring Operation: 98-69=29, Resulting Numbers: [9, 29] Generated Node #0,2,3: 38:[9, 29] Operation: 98-69=29 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 38:[9, 29], Operations: ['89-80=9', '98-69=29'] Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[80, 98, 89, 69], Operations: [] Exploring Operation: 89-80=9, Resulting Numbers: [98, 69, 9] Generated Node #0,2: 38:[98, 69, 9] Operation: 89-80=9 Moving to Node #0,2 Current State: 38:[98, 69, 9], Operations: ['89-80=9'] Exploring Operation: 98-69=29, Resulting Numbers: [9, 29] Generated Node #0,2,3: 38:[9, 29] Operation: 98-69=29 Moving to Node #0,2,3 Current State: 38:[9, 29], Operations: ['89-80=9', '98-69=29'] Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
mult_heuristic
[ 66, 62, 54, 24 ]
74
[ "66-62=4", "54+24=78", "78-4=74" ]
Current State: 74:[66, 62, 54, 24], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [54, 24, 4] Generated Node #2: [54, 24, 4] from Operation: 66-62=4 Current State: 74:[54, 24, 4], Operations: ['66-62=4'] Exploring Operation: 54+24=78, Resulting Numbers: [4, 78] Generated Node #3: [4, 78] from Operation: 54+24=78 Current State: 74:[4, 78], Operations: ['66-62=4', '54+24=78'] Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[66, 62, 54, 24], Operations: [] Exploring Operation: 54-24=30, Resulting Numbers: [66, 62, 30] Generated Node #0,0: 74:[66, 62, 30] Operation: 54-24=30 Exploring Operation: 62-24=38, Resulting Numbers: [66, 54, 38] Generated Node #0,1: 74:[66, 54, 38] Operation: 62-24=38 Exploring Operation: 54+24=78, Resulting Numbers: [66, 62, 78] Generated Node #0,2: 74:[66, 62, 78] Operation: 54+24=78 Exploring Operation: 62-54=8, Resulting Numbers: [66, 24, 8] Generated Node #0,3: 74:[66, 24, 8] Operation: 62-54=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[66, 62, 78], Operations: ['54+24=78'] Exploring Operation: 66-62=4, Resulting Numbers: [78, 4] Generated Node #0,2,0: 74:[78, 4] Operation: 66-62=4 Exploring Operation: 78-66=12, Resulting Numbers: [62, 12] Generated Node #0,2,1: 74:[62, 12] Operation: 78-66=12 Exploring Operation: 66+62=128, Resulting Numbers: [78, 128] Generated Node #0,2,2: 74:[78, 128] Operation: 66+62=128 Exploring Operation: 78-62=16, Resulting Numbers: [66, 16] Generated Node #0,2,3: 74:[66, 16] Operation: 78-62=16 Moving to Node #0,2,0 Current State: 74:[78, 4], Operations: ['54+24=78', '66-62=4'] Exploring Operation: 78+4=82, Resulting Numbers: [82] 82,74 unequal: No Solution Exploring Operation: 78*4=312, Resulting Numbers: [312] 312,74 unequal: No Solution Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[66, 62, 54, 24], Operations: [] Exploring Operation: 54+24=78, Resulting Numbers: [66, 62, 78] Generated Node #0,2: 74:[66, 62, 78] Operation: 54+24=78 Moving to Node #0,2 Current State: 74:[66, 62, 78], Operations: ['54+24=78'] Exploring Operation: 66-62=4, Resulting Numbers: [78, 4] Generated Node #0,2,0: 74:[78, 4] Operation: 66-62=4 Moving to Node #0,2,0 Current State: 74:[78, 4], Operations: ['54+24=78', '66-62=4'] Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 6, 30, 52, 12 ]
54
[ "30-6=24", "24/12=2", "52+2=54" ]
Current State: 54:[6, 30, 52, 12], Operations: [] Exploring Operation: 30-6=24, Resulting Numbers: [52, 12, 24] Generated Node #2: [52, 12, 24] from Operation: 30-6=24 Current State: 54:[52, 12, 24], Operations: ['30-6=24'] Exploring Operation: 24/12=2, Resulting Numbers: [52, 2] Generated Node #3: [52, 2] from Operation: 24/12=2 Current State: 54:[52, 2], Operations: ['30-6=24', '24/12=2'] Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[6, 30, 52, 12], Operations: [] Exploring Operation: 6+12=18, Resulting Numbers: [30, 52, 18] Generated Node #0,0: 54:[30, 52, 18] Operation: 6+12=18 Exploring Operation: 30-12=18, Resulting Numbers: [6, 52, 18] Generated Node #0,1: 54:[6, 52, 18] Operation: 30-12=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[6, 52, 18], Operations: ['30-12=18'] Exploring Operation: 18/6=3, Resulting Numbers: [52, 3] Generated Node #0,1,0: 54:[52, 3] Operation: 18/6=3 Exploring Operation: 6+52=58, Resulting Numbers: [18, 58] Generated Node #0,1,1: 54:[18, 58] Operation: 6+52=58 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 54:[52, 3], Operations: ['30-12=18', '18/6=3'] Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,54 unequal: No Solution Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,54 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 #0,1,1 Current State: 54:[18, 58], Operations: ['30-12=18', '6+52=58'] Exploring Operation: 18+58=76, Resulting Numbers: [76] 76,54 unequal: No Solution Exploring Operation: 58-18=40, Resulting Numbers: [40] 40,54 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 #0,0 Current State: 54:[30, 52, 18], Operations: ['6+12=18'] Exploring Operation: 52-30=22, Resulting Numbers: [18, 22] Generated Node #0,0,0: 54:[18, 22] Operation: 52-30=22 Exploring Operation: 30-18=12, Resulting Numbers: [52, 12] Generated Node #0,0,1: 54:[52, 12] Operation: 30-18=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[18, 22], Operations: ['6+12=18', '52-30=22'] Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,54 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,54 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 #0,0,1 Current State: 54:[52, 12], Operations: ['6+12=18', '30-18=12'] Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,54 unequal: No Solution Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,54 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 No solution found.
0
hs_2
sum_heuristic
[ 61, 2, 21, 78 ]
43
[ "61+21=82", "78/2=39", "82-39=43" ]
Current State: 43:[61, 2, 21, 78], Operations: [] Exploring Operation: 61+21=82, Resulting Numbers: [2, 78, 82] Generated Node #2: [2, 78, 82] from Operation: 61+21=82 Current State: 43:[2, 78, 82], Operations: ['61+21=82'] Exploring Operation: 78/2=39, Resulting Numbers: [82, 39] Generated Node #3: [82, 39] from Operation: 78/2=39 Current State: 43:[82, 39], Operations: ['61+21=82', '78/2=39'] Exploring Operation: 82-39=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[61, 2, 21, 78], Operations: [] Exploring Operation: 78/2=39, Resulting Numbers: [61, 21, 39] Generated Node #0,0: 43:[61, 21, 39] Operation: 78/2=39 Moving to Node #0,0 Current State: 43:[61, 21, 39], Operations: ['78/2=39'] Exploring Operation: 61-21=40, Resulting Numbers: [39, 40] Generated Node #0,0,0: 43:[39, 40] Operation: 61-21=40 Moving to Node #0,0,0 Current State: 43:[39, 40], Operations: ['78/2=39', '61-21=40'] Exploring Operation: 39+40=79, Resulting Numbers: [79] 79,43 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 11, 3, 4, 9 ]
24
[ "11*9=99", "99-3=96", "96/4=24" ]
Current State: 24:[11, 3, 4, 9], Operations: [] Exploring Operation: 11*9=99, Resulting Numbers: [3, 4, 99] Generated Node #2: [3, 4, 99] from Operation: 11*9=99 Current State: 24:[3, 4, 99], Operations: ['11*9=99'] Exploring Operation: 99-3=96, Resulting Numbers: [4, 96] Generated Node #3: [4, 96] from Operation: 99-3=96 Current State: 24:[4, 96], Operations: ['11*9=99', '99-3=96'] Exploring Operation: 96/4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[11, 3, 4, 9], Operations: [] Exploring Operation: 11-9=2, Resulting Numbers: [3, 4, 2] Generated Node #0,0: 24:[3, 4, 2] Operation: 11-9=2 Moving to Node #0,0 Current State: 24:[3, 4, 2], Operations: ['11-9=2'] Exploring Operation: 3*4=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 24:[2, 12] Operation: 3*4=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 24:[2, 12], Operations: ['11-9=2', '3*4=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[11, 3, 4, 9], Operations: [] Exploring Operation: 11-9=2, Resulting Numbers: [3, 4, 2] Generated Node #0,0: 24:[3, 4, 2] Operation: 11-9=2 Moving to Node #0,0 Current State: 24:[3, 4, 2], Operations: ['11-9=2'] Exploring Operation: 3*4=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 24:[2, 12] Operation: 3*4=12 Moving to Node #0,0,0 Current State: 24:[2, 12], Operations: ['11-9=2', '3*4=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 74, 26, 39, 61 ]
41
[ "74-61=13", "26/13=2", "39+2=41" ]
Current State: 41:[74, 26, 39, 61], Operations: [] Exploring Operation: 74-61=13, Resulting Numbers: [26, 39, 13] Generated Node #2: [26, 39, 13] from Operation: 74-61=13 Current State: 41:[26, 39, 13], Operations: ['74-61=13'] Exploring Operation: 26/13=2, Resulting Numbers: [39, 2] Generated Node #3: [39, 2] from Operation: 26/13=2 Current State: 41:[39, 2], Operations: ['74-61=13', '26/13=2'] Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[74, 26, 39, 61], Operations: [] Exploring Operation: 74-26=48, Resulting Numbers: [39, 61, 48] Generated Node #0,0: 41:[39, 61, 48] Operation: 74-26=48 Exploring Operation: 74-39=35, Resulting Numbers: [26, 61, 35] Generated Node #0,1: 41:[26, 61, 35] Operation: 74-39=35 Exploring Operation: 61-26=35, Resulting Numbers: [74, 39, 35] Generated Node #0,2: 41:[74, 39, 35] Operation: 61-26=35 Moving to Node #0,0 Current State: 41:[39, 61, 48], Operations: ['74-26=48'] Exploring Operation: 61-39=22, Resulting Numbers: [48, 22] Generated Node #0,0,0: 41:[48, 22] Operation: 61-39=22 Exploring Operation: 48-39=9, Resulting Numbers: [61, 9] Generated Node #0,0,1: 41:[61, 9] Operation: 48-39=9 Exploring Operation: 61-48=13, Resulting Numbers: [39, 13] Generated Node #0,0,2: 41:[39, 13] Operation: 61-48=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[48, 22], Operations: ['74-26=48', '61-39=22'] Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,41 unequal: No Solution Exploring Operation: 48+22=70, Resulting Numbers: [70] 70,41 unequal: No Solution Exploring Operation: 48*22=1056, Resulting Numbers: [1056] 1056,41 unequal: No Solution No 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: 41:[39, 13], Operations: ['74-26=48', '61-48=13'] Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,41 unequal: No Solution Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,41 unequal: No Solution No 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: 41:[61, 9], Operations: ['74-26=48', '48-39=9'] Exploring Operation: 61*9=549, Resulting Numbers: [549] 549,41 unequal: No Solution Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,41 unequal: No Solution Exploring Operation: 61+9=70, Resulting Numbers: [70] 70,41 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: 41:[26, 61, 35], Operations: ['74-39=35'] Exploring Operation: 61-26=35, Resulting Numbers: [35, 35] Generated Node #0,1,0: 41:[35, 35] Operation: 61-26=35 Exploring Operation: 61-35=26, Resulting Numbers: [26, 26] Generated Node #0,1,1: 41:[26, 26] Operation: 61-35=26 Exploring Operation: 26+35=61, Resulting Numbers: [61, 61] Generated Node #0,1,2: 41:[61, 61] Operation: 26+35=61 Moving to Node #0,2 Current State: 41:[74, 39, 35], Operations: ['61-26=35'] Exploring Operation: 39+35=74, Resulting Numbers: [74, 74] Generated Node #0,2,0: 41:[74, 74] Operation: 39+35=74 Exploring Operation: 74-35=39, Resulting Numbers: [39, 39] Generated Node #0,2,1: 41:[39, 39] Operation: 74-35=39 Exploring Operation: 74-39=35, Resulting Numbers: [35, 35] Generated Node #0,2,2: 41:[35, 35] Operation: 74-39=35 Moving to Node #0,2,1 Current State: 41:[39, 39], Operations: ['61-26=35', '74-35=39'] Exploring Operation: 39/39=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 39-39=0, Resulting Numbers: [0] 0,41 unequal: No Solution Exploring Operation: 39+39=78, Resulting Numbers: [78] 78,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[35, 35], Operations: ['74-39=35', '61-26=35'] Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,41 unequal: No Solution Exploring Operation: 35/35=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 35-35=0, Resulting Numbers: [0] 0,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[35, 35], Operations: ['61-26=35', '74-39=35'] Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,41 unequal: No Solution Exploring Operation: 35-35=0, Resulting Numbers: [0] 0,41 unequal: No Solution Exploring Operation: 35/35=1, Resulting Numbers: [1] 1,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[26, 26], Operations: ['74-39=35', '61-35=26'] Exploring Operation: 26-26=0, Resulting Numbers: [0] 0,41 unequal: No Solution Exploring Operation: 26/26=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 26+26=52, Resulting Numbers: [52] 52,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[61, 61], Operations: ['74-39=35', '26+35=61'] Exploring Operation: 61-61=0, Resulting Numbers: [0] 0,41 unequal: No Solution Exploring Operation: 61/61=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 61+61=122, Resulting Numbers: [122] 122,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[74, 74], Operations: ['61-26=35', '39+35=74'] Exploring Operation: 74/74=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 74-74=0, Resulting Numbers: [0] 0,41 unequal: No Solution Exploring Operation: 74+74=148, Resulting Numbers: [148] 148,41 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 35, 8, 20, 80 ]
10
[ "35*8=280", "280-80=200", "200/20=10" ]
Current State: 10:[35, 8, 20, 80], Operations: [] Exploring Operation: 35*8=280, Resulting Numbers: [20, 80, 280] Generated Node #2: [20, 80, 280] from Operation: 35*8=280 Current State: 10:[20, 80, 280], Operations: ['35*8=280'] Exploring Operation: 280-80=200, Resulting Numbers: [20, 200] Generated Node #3: [20, 200] from Operation: 280-80=200 Current State: 10:[20, 200], Operations: ['35*8=280', '280-80=200'] Exploring Operation: 200/20=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[35, 8, 20, 80], Operations: [] Exploring Operation: 80/20=4, Resulting Numbers: [35, 8, 4] Generated Node #0,0: 10:[35, 8, 4] Operation: 80/20=4 Moving to Node #0,0 Current State: 10:[35, 8, 4], Operations: ['80/20=4'] Exploring Operation: 35-8=27, Resulting Numbers: [4, 27] Generated Node #0,0,0: 10:[4, 27] Operation: 35-8=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[4, 27], Operations: ['80/20=4', '35-8=27'] Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,10 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
[ 36, 83, 62, 84 ]
40
[ "83-62=21", "84/21=4", "36+4=40" ]
Current State: 40:[36, 83, 62, 84], Operations: [] Exploring Operation: 83-62=21, Resulting Numbers: [36, 84, 21] Generated Node #2: [36, 84, 21] from Operation: 83-62=21 Current State: 40:[36, 84, 21], Operations: ['83-62=21'] Exploring Operation: 84/21=4, Resulting Numbers: [36, 4] Generated Node #3: [36, 4] from Operation: 84/21=4 Current State: 40:[36, 4], Operations: ['83-62=21', '84/21=4'] Exploring Operation: 36+4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[36, 83, 62, 84], Operations: [] Exploring Operation: 84-62=22, Resulting Numbers: [36, 83, 22] Generated Node #0,0: 40:[36, 83, 22] Operation: 84-62=22 Exploring Operation: 84-83=1, Resulting Numbers: [36, 62, 1] Generated Node #0,1: 40:[36, 62, 1] Operation: 84-83=1 Exploring Operation: 83-62=21, Resulting Numbers: [36, 84, 21] Generated Node #0,2: 40:[36, 84, 21] Operation: 83-62=21 Moving to Node #0,1 Current State: 40:[36, 62, 1], Operations: ['84-83=1'] Exploring Operation: 62-36=26, Resulting Numbers: [1, 26] Generated Node #0,1,0: 40:[1, 26] Operation: 62-36=26 Exploring Operation: 36+1=37, Resulting Numbers: [62, 37] Generated Node #0,1,1: 40:[62, 37] Operation: 36+1=37 Exploring Operation: 62-1=61, Resulting Numbers: [36, 61] Generated Node #0,1,2: 40:[36, 61] Operation: 62-1=61 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[1, 26], Operations: ['84-83=1', '62-36=26'] Exploring Operation: 1*26=26, Resulting Numbers: [26] 26,40 unequal: No Solution Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,40 unequal: No Solution Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,40 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:[62, 37], Operations: ['84-83=1', '36+1=37'] Exploring Operation: 62*37=2294, Resulting Numbers: [2294] 2294,40 unequal: No Solution Exploring Operation: 62+37=99, Resulting Numbers: [99] 99,40 unequal: No Solution Exploring Operation: 62-37=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 #0,1,2 Current State: 40:[36, 61], Operations: ['84-83=1', '62-1=61'] Exploring Operation: 61-36=25, Resulting Numbers: [25] 25,40 unequal: No Solution Exploring Operation: 36*61=2196, Resulting Numbers: [2196] 2196,40 unequal: No Solution Exploring Operation: 36+61=97, Resulting Numbers: [97] 97,40 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: 40:[36, 83, 22], Operations: ['84-62=22'] Exploring Operation: 83-22=61, Resulting Numbers: [36, 61] Generated Node #0,0,0: 40:[36, 61] Operation: 83-22=61 Exploring Operation: 36-22=14, Resulting Numbers: [83, 14] Generated Node #0,0,1: 40:[83, 14] Operation: 36-22=14 Exploring Operation: 83-36=47, Resulting Numbers: [22, 47] Generated Node #0,0,2: 40:[22, 47] Operation: 83-36=47 Moving to Node #0,2 Current State: 40:[36, 84, 21], Operations: ['83-62=21'] Exploring Operation: 84/21=4, Resulting Numbers: [36, 4] Generated Node #0,2,0: 40:[36, 4] Operation: 84/21=4 Exploring Operation: 84-21=63, Resulting Numbers: [36, 63] Generated Node #0,2,1: 40:[36, 63] Operation: 84-21=63 Exploring Operation: 84-36=48, Resulting Numbers: [21, 48] Generated Node #0,2,2: 40:[21, 48] Operation: 84-36=48 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 40:[36, 4], Operations: ['83-62=21', '84/21=4'] Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,40 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,40 unequal: No Solution Exploring Operation: 36+4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[36, 83, 62, 84], Operations: [] Exploring Operation: 83-62=21, Resulting Numbers: [36, 84, 21] Generated Node #0,2: 40:[36, 84, 21] Operation: 83-62=21 Moving to Node #0,2 Current State: 40:[36, 84, 21], Operations: ['83-62=21'] Exploring Operation: 84/21=4, Resulting Numbers: [36, 4] Generated Node #0,2,0: 40:[36, 4] Operation: 84/21=4 Moving to Node #0,2,0 Current State: 40:[36, 4], Operations: ['83-62=21', '84/21=4'] Exploring Operation: 36+4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_3
sum_heuristic
[ 44, 99, 46, 56 ]
41
[ "44+99=143", "46+56=102", "143-102=41" ]
Current State: 41:[44, 99, 46, 56], Operations: [] Exploring Operation: 44+99=143, Resulting Numbers: [46, 56, 143] Generated Node #2: [46, 56, 143] from Operation: 44+99=143 Current State: 41:[46, 56, 143], Operations: ['44+99=143'] Exploring Operation: 46+56=102, Resulting Numbers: [143, 102] Generated Node #3: [143, 102] from Operation: 46+56=102 Current State: 41:[143, 102], Operations: ['44+99=143', '46+56=102'] Exploring Operation: 143-102=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[44, 99, 46, 56], Operations: [] Exploring Operation: 99-56=43, Resulting Numbers: [44, 46, 43] Generated Node #0,0: 41:[44, 46, 43] Operation: 99-56=43 Exploring Operation: 99-46=53, Resulting Numbers: [44, 56, 53] Generated Node #0,1: 41:[44, 56, 53] Operation: 99-46=53 Moving to Node #0,0 Current State: 41:[44, 46, 43], Operations: ['99-56=43'] Exploring Operation: 46-44=2, Resulting Numbers: [43, 2] Generated Node #0,0,0: 41:[43, 2] Operation: 46-44=2 Exploring Operation: 46-43=3, Resulting Numbers: [44, 3] Generated Node #0,0,1: 41:[44, 3] Operation: 46-43=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[43, 2], Operations: ['99-56=43', '46-44=2'] Exploring Operation: 43+2=45, Resulting Numbers: [45] 45,41 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[44, 99, 46, 56], Operations: [] Exploring Operation: 99-56=43, Resulting Numbers: [44, 46, 43] Generated Node #0,0: 41:[44, 46, 43] Operation: 99-56=43 Moving to Node #0,0 Current State: 41:[44, 46, 43], Operations: ['99-56=43'] Exploring Operation: 46-44=2, Resulting Numbers: [43, 2] Generated Node #0,0,0: 41:[43, 2] Operation: 46-44=2 Moving to Node #0,0,0 Current State: 41:[43, 2], Operations: ['99-56=43', '46-44=2'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 51, 43, 14, 62 ]
40
[ "51-43=8", "62-14=48", "48-8=40" ]
Current State: 40:[51, 43, 14, 62], Operations: [] Exploring Operation: 51-43=8, Resulting Numbers: [14, 62, 8] Generated Node #2: [14, 62, 8] from Operation: 51-43=8 Current State: 40:[14, 62, 8], Operations: ['51-43=8'] Exploring Operation: 62-14=48, Resulting Numbers: [8, 48] Generated Node #3: [8, 48] from Operation: 62-14=48 Current State: 40:[8, 48], Operations: ['51-43=8', '62-14=48'] Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[51, 43, 14, 62], Operations: [] Exploring Operation: 62-51=11, Resulting Numbers: [43, 14, 11] Generated Node #0,0: 40:[43, 14, 11] Operation: 62-51=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[43, 14, 11], Operations: ['62-51=11'] Exploring Operation: 14-11=3, Resulting Numbers: [43, 3] Generated Node #0,0,0: 40:[43, 3] Operation: 14-11=3 Moving to Node #0,0,0 Current State: 40:[43, 3], Operations: ['62-51=11', '14-11=3'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[51, 43, 14, 62], Operations: [] Exploring Operation: 62-51=11, Resulting Numbers: [43, 14, 11] Generated Node #0,0: 40:[43, 14, 11] Operation: 62-51=11 Moving to Node #0,0 Current State: 40:[43, 14, 11], Operations: ['62-51=11'] Exploring Operation: 14-11=3, Resulting Numbers: [43, 3] Generated Node #0,0,0: 40:[43, 3] Operation: 14-11=3 Moving to Node #0,0,0 Current State: 40:[43, 3], Operations: ['62-51=11', '14-11=3'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 15, 66, 8, 62 ]
28
[ "15-8=7", "66-62=4", "7*4=28" ]
Current State: 28:[15, 66, 8, 62], Operations: [] Exploring Operation: 15-8=7, Resulting Numbers: [66, 62, 7] Generated Node #2: [66, 62, 7] from Operation: 15-8=7 Current State: 28:[66, 62, 7], Operations: ['15-8=7'] Exploring Operation: 66-62=4, Resulting Numbers: [7, 4] Generated Node #3: [7, 4] from Operation: 66-62=4 Current State: 28:[7, 4], Operations: ['15-8=7', '66-62=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[15, 66, 8, 62], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [15, 8, 4] Generated Node #0,0: 28:[15, 8, 4] Operation: 66-62=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[15, 8, 4], Operations: ['66-62=4'] Exploring Operation: 15-8=7, Resulting Numbers: [4, 7] Generated Node #0,0,0: 28:[4, 7] Operation: 15-8=7 Moving to Node #0,0,0 Current State: 28:[4, 7], Operations: ['66-62=4', '15-8=7'] Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[15, 66, 8, 62], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [15, 8, 4] Generated Node #0,0: 28:[15, 8, 4] Operation: 66-62=4 Moving to Node #0,0 Current State: 28:[15, 8, 4], Operations: ['66-62=4'] Exploring Operation: 15-8=7, Resulting Numbers: [4, 7] Generated Node #0,0,0: 28:[4, 7] Operation: 15-8=7 Moving to Node #0,0,0 Current State: 28:[4, 7], Operations: ['66-62=4', '15-8=7'] Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 55, 18, 16, 7 ]
31
[ "55+7=62", "18-16=2", "62/2=31" ]
Current State: 31:[55, 18, 16, 7], Operations: [] Exploring Operation: 55+7=62, Resulting Numbers: [18, 16, 62] Generated Node #2: [18, 16, 62] from Operation: 55+7=62 Current State: 31:[18, 16, 62], Operations: ['55+7=62'] Exploring Operation: 18-16=2, Resulting Numbers: [62, 2] Generated Node #3: [62, 2] from Operation: 18-16=2 Current State: 31:[62, 2], Operations: ['55+7=62', '18-16=2'] Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[55, 18, 16, 7], Operations: [] Exploring Operation: 55-7=48, Resulting Numbers: [18, 16, 48] Generated Node #0,0: 31:[18, 16, 48] Operation: 55-7=48 Exploring Operation: 18+7=25, Resulting Numbers: [55, 16, 25] Generated Node #0,1: 31:[55, 16, 25] Operation: 18+7=25 Exploring Operation: 55-18=37, Resulting Numbers: [16, 7, 37] Generated Node #0,2: 31:[16, 7, 37] Operation: 55-18=37 Exploring Operation: 55-16=39, Resulting Numbers: [18, 7, 39] Generated Node #0,3: 31:[18, 7, 39] Operation: 55-16=39 Exploring Operation: 16+7=23, Resulting Numbers: [55, 18, 23] Generated Node #0,4: 31:[55, 18, 23] Operation: 16+7=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[18, 16, 48], Operations: ['55-7=48'] Exploring Operation: 18-16=2, Resulting Numbers: [48, 2] Generated Node #0,0,0: 31:[48, 2] Operation: 18-16=2 Exploring Operation: 48-16=32, Resulting Numbers: [18, 32] Generated Node #0,0,1: 31:[18, 32] Operation: 48-16=32 Exploring Operation: 48/16=3, Resulting Numbers: [18, 3] Generated Node #0,0,2: 31:[18, 3] Operation: 48/16=3 Exploring Operation: 48-18=30, Resulting Numbers: [16, 30] Generated Node #0,0,3: 31:[16, 30] Operation: 48-18=30 Exploring Operation: 18+16=34, Resulting Numbers: [48, 34] Generated Node #0,0,4: 31:[48, 34] Operation: 18+16=34 Moving to Node #0,0,1 Current State: 31:[18, 32], Operations: ['55-7=48', '48-16=32'] Exploring Operation: 18+32=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 18*32=576, Resulting Numbers: [576] 576,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[16, 30], Operations: ['55-7=48', '48-18=30'] Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 16*30=480, Resulting Numbers: [480] 480,31 unequal: No Solution Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,31 unequal: No Solution Moving to Node #0,0,4 Current State: 31:[48, 34], Operations: ['55-7=48', '18+16=34'] Exploring Operation: 48*34=1632, Resulting Numbers: [1632] 1632,31 unequal: No Solution Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 48+34=82, Resulting Numbers: [82] 82,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[18, 3], Operations: ['55-7=48', '48/16=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,31 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[48, 2], Operations: ['55-7=48', '18-16=2'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,31 unequal: No Solution Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,31 unequal: No Solution Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,31 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:[55, 16, 25], Operations: ['18+7=25'] Exploring Operation: 55-16=39, Resulting Numbers: [25, 39] Generated Node #0,1,0: 31:[25, 39] Operation: 55-16=39 Exploring Operation: 16+25=41, Resulting Numbers: [55, 41] Generated Node #0,1,1: 31:[55, 41] Operation: 16+25=41 Exploring Operation: 55-25=30, Resulting Numbers: [16, 30] Generated Node #0,1,2: 31:[16, 30] Operation: 55-25=30 Exploring Operation: 25-16=9, Resulting Numbers: [55, 9] Generated Node #0,1,3: 31:[55, 9] Operation: 25-16=9 Exploring Operation: 55+16=71, Resulting Numbers: [25, 71] Generated Node #0,1,4: 31:[25, 71] Operation: 55+16=71 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 31:[25, 39], Operations: ['18+7=25', '55-16=39'] Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 25+39=64, Resulting Numbers: [64] 64,31 unequal: No Solution Exploring Operation: 25*39=975, Resulting Numbers: [975] 975,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 31:[16, 30], Operations: ['18+7=25', '55-25=30'] Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 16*30=480, Resulting Numbers: [480] 480,31 unequal: No Solution Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 31:[55, 41], Operations: ['18+7=25', '16+25=41'] Exploring Operation: 55*41=2255, Resulting Numbers: [2255] 2255,31 unequal: No Solution Exploring Operation: 55-41=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 55+41=96, Resulting Numbers: [96] 96,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 31:[55, 9], Operations: ['18+7=25', '25-16=9'] Exploring Operation: 55+9=64, Resulting Numbers: [64] 64,31 unequal: No Solution Exploring Operation: 55*9=495, Resulting Numbers: [495] 495,31 unequal: No Solution Exploring Operation: 55-9=46, Resulting Numbers: [46] 46,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 31:[25, 71], Operations: ['18+7=25', '55+16=71'] Exploring Operation: 71-25=46, Resulting Numbers: [46] 46,31 unequal: No Solution Exploring Operation: 25+71=96, Resulting Numbers: [96] 96,31 unequal: No Solution Exploring Operation: 25*71=1775, Resulting Numbers: [1775] 1775,31 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 #0,2 Current State: 31:[16, 7, 37], Operations: ['55-18=37'] Exploring Operation: 7+37=44, Resulting Numbers: [16, 44] Generated Node #0,2,0: 31:[16, 44] Operation: 7+37=44 Exploring Operation: 16+7=23, Resulting Numbers: [37, 23] Generated Node #0,2,1: 31:[37, 23] Operation: 16+7=23 Exploring Operation: 16-7=9, Resulting Numbers: [37, 9] Generated Node #0,2,2: 31:[37, 9] Operation: 16-7=9 Exploring Operation: 37-16=21, Resulting Numbers: [7, 21] Generated Node #0,2,3: 31:[7, 21] Operation: 37-16=21 Exploring Operation: 37-7=30, Resulting Numbers: [16, 30] Generated Node #0,2,4: 31:[16, 30] Operation: 37-7=30 Moving to Node #0,2,1 Current State: 31:[37, 23], Operations: ['55-18=37', '16+7=23'] Exploring Operation: 37+23=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 37*23=851, Resulting Numbers: [851] 851,31 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,31 unequal: No Solution Moving to Node #0,2,4 Current State: 31:[16, 30], Operations: ['55-18=37', '37-7=30'] Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,31 unequal: No Solution Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 16*30=480, Resulting Numbers: [480] 480,31 unequal: No Solution Moving to Node #0,2,0 Current State: 31:[16, 44], Operations: ['55-18=37', '7+37=44'] Exploring Operation: 44-16=28, Resulting Numbers: [28] 28,31 unequal: No Solution Exploring Operation: 16+44=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 16*44=704, Resulting Numbers: [704] 704,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[37, 9], Operations: ['55-18=37', '16-7=9'] Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,31 unequal: No Solution Exploring Operation: 37+9=46, Resulting Numbers: [46] 46,31 unequal: No Solution Exploring Operation: 37*9=333, Resulting Numbers: [333] 333,31 unequal: No Solution Moving to Node #0,2,3 Current State: 31:[7, 21], Operations: ['55-18=37', '37-16=21'] Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 7*21=147, Resulting Numbers: [147] 147,31 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,31 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 #0,3 Current State: 31:[18, 7, 39], Operations: ['55-16=39'] Exploring Operation: 39-7=32, Resulting Numbers: [18, 32] Generated Node #0,3,0: 31:[18, 32] Operation: 39-7=32 Exploring Operation: 18+7=25, Resulting Numbers: [39, 25] Generated Node #0,3,1: 31:[39, 25] Operation: 18+7=25 Exploring Operation: 18-7=11, Resulting Numbers: [39, 11] Generated Node #0,3,2: 31:[39, 11] Operation: 18-7=11 Exploring Operation: 7+39=46, Resulting Numbers: [18, 46] Generated Node #0,3,3: 31:[18, 46] Operation: 7+39=46 Exploring Operation: 39-18=21, Resulting Numbers: [7, 21] Generated Node #0,3,4: 31:[7, 21] Operation: 39-18=21 Moving to Node #0,3,0 Current State: 31:[18, 32], Operations: ['55-16=39', '39-7=32'] Exploring Operation: 18+32=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 18*32=576, Resulting Numbers: [576] 576,31 unequal: No Solution Moving to Node #0,3,1 Current State: 31:[39, 25], Operations: ['55-16=39', '18+7=25'] Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 39+25=64, Resulting Numbers: [64] 64,31 unequal: No Solution Exploring Operation: 39*25=975, Resulting Numbers: [975] 975,31 unequal: No Solution Moving to Node #0,3,2 Current State: 31:[39, 11], Operations: ['55-16=39', '18-7=11'] Exploring Operation: 39+11=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,31 unequal: No Solution Exploring Operation: 39*11=429, Resulting Numbers: [429] 429,31 unequal: No Solution Moving to Node #0,3,3 Current State: 31:[18, 46], Operations: ['55-16=39', '7+39=46'] Exploring Operation: 18*46=828, Resulting Numbers: [828] 828,31 unequal: No Solution Exploring Operation: 46-18=28, Resulting Numbers: [28] 28,31 unequal: No Solution Exploring Operation: 18+46=64, Resulting Numbers: [64] 64,31 unequal: No Solution Moving to Node #0,3,4 Current State: 31:[7, 21], Operations: ['55-16=39', '39-18=21'] Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,31 unequal: No Solution Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 7*21=147, Resulting Numbers: [147] 147,31 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,31 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 #0,4 Current State: 31:[55, 18, 23], Operations: ['16+7=23'] Exploring Operation: 55-18=37, Resulting Numbers: [23, 37] Generated Node #0,4,0: 31:[23, 37] Operation: 55-18=37 Exploring Operation: 18+23=41, Resulting Numbers: [55, 41] Generated Node #0,4,1: 31:[55, 41] Operation: 18+23=41 Exploring Operation: 55-23=32, Resulting Numbers: [18, 32] Generated Node #0,4,2: 31:[18, 32] Operation: 55-23=32 Exploring Operation: 55+18=73, Resulting Numbers: [23, 73] Generated Node #0,4,3: 31:[23, 73] Operation: 55+18=73 Exploring Operation: 23-18=5, Resulting Numbers: [55, 5] Generated Node #0,4,4: 31:[55, 5] Operation: 23-18=5 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 31:[23, 37], Operations: ['16+7=23', '55-18=37'] Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 23+37=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 23*37=851, Resulting Numbers: [851] 851,31 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 #0,4,2 Current State: 31:[18, 32], Operations: ['16+7=23', '55-23=32'] Exploring Operation: 18*32=576, Resulting Numbers: [576] 576,31 unequal: No Solution Exploring Operation: 18+32=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,31 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 #0,4,1 Current State: 31:[55, 41], Operations: ['16+7=23', '18+23=41'] Exploring Operation: 55-41=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 55+41=96, Resulting Numbers: [96] 96,31 unequal: No Solution Exploring Operation: 55*41=2255, Resulting Numbers: [2255] 2255,31 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 #0,4,3 Current State: 31:[23, 73], Operations: ['16+7=23', '55+18=73'] Exploring Operation: 23+73=96, Resulting Numbers: [96] 96,31 unequal: No Solution Exploring Operation: 73-23=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 23*73=1679, Resulting Numbers: [1679] 1679,31 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 #0,4,4 Current State: 31:[55, 5], Operations: ['16+7=23', '23-18=5'] Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,31 unequal: No Solution Exploring Operation: 55+5=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 55*5=275, Resulting Numbers: [275] 275,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 62, 34, 21, 39 ]
32
[ "62-34=28", "21+39=60", "60-28=32" ]
Current State: 32:[62, 34, 21, 39], Operations: [] Exploring Operation: 62-34=28, Resulting Numbers: [21, 39, 28] Generated Node #2: [21, 39, 28] from Operation: 62-34=28 Current State: 32:[21, 39, 28], Operations: ['62-34=28'] Exploring Operation: 21+39=60, Resulting Numbers: [28, 60] Generated Node #3: [28, 60] from Operation: 21+39=60 Current State: 32:[28, 60], Operations: ['62-34=28', '21+39=60'] Exploring Operation: 60-28=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[62, 34, 21, 39], Operations: [] Exploring Operation: 39-21=18, Resulting Numbers: [62, 34, 18] Generated Node #0,0: 32:[62, 34, 18] Operation: 39-21=18 Exploring Operation: 62-21=41, Resulting Numbers: [34, 39, 41] Generated Node #0,1: 32:[34, 39, 41] Operation: 62-21=41 Exploring Operation: 62-34=28, Resulting Numbers: [21, 39, 28] Generated Node #0,2: 32:[21, 39, 28] Operation: 62-34=28 Exploring Operation: 62-39=23, Resulting Numbers: [34, 21, 23] Generated Node #0,3: 32:[34, 21, 23] Operation: 62-39=23 Moving to Node #0,3 Current State: 32:[34, 21, 23], Operations: ['62-39=23'] Exploring Operation: 34-21=13, Resulting Numbers: [23, 13] Generated Node #0,3,0: 32:[23, 13] Operation: 34-21=13 Exploring Operation: 23-21=2, Resulting Numbers: [34, 2] Generated Node #0,3,1: 32:[34, 2] Operation: 23-21=2 Exploring Operation: 34-23=11, Resulting Numbers: [21, 11] Generated Node #0,3,2: 32:[21, 11] Operation: 34-23=11 Exploring Operation: 21+23=44, Resulting Numbers: [34, 44] Generated Node #0,3,3: 32:[34, 44] Operation: 21+23=44 Moving to Node #0,2 Current State: 32:[21, 39, 28], Operations: ['62-34=28'] Exploring Operation: 39-21=18, Resulting Numbers: [28, 18] Generated Node #0,2,0: 32:[28, 18] Operation: 39-21=18 Exploring Operation: 39-28=11, Resulting Numbers: [21, 11] Generated Node #0,2,1: 32:[21, 11] Operation: 39-28=11 Exploring Operation: 21+28=49, Resulting Numbers: [39, 49] Generated Node #0,2,2: 32:[39, 49] Operation: 21+28=49 Exploring Operation: 28-21=7, Resulting Numbers: [39, 7] Generated Node #0,2,3: 32:[39, 7] Operation: 28-21=7 Moving to Node #0,1 Current State: 32:[34, 39, 41], Operations: ['62-21=41'] Exploring Operation: 34+39=73, Resulting Numbers: [41, 73] Generated Node #0,1,0: 32:[41, 73] Operation: 34+39=73 Exploring Operation: 41-34=7, Resulting Numbers: [39, 7] Generated Node #0,1,1: 32:[39, 7] Operation: 41-34=7 Exploring Operation: 41-39=2, Resulting Numbers: [34, 2] Generated Node #0,1,2: 32:[34, 2] Operation: 41-39=2 Exploring Operation: 39-34=5, Resulting Numbers: [41, 5] Generated Node #0,1,3: 32:[41, 5] Operation: 39-34=5 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 32:[34, 2], Operations: ['62-21=41', '41-39=2'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[62, 34, 21, 39], Operations: [] Exploring Operation: 62-21=41, Resulting Numbers: [34, 39, 41] Generated Node #0,1: 32:[34, 39, 41] Operation: 62-21=41 Moving to Node #0,1 Current State: 32:[34, 39, 41], Operations: ['62-21=41'] Exploring Operation: 41-39=2, Resulting Numbers: [34, 2] Generated Node #0,1,2: 32:[34, 2] Operation: 41-39=2 Moving to Node #0,1,2 Current State: 32:[34, 2], Operations: ['62-21=41', '41-39=2'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 74, 73, 44, 22 ]
65
[ "74-73=1", "44+22=66", "66-1=65" ]
Current State: 65:[74, 73, 44, 22], Operations: [] Exploring Operation: 74-73=1, Resulting Numbers: [44, 22, 1] Generated Node #2: [44, 22, 1] from Operation: 74-73=1 Current State: 65:[44, 22, 1], Operations: ['74-73=1'] Exploring Operation: 44+22=66, Resulting Numbers: [1, 66] Generated Node #3: [1, 66] from Operation: 44+22=66 Current State: 65:[1, 66], Operations: ['74-73=1', '44+22=66'] Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[74, 73, 44, 22], Operations: [] Exploring Operation: 44-22=22, Resulting Numbers: [74, 73, 22] Generated Node #0,0: 65:[74, 73, 22] Operation: 44-22=22 Exploring Operation: 44/22=2, Resulting Numbers: [74, 73, 2] Generated Node #0,1: 65:[74, 73, 2] Operation: 44/22=2 Exploring Operation: 44+22=66, Resulting Numbers: [74, 73, 66] Generated Node #0,2: 65:[74, 73, 66] Operation: 44+22=66 Moving to Node #0,2 Current State: 65:[74, 73, 66], Operations: ['44+22=66'] Exploring Operation: 73-66=7, Resulting Numbers: [74, 7] Generated Node #0,2,0: 65:[74, 7] Operation: 73-66=7 Exploring Operation: 74-73=1, Resulting Numbers: [66, 1] Generated Node #0,2,1: 65:[66, 1] Operation: 74-73=1 Exploring Operation: 74-66=8, Resulting Numbers: [73, 8] Generated Node #0,2,2: 65:[73, 8] Operation: 74-66=8 Moving to Node #0,1 Current State: 65:[74, 73, 2], Operations: ['44/22=2'] Exploring Operation: 73-2=71, Resulting Numbers: [74, 71] Generated Node #0,1,0: 65:[74, 71] Operation: 73-2=71 Exploring Operation: 74-2=72, Resulting Numbers: [73, 72] Generated Node #0,1,1: 65:[73, 72] Operation: 74-2=72 Exploring Operation: 74-73=1, Resulting Numbers: [2, 1] Generated Node #0,1,2: 65:[2, 1] Operation: 74-73=1 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[2, 1], Operations: ['44/22=2', '74-73=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,65 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,65 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[74, 71], Operations: ['44/22=2', '73-2=71'] Exploring Operation: 74*71=5254, Resulting Numbers: [5254] 5254,65 unequal: No Solution Exploring Operation: 74+71=145, Resulting Numbers: [145] 145,65 unequal: No Solution Exploring Operation: 74-71=3, Resulting Numbers: [3] 3,65 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:[73, 72], Operations: ['44/22=2', '74-2=72'] Exploring Operation: 73*72=5256, Resulting Numbers: [5256] 5256,65 unequal: No Solution Exploring Operation: 73-72=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 73+72=145, Resulting Numbers: [145] 145,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 65:[74, 73, 22], Operations: ['44-22=22'] Exploring Operation: 73-22=51, Resulting Numbers: [74, 51] Generated Node #0,0,0: 65:[74, 51] Operation: 73-22=51 Exploring Operation: 74-22=52, Resulting Numbers: [73, 52] Generated Node #0,0,1: 65:[73, 52] Operation: 74-22=52 Exploring Operation: 74-73=1, Resulting Numbers: [22, 1] Generated Node #0,0,2: 65:[22, 1] Operation: 74-73=1 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 65:[22, 1], Operations: ['44-22=22', '74-73=1'] Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,65 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:[73, 52], Operations: ['44-22=22', '74-22=52'] Exploring Operation: 73+52=125, Resulting Numbers: [125] 125,65 unequal: No Solution Exploring Operation: 73-52=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 73*52=3796, Resulting Numbers: [3796] 3796,65 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:[74, 51], Operations: ['44-22=22', '73-22=51'] Exploring Operation: 74-51=23, Resulting Numbers: [23] 23,65 unequal: No Solution Exploring Operation: 74+51=125, Resulting Numbers: [125] 125,65 unequal: No Solution Exploring Operation: 74*51=3774, Resulting Numbers: [3774] 3774,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 65:[66, 1], Operations: ['44+22=66', '74-73=1'] Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[74, 73, 44, 22], Operations: [] Exploring Operation: 44+22=66, Resulting Numbers: [74, 73, 66] Generated Node #0,2: 65:[74, 73, 66] Operation: 44+22=66 Moving to Node #0,2 Current State: 65:[74, 73, 66], Operations: ['44+22=66'] Exploring Operation: 74-73=1, Resulting Numbers: [66, 1] Generated Node #0,2,1: 65:[66, 1] Operation: 74-73=1 Moving to Node #0,2,1 Current State: 65:[66, 1], Operations: ['44+22=66', '74-73=1'] Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
0.969618
hs_3
mult_heuristic
[ 23, 29, 7, 18 ]
55
[ "23*18=414", "414-29=385", "385/7=55" ]
Current State: 55:[23, 29, 7, 18], Operations: [] Exploring Operation: 23*18=414, Resulting Numbers: [29, 7, 414] Generated Node #2: [29, 7, 414] from Operation: 23*18=414 Current State: 55:[29, 7, 414], Operations: ['23*18=414'] Exploring Operation: 414-29=385, Resulting Numbers: [7, 385] Generated Node #3: [7, 385] from Operation: 414-29=385 Current State: 55:[7, 385], Operations: ['23*18=414', '414-29=385'] Exploring Operation: 385/7=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[23, 29, 7, 18], Operations: [] Exploring Operation: 29-23=6, Resulting Numbers: [7, 18, 6] Generated Node #0,0: 55:[7, 18, 6] Operation: 29-23=6 Exploring Operation: 23+29=52, Resulting Numbers: [7, 18, 52] Generated Node #0,1: 55:[7, 18, 52] Operation: 23+29=52 Exploring Operation: 23-18=5, Resulting Numbers: [29, 7, 5] Generated Node #0,2: 55:[29, 7, 5] Operation: 23-18=5 Exploring Operation: 29-18=11, Resulting Numbers: [23, 7, 11] Generated Node #0,3: 55:[23, 7, 11] Operation: 29-18=11 Moving to Node #0,0 Current State: 55:[7, 18, 6], Operations: ['29-23=6'] Exploring Operation: 7+6=13, Resulting Numbers: [18, 13] Generated Node #0,0,0: 55:[18, 13] Operation: 7+6=13 Exploring Operation: 18-6=12, Resulting Numbers: [7, 12] Generated Node #0,0,1: 55:[7, 12] Operation: 18-6=12 Exploring Operation: 18-7=11, Resulting Numbers: [6, 11] Generated Node #0,0,2: 55:[6, 11] Operation: 18-7=11 Exploring Operation: 18/6=3, Resulting Numbers: [7, 3] Generated Node #0,0,3: 55:[7, 3] Operation: 18/6=3 Moving to Node #0,1 Current State: 55:[7, 18, 52], Operations: ['23+29=52'] Exploring Operation: 18-7=11, Resulting Numbers: [52, 11] Generated Node #0,1,0: 55:[52, 11] Operation: 18-7=11 Exploring Operation: 52-7=45, Resulting Numbers: [18, 45] Generated Node #0,1,1: 55:[18, 45] Operation: 52-7=45 Exploring Operation: 7+18=25, Resulting Numbers: [52, 25] Generated Node #0,1,2: 55:[52, 25] Operation: 7+18=25 Exploring Operation: 7+52=59, Resulting Numbers: [18, 59] Generated Node #0,1,3: 55:[18, 59] Operation: 7+52=59 Moving to Node #0,3 Current State: 55:[23, 7, 11], Operations: ['29-18=11'] Exploring Operation: 23-11=12, Resulting Numbers: [7, 12] Generated Node #0,3,0: 55:[7, 12] Operation: 23-11=12 Exploring Operation: 23-7=16, Resulting Numbers: [11, 16] Generated Node #0,3,1: 55:[11, 16] Operation: 23-7=16 Exploring Operation: 23+7=30, Resulting Numbers: [11, 30] Generated Node #0,3,2: 55:[11, 30] Operation: 23+7=30 Exploring Operation: 11-7=4, Resulting Numbers: [23, 4] Generated Node #0,3,3: 55:[23, 4] Operation: 11-7=4 Moving to Node #0,2 Current State: 55:[29, 7, 5], Operations: ['23-18=5'] Exploring Operation: 7+5=12, Resulting Numbers: [29, 12] Generated Node #0,2,0: 55:[29, 12] Operation: 7+5=12 Exploring Operation: 29-5=24, Resulting Numbers: [7, 24] Generated Node #0,2,1: 55:[7, 24] Operation: 29-5=24 Exploring Operation: 29-7=22, Resulting Numbers: [5, 22] Generated Node #0,2,2: 55:[5, 22] Operation: 29-7=22 Exploring Operation: 29+7=36, Resulting Numbers: [5, 36] Generated Node #0,2,3: 55:[5, 36] Operation: 29+7=36 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 55:[5, 22], Operations: ['23-18=5', '29-7=22'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,55 unequal: No Solution Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,55 unequal: No Solution Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 55:[7, 24], Operations: ['23-18=5', '29-5=24'] Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,55 unequal: No Solution Exploring Operation: 7*24=168, Resulting Numbers: [168] 168,55 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 55:[29, 12], Operations: ['23-18=5', '7+5=12'] Exploring Operation: 29*12=348, Resulting Numbers: [348] 348,55 unequal: No Solution Exploring Operation: 29+12=41, Resulting Numbers: [41] 41,55 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 55:[5, 36], Operations: ['23-18=5', '29+7=36'] Exploring Operation: 5*36=180, Resulting Numbers: [180] 180,55 unequal: No Solution Exploring Operation: 5+36=41, Resulting Numbers: [41] 41,55 unequal: No Solution Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 55:[6, 11], Operations: ['29-23=6', '18-7=11'] Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,55 unequal: No Solution Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[7, 12], Operations: ['29-23=6', '18-6=12'] Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 7+12=19, Resulting Numbers: [19] 19,55 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,55 unequal: No Solution Moving to Node #0,1,0 Current State: 55:[52, 11], Operations: ['23+29=52', '18-7=11'] Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,55 unequal: No Solution Exploring Operation: 52+11=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 52*11=572, Resulting Numbers: [572] 572,55 unequal: No Solution Moving to Node #0,3,0 Current State: 55:[7, 12], Operations: ['29-18=11', '23-11=12'] Exploring Operation: 7+12=19, Resulting Numbers: [19] 19,55 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,55 unequal: No Solution Moving to Node #0,0,3 Current State: 55:[7, 3], Operations: ['29-23=6', '18/6=3'] Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,55 unequal: No Solution Moving to Node #0,3,1 Current State: 55:[11, 16], Operations: ['29-18=11', '23-7=16'] Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 11+16=27, Resulting Numbers: [27] 27,55 unequal: No Solution Exploring Operation: 11*16=176, Resulting Numbers: [176] 176,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[18, 13], Operations: ['29-23=6', '7+6=13'] Exploring Operation: 18+13=31, Resulting Numbers: [31] 31,55 unequal: No Solution Exploring Operation: 18-13=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 18*13=234, Resulting Numbers: [234] 234,55 unequal: No Solution Moving to Node #0,1,3 Current State: 55:[18, 59], Operations: ['23+29=52', '7+52=59'] Exploring Operation: 18+59=77, Resulting Numbers: [77] 77,55 unequal: No Solution Exploring Operation: 18*59=1062, Resulting Numbers: [1062] 1062,55 unequal: No Solution Exploring Operation: 59-18=41, Resulting Numbers: [41] 41,55 unequal: No Solution Moving to Node #0,3,3 Current State: 55:[23, 4], Operations: ['29-18=11', '11-7=4'] Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,55 unequal: No Solution Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,55 unequal: No Solution Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,55 unequal: No Solution Moving to Node #0,1,2 Current State: 55:[52, 25], Operations: ['23+29=52', '7+18=25'] Exploring Operation: 52-25=27, Resulting Numbers: [27] 27,55 unequal: No Solution Exploring Operation: 52+25=77, Resulting Numbers: [77] 77,55 unequal: No Solution Exploring Operation: 52*25=1300, Resulting Numbers: [1300] 1300,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[18, 45], Operations: ['23+29=52', '52-7=45'] Exploring Operation: 18+45=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 18*45=810, Resulting Numbers: [810] 810,55 unequal: No Solution Exploring Operation: 45-18=27, Resulting Numbers: [27] 27,55 unequal: No Solution Moving to Node #0,3,2 Current State: 55:[11, 30], Operations: ['29-18=11', '23+7=30'] Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,55 unequal: No Solution Exploring Operation: 11+30=41, Resulting Numbers: [41] 41,55 unequal: No Solution Exploring Operation: 11*30=330, Resulting Numbers: [330] 330,55 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 25, 10, 86, 66 ]
98
[ "25*10=250", "86+66=152", "250-152=98" ]
Current State: 98:[25, 10, 86, 66], Operations: [] Exploring Operation: 25*10=250, Resulting Numbers: [86, 66, 250] Generated Node #2: [86, 66, 250] from Operation: 25*10=250 Current State: 98:[86, 66, 250], Operations: ['25*10=250'] Exploring Operation: 86+66=152, Resulting Numbers: [250, 152] Generated Node #3: [250, 152] from Operation: 86+66=152 Current State: 98:[250, 152], Operations: ['25*10=250', '86+66=152'] Exploring Operation: 250-152=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[25, 10, 86, 66], Operations: [] Exploring Operation: 86-66=20, Resulting Numbers: [25, 10, 20] Generated Node #0,0: 98:[25, 10, 20] Operation: 86-66=20 Moving to Node #0,0 Current State: 98:[25, 10, 20], Operations: ['86-66=20'] Exploring Operation: 25-20=5, Resulting Numbers: [10, 5] Generated Node #0,0,0: 98:[10, 5] Operation: 25-20=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[10, 5], Operations: ['86-66=20', '25-20=5'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 61, 38, 32, 14 ]
41
[ "61-38=23", "32-14=18", "23+18=41" ]
Current State: 41:[61, 38, 32, 14], Operations: [] Exploring Operation: 61-38=23, Resulting Numbers: [32, 14, 23] Generated Node #2: [32, 14, 23] from Operation: 61-38=23 Current State: 41:[32, 14, 23], Operations: ['61-38=23'] Exploring Operation: 32-14=18, Resulting Numbers: [23, 18] Generated Node #3: [23, 18] from Operation: 32-14=18 Current State: 41:[23, 18], Operations: ['61-38=23', '32-14=18'] Exploring Operation: 23+18=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[61, 38, 32, 14], Operations: [] Exploring Operation: 61-14=47, Resulting Numbers: [38, 32, 47] Generated Node #0,0: 41:[38, 32, 47] Operation: 61-14=47 Exploring Operation: 32+14=46, Resulting Numbers: [61, 38, 46] Generated Node #0,1: 41:[61, 38, 46] Operation: 32+14=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[38, 32, 47], Operations: ['61-14=47'] Exploring Operation: 38+32=70, Resulting Numbers: [47, 70] Generated Node #0,0,0: 41:[47, 70] Operation: 38+32=70 Exploring Operation: 47-32=15, Resulting Numbers: [38, 15] Generated Node #0,0,1: 41:[38, 15] Operation: 47-32=15 Moving to Node #0,0,1 Current State: 41:[38, 15], Operations: ['61-14=47', '47-32=15'] Exploring Operation: 38+15=53, Resulting Numbers: [53] 53,41 unequal: No Solution Exploring Operation: 38-15=23, Resulting Numbers: [23] 23,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[47, 70], Operations: ['61-14=47', '38+32=70'] Exploring Operation: 47+70=117, Resulting Numbers: [117] 117,41 unequal: No Solution Exploring Operation: 70-47=23, Resulting Numbers: [23] 23,41 unequal: No Solution No 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: 41:[61, 38, 46], Operations: ['32+14=46'] Exploring Operation: 61-38=23, Resulting Numbers: [46, 23] Generated Node #0,1,0: 41:[46, 23] Operation: 61-38=23 Exploring Operation: 61-46=15, Resulting Numbers: [38, 15] Generated Node #0,1,1: 41:[38, 15] Operation: 61-46=15 Moving to Node #0,1,0 Current State: 41:[46, 23], Operations: ['32+14=46', '61-38=23'] Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 46+23=69, Resulting Numbers: [69] 69,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[38, 15], Operations: ['32+14=46', '61-46=15'] Exploring Operation: 38+15=53, Resulting Numbers: [53] 53,41 unequal: No Solution Exploring Operation: 38-15=23, Resulting Numbers: [23] 23,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 47, 73, 62, 32 ]
71
[ "62+32=94", "94/47=2", "73-2=71" ]
Current State: 71:[47, 73, 62, 32], Operations: [] Exploring Operation: 62+32=94, Resulting Numbers: [47, 73, 94] Generated Node #2: [47, 73, 94] from Operation: 62+32=94 Current State: 71:[47, 73, 94], Operations: ['62+32=94'] Exploring Operation: 94/47=2, Resulting Numbers: [73, 2] Generated Node #3: [73, 2] from Operation: 94/47=2 Current State: 71:[73, 2], Operations: ['62+32=94', '94/47=2'] Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[47, 73, 62, 32], Operations: [] Exploring Operation: 62+32=94, Resulting Numbers: [47, 73, 94] Generated Node #0,0: 71:[47, 73, 94] Operation: 62+32=94 Exploring Operation: 47+32=79, Resulting Numbers: [73, 62, 79] Generated Node #0,1: 71:[73, 62, 79] Operation: 47+32=79 Exploring Operation: 47-32=15, Resulting Numbers: [73, 62, 15] Generated Node #0,2: 71:[73, 62, 15] Operation: 47-32=15 Exploring Operation: 73-32=41, Resulting Numbers: [47, 62, 41] Generated Node #0,3: 71:[47, 62, 41] Operation: 73-32=41 Exploring Operation: 73+32=105, Resulting Numbers: [47, 62, 105] Generated Node #0,4: 71:[47, 62, 105] Operation: 73+32=105 Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[73, 62, 79], Operations: ['47+32=79'] Exploring Operation: 73+62=135, Resulting Numbers: [79, 135] Generated Node #0,1,0: 71:[79, 135] Operation: 73+62=135 Exploring Operation: 62+79=141, Resulting Numbers: [73, 141] Generated Node #0,1,1: 71:[73, 141] Operation: 62+79=141 Exploring Operation: 79-73=6, Resulting Numbers: [62, 6] Generated Node #0,1,2: 71:[62, 6] Operation: 79-73=6 Exploring Operation: 73-62=11, Resulting Numbers: [79, 11] Generated Node #0,1,3: 71:[79, 11] Operation: 73-62=11 Exploring Operation: 79-62=17, Resulting Numbers: [73, 17] Generated Node #0,1,4: 71:[73, 17] Operation: 79-62=17 Moving to Node #0,1,4 Current State: 71:[73, 17], Operations: ['47+32=79', '79-62=17'] Exploring Operation: 73-17=56, Resulting Numbers: [56] 56,71 unequal: No Solution Exploring Operation: 73+17=90, Resulting Numbers: [90] 90,71 unequal: No Solution Exploring Operation: 73*17=1241, Resulting Numbers: [1241] 1241,71 unequal: No Solution Moving to Node #0,1,3 Current State: 71:[79, 11], Operations: ['47+32=79', '73-62=11'] Exploring Operation: 79+11=90, Resulting Numbers: [90] 90,71 unequal: No Solution Exploring Operation: 79-11=68, Resulting Numbers: [68] 68,71 unequal: No Solution Exploring Operation: 79*11=869, Resulting Numbers: [869] 869,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[79, 135], Operations: ['47+32=79', '73+62=135'] Exploring Operation: 79*135=10665, Resulting Numbers: [10665] 10665,71 unequal: No Solution Exploring Operation: 135-79=56, Resulting Numbers: [56] 56,71 unequal: No Solution Exploring Operation: 79+135=214, Resulting Numbers: [214] 214,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[73, 141], Operations: ['47+32=79', '62+79=141'] Exploring Operation: 73+141=214, Resulting Numbers: [214] 214,71 unequal: No Solution Exploring Operation: 141-73=68, Resulting Numbers: [68] 68,71 unequal: No Solution Exploring Operation: 73*141=10293, Resulting Numbers: [10293] 10293,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[62, 6], Operations: ['47+32=79', '79-73=6'] Exploring Operation: 62+6=68, Resulting Numbers: [68] 68,71 unequal: No Solution Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,71 unequal: No Solution Exploring Operation: 62*6=372, Resulting Numbers: [372] 372,71 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:[47, 73, 94], Operations: ['62+32=94'] Exploring Operation: 73-47=26, Resulting Numbers: [94, 26] Generated Node #0,0,0: 71:[94, 26] Operation: 73-47=26 Exploring Operation: 47+94=141, Resulting Numbers: [73, 141] Generated Node #0,0,1: 71:[73, 141] Operation: 47+94=141 Exploring Operation: 94-47=47, Resulting Numbers: [73, 47] Generated Node #0,0,2: 71:[73, 47] Operation: 94-47=47 Exploring Operation: 94/47=2, Resulting Numbers: [73, 2] Generated Node #0,0,3: 71:[73, 2] Operation: 94/47=2 Exploring Operation: 47+73=120, Resulting Numbers: [94, 120] Generated Node #0,0,4: 71:[94, 120] Operation: 47+73=120 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 71:[73, 47], Operations: ['62+32=94', '94-47=47'] Exploring Operation: 73*47=3431, Resulting Numbers: [3431] 3431,71 unequal: No Solution Exploring Operation: 73+47=120, Resulting Numbers: [120] 120,71 unequal: No Solution Exploring Operation: 73-47=26, Resulting Numbers: [26] 26,71 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:[94, 26], Operations: ['62+32=94', '73-47=26'] Exploring Operation: 94*26=2444, Resulting Numbers: [2444] 2444,71 unequal: No Solution Exploring Operation: 94-26=68, Resulting Numbers: [68] 68,71 unequal: No Solution Exploring Operation: 94+26=120, Resulting Numbers: [120] 120,71 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 #0,0,3 Current State: 71:[73, 2], Operations: ['62+32=94', '94/47=2'] Exploring Operation: 73*2=146, Resulting Numbers: [146] 146,71 unequal: No Solution Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,71 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[47, 73, 62, 32], Operations: [] Exploring Operation: 62+32=94, Resulting Numbers: [47, 73, 94] Generated Node #0,0: 71:[47, 73, 94] Operation: 62+32=94 Moving to Node #0,0 Current State: 71:[47, 73, 94], Operations: ['62+32=94'] Exploring Operation: 94/47=2, Resulting Numbers: [73, 2] Generated Node #0,0,3: 71:[73, 2] Operation: 94/47=2 Moving to Node #0,0,3 Current State: 71:[73, 2], Operations: ['62+32=94', '94/47=2'] Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic
[ 90, 57, 55, 66 ]
65
[ "66-57=9", "90/9=10", "55+10=65" ]
Current State: 65:[90, 57, 55, 66], Operations: [] Exploring Operation: 66-57=9, Resulting Numbers: [90, 55, 9] Generated Node #2: [90, 55, 9] from Operation: 66-57=9 Current State: 65:[90, 55, 9], Operations: ['66-57=9'] Exploring Operation: 90/9=10, Resulting Numbers: [55, 10] Generated Node #3: [55, 10] from Operation: 90/9=10 Current State: 65:[55, 10], Operations: ['66-57=9', '90/9=10'] Exploring Operation: 55+10=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[90, 57, 55, 66], Operations: [] Exploring Operation: 57-55=2, Resulting Numbers: [90, 66, 2] Generated Node #0,0: 65:[90, 66, 2] Operation: 57-55=2 Exploring Operation: 90-57=33, Resulting Numbers: [55, 66, 33] Generated Node #0,1: 65:[55, 66, 33] Operation: 90-57=33 Exploring Operation: 90-66=24, Resulting Numbers: [57, 55, 24] Generated Node #0,2: 65:[57, 55, 24] Operation: 90-66=24 Moving to Node #0,0 Current State: 65:[90, 66, 2], Operations: ['57-55=2'] Exploring Operation: 90-66=24, Resulting Numbers: [2, 24] Generated Node #0,0,0: 65:[2, 24] Operation: 90-66=24 Exploring Operation: 90/2=45, Resulting Numbers: [66, 45] Generated Node #0,0,1: 65:[66, 45] Operation: 90/2=45 Exploring Operation: 90-2=88, Resulting Numbers: [66, 88] Generated Node #0,0,2: 65:[66, 88] Operation: 90-2=88 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[2, 24], Operations: ['57-55=2', '90-66=24'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,65 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:[66, 45], Operations: ['57-55=2', '90/2=45'] Exploring Operation: 66*45=2970, Resulting Numbers: [2970] 2970,65 unequal: No Solution Exploring Operation: 66+45=111, Resulting Numbers: [111] 111,65 unequal: No Solution Exploring Operation: 66-45=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 #0,0,2 Current State: 65:[66, 88], Operations: ['57-55=2', '90-2=88'] Exploring Operation: 66+88=154, Resulting Numbers: [154] 154,65 unequal: No Solution Exploring Operation: 88-66=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 66*88=5808, Resulting Numbers: [5808] 5808,65 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:[57, 55, 24], Operations: ['90-66=24'] Exploring Operation: 55+24=79, Resulting Numbers: [57, 79] Generated Node #0,2,0: 65:[57, 79] Operation: 55+24=79 Exploring Operation: 57-55=2, Resulting Numbers: [24, 2] Generated Node #0,2,1: 65:[24, 2] Operation: 57-55=2 Exploring Operation: 57+24=81, Resulting Numbers: [55, 81] Generated Node #0,2,2: 65:[55, 81] Operation: 57+24=81 Moving to Node #0,1 Current State: 65:[55, 66, 33], Operations: ['90-57=33'] Exploring Operation: 66-55=11, Resulting Numbers: [33, 11] Generated Node #0,1,0: 65:[33, 11] Operation: 66-55=11 Exploring Operation: 66/33=2, Resulting Numbers: [55, 2] Generated Node #0,1,1: 65:[55, 2] Operation: 66/33=2 Exploring Operation: 55-33=22, Resulting Numbers: [66, 22] Generated Node #0,1,2: 65:[66, 22] Operation: 55-33=22 Moving to Node #0,1,2 Current State: 65:[66, 22], Operations: ['90-57=33', '55-33=22'] Exploring Operation: 66+22=88, Resulting Numbers: [88] 88,65 unequal: No Solution Exploring Operation: 66-22=44, Resulting Numbers: [44] 44,65 unequal: No Solution Exploring Operation: 66/22=3, Resulting Numbers: [3] 3,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[55, 2], Operations: ['90-57=33', '66/33=2'] Exploring Operation: 55*2=110, Resulting Numbers: [110] 110,65 unequal: No Solution Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,65 unequal: No Solution Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[24, 2], Operations: ['90-66=24', '57-55=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,65 unequal: No Solution Moving to Node #0,1,0 Current State: 65:[33, 11], Operations: ['90-57=33', '66-55=11'] Exploring Operation: 33+11=44, Resulting Numbers: [44] 44,65 unequal: No Solution Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 33/11=3, Resulting Numbers: [3] 3,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[57, 79], Operations: ['90-66=24', '55+24=79'] Exploring Operation: 57*79=4503, Resulting Numbers: [4503] 4503,65 unequal: No Solution Exploring Operation: 79-57=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 57+79=136, Resulting Numbers: [136] 136,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[55, 81], Operations: ['90-66=24', '57+24=81'] Exploring Operation: 55*81=4455, Resulting Numbers: [4455] 4455,65 unequal: No Solution Exploring Operation: 55+81=136, Resulting Numbers: [136] 136,65 unequal: No Solution Exploring Operation: 81-55=26, Resulting Numbers: [26] 26,65 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 54, 9, 14, 90 ]
59
[ "54-9=45", "14+90=104", "104-45=59" ]
Current State: 59:[54, 9, 14, 90], Operations: [] Exploring Operation: 54-9=45, Resulting Numbers: [14, 90, 45] Generated Node #2: [14, 90, 45] from Operation: 54-9=45 Current State: 59:[14, 90, 45], Operations: ['54-9=45'] Exploring Operation: 14+90=104, Resulting Numbers: [45, 104] Generated Node #3: [45, 104] from Operation: 14+90=104 Current State: 59:[45, 104], Operations: ['54-9=45', '14+90=104'] Exploring Operation: 104-45=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[54, 9, 14, 90], Operations: [] Exploring Operation: 90-14=76, Resulting Numbers: [54, 9, 76] Generated Node #0,0: 59:[54, 9, 76] Operation: 90-14=76 Exploring Operation: 9+14=23, Resulting Numbers: [54, 90, 23] Generated Node #0,1: 59:[54, 90, 23] Operation: 9+14=23 Exploring Operation: 90-9=81, Resulting Numbers: [54, 14, 81] Generated Node #0,2: 59:[54, 14, 81] Operation: 90-9=81 Exploring Operation: 54+9=63, Resulting Numbers: [14, 90, 63] Generated Node #0,3: 59:[14, 90, 63] Operation: 54+9=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[54, 9, 76], Operations: ['90-14=76'] Exploring Operation: 54+9=63, Resulting Numbers: [76, 63] Generated Node #0,0,0: 59:[76, 63] Operation: 54+9=63 Exploring Operation: 54-9=45, Resulting Numbers: [76, 45] Generated Node #0,0,1: 59:[76, 45] Operation: 54-9=45 Exploring Operation: 76-9=67, Resulting Numbers: [54, 67] Generated Node #0,0,2: 59:[54, 67] Operation: 76-9=67 Exploring Operation: 9+76=85, Resulting Numbers: [54, 85] Generated Node #0,0,3: 59:[54, 85] Operation: 9+76=85 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 59:[54, 67], Operations: ['90-14=76', '76-9=67'] Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 54*67=3618, Resulting Numbers: [3618] 3618,59 unequal: No Solution Exploring Operation: 54+67=121, Resulting Numbers: [121] 121,59 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:[76, 63], Operations: ['90-14=76', '54+9=63'] Exploring Operation: 76+63=139, Resulting Numbers: [139] 139,59 unequal: No Solution Exploring Operation: 76-63=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 76*63=4788, Resulting Numbers: [4788] 4788,59 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 #0,0,1 Current State: 59:[76, 45], Operations: ['90-14=76', '54-9=45'] Exploring Operation: 76-45=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 76+45=121, Resulting Numbers: [121] 121,59 unequal: No Solution Exploring Operation: 76*45=3420, Resulting Numbers: [3420] 3420,59 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 #0,0,3 Current State: 59:[54, 85], Operations: ['90-14=76', '9+76=85'] Exploring Operation: 85-54=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 54+85=139, Resulting Numbers: [139] 139,59 unequal: No Solution Exploring Operation: 54*85=4590, Resulting Numbers: [4590] 4590,59 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:[54, 90, 23], Operations: ['9+14=23'] Exploring Operation: 90-23=67, Resulting Numbers: [54, 67] Generated Node #0,1,0: 59:[54, 67] Operation: 90-23=67 Exploring Operation: 90-54=36, Resulting Numbers: [23, 36] Generated Node #0,1,1: 59:[23, 36] Operation: 90-54=36 Exploring Operation: 54+23=77, Resulting Numbers: [90, 77] Generated Node #0,1,2: 59:[90, 77] Operation: 54+23=77 Exploring Operation: 54-23=31, Resulting Numbers: [90, 31] Generated Node #0,1,3: 59:[90, 31] Operation: 54-23=31 Moving to Node #0,1,0 Current State: 59:[54, 67], Operations: ['9+14=23', '90-23=67'] Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 54*67=3618, Resulting Numbers: [3618] 3618,59 unequal: No Solution Exploring Operation: 54+67=121, Resulting Numbers: [121] 121,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[90, 77], Operations: ['9+14=23', '54+23=77'] Exploring Operation: 90*77=6930, Resulting Numbers: [6930] 6930,59 unequal: No Solution Exploring Operation: 90-77=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 90+77=167, Resulting Numbers: [167] 167,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[90, 31], Operations: ['9+14=23', '54-23=31'] Exploring Operation: 90+31=121, Resulting Numbers: [121] 121,59 unequal: No Solution Exploring Operation: 90-31=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[54, 9, 14, 90], Operations: [] Exploring Operation: 9+14=23, Resulting Numbers: [54, 90, 23] Generated Node #0,1: 59:[54, 90, 23] Operation: 9+14=23 Moving to Node #0,1 Current State: 59:[54, 90, 23], Operations: ['9+14=23'] Exploring Operation: 54-23=31, Resulting Numbers: [90, 31] Generated Node #0,1,3: 59:[90, 31] Operation: 54-23=31 Moving to Node #0,1,3 Current State: 59:[90, 31], Operations: ['9+14=23', '54-23=31'] Exploring Operation: 90-31=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_4
mult_heuristic
[ 3, 48, 82, 28 ]
70
[ "48/3=16", "82-28=54", "16+54=70" ]
Current State: 70:[3, 48, 82, 28], Operations: [] Exploring Operation: 48/3=16, Resulting Numbers: [82, 28, 16] Generated Node #2: [82, 28, 16] from Operation: 48/3=16 Current State: 70:[82, 28, 16], Operations: ['48/3=16'] Exploring Operation: 82-28=54, Resulting Numbers: [16, 54] Generated Node #3: [16, 54] from Operation: 82-28=54 Current State: 70:[16, 54], Operations: ['48/3=16', '82-28=54'] Exploring Operation: 16+54=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[3, 48, 82, 28], Operations: [] Exploring Operation: 82-48=34, Resulting Numbers: [3, 28, 34] Generated Node #0,0: 70:[3, 28, 34] Operation: 82-48=34 Exploring Operation: 48+28=76, Resulting Numbers: [3, 82, 76] Generated Node #0,1: 70:[3, 82, 76] Operation: 48+28=76 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[3, 28, 34], Operations: ['82-48=34'] Exploring Operation: 3+28=31, Resulting Numbers: [34, 31] Generated Node #0,0,0: 70:[34, 31] Operation: 3+28=31 Exploring Operation: 34-28=6, Resulting Numbers: [3, 6] Generated Node #0,0,1: 70:[3, 6] Operation: 34-28=6 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 70:[3, 6], Operations: ['82-48=34', '34-28=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,70 unequal: No Solution No 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: 70:[34, 31], Operations: ['82-48=34', '3+28=31'] Exploring Operation: 34+31=65, Resulting Numbers: [65] 65,70 unequal: No Solution Exploring Operation: 34-31=3, Resulting Numbers: [3] 3,70 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: 70:[3, 82, 76], Operations: ['48+28=76'] Exploring Operation: 82-76=6, Resulting Numbers: [3, 6] Generated Node #0,1,0: 70:[3, 6] Operation: 82-76=6 Exploring Operation: 82-3=79, Resulting Numbers: [76, 79] Generated Node #0,1,1: 70:[76, 79] Operation: 82-3=79 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 70:[3, 6], Operations: ['48+28=76', '82-76=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,70 unequal: No Solution No 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: 70:[76, 79], Operations: ['48+28=76', '82-3=79'] Exploring Operation: 79-76=3, Resulting Numbers: [3] 3,70 unequal: No Solution Exploring Operation: 76+79=155, Resulting Numbers: [155] 155,70 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
[ 82, 65, 24, 80 ]
78
[ "65-24=41", "82/41=2", "80-2=78" ]
Current State: 78:[82, 65, 24, 80], Operations: [] Exploring Operation: 65-24=41, Resulting Numbers: [82, 80, 41] Generated Node #2: [82, 80, 41] from Operation: 65-24=41 Current State: 78:[82, 80, 41], Operations: ['65-24=41'] Exploring Operation: 82/41=2, Resulting Numbers: [80, 2] Generated Node #3: [80, 2] from Operation: 82/41=2 Current State: 78:[80, 2], Operations: ['65-24=41', '82/41=2'] Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[82, 65, 24, 80], Operations: [] Exploring Operation: 80-65=15, Resulting Numbers: [82, 24, 15] Generated Node #0,0: 78:[82, 24, 15] Operation: 80-65=15 Exploring Operation: 82-80=2, Resulting Numbers: [65, 24, 2] Generated Node #0,1: 78:[65, 24, 2] Operation: 82-80=2 Exploring Operation: 82-65=17, Resulting Numbers: [24, 80, 17] Generated Node #0,2: 78:[24, 80, 17] Operation: 82-65=17 Exploring Operation: 65-24=41, Resulting Numbers: [82, 80, 41] Generated Node #0,3: 78:[82, 80, 41] Operation: 65-24=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[82, 24, 15], Operations: ['80-65=15'] Exploring Operation: 82-24=58, Resulting Numbers: [15, 58] Generated Node #0,0,0: 78:[15, 58] Operation: 82-24=58 Exploring Operation: 82-15=67, Resulting Numbers: [24, 67] Generated Node #0,0,1: 78:[24, 67] Operation: 82-15=67 Exploring Operation: 24+15=39, Resulting Numbers: [82, 39] Generated Node #0,0,2: 78:[82, 39] Operation: 24+15=39 Exploring Operation: 24-15=9, Resulting Numbers: [82, 9] Generated Node #0,0,3: 78:[82, 9] Operation: 24-15=9 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 78:[82, 39], Operations: ['80-65=15', '24+15=39'] Exploring Operation: 82*39=3198, Resulting Numbers: [3198] 3198,78 unequal: No Solution Exploring Operation: 82+39=121, Resulting Numbers: [121] 121,78 unequal: No Solution Exploring Operation: 82-39=43, Resulting Numbers: [43] 43,78 unequal: No Solution No 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: 78:[82, 9], Operations: ['80-65=15', '24-15=9'] Exploring Operation: 82-9=73, Resulting Numbers: [73] 73,78 unequal: No Solution Exploring Operation: 82+9=91, Resulting Numbers: [91] 91,78 unequal: No Solution Exploring Operation: 82*9=738, Resulting Numbers: [738] 738,78 unequal: No Solution No 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: 78:[24, 67], Operations: ['80-65=15', '82-15=67'] Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,78 unequal: No Solution Exploring Operation: 24+67=91, Resulting Numbers: [91] 91,78 unequal: No Solution Exploring Operation: 24*67=1608, Resulting Numbers: [1608] 1608,78 unequal: No Solution No 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: 78:[15, 58], Operations: ['80-65=15', '82-24=58'] Exploring Operation: 15*58=870, Resulting Numbers: [870] 870,78 unequal: No Solution Exploring Operation: 15+58=73, Resulting Numbers: [73] 73,78 unequal: No Solution Exploring Operation: 58-15=43, Resulting Numbers: [43] 43,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 78:[24, 80, 17], Operations: ['82-65=17'] Exploring Operation: 80-24=56, Resulting Numbers: [17, 56] Generated Node #0,2,0: 78:[17, 56] Operation: 80-24=56 Exploring Operation: 80-17=63, Resulting Numbers: [24, 63] Generated Node #0,2,1: 78:[24, 63] Operation: 80-17=63 Exploring Operation: 24-17=7, Resulting Numbers: [80, 7] Generated Node #0,2,2: 78:[80, 7] Operation: 24-17=7 Exploring Operation: 24+17=41, Resulting Numbers: [80, 41] Generated Node #0,2,3: 78:[80, 41] Operation: 24+17=41 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 78:[80, 7], Operations: ['82-65=17', '24-17=7'] Exploring Operation: 80*7=560, Resulting Numbers: [560] 560,78 unequal: No Solution Exploring Operation: 80+7=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 80-7=73, Resulting Numbers: [73] 73,78 unequal: No Solution No 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: 78:[80, 41], Operations: ['82-65=17', '24+17=41'] Exploring Operation: 80*41=3280, Resulting Numbers: [3280] 3280,78 unequal: No Solution Exploring Operation: 80+41=121, Resulting Numbers: [121] 121,78 unequal: No Solution Exploring Operation: 80-41=39, Resulting Numbers: [39] 39,78 unequal: No Solution No 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: 78:[24, 63], Operations: ['82-65=17', '80-17=63'] Exploring Operation: 24+63=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 63-24=39, Resulting Numbers: [39] 39,78 unequal: No Solution Exploring Operation: 24*63=1512, Resulting Numbers: [1512] 1512,78 unequal: No Solution No 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: 78:[17, 56], Operations: ['82-65=17', '80-24=56'] Exploring Operation: 17*56=952, Resulting Numbers: [952] 952,78 unequal: No Solution Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,78 unequal: No Solution Exploring Operation: 17+56=73, Resulting Numbers: [73] 73,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 78:[82, 80, 41], Operations: ['65-24=41'] Exploring Operation: 80-41=39, Resulting Numbers: [82, 39] Generated Node #0,3,0: 78:[82, 39] Operation: 80-41=39 Exploring Operation: 82-80=2, Resulting Numbers: [41, 2] Generated Node #0,3,1: 78:[41, 2] Operation: 82-80=2 Exploring Operation: 82-41=41, Resulting Numbers: [80, 41] Generated Node #0,3,2: 78:[80, 41] Operation: 82-41=41 Exploring Operation: 82/41=2, Resulting Numbers: [80, 2] Generated Node #0,3,3: 78:[80, 2] Operation: 82/41=2 Moving to Node #0,3,1 Current State: 78:[41, 2], Operations: ['65-24=41', '82-80=2'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,78 unequal: No Solution Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,78 unequal: No Solution Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,78 unequal: No Solution Moving to Node #0,3,3 Current State: 78:[80, 2], Operations: ['65-24=41', '82/41=2'] Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,78 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[82, 65, 24, 80], Operations: [] Exploring Operation: 65-24=41, Resulting Numbers: [82, 80, 41] Generated Node #0,3: 78:[82, 80, 41] Operation: 65-24=41 Moving to Node #0,3 Current State: 78:[82, 80, 41], Operations: ['65-24=41'] Exploring Operation: 82/41=2, Resulting Numbers: [80, 2] Generated Node #0,3,3: 78:[80, 2] Operation: 82/41=2 Moving to Node #0,3,3 Current State: 78:[80, 2], Operations: ['65-24=41', '82/41=2'] Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.957465
hs_4
sum_heuristic
[ 35, 48, 44, 59 ]
39
[ "59-48=11", "44/11=4", "35+4=39" ]
Current State: 39:[35, 48, 44, 59], Operations: [] Exploring Operation: 59-48=11, Resulting Numbers: [35, 44, 11] Generated Node #2: [35, 44, 11] from Operation: 59-48=11 Current State: 39:[35, 44, 11], Operations: ['59-48=11'] Exploring Operation: 44/11=4, Resulting Numbers: [35, 4] Generated Node #3: [35, 4] from Operation: 44/11=4 Current State: 39:[35, 4], Operations: ['59-48=11', '44/11=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[35, 48, 44, 59], Operations: [] Exploring Operation: 59-44=15, Resulting Numbers: [35, 48, 15] Generated Node #0,0: 39:[35, 48, 15] Operation: 59-44=15 Exploring Operation: 48-35=13, Resulting Numbers: [44, 59, 13] Generated Node #0,1: 39:[44, 59, 13] Operation: 48-35=13 Exploring Operation: 59-48=11, Resulting Numbers: [35, 44, 11] Generated Node #0,2: 39:[35, 44, 11] Operation: 59-48=11 Moving to Node #0,2 Current State: 39:[35, 44, 11], Operations: ['59-48=11'] Exploring Operation: 44-35=9, Resulting Numbers: [11, 9] Generated Node #0,2,0: 39:[11, 9] Operation: 44-35=9 Exploring Operation: 44-11=33, Resulting Numbers: [35, 33] Generated Node #0,2,1: 39:[35, 33] Operation: 44-11=33 Exploring Operation: 44/11=4, Resulting Numbers: [35, 4] Generated Node #0,2,2: 39:[35, 4] Operation: 44/11=4 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 39:[35, 4], Operations: ['59-48=11', '44/11=4'] Exploring Operation: 35*4=140, Resulting Numbers: [140] 140,39 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[35, 48, 44, 59], Operations: [] Exploring Operation: 59-48=11, Resulting Numbers: [35, 44, 11] Generated Node #0,2: 39:[35, 44, 11] Operation: 59-48=11 Moving to Node #0,2 Current State: 39:[35, 44, 11], Operations: ['59-48=11'] Exploring Operation: 44/11=4, Resulting Numbers: [35, 4] Generated Node #0,2,2: 39:[35, 4] Operation: 44/11=4 Moving to Node #0,2,2 Current State: 39:[35, 4], Operations: ['59-48=11', '44/11=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 70, 51, 8, 32 ]
76
[ "70-51=19", "32/8=4", "19*4=76" ]
Current State: 76:[70, 51, 8, 32], Operations: [] Exploring Operation: 70-51=19, Resulting Numbers: [8, 32, 19] Generated Node #2: [8, 32, 19] from Operation: 70-51=19 Current State: 76:[8, 32, 19], Operations: ['70-51=19'] Exploring Operation: 32/8=4, Resulting Numbers: [19, 4] Generated Node #3: [19, 4] from Operation: 32/8=4 Current State: 76:[19, 4], Operations: ['70-51=19', '32/8=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[70, 51, 8, 32], Operations: [] Exploring Operation: 70-32=38, Resulting Numbers: [51, 8, 38] Generated Node #0,0: 76:[51, 8, 38] Operation: 70-32=38 Exploring Operation: 51-32=19, Resulting Numbers: [70, 8, 19] Generated Node #0,1: 76:[70, 8, 19] Operation: 51-32=19 Exploring Operation: 70-51=19, Resulting Numbers: [8, 32, 19] Generated Node #0,2: 76:[8, 32, 19] Operation: 70-51=19 Moving to Node #0,1 Current State: 76:[70, 8, 19], Operations: ['51-32=19'] Exploring Operation: 19-8=11, Resulting Numbers: [70, 11] Generated Node #0,1,0: 76:[70, 11] Operation: 19-8=11 Exploring Operation: 70-8=62, Resulting Numbers: [19, 62] Generated Node #0,1,1: 76:[19, 62] Operation: 70-8=62 Exploring Operation: 70+8=78, Resulting Numbers: [19, 78] Generated Node #0,1,2: 76:[19, 78] Operation: 70+8=78 Moving to Node #0,2 Current State: 76:[8, 32, 19], Operations: ['70-51=19'] Exploring Operation: 32-8=24, Resulting Numbers: [19, 24] Generated Node #0,2,0: 76:[19, 24] Operation: 32-8=24 Exploring Operation: 8+32=40, Resulting Numbers: [19, 40] Generated Node #0,2,1: 76:[19, 40] Operation: 8+32=40 Exploring Operation: 32/8=4, Resulting Numbers: [19, 4] Generated Node #0,2,2: 76:[19, 4] Operation: 32/8=4 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 76:[19, 4], Operations: ['70-51=19', '32/8=4'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,76 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,76 unequal: No Solution Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[70, 51, 8, 32], Operations: [] Exploring Operation: 70-51=19, Resulting Numbers: [8, 32, 19] Generated Node #0,2: 76:[8, 32, 19] Operation: 70-51=19 Moving to Node #0,2 Current State: 76:[8, 32, 19], Operations: ['70-51=19'] Exploring Operation: 32/8=4, Resulting Numbers: [19, 4] Generated Node #0,2,2: 76:[19, 4] Operation: 32/8=4 Moving to Node #0,2,2 Current State: 76:[19, 4], Operations: ['70-51=19', '32/8=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 64, 22, 33, 78 ]
69
[ "64-22=42", "33+78=111", "111-42=69" ]
Current State: 69:[64, 22, 33, 78], Operations: [] Exploring Operation: 64-22=42, Resulting Numbers: [33, 78, 42] Generated Node #2: [33, 78, 42] from Operation: 64-22=42 Current State: 69:[33, 78, 42], Operations: ['64-22=42'] Exploring Operation: 33+78=111, Resulting Numbers: [42, 111] Generated Node #3: [42, 111] from Operation: 33+78=111 Current State: 69:[42, 111], Operations: ['64-22=42', '33+78=111'] Exploring Operation: 111-42=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[64, 22, 33, 78], Operations: [] Exploring Operation: 78-64=14, Resulting Numbers: [22, 33, 14] Generated Node #0,0: 69:[22, 33, 14] Operation: 78-64=14 Exploring Operation: 64-33=31, Resulting Numbers: [22, 78, 31] Generated Node #0,1: 69:[22, 78, 31] Operation: 64-33=31 Exploring Operation: 33-22=11, Resulting Numbers: [64, 78, 11] Generated Node #0,2: 69:[64, 78, 11] Operation: 33-22=11 Exploring Operation: 22+33=55, Resulting Numbers: [64, 78, 55] Generated Node #0,3: 69:[64, 78, 55] Operation: 22+33=55 Moving to Node #0,1 Current State: 69:[22, 78, 31], Operations: ['64-33=31'] Exploring Operation: 78-22=56, Resulting Numbers: [31, 56] Generated Node #0,1,0: 69:[31, 56] Operation: 78-22=56 Exploring Operation: 78-31=47, Resulting Numbers: [22, 47] Generated Node #0,1,1: 69:[22, 47] Operation: 78-31=47 Exploring Operation: 31-22=9, Resulting Numbers: [78, 9] Generated Node #0,1,2: 69:[78, 9] Operation: 31-22=9 Exploring Operation: 22+31=53, Resulting Numbers: [78, 53] Generated Node #0,1,3: 69:[78, 53] Operation: 22+31=53 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[78, 9], Operations: ['64-33=31', '31-22=9'] Exploring Operation: 78-9=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[64, 22, 33, 78], Operations: [] Exploring Operation: 64-33=31, Resulting Numbers: [22, 78, 31] Generated Node #0,1: 69:[22, 78, 31] Operation: 64-33=31 Moving to Node #0,1 Current State: 69:[22, 78, 31], Operations: ['64-33=31'] Exploring Operation: 31-22=9, Resulting Numbers: [78, 9] Generated Node #0,1,2: 69:[78, 9] Operation: 31-22=9 Moving to Node #0,1,2 Current State: 69:[78, 9], Operations: ['64-33=31', '31-22=9'] Exploring Operation: 78-9=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 20, 10, 71, 15 ]
56
[ "20+10=30", "71+15=86", "86-30=56" ]
Current State: 56:[20, 10, 71, 15], Operations: [] Exploring Operation: 20+10=30, Resulting Numbers: [71, 15, 30] Generated Node #2: [71, 15, 30] from Operation: 20+10=30 Current State: 56:[71, 15, 30], Operations: ['20+10=30'] Exploring Operation: 71+15=86, Resulting Numbers: [30, 86] Generated Node #3: [30, 86] from Operation: 71+15=86 Current State: 56:[30, 86], Operations: ['20+10=30', '71+15=86'] Exploring Operation: 86-30=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[20, 10, 71, 15], Operations: [] Exploring Operation: 71-20=51, Resulting Numbers: [10, 15, 51] Generated Node #0,0: 56:[10, 15, 51] Operation: 71-20=51 Moving to Node #0,0 Current State: 56:[10, 15, 51], Operations: ['71-20=51'] Exploring Operation: 15-10=5, Resulting Numbers: [51, 5] Generated Node #0,0,0: 56:[51, 5] Operation: 15-10=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[51, 5], Operations: ['71-20=51', '15-10=5'] Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[20, 10, 71, 15], Operations: [] Exploring Operation: 71-20=51, Resulting Numbers: [10, 15, 51] Generated Node #0,0: 56:[10, 15, 51] Operation: 71-20=51 Moving to Node #0,0 Current State: 56:[10, 15, 51], Operations: ['71-20=51'] Exploring Operation: 15-10=5, Resulting Numbers: [51, 5] Generated Node #0,0,0: 56:[51, 5] Operation: 15-10=5 Moving to Node #0,0,0 Current State: 56:[51, 5], Operations: ['71-20=51', '15-10=5'] Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 93, 9, 25, 86 ]
23
[ "93-9=84", "86-25=61", "84-61=23" ]
Current State: 23:[93, 9, 25, 86], Operations: [] Exploring Operation: 93-9=84, Resulting Numbers: [25, 86, 84] Generated Node #2: [25, 86, 84] from Operation: 93-9=84 Current State: 23:[25, 86, 84], Operations: ['93-9=84'] Exploring Operation: 86-25=61, Resulting Numbers: [84, 61] Generated Node #3: [84, 61] from Operation: 86-25=61 Current State: 23:[84, 61], Operations: ['93-9=84', '86-25=61'] Exploring Operation: 84-61=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[93, 9, 25, 86], Operations: [] Exploring Operation: 93-86=7, Resulting Numbers: [9, 25, 7] Generated Node #0,0: 23:[9, 25, 7] Operation: 93-86=7 Exploring Operation: 93-25=68, Resulting Numbers: [9, 86, 68] Generated Node #0,1: 23:[9, 86, 68] Operation: 93-25=68 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[9, 25, 7], Operations: ['93-86=7'] Exploring Operation: 25-7=18, Resulting Numbers: [9, 18] Generated Node #0,0,0: 23:[9, 18] Operation: 25-7=18 Exploring Operation: 9+7=16, Resulting Numbers: [25, 16] Generated Node #0,0,1: 23:[25, 16] Operation: 9+7=16 Moving to Node #0,0,1 Current State: 23:[25, 16], Operations: ['93-86=7', '9+7=16'] Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,23 unequal: No Solution Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[9, 18], Operations: ['93-86=7', '25-7=18'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[9, 86, 68], Operations: ['93-25=68'] Exploring Operation: 86-68=18, Resulting Numbers: [9, 18] Generated Node #0,1,0: 23:[9, 18] Operation: 86-68=18 Exploring Operation: 86-9=77, Resulting Numbers: [68, 77] Generated Node #0,1,1: 23:[68, 77] Operation: 86-9=77 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 23:[9, 18], Operations: ['93-25=68', '86-68=18'] Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,23 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 23:[68, 77], Operations: ['93-25=68', '86-9=77'] Exploring Operation: 68+77=145, Resulting Numbers: [145] 145,23 unequal: No Solution Exploring Operation: 77-68=9, Resulting Numbers: [9] 9,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 35, 85, 40, 91 ]
19
[ "40*91=3640", "3640/35=104", "104-85=19" ]
Current State: 19:[35, 85, 40, 91], Operations: [] Exploring Operation: 40*91=3640, Resulting Numbers: [35, 85, 3640] Generated Node #2: [35, 85, 3640] from Operation: 40*91=3640 Current State: 19:[35, 85, 3640], Operations: ['40*91=3640'] Exploring Operation: 3640/35=104, Resulting Numbers: [85, 104] Generated Node #3: [85, 104] from Operation: 3640/35=104 Current State: 19:[85, 104], Operations: ['40*91=3640', '3640/35=104'] Exploring Operation: 104-85=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[35, 85, 40, 91], Operations: [] Exploring Operation: 91-85=6, Resulting Numbers: [35, 40, 6] Generated Node #0,0: 19:[35, 40, 6] Operation: 91-85=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[35, 40, 6], Operations: ['91-85=6'] Exploring Operation: 40-35=5, Resulting Numbers: [6, 5] Generated Node #0,0,0: 19:[6, 5] Operation: 40-35=5 Moving to Node #0,0,0 Current State: 19:[6, 5], Operations: ['91-85=6', '40-35=5'] Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 10, 72, 18, 18 ]
20
[ "10*72=720", "18+18=36", "720/36=20" ]
Current State: 20:[10, 72, 18, 18], Operations: [] Exploring Operation: 10*72=720, Resulting Numbers: [18, 18, 720] Generated Node #2: [18, 18, 720] from Operation: 10*72=720 Current State: 20:[18, 18, 720], Operations: ['10*72=720'] Exploring Operation: 18+18=36, Resulting Numbers: [720, 36] Generated Node #3: [720, 36] from Operation: 18+18=36 Current State: 20:[720, 36], Operations: ['10*72=720', '18+18=36'] Exploring Operation: 720/36=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[10, 72, 18, 18], Operations: [] Exploring Operation: 72/18=4, Resulting Numbers: [10, 18, 4] Generated Node #0,0: 20:[10, 18, 4] Operation: 72/18=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[10, 18, 4], Operations: ['72/18=4'] Exploring Operation: 18-10=8, Resulting Numbers: [4, 8] Generated Node #0,0,0: 20:[4, 8] Operation: 18-10=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 20:[4, 8], Operations: ['72/18=4', '18-10=8'] Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,20 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
[ 14, 37, 22, 54 ]
66
[ "14+37=51", "54-51=3", "22*3=66" ]
Current State: 66:[14, 37, 22, 54], Operations: [] Exploring Operation: 14+37=51, Resulting Numbers: [22, 54, 51] Generated Node #2: [22, 54, 51] from Operation: 14+37=51 Current State: 66:[22, 54, 51], Operations: ['14+37=51'] Exploring Operation: 54-51=3, Resulting Numbers: [22, 3] Generated Node #3: [22, 3] from Operation: 54-51=3 Current State: 66:[22, 3], Operations: ['14+37=51', '54-51=3'] Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[14, 37, 22, 54], Operations: [] Exploring Operation: 54-37=17, Resulting Numbers: [14, 22, 17] Generated Node #0,0: 66:[14, 22, 17] Operation: 54-37=17 Exploring Operation: 54-22=32, Resulting Numbers: [14, 37, 32] Generated Node #0,1: 66:[14, 37, 32] Operation: 54-22=32 Exploring Operation: 14+54=68, Resulting Numbers: [37, 22, 68] Generated Node #0,2: 66:[37, 22, 68] Operation: 14+54=68 Start Sub Search at level 1: Moving to Node #0,2 Current State: 66:[37, 22, 68], Operations: ['14+54=68'] Exploring Operation: 37+22=59, Resulting Numbers: [68, 59] Generated Node #0,2,0: 66:[68, 59] Operation: 37+22=59 Exploring Operation: 68-37=31, Resulting Numbers: [22, 31] Generated Node #0,2,1: 66:[22, 31] Operation: 68-37=31 Exploring Operation: 37-22=15, Resulting Numbers: [68, 15] Generated Node #0,2,2: 66:[68, 15] Operation: 37-22=15 Moving to Node #0,2,1 Current State: 66:[22, 31], Operations: ['14+54=68', '68-37=31'] Exploring Operation: 31-22=9, Resulting Numbers: [9] 9,66 unequal: No Solution Exploring Operation: 22+31=53, Resulting Numbers: [53] 53,66 unequal: No Solution Exploring Operation: 22*31=682, Resulting Numbers: [682] 682,66 unequal: No Solution Moving to Node #0,2,2 Current State: 66:[68, 15], Operations: ['14+54=68', '37-22=15'] Exploring Operation: 68-15=53, Resulting Numbers: [53] 53,66 unequal: No Solution Exploring Operation: 68*15=1020, Resulting Numbers: [1020] 1020,66 unequal: No Solution Exploring Operation: 68+15=83, Resulting Numbers: [83] 83,66 unequal: No Solution Moving to Node #0,2,0 Current State: 66:[68, 59], Operations: ['14+54=68', '37+22=59'] Exploring Operation: 68+59=127, Resulting Numbers: [127] 127,66 unequal: No Solution Exploring Operation: 68-59=9, Resulting Numbers: [9] 9,66 unequal: No Solution Exploring Operation: 68*59=4012, Resulting Numbers: [4012] 4012,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[14, 22, 17], Operations: ['54-37=17'] Exploring Operation: 17-14=3, Resulting Numbers: [22, 3] Generated Node #0,0,0: 66:[22, 3] Operation: 17-14=3 Exploring Operation: 22-17=5, Resulting Numbers: [14, 5] Generated Node #0,0,1: 66:[14, 5] Operation: 22-17=5 Exploring Operation: 14+17=31, Resulting Numbers: [22, 31] Generated Node #0,0,2: 66:[22, 31] Operation: 14+17=31 Moving to Node #0,0,0 Current State: 66:[22, 3], Operations: ['54-37=17', '17-14=3'] Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,66 unequal: No Solution Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[14, 37, 22, 54], Operations: [] Exploring Operation: 54-37=17, Resulting Numbers: [14, 22, 17] Generated Node #0,0: 66:[14, 22, 17] Operation: 54-37=17 Moving to Node #0,0 Current State: 66:[14, 22, 17], Operations: ['54-37=17'] Exploring Operation: 17-14=3, Resulting Numbers: [22, 3] Generated Node #0,0,0: 66:[22, 3] Operation: 17-14=3 Moving to Node #0,0,0 Current State: 66:[22, 3], Operations: ['54-37=17', '17-14=3'] Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 11, 15, 11, 67 ]
15
[ "11-11=0", "67*0=0", "15+0=15" ]
Current State: 15:[11, 15, 11, 67], Operations: [] Exploring Operation: 11-11=0, Resulting Numbers: [15, 67, 0] Generated Node #2: [15, 67, 0] from Operation: 11-11=0 Current State: 15:[15, 67, 0], Operations: ['11-11=0'] Exploring Operation: 67*0=0, Resulting Numbers: [15, 0] Generated Node #3: [15, 0] from Operation: 67*0=0 Current State: 15:[15, 0], Operations: ['11-11=0', '67*0=0'] Exploring Operation: 15+0=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[11, 15, 11, 67], Operations: [] Exploring Operation: 67-11=56, Resulting Numbers: [15, 11, 56] Generated Node #0,0: 15:[15, 11, 56] Operation: 67-11=56 Exploring Operation: 67-15=52, Resulting Numbers: [11, 11, 52] Generated Node #0,1: 15:[11, 11, 52] Operation: 67-15=52 Moving to Node #0,0 Current State: 15:[15, 11, 56], Operations: ['67-11=56'] Exploring Operation: 56-15=41, Resulting Numbers: [11, 41] Generated Node #0,0,0: 15:[11, 41] Operation: 56-15=41 Exploring Operation: 56-11=45, Resulting Numbers: [15, 45] Generated Node #0,0,1: 15:[15, 45] Operation: 56-11=45 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[11, 41], Operations: ['67-11=56', '56-15=41'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,15 unequal: No Solution Exploring Operation: 11+41=52, Resulting Numbers: [52] 52,15 unequal: No Solution No 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: 15:[15, 45], Operations: ['67-11=56', '56-11=45'] Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,15 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: 15:[11, 11, 52], Operations: ['67-15=52'] Exploring Operation: 52-11=41, Resulting Numbers: [11, 41] Generated Node #0,1,0: 15:[11, 41] Operation: 52-11=41 Exploring Operation: 52-11=41, Resulting Numbers: [11, 41] Generated Node #0,1,1: 15:[11, 41] Operation: 52-11=41 Moving to Node #0,1,0 Current State: 15:[11, 41], Operations: ['67-15=52', '52-11=41'] Exploring Operation: 11+41=52, Resulting Numbers: [52] 52,15 unequal: No Solution Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[11, 41], Operations: ['67-15=52', '52-11=41'] Exploring Operation: 11+41=52, Resulting Numbers: [52] 52,15 unequal: No Solution Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,15 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 77, 10, 5, 65 ]
11
[ "77*10=770", "5+65=70", "770/70=11" ]
Current State: 11:[77, 10, 5, 65], Operations: [] Exploring Operation: 77*10=770, Resulting Numbers: [5, 65, 770] Generated Node #2: [5, 65, 770] from Operation: 77*10=770 Current State: 11:[5, 65, 770], Operations: ['77*10=770'] Exploring Operation: 5+65=70, Resulting Numbers: [770, 70] Generated Node #3: [770, 70] from Operation: 5+65=70 Current State: 11:[770, 70], Operations: ['77*10=770', '5+65=70'] Exploring Operation: 770/70=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[77, 10, 5, 65], Operations: [] Exploring Operation: 77-65=12, Resulting Numbers: [10, 5, 12] Generated Node #0,0: 11:[10, 5, 12] Operation: 77-65=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[10, 5, 12], Operations: ['77-65=12'] Exploring Operation: 10+5=15, Resulting Numbers: [12, 15] Generated Node #0,0,0: 11:[12, 15] Operation: 10+5=15 Moving to Node #0,0,0 Current State: 11:[12, 15], Operations: ['77-65=12', '10+5=15'] Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 51, 12, 37, 55 ]
11
[ "55-51=4", "12*4=48", "48-37=11" ]
Current State: 11:[51, 12, 37, 55], Operations: [] Exploring Operation: 55-51=4, Resulting Numbers: [12, 37, 4] Generated Node #2: [12, 37, 4] from Operation: 55-51=4 Current State: 11:[12, 37, 4], Operations: ['55-51=4'] Exploring Operation: 12*4=48, Resulting Numbers: [37, 48] Generated Node #3: [37, 48] from Operation: 12*4=48 Current State: 11:[37, 48], Operations: ['55-51=4', '12*4=48'] Exploring Operation: 48-37=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[51, 12, 37, 55], Operations: [] Exploring Operation: 51-37=14, Resulting Numbers: [12, 55, 14] Generated Node #0,0: 11:[12, 55, 14] Operation: 51-37=14 Exploring Operation: 55-51=4, Resulting Numbers: [12, 37, 4] Generated Node #0,1: 11:[12, 37, 4] Operation: 55-51=4 Moving to Node #0,1 Current State: 11:[12, 37, 4], Operations: ['55-51=4'] Exploring Operation: 37-4=33, Resulting Numbers: [12, 33] Generated Node #0,1,0: 11:[12, 33] Operation: 37-4=33 Exploring Operation: 37-12=25, Resulting Numbers: [4, 25] Generated Node #0,1,1: 11:[4, 25] Operation: 37-12=25 Moving to Node #0,0 Current State: 11:[12, 55, 14], Operations: ['51-37=14'] Exploring Operation: 55-12=43, Resulting Numbers: [14, 43] Generated Node #0,0,0: 11:[14, 43] Operation: 55-12=43 Exploring Operation: 55-14=41, Resulting Numbers: [12, 41] Generated Node #0,0,1: 11:[12, 41] Operation: 55-14=41 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 11:[12, 41], Operations: ['51-37=14', '55-14=41'] Exploring Operation: 41-12=29, Resulting Numbers: [29] 29,11 unequal: No Solution Exploring Operation: 12+41=53, Resulting Numbers: [53] 53,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[14, 43], Operations: ['51-37=14', '55-12=43'] Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,11 unequal: No Solution Exploring Operation: 14+43=57, Resulting Numbers: [57] 57,11 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: 11:[4, 25], Operations: ['55-51=4', '37-12=25'] Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,11 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[12, 33], Operations: ['55-51=4', '37-4=33'] Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,11 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 67, 39, 66, 12 ]
26
[ "67-39=28", "66-12=54", "54-28=26" ]
Current State: 26:[67, 39, 66, 12], Operations: [] Exploring Operation: 67-39=28, Resulting Numbers: [66, 12, 28] Generated Node #2: [66, 12, 28] from Operation: 67-39=28 Current State: 26:[66, 12, 28], Operations: ['67-39=28'] Exploring Operation: 66-12=54, Resulting Numbers: [28, 54] Generated Node #3: [28, 54] from Operation: 66-12=54 Current State: 26:[28, 54], Operations: ['67-39=28', '66-12=54'] Exploring Operation: 54-28=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[67, 39, 66, 12], Operations: [] Exploring Operation: 67-66=1, Resulting Numbers: [39, 12, 1] Generated Node #0,0: 26:[39, 12, 1] Operation: 67-66=1 Exploring Operation: 67-39=28, Resulting Numbers: [66, 12, 28] Generated Node #0,1: 26:[66, 12, 28] Operation: 67-39=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[39, 12, 1], Operations: ['67-66=1'] Exploring Operation: 39-1=38, Resulting Numbers: [12, 38] Generated Node #0,0,0: 26:[12, 38] Operation: 39-1=38 Exploring Operation: 39-12=27, Resulting Numbers: [1, 27] Generated Node #0,0,1: 26:[1, 27] Operation: 39-12=27 Moving to Node #0,0,1 Current State: 26:[1, 27], Operations: ['67-66=1', '39-12=27'] Exploring Operation: 1*27=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[67, 39, 66, 12], Operations: [] Exploring Operation: 67-66=1, Resulting Numbers: [39, 12, 1] Generated Node #0,0: 26:[39, 12, 1] Operation: 67-66=1 Moving to Node #0,0 Current State: 26:[39, 12, 1], Operations: ['67-66=1'] Exploring Operation: 39-12=27, Resulting Numbers: [1, 27] Generated Node #0,0,1: 26:[1, 27] Operation: 39-12=27 Moving to Node #0,0,1 Current State: 26:[1, 27], Operations: ['67-66=1', '39-12=27'] Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic