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
[ 62, 76, 55, 50 ]
18
[ "62-55=7", "76+50=126", "126/7=18" ]
Current State: 18:[62, 76, 55, 50], Operations: [] Exploring Operation: 62-55=7, Resulting Numbers: [76, 50, 7] Generated Node #2: [76, 50, 7] from Operation: 62-55=7 Current State: 18:[76, 50, 7], Operations: ['62-55=7'] Exploring Operation: 76+50=126, Resulting Numbers: [7, 126] Generated Node #3: [7, 126] from Operation: 76+50=126 Current State: 18:[7, 126], Operations: ['62-55=7', '76+50=126'] Exploring Operation: 126/7=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[62, 76, 55, 50], Operations: [] Exploring Operation: 62-55=7, Resulting Numbers: [76, 50, 7] Generated Node #0,0: 18:[76, 50, 7] Operation: 62-55=7 Exploring Operation: 76-50=26, Resulting Numbers: [62, 55, 26] Generated Node #0,1: 18:[62, 55, 26] Operation: 76-50=26 Exploring Operation: 62-50=12, Resulting Numbers: [76, 55, 12] Generated Node #0,2: 18:[76, 55, 12] Operation: 62-50=12 Exploring Operation: 76-62=14, Resulting Numbers: [55, 50, 14] Generated Node #0,3: 18:[55, 50, 14] Operation: 76-62=14 Exploring Operation: 76-55=21, Resulting Numbers: [62, 50, 21] Generated Node #0,4: 18:[62, 50, 21] Operation: 76-55=21 Moving to Node #0,3 Current State: 18:[55, 50, 14], Operations: ['76-62=14'] Exploring Operation: 50-14=36, Resulting Numbers: [55, 36] Generated Node #0,3,0: 18:[55, 36] Operation: 50-14=36 Exploring Operation: 55+14=69, Resulting Numbers: [50, 69] Generated Node #0,3,1: 18:[50, 69] Operation: 55+14=69 Exploring Operation: 55-50=5, Resulting Numbers: [14, 5] Generated Node #0,3,2: 18:[14, 5] Operation: 55-50=5 Exploring Operation: 55-14=41, Resulting Numbers: [50, 41] Generated Node #0,3,3: 18:[50, 41] Operation: 55-14=41 Exploring Operation: 50+14=64, Resulting Numbers: [55, 64] Generated Node #0,3,4: 18:[55, 64] Operation: 50+14=64 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 18:[14, 5], Operations: ['76-62=14', '55-50=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,18 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,18 unequal: No Solution No 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: 18:[55, 36], Operations: ['76-62=14', '50-14=36'] Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 55+36=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 55*36=1980, Resulting Numbers: [1980] 1980,18 unequal: No Solution No 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: 18:[50, 41], Operations: ['76-62=14', '55-14=41'] Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 50*41=2050, Resulting Numbers: [2050] 2050,18 unequal: No Solution Exploring Operation: 50+41=91, Resulting Numbers: [91] 91,18 unequal: No Solution No 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: 18:[50, 69], Operations: ['76-62=14', '55+14=69'] Exploring Operation: 50+69=119, Resulting Numbers: [119] 119,18 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 50*69=3450, Resulting Numbers: [3450] 3450,18 unequal: No Solution No 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: 18:[55, 64], Operations: ['76-62=14', '50+14=64'] Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 55+64=119, Resulting Numbers: [119] 119,18 unequal: No Solution Exploring Operation: 55*64=3520, Resulting Numbers: [3520] 3520,18 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: 18:[62, 50, 21], Operations: ['76-55=21'] Exploring Operation: 50-21=29, Resulting Numbers: [62, 29] Generated Node #0,4,0: 18:[62, 29] Operation: 50-21=29 Exploring Operation: 62-21=41, Resulting Numbers: [50, 41] Generated Node #0,4,1: 18:[50, 41] Operation: 62-21=41 Exploring Operation: 62-50=12, Resulting Numbers: [21, 12] Generated Node #0,4,2: 18:[21, 12] Operation: 62-50=12 Exploring Operation: 62+21=83, Resulting Numbers: [50, 83] Generated Node #0,4,3: 18:[50, 83] Operation: 62+21=83 Exploring Operation: 62+50=112, Resulting Numbers: [21, 112] Generated Node #0,4,4: 18:[21, 112] Operation: 62+50=112 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 18:[21, 12], Operations: ['76-55=21', '62-50=12'] Exploring Operation: 21*12=252, Resulting Numbers: [252] 252,18 unequal: No Solution Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,18 unequal: No Solution No 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: 18:[62, 29], Operations: ['76-55=21', '50-21=29'] Exploring Operation: 62*29=1798, Resulting Numbers: [1798] 1798,18 unequal: No Solution Exploring Operation: 62-29=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 62+29=91, Resulting Numbers: [91] 91,18 unequal: No Solution No 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: 18:[50, 41], Operations: ['76-55=21', '62-21=41'] Exploring Operation: 50*41=2050, Resulting Numbers: [2050] 2050,18 unequal: No Solution Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 50+41=91, Resulting Numbers: [91] 91,18 unequal: No Solution No 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: 18:[50, 83], Operations: ['76-55=21', '62+21=83'] Exploring Operation: 50+83=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 50*83=4150, Resulting Numbers: [4150] 4150,18 unequal: No Solution Exploring Operation: 83-50=33, Resulting Numbers: [33] 33,18 unequal: No Solution No 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: 18:[21, 112], Operations: ['76-55=21', '62+50=112'] Exploring Operation: 112-21=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 21*112=2352, Resulting Numbers: [2352] 2352,18 unequal: No Solution Exploring Operation: 21+112=133, Resulting Numbers: [133] 133,18 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: 18:[62, 55, 26], Operations: ['76-50=26'] Exploring Operation: 62-26=36, Resulting Numbers: [55, 36] Generated Node #0,1,0: 18:[55, 36] Operation: 62-26=36 Exploring Operation: 62+26=88, Resulting Numbers: [55, 88] Generated Node #0,1,1: 18:[55, 88] Operation: 62+26=88 Exploring Operation: 55-26=29, Resulting Numbers: [62, 29] Generated Node #0,1,2: 18:[62, 29] Operation: 55-26=29 Exploring Operation: 62-55=7, Resulting Numbers: [26, 7] Generated Node #0,1,3: 18:[26, 7] Operation: 62-55=7 Exploring Operation: 62+55=117, Resulting Numbers: [26, 117] Generated Node #0,1,4: 18:[26, 117] Operation: 62+55=117 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[26, 7], Operations: ['76-50=26', '62-55=7'] Exploring Operation: 26+7=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 26*7=182, Resulting Numbers: [182] 182,18 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,18 unequal: No Solution No 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: 18:[55, 36], Operations: ['76-50=26', '62-26=36'] Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 55*36=1980, Resulting Numbers: [1980] 1980,18 unequal: No Solution Exploring Operation: 55+36=91, Resulting Numbers: [91] 91,18 unequal: No Solution No 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: 18:[62, 29], Operations: ['76-50=26', '55-26=29'] Exploring Operation: 62*29=1798, Resulting Numbers: [1798] 1798,18 unequal: No Solution Exploring Operation: 62+29=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 62-29=33, Resulting Numbers: [33] 33,18 unequal: No Solution No 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: 18:[55, 88], Operations: ['76-50=26', '62+26=88'] Exploring Operation: 55*88=4840, Resulting Numbers: [4840] 4840,18 unequal: No Solution Exploring Operation: 55+88=143, Resulting Numbers: [143] 143,18 unequal: No Solution Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 18:[26, 117], Operations: ['76-50=26', '62+55=117'] Exploring Operation: 26*117=3042, Resulting Numbers: [3042] 3042,18 unequal: No Solution Exploring Operation: 117-26=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 26+117=143, Resulting Numbers: [143] 143,18 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: 18:[76, 50, 7], Operations: ['62-55=7'] Exploring Operation: 76-7=69, Resulting Numbers: [50, 69] Generated Node #0,0,0: 18:[50, 69] Operation: 76-7=69 Exploring Operation: 76+7=83, Resulting Numbers: [50, 83] Generated Node #0,0,1: 18:[50, 83] Operation: 76+7=83 Exploring Operation: 50-7=43, Resulting Numbers: [76, 43] Generated Node #0,0,2: 18:[76, 43] Operation: 50-7=43 Exploring Operation: 76-50=26, Resulting Numbers: [7, 26] Generated Node #0,0,3: 18:[7, 26] Operation: 76-50=26 Exploring Operation: 50+7=57, Resulting Numbers: [76, 57] Generated Node #0,0,4: 18:[76, 57] Operation: 50+7=57 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 18:[7, 26], Operations: ['62-55=7', '76-50=26'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 7*26=182, Resulting Numbers: [182] 182,18 unequal: No Solution Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,18 unequal: No Solution No 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: 18:[50, 69], Operations: ['62-55=7', '76-7=69'] Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 50*69=3450, Resulting Numbers: [3450] 3450,18 unequal: No Solution Exploring Operation: 50+69=119, Resulting Numbers: [119] 119,18 unequal: No Solution No 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: 18:[76, 43], Operations: ['62-55=7', '50-7=43'] Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,18 unequal: No Solution Exploring Operation: 76*43=3268, Resulting Numbers: [3268] 3268,18 unequal: No Solution No 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: 18:[50, 83], Operations: ['62-55=7', '76+7=83'] Exploring Operation: 50+83=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 83-50=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 50*83=4150, Resulting Numbers: [4150] 4150,18 unequal: No Solution No 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: 18:[76, 57], Operations: ['62-55=7', '50+7=57'] Exploring Operation: 76+57=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 76-57=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 76*57=4332, Resulting Numbers: [4332] 4332,18 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: 18:[76, 55, 12], Operations: ['62-50=12'] Exploring Operation: 76-12=64, Resulting Numbers: [55, 64] Generated Node #0,2,0: 18:[55, 64] Operation: 76-12=64 Exploring Operation: 76+12=88, Resulting Numbers: [55, 88] Generated Node #0,2,1: 18:[55, 88] Operation: 76+12=88 Exploring Operation: 55-12=43, Resulting Numbers: [76, 43] Generated Node #0,2,2: 18:[76, 43] Operation: 55-12=43 Exploring Operation: 55+12=67, Resulting Numbers: [76, 67] Generated Node #0,2,3: 18:[76, 67] Operation: 55+12=67 Exploring Operation: 76-55=21, Resulting Numbers: [12, 21] Generated Node #0,2,4: 18:[12, 21] Operation: 76-55=21 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 18:[12, 21], Operations: ['62-50=12', '76-55=21'] Exploring Operation: 12*21=252, Resulting Numbers: [252] 252,18 unequal: No Solution Exploring Operation: 12+21=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,18 unequal: No Solution No 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: 18:[55, 64], Operations: ['62-50=12', '76-12=64'] Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 55*64=3520, Resulting Numbers: [3520] 3520,18 unequal: No Solution Exploring Operation: 55+64=119, Resulting Numbers: [119] 119,18 unequal: No Solution No 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: 18:[76, 43], Operations: ['62-50=12', '55-12=43'] Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,18 unequal: No Solution Exploring Operation: 76*43=3268, Resulting Numbers: [3268] 3268,18 unequal: No Solution No 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: 18:[55, 88], Operations: ['62-50=12', '76+12=88'] Exploring Operation: 55+88=143, Resulting Numbers: [143] 143,18 unequal: No Solution Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 55*88=4840, Resulting Numbers: [4840] 4840,18 unequal: No Solution No 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: 18:[76, 67], Operations: ['62-50=12', '55+12=67'] Exploring Operation: 76+67=143, Resulting Numbers: [143] 143,18 unequal: No Solution Exploring Operation: 76-67=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 76*67=5092, Resulting Numbers: [5092] 5092,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 25, 83, 47, 4 ]
57
[ "25+83=108", "47+4=51", "108-51=57" ]
Current State: 57:[25, 83, 47, 4], Operations: [] Exploring Operation: 25+83=108, Resulting Numbers: [47, 4, 108] Generated Node #2: [47, 4, 108] from Operation: 25+83=108 Current State: 57:[47, 4, 108], Operations: ['25+83=108'] Exploring Operation: 47+4=51, Resulting Numbers: [108, 51] Generated Node #3: [108, 51] from Operation: 47+4=51 Current State: 57:[108, 51], Operations: ['25+83=108', '47+4=51'] Exploring Operation: 108-51=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[25, 83, 47, 4], Operations: [] Exploring Operation: 25-4=21, Resulting Numbers: [83, 47, 21] Generated Node #0,0: 57:[83, 47, 21] Operation: 25-4=21 Exploring Operation: 47-25=22, Resulting Numbers: [83, 4, 22] Generated Node #0,1: 57:[83, 4, 22] Operation: 47-25=22 Exploring Operation: 83-25=58, Resulting Numbers: [47, 4, 58] Generated Node #0,2: 57:[47, 4, 58] Operation: 83-25=58 Exploring Operation: 83-47=36, Resulting Numbers: [25, 4, 36] Generated Node #0,3: 57:[25, 4, 36] Operation: 83-47=36 Moving to Node #0,2 Current State: 57:[47, 4, 58], Operations: ['83-25=58'] Exploring Operation: 58-4=54, Resulting Numbers: [47, 54] Generated Node #0,2,0: 57:[47, 54] Operation: 58-4=54 Exploring Operation: 58-47=11, Resulting Numbers: [4, 11] Generated Node #0,2,1: 57:[4, 11] Operation: 58-47=11 Exploring Operation: 47+4=51, Resulting Numbers: [58, 51] Generated Node #0,2,2: 57:[58, 51] Operation: 47+4=51 Exploring Operation: 47-4=43, Resulting Numbers: [58, 43] Generated Node #0,2,3: 57:[58, 43] Operation: 47-4=43 Moving to Node #0,3 Current State: 57:[25, 4, 36], Operations: ['83-47=36'] Exploring Operation: 25+36=61, Resulting Numbers: [4, 61] Generated Node #0,3,0: 57:[4, 61] Operation: 25+36=61 Exploring Operation: 36-25=11, Resulting Numbers: [4, 11] Generated Node #0,3,1: 57:[4, 11] Operation: 36-25=11 Exploring Operation: 25-4=21, Resulting Numbers: [36, 21] Generated Node #0,3,2: 57:[36, 21] Operation: 25-4=21 Exploring Operation: 36/4=9, Resulting Numbers: [25, 9] Generated Node #0,3,3: 57:[25, 9] Operation: 36/4=9 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 57:[4, 61], Operations: ['83-47=36', '25+36=61'] Exploring Operation: 4+61=65, Resulting Numbers: [65] 65,57 unequal: No Solution Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[25, 83, 47, 4], Operations: [] Exploring Operation: 83-47=36, Resulting Numbers: [25, 4, 36] Generated Node #0,3: 57:[25, 4, 36] Operation: 83-47=36 Moving to Node #0,3 Current State: 57:[25, 4, 36], Operations: ['83-47=36'] Exploring Operation: 25+36=61, Resulting Numbers: [4, 61] Generated Node #0,3,0: 57:[4, 61] Operation: 25+36=61 Moving to Node #0,3,0 Current State: 57:[4, 61], Operations: ['83-47=36', '25+36=61'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 97, 83, 53, 90 ]
23
[ "97-83=14", "90-53=37", "37-14=23" ]
Current State: 23:[97, 83, 53, 90], Operations: [] Exploring Operation: 97-83=14, Resulting Numbers: [53, 90, 14] Generated Node #2: [53, 90, 14] from Operation: 97-83=14 Current State: 23:[53, 90, 14], Operations: ['97-83=14'] Exploring Operation: 90-53=37, Resulting Numbers: [14, 37] Generated Node #3: [14, 37] from Operation: 90-53=37 Current State: 23:[14, 37], Operations: ['97-83=14', '90-53=37'] Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[97, 83, 53, 90], Operations: [] Exploring Operation: 97-83=14, Resulting Numbers: [53, 90, 14] Generated Node #0,0: 23:[53, 90, 14] Operation: 97-83=14 Exploring Operation: 90-83=7, Resulting Numbers: [97, 53, 7] Generated Node #0,1: 23:[97, 53, 7] Operation: 90-83=7 Exploring Operation: 97-90=7, Resulting Numbers: [83, 53, 7] Generated Node #0,2: 23:[83, 53, 7] Operation: 97-90=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[53, 90, 14], Operations: ['97-83=14'] Exploring Operation: 53-14=39, Resulting Numbers: [90, 39] Generated Node #0,0,0: 23:[90, 39] Operation: 53-14=39 Exploring Operation: 90-14=76, Resulting Numbers: [53, 76] Generated Node #0,0,1: 23:[53, 76] Operation: 90-14=76 Exploring Operation: 90-53=37, Resulting Numbers: [14, 37] Generated Node #0,0,2: 23:[14, 37] Operation: 90-53=37 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 23:[14, 37], Operations: ['97-83=14', '90-53=37'] Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[97, 83, 53, 90], Operations: [] Exploring Operation: 97-83=14, Resulting Numbers: [53, 90, 14] Generated Node #0,0: 23:[53, 90, 14] Operation: 97-83=14 Moving to Node #0,0 Current State: 23:[53, 90, 14], Operations: ['97-83=14'] Exploring Operation: 90-53=37, Resulting Numbers: [14, 37] Generated Node #0,0,2: 23:[14, 37] Operation: 90-53=37 Moving to Node #0,0,2 Current State: 23:[14, 37], Operations: ['97-83=14', '90-53=37'] Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 29, 76, 35, 13 ]
25
[ "76-29=47", "35-13=22", "47-22=25" ]
Current State: 25:[29, 76, 35, 13], Operations: [] Exploring Operation: 76-29=47, Resulting Numbers: [35, 13, 47] Generated Node #2: [35, 13, 47] from Operation: 76-29=47 Current State: 25:[35, 13, 47], Operations: ['76-29=47'] Exploring Operation: 35-13=22, Resulting Numbers: [47, 22] Generated Node #3: [47, 22] from Operation: 35-13=22 Current State: 25:[47, 22], Operations: ['76-29=47', '35-13=22'] Exploring Operation: 47-22=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[29, 76, 35, 13], Operations: [] Exploring Operation: 35-29=6, Resulting Numbers: [76, 13, 6] Generated Node #0,0: 25:[76, 13, 6] Operation: 35-29=6 Exploring Operation: 76-13=63, Resulting Numbers: [29, 35, 63] Generated Node #0,1: 25:[29, 35, 63] Operation: 76-13=63 Exploring Operation: 76-35=41, Resulting Numbers: [29, 13, 41] Generated Node #0,2: 25:[29, 13, 41] Operation: 76-35=41 Exploring Operation: 35-13=22, Resulting Numbers: [29, 76, 22] Generated Node #0,3: 25:[29, 76, 22] Operation: 35-13=22 Exploring Operation: 76-29=47, Resulting Numbers: [35, 13, 47] Generated Node #0,4: 25:[35, 13, 47] Operation: 76-29=47 Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[29, 13, 41], Operations: ['76-35=41'] Exploring Operation: 41-13=28, Resulting Numbers: [29, 28] Generated Node #0,2,0: 25:[29, 28] Operation: 41-13=28 Exploring Operation: 41-29=12, Resulting Numbers: [13, 12] Generated Node #0,2,1: 25:[13, 12] Operation: 41-29=12 Exploring Operation: 29-13=16, Resulting Numbers: [41, 16] Generated Node #0,2,2: 25:[41, 16] Operation: 29-13=16 Exploring Operation: 13+41=54, Resulting Numbers: [29, 54] Generated Node #0,2,3: 25:[29, 54] Operation: 13+41=54 Exploring Operation: 29+13=42, Resulting Numbers: [41, 42] Generated Node #0,2,4: 25:[41, 42] Operation: 29+13=42 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 25:[29, 28], Operations: ['76-35=41', '41-13=28'] Exploring Operation: 29*28=812, Resulting Numbers: [812] 812,25 unequal: No Solution Exploring Operation: 29+28=57, Resulting Numbers: [57] 57,25 unequal: No Solution Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 25:[13, 12], Operations: ['76-35=41', '41-29=12'] Exploring Operation: 13*12=156, Resulting Numbers: [156] 156,25 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 13+12=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[29, 76, 35, 13], Operations: [] Exploring Operation: 76-35=41, Resulting Numbers: [29, 13, 41] Generated Node #0,2: 25:[29, 13, 41] Operation: 76-35=41 Moving to Node #0,2 Current State: 25:[29, 13, 41], Operations: ['76-35=41'] Exploring Operation: 41-29=12, Resulting Numbers: [13, 12] Generated Node #0,2,1: 25:[13, 12] Operation: 41-29=12 Moving to Node #0,2,1 Current State: 25:[13, 12], Operations: ['76-35=41', '41-29=12'] Exploring Operation: 13+12=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 23, 95, 17, 22 ]
33
[ "95-23=72", "17+22=39", "72-39=33" ]
Current State: 33:[23, 95, 17, 22], Operations: [] Exploring Operation: 95-23=72, Resulting Numbers: [17, 22, 72] Generated Node #2: [17, 22, 72] from Operation: 95-23=72 Current State: 33:[17, 22, 72], Operations: ['95-23=72'] Exploring Operation: 17+22=39, Resulting Numbers: [72, 39] Generated Node #3: [72, 39] from Operation: 17+22=39 Current State: 33:[72, 39], Operations: ['95-23=72', '17+22=39'] Exploring Operation: 72-39=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[23, 95, 17, 22], Operations: [] Exploring Operation: 95-22=73, Resulting Numbers: [23, 17, 73] Generated Node #0,0: 33:[23, 17, 73] Operation: 95-22=73 Exploring Operation: 23-22=1, Resulting Numbers: [95, 17, 1] Generated Node #0,1: 33:[95, 17, 1] Operation: 23-22=1 Exploring Operation: 95-17=78, Resulting Numbers: [23, 22, 78] Generated Node #0,2: 33:[23, 22, 78] Operation: 95-17=78 Exploring Operation: 95-23=72, Resulting Numbers: [17, 22, 72] Generated Node #0,3: 33:[17, 22, 72] Operation: 95-23=72 Moving to Node #0,0 Current State: 33:[23, 17, 73], Operations: ['95-22=73'] Exploring Operation: 23+17=40, Resulting Numbers: [73, 40] Generated Node #0,0,0: 33:[73, 40] Operation: 23+17=40 Exploring Operation: 73-17=56, Resulting Numbers: [23, 56] Generated Node #0,0,1: 33:[23, 56] Operation: 73-17=56 Exploring Operation: 23-17=6, Resulting Numbers: [73, 6] Generated Node #0,0,2: 33:[73, 6] Operation: 23-17=6 Exploring Operation: 73-23=50, Resulting Numbers: [17, 50] Generated Node #0,0,3: 33:[17, 50] Operation: 73-23=50 Moving to Node #0,3 Current State: 33:[17, 22, 72], Operations: ['95-23=72'] Exploring Operation: 72-17=55, Resulting Numbers: [22, 55] Generated Node #0,3,0: 33:[22, 55] Operation: 72-17=55 Exploring Operation: 22-17=5, Resulting Numbers: [72, 5] Generated Node #0,3,1: 33:[72, 5] Operation: 22-17=5 Exploring Operation: 17+22=39, Resulting Numbers: [72, 39] Generated Node #0,3,2: 33:[72, 39] Operation: 17+22=39 Exploring Operation: 72-22=50, Resulting Numbers: [17, 50] Generated Node #0,3,3: 33:[17, 50] Operation: 72-22=50 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 33:[17, 50], Operations: ['95-23=72', '72-22=50'] Exploring Operation: 17+50=67, Resulting Numbers: [67] 67,33 unequal: No Solution Exploring Operation: 17*50=850, Resulting Numbers: [850] 850,33 unequal: No Solution Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[23, 95, 17, 22], Operations: [] Exploring Operation: 95-23=72, Resulting Numbers: [17, 22, 72] Generated Node #0,3: 33:[17, 22, 72] Operation: 95-23=72 Moving to Node #0,3 Current State: 33:[17, 22, 72], Operations: ['95-23=72'] Exploring Operation: 72-22=50, Resulting Numbers: [17, 50] Generated Node #0,3,3: 33:[17, 50] Operation: 72-22=50 Moving to Node #0,3,3 Current State: 33:[17, 50], Operations: ['95-23=72', '72-22=50'] Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 74, 23, 26, 20 ]
97
[ "74-23=51", "26+20=46", "51+46=97" ]
Current State: 97:[74, 23, 26, 20], Operations: [] Exploring Operation: 74-23=51, Resulting Numbers: [26, 20, 51] Generated Node #2: [26, 20, 51] from Operation: 74-23=51 Current State: 97:[26, 20, 51], Operations: ['74-23=51'] Exploring Operation: 26+20=46, Resulting Numbers: [51, 46] Generated Node #3: [51, 46] from Operation: 26+20=46 Current State: 97:[51, 46], Operations: ['74-23=51', '26+20=46'] Exploring Operation: 51+46=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[74, 23, 26, 20], Operations: [] Exploring Operation: 23+26=49, Resulting Numbers: [74, 20, 49] Generated Node #0,0: 97:[74, 20, 49] Operation: 23+26=49 Exploring Operation: 74+20=94, Resulting Numbers: [23, 26, 94] Generated Node #0,1: 97:[23, 26, 94] Operation: 74+20=94 Exploring Operation: 74+23=97, Resulting Numbers: [26, 20, 97] Generated Node #0,2: 97:[26, 20, 97] Operation: 74+23=97 Exploring Operation: 23+20=43, Resulting Numbers: [74, 26, 43] Generated Node #0,3: 97:[74, 26, 43] Operation: 23+20=43 Exploring Operation: 26+20=46, Resulting Numbers: [74, 23, 46] Generated Node #0,4: 97:[74, 23, 46] Operation: 26+20=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[74, 20, 49], Operations: ['23+26=49'] Exploring Operation: 20+49=69, Resulting Numbers: [74, 69] Generated Node #0,0,0: 97:[74, 69] Operation: 20+49=69 Exploring Operation: 74+20=94, Resulting Numbers: [49, 94] Generated Node #0,0,1: 97:[49, 94] Operation: 74+20=94 Exploring Operation: 74+49=123, Resulting Numbers: [20, 123] Generated Node #0,0,2: 97:[20, 123] Operation: 74+49=123 Exploring Operation: 74-20=54, Resulting Numbers: [49, 54] Generated Node #0,0,3: 97:[49, 54] Operation: 74-20=54 Exploring Operation: 49-20=29, Resulting Numbers: [74, 29] Generated Node #0,0,4: 97:[74, 29] Operation: 49-20=29 Moving to Node #0,0,0 Current State: 97:[74, 69], Operations: ['23+26=49', '20+49=69'] Exploring Operation: 74-69=5, Resulting Numbers: [5] 5,97 unequal: No Solution Exploring Operation: 74+69=143, Resulting Numbers: [143] 143,97 unequal: No Solution Exploring Operation: 74*69=5106, Resulting Numbers: [5106] 5106,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[49, 94], Operations: ['23+26=49', '74+20=94'] Exploring Operation: 49+94=143, Resulting Numbers: [143] 143,97 unequal: No Solution Exploring Operation: 94-49=45, Resulting Numbers: [45] 45,97 unequal: No Solution Exploring Operation: 49*94=4606, Resulting Numbers: [4606] 4606,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[49, 54], Operations: ['23+26=49', '74-20=54'] Exploring Operation: 49+54=103, Resulting Numbers: [103] 103,97 unequal: No Solution Exploring Operation: 49*54=2646, Resulting Numbers: [2646] 2646,97 unequal: No Solution Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,97 unequal: No Solution Moving to Node #0,0,4 Current State: 97:[74, 29], Operations: ['23+26=49', '49-20=29'] Exploring Operation: 74-29=45, Resulting Numbers: [45] 45,97 unequal: No Solution Exploring Operation: 74*29=2146, Resulting Numbers: [2146] 2146,97 unequal: No Solution Exploring Operation: 74+29=103, Resulting Numbers: [103] 103,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[20, 123], Operations: ['23+26=49', '74+49=123'] Exploring Operation: 20*123=2460, Resulting Numbers: [2460] 2460,97 unequal: No Solution Exploring Operation: 123-20=103, Resulting Numbers: [103] 103,97 unequal: No Solution Exploring Operation: 20+123=143, Resulting Numbers: [143] 143,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[23, 26, 94], Operations: ['74+20=94'] Exploring Operation: 94-23=71, Resulting Numbers: [26, 71] Generated Node #0,1,0: 97:[26, 71] Operation: 94-23=71 Exploring Operation: 26-23=3, Resulting Numbers: [94, 3] Generated Node #0,1,1: 97:[94, 3] Operation: 26-23=3 Exploring Operation: 26+94=120, Resulting Numbers: [23, 120] Generated Node #0,1,2: 97:[23, 120] Operation: 26+94=120 Exploring Operation: 23+26=49, Resulting Numbers: [94, 49] Generated Node #0,1,3: 97:[94, 49] Operation: 23+26=49 Exploring Operation: 23+94=117, Resulting Numbers: [26, 117] Generated Node #0,1,4: 97:[26, 117] Operation: 23+94=117 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 97:[94, 49], Operations: ['74+20=94', '23+26=49'] Exploring Operation: 94+49=143, Resulting Numbers: [143] 143,97 unequal: No Solution Exploring Operation: 94*49=4606, Resulting Numbers: [4606] 4606,97 unequal: No Solution Exploring Operation: 94-49=45, Resulting Numbers: [45] 45,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 97:[26, 117], Operations: ['74+20=94', '23+94=117'] Exploring Operation: 26+117=143, Resulting Numbers: [143] 143,97 unequal: No Solution Exploring Operation: 26*117=3042, Resulting Numbers: [3042] 3042,97 unequal: No Solution Exploring Operation: 117-26=91, Resulting Numbers: [91] 91,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[26, 71], Operations: ['74+20=94', '94-23=71'] Exploring Operation: 26+71=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[74, 23, 26, 20], Operations: [] Exploring Operation: 74+20=94, Resulting Numbers: [23, 26, 94] Generated Node #0,1: 97:[23, 26, 94] Operation: 74+20=94 Moving to Node #0,1 Current State: 97:[23, 26, 94], Operations: ['74+20=94'] Exploring Operation: 94-23=71, Resulting Numbers: [26, 71] Generated Node #0,1,0: 97:[26, 71] Operation: 94-23=71 Moving to Node #0,1,0 Current State: 97:[26, 71], Operations: ['74+20=94', '94-23=71'] Exploring Operation: 26+71=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 4, 11, 6, 60 ]
34
[ "4*11=44", "60/6=10", "44-10=34" ]
Current State: 34:[4, 11, 6, 60], Operations: [] Exploring Operation: 4*11=44, Resulting Numbers: [6, 60, 44] Generated Node #2: [6, 60, 44] from Operation: 4*11=44 Current State: 34:[6, 60, 44], Operations: ['4*11=44'] Exploring Operation: 60/6=10, Resulting Numbers: [44, 10] Generated Node #3: [44, 10] from Operation: 60/6=10 Current State: 34:[44, 10], Operations: ['4*11=44', '60/6=10'] Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[4, 11, 6, 60], Operations: [] Exploring Operation: 60/4=15, Resulting Numbers: [11, 6, 15] Generated Node #0,0: 34:[11, 6, 15] Operation: 60/4=15 Exploring Operation: 11+6=17, Resulting Numbers: [4, 60, 17] Generated Node #0,1: 34:[4, 60, 17] Operation: 11+6=17 Exploring Operation: 60-6=54, Resulting Numbers: [4, 11, 54] Generated Node #0,2: 34:[4, 11, 54] Operation: 60-6=54 Exploring Operation: 60-11=49, Resulting Numbers: [4, 6, 49] Generated Node #0,3: 34:[4, 6, 49] Operation: 60-11=49 Exploring Operation: 60/6=10, Resulting Numbers: [4, 11, 10] Generated Node #0,4: 34:[4, 11, 10] Operation: 60/6=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[11, 6, 15], Operations: ['60/4=15'] Exploring Operation: 11+6=17, Resulting Numbers: [15, 17] Generated Node #0,0,0: 34:[15, 17] Operation: 11+6=17 Exploring Operation: 11+15=26, Resulting Numbers: [6, 26] Generated Node #0,0,1: 34:[6, 26] Operation: 11+15=26 Exploring Operation: 11-6=5, Resulting Numbers: [15, 5] Generated Node #0,0,2: 34:[15, 5] Operation: 11-6=5 Exploring Operation: 15-11=4, Resulting Numbers: [6, 4] Generated Node #0,0,3: 34:[6, 4] Operation: 15-11=4 Exploring Operation: 6+15=21, Resulting Numbers: [11, 21] Generated Node #0,0,4: 34:[11, 21] Operation: 6+15=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[15, 17], Operations: ['60/4=15', '11+6=17'] Exploring Operation: 15*17=255, Resulting Numbers: [255] 255,34 unequal: No Solution Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,34 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 34:[15, 5], Operations: ['60/4=15', '11-6=5'] Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,34 unequal: No Solution Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 34:[6, 4], Operations: ['60/4=15', '15-11=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,34 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,34 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 34:[11, 21], Operations: ['60/4=15', '6+15=21'] Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,34 unequal: No Solution Exploring Operation: 11+21=32, Resulting Numbers: [32] 32,34 unequal: No Solution Exploring Operation: 11*21=231, Resulting Numbers: [231] 231,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 34:[6, 26], Operations: ['60/4=15', '11+15=26'] Exploring Operation: 6*26=156, Resulting Numbers: [156] 156,34 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 34:[4, 11, 10], Operations: ['60/6=10'] Exploring Operation: 11-10=1, Resulting Numbers: [4, 1] Generated Node #0,4,0: 34:[4, 1] Operation: 11-10=1 Exploring Operation: 11+10=21, Resulting Numbers: [4, 21] Generated Node #0,4,1: 34:[4, 21] Operation: 11+10=21 Exploring Operation: 4+11=15, Resulting Numbers: [10, 15] Generated Node #0,4,2: 34:[10, 15] Operation: 4+11=15 Exploring Operation: 4+10=14, Resulting Numbers: [11, 14] Generated Node #0,4,3: 34:[11, 14] Operation: 4+10=14 Exploring Operation: 10-4=6, Resulting Numbers: [11, 6] Generated Node #0,4,4: 34:[11, 6] Operation: 10-4=6 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 34:[4, 1], Operations: ['60/6=10', '11-10=1'] Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,34 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 34:[4, 21], Operations: ['60/6=10', '11+10=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,34 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 34:[10, 15], Operations: ['60/6=10', '4+11=15'] Exploring Operation: 10*15=150, Resulting Numbers: [150] 150,34 unequal: No Solution Exploring Operation: 10+15=25, Resulting Numbers: [25] 25,34 unequal: No Solution Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 34:[11, 14], Operations: ['60/6=10', '4+10=14'] Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,34 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,34 unequal: No Solution Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 34:[11, 6], Operations: ['60/6=10', '10-4=6'] Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,34 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 34:[4, 6, 49], Operations: ['60-11=49'] Exploring Operation: 4+6=10, Resulting Numbers: [49, 10] Generated Node #0,3,0: 34:[49, 10] Operation: 4+6=10 Exploring Operation: 49-4=45, Resulting Numbers: [6, 45] Generated Node #0,3,1: 34:[6, 45] Operation: 49-4=45 Exploring Operation: 4*6=24, Resulting Numbers: [49, 24] Generated Node #0,3,2: 34:[49, 24] Operation: 4*6=24 Exploring Operation: 6-4=2, Resulting Numbers: [49, 2] Generated Node #0,3,3: 34:[49, 2] Operation: 6-4=2 Exploring Operation: 49-6=43, Resulting Numbers: [4, 43] Generated Node #0,3,4: 34:[4, 43] Operation: 49-6=43 Moving to Node #0,3,4 Current State: 34:[4, 43], Operations: ['60-11=49', '49-6=43'] Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 4+43=47, Resulting Numbers: [47] 47,34 unequal: No Solution Exploring Operation: 4*43=172, Resulting Numbers: [172] 172,34 unequal: No Solution Moving to Node #0,3,3 Current State: 34:[49, 2], Operations: ['60-11=49', '6-4=2'] Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,34 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,34 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,34 unequal: No Solution Moving to Node #0,3,1 Current State: 34:[6, 45], Operations: ['60-11=49', '49-4=45'] Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,34 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 6*45=270, Resulting Numbers: [270] 270,34 unequal: No Solution Moving to Node #0,3,0 Current State: 34:[49, 10], Operations: ['60-11=49', '4+6=10'] Exploring Operation: 49*10=490, Resulting Numbers: [490] 490,34 unequal: No Solution Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,34 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,34 unequal: No Solution Moving to Node #0,3,2 Current State: 34:[49, 24], Operations: ['60-11=49', '4*6=24'] Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,34 unequal: No Solution Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,34 unequal: No Solution Exploring Operation: 49*24=1176, Resulting Numbers: [1176] 1176,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[4, 60, 17], Operations: ['11+6=17'] Exploring Operation: 60/4=15, Resulting Numbers: [17, 15] Generated Node #0,1,0: 34:[17, 15] Operation: 60/4=15 Exploring Operation: 4+60=64, Resulting Numbers: [17, 64] Generated Node #0,1,1: 34:[17, 64] Operation: 4+60=64 Exploring Operation: 4+17=21, Resulting Numbers: [60, 21] Generated Node #0,1,2: 34:[60, 21] Operation: 4+17=21 Exploring Operation: 60-17=43, Resulting Numbers: [4, 43] Generated Node #0,1,3: 34:[4, 43] Operation: 60-17=43 Exploring Operation: 60-4=56, Resulting Numbers: [17, 56] Generated Node #0,1,4: 34:[17, 56] Operation: 60-4=56 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 34:[17, 15], Operations: ['11+6=17', '60/4=15'] Exploring Operation: 17*15=255, Resulting Numbers: [255] 255,34 unequal: No Solution Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,34 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 34:[4, 43], Operations: ['11+6=17', '60-17=43'] Exploring Operation: 4*43=172, Resulting Numbers: [172] 172,34 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 4+43=47, Resulting Numbers: [47] 47,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 34:[17, 56], Operations: ['11+6=17', '60-4=56'] Exploring Operation: 17+56=73, Resulting Numbers: [73] 73,34 unequal: No Solution Exploring Operation: 17*56=952, Resulting Numbers: [952] 952,34 unequal: No Solution Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 34:[17, 64], Operations: ['11+6=17', '4+60=64'] Exploring Operation: 17*64=1088, Resulting Numbers: [1088] 1088,34 unequal: No Solution Exploring Operation: 17+64=81, Resulting Numbers: [81] 81,34 unequal: No Solution Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 34:[60, 21], Operations: ['11+6=17', '4+17=21'] Exploring Operation: 60*21=1260, Resulting Numbers: [1260] 1260,34 unequal: No Solution Exploring Operation: 60+21=81, Resulting Numbers: [81] 81,34 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[4, 11, 54], Operations: ['60-6=54'] Exploring Operation: 4*11=44, Resulting Numbers: [54, 44] Generated Node #0,2,0: 34:[54, 44] Operation: 4*11=44 Exploring Operation: 11-4=7, Resulting Numbers: [54, 7] Generated Node #0,2,1: 34:[54, 7] Operation: 11-4=7 Exploring Operation: 54-11=43, Resulting Numbers: [4, 43] Generated Node #0,2,2: 34:[4, 43] Operation: 54-11=43 Exploring Operation: 54-4=50, Resulting Numbers: [11, 50] Generated Node #0,2,3: 34:[11, 50] Operation: 54-4=50 Exploring Operation: 4+11=15, Resulting Numbers: [54, 15] Generated Node #0,2,4: 34:[54, 15] Operation: 4+11=15 Moving to Node #0,2,2 Current State: 34:[4, 43], Operations: ['60-6=54', '54-11=43'] Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 4*43=172, Resulting Numbers: [172] 172,34 unequal: No Solution Exploring Operation: 4+43=47, Resulting Numbers: [47] 47,34 unequal: No Solution Moving to Node #0,2,4 Current State: 34:[54, 15], Operations: ['60-6=54', '4+11=15'] Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,34 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,34 unequal: No Solution Moving to Node #0,2,3 Current State: 34:[11, 50], Operations: ['60-6=54', '54-4=50'] Exploring Operation: 11*50=550, Resulting Numbers: [550] 550,34 unequal: No Solution Exploring Operation: 50-11=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 11+50=61, Resulting Numbers: [61] 61,34 unequal: No Solution Moving to Node #0,2,1 Current State: 34:[54, 7], Operations: ['60-6=54', '11-4=7'] Exploring Operation: 54*7=378, Resulting Numbers: [378] 378,34 unequal: No Solution Exploring Operation: 54+7=61, Resulting Numbers: [61] 61,34 unequal: No Solution Exploring Operation: 54-7=47, Resulting Numbers: [47] 47,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[54, 44], Operations: ['60-6=54', '4*11=44'] Exploring Operation: 54*44=2376, Resulting Numbers: [2376] 2376,34 unequal: No Solution Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,34 unequal: No Solution Exploring Operation: 54+44=98, Resulting Numbers: [98] 98,34 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
[ 83, 80, 63, 2 ]
37
[ "83+80=163", "63*2=126", "163-126=37" ]
Current State: 37:[83, 80, 63, 2], Operations: [] Exploring Operation: 83+80=163, Resulting Numbers: [63, 2, 163] Generated Node #2: [63, 2, 163] from Operation: 83+80=163 Current State: 37:[63, 2, 163], Operations: ['83+80=163'] Exploring Operation: 63*2=126, Resulting Numbers: [163, 126] Generated Node #3: [163, 126] from Operation: 63*2=126 Current State: 37:[163, 126], Operations: ['83+80=163', '63*2=126'] Exploring Operation: 163-126=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[83, 80, 63, 2], Operations: [] Exploring Operation: 83-80=3, Resulting Numbers: [63, 2, 3] Generated Node #0,0: 37:[63, 2, 3] Operation: 83-80=3 Exploring Operation: 80-63=17, Resulting Numbers: [83, 2, 17] Generated Node #0,1: 37:[83, 2, 17] Operation: 80-63=17 Exploring Operation: 80/2=40, Resulting Numbers: [83, 63, 40] Generated Node #0,2: 37:[83, 63, 40] Operation: 80/2=40 Exploring Operation: 83-63=20, Resulting Numbers: [80, 2, 20] Generated Node #0,3: 37:[80, 2, 20] Operation: 83-63=20 Exploring Operation: 83-2=81, Resulting Numbers: [80, 63, 81] Generated Node #0,4: 37:[80, 63, 81] Operation: 83-2=81 Start Sub Search at level 1: Moving to Node #0,2 Current State: 37:[83, 63, 40], Operations: ['80/2=40'] Exploring Operation: 83-40=43, Resulting Numbers: [63, 43] Generated Node #0,2,0: 37:[63, 43] Operation: 83-40=43 Exploring Operation: 83+63=146, Resulting Numbers: [40, 146] Generated Node #0,2,1: 37:[40, 146] Operation: 83+63=146 Exploring Operation: 83-63=20, Resulting Numbers: [40, 20] Generated Node #0,2,2: 37:[40, 20] Operation: 83-63=20 Exploring Operation: 83+40=123, Resulting Numbers: [63, 123] Generated Node #0,2,3: 37:[63, 123] Operation: 83+40=123 Exploring Operation: 63-40=23, Resulting Numbers: [83, 23] Generated Node #0,2,4: 37:[83, 23] Operation: 63-40=23 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 37:[40, 20], Operations: ['80/2=40', '83-63=20'] Exploring Operation: 40+20=60, Resulting Numbers: [60] 60,37 unequal: No Solution Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,37 unequal: No Solution Exploring Operation: 40*20=800, Resulting Numbers: [800] 800,37 unequal: No Solution Exploring Operation: 40/20=2, Resulting Numbers: [2] 2,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 37:[63, 43], Operations: ['80/2=40', '83-40=43'] Exploring Operation: 63+43=106, Resulting Numbers: [106] 106,37 unequal: No Solution Exploring Operation: 63-43=20, Resulting Numbers: [20] 20,37 unequal: No Solution Exploring Operation: 63*43=2709, Resulting Numbers: [2709] 2709,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 37:[83, 23], Operations: ['80/2=40', '63-40=23'] Exploring Operation: 83*23=1909, Resulting Numbers: [1909] 1909,37 unequal: No Solution Exploring Operation: 83+23=106, Resulting Numbers: [106] 106,37 unequal: No Solution Exploring Operation: 83-23=60, Resulting Numbers: [60] 60,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 37:[40, 146], Operations: ['80/2=40', '83+63=146'] Exploring Operation: 40+146=186, Resulting Numbers: [186] 186,37 unequal: No Solution Exploring Operation: 146-40=106, Resulting Numbers: [106] 106,37 unequal: No Solution Exploring Operation: 40*146=5840, Resulting Numbers: [5840] 5840,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 37:[63, 123], Operations: ['80/2=40', '83+40=123'] Exploring Operation: 63*123=7749, Resulting Numbers: [7749] 7749,37 unequal: No Solution Exploring Operation: 63+123=186, Resulting Numbers: [186] 186,37 unequal: No Solution Exploring Operation: 123-63=60, Resulting Numbers: [60] 60,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[63, 2, 3], Operations: ['83-80=3'] Exploring Operation: 2+3=5, Resulting Numbers: [63, 5] Generated Node #0,0,0: 37:[63, 5] Operation: 2+3=5 Exploring Operation: 63-2=61, Resulting Numbers: [3, 61] Generated Node #0,0,1: 37:[3, 61] Operation: 63-2=61 Exploring Operation: 63/3=21, Resulting Numbers: [2, 21] Generated Node #0,0,2: 37:[2, 21] Operation: 63/3=21 Exploring Operation: 2*3=6, Resulting Numbers: [63, 6] Generated Node #0,0,3: 37:[63, 6] Operation: 2*3=6 Exploring Operation: 63-3=60, Resulting Numbers: [2, 60] Generated Node #0,0,4: 37:[2, 60] Operation: 63-3=60 Moving to Node #0,0,2 Current State: 37:[2, 21], Operations: ['83-80=3', '63/3=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,37 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,37 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,37 unequal: No Solution Moving to Node #0,0,3 Current State: 37:[63, 6], Operations: ['83-80=3', '2*3=6'] Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,37 unequal: No Solution Exploring Operation: 63*6=378, Resulting Numbers: [378] 378,37 unequal: No Solution Exploring Operation: 63+6=69, Resulting Numbers: [69] 69,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[63, 5], Operations: ['83-80=3', '2+3=5'] Exploring Operation: 63+5=68, Resulting Numbers: [68] 68,37 unequal: No Solution Exploring Operation: 63-5=58, Resulting Numbers: [58] 58,37 unequal: No Solution Exploring Operation: 63*5=315, Resulting Numbers: [315] 315,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[3, 61], Operations: ['83-80=3', '63-2=61'] Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,37 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,37 unequal: No Solution Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,37 unequal: No Solution Moving to Node #0,0,4 Current State: 37:[2, 60], Operations: ['83-80=3', '63-3=60'] Exploring Operation: 2*60=120, Resulting Numbers: [120] 120,37 unequal: No Solution Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,37 unequal: No Solution Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 37:[80, 2, 20], Operations: ['83-63=20'] Exploring Operation: 80-2=78, Resulting Numbers: [20, 78] Generated Node #0,3,0: 37:[20, 78] Operation: 80-2=78 Exploring Operation: 80-20=60, Resulting Numbers: [2, 60] Generated Node #0,3,1: 37:[2, 60] Operation: 80-20=60 Exploring Operation: 2+20=22, Resulting Numbers: [80, 22] Generated Node #0,3,2: 37:[80, 22] Operation: 2+20=22 Exploring Operation: 80/2=40, Resulting Numbers: [20, 40] Generated Node #0,3,3: 37:[20, 40] Operation: 80/2=40 Exploring Operation: 2*20=40, Resulting Numbers: [80, 40] Generated Node #0,3,4: 37:[80, 40] Operation: 2*20=40 Moving to Node #0,3,3 Current State: 37:[20, 40], Operations: ['83-63=20', '80/2=40'] Exploring Operation: 40/20=2, Resulting Numbers: [2] 2,37 unequal: No Solution Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,37 unequal: No Solution Exploring Operation: 20*40=800, Resulting Numbers: [800] 800,37 unequal: No Solution Exploring Operation: 20+40=60, Resulting Numbers: [60] 60,37 unequal: No Solution Moving to Node #0,3,4 Current State: 37:[80, 40], Operations: ['83-63=20', '2*20=40'] Exploring Operation: 80*40=3200, Resulting Numbers: [3200] 3200,37 unequal: No Solution Exploring Operation: 80+40=120, Resulting Numbers: [120] 120,37 unequal: No Solution Exploring Operation: 80-40=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 80/40=2, Resulting Numbers: [2] 2,37 unequal: No Solution Moving to Node #0,3,0 Current State: 37:[20, 78], Operations: ['83-63=20', '80-2=78'] Exploring Operation: 20*78=1560, Resulting Numbers: [1560] 1560,37 unequal: No Solution Exploring Operation: 20+78=98, Resulting Numbers: [98] 98,37 unequal: No Solution Exploring Operation: 78-20=58, Resulting Numbers: [58] 58,37 unequal: No Solution Moving to Node #0,3,1 Current State: 37:[2, 60], Operations: ['83-63=20', '80-20=60'] Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,37 unequal: No Solution Exploring Operation: 2*60=120, Resulting Numbers: [120] 120,37 unequal: No Solution Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,37 unequal: No Solution Moving to Node #0,3,2 Current State: 37:[80, 22], Operations: ['83-63=20', '2+20=22'] Exploring Operation: 80-22=58, Resulting Numbers: [58] 58,37 unequal: No Solution Exploring Operation: 80*22=1760, Resulting Numbers: [1760] 1760,37 unequal: No Solution Exploring Operation: 80+22=102, Resulting Numbers: [102] 102,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[83, 2, 17], Operations: ['80-63=17'] Exploring Operation: 2+17=19, Resulting Numbers: [83, 19] Generated Node #0,1,0: 37:[83, 19] Operation: 2+17=19 Exploring Operation: 83+2=85, Resulting Numbers: [17, 85] Generated Node #0,1,1: 37:[17, 85] Operation: 83+2=85 Exploring Operation: 83-17=66, Resulting Numbers: [2, 66] Generated Node #0,1,2: 37:[2, 66] Operation: 83-17=66 Exploring Operation: 2*17=34, Resulting Numbers: [83, 34] Generated Node #0,1,3: 37:[83, 34] Operation: 2*17=34 Exploring Operation: 83-2=81, Resulting Numbers: [17, 81] Generated Node #0,1,4: 37:[17, 81] Operation: 83-2=81 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 37:[83, 34], Operations: ['80-63=17', '2*17=34'] Exploring Operation: 83-34=49, Resulting Numbers: [49] 49,37 unequal: No Solution Exploring Operation: 83+34=117, Resulting Numbers: [117] 117,37 unequal: No Solution Exploring Operation: 83*34=2822, Resulting Numbers: [2822] 2822,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 37:[83, 19], Operations: ['80-63=17', '2+17=19'] Exploring Operation: 83+19=102, Resulting Numbers: [102] 102,37 unequal: No Solution Exploring Operation: 83*19=1577, Resulting Numbers: [1577] 1577,37 unequal: No Solution Exploring Operation: 83-19=64, Resulting Numbers: [64] 64,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 37:[2, 66], Operations: ['80-63=17', '83-17=66'] Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,37 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,37 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,37 unequal: No Solution Exploring Operation: 2*66=132, Resulting Numbers: [132] 132,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 37:[17, 81], Operations: ['80-63=17', '83-2=81'] Exploring Operation: 17*81=1377, Resulting Numbers: [1377] 1377,37 unequal: No Solution Exploring Operation: 81-17=64, Resulting Numbers: [64] 64,37 unequal: No Solution Exploring Operation: 17+81=98, Resulting Numbers: [98] 98,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 37:[17, 85], Operations: ['80-63=17', '83+2=85'] Exploring Operation: 85/17=5, Resulting Numbers: [5] 5,37 unequal: No Solution Exploring Operation: 17*85=1445, Resulting Numbers: [1445] 1445,37 unequal: No Solution Exploring Operation: 85-17=68, Resulting Numbers: [68] 68,37 unequal: No Solution Exploring Operation: 17+85=102, Resulting Numbers: [102] 102,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 37:[80, 63, 81], Operations: ['83-2=81'] Exploring Operation: 81-80=1, Resulting Numbers: [63, 1] Generated Node #0,4,0: 37:[63, 1] Operation: 81-80=1 Exploring Operation: 80-63=17, Resulting Numbers: [81, 17] Generated Node #0,4,1: 37:[81, 17] Operation: 80-63=17 Exploring Operation: 80+63=143, Resulting Numbers: [81, 143] Generated Node #0,4,2: 37:[81, 143] Operation: 80+63=143 Exploring Operation: 81-63=18, Resulting Numbers: [80, 18] Generated Node #0,4,3: 37:[80, 18] Operation: 81-63=18 Exploring Operation: 80+81=161, Resulting Numbers: [63, 161] Generated Node #0,4,4: 37:[63, 161] Operation: 80+81=161 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 37:[63, 1], Operations: ['83-2=81', '81-80=1'] Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 63*1=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 63+1=64, Resulting Numbers: [64] 64,37 unequal: No Solution Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 37:[80, 18], Operations: ['83-2=81', '81-63=18'] Exploring Operation: 80*18=1440, Resulting Numbers: [1440] 1440,37 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 37:[81, 17], Operations: ['83-2=81', '80-63=17'] Exploring Operation: 81*17=1377, Resulting Numbers: [1377] 1377,37 unequal: No Solution Exploring Operation: 81+17=98, Resulting Numbers: [98] 98,37 unequal: No Solution Exploring Operation: 81-17=64, Resulting Numbers: [64] 64,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 37:[81, 143], Operations: ['83-2=81', '80+63=143'] Exploring Operation: 143-81=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 81+143=224, Resulting Numbers: [224] 224,37 unequal: No Solution Exploring Operation: 81*143=11583, Resulting Numbers: [11583] 11583,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 37:[63, 161], Operations: ['83-2=81', '80+81=161'] Exploring Operation: 161-63=98, Resulting Numbers: [98] 98,37 unequal: No Solution Exploring Operation: 63+161=224, Resulting Numbers: [224] 224,37 unequal: No Solution Exploring Operation: 63*161=10143, Resulting Numbers: [10143] 10143,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 91, 13, 18, 27 ]
87
[ "91-13=78", "27-18=9", "78+9=87" ]
Current State: 87:[91, 13, 18, 27], Operations: [] Exploring Operation: 91-13=78, Resulting Numbers: [18, 27, 78] Generated Node #2: [18, 27, 78] from Operation: 91-13=78 Current State: 87:[18, 27, 78], Operations: ['91-13=78'] Exploring Operation: 27-18=9, Resulting Numbers: [78, 9] Generated Node #3: [78, 9] from Operation: 27-18=9 Current State: 87:[78, 9], Operations: ['91-13=78', '27-18=9'] Exploring Operation: 78+9=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[91, 13, 18, 27], Operations: [] Exploring Operation: 13+18=31, Resulting Numbers: [91, 27, 31] Generated Node #0,0: 87:[91, 27, 31] Operation: 13+18=31 Exploring Operation: 18-13=5, Resulting Numbers: [91, 27, 5] Generated Node #0,1: 87:[91, 27, 5] Operation: 18-13=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[91, 27, 31], Operations: ['13+18=31'] Exploring Operation: 91-27=64, Resulting Numbers: [31, 64] Generated Node #0,0,0: 87:[31, 64] Operation: 91-27=64 Exploring Operation: 31-27=4, Resulting Numbers: [91, 4] Generated Node #0,0,1: 87:[91, 4] Operation: 31-27=4 Moving to Node #0,0,1 Current State: 87:[91, 4], Operations: ['13+18=31', '31-27=4'] Exploring Operation: 91+4=95, Resulting Numbers: [95] 95,87 unequal: No Solution Exploring Operation: 91-4=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[91, 13, 18, 27], Operations: [] Exploring Operation: 13+18=31, Resulting Numbers: [91, 27, 31] Generated Node #0,0: 87:[91, 27, 31] Operation: 13+18=31 Moving to Node #0,0 Current State: 87:[91, 27, 31], Operations: ['13+18=31'] Exploring Operation: 31-27=4, Resulting Numbers: [91, 4] Generated Node #0,0,1: 87:[91, 4] Operation: 31-27=4 Moving to Node #0,0,1 Current State: 87:[91, 4], Operations: ['13+18=31', '31-27=4'] Exploring Operation: 91-4=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 59, 94, 81, 66 ]
97
[ "81-59=22", "66/22=3", "94+3=97" ]
Current State: 97:[59, 94, 81, 66], Operations: [] Exploring Operation: 81-59=22, Resulting Numbers: [94, 66, 22] Generated Node #2: [94, 66, 22] from Operation: 81-59=22 Current State: 97:[94, 66, 22], Operations: ['81-59=22'] Exploring Operation: 66/22=3, Resulting Numbers: [94, 3] Generated Node #3: [94, 3] from Operation: 66/22=3 Current State: 97:[94, 3], Operations: ['81-59=22', '66/22=3'] Exploring Operation: 94+3=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[59, 94, 81, 66], Operations: [] Exploring Operation: 81+66=147, Resulting Numbers: [59, 94, 147] Generated Node #0,0: 97:[59, 94, 147] Operation: 81+66=147 Exploring Operation: 59+66=125, Resulting Numbers: [94, 81, 125] Generated Node #0,1: 97:[94, 81, 125] Operation: 59+66=125 Exploring Operation: 59+81=140, Resulting Numbers: [94, 66, 140] Generated Node #0,2: 97:[94, 66, 140] Operation: 59+81=140 Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[94, 81, 125], Operations: ['59+66=125'] Exploring Operation: 125-81=44, Resulting Numbers: [94, 44] Generated Node #0,1,0: 97:[94, 44] Operation: 125-81=44 Exploring Operation: 94+81=175, Resulting Numbers: [125, 175] Generated Node #0,1,1: 97:[125, 175] Operation: 94+81=175 Exploring Operation: 125-94=31, Resulting Numbers: [81, 31] Generated Node #0,1,2: 97:[81, 31] Operation: 125-94=31 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[94, 44], Operations: ['59+66=125', '125-81=44'] Exploring Operation: 94+44=138, Resulting Numbers: [138] 138,97 unequal: No Solution Exploring Operation: 94*44=4136, Resulting Numbers: [4136] 4136,97 unequal: No Solution Exploring Operation: 94-44=50, Resulting Numbers: [50] 50,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 97:[81, 31], Operations: ['59+66=125', '125-94=31'] Exploring Operation: 81+31=112, Resulting Numbers: [112] 112,97 unequal: No Solution Exploring Operation: 81*31=2511, Resulting Numbers: [2511] 2511,97 unequal: No Solution Exploring Operation: 81-31=50, Resulting Numbers: [50] 50,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 97:[125, 175], Operations: ['59+66=125', '94+81=175'] Exploring Operation: 125*175=21875, Resulting Numbers: [21875] 21875,97 unequal: No Solution Exploring Operation: 175-125=50, Resulting Numbers: [50] 50,97 unequal: No Solution Exploring Operation: 125+175=300, Resulting Numbers: [300] 300,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[94, 66, 140], Operations: ['59+81=140'] Exploring Operation: 140-94=46, Resulting Numbers: [66, 46] Generated Node #0,2,0: 97:[66, 46] Operation: 140-94=46 Exploring Operation: 94+66=160, Resulting Numbers: [140, 160] Generated Node #0,2,1: 97:[140, 160] Operation: 94+66=160 Exploring Operation: 140-66=74, Resulting Numbers: [94, 74] Generated Node #0,2,2: 97:[94, 74] Operation: 140-66=74 Moving to Node #0,2,2 Current State: 97:[94, 74], Operations: ['59+81=140', '140-66=74'] Exploring Operation: 94-74=20, Resulting Numbers: [20] 20,97 unequal: No Solution Exploring Operation: 94+74=168, Resulting Numbers: [168] 168,97 unequal: No Solution Exploring Operation: 94*74=6956, Resulting Numbers: [6956] 6956,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[66, 46], Operations: ['59+81=140', '140-94=46'] Exploring Operation: 66+46=112, Resulting Numbers: [112] 112,97 unequal: No Solution Exploring Operation: 66-46=20, Resulting Numbers: [20] 20,97 unequal: No Solution Exploring Operation: 66*46=3036, Resulting Numbers: [3036] 3036,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[140, 160], Operations: ['59+81=140', '94+66=160'] Exploring Operation: 140+160=300, Resulting Numbers: [300] 300,97 unequal: No Solution Exploring Operation: 160-140=20, Resulting Numbers: [20] 20,97 unequal: No Solution Exploring Operation: 140*160=22400, Resulting Numbers: [22400] 22400,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[59, 94, 147], Operations: ['81+66=147'] Exploring Operation: 147-94=53, Resulting Numbers: [59, 53] Generated Node #0,0,0: 97:[59, 53] Operation: 147-94=53 Exploring Operation: 59+94=153, Resulting Numbers: [147, 153] Generated Node #0,0,1: 97:[147, 153] Operation: 59+94=153 Exploring Operation: 147-59=88, Resulting Numbers: [94, 88] Generated Node #0,0,2: 97:[94, 88] Operation: 147-59=88 Moving to Node #0,0,2 Current State: 97:[94, 88], Operations: ['81+66=147', '147-59=88'] Exploring Operation: 94*88=8272, Resulting Numbers: [8272] 8272,97 unequal: No Solution Exploring Operation: 94-88=6, Resulting Numbers: [6] 6,97 unequal: No Solution Exploring Operation: 94+88=182, Resulting Numbers: [182] 182,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[59, 53], Operations: ['81+66=147', '147-94=53'] Exploring Operation: 59*53=3127, Resulting Numbers: [3127] 3127,97 unequal: No Solution Exploring Operation: 59+53=112, Resulting Numbers: [112] 112,97 unequal: No Solution Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[147, 153], Operations: ['81+66=147', '59+94=153'] Exploring Operation: 153-147=6, Resulting Numbers: [6] 6,97 unequal: No Solution Exploring Operation: 147*153=22491, Resulting Numbers: [22491] 22491,97 unequal: No Solution Exploring Operation: 147+153=300, Resulting Numbers: [300] 300,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 80, 49, 62, 51 ]
36
[ "80-62=18", "51-49=2", "18*2=36" ]
Current State: 36:[80, 49, 62, 51], Operations: [] Exploring Operation: 80-62=18, Resulting Numbers: [49, 51, 18] Generated Node #2: [49, 51, 18] from Operation: 80-62=18 Current State: 36:[49, 51, 18], Operations: ['80-62=18'] Exploring Operation: 51-49=2, Resulting Numbers: [18, 2] Generated Node #3: [18, 2] from Operation: 51-49=2 Current State: 36:[18, 2], Operations: ['80-62=18', '51-49=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[80, 49, 62, 51], Operations: [] Exploring Operation: 80-49=31, Resulting Numbers: [62, 51, 31] Generated Node #0,0: 36:[62, 51, 31] Operation: 80-49=31 Exploring Operation: 80-62=18, Resulting Numbers: [49, 51, 18] Generated Node #0,1: 36:[49, 51, 18] Operation: 80-62=18 Moving to Node #0,1 Current State: 36:[49, 51, 18], Operations: ['80-62=18'] Exploring Operation: 51-18=33, Resulting Numbers: [49, 33] Generated Node #0,1,0: 36:[49, 33] Operation: 51-18=33 Exploring Operation: 51-49=2, Resulting Numbers: [18, 2] Generated Node #0,1,1: 36:[18, 2] Operation: 51-49=2 Moving to Node #0,0 Current State: 36:[62, 51, 31], Operations: ['80-49=31'] Exploring Operation: 62/31=2, Resulting Numbers: [51, 2] Generated Node #0,0,0: 36:[51, 2] Operation: 62/31=2 Exploring Operation: 62-51=11, Resulting Numbers: [31, 11] Generated Node #0,0,1: 36:[31, 11] Operation: 62-51=11 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[31, 11], Operations: ['80-49=31', '62-51=11'] Exploring Operation: 31+11=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[51, 2], Operations: ['80-49=31', '62/31=2'] Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,36 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,36 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: 36:[18, 2], Operations: ['80-62=18', '51-49=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[80, 49, 62, 51], Operations: [] Exploring Operation: 80-62=18, Resulting Numbers: [49, 51, 18] Generated Node #0,1: 36:[49, 51, 18] Operation: 80-62=18 Moving to Node #0,1 Current State: 36:[49, 51, 18], Operations: ['80-62=18'] Exploring Operation: 51-49=2, Resulting Numbers: [18, 2] Generated Node #0,1,1: 36:[18, 2] Operation: 51-49=2 Moving to Node #0,1,1 Current State: 36:[18, 2], Operations: ['80-62=18', '51-49=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 5, 19, 2, 30 ]
67
[ "5*19=95", "30-2=28", "95-28=67" ]
Current State: 67:[5, 19, 2, 30], Operations: [] Exploring Operation: 5*19=95, Resulting Numbers: [2, 30, 95] Generated Node #2: [2, 30, 95] from Operation: 5*19=95 Current State: 67:[2, 30, 95], Operations: ['5*19=95'] Exploring Operation: 30-2=28, Resulting Numbers: [95, 28] Generated Node #3: [95, 28] from Operation: 30-2=28 Current State: 67:[95, 28], Operations: ['5*19=95', '30-2=28'] Exploring Operation: 95-28=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[5, 19, 2, 30], Operations: [] Exploring Operation: 5*19=95, Resulting Numbers: [2, 30, 95] Generated Node #0,0: 67:[2, 30, 95] Operation: 5*19=95 Exploring Operation: 2*30=60, Resulting Numbers: [5, 19, 60] Generated Node #0,1: 67:[5, 19, 60] Operation: 2*30=60 Exploring Operation: 19*2=38, Resulting Numbers: [5, 30, 38] Generated Node #0,2: 67:[5, 30, 38] Operation: 19*2=38 Moving to Node #0,1 Current State: 67:[5, 19, 60], Operations: ['2*30=60'] Exploring Operation: 5+60=65, Resulting Numbers: [19, 65] Generated Node #0,1,0: 67:[19, 65] Operation: 5+60=65 Exploring Operation: 5+19=24, Resulting Numbers: [60, 24] Generated Node #0,1,1: 67:[60, 24] Operation: 5+19=24 Exploring Operation: 5*19=95, Resulting Numbers: [60, 95] Generated Node #0,1,2: 67:[60, 95] Operation: 5*19=95 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 67:[60, 95], Operations: ['2*30=60', '5*19=95'] Exploring Operation: 60*95=5700, Resulting Numbers: [5700] 5700,67 unequal: No Solution Exploring Operation: 95-60=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 60+95=155, Resulting Numbers: [155] 155,67 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 #0,1,0 Current State: 67:[19, 65], Operations: ['2*30=60', '5+60=65'] Exploring Operation: 19+65=84, Resulting Numbers: [84] 84,67 unequal: No Solution Exploring Operation: 65-19=46, Resulting Numbers: [46] 46,67 unequal: No Solution Exploring Operation: 19*65=1235, Resulting Numbers: [1235] 1235,67 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 #0,1,1 Current State: 67:[60, 24], Operations: ['2*30=60', '5+19=24'] Exploring Operation: 60+24=84, Resulting Numbers: [84] 84,67 unequal: No Solution Exploring Operation: 60-24=36, Resulting Numbers: [36] 36,67 unequal: No Solution Exploring Operation: 60*24=1440, Resulting Numbers: [1440] 1440,67 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: 67:[5, 30, 38], Operations: ['19*2=38'] Exploring Operation: 5+30=35, Resulting Numbers: [38, 35] Generated Node #0,2,0: 67:[38, 35] Operation: 5+30=35 Exploring Operation: 30+38=68, Resulting Numbers: [5, 68] Generated Node #0,2,1: 67:[5, 68] Operation: 30+38=68 Exploring Operation: 5+38=43, Resulting Numbers: [30, 43] Generated Node #0,2,2: 67:[30, 43] Operation: 5+38=43 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[38, 35], Operations: ['19*2=38', '5+30=35'] Exploring Operation: 38-35=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 38+35=73, Resulting Numbers: [73] 73,67 unequal: No Solution Exploring Operation: 38*35=1330, Resulting Numbers: [1330] 1330,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 67:[30, 43], Operations: ['19*2=38', '5+38=43'] Exploring Operation: 30+43=73, Resulting Numbers: [73] 73,67 unequal: No Solution Exploring Operation: 43-30=13, Resulting Numbers: [13] 13,67 unequal: No Solution Exploring Operation: 30*43=1290, Resulting Numbers: [1290] 1290,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[5, 68], Operations: ['19*2=38', '30+38=68'] Exploring Operation: 5+68=73, Resulting Numbers: [73] 73,67 unequal: No Solution Exploring Operation: 5*68=340, Resulting Numbers: [340] 340,67 unequal: No Solution Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 67:[2, 30, 95], Operations: ['5*19=95'] Exploring Operation: 2+30=32, Resulting Numbers: [95, 32] Generated Node #0,0,0: 67:[95, 32] Operation: 2+30=32 Exploring Operation: 2*30=60, Resulting Numbers: [95, 60] Generated Node #0,0,1: 67:[95, 60] Operation: 2*30=60 Exploring Operation: 95-2=93, Resulting Numbers: [30, 93] Generated Node #0,0,2: 67:[30, 93] Operation: 95-2=93 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[95, 60], Operations: ['5*19=95', '2*30=60'] Exploring Operation: 95-60=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 95+60=155, Resulting Numbers: [155] 155,67 unequal: No Solution Exploring Operation: 95*60=5700, Resulting Numbers: [5700] 5700,67 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 #0,0,0 Current State: 67:[95, 32], Operations: ['5*19=95', '2+30=32'] Exploring Operation: 95*32=3040, Resulting Numbers: [3040] 3040,67 unequal: No Solution Exploring Operation: 95+32=127, Resulting Numbers: [127] 127,67 unequal: No Solution Exploring Operation: 95-32=63, Resulting Numbers: [63] 63,67 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 #0,0,2 Current State: 67:[30, 93], Operations: ['5*19=95', '95-2=93'] Exploring Operation: 93-30=63, Resulting Numbers: [63] 63,67 unequal: No Solution Exploring Operation: 30+93=123, Resulting Numbers: [123] 123,67 unequal: No Solution Exploring Operation: 30*93=2790, Resulting Numbers: [2790] 2790,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 46, 58, 18, 67 ]
55
[ "46+58=104", "67-18=49", "104-49=55" ]
Current State: 55:[46, 58, 18, 67], Operations: [] Exploring Operation: 46+58=104, Resulting Numbers: [18, 67, 104] Generated Node #2: [18, 67, 104] from Operation: 46+58=104 Current State: 55:[18, 67, 104], Operations: ['46+58=104'] Exploring Operation: 67-18=49, Resulting Numbers: [104, 49] Generated Node #3: [104, 49] from Operation: 67-18=49 Current State: 55:[104, 49], Operations: ['46+58=104', '67-18=49'] Exploring Operation: 104-49=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[46, 58, 18, 67], Operations: [] Exploring Operation: 67-58=9, Resulting Numbers: [46, 18, 9] Generated Node #0,0: 55:[46, 18, 9] Operation: 67-58=9 Exploring Operation: 67-46=21, Resulting Numbers: [58, 18, 21] Generated Node #0,1: 55:[58, 18, 21] Operation: 67-46=21 Exploring Operation: 67-18=49, Resulting Numbers: [46, 58, 49] Generated Node #0,2: 55:[46, 58, 49] Operation: 67-18=49 Exploring Operation: 58-46=12, Resulting Numbers: [18, 67, 12] Generated Node #0,3: 55:[18, 67, 12] Operation: 58-46=12 Moving to Node #0,0 Current State: 55:[46, 18, 9], Operations: ['67-58=9'] Exploring Operation: 18-9=9, Resulting Numbers: [46, 9] Generated Node #0,0,0: 55:[46, 9] Operation: 18-9=9 Exploring Operation: 18/9=2, Resulting Numbers: [46, 2] Generated Node #0,0,1: 55:[46, 2] Operation: 18/9=2 Exploring Operation: 46+9=55, Resulting Numbers: [18, 55] Generated Node #0,0,2: 55:[18, 55] Operation: 46+9=55 Exploring Operation: 46+18=64, Resulting Numbers: [9, 64] Generated Node #0,0,3: 55:[9, 64] Operation: 46+18=64 Moving to Node #0,2 Current State: 55:[46, 58, 49], Operations: ['67-18=49'] Exploring Operation: 58-46=12, Resulting Numbers: [49, 12] Generated Node #0,2,0: 55:[49, 12] Operation: 58-46=12 Exploring Operation: 46+49=95, Resulting Numbers: [58, 95] Generated Node #0,2,1: 55:[58, 95] Operation: 46+49=95 Exploring Operation: 49-46=3, Resulting Numbers: [58, 3] Generated Node #0,2,2: 55:[58, 3] Operation: 49-46=3 Exploring Operation: 58-49=9, Resulting Numbers: [46, 9] Generated Node #0,2,3: 55:[46, 9] Operation: 58-49=9 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 55:[58, 3], Operations: ['67-18=49', '49-46=3'] Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,55 unequal: No Solution Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,55 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[46, 58, 18, 67], Operations: [] Exploring Operation: 67-18=49, Resulting Numbers: [46, 58, 49] Generated Node #0,2: 55:[46, 58, 49] Operation: 67-18=49 Moving to Node #0,2 Current State: 55:[46, 58, 49], Operations: ['67-18=49'] Exploring Operation: 49-46=3, Resulting Numbers: [58, 3] Generated Node #0,2,2: 55:[58, 3] Operation: 49-46=3 Moving to Node #0,2,2 Current State: 55:[58, 3], Operations: ['67-18=49', '49-46=3'] Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 13, 77, 81, 88 ]
83
[ "13+77=90", "88-81=7", "90-7=83" ]
Current State: 83:[13, 77, 81, 88], Operations: [] Exploring Operation: 13+77=90, Resulting Numbers: [81, 88, 90] Generated Node #2: [81, 88, 90] from Operation: 13+77=90 Current State: 83:[81, 88, 90], Operations: ['13+77=90'] Exploring Operation: 88-81=7, Resulting Numbers: [90, 7] Generated Node #3: [90, 7] from Operation: 88-81=7 Current State: 83:[90, 7], Operations: ['13+77=90', '88-81=7'] Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[13, 77, 81, 88], Operations: [] Exploring Operation: 13+77=90, Resulting Numbers: [81, 88, 90] Generated Node #0,0: 83:[81, 88, 90] Operation: 13+77=90 Exploring Operation: 88-13=75, Resulting Numbers: [77, 81, 75] Generated Node #0,1: 83:[77, 81, 75] Operation: 88-13=75 Moving to Node #0,0 Current State: 83:[81, 88, 90], Operations: ['13+77=90'] Exploring Operation: 88-81=7, Resulting Numbers: [90, 7] Generated Node #0,0,0: 83:[90, 7] Operation: 88-81=7 Exploring Operation: 90-81=9, Resulting Numbers: [88, 9] Generated Node #0,0,1: 83:[88, 9] Operation: 90-81=9 Moving to Node #0,1 Current State: 83:[77, 81, 75], Operations: ['88-13=75'] Exploring Operation: 81+75=156, Resulting Numbers: [77, 156] Generated Node #0,1,0: 83:[77, 156] Operation: 81+75=156 Exploring Operation: 77+75=152, Resulting Numbers: [81, 152] Generated Node #0,1,1: 83:[81, 152] Operation: 77+75=152 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 83:[81, 152], Operations: ['88-13=75', '77+75=152'] Exploring Operation: 81+152=233, Resulting Numbers: [233] 233,83 unequal: No Solution Exploring Operation: 152-81=71, Resulting Numbers: [71] 71,83 unequal: No Solution No 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: 83:[77, 156], Operations: ['88-13=75', '81+75=156'] Exploring Operation: 77+156=233, Resulting Numbers: [233] 233,83 unequal: No Solution Exploring Operation: 156-77=79, Resulting Numbers: [79] 79,83 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: 83:[88, 9], Operations: ['13+77=90', '90-81=9'] Exploring Operation: 88+9=97, Resulting Numbers: [97] 97,83 unequal: No Solution Exploring Operation: 88-9=79, Resulting Numbers: [79] 79,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[90, 7], Operations: ['13+77=90', '88-81=7'] Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[13, 77, 81, 88], Operations: [] Exploring Operation: 13+77=90, Resulting Numbers: [81, 88, 90] Generated Node #0,0: 83:[81, 88, 90] Operation: 13+77=90 Moving to Node #0,0 Current State: 83:[81, 88, 90], Operations: ['13+77=90'] Exploring Operation: 88-81=7, Resulting Numbers: [90, 7] Generated Node #0,0,0: 83:[90, 7] Operation: 88-81=7 Moving to Node #0,0,0 Current State: 83:[90, 7], Operations: ['13+77=90', '88-81=7'] Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
0.985243
hs_2
sum_heuristic
[ 17, 26, 54, 25 ]
14
[ "17+26=43", "54-25=29", "43-29=14" ]
Current State: 14:[17, 26, 54, 25], Operations: [] Exploring Operation: 17+26=43, Resulting Numbers: [54, 25, 43] Generated Node #2: [54, 25, 43] from Operation: 17+26=43 Current State: 14:[54, 25, 43], Operations: ['17+26=43'] Exploring Operation: 54-25=29, Resulting Numbers: [43, 29] Generated Node #3: [43, 29] from Operation: 54-25=29 Current State: 14:[43, 29], Operations: ['17+26=43', '54-25=29'] Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[17, 26, 54, 25], Operations: [] Exploring Operation: 54-26=28, Resulting Numbers: [17, 25, 28] Generated Node #0,0: 14:[17, 25, 28] Operation: 54-26=28 Moving to Node #0,0 Current State: 14:[17, 25, 28], Operations: ['54-26=28'] Exploring Operation: 28-25=3, Resulting Numbers: [17, 3] Generated Node #0,0,0: 14:[17, 3] Operation: 28-25=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[17, 3], Operations: ['54-26=28', '28-25=3'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[17, 26, 54, 25], Operations: [] Exploring Operation: 54-26=28, Resulting Numbers: [17, 25, 28] Generated Node #0,0: 14:[17, 25, 28] Operation: 54-26=28 Moving to Node #0,0 Current State: 14:[17, 25, 28], Operations: ['54-26=28'] Exploring Operation: 28-25=3, Resulting Numbers: [17, 3] Generated Node #0,0,0: 14:[17, 3] Operation: 28-25=3 Moving to Node #0,0,0 Current State: 14:[17, 3], Operations: ['54-26=28', '28-25=3'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 50, 93, 11, 41 ]
52
[ "93-11=82", "82/41=2", "50+2=52" ]
Current State: 52:[50, 93, 11, 41], Operations: [] Exploring Operation: 93-11=82, Resulting Numbers: [50, 41, 82] Generated Node #2: [50, 41, 82] from Operation: 93-11=82 Current State: 52:[50, 41, 82], Operations: ['93-11=82'] Exploring Operation: 82/41=2, Resulting Numbers: [50, 2] Generated Node #3: [50, 2] from Operation: 82/41=2 Current State: 52:[50, 2], Operations: ['93-11=82', '82/41=2'] Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[50, 93, 11, 41], Operations: [] Exploring Operation: 93-41=52, Resulting Numbers: [50, 11, 52] Generated Node #0,0: 52:[50, 11, 52] Operation: 93-41=52 Moving to Node #0,0 Current State: 52:[50, 11, 52], Operations: ['93-41=52'] Exploring Operation: 52-50=2, Resulting Numbers: [11, 2] Generated Node #0,0,0: 52:[11, 2] Operation: 52-50=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[11, 2], Operations: ['93-41=52', '52-50=2'] Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 14, 12, 94, 30 ]
39
[ "14+94=108", "108/12=9", "30+9=39" ]
Current State: 39:[14, 12, 94, 30], Operations: [] Exploring Operation: 14+94=108, Resulting Numbers: [12, 30, 108] Generated Node #2: [12, 30, 108] from Operation: 14+94=108 Current State: 39:[12, 30, 108], Operations: ['14+94=108'] Exploring Operation: 108/12=9, Resulting Numbers: [30, 9] Generated Node #3: [30, 9] from Operation: 108/12=9 Current State: 39:[30, 9], Operations: ['14+94=108', '108/12=9'] Exploring Operation: 30+9=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[14, 12, 94, 30], Operations: [] Exploring Operation: 94-14=80, Resulting Numbers: [12, 30, 80] Generated Node #0,0: 39:[12, 30, 80] Operation: 94-14=80 Exploring Operation: 94-12=82, Resulting Numbers: [14, 30, 82] Generated Node #0,1: 39:[14, 30, 82] Operation: 94-12=82 Exploring Operation: 30-14=16, Resulting Numbers: [12, 94, 16] Generated Node #0,2: 39:[12, 94, 16] Operation: 30-14=16 Exploring Operation: 12+30=42, Resulting Numbers: [14, 94, 42] Generated Node #0,3: 39:[14, 94, 42] Operation: 12+30=42 Exploring Operation: 94-30=64, Resulting Numbers: [14, 12, 64] Generated Node #0,4: 39:[14, 12, 64] Operation: 94-30=64 Start Sub Search at level 1: Moving to Node #0,4 Current State: 39:[14, 12, 64], Operations: ['94-30=64'] Exploring Operation: 64-14=50, Resulting Numbers: [12, 50] Generated Node #0,4,0: 39:[12, 50] Operation: 64-14=50 Exploring Operation: 14+12=26, Resulting Numbers: [64, 26] Generated Node #0,4,1: 39:[64, 26] Operation: 14+12=26 Exploring Operation: 12+64=76, Resulting Numbers: [14, 76] Generated Node #0,4,2: 39:[14, 76] Operation: 12+64=76 Exploring Operation: 64-12=52, Resulting Numbers: [14, 52] Generated Node #0,4,3: 39:[14, 52] Operation: 64-12=52 Exploring Operation: 14-12=2, Resulting Numbers: [64, 2] Generated Node #0,4,4: 39:[64, 2] Operation: 14-12=2 Moving to Node #0,4,0 Current State: 39:[12, 50], Operations: ['94-30=64', '64-14=50'] Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 12*50=600, Resulting Numbers: [600] 600,39 unequal: No Solution Exploring Operation: 12+50=62, Resulting Numbers: [62] 62,39 unequal: No Solution Moving to Node #0,4,3 Current State: 39:[14, 52], Operations: ['94-30=64', '64-12=52'] Exploring Operation: 14+52=66, Resulting Numbers: [66] 66,39 unequal: No Solution Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 14*52=728, Resulting Numbers: [728] 728,39 unequal: No Solution Moving to Node #0,4,4 Current State: 39:[64, 2], Operations: ['94-30=64', '14-12=2'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,39 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,39 unequal: No Solution Exploring Operation: 64*2=128, Resulting Numbers: [128] 128,39 unequal: No Solution Moving to Node #0,4,1 Current State: 39:[64, 26], Operations: ['94-30=64', '14+12=26'] Exploring Operation: 64-26=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 64*26=1664, Resulting Numbers: [1664] 1664,39 unequal: No Solution Exploring Operation: 64+26=90, Resulting Numbers: [90] 90,39 unequal: No Solution Moving to Node #0,4,2 Current State: 39:[14, 76], Operations: ['94-30=64', '12+64=76'] Exploring Operation: 14+76=90, Resulting Numbers: [90] 90,39 unequal: No Solution Exploring Operation: 14*76=1064, Resulting Numbers: [1064] 1064,39 unequal: No Solution Exploring Operation: 76-14=62, Resulting Numbers: [62] 62,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[12, 30, 80], Operations: ['94-14=80'] Exploring Operation: 12+30=42, Resulting Numbers: [80, 42] Generated Node #0,0,0: 39:[80, 42] Operation: 12+30=42 Exploring Operation: 30-12=18, Resulting Numbers: [80, 18] Generated Node #0,0,1: 39:[80, 18] Operation: 30-12=18 Exploring Operation: 80-12=68, Resulting Numbers: [30, 68] Generated Node #0,0,2: 39:[30, 68] Operation: 80-12=68 Exploring Operation: 12+80=92, Resulting Numbers: [30, 92] Generated Node #0,0,3: 39:[30, 92] Operation: 12+80=92 Exploring Operation: 80-30=50, Resulting Numbers: [12, 50] Generated Node #0,0,4: 39:[12, 50] Operation: 80-30=50 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 39:[12, 50], Operations: ['94-14=80', '80-30=50'] Exploring Operation: 12*50=600, Resulting Numbers: [600] 600,39 unequal: No Solution Exploring Operation: 12+50=62, Resulting Numbers: [62] 62,39 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,39 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:[30, 68], Operations: ['94-14=80', '80-12=68'] Exploring Operation: 30+68=98, Resulting Numbers: [98] 98,39 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 30*68=2040, Resulting Numbers: [2040] 2040,39 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:[80, 42], Operations: ['94-14=80', '12+30=42'] Exploring Operation: 80+42=122, Resulting Numbers: [122] 122,39 unequal: No Solution Exploring Operation: 80-42=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 80*42=3360, Resulting Numbers: [3360] 3360,39 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 #0,0,1 Current State: 39:[80, 18], Operations: ['94-14=80', '30-12=18'] Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,39 unequal: No Solution Exploring Operation: 80*18=1440, Resulting Numbers: [1440] 1440,39 unequal: No Solution Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,39 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 #0,0,3 Current State: 39:[30, 92], Operations: ['94-14=80', '12+80=92'] Exploring Operation: 30+92=122, Resulting Numbers: [122] 122,39 unequal: No Solution Exploring Operation: 30*92=2760, Resulting Numbers: [2760] 2760,39 unequal: No Solution Exploring Operation: 92-30=62, Resulting Numbers: [62] 62,39 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 #0,1 Current State: 39:[14, 30, 82], Operations: ['94-12=82'] Exploring Operation: 14+82=96, Resulting Numbers: [30, 96] Generated Node #0,1,0: 39:[30, 96] Operation: 14+82=96 Exploring Operation: 30-14=16, Resulting Numbers: [82, 16] Generated Node #0,1,1: 39:[82, 16] Operation: 30-14=16 Exploring Operation: 14+30=44, Resulting Numbers: [82, 44] Generated Node #0,1,2: 39:[82, 44] Operation: 14+30=44 Exploring Operation: 82-30=52, Resulting Numbers: [14, 52] Generated Node #0,1,3: 39:[14, 52] Operation: 82-30=52 Exploring Operation: 82-14=68, Resulting Numbers: [30, 68] Generated Node #0,1,4: 39:[30, 68] Operation: 82-14=68 Moving to Node #0,1,3 Current State: 39:[14, 52], Operations: ['94-12=82', '82-30=52'] Exploring Operation: 14+52=66, Resulting Numbers: [66] 66,39 unequal: No Solution Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 14*52=728, Resulting Numbers: [728] 728,39 unequal: No Solution Moving to Node #0,1,4 Current State: 39:[30, 68], Operations: ['94-12=82', '82-14=68'] Exploring Operation: 30*68=2040, Resulting Numbers: [2040] 2040,39 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 30+68=98, Resulting Numbers: [98] 98,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[82, 16], Operations: ['94-12=82', '30-14=16'] Exploring Operation: 82+16=98, Resulting Numbers: [98] 98,39 unequal: No Solution Exploring Operation: 82*16=1312, Resulting Numbers: [1312] 1312,39 unequal: No Solution Exploring Operation: 82-16=66, Resulting Numbers: [66] 66,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[82, 44], Operations: ['94-12=82', '14+30=44'] Exploring Operation: 82*44=3608, Resulting Numbers: [3608] 3608,39 unequal: No Solution Exploring Operation: 82-44=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 82+44=126, Resulting Numbers: [126] 126,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[30, 96], Operations: ['94-12=82', '14+82=96'] Exploring Operation: 30+96=126, Resulting Numbers: [126] 126,39 unequal: No Solution Exploring Operation: 96-30=66, Resulting Numbers: [66] 66,39 unequal: No Solution Exploring Operation: 30*96=2880, Resulting Numbers: [2880] 2880,39 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:[12, 94, 16], Operations: ['30-14=16'] Exploring Operation: 94-12=82, Resulting Numbers: [16, 82] Generated Node #0,2,0: 39:[16, 82] Operation: 94-12=82 Exploring Operation: 16-12=4, Resulting Numbers: [94, 4] Generated Node #0,2,1: 39:[94, 4] Operation: 16-12=4 Exploring Operation: 12+16=28, Resulting Numbers: [94, 28] Generated Node #0,2,2: 39:[94, 28] Operation: 12+16=28 Exploring Operation: 12+94=106, Resulting Numbers: [16, 106] Generated Node #0,2,3: 39:[16, 106] Operation: 12+94=106 Exploring Operation: 94-16=78, Resulting Numbers: [12, 78] Generated Node #0,2,4: 39:[12, 78] Operation: 94-16=78 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 39:[12, 78], Operations: ['30-14=16', '94-16=78'] Exploring Operation: 78-12=66, Resulting Numbers: [66] 66,39 unequal: No Solution Exploring Operation: 12+78=90, Resulting Numbers: [90] 90,39 unequal: No Solution Exploring Operation: 12*78=936, Resulting Numbers: [936] 936,39 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:[16, 82], Operations: ['30-14=16', '94-12=82'] Exploring Operation: 82-16=66, Resulting Numbers: [66] 66,39 unequal: No Solution Exploring Operation: 16*82=1312, Resulting Numbers: [1312] 1312,39 unequal: No Solution Exploring Operation: 16+82=98, Resulting Numbers: [98] 98,39 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 #0,2,1 Current State: 39:[94, 4], Operations: ['30-14=16', '16-12=4'] Exploring Operation: 94-4=90, Resulting Numbers: [90] 90,39 unequal: No Solution Exploring Operation: 94*4=376, Resulting Numbers: [376] 376,39 unequal: No Solution Exploring Operation: 94+4=98, Resulting Numbers: [98] 98,39 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:[94, 28], Operations: ['30-14=16', '12+16=28'] Exploring Operation: 94*28=2632, Resulting Numbers: [2632] 2632,39 unequal: No Solution Exploring Operation: 94+28=122, Resulting Numbers: [122] 122,39 unequal: No Solution Exploring Operation: 94-28=66, Resulting Numbers: [66] 66,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 39:[16, 106], Operations: ['30-14=16', '12+94=106'] Exploring Operation: 16+106=122, Resulting Numbers: [122] 122,39 unequal: No Solution Exploring Operation: 106-16=90, Resulting Numbers: [90] 90,39 unequal: No Solution Exploring Operation: 16*106=1696, Resulting Numbers: [1696] 1696,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 39:[14, 94, 42], Operations: ['12+30=42'] Exploring Operation: 14+94=108, Resulting Numbers: [42, 108] Generated Node #0,3,0: 39:[42, 108] Operation: 14+94=108 Exploring Operation: 94-42=52, Resulting Numbers: [14, 52] Generated Node #0,3,1: 39:[14, 52] Operation: 94-42=52 Exploring Operation: 42-14=28, Resulting Numbers: [94, 28] Generated Node #0,3,2: 39:[94, 28] Operation: 42-14=28 Exploring Operation: 42/14=3, Resulting Numbers: [94, 3] Generated Node #0,3,3: 39:[94, 3] Operation: 42/14=3 Exploring Operation: 94-14=80, Resulting Numbers: [42, 80] Generated Node #0,3,4: 39:[42, 80] Operation: 94-14=80 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 39:[14, 52], Operations: ['12+30=42', '94-42=52'] Exploring Operation: 14*52=728, Resulting Numbers: [728] 728,39 unequal: No Solution Exploring Operation: 14+52=66, Resulting Numbers: [66] 66,39 unequal: No Solution Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 39:[42, 80], Operations: ['12+30=42', '94-14=80'] Exploring Operation: 80-42=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 42+80=122, Resulting Numbers: [122] 122,39 unequal: No Solution Exploring Operation: 42*80=3360, Resulting Numbers: [3360] 3360,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 39:[94, 3], Operations: ['12+30=42', '42/14=3'] Exploring Operation: 94+3=97, Resulting Numbers: [97] 97,39 unequal: No Solution Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,39 unequal: No Solution Exploring Operation: 94*3=282, Resulting Numbers: [282] 282,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 39:[94, 28], Operations: ['12+30=42', '42-14=28'] Exploring Operation: 94+28=122, Resulting Numbers: [122] 122,39 unequal: No Solution Exploring Operation: 94*28=2632, Resulting Numbers: [2632] 2632,39 unequal: No Solution Exploring Operation: 94-28=66, Resulting Numbers: [66] 66,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 39:[42, 108], Operations: ['12+30=42', '14+94=108'] Exploring Operation: 42+108=150, Resulting Numbers: [150] 150,39 unequal: No Solution Exploring Operation: 42*108=4536, Resulting Numbers: [4536] 4536,39 unequal: No Solution Exploring Operation: 108-42=66, Resulting Numbers: [66] 66,39 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_5
sum_heuristic
[ 76, 33, 59, 13 ]
89
[ "76-33=43", "59-13=46", "43+46=89" ]
Current State: 89:[76, 33, 59, 13], Operations: [] Exploring Operation: 76-33=43, Resulting Numbers: [59, 13, 43] Generated Node #2: [59, 13, 43] from Operation: 76-33=43 Current State: 89:[59, 13, 43], Operations: ['76-33=43'] Exploring Operation: 59-13=46, Resulting Numbers: [43, 46] Generated Node #3: [43, 46] from Operation: 59-13=46 Current State: 89:[43, 46], Operations: ['76-33=43', '59-13=46'] Exploring Operation: 43+46=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[76, 33, 59, 13], Operations: [] Exploring Operation: 33+13=46, Resulting Numbers: [76, 59, 46] Generated Node #0,0: 89:[76, 59, 46] Operation: 33+13=46 Exploring Operation: 76+13=89, Resulting Numbers: [33, 59, 89] Generated Node #0,1: 89:[33, 59, 89] Operation: 76+13=89 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[76, 59, 46], Operations: ['33+13=46'] Exploring Operation: 76+46=122, Resulting Numbers: [59, 122] Generated Node #0,0,0: 89:[59, 122] Operation: 76+46=122 Exploring Operation: 59+46=105, Resulting Numbers: [76, 105] Generated Node #0,0,1: 89:[76, 105] Operation: 59+46=105 Moving to Node #0,0,1 Current State: 89:[76, 105], Operations: ['33+13=46', '59+46=105'] Exploring Operation: 76+105=181, Resulting Numbers: [181] 181,89 unequal: No Solution Exploring Operation: 105-76=29, Resulting Numbers: [29] 29,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[59, 122], Operations: ['33+13=46', '76+46=122'] Exploring Operation: 122-59=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 59+122=181, Resulting Numbers: [181] 181,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[33, 59, 89], Operations: ['76+13=89'] Exploring Operation: 33+59=92, Resulting Numbers: [89, 92] Generated Node #0,1,0: 89:[89, 92] Operation: 33+59=92 Exploring Operation: 59-33=26, Resulting Numbers: [89, 26] Generated Node #0,1,1: 89:[89, 26] Operation: 59-33=26 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[89, 92], Operations: ['76+13=89', '33+59=92'] Exploring Operation: 92-89=3, Resulting Numbers: [3] 3,89 unequal: No Solution Exploring Operation: 89+92=181, Resulting Numbers: [181] 181,89 unequal: No Solution No 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: 89:[89, 26], Operations: ['76+13=89', '59-33=26'] Exploring Operation: 89+26=115, Resulting Numbers: [115] 115,89 unequal: No Solution Exploring Operation: 89-26=63, Resulting Numbers: [63] 63,89 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
[ 39, 82, 10, 72 ]
39
[ "39+82=121", "10+72=82", "121-82=39" ]
Current State: 39:[39, 82, 10, 72], Operations: [] Exploring Operation: 39+82=121, Resulting Numbers: [10, 72, 121] Generated Node #2: [10, 72, 121] from Operation: 39+82=121 Current State: 39:[10, 72, 121], Operations: ['39+82=121'] Exploring Operation: 10+72=82, Resulting Numbers: [121, 82] Generated Node #3: [121, 82] from Operation: 10+72=82 Current State: 39:[121, 82], Operations: ['39+82=121', '10+72=82'] Exploring Operation: 121-82=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[39, 82, 10, 72], Operations: [] Exploring Operation: 82-39=43, Resulting Numbers: [10, 72, 43] Generated Node #0,0: 39:[10, 72, 43] Operation: 82-39=43 Exploring Operation: 72-39=33, Resulting Numbers: [82, 10, 33] Generated Node #0,1: 39:[82, 10, 33] Operation: 72-39=33 Exploring Operation: 82-10=72, Resulting Numbers: [39, 72, 72] Generated Node #0,2: 39:[39, 72, 72] Operation: 82-10=72 Exploring Operation: 82-72=10, Resulting Numbers: [39, 10, 10] Generated Node #0,3: 39:[39, 10, 10] Operation: 82-72=10 Moving to Node #0,3 Current State: 39:[39, 10, 10], Operations: ['82-72=10'] Exploring Operation: 10+10=20, Resulting Numbers: [39, 20] Generated Node #0,3,0: 39:[39, 20] Operation: 10+10=20 Exploring Operation: 10-10=0, Resulting Numbers: [39, 0] Generated Node #0,3,1: 39:[39, 0] Operation: 10-10=0 Exploring Operation: 10/10=1, Resulting Numbers: [39, 1] Generated Node #0,3,2: 39:[39, 1] Operation: 10/10=1 Exploring Operation: 39+10=49, Resulting Numbers: [10, 49] Generated Node #0,3,3: 39:[10, 49] Operation: 39+10=49 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 39:[39, 1], Operations: ['82-72=10', '10/10=1'] Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,39 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[39, 82, 10, 72], Operations: [] Exploring Operation: 82-72=10, Resulting Numbers: [39, 10, 10] Generated Node #0,3: 39:[39, 10, 10] Operation: 82-72=10 Moving to Node #0,3 Current State: 39:[39, 10, 10], Operations: ['82-72=10'] Exploring Operation: 10/10=1, Resulting Numbers: [39, 1] Generated Node #0,3,2: 39:[39, 1] Operation: 10/10=1 Moving to Node #0,3,2 Current State: 39:[39, 1], Operations: ['82-72=10', '10/10=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 1, 73, 91, 95 ]
77
[ "1*73=73", "95-91=4", "73+4=77" ]
Current State: 77:[1, 73, 91, 95], Operations: [] Exploring Operation: 1*73=73, Resulting Numbers: [91, 95, 73] Generated Node #2: [91, 95, 73] from Operation: 1*73=73 Current State: 77:[91, 95, 73], Operations: ['1*73=73'] Exploring Operation: 95-91=4, Resulting Numbers: [73, 4] Generated Node #3: [73, 4] from Operation: 95-91=4 Current State: 77:[73, 4], Operations: ['1*73=73', '95-91=4'] Exploring Operation: 73+4=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[1, 73, 91, 95], Operations: [] Exploring Operation: 95-91=4, Resulting Numbers: [1, 73, 4] Generated Node #0,0: 77:[1, 73, 4] Operation: 95-91=4 Exploring Operation: 91-73=18, Resulting Numbers: [1, 95, 18] Generated Node #0,1: 77:[1, 95, 18] Operation: 91-73=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[1, 73, 4], Operations: ['95-91=4'] Exploring Operation: 1+4=5, Resulting Numbers: [73, 5] Generated Node #0,0,0: 77:[73, 5] Operation: 1+4=5 Exploring Operation: 1+73=74, Resulting Numbers: [4, 74] Generated Node #0,0,1: 77:[4, 74] Operation: 1+73=74 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[73, 5], Operations: ['95-91=4', '1+4=5'] Exploring Operation: 73-5=68, Resulting Numbers: [68] 68,77 unequal: No Solution Exploring Operation: 73+5=78, Resulting Numbers: [78] 78,77 unequal: No Solution No 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: 77:[4, 74], Operations: ['95-91=4', '1+73=74'] Exploring Operation: 4+74=78, Resulting Numbers: [78] 78,77 unequal: No Solution Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,77 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: 77:[1, 95, 18], Operations: ['91-73=18'] Exploring Operation: 95-18=77, Resulting Numbers: [1, 77] Generated Node #0,1,0: 77:[1, 77] Operation: 95-18=77 Exploring Operation: 95-1=94, Resulting Numbers: [18, 94] Generated Node #0,1,1: 77:[18, 94] Operation: 95-1=94 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 77:[1, 77], Operations: ['91-73=18', '95-18=77'] Exploring Operation: 1*77=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[1, 73, 91, 95], Operations: [] Exploring Operation: 91-73=18, Resulting Numbers: [1, 95, 18] Generated Node #0,1: 77:[1, 95, 18] Operation: 91-73=18 Moving to Node #0,1 Current State: 77:[1, 95, 18], Operations: ['91-73=18'] Exploring Operation: 95-18=77, Resulting Numbers: [1, 77] Generated Node #0,1,0: 77:[1, 77] Operation: 95-18=77 Moving to Node #0,1,0 Current State: 77:[1, 77], Operations: ['91-73=18', '95-18=77'] Exploring Operation: 1*77=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 3, 68, 94, 72 ]
54
[ "3*72=216", "68+94=162", "216-162=54" ]
Current State: 54:[3, 68, 94, 72], Operations: [] Exploring Operation: 3*72=216, Resulting Numbers: [68, 94, 216] Generated Node #2: [68, 94, 216] from Operation: 3*72=216 Current State: 54:[68, 94, 216], Operations: ['3*72=216'] Exploring Operation: 68+94=162, Resulting Numbers: [216, 162] Generated Node #3: [216, 162] from Operation: 68+94=162 Current State: 54:[216, 162], Operations: ['3*72=216', '68+94=162'] Exploring Operation: 216-162=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[3, 68, 94, 72], Operations: [] Exploring Operation: 94-68=26, Resulting Numbers: [3, 72, 26] Generated Node #0,0: 54:[3, 72, 26] Operation: 94-68=26 Exploring Operation: 94-72=22, Resulting Numbers: [3, 68, 22] Generated Node #0,1: 54:[3, 68, 22] Operation: 94-72=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[3, 68, 22], Operations: ['94-72=22'] Exploring Operation: 68-22=46, Resulting Numbers: [3, 46] Generated Node #0,1,0: 54:[3, 46] Operation: 68-22=46 Exploring Operation: 68-3=65, Resulting Numbers: [22, 65] Generated Node #0,1,1: 54:[22, 65] Operation: 68-3=65 Moving to Node #0,1,0 Current State: 54:[3, 46], Operations: ['94-72=22', '68-22=46'] Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,54 unequal: No Solution Exploring Operation: 3+46=49, Resulting Numbers: [49] 49,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[22, 65], Operations: ['94-72=22', '68-3=65'] Exploring Operation: 65-22=43, Resulting Numbers: [43] 43,54 unequal: No Solution Exploring Operation: 22+65=87, Resulting Numbers: [87] 87,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[3, 72, 26], Operations: ['94-68=26'] Exploring Operation: 72-26=46, Resulting Numbers: [3, 46] Generated Node #0,0,0: 54:[3, 46] Operation: 72-26=46 Exploring Operation: 72/3=24, Resulting Numbers: [26, 24] Generated Node #0,0,1: 54:[26, 24] Operation: 72/3=24 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 54:[26, 24], Operations: ['94-68=26', '72/3=24'] Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 26+24=50, Resulting Numbers: [50] 50,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[3, 46], Operations: ['94-68=26', '72-26=46'] Exploring Operation: 3+46=49, Resulting Numbers: [49] 49,54 unequal: No Solution Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,54 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
[ 12, 87, 7, 31 ]
75
[ "12+87=99", "31-7=24", "99-24=75" ]
Current State: 75:[12, 87, 7, 31], Operations: [] Exploring Operation: 12+87=99, Resulting Numbers: [7, 31, 99] Generated Node #2: [7, 31, 99] from Operation: 12+87=99 Current State: 75:[7, 31, 99], Operations: ['12+87=99'] Exploring Operation: 31-7=24, Resulting Numbers: [99, 24] Generated Node #3: [99, 24] from Operation: 31-7=24 Current State: 75:[99, 24], Operations: ['12+87=99', '31-7=24'] Exploring Operation: 99-24=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[12, 87, 7, 31], Operations: [] Exploring Operation: 87-7=80, Resulting Numbers: [12, 31, 80] Generated Node #0,0: 75:[12, 31, 80] Operation: 87-7=80 Exploring Operation: 12-7=5, Resulting Numbers: [87, 31, 5] Generated Node #0,1: 75:[87, 31, 5] Operation: 12-7=5 Exploring Operation: 31-7=24, Resulting Numbers: [12, 87, 24] Generated Node #0,2: 75:[12, 87, 24] Operation: 31-7=24 Exploring Operation: 87-12=75, Resulting Numbers: [7, 31, 75] Generated Node #0,3: 75:[7, 31, 75] Operation: 87-12=75 Start Sub Search at level 1: Moving to Node #0,3 Current State: 75:[7, 31, 75], Operations: ['87-12=75'] Exploring Operation: 7+75=82, Resulting Numbers: [31, 82] Generated Node #0,3,0: 75:[31, 82] Operation: 7+75=82 Exploring Operation: 75-7=68, Resulting Numbers: [31, 68] Generated Node #0,3,1: 75:[31, 68] Operation: 75-7=68 Exploring Operation: 31-7=24, Resulting Numbers: [75, 24] Generated Node #0,3,2: 75:[75, 24] Operation: 31-7=24 Exploring Operation: 7+31=38, Resulting Numbers: [75, 38] Generated Node #0,3,3: 75:[75, 38] Operation: 7+31=38 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 75:[75, 24], Operations: ['87-12=75', '31-7=24'] Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,75 unequal: No Solution Exploring Operation: 75*24=1800, Resulting Numbers: [1800] 1800,75 unequal: No Solution Exploring Operation: 75+24=99, Resulting Numbers: [99] 99,75 unequal: No Solution No 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: 75:[31, 82], Operations: ['87-12=75', '7+75=82'] Exploring Operation: 31*82=2542, Resulting Numbers: [2542] 2542,75 unequal: No Solution Exploring Operation: 31+82=113, Resulting Numbers: [113] 113,75 unequal: No Solution Exploring Operation: 82-31=51, Resulting Numbers: [51] 51,75 unequal: No Solution No 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: 75:[31, 68], Operations: ['87-12=75', '75-7=68'] Exploring Operation: 68-31=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 31*68=2108, Resulting Numbers: [2108] 2108,75 unequal: No Solution Exploring Operation: 31+68=99, Resulting Numbers: [99] 99,75 unequal: No Solution No 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: 75:[75, 38], Operations: ['87-12=75', '7+31=38'] Exploring Operation: 75+38=113, Resulting Numbers: [113] 113,75 unequal: No Solution Exploring Operation: 75*38=2850, Resulting Numbers: [2850] 2850,75 unequal: No Solution Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,75 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: 75:[12, 31, 80], Operations: ['87-7=80'] Exploring Operation: 80-12=68, Resulting Numbers: [31, 68] Generated Node #0,0,0: 75:[31, 68] Operation: 80-12=68 Exploring Operation: 12+31=43, Resulting Numbers: [80, 43] Generated Node #0,0,1: 75:[80, 43] Operation: 12+31=43 Exploring Operation: 12+80=92, Resulting Numbers: [31, 92] Generated Node #0,0,2: 75:[31, 92] Operation: 12+80=92 Exploring Operation: 31-12=19, Resulting Numbers: [80, 19] Generated Node #0,0,3: 75:[80, 19] Operation: 31-12=19 Moving to Node #0,0,3 Current State: 75:[80, 19], Operations: ['87-7=80', '31-12=19'] Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,75 unequal: No Solution Exploring Operation: 80*19=1520, Resulting Numbers: [1520] 1520,75 unequal: No Solution Exploring Operation: 80+19=99, Resulting Numbers: [99] 99,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[31, 68], Operations: ['87-7=80', '80-12=68'] Exploring Operation: 68-31=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 31*68=2108, Resulting Numbers: [2108] 2108,75 unequal: No Solution Exploring Operation: 31+68=99, Resulting Numbers: [99] 99,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[31, 92], Operations: ['87-7=80', '12+80=92'] Exploring Operation: 92-31=61, Resulting Numbers: [61] 61,75 unequal: No Solution Exploring Operation: 31*92=2852, Resulting Numbers: [2852] 2852,75 unequal: No Solution Exploring Operation: 31+92=123, Resulting Numbers: [123] 123,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[80, 43], Operations: ['87-7=80', '12+31=43'] Exploring Operation: 80+43=123, Resulting Numbers: [123] 123,75 unequal: No Solution Exploring Operation: 80*43=3440, Resulting Numbers: [3440] 3440,75 unequal: No Solution Exploring Operation: 80-43=37, Resulting Numbers: [37] 37,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[12, 87, 24], Operations: ['31-7=24'] Exploring Operation: 87-12=75, Resulting Numbers: [24, 75] Generated Node #0,2,0: 75:[24, 75] Operation: 87-12=75 Exploring Operation: 24-12=12, Resulting Numbers: [87, 12] Generated Node #0,2,1: 75:[87, 12] Operation: 24-12=12 Exploring Operation: 87-24=63, Resulting Numbers: [12, 63] Generated Node #0,2,2: 75:[12, 63] Operation: 87-24=63 Exploring Operation: 24/12=2, Resulting Numbers: [87, 2] Generated Node #0,2,3: 75:[87, 2] Operation: 24/12=2 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 75:[24, 75], Operations: ['31-7=24', '87-12=75'] Exploring Operation: 24+75=99, Resulting Numbers: [99] 99,75 unequal: No Solution Exploring Operation: 24*75=1800, Resulting Numbers: [1800] 1800,75 unequal: No Solution Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,75 unequal: No Solution No 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: 75:[87, 2], Operations: ['31-7=24', '24/12=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,75 unequal: No Solution Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,75 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,75 unequal: No Solution No 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: 75:[87, 12], Operations: ['31-7=24', '24-12=12'] Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[12, 87, 7, 31], Operations: [] Exploring Operation: 31-7=24, Resulting Numbers: [12, 87, 24] Generated Node #0,2: 75:[12, 87, 24] Operation: 31-7=24 Moving to Node #0,2 Current State: 75:[12, 87, 24], Operations: ['31-7=24'] Exploring Operation: 24-12=12, Resulting Numbers: [87, 12] Generated Node #0,2,1: 75:[87, 12] Operation: 24-12=12 Moving to Node #0,2,1 Current State: 75:[87, 12], Operations: ['31-7=24', '24-12=12'] Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.955729
hs_4
sum_heuristic
[ 8, 25, 95, 11 ]
89
[ "25-8=17", "95+11=106", "106-17=89" ]
Current State: 89:[8, 25, 95, 11], Operations: [] Exploring Operation: 25-8=17, Resulting Numbers: [95, 11, 17] Generated Node #2: [95, 11, 17] from Operation: 25-8=17 Current State: 89:[95, 11, 17], Operations: ['25-8=17'] Exploring Operation: 95+11=106, Resulting Numbers: [17, 106] Generated Node #3: [17, 106] from Operation: 95+11=106 Current State: 89:[17, 106], Operations: ['25-8=17', '95+11=106'] Exploring Operation: 106-17=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[8, 25, 95, 11], Operations: [] Exploring Operation: 8+11=19, Resulting Numbers: [25, 95, 19] Generated Node #0,0: 89:[25, 95, 19] Operation: 8+11=19 Exploring Operation: 8+25=33, Resulting Numbers: [95, 11, 33] Generated Node #0,1: 89:[95, 11, 33] Operation: 8+25=33 Exploring Operation: 8*11=88, Resulting Numbers: [25, 95, 88] Generated Node #0,2: 89:[25, 95, 88] Operation: 8*11=88 Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[25, 95, 88], Operations: ['8*11=88'] Exploring Operation: 25+88=113, Resulting Numbers: [95, 113] Generated Node #0,2,0: 89:[95, 113] Operation: 25+88=113 Exploring Operation: 25+95=120, Resulting Numbers: [88, 120] Generated Node #0,2,1: 89:[88, 120] Operation: 25+95=120 Exploring Operation: 95-25=70, Resulting Numbers: [88, 70] Generated Node #0,2,2: 89:[88, 70] Operation: 95-25=70 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 89:[88, 70], Operations: ['8*11=88', '95-25=70'] Exploring Operation: 88+70=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 88*70=6160, Resulting Numbers: [6160] 6160,89 unequal: No Solution Exploring Operation: 88-70=18, Resulting Numbers: [18] 18,89 unequal: No Solution No 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: 89:[95, 113], Operations: ['8*11=88', '25+88=113'] Exploring Operation: 113-95=18, Resulting Numbers: [18] 18,89 unequal: No Solution Exploring Operation: 95*113=10735, Resulting Numbers: [10735] 10735,89 unequal: No Solution Exploring Operation: 95+113=208, Resulting Numbers: [208] 208,89 unequal: No Solution No 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: 89:[88, 120], Operations: ['8*11=88', '25+95=120'] Exploring Operation: 88+120=208, Resulting Numbers: [208] 208,89 unequal: No Solution Exploring Operation: 88*120=10560, Resulting Numbers: [10560] 10560,89 unequal: No Solution Exploring Operation: 120-88=32, Resulting Numbers: [32] 32,89 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: 89:[25, 95, 19], Operations: ['8+11=19'] Exploring Operation: 95-25=70, Resulting Numbers: [19, 70] Generated Node #0,0,0: 89:[19, 70] Operation: 95-25=70 Exploring Operation: 25+19=44, Resulting Numbers: [95, 44] Generated Node #0,0,1: 89:[95, 44] Operation: 25+19=44 Exploring Operation: 95-19=76, Resulting Numbers: [25, 76] Generated Node #0,0,2: 89:[25, 76] Operation: 95-19=76 Moving to Node #0,0,1 Current State: 89:[95, 44], Operations: ['8+11=19', '25+19=44'] Exploring Operation: 95*44=4180, Resulting Numbers: [4180] 4180,89 unequal: No Solution Exploring Operation: 95+44=139, Resulting Numbers: [139] 139,89 unequal: No Solution Exploring Operation: 95-44=51, Resulting Numbers: [51] 51,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[25, 76], Operations: ['8+11=19', '95-19=76'] Exploring Operation: 25*76=1900, Resulting Numbers: [1900] 1900,89 unequal: No Solution Exploring Operation: 25+76=101, Resulting Numbers: [101] 101,89 unequal: No Solution Exploring Operation: 76-25=51, Resulting Numbers: [51] 51,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[19, 70], Operations: ['8+11=19', '95-25=70'] Exploring Operation: 19+70=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[8, 25, 95, 11], Operations: [] Exploring Operation: 8+11=19, Resulting Numbers: [25, 95, 19] Generated Node #0,0: 89:[25, 95, 19] Operation: 8+11=19 Moving to Node #0,0 Current State: 89:[25, 95, 19], Operations: ['8+11=19'] Exploring Operation: 95-25=70, Resulting Numbers: [19, 70] Generated Node #0,0,0: 89:[19, 70] Operation: 95-25=70 Moving to Node #0,0,0 Current State: 89:[19, 70], Operations: ['8+11=19', '95-25=70'] Exploring Operation: 19+70=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
mult_heuristic
[ 85, 78, 77, 12 ]
74
[ "85+78=163", "77+12=89", "163-89=74" ]
Current State: 74:[85, 78, 77, 12], Operations: [] Exploring Operation: 85+78=163, Resulting Numbers: [77, 12, 163] Generated Node #2: [77, 12, 163] from Operation: 85+78=163 Current State: 74:[77, 12, 163], Operations: ['85+78=163'] Exploring Operation: 77+12=89, Resulting Numbers: [163, 89] Generated Node #3: [163, 89] from Operation: 77+12=89 Current State: 74:[163, 89], Operations: ['85+78=163', '77+12=89'] Exploring Operation: 163-89=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[85, 78, 77, 12], Operations: [] Exploring Operation: 85-12=73, Resulting Numbers: [78, 77, 73] Generated Node #0,0: 74:[78, 77, 73] Operation: 85-12=73 Moving to Node #0,0 Current State: 74:[78, 77, 73], Operations: ['85-12=73'] Exploring Operation: 78-77=1, Resulting Numbers: [73, 1] Generated Node #0,0,0: 74:[73, 1] Operation: 78-77=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[73, 1], Operations: ['85-12=73', '78-77=1'] Exploring Operation: 73+1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[85, 78, 77, 12], Operations: [] Exploring Operation: 85-12=73, Resulting Numbers: [78, 77, 73] Generated Node #0,0: 74:[78, 77, 73] Operation: 85-12=73 Moving to Node #0,0 Current State: 74:[78, 77, 73], Operations: ['85-12=73'] Exploring Operation: 78-77=1, Resulting Numbers: [73, 1] Generated Node #0,0,0: 74:[73, 1] Operation: 78-77=1 Moving to Node #0,0,0 Current State: 74:[73, 1], Operations: ['85-12=73', '78-77=1'] Exploring Operation: 73+1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 57, 18, 16, 35 ]
57
[ "18+16=34", "35-34=1", "57*1=57" ]
Current State: 57:[57, 18, 16, 35], Operations: [] Exploring Operation: 18+16=34, Resulting Numbers: [57, 35, 34] Generated Node #2: [57, 35, 34] from Operation: 18+16=34 Current State: 57:[57, 35, 34], Operations: ['18+16=34'] Exploring Operation: 35-34=1, Resulting Numbers: [57, 1] Generated Node #3: [57, 1] from Operation: 35-34=1 Current State: 57:[57, 1], Operations: ['18+16=34', '35-34=1'] Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[57, 18, 16, 35], Operations: [] Exploring Operation: 35-16=19, Resulting Numbers: [57, 18, 19] Generated Node #0,0: 57:[57, 18, 19] Operation: 35-16=19 Exploring Operation: 57-35=22, Resulting Numbers: [18, 16, 22] Generated Node #0,1: 57:[18, 16, 22] Operation: 57-35=22 Exploring Operation: 35-18=17, Resulting Numbers: [57, 16, 17] Generated Node #0,2: 57:[57, 16, 17] Operation: 35-18=17 Exploring Operation: 18+35=53, Resulting Numbers: [57, 16, 53] Generated Node #0,3: 57:[57, 16, 53] Operation: 18+35=53 Exploring Operation: 16+35=51, Resulting Numbers: [57, 18, 51] Generated Node #0,4: 57:[57, 18, 51] Operation: 16+35=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[57, 18, 19], Operations: ['35-16=19'] Exploring Operation: 57/19=3, Resulting Numbers: [18, 3] Generated Node #0,0,0: 57:[18, 3] Operation: 57/19=3 Exploring Operation: 57+18=75, Resulting Numbers: [19, 75] Generated Node #0,0,1: 57:[19, 75] Operation: 57+18=75 Exploring Operation: 18+19=37, Resulting Numbers: [57, 37] Generated Node #0,0,2: 57:[57, 37] Operation: 18+19=37 Exploring Operation: 19-18=1, Resulting Numbers: [57, 1] Generated Node #0,0,3: 57:[57, 1] Operation: 19-18=1 Exploring Operation: 57-18=39, Resulting Numbers: [19, 39] Generated Node #0,0,4: 57:[19, 39] Operation: 57-18=39 Moving to Node #0,0,0 Current State: 57:[18, 3], Operations: ['35-16=19', '57/19=3'] Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,57 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,57 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,57 unequal: No Solution Moving to Node #0,0,3 Current State: 57:[57, 1], Operations: ['35-16=19', '19-18=1'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,57 unequal: No Solution Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[57, 18, 16, 35], Operations: [] Exploring Operation: 35-16=19, Resulting Numbers: [57, 18, 19] Generated Node #0,0: 57:[57, 18, 19] Operation: 35-16=19 Moving to Node #0,0 Current State: 57:[57, 18, 19], Operations: ['35-16=19'] Exploring Operation: 19-18=1, Resulting Numbers: [57, 1] Generated Node #0,0,3: 57:[57, 1] Operation: 19-18=1 Moving to Node #0,0,3 Current State: 57:[57, 1], Operations: ['35-16=19', '19-18=1'] Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 6, 78, 91, 70 ]
93
[ "78-6=72", "91-70=21", "72+21=93" ]
Current State: 93:[6, 78, 91, 70], Operations: [] Exploring Operation: 78-6=72, Resulting Numbers: [91, 70, 72] Generated Node #2: [91, 70, 72] from Operation: 78-6=72 Current State: 93:[91, 70, 72], Operations: ['78-6=72'] Exploring Operation: 91-70=21, Resulting Numbers: [72, 21] Generated Node #3: [72, 21] from Operation: 91-70=21 Current State: 93:[72, 21], Operations: ['78-6=72', '91-70=21'] Exploring Operation: 72+21=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[6, 78, 91, 70], Operations: [] Exploring Operation: 6+70=76, Resulting Numbers: [78, 91, 76] Generated Node #0,0: 93:[78, 91, 76] Operation: 6+70=76 Exploring Operation: 6+78=84, Resulting Numbers: [91, 70, 84] Generated Node #0,1: 93:[91, 70, 84] Operation: 6+78=84 Exploring Operation: 91-70=21, Resulting Numbers: [6, 78, 21] Generated Node #0,2: 93:[6, 78, 21] Operation: 91-70=21 Exploring Operation: 78-70=8, Resulting Numbers: [6, 91, 8] Generated Node #0,3: 93:[6, 91, 8] Operation: 78-70=8 Exploring Operation: 78/6=13, Resulting Numbers: [91, 70, 13] Generated Node #0,4: 93:[91, 70, 13] Operation: 78/6=13 Moving to Node #0,3 Current State: 93:[6, 91, 8], Operations: ['78-70=8'] Exploring Operation: 91+8=99, Resulting Numbers: [6, 99] Generated Node #0,3,0: 93:[6, 99] Operation: 91+8=99 Exploring Operation: 6+8=14, Resulting Numbers: [91, 14] Generated Node #0,3,1: 93:[91, 14] Operation: 6+8=14 Exploring Operation: 8-6=2, Resulting Numbers: [91, 2] Generated Node #0,3,2: 93:[91, 2] Operation: 8-6=2 Exploring Operation: 6+91=97, Resulting Numbers: [8, 97] Generated Node #0,3,3: 93:[8, 97] Operation: 6+91=97 Exploring Operation: 91-6=85, Resulting Numbers: [8, 85] Generated Node #0,3,4: 93:[8, 85] Operation: 91-6=85 Moving to Node #0,2 Current State: 93:[6, 78, 21], Operations: ['91-70=21'] Exploring Operation: 21-6=15, Resulting Numbers: [78, 15] Generated Node #0,2,0: 93:[78, 15] Operation: 21-6=15 Exploring Operation: 6+78=84, Resulting Numbers: [21, 84] Generated Node #0,2,1: 93:[21, 84] Operation: 6+78=84 Exploring Operation: 78/6=13, Resulting Numbers: [21, 13] Generated Node #0,2,2: 93:[21, 13] Operation: 78/6=13 Exploring Operation: 6+21=27, Resulting Numbers: [78, 27] Generated Node #0,2,3: 93:[78, 27] Operation: 6+21=27 Exploring Operation: 78+21=99, Resulting Numbers: [6, 99] Generated Node #0,2,4: 93:[6, 99] Operation: 78+21=99 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 93:[6, 99], Operations: ['91-70=21', '78+21=99'] Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[6, 78, 91, 70], Operations: [] Exploring Operation: 91-70=21, Resulting Numbers: [6, 78, 21] Generated Node #0,2: 93:[6, 78, 21] Operation: 91-70=21 Moving to Node #0,2 Current State: 93:[6, 78, 21], Operations: ['91-70=21'] Exploring Operation: 78+21=99, Resulting Numbers: [6, 99] Generated Node #0,2,4: 93:[6, 99] Operation: 78+21=99 Moving to Node #0,2,4 Current State: 93:[6, 99], Operations: ['91-70=21', '78+21=99'] Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 88, 44, 22, 81 ]
29
[ "88+44=132", "22+81=103", "132-103=29" ]
Current State: 29:[88, 44, 22, 81], Operations: [] Exploring Operation: 88+44=132, Resulting Numbers: [22, 81, 132] Generated Node #2: [22, 81, 132] from Operation: 88+44=132 Current State: 29:[22, 81, 132], Operations: ['88+44=132'] Exploring Operation: 22+81=103, Resulting Numbers: [132, 103] Generated Node #3: [132, 103] from Operation: 22+81=103 Current State: 29:[132, 103], Operations: ['88+44=132', '22+81=103'] Exploring Operation: 132-103=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[88, 44, 22, 81], Operations: [] Exploring Operation: 88-81=7, Resulting Numbers: [44, 22, 7] Generated Node #0,0: 29:[44, 22, 7] Operation: 88-81=7 Exploring Operation: 81-44=37, Resulting Numbers: [88, 22, 37] Generated Node #0,1: 29:[88, 22, 37] Operation: 81-44=37 Exploring Operation: 88-44=44, Resulting Numbers: [22, 81, 44] Generated Node #0,2: 29:[22, 81, 44] Operation: 88-44=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[44, 22, 7], Operations: ['88-81=7'] Exploring Operation: 44-22=22, Resulting Numbers: [7, 22] Generated Node #0,0,0: 29:[7, 22] Operation: 44-22=22 Exploring Operation: 44-7=37, Resulting Numbers: [22, 37] Generated Node #0,0,1: 29:[22, 37] Operation: 44-7=37 Exploring Operation: 22+7=29, Resulting Numbers: [44, 29] Generated Node #0,0,2: 29:[44, 29] Operation: 22+7=29 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 29:[22, 37], Operations: ['88-81=7', '44-7=37'] Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,29 unequal: No Solution Exploring Operation: 22*37=814, Resulting Numbers: [814] 814,29 unequal: No Solution Exploring Operation: 22+37=59, Resulting Numbers: [59] 59,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 29:[44, 29], Operations: ['88-81=7', '22+7=29'] Exploring Operation: 44*29=1276, Resulting Numbers: [1276] 1276,29 unequal: No Solution Exploring Operation: 44+29=73, Resulting Numbers: [73] 73,29 unequal: No Solution Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[7, 22], Operations: ['88-81=7', '44-22=22'] Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[88, 44, 22, 81], Operations: [] Exploring Operation: 88-81=7, Resulting Numbers: [44, 22, 7] Generated Node #0,0: 29:[44, 22, 7] Operation: 88-81=7 Moving to Node #0,0 Current State: 29:[44, 22, 7], Operations: ['88-81=7'] Exploring Operation: 44-22=22, Resulting Numbers: [7, 22] Generated Node #0,0,0: 29:[7, 22] Operation: 44-22=22 Moving to Node #0,0,0 Current State: 29:[7, 22], Operations: ['88-81=7', '44-22=22'] Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 68, 78, 47, 16 ]
70
[ "78+16=94", "94/47=2", "68+2=70" ]
Current State: 70:[68, 78, 47, 16], Operations: [] Exploring Operation: 78+16=94, Resulting Numbers: [68, 47, 94] Generated Node #2: [68, 47, 94] from Operation: 78+16=94 Current State: 70:[68, 47, 94], Operations: ['78+16=94'] Exploring Operation: 94/47=2, Resulting Numbers: [68, 2] Generated Node #3: [68, 2] from Operation: 94/47=2 Current State: 70:[68, 2], Operations: ['78+16=94', '94/47=2'] Exploring Operation: 68+2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[68, 78, 47, 16], Operations: [] Exploring Operation: 78-47=31, Resulting Numbers: [68, 16, 31] Generated Node #0,0: 70:[68, 16, 31] Operation: 78-47=31 Exploring Operation: 78-68=10, Resulting Numbers: [47, 16, 10] Generated Node #0,1: 70:[47, 16, 10] Operation: 78-68=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[68, 16, 31], Operations: ['78-47=31'] Exploring Operation: 31-16=15, Resulting Numbers: [68, 15] Generated Node #0,0,0: 70:[68, 15] Operation: 31-16=15 Exploring Operation: 68-31=37, Resulting Numbers: [16, 37] Generated Node #0,0,1: 70:[16, 37] Operation: 68-31=37 Moving to Node #0,0,0 Current State: 70:[68, 15], Operations: ['78-47=31', '31-16=15'] Exploring Operation: 68+15=83, Resulting Numbers: [83] 83,70 unequal: No Solution Exploring Operation: 68-15=53, Resulting Numbers: [53] 53,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[16, 37], Operations: ['78-47=31', '68-31=37'] Exploring Operation: 16+37=53, Resulting Numbers: [53] 53,70 unequal: No Solution Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[47, 16, 10], Operations: ['78-68=10'] Exploring Operation: 47-16=31, Resulting Numbers: [10, 31] Generated Node #0,1,0: 70:[10, 31] Operation: 47-16=31 Exploring Operation: 47-10=37, Resulting Numbers: [16, 37] Generated Node #0,1,1: 70:[16, 37] Operation: 47-10=37 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 70:[10, 31], Operations: ['78-68=10', '47-16=31'] Exploring Operation: 10+31=41, Resulting Numbers: [41] 41,70 unequal: No Solution Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,70 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:[16, 37], Operations: ['78-68=10', '47-10=37'] Exploring Operation: 16+37=53, Resulting Numbers: [53] 53,70 unequal: No Solution Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,70 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
[ 44, 59, 32, 50 ]
97
[ "59-44=15", "32+50=82", "15+82=97" ]
Current State: 97:[44, 59, 32, 50], Operations: [] Exploring Operation: 59-44=15, Resulting Numbers: [32, 50, 15] Generated Node #2: [32, 50, 15] from Operation: 59-44=15 Current State: 97:[32, 50, 15], Operations: ['59-44=15'] Exploring Operation: 32+50=82, Resulting Numbers: [15, 82] Generated Node #3: [15, 82] from Operation: 32+50=82 Current State: 97:[15, 82], Operations: ['59-44=15', '32+50=82'] Exploring Operation: 15+82=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[44, 59, 32, 50], Operations: [] Exploring Operation: 44+32=76, Resulting Numbers: [59, 50, 76] Generated Node #0,0: 97:[59, 50, 76] Operation: 44+32=76 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[59, 50, 76], Operations: ['44+32=76'] Exploring Operation: 59+50=109, Resulting Numbers: [76, 109] Generated Node #0,0,0: 97:[76, 109] Operation: 59+50=109 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[76, 109], Operations: ['44+32=76', '59+50=109'] Exploring Operation: 109-76=33, Resulting Numbers: [33] 33,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 17, 21, 29, 92 ]
59
[ "21-17=4", "92-29=63", "63-4=59" ]
Current State: 59:[17, 21, 29, 92], Operations: [] Exploring Operation: 21-17=4, Resulting Numbers: [29, 92, 4] Generated Node #2: [29, 92, 4] from Operation: 21-17=4 Current State: 59:[29, 92, 4], Operations: ['21-17=4'] Exploring Operation: 92-29=63, Resulting Numbers: [4, 63] Generated Node #3: [4, 63] from Operation: 92-29=63 Current State: 59:[4, 63], Operations: ['21-17=4', '92-29=63'] Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[17, 21, 29, 92], Operations: [] Exploring Operation: 17+21=38, Resulting Numbers: [29, 92, 38] Generated Node #0,0: 59:[29, 92, 38] Operation: 17+21=38 Moving to Node #0,0 Current State: 59:[29, 92, 38], Operations: ['17+21=38'] Exploring Operation: 92-29=63, Resulting Numbers: [38, 63] Generated Node #0,0,0: 59:[38, 63] Operation: 92-29=63 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[38, 63], Operations: ['17+21=38', '92-29=63'] Exploring Operation: 63-38=25, Resulting Numbers: [25] 25,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 43, 2, 89, 86 ]
85
[ "86/43=2", "89-2=87", "87-2=85" ]
Current State: 85:[43, 2, 89, 86], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [2, 89, 2] Generated Node #2: [2, 89, 2] from Operation: 86/43=2 Current State: 85:[2, 89, 2], Operations: ['86/43=2'] Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,85 equal: Goal Reached Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[43, 2, 89, 86], Operations: [] Exploring Operation: 43*2=86, Resulting Numbers: [89, 86, 86] Generated Node #0,0: 85:[89, 86, 86] Operation: 43*2=86 Exploring Operation: 86/43=2, Resulting Numbers: [2, 89, 2] Generated Node #0,1: 85:[2, 89, 2] Operation: 86/43=2 Exploring Operation: 43-2=41, Resulting Numbers: [89, 86, 41] Generated Node #0,2: 85:[89, 86, 41] Operation: 43-2=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[89, 86, 86], Operations: ['43*2=86'] Exploring Operation: 86/86=1, Resulting Numbers: [89, 1] Generated Node #0,0,0: 85:[89, 1] Operation: 86/86=1 Exploring Operation: 89-86=3, Resulting Numbers: [86, 3] Generated Node #0,0,1: 85:[86, 3] Operation: 89-86=3 Exploring Operation: 89-86=3, Resulting Numbers: [86, 3] Generated Node #0,0,2: 85:[86, 3] Operation: 89-86=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 85:[86, 3], Operations: ['43*2=86', '89-86=3'] Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,85 unequal: No Solution Exploring Operation: 86*3=258, Resulting Numbers: [258] 258,85 unequal: No Solution Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 85:[86, 3], Operations: ['43*2=86', '89-86=3'] Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,85 unequal: No Solution Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,85 unequal: No Solution Exploring Operation: 86*3=258, Resulting Numbers: [258] 258,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[89, 1], Operations: ['43*2=86', '86/86=1'] Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,85 unequal: No Solution Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,85 unequal: No Solution Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[2, 89, 2], Operations: ['86/43=2'] Exploring Operation: 89-2=87, Resulting Numbers: [2, 87] Generated Node #0,1,0: 85:[2, 87] Operation: 89-2=87 Exploring Operation: 2+2=4, Resulting Numbers: [89, 4] Generated Node #0,1,1: 85:[89, 4] Operation: 2+2=4 Exploring Operation: 2*2=4, Resulting Numbers: [89, 4] Generated Node #0,1,2: 85:[89, 4] Operation: 2*2=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 85:[2, 87], Operations: ['86/43=2', '89-2=87'] Exploring Operation: 2*87=174, Resulting Numbers: [174] 174,85 unequal: No Solution Exploring Operation: 2+87=89, Resulting Numbers: [89] 89,85 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[43, 2, 89, 86], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [2, 89, 2] Generated Node #0,1: 85:[2, 89, 2] Operation: 86/43=2 Moving to Node #0,1 Current State: 85:[2, 89, 2], Operations: ['86/43=2'] Exploring Operation: 89-2=87, Resulting Numbers: [2, 87] Generated Node #0,1,0: 85:[2, 87] Operation: 89-2=87 Moving to Node #0,1,0 Current State: 85:[2, 87], Operations: ['86/43=2', '89-2=87'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_3
sum_heuristic
[ 53, 82, 11, 2 ]
61
[ "53-11=42", "42/2=21", "82-21=61" ]
Current State: 61:[53, 82, 11, 2], Operations: [] Exploring Operation: 53-11=42, Resulting Numbers: [82, 2, 42] Generated Node #2: [82, 2, 42] from Operation: 53-11=42 Current State: 61:[82, 2, 42], Operations: ['53-11=42'] Exploring Operation: 42/2=21, Resulting Numbers: [82, 21] Generated Node #3: [82, 21] from Operation: 42/2=21 Current State: 61:[82, 21], Operations: ['53-11=42', '42/2=21'] Exploring Operation: 82-21=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[53, 82, 11, 2], Operations: [] Exploring Operation: 11*2=22, Resulting Numbers: [53, 82, 22] Generated Node #0,0: 61:[53, 82, 22] Operation: 11*2=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[53, 82, 22], Operations: ['11*2=22'] Exploring Operation: 82-22=60, Resulting Numbers: [53, 60] Generated Node #0,0,0: 61:[53, 60] Operation: 82-22=60 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[53, 60], Operations: ['11*2=22', '82-22=60'] Exploring Operation: 53+60=113, Resulting Numbers: [113] 113,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 92, 54, 49, 4 ]
83
[ "92-54=38", "49-4=45", "38+45=83" ]
Current State: 83:[92, 54, 49, 4], Operations: [] Exploring Operation: 92-54=38, Resulting Numbers: [49, 4, 38] Generated Node #2: [49, 4, 38] from Operation: 92-54=38 Current State: 83:[49, 4, 38], Operations: ['92-54=38'] Exploring Operation: 49-4=45, Resulting Numbers: [38, 45] Generated Node #3: [38, 45] from Operation: 49-4=45 Current State: 83:[38, 45], Operations: ['92-54=38', '49-4=45'] Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[92, 54, 49, 4], Operations: [] Exploring Operation: 54+4=58, Resulting Numbers: [92, 49, 58] Generated Node #0,0: 83:[92, 49, 58] Operation: 54+4=58 Exploring Operation: 92+4=96, Resulting Numbers: [54, 49, 96] Generated Node #0,1: 83:[54, 49, 96] Operation: 92+4=96 Exploring Operation: 92-4=88, Resulting Numbers: [54, 49, 88] Generated Node #0,2: 83:[54, 49, 88] Operation: 92-4=88 Exploring Operation: 54-4=50, Resulting Numbers: [92, 49, 50] Generated Node #0,3: 83:[92, 49, 50] Operation: 54-4=50 Exploring Operation: 49+4=53, Resulting Numbers: [92, 54, 53] Generated Node #0,4: 83:[92, 54, 53] Operation: 49+4=53 Moving to Node #0,0 Current State: 83:[92, 49, 58], Operations: ['54+4=58'] Exploring Operation: 92+49=141, Resulting Numbers: [58, 141] Generated Node #0,0,0: 83:[58, 141] Operation: 92+49=141 Exploring Operation: 49+58=107, Resulting Numbers: [92, 107] Generated Node #0,0,1: 83:[92, 107] Operation: 49+58=107 Exploring Operation: 58-49=9, Resulting Numbers: [92, 9] Generated Node #0,0,2: 83:[92, 9] Operation: 58-49=9 Exploring Operation: 92-58=34, Resulting Numbers: [49, 34] Generated Node #0,0,3: 83:[49, 34] Operation: 92-58=34 Exploring Operation: 92-49=43, Resulting Numbers: [58, 43] Generated Node #0,0,4: 83:[58, 43] Operation: 92-49=43 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[92, 107], Operations: ['54+4=58', '49+58=107'] Exploring Operation: 92*107=9844, Resulting Numbers: [9844] 9844,83 unequal: No Solution Exploring Operation: 107-92=15, Resulting Numbers: [15] 15,83 unequal: No Solution Exploring Operation: 92+107=199, Resulting Numbers: [199] 199,83 unequal: No Solution No 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: 83:[58, 43], Operations: ['54+4=58', '92-49=43'] Exploring Operation: 58-43=15, Resulting Numbers: [15] 15,83 unequal: No Solution Exploring Operation: 58+43=101, Resulting Numbers: [101] 101,83 unequal: No Solution Exploring Operation: 58*43=2494, Resulting Numbers: [2494] 2494,83 unequal: No Solution No 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: 83:[58, 141], Operations: ['54+4=58', '92+49=141'] Exploring Operation: 141-58=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[92, 54, 49, 4], Operations: [] Exploring Operation: 54+4=58, Resulting Numbers: [92, 49, 58] Generated Node #0,0: 83:[92, 49, 58] Operation: 54+4=58 Moving to Node #0,0 Current State: 83:[92, 49, 58], Operations: ['54+4=58'] Exploring Operation: 92+49=141, Resulting Numbers: [58, 141] Generated Node #0,0,0: 83:[58, 141] Operation: 92+49=141 Moving to Node #0,0,0 Current State: 83:[58, 141], Operations: ['54+4=58', '92+49=141'] Exploring Operation: 141-58=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 23, 92, 42, 1 ]
73
[ "23+92=115", "42*1=42", "115-42=73" ]
Current State: 73:[23, 92, 42, 1], Operations: [] Exploring Operation: 23+92=115, Resulting Numbers: [42, 1, 115] Generated Node #2: [42, 1, 115] from Operation: 23+92=115 Current State: 73:[42, 1, 115], Operations: ['23+92=115'] Exploring Operation: 42*1=42, Resulting Numbers: [115, 42] Generated Node #3: [115, 42] from Operation: 42*1=42 Current State: 73:[115, 42], Operations: ['23+92=115', '42*1=42'] Exploring Operation: 115-42=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[23, 92, 42, 1], Operations: [] Exploring Operation: 23+42=65, Resulting Numbers: [92, 1, 65] Generated Node #0,0: 73:[92, 1, 65] Operation: 23+42=65 Moving to Node #0,0 Current State: 73:[92, 1, 65], Operations: ['23+42=65'] Exploring Operation: 92-1=91, Resulting Numbers: [65, 91] Generated Node #0,0,0: 73:[65, 91] Operation: 92-1=91 Moving to Node #0,0,0 Current State: 73:[65, 91], Operations: ['23+42=65', '92-1=91'] Exploring Operation: 91-65=26, Resulting Numbers: [26] 26,73 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 54, 82, 95, 26 ]
97
[ "82-54=28", "95-26=69", "28+69=97" ]
Current State: 97:[54, 82, 95, 26], Operations: [] Exploring Operation: 82-54=28, Resulting Numbers: [95, 26, 28] Generated Node #2: [95, 26, 28] from Operation: 82-54=28 Current State: 97:[95, 26, 28], Operations: ['82-54=28'] Exploring Operation: 95-26=69, Resulting Numbers: [28, 69] Generated Node #3: [28, 69] from Operation: 95-26=69 Current State: 97:[28, 69], Operations: ['82-54=28', '95-26=69'] Exploring Operation: 28+69=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[54, 82, 95, 26], Operations: [] Exploring Operation: 82+26=108, Resulting Numbers: [54, 95, 108] Generated Node #0,0: 97:[54, 95, 108] Operation: 82+26=108 Exploring Operation: 54+26=80, Resulting Numbers: [82, 95, 80] Generated Node #0,1: 97:[82, 95, 80] Operation: 54+26=80 Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[82, 95, 80], Operations: ['54+26=80'] Exploring Operation: 82+80=162, Resulting Numbers: [95, 162] Generated Node #0,1,0: 97:[95, 162] Operation: 82+80=162 Exploring Operation: 95+80=175, Resulting Numbers: [82, 175] Generated Node #0,1,1: 97:[82, 175] Operation: 95+80=175 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[95, 162], Operations: ['54+26=80', '82+80=162'] Exploring Operation: 162-95=67, Resulting Numbers: [67] 67,97 unequal: No Solution Exploring Operation: 95+162=257, Resulting Numbers: [257] 257,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 97:[82, 175], Operations: ['54+26=80', '95+80=175'] Exploring Operation: 82+175=257, Resulting Numbers: [257] 257,97 unequal: No Solution Exploring Operation: 175-82=93, Resulting Numbers: [93] 93,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[54, 95, 108], Operations: ['82+26=108'] Exploring Operation: 108-54=54, Resulting Numbers: [95, 54] Generated Node #0,0,0: 97:[95, 54] Operation: 108-54=54 Exploring Operation: 54+95=149, Resulting Numbers: [108, 149] Generated Node #0,0,1: 97:[108, 149] Operation: 54+95=149 Moving to Node #0,0,0 Current State: 97:[95, 54], Operations: ['82+26=108', '108-54=54'] Exploring Operation: 95+54=149, Resulting Numbers: [149] 149,97 unequal: No Solution Exploring Operation: 95-54=41, Resulting Numbers: [41] 41,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[108, 149], Operations: ['82+26=108', '54+95=149'] Exploring Operation: 108+149=257, Resulting Numbers: [257] 257,97 unequal: No Solution Exploring Operation: 149-108=41, Resulting Numbers: [41] 41,97 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
[ 17, 75, 88, 17 ]
14
[ "17/17=1", "88-75=13", "1+13=14" ]
Current State: 14:[17, 75, 88, 17], Operations: [] Exploring Operation: 17/17=1, Resulting Numbers: [75, 88, 1] Generated Node #2: [75, 88, 1] from Operation: 17/17=1 Current State: 14:[75, 88, 1], Operations: ['17/17=1'] Exploring Operation: 88-75=13, Resulting Numbers: [1, 13] Generated Node #3: [1, 13] from Operation: 88-75=13 Current State: 14:[1, 13], Operations: ['17/17=1', '88-75=13'] Exploring Operation: 1+13=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[17, 75, 88, 17], Operations: [] Exploring Operation: 75-17=58, Resulting Numbers: [17, 88, 58] Generated Node #0,0: 14:[17, 88, 58] Operation: 75-17=58 Exploring Operation: 75-17=58, Resulting Numbers: [88, 17, 58] Generated Node #0,1: 14:[88, 17, 58] Operation: 75-17=58 Exploring Operation: 88-17=71, Resulting Numbers: [75, 17, 71] Generated Node #0,2: 14:[75, 17, 71] Operation: 88-17=71 Exploring Operation: 88-75=13, Resulting Numbers: [17, 17, 13] Generated Node #0,3: 14:[17, 17, 13] Operation: 88-75=13 Start Sub Search at level 1: Moving to Node #0,3 Current State: 14:[17, 17, 13], Operations: ['88-75=13'] Exploring Operation: 17-17=0, Resulting Numbers: [13, 0] Generated Node #0,3,0: 14:[13, 0] Operation: 17-17=0 Exploring Operation: 17/17=1, Resulting Numbers: [13, 1] Generated Node #0,3,1: 14:[13, 1] Operation: 17/17=1 Exploring Operation: 17-13=4, Resulting Numbers: [17, 4] Generated Node #0,3,2: 14:[17, 4] Operation: 17-13=4 Exploring Operation: 17-13=4, Resulting Numbers: [17, 4] Generated Node #0,3,3: 14:[17, 4] Operation: 17-13=4 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 14:[13, 1], Operations: ['88-75=13', '17/17=1'] Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,14 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[17, 75, 88, 17], Operations: [] Exploring Operation: 88-75=13, Resulting Numbers: [17, 17, 13] Generated Node #0,3: 14:[17, 17, 13] Operation: 88-75=13 Moving to Node #0,3 Current State: 14:[17, 17, 13], Operations: ['88-75=13'] Exploring Operation: 17/17=1, Resulting Numbers: [13, 1] Generated Node #0,3,1: 14:[13, 1] Operation: 17/17=1 Moving to Node #0,3,1 Current State: 14:[13, 1], Operations: ['88-75=13', '17/17=1'] Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 3, 54, 36, 21 ]
73
[ "36+21=57", "57/3=19", "54+19=73" ]
Current State: 73:[3, 54, 36, 21], Operations: [] Exploring Operation: 36+21=57, Resulting Numbers: [3, 54, 57] Generated Node #2: [3, 54, 57] from Operation: 36+21=57 Current State: 73:[3, 54, 57], Operations: ['36+21=57'] Exploring Operation: 57/3=19, Resulting Numbers: [54, 19] Generated Node #3: [54, 19] from Operation: 57/3=19 Current State: 73:[54, 19], Operations: ['36+21=57', '57/3=19'] Exploring Operation: 54+19=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[3, 54, 36, 21], Operations: [] Exploring Operation: 3+21=24, Resulting Numbers: [54, 36, 24] Generated Node #0,0: 73:[54, 36, 24] Operation: 3+21=24 Exploring Operation: 3+36=39, Resulting Numbers: [54, 21, 39] Generated Node #0,1: 73:[54, 21, 39] Operation: 3+36=39 Exploring Operation: 3+54=57, Resulting Numbers: [36, 21, 57] Generated Node #0,2: 73:[36, 21, 57] Operation: 3+54=57 Exploring Operation: 3*21=63, Resulting Numbers: [54, 36, 63] Generated Node #0,3: 73:[54, 36, 63] Operation: 3*21=63 Moving to Node #0,3 Current State: 73:[54, 36, 63], Operations: ['3*21=63'] Exploring Operation: 54+36=90, Resulting Numbers: [63, 90] Generated Node #0,3,0: 73:[63, 90] Operation: 54+36=90 Exploring Operation: 54-36=18, Resulting Numbers: [63, 18] Generated Node #0,3,1: 73:[63, 18] Operation: 54-36=18 Exploring Operation: 36+63=99, Resulting Numbers: [54, 99] Generated Node #0,3,2: 73:[54, 99] Operation: 36+63=99 Exploring Operation: 63-36=27, Resulting Numbers: [54, 27] Generated Node #0,3,3: 73:[54, 27] Operation: 63-36=27 Moving to Node #0,1 Current State: 73:[54, 21, 39], Operations: ['3+36=39'] Exploring Operation: 21+39=60, Resulting Numbers: [54, 60] Generated Node #0,1,0: 73:[54, 60] Operation: 21+39=60 Exploring Operation: 54-21=33, Resulting Numbers: [39, 33] Generated Node #0,1,1: 73:[39, 33] Operation: 54-21=33 Exploring Operation: 54+39=93, Resulting Numbers: [21, 93] Generated Node #0,1,2: 73:[21, 93] Operation: 54+39=93 Exploring Operation: 54+21=75, Resulting Numbers: [39, 75] Generated Node #0,1,3: 73:[39, 75] Operation: 54+21=75 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[54, 60], Operations: ['3+36=39', '21+39=60'] Exploring Operation: 54+60=114, Resulting Numbers: [114] 114,73 unequal: No Solution Exploring Operation: 60-54=6, Resulting Numbers: [6] 6,73 unequal: No Solution Exploring Operation: 54*60=3240, Resulting Numbers: [3240] 3240,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 73:[39, 75], Operations: ['3+36=39', '54+21=75'] Exploring Operation: 39+75=114, Resulting Numbers: [114] 114,73 unequal: No Solution Exploring Operation: 39*75=2925, Resulting Numbers: [2925] 2925,73 unequal: No Solution Exploring Operation: 75-39=36, Resulting Numbers: [36] 36,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 73:[21, 93], Operations: ['3+36=39', '54+39=93'] Exploring Operation: 21+93=114, Resulting Numbers: [114] 114,73 unequal: No Solution Exploring Operation: 21*93=1953, Resulting Numbers: [1953] 1953,73 unequal: No Solution Exploring Operation: 93-21=72, Resulting Numbers: [72] 72,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[39, 33], Operations: ['3+36=39', '54-21=33'] Exploring Operation: 39*33=1287, Resulting Numbers: [1287] 1287,73 unequal: No Solution Exploring Operation: 39+33=72, Resulting Numbers: [72] 72,73 unequal: No Solution Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,73 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: 73:[54, 36, 24], Operations: ['3+21=24'] Exploring Operation: 54+24=78, Resulting Numbers: [36, 78] Generated Node #0,0,0: 73:[36, 78] Operation: 54+24=78 Exploring Operation: 54-24=30, Resulting Numbers: [36, 30] Generated Node #0,0,1: 73:[36, 30] Operation: 54-24=30 Exploring Operation: 54+36=90, Resulting Numbers: [24, 90] Generated Node #0,0,2: 73:[24, 90] Operation: 54+36=90 Exploring Operation: 36+24=60, Resulting Numbers: [54, 60] Generated Node #0,0,3: 73:[54, 60] Operation: 36+24=60 Moving to Node #0,2 Current State: 73:[36, 21, 57], Operations: ['3+54=57'] Exploring Operation: 36+21=57, Resulting Numbers: [57, 57] Generated Node #0,2,0: 73:[57, 57] Operation: 36+21=57 Exploring Operation: 36-21=15, Resulting Numbers: [57, 15] Generated Node #0,2,1: 73:[57, 15] Operation: 36-21=15 Exploring Operation: 36+57=93, Resulting Numbers: [21, 93] Generated Node #0,2,2: 73:[21, 93] Operation: 36+57=93 Exploring Operation: 21+57=78, Resulting Numbers: [36, 78] Generated Node #0,2,3: 73:[36, 78] Operation: 21+57=78 Moving to Node #0,3,0 Current State: 73:[63, 90], Operations: ['3*21=63', '54+36=90'] Exploring Operation: 63+90=153, Resulting Numbers: [153] 153,73 unequal: No Solution Exploring Operation: 63*90=5670, Resulting Numbers: [5670] 5670,73 unequal: No Solution Exploring Operation: 90-63=27, Resulting Numbers: [27] 27,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[54, 60], Operations: ['3+21=24', '36+24=60'] Exploring Operation: 54+60=114, Resulting Numbers: [114] 114,73 unequal: No Solution Exploring Operation: 54*60=3240, Resulting Numbers: [3240] 3240,73 unequal: No Solution Exploring Operation: 60-54=6, Resulting Numbers: [6] 6,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[57, 57], Operations: ['3+54=57', '36+21=57'] Exploring Operation: 57/57=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 57+57=114, Resulting Numbers: [114] 114,73 unequal: No Solution Exploring Operation: 57*57=3249, Resulting Numbers: [3249] 3249,73 unequal: No Solution Exploring Operation: 57-57=0, Resulting Numbers: [0] 0,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[36, 78], Operations: ['3+21=24', '54+24=78'] Exploring Operation: 36*78=2808, Resulting Numbers: [2808] 2808,73 unequal: No Solution Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,73 unequal: No Solution Exploring Operation: 36+78=114, Resulting Numbers: [114] 114,73 unequal: No Solution Moving to Node #0,2,3 Current State: 73:[36, 78], Operations: ['3+54=57', '21+57=78'] Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,73 unequal: No Solution Exploring Operation: 36+78=114, Resulting Numbers: [114] 114,73 unequal: No Solution Exploring Operation: 36*78=2808, Resulting Numbers: [2808] 2808,73 unequal: No Solution Moving to Node #0,3,2 Current State: 73:[54, 99], Operations: ['3*21=63', '36+63=99'] Exploring Operation: 99-54=45, Resulting Numbers: [45] 45,73 unequal: No Solution Exploring Operation: 54+99=153, Resulting Numbers: [153] 153,73 unequal: No Solution Exploring Operation: 54*99=5346, Resulting Numbers: [5346] 5346,73 unequal: No Solution Moving to Node #0,3,1 Current State: 73:[63, 18], Operations: ['3*21=63', '54-36=18'] Exploring Operation: 63-18=45, Resulting Numbers: [45] 45,73 unequal: No Solution Exploring Operation: 63+18=81, Resulting Numbers: [81] 81,73 unequal: No Solution Exploring Operation: 63*18=1134, Resulting Numbers: [1134] 1134,73 unequal: No Solution Moving to Node #0,3,3 Current State: 73:[54, 27], Operations: ['3*21=63', '63-36=27'] Exploring Operation: 54+27=81, Resulting Numbers: [81] 81,73 unequal: No Solution Exploring Operation: 54-27=27, Resulting Numbers: [27] 27,73 unequal: No Solution Exploring Operation: 54/27=2, Resulting Numbers: [2] 2,73 unequal: No Solution Exploring Operation: 54*27=1458, Resulting Numbers: [1458] 1458,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[24, 90], Operations: ['3+21=24', '54+36=90'] Exploring Operation: 90-24=66, Resulting Numbers: [66] 66,73 unequal: No Solution Exploring Operation: 24*90=2160, Resulting Numbers: [2160] 2160,73 unequal: No Solution Exploring Operation: 24+90=114, Resulting Numbers: [114] 114,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[21, 93], Operations: ['3+54=57', '36+57=93'] Exploring Operation: 21+93=114, Resulting Numbers: [114] 114,73 unequal: No Solution Exploring Operation: 21*93=1953, Resulting Numbers: [1953] 1953,73 unequal: No Solution Exploring Operation: 93-21=72, Resulting Numbers: [72] 72,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[57, 15], Operations: ['3+54=57', '36-21=15'] Exploring Operation: 57*15=855, Resulting Numbers: [855] 855,73 unequal: No Solution Exploring Operation: 57+15=72, Resulting Numbers: [72] 72,73 unequal: No Solution Exploring Operation: 57-15=42, Resulting Numbers: [42] 42,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[36, 30], Operations: ['3+21=24', '54-24=30'] Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,73 unequal: No Solution Exploring Operation: 36*30=1080, Resulting Numbers: [1080] 1080,73 unequal: No Solution Exploring Operation: 36+30=66, Resulting Numbers: [66] 66,73 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 51, 52, 58, 98 ]
66
[ "58-51=7", "98/7=14", "52+14=66" ]
Current State: 66:[51, 52, 58, 98], Operations: [] Exploring Operation: 58-51=7, Resulting Numbers: [52, 98, 7] Generated Node #2: [52, 98, 7] from Operation: 58-51=7 Current State: 66:[52, 98, 7], Operations: ['58-51=7'] Exploring Operation: 98/7=14, Resulting Numbers: [52, 14] Generated Node #3: [52, 14] from Operation: 98/7=14 Current State: 66:[52, 14], Operations: ['58-51=7', '98/7=14'] Exploring Operation: 52+14=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[51, 52, 58, 98], Operations: [] Exploring Operation: 98-51=47, Resulting Numbers: [52, 58, 47] Generated Node #0,0: 66:[52, 58, 47] Operation: 98-51=47 Exploring Operation: 52-51=1, Resulting Numbers: [58, 98, 1] Generated Node #0,1: 66:[58, 98, 1] Operation: 52-51=1 Exploring Operation: 98-58=40, Resulting Numbers: [51, 52, 40] Generated Node #0,2: 66:[51, 52, 40] Operation: 98-58=40 Exploring Operation: 98-52=46, Resulting Numbers: [51, 58, 46] Generated Node #0,3: 66:[51, 58, 46] Operation: 98-52=46 Moving to Node #0,0 Current State: 66:[52, 58, 47], Operations: ['98-51=47'] Exploring Operation: 58-52=6, Resulting Numbers: [47, 6] Generated Node #0,0,0: 66:[47, 6] Operation: 58-52=6 Exploring Operation: 58-47=11, Resulting Numbers: [52, 11] Generated Node #0,0,1: 66:[52, 11] Operation: 58-47=11 Exploring Operation: 52-47=5, Resulting Numbers: [58, 5] Generated Node #0,0,2: 66:[58, 5] Operation: 52-47=5 Exploring Operation: 52+47=99, Resulting Numbers: [58, 99] Generated Node #0,0,3: 66:[58, 99] Operation: 52+47=99 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 66:[58, 5], Operations: ['98-51=47', '52-47=5'] Exploring Operation: 58*5=290, Resulting Numbers: [290] 290,66 unequal: No Solution Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,66 unequal: No Solution Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,66 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 #0,0,0 Current State: 66:[47, 6], Operations: ['98-51=47', '58-52=6'] Exploring Operation: 47*6=282, Resulting Numbers: [282] 282,66 unequal: No Solution Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,66 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 66:[52, 11], Operations: ['98-51=47', '58-47=11'] Exploring Operation: 52+11=63, Resulting Numbers: [63] 63,66 unequal: No Solution Exploring Operation: 52*11=572, Resulting Numbers: [572] 572,66 unequal: No Solution Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 66:[58, 99], Operations: ['98-51=47', '52+47=99'] Exploring Operation: 58*99=5742, Resulting Numbers: [5742] 5742,66 unequal: No Solution Exploring Operation: 99-58=41, Resulting Numbers: [41] 41,66 unequal: No Solution Exploring Operation: 58+99=157, Resulting Numbers: [157] 157,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 66:[51, 58, 46], Operations: ['98-52=46'] Exploring Operation: 58-46=12, Resulting Numbers: [51, 12] Generated Node #0,3,0: 66:[51, 12] Operation: 58-46=12 Exploring Operation: 51+46=97, Resulting Numbers: [58, 97] Generated Node #0,3,1: 66:[58, 97] Operation: 51+46=97 Exploring Operation: 58-51=7, Resulting Numbers: [46, 7] Generated Node #0,3,2: 66:[46, 7] Operation: 58-51=7 Exploring Operation: 51-46=5, Resulting Numbers: [58, 5] Generated Node #0,3,3: 66:[58, 5] Operation: 51-46=5 Moving to Node #0,2 Current State: 66:[51, 52, 40], Operations: ['98-58=40'] Exploring Operation: 52-51=1, Resulting Numbers: [40, 1] Generated Node #0,2,0: 66:[40, 1] Operation: 52-51=1 Exploring Operation: 51-40=11, Resulting Numbers: [52, 11] Generated Node #0,2,1: 66:[52, 11] Operation: 51-40=11 Exploring Operation: 51+40=91, Resulting Numbers: [52, 91] Generated Node #0,2,2: 66:[52, 91] Operation: 51+40=91 Exploring Operation: 52-40=12, Resulting Numbers: [51, 12] Generated Node #0,2,3: 66:[51, 12] Operation: 52-40=12 Moving to Node #0,1 Current State: 66:[58, 98, 1], Operations: ['52-51=1'] Exploring Operation: 58+1=59, Resulting Numbers: [98, 59] Generated Node #0,1,0: 66:[98, 59] Operation: 58+1=59 Exploring Operation: 58*1=58, Resulting Numbers: [98, 58] Generated Node #0,1,1: 66:[98, 58] Operation: 58*1=58 Exploring Operation: 98-58=40, Resulting Numbers: [1, 40] Generated Node #0,1,2: 66:[1, 40] Operation: 98-58=40 Exploring Operation: 98-1=97, Resulting Numbers: [58, 97] Generated Node #0,1,3: 66:[58, 97] Operation: 98-1=97 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 66:[1, 40], Operations: ['52-51=1', '98-58=40'] Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,66 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,66 unequal: No Solution Exploring Operation: 1+40=41, Resulting Numbers: [41] 41,66 unequal: No Solution Exploring Operation: 1*40=40, Resulting Numbers: [40] 40,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 66:[98, 59], Operations: ['52-51=1', '58+1=59'] Exploring Operation: 98-59=39, Resulting Numbers: [39] 39,66 unequal: No Solution Exploring Operation: 98*59=5782, Resulting Numbers: [5782] 5782,66 unequal: No Solution Exploring Operation: 98+59=157, Resulting Numbers: [157] 157,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 66:[58, 97], Operations: ['52-51=1', '98-1=97'] Exploring Operation: 58+97=155, Resulting Numbers: [155] 155,66 unequal: No Solution Exploring Operation: 58*97=5626, Resulting Numbers: [5626] 5626,66 unequal: No Solution Exploring Operation: 97-58=39, Resulting Numbers: [39] 39,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 66:[98, 58], Operations: ['52-51=1', '58*1=58'] Exploring Operation: 98*58=5684, Resulting Numbers: [5684] 5684,66 unequal: No Solution Exploring Operation: 98-58=40, Resulting Numbers: [40] 40,66 unequal: No Solution Exploring Operation: 98+58=156, Resulting Numbers: [156] 156,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 66:[40, 1], Operations: ['98-58=40', '52-51=1'] Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,66 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,66 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,66 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,66 unequal: No Solution Moving to Node #0,3,3 Current State: 66:[58, 5], Operations: ['98-52=46', '51-46=5'] Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,66 unequal: No Solution Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,66 unequal: No Solution Exploring Operation: 58*5=290, Resulting Numbers: [290] 290,66 unequal: No Solution Moving to Node #0,2,1 Current State: 66:[52, 11], Operations: ['98-58=40', '51-40=11'] Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,66 unequal: No Solution Exploring Operation: 52*11=572, Resulting Numbers: [572] 572,66 unequal: No Solution Exploring Operation: 52+11=63, Resulting Numbers: [63] 63,66 unequal: No Solution Moving to Node #0,3,2 Current State: 66:[46, 7], Operations: ['98-52=46', '58-51=7'] Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,66 unequal: No Solution Exploring Operation: 46+7=53, Resulting Numbers: [53] 53,66 unequal: No Solution Exploring Operation: 46*7=322, Resulting Numbers: [322] 322,66 unequal: No Solution Moving to Node #0,3,0 Current State: 66:[51, 12], Operations: ['98-52=46', '58-46=12'] Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,66 unequal: No Solution Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,66 unequal: No Solution Exploring Operation: 51*12=612, Resulting Numbers: [612] 612,66 unequal: No Solution Moving to Node #0,2,3 Current State: 66:[51, 12], Operations: ['98-58=40', '52-40=12'] Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,66 unequal: No Solution Exploring Operation: 51*12=612, Resulting Numbers: [612] 612,66 unequal: No Solution Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,66 unequal: No Solution Moving to Node #0,3,1 Current State: 66:[58, 97], Operations: ['98-52=46', '51+46=97'] Exploring Operation: 58*97=5626, Resulting Numbers: [5626] 5626,66 unequal: No Solution Exploring Operation: 97-58=39, Resulting Numbers: [39] 39,66 unequal: No Solution Exploring Operation: 58+97=155, Resulting Numbers: [155] 155,66 unequal: No Solution Moving to Node #0,2,2 Current State: 66:[52, 91], Operations: ['98-58=40', '51+40=91'] Exploring Operation: 52+91=143, Resulting Numbers: [143] 143,66 unequal: No Solution Exploring Operation: 52*91=4732, Resulting Numbers: [4732] 4732,66 unequal: No Solution Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,66 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 27, 31, 24, 28 ]
68
[ "31-27=4", "24*4=96", "96-28=68" ]
Current State: 68:[27, 31, 24, 28], Operations: [] Exploring Operation: 31-27=4, Resulting Numbers: [24, 28, 4] Generated Node #2: [24, 28, 4] from Operation: 31-27=4 Current State: 68:[24, 28, 4], Operations: ['31-27=4'] Exploring Operation: 24*4=96, Resulting Numbers: [28, 96] Generated Node #3: [28, 96] from Operation: 24*4=96 Current State: 68:[28, 96], Operations: ['31-27=4', '24*4=96'] Exploring Operation: 96-28=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[27, 31, 24, 28], Operations: [] Exploring Operation: 27-24=3, Resulting Numbers: [31, 28, 3] Generated Node #0,0: 68:[31, 28, 3] Operation: 27-24=3 Moving to Node #0,0 Current State: 68:[31, 28, 3], Operations: ['27-24=3'] Exploring Operation: 31-28=3, Resulting Numbers: [3, 3] Generated Node #0,0,0: 68:[3, 3] Operation: 31-28=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[3, 3], Operations: ['27-24=3', '31-28=3'] Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,68 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
[ 80, 47, 94, 12 ]
46
[ "80+12=92", "94/47=2", "92/2=46" ]
Current State: 46:[80, 47, 94, 12], Operations: [] Exploring Operation: 80+12=92, Resulting Numbers: [47, 94, 92] Generated Node #2: [47, 94, 92] from Operation: 80+12=92 Current State: 46:[47, 94, 92], Operations: ['80+12=92'] Exploring Operation: 94/47=2, Resulting Numbers: [92, 2] Generated Node #3: [92, 2] from Operation: 94/47=2 Current State: 46:[92, 2], Operations: ['80+12=92', '94/47=2'] Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[80, 47, 94, 12], Operations: [] Exploring Operation: 94-80=14, Resulting Numbers: [47, 12, 14] Generated Node #0,0: 46:[47, 12, 14] Operation: 94-80=14 Exploring Operation: 94/47=2, Resulting Numbers: [80, 12, 2] Generated Node #0,1: 46:[80, 12, 2] Operation: 94/47=2 Exploring Operation: 94-47=47, Resulting Numbers: [80, 12, 47] Generated Node #0,2: 46:[80, 12, 47] Operation: 94-47=47 Moving to Node #0,0 Current State: 46:[47, 12, 14], Operations: ['94-80=14'] Exploring Operation: 12+14=26, Resulting Numbers: [47, 26] Generated Node #0,0,0: 46:[47, 26] Operation: 12+14=26 Exploring Operation: 14-12=2, Resulting Numbers: [47, 2] Generated Node #0,0,1: 46:[47, 2] Operation: 14-12=2 Exploring Operation: 47-12=35, Resulting Numbers: [14, 35] Generated Node #0,0,2: 46:[14, 35] Operation: 47-12=35 Moving to Node #0,1 Current State: 46:[80, 12, 2], Operations: ['94/47=2'] Exploring Operation: 80-12=68, Resulting Numbers: [2, 68] Generated Node #0,1,0: 46:[2, 68] Operation: 80-12=68 Exploring Operation: 12*2=24, Resulting Numbers: [80, 24] Generated Node #0,1,1: 46:[80, 24] Operation: 12*2=24 Exploring Operation: 80/2=40, Resulting Numbers: [12, 40] Generated Node #0,1,2: 46:[12, 40] Operation: 80/2=40 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 46:[12, 40], Operations: ['94/47=2', '80/2=40'] Exploring Operation: 12+40=52, Resulting Numbers: [52] 52,46 unequal: No Solution Exploring Operation: 12*40=480, Resulting Numbers: [480] 480,46 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,46 unequal: No Solution No 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: 46:[2, 68], Operations: ['94/47=2', '80-12=68'] Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,46 unequal: No Solution Exploring Operation: 2+68=70, Resulting Numbers: [70] 70,46 unequal: No Solution Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,46 unequal: No Solution No 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: 46:[80, 24], Operations: ['94/47=2', '12*2=24'] Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,46 unequal: No Solution Exploring Operation: 80+24=104, Resulting Numbers: [104] 104,46 unequal: No Solution Exploring Operation: 80*24=1920, Resulting Numbers: [1920] 1920,46 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: 46:[80, 12, 47], Operations: ['94-47=47'] Exploring Operation: 80-12=68, Resulting Numbers: [47, 68] Generated Node #0,2,0: 46:[47, 68] Operation: 80-12=68 Exploring Operation: 80-47=33, Resulting Numbers: [12, 33] Generated Node #0,2,1: 46:[12, 33] Operation: 80-47=33 Exploring Operation: 47-12=35, Resulting Numbers: [80, 35] Generated Node #0,2,2: 46:[80, 35] Operation: 47-12=35 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 46:[12, 33], Operations: ['94-47=47', '80-47=33'] Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 12*33=396, Resulting Numbers: [396] 396,46 unequal: No Solution Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,46 unequal: No Solution No 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: 46:[47, 68], Operations: ['94-47=47', '80-12=68'] Exploring Operation: 47+68=115, Resulting Numbers: [115] 115,46 unequal: No Solution Exploring Operation: 47*68=3196, Resulting Numbers: [3196] 3196,46 unequal: No Solution Exploring Operation: 68-47=21, Resulting Numbers: [21] 21,46 unequal: No Solution No 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: 46:[80, 35], Operations: ['94-47=47', '47-12=35'] Exploring Operation: 80*35=2800, Resulting Numbers: [2800] 2800,46 unequal: No Solution Exploring Operation: 80+35=115, Resulting Numbers: [115] 115,46 unequal: No Solution Exploring Operation: 80-35=45, Resulting Numbers: [45] 45,46 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: 46:[47, 2], Operations: ['94-80=14', '14-12=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,46 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,46 unequal: No Solution Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[47, 26], Operations: ['94-80=14', '12+14=26'] Exploring Operation: 47+26=73, Resulting Numbers: [73] 73,46 unequal: No Solution Exploring Operation: 47*26=1222, Resulting Numbers: [1222] 1222,46 unequal: No Solution Exploring Operation: 47-26=21, Resulting Numbers: [21] 21,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[14, 35], Operations: ['94-80=14', '47-12=35'] Exploring Operation: 14+35=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 14*35=490, Resulting Numbers: [490] 490,46 unequal: No Solution Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,46 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 9, 12, 84, 21 ]
83
[ "9+12=21", "21/21=1", "84-1=83" ]
Current State: 83:[9, 12, 84, 21], Operations: [] Exploring Operation: 9+12=21, Resulting Numbers: [84, 21, 21] Generated Node #2: [84, 21, 21] from Operation: 9+12=21 Current State: 83:[84, 21, 21], Operations: ['9+12=21'] Exploring Operation: 21/21=1, Resulting Numbers: [84, 1] Generated Node #3: [84, 1] from Operation: 21/21=1 Current State: 83:[84, 1], Operations: ['9+12=21', '21/21=1'] Exploring Operation: 84-1=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[9, 12, 84, 21], Operations: [] Exploring Operation: 9*12=108, Resulting Numbers: [84, 21, 108] Generated Node #0,0: 83:[84, 21, 108] Operation: 9*12=108 Exploring Operation: 12+21=33, Resulting Numbers: [9, 84, 33] Generated Node #0,1: 83:[9, 84, 33] Operation: 12+21=33 Exploring Operation: 9+21=30, Resulting Numbers: [12, 84, 30] Generated Node #0,2: 83:[12, 84, 30] Operation: 9+21=30 Exploring Operation: 9+12=21, Resulting Numbers: [84, 21, 21] Generated Node #0,3: 83:[84, 21, 21] Operation: 9+12=21 Moving to Node #0,0 Current State: 83:[84, 21, 108], Operations: ['9*12=108'] Exploring Operation: 84-21=63, Resulting Numbers: [108, 63] Generated Node #0,0,0: 83:[108, 63] Operation: 84-21=63 Exploring Operation: 21+108=129, Resulting Numbers: [84, 129] Generated Node #0,0,1: 83:[84, 129] Operation: 21+108=129 Exploring Operation: 84+21=105, Resulting Numbers: [108, 105] Generated Node #0,0,2: 83:[108, 105] Operation: 84+21=105 Exploring Operation: 108-21=87, Resulting Numbers: [84, 87] Generated Node #0,0,3: 83:[84, 87] Operation: 108-21=87 Moving to Node #0,2 Current State: 83:[12, 84, 30], Operations: ['9+21=30'] Exploring Operation: 12+30=42, Resulting Numbers: [84, 42] Generated Node #0,2,0: 83:[84, 42] Operation: 12+30=42 Exploring Operation: 30-12=18, Resulting Numbers: [84, 18] Generated Node #0,2,1: 83:[84, 18] Operation: 30-12=18 Exploring Operation: 12+84=96, Resulting Numbers: [30, 96] Generated Node #0,2,2: 83:[30, 96] Operation: 12+84=96 Exploring Operation: 84-12=72, Resulting Numbers: [30, 72] Generated Node #0,2,3: 83:[30, 72] Operation: 84-12=72 Moving to Node #0,1 Current State: 83:[9, 84, 33], Operations: ['12+21=33'] Exploring Operation: 9+84=93, Resulting Numbers: [33, 93] Generated Node #0,1,0: 83:[33, 93] Operation: 9+84=93 Exploring Operation: 84-9=75, Resulting Numbers: [33, 75] Generated Node #0,1,1: 83:[33, 75] Operation: 84-9=75 Exploring Operation: 9+33=42, Resulting Numbers: [84, 42] Generated Node #0,1,2: 83:[84, 42] Operation: 9+33=42 Exploring Operation: 33-9=24, Resulting Numbers: [84, 24] Generated Node #0,1,3: 83:[84, 24] Operation: 33-9=24 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 83:[84, 42], Operations: ['12+21=33', '9+33=42'] Exploring Operation: 84/42=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 84+42=126, Resulting Numbers: [126] 126,83 unequal: No Solution Exploring Operation: 84*42=3528, Resulting Numbers: [3528] 3528,83 unequal: No Solution Exploring Operation: 84-42=42, Resulting Numbers: [42] 42,83 unequal: No Solution No 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: 83:[33, 75], Operations: ['12+21=33', '84-9=75'] Exploring Operation: 33+75=108, Resulting Numbers: [108] 108,83 unequal: No Solution Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,83 unequal: No Solution Exploring Operation: 33*75=2475, Resulting Numbers: [2475] 2475,83 unequal: No Solution No 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: 83:[33, 93], Operations: ['12+21=33', '9+84=93'] Exploring Operation: 93-33=60, Resulting Numbers: [60] 60,83 unequal: No Solution Exploring Operation: 33+93=126, Resulting Numbers: [126] 126,83 unequal: No Solution Exploring Operation: 33*93=3069, Resulting Numbers: [3069] 3069,83 unequal: No Solution No 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: 83:[84, 24], Operations: ['12+21=33', '33-9=24'] Exploring Operation: 84-24=60, Resulting Numbers: [60] 60,83 unequal: No Solution Exploring Operation: 84*24=2016, Resulting Numbers: [2016] 2016,83 unequal: No Solution Exploring Operation: 84+24=108, Resulting Numbers: [108] 108,83 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: 83:[84, 21, 21], Operations: ['9+12=21'] Exploring Operation: 21/21=1, Resulting Numbers: [84, 1] Generated Node #0,3,0: 83:[84, 1] Operation: 21/21=1 Exploring Operation: 84-21=63, Resulting Numbers: [21, 63] Generated Node #0,3,1: 83:[21, 63] Operation: 84-21=63 Exploring Operation: 84-21=63, Resulting Numbers: [21, 63] Generated Node #0,3,2: 83:[21, 63] Operation: 84-21=63 Exploring Operation: 21+21=42, Resulting Numbers: [84, 42] Generated Node #0,3,3: 83:[84, 42] Operation: 21+21=42 Moving to Node #0,0,3 Current State: 83:[84, 87], Operations: ['9*12=108', '108-21=87'] Exploring Operation: 87-84=3, Resulting Numbers: [3] 3,83 unequal: No Solution Exploring Operation: 84+87=171, Resulting Numbers: [171] 171,83 unequal: No Solution Exploring Operation: 84*87=7308, Resulting Numbers: [7308] 7308,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[84, 42], Operations: ['9+21=30', '12+30=42'] Exploring Operation: 84/42=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 84-42=42, Resulting Numbers: [42] 42,83 unequal: No Solution Exploring Operation: 84*42=3528, Resulting Numbers: [3528] 3528,83 unequal: No Solution Exploring Operation: 84+42=126, Resulting Numbers: [126] 126,83 unequal: No Solution Moving to Node #0,3,3 Current State: 83:[84, 42], Operations: ['9+12=21', '21+21=42'] Exploring Operation: 84+42=126, Resulting Numbers: [126] 126,83 unequal: No Solution Exploring Operation: 84*42=3528, Resulting Numbers: [3528] 3528,83 unequal: No Solution Exploring Operation: 84-42=42, Resulting Numbers: [42] 42,83 unequal: No Solution Exploring Operation: 84/42=2, Resulting Numbers: [2] 2,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[108, 63], Operations: ['9*12=108', '84-21=63'] Exploring Operation: 108*63=6804, Resulting Numbers: [6804] 6804,83 unequal: No Solution Exploring Operation: 108-63=45, Resulting Numbers: [45] 45,83 unequal: No Solution Exploring Operation: 108+63=171, Resulting Numbers: [171] 171,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[84, 129], Operations: ['9*12=108', '21+108=129'] Exploring Operation: 129-84=45, Resulting Numbers: [45] 45,83 unequal: No Solution Exploring Operation: 84*129=10836, Resulting Numbers: [10836] 10836,83 unequal: No Solution Exploring Operation: 84+129=213, Resulting Numbers: [213] 213,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[108, 105], Operations: ['9*12=108', '84+21=105'] Exploring Operation: 108*105=11340, Resulting Numbers: [11340] 11340,83 unequal: No Solution Exploring Operation: 108-105=3, Resulting Numbers: [3] 3,83 unequal: No Solution Exploring Operation: 108+105=213, Resulting Numbers: [213] 213,83 unequal: No Solution Moving to Node #0,2,3 Current State: 83:[30, 72], Operations: ['9+21=30', '84-12=72'] Exploring Operation: 30+72=102, Resulting Numbers: [102] 102,83 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,83 unequal: No Solution Exploring Operation: 30*72=2160, Resulting Numbers: [2160] 2160,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[84, 18], Operations: ['9+21=30', '30-12=18'] Exploring Operation: 84*18=1512, Resulting Numbers: [1512] 1512,83 unequal: No Solution Exploring Operation: 84-18=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 84+18=102, Resulting Numbers: [102] 102,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[30, 96], Operations: ['9+21=30', '12+84=96'] Exploring Operation: 30*96=2880, Resulting Numbers: [2880] 2880,83 unequal: No Solution Exploring Operation: 30+96=126, Resulting Numbers: [126] 126,83 unequal: No Solution Exploring Operation: 96-30=66, Resulting Numbers: [66] 66,83 unequal: No Solution Moving to Node #0,3,2 Current State: 83:[21, 63], Operations: ['9+12=21', '84-21=63'] Exploring Operation: 21+63=84, Resulting Numbers: [84] 84,83 unequal: No Solution Exploring Operation: 21*63=1323, Resulting Numbers: [1323] 1323,83 unequal: No Solution Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,83 unequal: No Solution Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,83 unequal: No Solution Moving to Node #0,3,1 Current State: 83:[21, 63], Operations: ['9+12=21', '84-21=63'] Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,83 unequal: No Solution Exploring Operation: 21*63=1323, Resulting Numbers: [1323] 1323,83 unequal: No Solution Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,83 unequal: No Solution Exploring Operation: 21+63=84, Resulting Numbers: [84] 84,83 unequal: No Solution Moving to Node #0,3,0 Current State: 83:[84, 1], Operations: ['9+12=21', '21/21=1'] Exploring Operation: 84/1=84, Resulting Numbers: [84] 84,83 unequal: No Solution Exploring Operation: 84*1=84, Resulting Numbers: [84] 84,83 unequal: No Solution Exploring Operation: 84-1=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[9, 12, 84, 21], Operations: [] Exploring Operation: 9+12=21, Resulting Numbers: [84, 21, 21] Generated Node #0,3: 83:[84, 21, 21] Operation: 9+12=21 Moving to Node #0,3 Current State: 83:[84, 21, 21], Operations: ['9+12=21'] Exploring Operation: 21/21=1, Resulting Numbers: [84, 1] Generated Node #0,3,0: 83:[84, 1] Operation: 21/21=1 Moving to Node #0,3,0 Current State: 83:[84, 1], Operations: ['9+12=21', '21/21=1'] Exploring Operation: 84-1=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
0.93316
hs_4
mult_heuristic
[ 5, 4, 2, 68 ]
83
[ "5*68=340", "340/4=85", "85-2=83" ]
Current State: 83:[5, 4, 2, 68], Operations: [] Exploring Operation: 5*68=340, Resulting Numbers: [4, 2, 340] Generated Node #2: [4, 2, 340] from Operation: 5*68=340 Current State: 83:[4, 2, 340], Operations: ['5*68=340'] Exploring Operation: 340/4=85, Resulting Numbers: [2, 85] Generated Node #3: [2, 85] from Operation: 340/4=85 Current State: 83:[2, 85], Operations: ['5*68=340', '340/4=85'] Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[5, 4, 2, 68], Operations: [] Exploring Operation: 5*4=20, Resulting Numbers: [2, 68, 20] Generated Node #0,0: 83:[2, 68, 20] Operation: 5*4=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[2, 68, 20], Operations: ['5*4=20'] Exploring Operation: 2*20=40, Resulting Numbers: [68, 40] Generated Node #0,0,0: 83:[68, 40] Operation: 2*20=40 Moving to Node #0,0,0 Current State: 83:[68, 40], Operations: ['5*4=20', '2*20=40'] Exploring Operation: 68+40=108, Resulting Numbers: [108] 108,83 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
[ 4, 5, 70, 11 ]
90
[ "4+5=9", "70+11=81", "9+81=90" ]
Current State: 90:[4, 5, 70, 11], Operations: [] Exploring Operation: 4+5=9, Resulting Numbers: [70, 11, 9] Generated Node #2: [70, 11, 9] from Operation: 4+5=9 Current State: 90:[70, 11, 9], Operations: ['4+5=9'] Exploring Operation: 70+11=81, Resulting Numbers: [9, 81] Generated Node #3: [9, 81] from Operation: 70+11=81 Current State: 90:[9, 81], Operations: ['4+5=9', '70+11=81'] Exploring Operation: 9+81=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[4, 5, 70, 11], Operations: [] Exploring Operation: 70/5=14, Resulting Numbers: [4, 11, 14] Generated Node #0,0: 90:[4, 11, 14] Operation: 70/5=14 Moving to Node #0,0 Current State: 90:[4, 11, 14], Operations: ['70/5=14'] Exploring Operation: 4+11=15, Resulting Numbers: [14, 15] Generated Node #0,0,0: 90:[14, 15] Operation: 4+11=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[14, 15], Operations: ['70/5=14', '4+11=15'] Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 74, 90, 82, 81 ]
17
[ "90-74=16", "82-81=1", "16+1=17" ]
Current State: 17:[74, 90, 82, 81], Operations: [] Exploring Operation: 90-74=16, Resulting Numbers: [82, 81, 16] Generated Node #2: [82, 81, 16] from Operation: 90-74=16 Current State: 17:[82, 81, 16], Operations: ['90-74=16'] Exploring Operation: 82-81=1, Resulting Numbers: [16, 1] Generated Node #3: [16, 1] from Operation: 82-81=1 Current State: 17:[16, 1], Operations: ['90-74=16', '82-81=1'] Exploring Operation: 16+1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[74, 90, 82, 81], Operations: [] Exploring Operation: 90-74=16, Resulting Numbers: [82, 81, 16] Generated Node #0,0: 17:[82, 81, 16] Operation: 90-74=16 Exploring Operation: 90-81=9, Resulting Numbers: [74, 82, 9] Generated Node #0,1: 17:[74, 82, 9] Operation: 90-81=9 Exploring Operation: 90-82=8, Resulting Numbers: [74, 81, 8] Generated Node #0,2: 17:[74, 81, 8] Operation: 90-82=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[82, 81, 16], Operations: ['90-74=16'] Exploring Operation: 82-16=66, Resulting Numbers: [81, 66] Generated Node #0,0,0: 17:[81, 66] Operation: 82-16=66 Exploring Operation: 81-16=65, Resulting Numbers: [82, 65] Generated Node #0,0,1: 17:[82, 65] Operation: 81-16=65 Exploring Operation: 82-81=1, Resulting Numbers: [16, 1] Generated Node #0,0,2: 17:[16, 1] Operation: 82-81=1 Moving to Node #0,0,2 Current State: 17:[16, 1], Operations: ['90-74=16', '82-81=1'] Exploring Operation: 16+1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[74, 90, 82, 81], Operations: [] Exploring Operation: 90-74=16, Resulting Numbers: [82, 81, 16] Generated Node #0,0: 17:[82, 81, 16] Operation: 90-74=16 Moving to Node #0,0 Current State: 17:[82, 81, 16], Operations: ['90-74=16'] Exploring Operation: 82-81=1, Resulting Numbers: [16, 1] Generated Node #0,0,2: 17:[16, 1] Operation: 82-81=1 Moving to Node #0,0,2 Current State: 17:[16, 1], Operations: ['90-74=16', '82-81=1'] Exploring Operation: 16+1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 39, 81, 55, 53 ]
66
[ "81-39=42", "55+53=108", "108-42=66" ]
Current State: 66:[39, 81, 55, 53], Operations: [] Exploring Operation: 81-39=42, Resulting Numbers: [55, 53, 42] Generated Node #2: [55, 53, 42] from Operation: 81-39=42 Current State: 66:[55, 53, 42], Operations: ['81-39=42'] Exploring Operation: 55+53=108, Resulting Numbers: [42, 108] Generated Node #3: [42, 108] from Operation: 55+53=108 Current State: 66:[42, 108], Operations: ['81-39=42', '55+53=108'] Exploring Operation: 108-42=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[39, 81, 55, 53], Operations: [] Exploring Operation: 53-39=14, Resulting Numbers: [81, 55, 14] Generated Node #0,0: 66:[81, 55, 14] Operation: 53-39=14 Exploring Operation: 55-53=2, Resulting Numbers: [39, 81, 2] Generated Node #0,1: 66:[39, 81, 2] Operation: 55-53=2 Exploring Operation: 81-53=28, Resulting Numbers: [39, 55, 28] Generated Node #0,2: 66:[39, 55, 28] Operation: 81-53=28 Exploring Operation: 81-55=26, Resulting Numbers: [39, 53, 26] Generated Node #0,3: 66:[39, 53, 26] Operation: 81-55=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[39, 81, 2], Operations: ['55-53=2'] Exploring Operation: 81-2=79, Resulting Numbers: [39, 79] Generated Node #0,1,0: 66:[39, 79] Operation: 81-2=79 Exploring Operation: 39-2=37, Resulting Numbers: [81, 37] Generated Node #0,1,1: 66:[81, 37] Operation: 39-2=37 Exploring Operation: 81-39=42, Resulting Numbers: [2, 42] Generated Node #0,1,2: 66:[2, 42] Operation: 81-39=42 Exploring Operation: 39+2=41, Resulting Numbers: [81, 41] Generated Node #0,1,3: 66:[81, 41] Operation: 39+2=41 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 66:[2, 42], Operations: ['55-53=2', '81-39=42'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,66 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,66 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,66 unequal: No Solution Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 66:[39, 79], Operations: ['55-53=2', '81-2=79'] Exploring Operation: 39+79=118, Resulting Numbers: [118] 118,66 unequal: No Solution Exploring Operation: 79-39=40, Resulting Numbers: [40] 40,66 unequal: No Solution Exploring Operation: 39*79=3081, Resulting Numbers: [3081] 3081,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 66:[81, 37], Operations: ['55-53=2', '39-2=37'] Exploring Operation: 81-37=44, Resulting Numbers: [44] 44,66 unequal: No Solution Exploring Operation: 81+37=118, Resulting Numbers: [118] 118,66 unequal: No Solution Exploring Operation: 81*37=2997, Resulting Numbers: [2997] 2997,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 66:[81, 41], Operations: ['55-53=2', '39+2=41'] Exploring Operation: 81-41=40, Resulting Numbers: [40] 40,66 unequal: No Solution Exploring Operation: 81*41=3321, Resulting Numbers: [3321] 3321,66 unequal: No Solution Exploring Operation: 81+41=122, Resulting Numbers: [122] 122,66 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: 66:[39, 55, 28], Operations: ['81-53=28'] Exploring Operation: 39+28=67, Resulting Numbers: [55, 67] Generated Node #0,2,0: 66:[55, 67] Operation: 39+28=67 Exploring Operation: 55-28=27, Resulting Numbers: [39, 27] Generated Node #0,2,1: 66:[39, 27] Operation: 55-28=27 Exploring Operation: 39-28=11, Resulting Numbers: [55, 11] Generated Node #0,2,2: 66:[55, 11] Operation: 39-28=11 Exploring Operation: 55-39=16, Resulting Numbers: [28, 16] Generated Node #0,2,3: 66:[28, 16] Operation: 55-39=16 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 66:[28, 16], Operations: ['81-53=28', '55-39=16'] Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,66 unequal: No Solution Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,66 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 66:[39, 27], Operations: ['81-53=28', '55-28=27'] Exploring Operation: 39*27=1053, Resulting Numbers: [1053] 1053,66 unequal: No Solution Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[39, 81, 55, 53], Operations: [] Exploring Operation: 81-53=28, Resulting Numbers: [39, 55, 28] Generated Node #0,2: 66:[39, 55, 28] Operation: 81-53=28 Moving to Node #0,2 Current State: 66:[39, 55, 28], Operations: ['81-53=28'] Exploring Operation: 55-28=27, Resulting Numbers: [39, 27] Generated Node #0,2,1: 66:[39, 27] Operation: 55-28=27 Moving to Node #0,2,1 Current State: 66:[39, 27], Operations: ['81-53=28', '55-28=27'] Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.970486
hs_4
sum_heuristic
[ 48, 70, 6, 66 ]
96
[ "70-6=64", "66-64=2", "48*2=96" ]
Current State: 96:[48, 70, 6, 66], Operations: [] Exploring Operation: 70-6=64, Resulting Numbers: [48, 66, 64] Generated Node #2: [48, 66, 64] from Operation: 70-6=64 Current State: 96:[48, 66, 64], Operations: ['70-6=64'] Exploring Operation: 66-64=2, Resulting Numbers: [48, 2] Generated Node #3: [48, 2] from Operation: 66-64=2 Current State: 96:[48, 2], Operations: ['70-6=64', '66-64=2'] Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[48, 70, 6, 66], Operations: [] Exploring Operation: 70-66=4, Resulting Numbers: [48, 6, 4] Generated Node #0,0: 96:[48, 6, 4] Operation: 70-66=4 Exploring Operation: 66/6=11, Resulting Numbers: [48, 70, 11] Generated Node #0,1: 96:[48, 70, 11] Operation: 66/6=11 Exploring Operation: 66-48=18, Resulting Numbers: [70, 6, 18] Generated Node #0,2: 96:[70, 6, 18] Operation: 66-48=18 Exploring Operation: 70-48=22, Resulting Numbers: [6, 66, 22] Generated Node #0,3: 96:[6, 66, 22] Operation: 70-48=22 Moving to Node #0,0 Current State: 96:[48, 6, 4], Operations: ['70-66=4'] Exploring Operation: 48/4=12, Resulting Numbers: [6, 12] Generated Node #0,0,0: 96:[6, 12] Operation: 48/4=12 Exploring Operation: 48/6=8, Resulting Numbers: [4, 8] Generated Node #0,0,1: 96:[4, 8] Operation: 48/6=8 Exploring Operation: 6-4=2, Resulting Numbers: [48, 2] Generated Node #0,0,2: 96:[48, 2] Operation: 6-4=2 Exploring Operation: 6*4=24, Resulting Numbers: [48, 24] Generated Node #0,0,3: 96:[48, 24] Operation: 6*4=24 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[6, 12], Operations: ['70-66=4', '48/4=12'] Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,96 unequal: No Solution Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,96 unequal: No Solution Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 96:[4, 8], Operations: ['70-66=4', '48/6=8'] Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 96:[48, 2], Operations: ['70-66=4', '6-4=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,96 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[48, 70, 6, 66], Operations: [] Exploring Operation: 70-66=4, Resulting Numbers: [48, 6, 4] Generated Node #0,0: 96:[48, 6, 4] Operation: 70-66=4 Moving to Node #0,0 Current State: 96:[48, 6, 4], Operations: ['70-66=4'] Exploring Operation: 6-4=2, Resulting Numbers: [48, 2] Generated Node #0,0,2: 96:[48, 2] Operation: 6-4=2 Moving to Node #0,0,2 Current State: 96:[48, 2], Operations: ['70-66=4', '6-4=2'] Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
mult_heuristic
[ 30, 55, 93, 99 ]
31
[ "55-30=25", "99-93=6", "25+6=31" ]
Current State: 31:[30, 55, 93, 99], Operations: [] Exploring Operation: 55-30=25, Resulting Numbers: [93, 99, 25] Generated Node #2: [93, 99, 25] from Operation: 55-30=25 Current State: 31:[93, 99, 25], Operations: ['55-30=25'] Exploring Operation: 99-93=6, Resulting Numbers: [25, 6] Generated Node #3: [25, 6] from Operation: 99-93=6 Current State: 31:[25, 6], Operations: ['55-30=25', '99-93=6'] Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[30, 55, 93, 99], Operations: [] Exploring Operation: 99-55=44, Resulting Numbers: [30, 93, 44] Generated Node #0,0: 31:[30, 93, 44] Operation: 99-55=44 Exploring Operation: 93-30=63, Resulting Numbers: [55, 99, 63] Generated Node #0,1: 31:[55, 99, 63] Operation: 93-30=63 Exploring Operation: 99-93=6, Resulting Numbers: [30, 55, 6] Generated Node #0,2: 31:[30, 55, 6] Operation: 99-93=6 Exploring Operation: 93-55=38, Resulting Numbers: [30, 99, 38] Generated Node #0,3: 31:[30, 99, 38] Operation: 93-55=38 Start Sub Search at level 1: Moving to Node #0,2 Current State: 31:[30, 55, 6], Operations: ['99-93=6'] Exploring Operation: 55-30=25, Resulting Numbers: [6, 25] Generated Node #0,2,0: 31:[6, 25] Operation: 55-30=25 Exploring Operation: 30-6=24, Resulting Numbers: [55, 24] Generated Node #0,2,1: 31:[55, 24] Operation: 30-6=24 Exploring Operation: 55-6=49, Resulting Numbers: [30, 49] Generated Node #0,2,2: 31:[30, 49] Operation: 55-6=49 Exploring Operation: 30+6=36, Resulting Numbers: [55, 36] Generated Node #0,2,3: 31:[55, 36] Operation: 30+6=36 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 31:[30, 49], Operations: ['99-93=6', '55-6=49'] Exploring Operation: 49-30=19, Resulting Numbers: [19] 19,31 unequal: No Solution Exploring Operation: 30+49=79, Resulting Numbers: [79] 79,31 unequal: No Solution Exploring Operation: 30*49=1470, Resulting Numbers: [1470] 1470,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 31:[55, 36], Operations: ['99-93=6', '30+6=36'] Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,31 unequal: No Solution Exploring Operation: 55*36=1980, Resulting Numbers: [1980] 1980,31 unequal: No Solution Exploring Operation: 55+36=91, Resulting Numbers: [91] 91,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 31:[6, 25], Operations: ['99-93=6', '55-30=25'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,31 unequal: No Solution Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[30, 55, 93, 99], Operations: [] Exploring Operation: 99-93=6, Resulting Numbers: [30, 55, 6] Generated Node #0,2: 31:[30, 55, 6] Operation: 99-93=6 Moving to Node #0,2 Current State: 31:[30, 55, 6], Operations: ['99-93=6'] Exploring Operation: 55-30=25, Resulting Numbers: [6, 25] Generated Node #0,2,0: 31:[6, 25] Operation: 55-30=25 Moving to Node #0,2,0 Current State: 31:[6, 25], Operations: ['99-93=6', '55-30=25'] Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 66, 4, 33, 13 ]
50
[ "66+4=70", "33-13=20", "70-20=50" ]
Current State: 50:[66, 4, 33, 13], Operations: [] Exploring Operation: 66+4=70, Resulting Numbers: [33, 13, 70] Generated Node #2: [33, 13, 70] from Operation: 66+4=70 Current State: 50:[33, 13, 70], Operations: ['66+4=70'] Exploring Operation: 33-13=20, Resulting Numbers: [70, 20] Generated Node #3: [70, 20] from Operation: 33-13=20 Current State: 50:[70, 20], Operations: ['66+4=70', '33-13=20'] Exploring Operation: 70-20=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[66, 4, 33, 13], Operations: [] Exploring Operation: 66-33=33, Resulting Numbers: [4, 13, 33] Generated Node #0,0: 50:[4, 13, 33] Operation: 66-33=33 Exploring Operation: 66/33=2, Resulting Numbers: [4, 13, 2] Generated Node #0,1: 50:[4, 13, 2] Operation: 66/33=2 Moving to Node #0,1 Current State: 50:[4, 13, 2], Operations: ['66/33=2'] Exploring Operation: 13-4=9, Resulting Numbers: [2, 9] Generated Node #0,1,0: 50:[2, 9] Operation: 13-4=9 Exploring Operation: 4*13=52, Resulting Numbers: [2, 52] Generated Node #0,1,1: 50:[2, 52] Operation: 4*13=52 Moving to Node #0,0 Current State: 50:[4, 13, 33], Operations: ['66-33=33'] Exploring Operation: 33-13=20, Resulting Numbers: [4, 20] Generated Node #0,0,0: 50:[4, 20] Operation: 33-13=20 Exploring Operation: 13+33=46, Resulting Numbers: [4, 46] Generated Node #0,0,1: 50:[4, 46] Operation: 13+33=46 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 50:[4, 46], Operations: ['66-33=33', '13+33=46'] Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[66, 4, 33, 13], Operations: [] Exploring Operation: 66-33=33, Resulting Numbers: [4, 13, 33] Generated Node #0,0: 50:[4, 13, 33] Operation: 66-33=33 Moving to Node #0,0 Current State: 50:[4, 13, 33], Operations: ['66-33=33'] Exploring Operation: 13+33=46, Resulting Numbers: [4, 46] Generated Node #0,0,1: 50:[4, 46] Operation: 13+33=46 Moving to Node #0,0,1 Current State: 50:[4, 46], Operations: ['66-33=33', '13+33=46'] Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 85, 53, 36, 84 ]
79
[ "53-36=17", "85/17=5", "84-5=79" ]
Current State: 79:[85, 53, 36, 84], Operations: [] Exploring Operation: 53-36=17, Resulting Numbers: [85, 84, 17] Generated Node #2: [85, 84, 17] from Operation: 53-36=17 Current State: 79:[85, 84, 17], Operations: ['53-36=17'] Exploring Operation: 85/17=5, Resulting Numbers: [84, 5] Generated Node #3: [84, 5] from Operation: 85/17=5 Current State: 79:[84, 5], Operations: ['53-36=17', '85/17=5'] Exploring Operation: 84-5=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[85, 53, 36, 84], Operations: [] Exploring Operation: 53+36=89, Resulting Numbers: [85, 84, 89] Generated Node #0,0: 79:[85, 84, 89] Operation: 53+36=89 Moving to Node #0,0 Current State: 79:[85, 84, 89], Operations: ['53+36=89'] Exploring Operation: 89-85=4, Resulting Numbers: [84, 4] Generated Node #0,0,0: 79:[84, 4] Operation: 89-85=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[84, 4], Operations: ['53+36=89', '89-85=4'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,79 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
[ 33, 21, 34, 19 ]
100
[ "21-19=2", "33*2=66", "34+66=100" ]
Current State: 100:[33, 21, 34, 19], Operations: [] Exploring Operation: 21-19=2, Resulting Numbers: [33, 34, 2] Generated Node #2: [33, 34, 2] from Operation: 21-19=2 Current State: 100:[33, 34, 2], Operations: ['21-19=2'] Exploring Operation: 33*2=66, Resulting Numbers: [34, 66] Generated Node #3: [34, 66] from Operation: 33*2=66 Current State: 100:[34, 66], Operations: ['21-19=2', '33*2=66'] Exploring Operation: 34+66=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[33, 21, 34, 19], Operations: [] Exploring Operation: 33-21=12, Resulting Numbers: [34, 19, 12] Generated Node #0,0: 100:[34, 19, 12] Operation: 33-21=12 Exploring Operation: 34-33=1, Resulting Numbers: [21, 19, 1] Generated Node #0,1: 100:[21, 19, 1] Operation: 34-33=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[21, 19, 1], Operations: ['34-33=1'] Exploring Operation: 21-1=20, Resulting Numbers: [19, 20] Generated Node #0,1,0: 100:[19, 20] Operation: 21-1=20 Exploring Operation: 21-19=2, Resulting Numbers: [1, 2] Generated Node #0,1,1: 100:[1, 2] Operation: 21-19=2 Moving to Node #0,1,0 Current State: 100:[19, 20], Operations: ['34-33=1', '21-1=20'] Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[1, 2], Operations: ['34-33=1', '21-19=2'] Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,100 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 Current State: 100:[34, 19, 12], Operations: ['33-21=12'] Exploring Operation: 34+19=53, Resulting Numbers: [12, 53] Generated Node #0,0,0: 100:[12, 53] Operation: 34+19=53 Exploring Operation: 34-12=22, Resulting Numbers: [19, 22] Generated Node #0,0,1: 100:[19, 22] Operation: 34-12=22 Moving to Node #0,0,1 Current State: 100:[19, 22], Operations: ['33-21=12', '34-12=22'] Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[12, 53], Operations: ['33-21=12', '34+19=53'] Exploring Operation: 53-12=41, Resulting Numbers: [41] 41,100 unequal: No Solution Exploring Operation: 12+53=65, Resulting Numbers: [65] 65,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 7, 42, 83, 64 ]
13
[ "42/7=6", "83-64=19", "19-6=13" ]
Current State: 13:[7, 42, 83, 64], Operations: [] Exploring Operation: 42/7=6, Resulting Numbers: [83, 64, 6] Generated Node #2: [83, 64, 6] from Operation: 42/7=6 Current State: 13:[83, 64, 6], Operations: ['42/7=6'] Exploring Operation: 83-64=19, Resulting Numbers: [6, 19] Generated Node #3: [6, 19] from Operation: 83-64=19 Current State: 13:[6, 19], Operations: ['42/7=6', '83-64=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[7, 42, 83, 64], Operations: [] Exploring Operation: 83-42=41, Resulting Numbers: [7, 64, 41] Generated Node #0,0: 13:[7, 64, 41] Operation: 83-42=41 Exploring Operation: 83-64=19, Resulting Numbers: [7, 42, 19] Generated Node #0,1: 13:[7, 42, 19] Operation: 83-64=19 Exploring Operation: 64-42=22, Resulting Numbers: [7, 83, 22] Generated Node #0,2: 13:[7, 83, 22] Operation: 64-42=22 Moving to Node #0,1 Current State: 13:[7, 42, 19], Operations: ['83-64=19'] Exploring Operation: 42-19=23, Resulting Numbers: [7, 23] Generated Node #0,1,0: 13:[7, 23] Operation: 42-19=23 Exploring Operation: 42-7=35, Resulting Numbers: [19, 35] Generated Node #0,1,1: 13:[19, 35] Operation: 42-7=35 Exploring Operation: 42/7=6, Resulting Numbers: [19, 6] Generated Node #0,1,2: 13:[19, 6] Operation: 42/7=6 Moving to Node #0,0 Current State: 13:[7, 64, 41], Operations: ['83-42=41'] Exploring Operation: 64-41=23, Resulting Numbers: [7, 23] Generated Node #0,0,0: 13:[7, 23] Operation: 64-41=23 Exploring Operation: 64-7=57, Resulting Numbers: [41, 57] Generated Node #0,0,1: 13:[41, 57] Operation: 64-7=57 Exploring Operation: 41-7=34, Resulting Numbers: [64, 34] Generated Node #0,0,2: 13:[64, 34] Operation: 41-7=34 Moving to Node #0,2 Current State: 13:[7, 83, 22], Operations: ['64-42=22'] Exploring Operation: 22-7=15, Resulting Numbers: [83, 15] Generated Node #0,2,0: 13:[83, 15] Operation: 22-7=15 Exploring Operation: 83-7=76, Resulting Numbers: [22, 76] Generated Node #0,2,1: 13:[22, 76] Operation: 83-7=76 Exploring Operation: 83-22=61, Resulting Numbers: [7, 61] Generated Node #0,2,2: 13:[7, 61] Operation: 83-22=61 Moving to Node #0,1,2 Current State: 13:[19, 6], Operations: ['83-64=19', '42/7=6'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[7, 42, 83, 64], Operations: [] Exploring Operation: 83-64=19, Resulting Numbers: [7, 42, 19] Generated Node #0,1: 13:[7, 42, 19] Operation: 83-64=19 Moving to Node #0,1 Current State: 13:[7, 42, 19], Operations: ['83-64=19'] Exploring Operation: 42/7=6, Resulting Numbers: [19, 6] Generated Node #0,1,2: 13:[19, 6] Operation: 42/7=6 Moving to Node #0,1,2 Current State: 13:[19, 6], Operations: ['83-64=19', '42/7=6'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
0.985243
hs_3
sum_heuristic
[ 30, 2, 35, 85 ]
55
[ "85-35=50", "50/2=25", "30+25=55" ]
Current State: 55:[30, 2, 35, 85], Operations: [] Exploring Operation: 85-35=50, Resulting Numbers: [30, 2, 50] Generated Node #2: [30, 2, 50] from Operation: 85-35=50 Current State: 55:[30, 2, 50], Operations: ['85-35=50'] Exploring Operation: 50/2=25, Resulting Numbers: [30, 25] Generated Node #3: [30, 25] from Operation: 50/2=25 Current State: 55:[30, 25], Operations: ['85-35=50', '50/2=25'] Exploring Operation: 30+25=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[30, 2, 35, 85], Operations: [] Exploring Operation: 85-30=55, Resulting Numbers: [2, 35, 55] Generated Node #0,0: 55:[2, 35, 55] Operation: 85-30=55 Moving to Node #0,0 Current State: 55:[2, 35, 55], Operations: ['85-30=55'] Exploring Operation: 55-35=20, Resulting Numbers: [2, 20] Generated Node #0,0,0: 55:[2, 20] Operation: 55-35=20 Moving to Node #0,0,0 Current State: 55:[2, 20], Operations: ['85-30=55', '55-35=20'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,55 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 72, 51, 51, 99 ]
99
[ "51-51=0", "72*0=0", "99+0=99" ]
Current State: 99:[72, 51, 51, 99], Operations: [] Exploring Operation: 51-51=0, Resulting Numbers: [72, 99, 0] Generated Node #2: [72, 99, 0] from Operation: 51-51=0 Current State: 99:[72, 99, 0], Operations: ['51-51=0'] Exploring Operation: 72*0=0, Resulting Numbers: [99, 0] Generated Node #3: [99, 0] from Operation: 72*0=0 Current State: 99:[99, 0], Operations: ['51-51=0', '72*0=0'] Exploring Operation: 99+0=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[72, 51, 51, 99], Operations: [] Exploring Operation: 51+51=102, Resulting Numbers: [72, 99, 102] Generated Node #0,0: 99:[72, 99, 102] Operation: 51+51=102 Exploring Operation: 51/51=1, Resulting Numbers: [72, 99, 1] Generated Node #0,1: 99:[72, 99, 1] Operation: 51/51=1 Exploring Operation: 51-51=0, Resulting Numbers: [72, 99, 0] Generated Node #0,2: 99:[72, 99, 0] Operation: 51-51=0 Exploring Operation: 72-51=21, Resulting Numbers: [51, 99, 21] Generated Node #0,3: 99:[51, 99, 21] Operation: 72-51=21 Exploring Operation: 72-51=21, Resulting Numbers: [51, 99, 21] Generated Node #0,4: 99:[51, 99, 21] Operation: 72-51=21 Moving to Node #0,3 Current State: 99:[51, 99, 21], Operations: ['72-51=21'] Exploring Operation: 51-21=30, Resulting Numbers: [99, 30] Generated Node #0,3,0: 99:[99, 30] Operation: 51-21=30 Exploring Operation: 99+21=120, Resulting Numbers: [51, 120] Generated Node #0,3,1: 99:[51, 120] Operation: 99+21=120 Exploring Operation: 99-51=48, Resulting Numbers: [21, 48] Generated Node #0,3,2: 99:[21, 48] Operation: 99-51=48 Exploring Operation: 99-21=78, Resulting Numbers: [51, 78] Generated Node #0,3,3: 99:[51, 78] Operation: 99-21=78 Exploring Operation: 51+21=72, Resulting Numbers: [99, 72] Generated Node #0,3,4: 99:[99, 72] Operation: 51+21=72 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 99:[99, 30], Operations: ['72-51=21', '51-21=30'] Exploring Operation: 99+30=129, Resulting Numbers: [129] 129,99 unequal: No Solution Exploring Operation: 99*30=2970, Resulting Numbers: [2970] 2970,99 unequal: No Solution Exploring Operation: 99-30=69, Resulting Numbers: [69] 69,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 99:[21, 48], Operations: ['72-51=21', '99-51=48'] Exploring Operation: 21+48=69, Resulting Numbers: [69] 69,99 unequal: No Solution Exploring Operation: 21*48=1008, Resulting Numbers: [1008] 1008,99 unequal: No Solution Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 99:[99, 72], Operations: ['72-51=21', '51+21=72'] Exploring Operation: 99-72=27, Resulting Numbers: [27] 27,99 unequal: No Solution Exploring Operation: 99*72=7128, Resulting Numbers: [7128] 7128,99 unequal: No Solution Exploring Operation: 99+72=171, Resulting Numbers: [171] 171,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 99:[51, 120], Operations: ['72-51=21', '99+21=120'] Exploring Operation: 51*120=6120, Resulting Numbers: [6120] 6120,99 unequal: No Solution Exploring Operation: 120-51=69, Resulting Numbers: [69] 69,99 unequal: No Solution Exploring Operation: 51+120=171, Resulting Numbers: [171] 171,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 99:[51, 78], Operations: ['72-51=21', '99-21=78'] Exploring Operation: 51*78=3978, Resulting Numbers: [3978] 3978,99 unequal: No Solution Exploring Operation: 51+78=129, Resulting Numbers: [129] 129,99 unequal: No Solution Exploring Operation: 78-51=27, Resulting Numbers: [27] 27,99 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: 99:[51, 99, 21], Operations: ['72-51=21'] Exploring Operation: 99-51=48, Resulting Numbers: [21, 48] Generated Node #0,4,0: 99:[21, 48] Operation: 99-51=48 Exploring Operation: 99-21=78, Resulting Numbers: [51, 78] Generated Node #0,4,1: 99:[51, 78] Operation: 99-21=78 Exploring Operation: 99+21=120, Resulting Numbers: [51, 120] Generated Node #0,4,2: 99:[51, 120] Operation: 99+21=120 Exploring Operation: 51-21=30, Resulting Numbers: [99, 30] Generated Node #0,4,3: 99:[99, 30] Operation: 51-21=30 Exploring Operation: 51+21=72, Resulting Numbers: [99, 72] Generated Node #0,4,4: 99:[99, 72] Operation: 51+21=72 Moving to Node #0,1 Current State: 99:[72, 99, 1], Operations: ['51/51=1'] Exploring Operation: 99-72=27, Resulting Numbers: [1, 27] Generated Node #0,1,0: 99:[1, 27] Operation: 99-72=27 Exploring Operation: 99*1=99, Resulting Numbers: [72, 99] Generated Node #0,1,1: 99:[72, 99] Operation: 99*1=99 Exploring Operation: 72/1=72, Resulting Numbers: [99, 72] Generated Node #0,1,2: 99:[99, 72] Operation: 72/1=72 Exploring Operation: 72+1=73, Resulting Numbers: [99, 73] Generated Node #0,1,3: 99:[99, 73] Operation: 72+1=73 Exploring Operation: 72*1=72, Resulting Numbers: [99, 72] Generated Node #0,1,4: 99:[99, 72] Operation: 72*1=72 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[1, 27], Operations: ['51/51=1', '99-72=27'] Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,99 unequal: No Solution Exploring Operation: 1+27=28, Resulting Numbers: [28] 28,99 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,99 unequal: No Solution Exploring Operation: 1*27=27, Resulting Numbers: [27] 27,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 99:[99, 73], Operations: ['51/51=1', '72+1=73'] Exploring Operation: 99*73=7227, Resulting Numbers: [7227] 7227,99 unequal: No Solution Exploring Operation: 99+73=172, Resulting Numbers: [172] 172,99 unequal: No Solution Exploring Operation: 99-73=26, Resulting Numbers: [26] 26,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[72, 99], Operations: ['51/51=1', '99*1=99'] Exploring Operation: 72*99=7128, Resulting Numbers: [7128] 7128,99 unequal: No Solution Exploring Operation: 72+99=171, Resulting Numbers: [171] 171,99 unequal: No Solution Exploring Operation: 99-72=27, Resulting Numbers: [27] 27,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 99:[99, 72], Operations: ['51/51=1', '72/1=72'] Exploring Operation: 99+72=171, Resulting Numbers: [171] 171,99 unequal: No Solution Exploring Operation: 99-72=27, Resulting Numbers: [27] 27,99 unequal: No Solution Exploring Operation: 99*72=7128, Resulting Numbers: [7128] 7128,99 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 #0,1,4 Current State: 99:[99, 72], Operations: ['51/51=1', '72*1=72'] Exploring Operation: 99*72=7128, Resulting Numbers: [7128] 7128,99 unequal: No Solution Exploring Operation: 99+72=171, Resulting Numbers: [171] 171,99 unequal: No Solution Exploring Operation: 99-72=27, Resulting Numbers: [27] 27,99 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: 99:[72, 99, 102], Operations: ['51+51=102'] Exploring Operation: 72+99=171, Resulting Numbers: [102, 171] Generated Node #0,0,0: 99:[102, 171] Operation: 72+99=171 Exploring Operation: 102-72=30, Resulting Numbers: [99, 30] Generated Node #0,0,1: 99:[99, 30] Operation: 102-72=30 Exploring Operation: 99-72=27, Resulting Numbers: [102, 27] Generated Node #0,0,2: 99:[102, 27] Operation: 99-72=27 Exploring Operation: 102-99=3, Resulting Numbers: [72, 3] Generated Node #0,0,3: 99:[72, 3] Operation: 102-99=3 Exploring Operation: 72+102=174, Resulting Numbers: [99, 174] Generated Node #0,0,4: 99:[99, 174] Operation: 72+102=174 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[99, 30], Operations: ['51+51=102', '102-72=30'] Exploring Operation: 99+30=129, Resulting Numbers: [129] 129,99 unequal: No Solution Exploring Operation: 99*30=2970, Resulting Numbers: [2970] 2970,99 unequal: No Solution Exploring Operation: 99-30=69, Resulting Numbers: [69] 69,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 99:[102, 27], Operations: ['51+51=102', '99-72=27'] Exploring Operation: 102-27=75, Resulting Numbers: [75] 75,99 unequal: No Solution Exploring Operation: 102*27=2754, Resulting Numbers: [2754] 2754,99 unequal: No Solution Exploring Operation: 102+27=129, Resulting Numbers: [129] 129,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 99:[72, 3], Operations: ['51+51=102', '102-99=3'] Exploring Operation: 72*3=216, Resulting Numbers: [216] 216,99 unequal: No Solution Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,99 unequal: No Solution Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,99 unequal: No Solution Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[102, 171], Operations: ['51+51=102', '72+99=171'] Exploring Operation: 102*171=17442, Resulting Numbers: [17442] 17442,99 unequal: No Solution Exploring Operation: 102+171=273, Resulting Numbers: [273] 273,99 unequal: No Solution Exploring Operation: 171-102=69, Resulting Numbers: [69] 69,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 99:[99, 174], Operations: ['51+51=102', '72+102=174'] Exploring Operation: 99+174=273, Resulting Numbers: [273] 273,99 unequal: No Solution Exploring Operation: 99*174=17226, Resulting Numbers: [17226] 17226,99 unequal: No Solution Exploring Operation: 174-99=75, Resulting Numbers: [75] 75,99 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: 99:[72, 99, 0], Operations: ['51-51=0'] Exploring Operation: 72-0=72, Resulting Numbers: [99, 72] Generated Node #0,2,0: 99:[99, 72] Operation: 72-0=72 Exploring Operation: 72+0=72, Resulting Numbers: [99, 72] Generated Node #0,2,1: 99:[99, 72] Operation: 72+0=72 Exploring Operation: 99-72=27, Resulting Numbers: [0, 27] Generated Node #0,2,2: 99:[0, 27] Operation: 99-72=27 Exploring Operation: 72*0=0, Resulting Numbers: [99, 0] Generated Node #0,2,3: 99:[99, 0] Operation: 72*0=0 Exploring Operation: 99+0=99, Resulting Numbers: [72, 99] Generated Node #0,2,4: 99:[72, 99] Operation: 99+0=99 Moving to Node #0,4,3 Current State: 99:[99, 30], Operations: ['72-51=21', '51-21=30'] Exploring Operation: 99-30=69, Resulting Numbers: [69] 69,99 unequal: No Solution Exploring Operation: 99+30=129, Resulting Numbers: [129] 129,99 unequal: No Solution Exploring Operation: 99*30=2970, Resulting Numbers: [2970] 2970,99 unequal: No Solution Moving to Node #0,2,3 Current State: 99:[99, 0], Operations: ['51-51=0', '72*0=0'] Exploring Operation: 99+0=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[72, 51, 51, 99], Operations: [] Exploring Operation: 51-51=0, Resulting Numbers: [72, 99, 0] Generated Node #0,2: 99:[72, 99, 0] Operation: 51-51=0 Moving to Node #0,2 Current State: 99:[72, 99, 0], Operations: ['51-51=0'] Exploring Operation: 72*0=0, Resulting Numbers: [99, 0] Generated Node #0,2,3: 99:[99, 0] Operation: 72*0=0 Moving to Node #0,2,3 Current State: 99:[99, 0], Operations: ['51-51=0', '72*0=0'] Exploring Operation: 99+0=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
0.926215
hs_5
mult_heuristic
[ 90, 87, 27, 65 ]
16
[ "90-87=3", "27*3=81", "81-65=16" ]
Current State: 16:[90, 87, 27, 65], Operations: [] Exploring Operation: 90-87=3, Resulting Numbers: [27, 65, 3] Generated Node #2: [27, 65, 3] from Operation: 90-87=3 Current State: 16:[27, 65, 3], Operations: ['90-87=3'] Exploring Operation: 27*3=81, Resulting Numbers: [65, 81] Generated Node #3: [65, 81] from Operation: 27*3=81 Current State: 16:[65, 81], Operations: ['90-87=3', '27*3=81'] Exploring Operation: 81-65=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[90, 87, 27, 65], Operations: [] Exploring Operation: 87-65=22, Resulting Numbers: [90, 27, 22] Generated Node #0,0: 16:[90, 27, 22] Operation: 87-65=22 Exploring Operation: 90-27=63, Resulting Numbers: [87, 65, 63] Generated Node #0,1: 16:[87, 65, 63] Operation: 90-27=63 Exploring Operation: 90-87=3, Resulting Numbers: [27, 65, 3] Generated Node #0,2: 16:[27, 65, 3] Operation: 90-87=3 Exploring Operation: 90-65=25, Resulting Numbers: [87, 27, 25] Generated Node #0,3: 16:[87, 27, 25] Operation: 90-65=25 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[27, 65, 3], Operations: ['90-87=3'] Exploring Operation: 65-3=62, Resulting Numbers: [27, 62] Generated Node #0,2,0: 16:[27, 62] Operation: 65-3=62 Exploring Operation: 65-27=38, Resulting Numbers: [3, 38] Generated Node #0,2,1: 16:[3, 38] Operation: 65-27=38 Exploring Operation: 27-3=24, Resulting Numbers: [65, 24] Generated Node #0,2,2: 16:[65, 24] Operation: 27-3=24 Exploring Operation: 27/3=9, Resulting Numbers: [65, 9] Generated Node #0,2,3: 16:[65, 9] Operation: 27/3=9 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 16:[3, 38], Operations: ['90-87=3', '65-27=38'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,16 unequal: No Solution Exploring Operation: 3*38=114, Resulting Numbers: [114] 114,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 16:[65, 9], Operations: ['90-87=3', '27/3=9'] Exploring Operation: 65*9=585, Resulting Numbers: [585] 585,16 unequal: No Solution Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,16 unequal: No Solution Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 16:[27, 62], Operations: ['90-87=3', '65-3=62'] Exploring Operation: 62-27=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 27*62=1674, Resulting Numbers: [1674] 1674,16 unequal: No Solution Exploring Operation: 27+62=89, Resulting Numbers: [89] 89,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 16:[65, 24], Operations: ['90-87=3', '27-3=24'] Exploring Operation: 65+24=89, Resulting Numbers: [89] 89,16 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,16 unequal: No Solution Exploring Operation: 65*24=1560, Resulting Numbers: [1560] 1560,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[90, 27, 22], Operations: ['87-65=22'] Exploring Operation: 90+27=117, Resulting Numbers: [22, 117] Generated Node #0,0,0: 16:[22, 117] Operation: 90+27=117 Exploring Operation: 90-22=68, Resulting Numbers: [27, 68] Generated Node #0,0,1: 16:[27, 68] Operation: 90-22=68 Exploring Operation: 27-22=5, Resulting Numbers: [90, 5] Generated Node #0,0,2: 16:[90, 5] Operation: 27-22=5 Exploring Operation: 90-27=63, Resulting Numbers: [22, 63] Generated Node #0,0,3: 16:[22, 63] Operation: 90-27=63 Moving to Node #0,0,3 Current State: 16:[22, 63], Operations: ['87-65=22', '90-27=63'] Exploring Operation: 22*63=1386, Resulting Numbers: [1386] 1386,16 unequal: No Solution Exploring Operation: 22+63=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[27, 68], Operations: ['87-65=22', '90-22=68'] Exploring Operation: 68-27=41, Resulting Numbers: [41] 41,16 unequal: No Solution Exploring Operation: 27+68=95, Resulting Numbers: [95] 95,16 unequal: No Solution Exploring Operation: 27*68=1836, Resulting Numbers: [1836] 1836,16 unequal: No Solution Moving to Node #0,0,2 Current State: 16:[90, 5], Operations: ['87-65=22', '27-22=5'] Exploring Operation: 90*5=450, Resulting Numbers: [450] 450,16 unequal: No Solution Exploring Operation: 90+5=95, Resulting Numbers: [95] 95,16 unequal: No Solution Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,16 unequal: No Solution Exploring Operation: 90-5=85, Resulting Numbers: [85] 85,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[22, 117], Operations: ['87-65=22', '90+27=117'] Exploring Operation: 22+117=139, Resulting Numbers: [139] 139,16 unequal: No Solution Exploring Operation: 117-22=95, Resulting Numbers: [95] 95,16 unequal: No Solution Exploring Operation: 22*117=2574, Resulting Numbers: [2574] 2574,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 16:[87, 27, 25], Operations: ['90-65=25'] Exploring Operation: 87+27=114, Resulting Numbers: [25, 114] Generated Node #0,3,0: 16:[25, 114] Operation: 87+27=114 Exploring Operation: 87-27=60, Resulting Numbers: [25, 60] Generated Node #0,3,1: 16:[25, 60] Operation: 87-27=60 Exploring Operation: 27-25=2, Resulting Numbers: [87, 2] Generated Node #0,3,2: 16:[87, 2] Operation: 27-25=2 Exploring Operation: 87-25=62, Resulting Numbers: [27, 62] Generated Node #0,3,3: 16:[27, 62] Operation: 87-25=62 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 16:[25, 60], Operations: ['90-65=25', '87-27=60'] Exploring Operation: 25+60=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 25*60=1500, Resulting Numbers: [1500] 1500,16 unequal: No Solution Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 16:[27, 62], Operations: ['90-65=25', '87-25=62'] Exploring Operation: 62-27=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 27+62=89, Resulting Numbers: [89] 89,16 unequal: No Solution Exploring Operation: 27*62=1674, Resulting Numbers: [1674] 1674,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 16:[87, 2], Operations: ['90-65=25', '27-25=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,16 unequal: No Solution Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 16:[25, 114], Operations: ['90-65=25', '87+27=114'] Exploring Operation: 25*114=2850, Resulting Numbers: [2850] 2850,16 unequal: No Solution Exploring Operation: 25+114=139, Resulting Numbers: [139] 139,16 unequal: No Solution Exploring Operation: 114-25=89, Resulting Numbers: [89] 89,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[87, 65, 63], Operations: ['90-27=63'] Exploring Operation: 87-65=22, Resulting Numbers: [63, 22] Generated Node #0,1,0: 16:[63, 22] Operation: 87-65=22 Exploring Operation: 65-63=2, Resulting Numbers: [87, 2] Generated Node #0,1,1: 16:[87, 2] Operation: 65-63=2 Exploring Operation: 87-63=24, Resulting Numbers: [65, 24] Generated Node #0,1,2: 16:[65, 24] Operation: 87-63=24 Exploring Operation: 87+65=152, Resulting Numbers: [63, 152] Generated Node #0,1,3: 16:[63, 152] Operation: 87+65=152 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[63, 22], Operations: ['90-27=63', '87-65=22'] Exploring Operation: 63+22=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,16 unequal: No Solution Exploring Operation: 63*22=1386, Resulting Numbers: [1386] 1386,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 16:[65, 24], Operations: ['90-27=63', '87-63=24'] Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,16 unequal: No Solution Exploring Operation: 65*24=1560, Resulting Numbers: [1560] 1560,16 unequal: No Solution Exploring Operation: 65+24=89, Resulting Numbers: [89] 89,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[87, 2], Operations: ['90-27=63', '65-63=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,16 unequal: No Solution Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,16 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 16:[63, 152], Operations: ['90-27=63', '87+65=152'] Exploring Operation: 63*152=9576, Resulting Numbers: [9576] 9576,16 unequal: No Solution Exploring Operation: 63+152=215, Resulting Numbers: [215] 215,16 unequal: No Solution Exploring Operation: 152-63=89, Resulting Numbers: [89] 89,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 54, 22, 51, 47 ]
19
[ "54+22=76", "51-47=4", "76/4=19" ]
Current State: 19:[54, 22, 51, 47], Operations: [] Exploring Operation: 54+22=76, Resulting Numbers: [51, 47, 76] Generated Node #2: [51, 47, 76] from Operation: 54+22=76 Current State: 19:[51, 47, 76], Operations: ['54+22=76'] Exploring Operation: 51-47=4, Resulting Numbers: [76, 4] Generated Node #3: [76, 4] from Operation: 51-47=4 Current State: 19:[76, 4], Operations: ['54+22=76', '51-47=4'] Exploring Operation: 76/4=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[54, 22, 51, 47], Operations: [] Exploring Operation: 54-51=3, Resulting Numbers: [22, 47, 3] Generated Node #0,0: 19:[22, 47, 3] Operation: 54-51=3 Exploring Operation: 54-22=32, Resulting Numbers: [51, 47, 32] Generated Node #0,1: 19:[51, 47, 32] Operation: 54-22=32 Exploring Operation: 51-47=4, Resulting Numbers: [54, 22, 4] Generated Node #0,2: 19:[54, 22, 4] Operation: 51-47=4 Exploring Operation: 54-47=7, Resulting Numbers: [22, 51, 7] Generated Node #0,3: 19:[22, 51, 7] Operation: 54-47=7 Moving to Node #0,0 Current State: 19:[22, 47, 3], Operations: ['54-51=3'] Exploring Operation: 47-22=25, Resulting Numbers: [3, 25] Generated Node #0,0,0: 19:[3, 25] Operation: 47-22=25 Exploring Operation: 22+3=25, Resulting Numbers: [47, 25] Generated Node #0,0,1: 19:[47, 25] Operation: 22+3=25 Exploring Operation: 47-3=44, Resulting Numbers: [22, 44] Generated Node #0,0,2: 19:[22, 44] Operation: 47-3=44 Exploring Operation: 22-3=19, Resulting Numbers: [47, 19] Generated Node #0,0,3: 19:[47, 19] Operation: 22-3=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[3, 25], Operations: ['54-51=3', '47-22=25'] Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,19 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,19 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 #0,0,2 Current State: 19:[22, 44], Operations: ['54-51=3', '47-3=44'] Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 22*44=968, Resulting Numbers: [968] 968,19 unequal: No Solution Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,19 unequal: No Solution Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,19 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 #0,0,3 Current State: 19:[47, 19], Operations: ['54-51=3', '22-3=19'] Exploring Operation: 47-19=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 47+19=66, Resulting Numbers: [66] 66,19 unequal: No Solution Exploring Operation: 47*19=893, Resulting Numbers: [893] 893,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 19:[47, 25], Operations: ['54-51=3', '22+3=25'] Exploring Operation: 47+25=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 47*25=1175, Resulting Numbers: [1175] 1175,19 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: 19:[22, 51, 7], Operations: ['54-47=7'] Exploring Operation: 22-7=15, Resulting Numbers: [51, 15] Generated Node #0,3,0: 19:[51, 15] Operation: 22-7=15 Exploring Operation: 51-22=29, Resulting Numbers: [7, 29] Generated Node #0,3,1: 19:[7, 29] Operation: 51-22=29 Exploring Operation: 51-7=44, Resulting Numbers: [22, 44] Generated Node #0,3,2: 19:[22, 44] Operation: 51-7=44 Exploring Operation: 22+7=29, Resulting Numbers: [51, 29] Generated Node #0,3,3: 19:[51, 29] Operation: 22+7=29 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 19:[7, 29], Operations: ['54-47=7', '51-22=29'] Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,19 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,19 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 #0,3,2 Current State: 19:[22, 44], Operations: ['54-47=7', '51-7=44'] Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 22*44=968, Resulting Numbers: [968] 968,19 unequal: No Solution Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,19 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 #0,3,0 Current State: 19:[51, 15], Operations: ['54-47=7', '22-7=15'] Exploring Operation: 51*15=765, Resulting Numbers: [765] 765,19 unequal: No Solution Exploring Operation: 51-15=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 51+15=66, Resulting Numbers: [66] 66,19 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 #0,3,3 Current State: 19:[51, 29], Operations: ['54-47=7', '22+7=29'] Exploring Operation: 51*29=1479, Resulting Numbers: [1479] 1479,19 unequal: No Solution Exploring Operation: 51-29=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 51+29=80, Resulting Numbers: [80] 80,19 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: 19:[54, 22, 4], Operations: ['51-47=4'] Exploring Operation: 54-22=32, Resulting Numbers: [4, 32] Generated Node #0,2,0: 19:[4, 32] Operation: 54-22=32 Exploring Operation: 22-4=18, Resulting Numbers: [54, 18] Generated Node #0,2,1: 19:[54, 18] Operation: 22-4=18 Exploring Operation: 54-4=50, Resulting Numbers: [22, 50] Generated Node #0,2,2: 19:[22, 50] Operation: 54-4=50 Exploring Operation: 54+4=58, Resulting Numbers: [22, 58] Generated Node #0,2,3: 19:[22, 58] Operation: 54+4=58 Moving to Node #0,1 Current State: 19:[51, 47, 32], Operations: ['54-22=32'] Exploring Operation: 51-32=19, Resulting Numbers: [47, 19] Generated Node #0,1,0: 19:[47, 19] Operation: 51-32=19 Exploring Operation: 47-32=15, Resulting Numbers: [51, 15] Generated Node #0,1,1: 19:[51, 15] Operation: 47-32=15 Exploring Operation: 51+47=98, Resulting Numbers: [32, 98] Generated Node #0,1,2: 19:[32, 98] Operation: 51+47=98 Exploring Operation: 51-47=4, Resulting Numbers: [32, 4] Generated Node #0,1,3: 19:[32, 4] Operation: 51-47=4 Moving to Node #0,2,0 Current State: 19:[4, 32], Operations: ['51-47=4', '54-22=32'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,19 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,19 unequal: No Solution Moving to Node #0,1,3 Current State: 19:[32, 4], Operations: ['54-22=32', '51-47=4'] Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 32*4=128, Resulting Numbers: [128] 128,19 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,19 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,19 unequal: No Solution Moving to Node #0,1,0 Current State: 19:[47, 19], Operations: ['54-22=32', '51-32=19'] Exploring Operation: 47-19=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 47*19=893, Resulting Numbers: [893] 893,19 unequal: No Solution Exploring Operation: 47+19=66, Resulting Numbers: [66] 66,19 unequal: No Solution Moving to Node #0,2,2 Current State: 19:[22, 50], Operations: ['51-47=4', '54-4=50'] Exploring Operation: 22+50=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 22*50=1100, Resulting Numbers: [1100] 1100,19 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,19 unequal: No Solution Moving to Node #0,1,1 Current State: 19:[51, 15], Operations: ['54-22=32', '47-32=15'] Exploring Operation: 51*15=765, Resulting Numbers: [765] 765,19 unequal: No Solution Exploring Operation: 51-15=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 51+15=66, Resulting Numbers: [66] 66,19 unequal: No Solution Moving to Node #0,2,1 Current State: 19:[54, 18], Operations: ['51-47=4', '22-4=18'] Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 54*18=972, Resulting Numbers: [972] 972,19 unequal: No Solution Exploring Operation: 54+18=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,19 unequal: No Solution Moving to Node #0,2,3 Current State: 19:[22, 58], Operations: ['51-47=4', '54+4=58'] Exploring Operation: 22*58=1276, Resulting Numbers: [1276] 1276,19 unequal: No Solution Exploring Operation: 58-22=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 22+58=80, Resulting Numbers: [80] 80,19 unequal: No Solution Moving to Node #0,1,2 Current State: 19:[32, 98], Operations: ['54-22=32', '51+47=98'] Exploring Operation: 32*98=3136, Resulting Numbers: [3136] 3136,19 unequal: No Solution Exploring Operation: 98-32=66, Resulting Numbers: [66] 66,19 unequal: No Solution Exploring Operation: 32+98=130, Resulting Numbers: [130] 130,19 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 23, 70, 10, 57 ]
46
[ "23+70=93", "57-10=47", "93-47=46" ]
Current State: 46:[23, 70, 10, 57], Operations: [] Exploring Operation: 23+70=93, Resulting Numbers: [10, 57, 93] Generated Node #2: [10, 57, 93] from Operation: 23+70=93 Current State: 46:[10, 57, 93], Operations: ['23+70=93'] Exploring Operation: 57-10=47, Resulting Numbers: [93, 47] Generated Node #3: [93, 47] from Operation: 57-10=47 Current State: 46:[93, 47], Operations: ['23+70=93', '57-10=47'] Exploring Operation: 93-47=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[23, 70, 10, 57], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [23, 57, 7] Generated Node #0,0: 46:[23, 57, 7] Operation: 70/10=7 Exploring Operation: 70-57=13, Resulting Numbers: [23, 10, 13] Generated Node #0,1: 46:[23, 10, 13] Operation: 70-57=13 Exploring Operation: 70-23=47, Resulting Numbers: [10, 57, 47] Generated Node #0,2: 46:[10, 57, 47] Operation: 70-23=47 Exploring Operation: 70-10=60, Resulting Numbers: [23, 57, 60] Generated Node #0,3: 46:[23, 57, 60] Operation: 70-10=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[23, 57, 7], Operations: ['70/10=7'] Exploring Operation: 57-7=50, Resulting Numbers: [23, 50] Generated Node #0,0,0: 46:[23, 50] Operation: 57-7=50 Exploring Operation: 23+7=30, Resulting Numbers: [57, 30] Generated Node #0,0,1: 46:[57, 30] Operation: 23+7=30 Exploring Operation: 23-7=16, Resulting Numbers: [57, 16] Generated Node #0,0,2: 46:[57, 16] Operation: 23-7=16 Exploring Operation: 57-23=34, Resulting Numbers: [7, 34] Generated Node #0,0,3: 46:[7, 34] Operation: 57-23=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[23, 50], Operations: ['70/10=7', '57-7=50'] Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 23*50=1150, Resulting Numbers: [1150] 1150,46 unequal: No Solution Exploring Operation: 23+50=73, Resulting Numbers: [73] 73,46 unequal: No Solution No 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: 46:[7, 34], Operations: ['70/10=7', '57-23=34'] Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,46 unequal: No Solution Exploring Operation: 7*34=238, Resulting Numbers: [238] 238,46 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,46 unequal: No Solution No 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: 46:[57, 30], Operations: ['70/10=7', '23+7=30'] Exploring Operation: 57-30=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 57*30=1710, Resulting Numbers: [1710] 1710,46 unequal: No Solution Exploring Operation: 57+30=87, Resulting Numbers: [87] 87,46 unequal: No Solution No 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: 46:[57, 16], Operations: ['70/10=7', '23-7=16'] Exploring Operation: 57-16=41, Resulting Numbers: [41] 41,46 unequal: No Solution Exploring Operation: 57*16=912, Resulting Numbers: [912] 912,46 unequal: No Solution Exploring Operation: 57+16=73, Resulting Numbers: [73] 73,46 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: 46:[23, 10, 13], Operations: ['70-57=13'] Exploring Operation: 10+13=23, Resulting Numbers: [23, 23] Generated Node #0,1,0: 46:[23, 23] Operation: 10+13=23 Exploring Operation: 23+13=36, Resulting Numbers: [10, 36] Generated Node #0,1,1: 46:[10, 36] Operation: 23+13=36 Exploring Operation: 13-10=3, Resulting Numbers: [23, 3] Generated Node #0,1,2: 46:[23, 3] Operation: 13-10=3 Exploring Operation: 23-13=10, Resulting Numbers: [10, 10] Generated Node #0,1,3: 46:[10, 10] Operation: 23-13=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[23, 23], Operations: ['70-57=13', '10+13=23'] Exploring Operation: 23*23=529, Resulting Numbers: [529] 529,46 unequal: No Solution Exploring Operation: 23-23=0, Resulting Numbers: [0] 0,46 unequal: No Solution Exploring Operation: 23/23=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 23+23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[23, 70, 10, 57], Operations: [] Exploring Operation: 70-57=13, Resulting Numbers: [23, 10, 13] Generated Node #0,1: 46:[23, 10, 13] Operation: 70-57=13 Moving to Node #0,1 Current State: 46:[23, 10, 13], Operations: ['70-57=13'] Exploring Operation: 10+13=23, Resulting Numbers: [23, 23] Generated Node #0,1,0: 46:[23, 23] Operation: 10+13=23 Moving to Node #0,1,0 Current State: 46:[23, 23], Operations: ['70-57=13', '10+13=23'] Exploring Operation: 23+23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 27, 50, 63, 63 ]
22
[ "50-27=23", "63/63=1", "23-1=22" ]
Current State: 22:[27, 50, 63, 63], Operations: [] Exploring Operation: 50-27=23, Resulting Numbers: [63, 63, 23] Generated Node #2: [63, 63, 23] from Operation: 50-27=23 Current State: 22:[63, 63, 23], Operations: ['50-27=23'] Exploring Operation: 63/63=1, Resulting Numbers: [23, 1] Generated Node #3: [23, 1] from Operation: 63/63=1 Current State: 22:[23, 1], Operations: ['50-27=23', '63/63=1'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[27, 50, 63, 63], Operations: [] Exploring Operation: 63-50=13, Resulting Numbers: [27, 63, 13] Generated Node #0,0: 22:[27, 63, 13] Operation: 63-50=13 Exploring Operation: 63/63=1, Resulting Numbers: [27, 50, 1] Generated Node #0,1: 22:[27, 50, 1] Operation: 63/63=1 Exploring Operation: 63-63=0, Resulting Numbers: [27, 50, 0] Generated Node #0,2: 22:[27, 50, 0] Operation: 63-63=0 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[27, 50, 1], Operations: ['63/63=1'] Exploring Operation: 50-1=49, Resulting Numbers: [27, 49] Generated Node #0,1,0: 22:[27, 49] Operation: 50-1=49 Exploring Operation: 50-27=23, Resulting Numbers: [1, 23] Generated Node #0,1,1: 22:[1, 23] Operation: 50-27=23 Exploring Operation: 27-1=26, Resulting Numbers: [50, 26] Generated Node #0,1,2: 22:[50, 26] Operation: 27-1=26 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 22:[1, 23], Operations: ['63/63=1', '50-27=23'] Exploring Operation: 1*23=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[27, 50, 63, 63], Operations: [] Exploring Operation: 63/63=1, Resulting Numbers: [27, 50, 1] Generated Node #0,1: 22:[27, 50, 1] Operation: 63/63=1 Moving to Node #0,1 Current State: 22:[27, 50, 1], Operations: ['63/63=1'] Exploring Operation: 50-27=23, Resulting Numbers: [1, 23] Generated Node #0,1,1: 22:[1, 23] Operation: 50-27=23 Moving to Node #0,1,1 Current State: 22:[1, 23], Operations: ['63/63=1', '50-27=23'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 14, 8, 17, 82 ]
43
[ "14+8=22", "82-17=65", "65-22=43" ]
Current State: 43:[14, 8, 17, 82], Operations: [] Exploring Operation: 14+8=22, Resulting Numbers: [17, 82, 22] Generated Node #2: [17, 82, 22] from Operation: 14+8=22 Current State: 43:[17, 82, 22], Operations: ['14+8=22'] Exploring Operation: 82-17=65, Resulting Numbers: [22, 65] Generated Node #3: [22, 65] from Operation: 82-17=65 Current State: 43:[22, 65], Operations: ['14+8=22', '82-17=65'] Exploring Operation: 65-22=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[14, 8, 17, 82], Operations: [] Exploring Operation: 14+17=31, Resulting Numbers: [8, 82, 31] Generated Node #0,0: 43:[8, 82, 31] Operation: 14+17=31 Exploring Operation: 14+8=22, Resulting Numbers: [17, 82, 22] Generated Node #0,1: 43:[17, 82, 22] Operation: 14+8=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[8, 82, 31], Operations: ['14+17=31'] Exploring Operation: 82-8=74, Resulting Numbers: [31, 74] Generated Node #0,0,0: 43:[31, 74] Operation: 82-8=74 Exploring Operation: 8+31=39, Resulting Numbers: [82, 39] Generated Node #0,0,1: 43:[82, 39] Operation: 8+31=39 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[31, 74], Operations: ['14+17=31', '82-8=74'] Exploring Operation: 31+74=105, Resulting Numbers: [105] 105,43 unequal: No Solution Exploring Operation: 74-31=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[14, 8, 17, 82], Operations: [] Exploring Operation: 14+17=31, Resulting Numbers: [8, 82, 31] Generated Node #0,0: 43:[8, 82, 31] Operation: 14+17=31 Moving to Node #0,0 Current State: 43:[8, 82, 31], Operations: ['14+17=31'] Exploring Operation: 82-8=74, Resulting Numbers: [31, 74] Generated Node #0,0,0: 43:[31, 74] Operation: 82-8=74 Moving to Node #0,0,0 Current State: 43:[31, 74], Operations: ['14+17=31', '82-8=74'] Exploring Operation: 74-31=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 68, 6, 39, 73 ]
39
[ "68+6=74", "74-73=1", "39*1=39" ]
Current State: 39:[68, 6, 39, 73], Operations: [] Exploring Operation: 68+6=74, Resulting Numbers: [39, 73, 74] Generated Node #2: [39, 73, 74] from Operation: 68+6=74 Current State: 39:[39, 73, 74], Operations: ['68+6=74'] Exploring Operation: 74-73=1, Resulting Numbers: [39, 1] Generated Node #3: [39, 1] from Operation: 74-73=1 Current State: 39:[39, 1], Operations: ['68+6=74', '74-73=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[68, 6, 39, 73], Operations: [] Exploring Operation: 73-39=34, Resulting Numbers: [68, 6, 34] Generated Node #0,0: 39:[68, 6, 34] Operation: 73-39=34 Exploring Operation: 73-68=5, Resulting Numbers: [6, 39, 5] Generated Node #0,1: 39:[6, 39, 5] Operation: 73-68=5 Moving to Node #0,1 Current State: 39:[6, 39, 5], Operations: ['73-68=5'] Exploring Operation: 6+5=11, Resulting Numbers: [39, 11] Generated Node #0,1,0: 39:[39, 11] Operation: 6+5=11 Exploring Operation: 6-5=1, Resulting Numbers: [39, 1] Generated Node #0,1,1: 39:[39, 1] Operation: 6-5=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[39, 11], Operations: ['73-68=5', '6+5=11'] Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,39 unequal: No Solution Exploring Operation: 39+11=50, Resulting Numbers: [50] 50,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[39, 1], Operations: ['73-68=5', '6-5=1'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[68, 6, 39, 73], Operations: [] Exploring Operation: 73-68=5, Resulting Numbers: [6, 39, 5] Generated Node #0,1: 39:[6, 39, 5] Operation: 73-68=5 Moving to Node #0,1 Current State: 39:[6, 39, 5], Operations: ['73-68=5'] Exploring Operation: 6-5=1, Resulting Numbers: [39, 1] Generated Node #0,1,1: 39:[39, 1] Operation: 6-5=1 Moving to Node #0,1,1 Current State: 39:[39, 1], Operations: ['73-68=5', '6-5=1'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 18, 89, 24, 6 ]
62
[ "18/6=3", "89-24=65", "65-3=62" ]
Current State: 62:[18, 89, 24, 6], Operations: [] Exploring Operation: 18/6=3, Resulting Numbers: [89, 24, 3] Generated Node #2: [89, 24, 3] from Operation: 18/6=3 Current State: 62:[89, 24, 3], Operations: ['18/6=3'] Exploring Operation: 89-24=65, Resulting Numbers: [3, 65] Generated Node #3: [3, 65] from Operation: 89-24=65 Current State: 62:[3, 65], Operations: ['18/6=3', '89-24=65'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[18, 89, 24, 6], Operations: [] Exploring Operation: 89-18=71, Resulting Numbers: [24, 6, 71] Generated Node #0,0: 62:[24, 6, 71] Operation: 89-18=71 Exploring Operation: 89-24=65, Resulting Numbers: [18, 6, 65] Generated Node #0,1: 62:[18, 6, 65] Operation: 89-24=65 Exploring Operation: 24-18=6, Resulting Numbers: [89, 6, 6] Generated Node #0,2: 62:[89, 6, 6] Operation: 24-18=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[24, 6, 71], Operations: ['89-18=71'] Exploring Operation: 24/6=4, Resulting Numbers: [71, 4] Generated Node #0,0,0: 62:[71, 4] Operation: 24/6=4 Exploring Operation: 24+6=30, Resulting Numbers: [71, 30] Generated Node #0,0,1: 62:[71, 30] Operation: 24+6=30 Exploring Operation: 71-6=65, Resulting Numbers: [24, 65] Generated Node #0,0,2: 62:[24, 65] Operation: 71-6=65 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 62:[71, 30], Operations: ['89-18=71', '24+6=30'] Exploring Operation: 71*30=2130, Resulting Numbers: [2130] 2130,62 unequal: No Solution Exploring Operation: 71+30=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 62:[24, 65], Operations: ['89-18=71', '71-6=65'] Exploring Operation: 24+65=89, Resulting Numbers: [89] 89,62 unequal: No Solution Exploring Operation: 24*65=1560, Resulting Numbers: [1560] 1560,62 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[71, 4], Operations: ['89-18=71', '24/6=4'] Exploring Operation: 71+4=75, Resulting Numbers: [75] 75,62 unequal: No Solution Exploring Operation: 71*4=284, Resulting Numbers: [284] 284,62 unequal: No Solution Exploring Operation: 71-4=67, Resulting Numbers: [67] 67,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[18, 6, 65], Operations: ['89-24=65'] Exploring Operation: 18-6=12, Resulting Numbers: [65, 12] Generated Node #0,1,0: 62:[65, 12] Operation: 18-6=12 Exploring Operation: 18/6=3, Resulting Numbers: [65, 3] Generated Node #0,1,1: 62:[65, 3] Operation: 18/6=3 Exploring Operation: 18+6=24, Resulting Numbers: [65, 24] Generated Node #0,1,2: 62:[65, 24] Operation: 18+6=24 Moving to Node #0,1,1 Current State: 62:[65, 3], Operations: ['89-24=65', '18/6=3'] Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,62 unequal: No Solution Exploring Operation: 65*3=195, Resulting Numbers: [195] 195,62 unequal: No Solution Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[18, 89, 24, 6], Operations: [] Exploring Operation: 89-24=65, Resulting Numbers: [18, 6, 65] Generated Node #0,1: 62:[18, 6, 65] Operation: 89-24=65 Moving to Node #0,1 Current State: 62:[18, 6, 65], Operations: ['89-24=65'] Exploring Operation: 18/6=3, Resulting Numbers: [65, 3] Generated Node #0,1,1: 62:[65, 3] Operation: 18/6=3 Moving to Node #0,1,1 Current State: 62:[65, 3], Operations: ['89-24=65', '18/6=3'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 18, 9, 82, 68 ]
54
[ "18/9=2", "68*2=136", "136-82=54" ]
Current State: 54:[18, 9, 82, 68], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [82, 68, 2] Generated Node #2: [82, 68, 2] from Operation: 18/9=2 Current State: 54:[82, 68, 2], Operations: ['18/9=2'] Exploring Operation: 68*2=136, Resulting Numbers: [82, 136] Generated Node #3: [82, 136] from Operation: 68*2=136 Current State: 54:[82, 136], Operations: ['18/9=2', '68*2=136'] Exploring Operation: 136-82=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[18, 9, 82, 68], Operations: [] Exploring Operation: 82-18=64, Resulting Numbers: [9, 68, 64] Generated Node #0,0: 54:[9, 68, 64] Operation: 82-18=64 Exploring Operation: 82-68=14, Resulting Numbers: [18, 9, 14] Generated Node #0,1: 54:[18, 9, 14] Operation: 82-68=14 Exploring Operation: 68-18=50, Resulting Numbers: [9, 82, 50] Generated Node #0,2: 54:[9, 82, 50] Operation: 68-18=50 Moving to Node #0,1 Current State: 54:[18, 9, 14], Operations: ['82-68=14'] Exploring Operation: 14-9=5, Resulting Numbers: [18, 5] Generated Node #0,1,0: 54:[18, 5] Operation: 14-9=5 Exploring Operation: 18+9=27, Resulting Numbers: [14, 27] Generated Node #0,1,1: 54:[14, 27] Operation: 18+9=27 Exploring Operation: 18-14=4, Resulting Numbers: [9, 4] Generated Node #0,1,2: 54:[9, 4] Operation: 18-14=4 Moving to Node #0,0 Current State: 54:[9, 68, 64], Operations: ['82-18=64'] Exploring Operation: 64-9=55, Resulting Numbers: [68, 55] Generated Node #0,0,0: 54:[68, 55] Operation: 64-9=55 Exploring Operation: 68-9=59, Resulting Numbers: [64, 59] Generated Node #0,0,1: 54:[64, 59] Operation: 68-9=59 Exploring Operation: 68-64=4, Resulting Numbers: [9, 4] Generated Node #0,0,2: 54:[9, 4] Operation: 68-64=4 Moving to Node #0,2 Current State: 54:[9, 82, 50], Operations: ['68-18=50'] Exploring Operation: 82-9=73, Resulting Numbers: [50, 73] Generated Node #0,2,0: 54:[50, 73] Operation: 82-9=73 Exploring Operation: 82-50=32, Resulting Numbers: [9, 32] Generated Node #0,2,1: 54:[9, 32] Operation: 82-50=32 Exploring Operation: 9+50=59, Resulting Numbers: [82, 59] Generated Node #0,2,2: 54:[82, 59] Operation: 9+50=59 Moving to Node #0,1,0 Current State: 54:[18, 5], Operations: ['82-68=14', '14-9=5'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,54 unequal: No Solution Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[9, 4], Operations: ['82-68=14', '18-14=4'] Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,54 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[9, 4], Operations: ['82-18=64', '68-64=4'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,54 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[14, 27], Operations: ['82-68=14', '18+9=27'] Exploring Operation: 14+27=41, Resulting Numbers: [41] 41,54 unequal: No Solution Exploring Operation: 14*27=378, Resulting Numbers: [378] 378,54 unequal: No Solution Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,54 unequal: No Solution Moving to Node #0,2,1 Current State: 54:[9, 32], Operations: ['68-18=50', '82-50=32'] Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,54 unequal: No Solution Exploring Operation: 9+32=41, Resulting Numbers: [41] 41,54 unequal: No Solution Exploring Operation: 9*32=288, Resulting Numbers: [288] 288,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[64, 59], Operations: ['82-18=64', '68-9=59'] Exploring Operation: 64-59=5, Resulting Numbers: [5] 5,54 unequal: No Solution Exploring Operation: 64+59=123, Resulting Numbers: [123] 123,54 unequal: No Solution Exploring Operation: 64*59=3776, Resulting Numbers: [3776] 3776,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[68, 55], Operations: ['82-18=64', '64-9=55'] Exploring Operation: 68*55=3740, Resulting Numbers: [3740] 3740,54 unequal: No Solution Exploring Operation: 68-55=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 68+55=123, Resulting Numbers: [123] 123,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[50, 73], Operations: ['68-18=50', '82-9=73'] Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,54 unequal: No Solution Exploring Operation: 50*73=3650, Resulting Numbers: [3650] 3650,54 unequal: No Solution Exploring Operation: 50+73=123, Resulting Numbers: [123] 123,54 unequal: No Solution Moving to Node #0,2,2 Current State: 54:[82, 59], Operations: ['68-18=50', '9+50=59'] Exploring Operation: 82+59=141, Resulting Numbers: [141] 141,54 unequal: No Solution Exploring Operation: 82*59=4838, Resulting Numbers: [4838] 4838,54 unequal: No Solution Exploring Operation: 82-59=23, Resulting Numbers: [23] 23,54 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 88, 15, 46, 77 ]
42
[ "88-15=73", "77-46=31", "73-31=42" ]
Current State: 42:[88, 15, 46, 77], Operations: [] Exploring Operation: 88-15=73, Resulting Numbers: [46, 77, 73] Generated Node #2: [46, 77, 73] from Operation: 88-15=73 Current State: 42:[46, 77, 73], Operations: ['88-15=73'] Exploring Operation: 77-46=31, Resulting Numbers: [73, 31] Generated Node #3: [73, 31] from Operation: 77-46=31 Current State: 42:[73, 31], Operations: ['88-15=73', '77-46=31'] Exploring Operation: 73-31=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[88, 15, 46, 77], Operations: [] Exploring Operation: 77-46=31, Resulting Numbers: [88, 15, 31] Generated Node #0,0: 42:[88, 15, 31] Operation: 77-46=31 Exploring Operation: 88-46=42, Resulting Numbers: [15, 77, 42] Generated Node #0,1: 42:[15, 77, 42] Operation: 88-46=42 Exploring Operation: 88-77=11, Resulting Numbers: [15, 46, 11] Generated Node #0,2: 42:[15, 46, 11] Operation: 88-77=11 Exploring Operation: 88-15=73, Resulting Numbers: [46, 77, 73] Generated Node #0,3: 42:[46, 77, 73] Operation: 88-15=73 Start Sub Search at level 1: Moving to Node #0,2 Current State: 42:[15, 46, 11], Operations: ['88-77=11'] Exploring Operation: 15+11=26, Resulting Numbers: [46, 26] Generated Node #0,2,0: 42:[46, 26] Operation: 15+11=26 Exploring Operation: 46-15=31, Resulting Numbers: [11, 31] Generated Node #0,2,1: 42:[11, 31] Operation: 46-15=31 Exploring Operation: 15-11=4, Resulting Numbers: [46, 4] Generated Node #0,2,2: 42:[46, 4] Operation: 15-11=4 Exploring Operation: 46-11=35, Resulting Numbers: [15, 35] Generated Node #0,2,3: 42:[15, 35] Operation: 46-11=35 Moving to Node #0,2,2 Current State: 42:[46, 4], Operations: ['88-77=11', '15-11=4'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[88, 15, 46, 77], Operations: [] Exploring Operation: 88-77=11, Resulting Numbers: [15, 46, 11] Generated Node #0,2: 42:[15, 46, 11] Operation: 88-77=11 Moving to Node #0,2 Current State: 42:[15, 46, 11], Operations: ['88-77=11'] Exploring Operation: 15-11=4, Resulting Numbers: [46, 4] Generated Node #0,2,2: 42:[46, 4] Operation: 15-11=4 Moving to Node #0,2,2 Current State: 42:[46, 4], Operations: ['88-77=11', '15-11=4'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 20, 60, 37, 1 ]
39
[ "60/20=3", "37-1=36", "3+36=39" ]
Current State: 39:[20, 60, 37, 1], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [37, 1, 3] Generated Node #2: [37, 1, 3] from Operation: 60/20=3 Current State: 39:[37, 1, 3], Operations: ['60/20=3'] Exploring Operation: 37-1=36, Resulting Numbers: [3, 36] Generated Node #3: [3, 36] from Operation: 37-1=36 Current State: 39:[3, 36], Operations: ['60/20=3', '37-1=36'] Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[20, 60, 37, 1], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [37, 1, 3] Generated Node #0,0: 39:[37, 1, 3] Operation: 60/20=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[37, 1, 3], Operations: ['60/20=3'] Exploring Operation: 37+1=38, Resulting Numbers: [3, 38] Generated Node #0,0,0: 39:[3, 38] Operation: 37+1=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[3, 38], Operations: ['60/20=3', '37+1=38'] Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,39 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_1
mult_heuristic
[ 7, 9, 18, 96 ]
91
[ "96-7=89", "18/9=2", "89+2=91" ]
Current State: 91:[7, 9, 18, 96], Operations: [] Exploring Operation: 96-7=89, Resulting Numbers: [9, 18, 89] Generated Node #2: [9, 18, 89] from Operation: 96-7=89 Current State: 91:[9, 18, 89], Operations: ['96-7=89'] Exploring Operation: 18/9=2, Resulting Numbers: [89, 2] Generated Node #3: [89, 2] from Operation: 18/9=2 Current State: 91:[89, 2], Operations: ['96-7=89', '18/9=2'] Exploring Operation: 89+2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[7, 9, 18, 96], Operations: [] Exploring Operation: 18-7=11, Resulting Numbers: [9, 96, 11] Generated Node #0,0: 91:[9, 96, 11] Operation: 18-7=11 Exploring Operation: 96-7=89, Resulting Numbers: [9, 18, 89] Generated Node #0,1: 91:[9, 18, 89] Operation: 96-7=89 Exploring Operation: 96-9=87, Resulting Numbers: [7, 18, 87] Generated Node #0,2: 91:[7, 18, 87] Operation: 96-9=87 Exploring Operation: 18-9=9, Resulting Numbers: [7, 96, 9] Generated Node #0,3: 91:[7, 96, 9] Operation: 18-9=9 Start Sub Search at level 1: Moving to Node #0,3 Current State: 91:[7, 96, 9], Operations: ['18-9=9'] Exploring Operation: 96-7=89, Resulting Numbers: [9, 89] Generated Node #0,3,0: 91:[9, 89] Operation: 96-7=89 Exploring Operation: 96-9=87, Resulting Numbers: [7, 87] Generated Node #0,3,1: 91:[7, 87] Operation: 96-9=87 Exploring Operation: 9-7=2, Resulting Numbers: [96, 2] Generated Node #0,3,2: 91:[96, 2] Operation: 9-7=2 Exploring Operation: 7+9=16, Resulting Numbers: [96, 16] Generated Node #0,3,3: 91:[96, 16] Operation: 7+9=16 Moving to Node #0,3,0 Current State: 91:[9, 89], Operations: ['18-9=9', '96-7=89'] Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,91 unequal: No Solution Exploring Operation: 9*89=801, Resulting Numbers: [801] 801,91 unequal: No Solution Exploring Operation: 9+89=98, Resulting Numbers: [98] 98,91 unequal: No Solution Moving to Node #0,3,1 Current State: 91:[7, 87], Operations: ['18-9=9', '96-9=87'] Exploring Operation: 7+87=94, Resulting Numbers: [94] 94,91 unequal: No Solution Exploring Operation: 87-7=80, Resulting Numbers: [80] 80,91 unequal: No Solution Exploring Operation: 7*87=609, Resulting Numbers: [609] 609,91 unequal: No Solution Moving to Node #0,3,3 Current State: 91:[96, 16], Operations: ['18-9=9', '7+9=16'] Exploring Operation: 96+16=112, Resulting Numbers: [112] 112,91 unequal: No Solution Exploring Operation: 96*16=1536, Resulting Numbers: [1536] 1536,91 unequal: No Solution Exploring Operation: 96/16=6, Resulting Numbers: [6] 6,91 unequal: No Solution Exploring Operation: 96-16=80, Resulting Numbers: [80] 80,91 unequal: No Solution Moving to Node #0,3,2 Current State: 91:[96, 2], Operations: ['18-9=9', '9-7=2'] Exploring Operation: 96*2=192, Resulting Numbers: [192] 192,91 unequal: No Solution Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,91 unequal: No Solution Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,91 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[9, 96, 11], Operations: ['18-7=11'] Exploring Operation: 9+11=20, Resulting Numbers: [96, 20] Generated Node #0,0,0: 91:[96, 20] Operation: 9+11=20 Exploring Operation: 96-11=85, Resulting Numbers: [9, 85] Generated Node #0,0,1: 91:[9, 85] Operation: 96-11=85 Exploring Operation: 96-9=87, Resulting Numbers: [11, 87] Generated Node #0,0,2: 91:[11, 87] Operation: 96-9=87 Exploring Operation: 11-9=2, Resulting Numbers: [96, 2] Generated Node #0,0,3: 91:[96, 2] Operation: 11-9=2 Moving to Node #0,0,2 Current State: 91:[11, 87], Operations: ['18-7=11', '96-9=87'] Exploring Operation: 11+87=98, Resulting Numbers: [98] 98,91 unequal: No Solution Exploring Operation: 11*87=957, Resulting Numbers: [957] 957,91 unequal: No Solution Exploring Operation: 87-11=76, Resulting Numbers: [76] 76,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[9, 85], Operations: ['18-7=11', '96-11=85'] Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,91 unequal: No Solution Exploring Operation: 9+85=94, Resulting Numbers: [94] 94,91 unequal: No Solution Exploring Operation: 9*85=765, Resulting Numbers: [765] 765,91 unequal: No Solution Moving to Node #0,0,3 Current State: 91:[96, 2], Operations: ['18-7=11', '11-9=2'] Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,91 unequal: No Solution Exploring Operation: 96*2=192, Resulting Numbers: [192] 192,91 unequal: No Solution Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,91 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,91 unequal: No Solution Moving to Node #0,0,0 Current State: 91:[96, 20], Operations: ['18-7=11', '9+11=20'] Exploring Operation: 96*20=1920, Resulting Numbers: [1920] 1920,91 unequal: No Solution Exploring Operation: 96-20=76, Resulting Numbers: [76] 76,91 unequal: No Solution Exploring Operation: 96+20=116, Resulting Numbers: [116] 116,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[9, 18, 89], Operations: ['96-7=89'] Exploring Operation: 9+18=27, Resulting Numbers: [89, 27] Generated Node #0,1,0: 91:[89, 27] Operation: 9+18=27 Exploring Operation: 18-9=9, Resulting Numbers: [89, 9] Generated Node #0,1,1: 91:[89, 9] Operation: 18-9=9 Exploring Operation: 9+89=98, Resulting Numbers: [18, 98] Generated Node #0,1,2: 91:[18, 98] Operation: 9+89=98 Exploring Operation: 18/9=2, Resulting Numbers: [89, 2] Generated Node #0,1,3: 91:[89, 2] Operation: 18/9=2 Moving to Node #0,1,1 Current State: 91:[89, 9], Operations: ['96-7=89', '18-9=9'] Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,91 unequal: No Solution Exploring Operation: 89+9=98, Resulting Numbers: [98] 98,91 unequal: No Solution Exploring Operation: 89*9=801, Resulting Numbers: [801] 801,91 unequal: No Solution Moving to Node #0,1,3 Current State: 91:[89, 2], Operations: ['96-7=89', '18/9=2'] Exploring Operation: 89*2=178, Resulting Numbers: [178] 178,91 unequal: No Solution Exploring Operation: 89+2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[7, 9, 18, 96], Operations: [] Exploring Operation: 96-7=89, Resulting Numbers: [9, 18, 89] Generated Node #0,1: 91:[9, 18, 89] Operation: 96-7=89 Moving to Node #0,1 Current State: 91:[9, 18, 89], Operations: ['96-7=89'] Exploring Operation: 18/9=2, Resulting Numbers: [89, 2] Generated Node #0,1,3: 91:[89, 2] Operation: 18/9=2 Moving to Node #0,1,3 Current State: 91:[89, 2], Operations: ['96-7=89', '18/9=2'] Exploring Operation: 89+2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.954861
hs_4
sum_heuristic
[ 44, 21, 7, 87 ]
57
[ "44-21=23", "87-7=80", "80-23=57" ]
Current State: 57:[44, 21, 7, 87], Operations: [] Exploring Operation: 44-21=23, Resulting Numbers: [7, 87, 23] Generated Node #2: [7, 87, 23] from Operation: 44-21=23 Current State: 57:[7, 87, 23], Operations: ['44-21=23'] Exploring Operation: 87-7=80, Resulting Numbers: [23, 80] Generated Node #3: [23, 80] from Operation: 87-7=80 Current State: 57:[23, 80], Operations: ['44-21=23', '87-7=80'] Exploring Operation: 80-23=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[44, 21, 7, 87], Operations: [] Exploring Operation: 87-21=66, Resulting Numbers: [44, 7, 66] Generated Node #0,0: 57:[44, 7, 66] Operation: 87-21=66 Exploring Operation: 44+7=51, Resulting Numbers: [21, 87, 51] Generated Node #0,1: 57:[21, 87, 51] Operation: 44+7=51 Exploring Operation: 44-21=23, Resulting Numbers: [7, 87, 23] Generated Node #0,2: 57:[7, 87, 23] Operation: 44-21=23 Exploring Operation: 87-44=43, Resulting Numbers: [21, 7, 43] Generated Node #0,3: 57:[21, 7, 43] Operation: 87-44=43 Exploring Operation: 87-7=80, Resulting Numbers: [44, 21, 80] Generated Node #0,4: 57:[44, 21, 80] Operation: 87-7=80 Start Sub Search at level 1: Moving to Node #0,3 Current State: 57:[21, 7, 43], Operations: ['87-44=43'] Exploring Operation: 43-21=22, Resulting Numbers: [7, 22] Generated Node #0,3,0: 57:[7, 22] Operation: 43-21=22 Exploring Operation: 21+43=64, Resulting Numbers: [7, 64] Generated Node #0,3,1: 57:[7, 64] Operation: 21+43=64 Exploring Operation: 7+43=50, Resulting Numbers: [21, 50] Generated Node #0,3,2: 57:[21, 50] Operation: 7+43=50 Exploring Operation: 21-7=14, Resulting Numbers: [43, 14] Generated Node #0,3,3: 57:[43, 14] Operation: 21-7=14 Exploring Operation: 21/7=3, Resulting Numbers: [43, 3] Generated Node #0,3,4: 57:[43, 3] Operation: 21/7=3 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 57:[7, 22], Operations: ['87-44=43', '43-21=22'] Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,57 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,57 unequal: No Solution Exploring Operation: 7*22=154, Resulting Numbers: [154] 154,57 unequal: No Solution No 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: 57:[21, 50], Operations: ['87-44=43', '7+43=50'] Exploring Operation: 21*50=1050, Resulting Numbers: [1050] 1050,57 unequal: No Solution Exploring Operation: 21+50=71, Resulting Numbers: [71] 71,57 unequal: No Solution Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,57 unequal: No Solution No 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: 57:[7, 64], Operations: ['87-44=43', '21+43=64'] Exploring Operation: 7*64=448, Resulting Numbers: [448] 448,57 unequal: No Solution Exploring Operation: 7+64=71, Resulting Numbers: [71] 71,57 unequal: No Solution Exploring Operation: 64-7=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[44, 21, 7, 87], Operations: [] Exploring Operation: 87-44=43, Resulting Numbers: [21, 7, 43] Generated Node #0,3: 57:[21, 7, 43] Operation: 87-44=43 Moving to Node #0,3 Current State: 57:[21, 7, 43], Operations: ['87-44=43'] Exploring Operation: 21+43=64, Resulting Numbers: [7, 64] Generated Node #0,3,1: 57:[7, 64] Operation: 21+43=64 Moving to Node #0,3,1 Current State: 57:[7, 64], Operations: ['87-44=43', '21+43=64'] Exploring Operation: 64-7=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 34, 12, 19, 24 ]
87
[ "34*24=816", "816/12=68", "19+68=87" ]
Current State: 87:[34, 12, 19, 24], Operations: [] Exploring Operation: 34*24=816, Resulting Numbers: [12, 19, 816] Generated Node #2: [12, 19, 816] from Operation: 34*24=816 Current State: 87:[12, 19, 816], Operations: ['34*24=816'] Exploring Operation: 816/12=68, Resulting Numbers: [19, 68] Generated Node #3: [19, 68] from Operation: 816/12=68 Current State: 87:[19, 68], Operations: ['34*24=816', '816/12=68'] Exploring Operation: 19+68=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[34, 12, 19, 24], Operations: [] Exploring Operation: 12+19=31, Resulting Numbers: [34, 24, 31] Generated Node #0,0: 87:[34, 24, 31] Operation: 12+19=31 Exploring Operation: 24-19=5, Resulting Numbers: [34, 12, 5] Generated Node #0,1: 87:[34, 12, 5] Operation: 24-19=5 Exploring Operation: 34-12=22, Resulting Numbers: [19, 24, 22] Generated Node #0,2: 87:[19, 24, 22] Operation: 34-12=22 Exploring Operation: 24/12=2, Resulting Numbers: [34, 19, 2] Generated Node #0,3: 87:[34, 19, 2] Operation: 24/12=2 Exploring Operation: 19-12=7, Resulting Numbers: [34, 24, 7] Generated Node #0,4: 87:[34, 24, 7] Operation: 19-12=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[34, 24, 31], Operations: ['12+19=31'] Exploring Operation: 34-24=10, Resulting Numbers: [31, 10] Generated Node #0,0,0: 87:[31, 10] Operation: 34-24=10 Exploring Operation: 31-24=7, Resulting Numbers: [34, 7] Generated Node #0,0,1: 87:[34, 7] Operation: 31-24=7 Exploring Operation: 34+31=65, Resulting Numbers: [24, 65] Generated Node #0,0,2: 87:[24, 65] Operation: 34+31=65 Exploring Operation: 34-31=3, Resulting Numbers: [24, 3] Generated Node #0,0,3: 87:[24, 3] Operation: 34-31=3 Exploring Operation: 34+24=58, Resulting Numbers: [31, 58] Generated Node #0,0,4: 87:[31, 58] Operation: 34+24=58 Moving to Node #0,0,3 Current State: 87:[24, 3], Operations: ['12+19=31', '34-31=3'] Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,87 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,87 unequal: No Solution Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,87 unequal: No Solution Moving to Node #0,0,1 Current State: 87:[34, 7], Operations: ['12+19=31', '31-24=7'] Exploring Operation: 34+7=41, Resulting Numbers: [41] 41,87 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,87 unequal: No Solution Exploring Operation: 34*7=238, Resulting Numbers: [238] 238,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[31, 10], Operations: ['12+19=31', '34-24=10'] Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,87 unequal: No Solution Exploring Operation: 31*10=310, Resulting Numbers: [310] 310,87 unequal: No Solution Exploring Operation: 31+10=41, Resulting Numbers: [41] 41,87 unequal: No Solution Moving to Node #0,0,2 Current State: 87:[24, 65], Operations: ['12+19=31', '34+31=65'] Exploring Operation: 24*65=1560, Resulting Numbers: [1560] 1560,87 unequal: No Solution Exploring Operation: 24+65=89, Resulting Numbers: [89] 89,87 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,87 unequal: No Solution Moving to Node #0,0,4 Current State: 87:[31, 58], Operations: ['12+19=31', '34+24=58'] Exploring Operation: 58-31=27, Resulting Numbers: [27] 27,87 unequal: No Solution Exploring Operation: 31*58=1798, Resulting Numbers: [1798] 1798,87 unequal: No Solution Exploring Operation: 31+58=89, Resulting Numbers: [89] 89,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 87:[34, 24, 7], Operations: ['19-12=7'] Exploring Operation: 34-24=10, Resulting Numbers: [7, 10] Generated Node #0,4,0: 87:[7, 10] Operation: 34-24=10 Exploring Operation: 24-7=17, Resulting Numbers: [34, 17] Generated Node #0,4,1: 87:[34, 17] Operation: 24-7=17 Exploring Operation: 34-7=27, Resulting Numbers: [24, 27] Generated Node #0,4,2: 87:[24, 27] Operation: 34-7=27 Exploring Operation: 24+7=31, Resulting Numbers: [34, 31] Generated Node #0,4,3: 87:[34, 31] Operation: 24+7=31 Exploring Operation: 34+7=41, Resulting Numbers: [24, 41] Generated Node #0,4,4: 87:[24, 41] Operation: 34+7=41 Moving to Node #0,4,2 Current State: 87:[24, 27], Operations: ['19-12=7', '34-7=27'] Exploring Operation: 24+27=51, Resulting Numbers: [51] 51,87 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,87 unequal: No Solution Exploring Operation: 24*27=648, Resulting Numbers: [648] 648,87 unequal: No Solution Moving to Node #0,4,3 Current State: 87:[34, 31], Operations: ['19-12=7', '24+7=31'] Exploring Operation: 34+31=65, Resulting Numbers: [65] 65,87 unequal: No Solution Exploring Operation: 34-31=3, Resulting Numbers: [3] 3,87 unequal: No Solution Exploring Operation: 34*31=1054, Resulting Numbers: [1054] 1054,87 unequal: No Solution Moving to Node #0,4,0 Current State: 87:[7, 10], Operations: ['19-12=7', '34-24=10'] Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,87 unequal: No Solution Moving to Node #0,4,1 Current State: 87:[34, 17], Operations: ['19-12=7', '24-7=17'] Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,87 unequal: No Solution Exploring Operation: 34*17=578, Resulting Numbers: [578] 578,87 unequal: No Solution Exploring Operation: 34+17=51, Resulting Numbers: [51] 51,87 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,87 unequal: No Solution Moving to Node #0,4,4 Current State: 87:[24, 41], Operations: ['19-12=7', '34+7=41'] Exploring Operation: 24*41=984, Resulting Numbers: [984] 984,87 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 24+41=65, Resulting Numbers: [65] 65,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[34, 12, 5], Operations: ['24-19=5'] Exploring Operation: 34-12=22, Resulting Numbers: [5, 22] Generated Node #0,1,0: 87:[5, 22] Operation: 34-12=22 Exploring Operation: 12+5=17, Resulting Numbers: [34, 17] Generated Node #0,1,1: 87:[34, 17] Operation: 12+5=17 Exploring Operation: 12-5=7, Resulting Numbers: [34, 7] Generated Node #0,1,2: 87:[34, 7] Operation: 12-5=7 Exploring Operation: 34-5=29, Resulting Numbers: [12, 29] Generated Node #0,1,3: 87:[12, 29] Operation: 34-5=29 Exploring Operation: 34+12=46, Resulting Numbers: [5, 46] Generated Node #0,1,4: 87:[5, 46] Operation: 34+12=46 Moving to Node #0,1,0 Current State: 87:[5, 22], Operations: ['24-19=5', '34-12=22'] Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,87 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,87 unequal: No Solution Moving to Node #0,1,3 Current State: 87:[12, 29], Operations: ['24-19=5', '34-5=29'] Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 12*29=348, Resulting Numbers: [348] 348,87 unequal: No Solution Exploring Operation: 12+29=41, Resulting Numbers: [41] 41,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[34, 7], Operations: ['24-19=5', '12-5=7'] Exploring Operation: 34*7=238, Resulting Numbers: [238] 238,87 unequal: No Solution Exploring Operation: 34+7=41, Resulting Numbers: [41] 41,87 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[34, 17], Operations: ['24-19=5', '12+5=17'] Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,87 unequal: No Solution Exploring Operation: 34*17=578, Resulting Numbers: [578] 578,87 unequal: No Solution Exploring Operation: 34+17=51, Resulting Numbers: [51] 51,87 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,87 unequal: No Solution Moving to Node #0,1,4 Current State: 87:[5, 46], Operations: ['24-19=5', '34+12=46'] Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,87 unequal: No Solution Exploring Operation: 5*46=230, Resulting Numbers: [230] 230,87 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 87:[34, 19, 2], Operations: ['24/12=2'] Exploring Operation: 34+2=36, Resulting Numbers: [19, 36] Generated Node #0,3,0: 87:[19, 36] Operation: 34+2=36 Exploring Operation: 19*2=38, Resulting Numbers: [34, 38] Generated Node #0,3,1: 87:[34, 38] Operation: 19*2=38 Exploring Operation: 19+2=21, Resulting Numbers: [34, 21] Generated Node #0,3,2: 87:[34, 21] Operation: 19+2=21 Exploring Operation: 34-2=32, Resulting Numbers: [19, 32] Generated Node #0,3,3: 87:[19, 32] Operation: 34-2=32 Exploring Operation: 34-19=15, Resulting Numbers: [2, 15] Generated Node #0,3,4: 87:[2, 15] Operation: 34-19=15 Moving to Node #0,3,2 Current State: 87:[34, 21], Operations: ['24/12=2', '19+2=21'] Exploring Operation: 34-21=13, Resulting Numbers: [13] 13,87 unequal: No Solution Exploring Operation: 34+21=55, Resulting Numbers: [55] 55,87 unequal: No Solution Exploring Operation: 34*21=714, Resulting Numbers: [714] 714,87 unequal: No Solution Moving to Node #0,3,4 Current State: 87:[2, 15], Operations: ['24/12=2', '34-19=15'] Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,87 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,87 unequal: No Solution Moving to Node #0,3,3 Current State: 87:[19, 32], Operations: ['24/12=2', '34-2=32'] Exploring Operation: 19+32=51, Resulting Numbers: [51] 51,87 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,87 unequal: No Solution Exploring Operation: 19*32=608, Resulting Numbers: [608] 608,87 unequal: No Solution Moving to Node #0,3,1 Current State: 87:[34, 38], Operations: ['24/12=2', '19*2=38'] Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,87 unequal: No Solution Exploring Operation: 34*38=1292, Resulting Numbers: [1292] 1292,87 unequal: No Solution Exploring Operation: 34+38=72, Resulting Numbers: [72] 72,87 unequal: No Solution Moving to Node #0,3,0 Current State: 87:[19, 36], Operations: ['24/12=2', '34+2=36'] Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,87 unequal: No Solution Exploring Operation: 19*36=684, Resulting Numbers: [684] 684,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[19, 24, 22], Operations: ['34-12=22'] Exploring Operation: 24-19=5, Resulting Numbers: [22, 5] Generated Node #0,2,0: 87:[22, 5] Operation: 24-19=5 Exploring Operation: 24-22=2, Resulting Numbers: [19, 2] Generated Node #0,2,1: 87:[19, 2] Operation: 24-22=2 Exploring Operation: 19+24=43, Resulting Numbers: [22, 43] Generated Node #0,2,2: 87:[22, 43] Operation: 19+24=43 Exploring Operation: 22-19=3, Resulting Numbers: [24, 3] Generated Node #0,2,3: 87:[24, 3] Operation: 22-19=3 Exploring Operation: 19+22=41, Resulting Numbers: [24, 41] Generated Node #0,2,4: 87:[24, 41] Operation: 19+22=41 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 87:[24, 3], Operations: ['34-12=22', '22-19=3'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,87 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,87 unequal: No Solution Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,87 unequal: No Solution No 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: 87:[22, 5], Operations: ['34-12=22', '24-19=5'] Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,87 unequal: No Solution Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,87 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,87 unequal: No Solution No 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: 87:[19, 2], Operations: ['34-12=22', '24-22=2'] Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,87 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 19+2=21, Resulting Numbers: [21] 21,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 87:[24, 41], Operations: ['34-12=22', '19+22=41'] Exploring Operation: 24+41=65, Resulting Numbers: [65] 65,87 unequal: No Solution Exploring Operation: 24*41=984, Resulting Numbers: [984] 984,87 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,87 unequal: No Solution No 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: 87:[22, 43], Operations: ['34-12=22', '19+24=43'] Exploring Operation: 43-22=21, Resulting Numbers: [21] 21,87 unequal: No Solution Exploring Operation: 22+43=65, Resulting Numbers: [65] 65,87 unequal: No Solution Exploring Operation: 22*43=946, Resulting Numbers: [946] 946,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 3, 58, 5, 12 ]
99
[ "3*12=36", "58+5=63", "36+63=99" ]
Current State: 99:[3, 58, 5, 12], Operations: [] Exploring Operation: 3*12=36, Resulting Numbers: [58, 5, 36] Generated Node #2: [58, 5, 36] from Operation: 3*12=36 Current State: 99:[58, 5, 36], Operations: ['3*12=36'] Exploring Operation: 58+5=63, Resulting Numbers: [36, 63] Generated Node #3: [36, 63] from Operation: 58+5=63 Current State: 99:[36, 63], Operations: ['3*12=36', '58+5=63'] Exploring Operation: 36+63=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[3, 58, 5, 12], Operations: [] Exploring Operation: 58-3=55, Resulting Numbers: [5, 12, 55] Generated Node #0,0: 99:[5, 12, 55] Operation: 58-3=55 Exploring Operation: 3+5=8, Resulting Numbers: [58, 12, 8] Generated Node #0,1: 99:[58, 12, 8] Operation: 3+5=8 Exploring Operation: 58-5=53, Resulting Numbers: [3, 12, 53] Generated Node #0,2: 99:[3, 12, 53] Operation: 58-5=53 Exploring Operation: 58-12=46, Resulting Numbers: [3, 5, 46] Generated Node #0,3: 99:[3, 5, 46] Operation: 58-12=46 Start Sub Search at level 1: Moving to Node #0,3 Current State: 99:[3, 5, 46], Operations: ['58-12=46'] Exploring Operation: 5-3=2, Resulting Numbers: [46, 2] Generated Node #0,3,0: 99:[46, 2] Operation: 5-3=2 Exploring Operation: 46-3=43, Resulting Numbers: [5, 43] Generated Node #0,3,1: 99:[5, 43] Operation: 46-3=43 Exploring Operation: 3+5=8, Resulting Numbers: [46, 8] Generated Node #0,3,2: 99:[46, 8] Operation: 3+5=8 Exploring Operation: 46-5=41, Resulting Numbers: [3, 41] Generated Node #0,3,3: 99:[3, 41] Operation: 46-5=41 Moving to Node #0,3,3 Current State: 99:[3, 41], Operations: ['58-12=46', '46-5=41'] Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,99 unequal: No Solution Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,99 unequal: No Solution Moving to Node #0,3,1 Current State: 99:[5, 43], Operations: ['58-12=46', '46-3=43'] Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,99 unequal: No Solution Exploring Operation: 5*43=215, Resulting Numbers: [215] 215,99 unequal: No Solution Moving to Node #0,3,2 Current State: 99:[46, 8], Operations: ['58-12=46', '3+5=8'] Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,99 unequal: No Solution Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 46*8=368, Resulting Numbers: [368] 368,99 unequal: No Solution Moving to Node #0,3,0 Current State: 99:[46, 2], Operations: ['58-12=46', '5-3=2'] Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,99 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[3, 12, 53], Operations: ['58-5=53'] Exploring Operation: 12-3=9, Resulting Numbers: [53, 9] Generated Node #0,2,0: 99:[53, 9] Operation: 12-3=9 Exploring Operation: 12/3=4, Resulting Numbers: [53, 4] Generated Node #0,2,1: 99:[53, 4] Operation: 12/3=4 Exploring Operation: 53-12=41, Resulting Numbers: [3, 41] Generated Node #0,2,2: 99:[3, 41] Operation: 53-12=41 Exploring Operation: 53-3=50, Resulting Numbers: [12, 50] Generated Node #0,2,3: 99:[12, 50] Operation: 53-3=50 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 99:[3, 41], Operations: ['58-5=53', '53-12=41'] Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,99 unequal: No Solution Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 99:[12, 50], Operations: ['58-5=53', '53-3=50'] Exploring Operation: 12*50=600, Resulting Numbers: [600] 600,99 unequal: No Solution Exploring Operation: 12+50=62, Resulting Numbers: [62] 62,99 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 99:[53, 9], Operations: ['58-5=53', '12-3=9'] Exploring Operation: 53+9=62, Resulting Numbers: [62] 62,99 unequal: No Solution Exploring Operation: 53*9=477, Resulting Numbers: [477] 477,99 unequal: No Solution Exploring Operation: 53-9=44, Resulting Numbers: [44] 44,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 99:[53, 4], Operations: ['58-5=53', '12/3=4'] Exploring Operation: 53*4=212, Resulting Numbers: [212] 212,99 unequal: No Solution Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,99 unequal: No Solution Exploring Operation: 53+4=57, Resulting Numbers: [57] 57,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[5, 12, 55], Operations: ['58-3=55'] Exploring Operation: 12-5=7, Resulting Numbers: [55, 7] Generated Node #0,0,0: 99:[55, 7] Operation: 12-5=7 Exploring Operation: 55-5=50, Resulting Numbers: [12, 50] Generated Node #0,0,1: 99:[12, 50] Operation: 55-5=50 Exploring Operation: 55-12=43, Resulting Numbers: [5, 43] Generated Node #0,0,2: 99:[5, 43] Operation: 55-12=43 Exploring Operation: 55/5=11, Resulting Numbers: [12, 11] Generated Node #0,0,3: 99:[12, 11] Operation: 55/5=11 Moving to Node #0,0,3 Current State: 99:[12, 11], Operations: ['58-3=55', '55/5=11'] Exploring Operation: 12*11=132, Resulting Numbers: [132] 132,99 unequal: No Solution Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,99 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[5, 43], Operations: ['58-3=55', '55-12=43'] Exploring Operation: 5*43=215, Resulting Numbers: [215] 215,99 unequal: No Solution Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[12, 50], Operations: ['58-3=55', '55-5=50'] Exploring Operation: 12*50=600, Resulting Numbers: [600] 600,99 unequal: No Solution Exploring Operation: 12+50=62, Resulting Numbers: [62] 62,99 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[55, 7], Operations: ['58-3=55', '12-5=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,99 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,99 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:[58, 12, 8], Operations: ['3+5=8'] Exploring Operation: 12*8=96, Resulting Numbers: [58, 96] Generated Node #0,1,0: 99:[58, 96] Operation: 12*8=96 Exploring Operation: 58-12=46, Resulting Numbers: [8, 46] Generated Node #0,1,1: 99:[8, 46] Operation: 58-12=46 Exploring Operation: 58-8=50, Resulting Numbers: [12, 50] Generated Node #0,1,2: 99:[12, 50] Operation: 58-8=50 Exploring Operation: 12-8=4, Resulting Numbers: [58, 4] Generated Node #0,1,3: 99:[58, 4] Operation: 12-8=4 Moving to Node #0,1,1 Current State: 99:[8, 46], Operations: ['3+5=8', '58-12=46'] Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 8*46=368, Resulting Numbers: [368] 368,99 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[12, 50], Operations: ['3+5=8', '58-8=50'] Exploring Operation: 12*50=600, Resulting Numbers: [600] 600,99 unequal: No Solution Exploring Operation: 12+50=62, Resulting Numbers: [62] 62,99 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,99 unequal: No Solution Moving to Node #0,1,3 Current State: 99:[58, 4], Operations: ['3+5=8', '12-8=4'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 58*4=232, Resulting Numbers: [232] 232,99 unequal: No Solution Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[58, 96], Operations: ['3+5=8', '12*8=96'] Exploring Operation: 96-58=38, Resulting Numbers: [38] 38,99 unequal: No Solution Exploring Operation: 58+96=154, Resulting Numbers: [154] 154,99 unequal: No Solution Exploring Operation: 58*96=5568, Resulting Numbers: [5568] 5568,99 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
[ 25, 51, 31, 4 ]
12
[ "25+51=76", "76/4=19", "31-19=12" ]
Current State: 12:[25, 51, 31, 4], Operations: [] Exploring Operation: 25+51=76, Resulting Numbers: [31, 4, 76] Generated Node #2: [31, 4, 76] from Operation: 25+51=76 Current State: 12:[31, 4, 76], Operations: ['25+51=76'] Exploring Operation: 76/4=19, Resulting Numbers: [31, 19] Generated Node #3: [31, 19] from Operation: 76/4=19 Current State: 12:[31, 19], Operations: ['25+51=76', '76/4=19'] Exploring Operation: 31-19=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[25, 51, 31, 4], Operations: [] Exploring Operation: 51-25=26, Resulting Numbers: [31, 4, 26] Generated Node #0,0: 12:[31, 4, 26] Operation: 51-25=26 Exploring Operation: 51-4=47, Resulting Numbers: [25, 31, 47] Generated Node #0,1: 12:[25, 31, 47] Operation: 51-4=47 Exploring Operation: 51-31=20, Resulting Numbers: [25, 4, 20] Generated Node #0,2: 12:[25, 4, 20] Operation: 51-31=20 Exploring Operation: 31-25=6, Resulting Numbers: [51, 4, 6] Generated Node #0,3: 12:[51, 4, 6] Operation: 31-25=6 Exploring Operation: 25-4=21, Resulting Numbers: [51, 31, 21] Generated Node #0,4: 12:[51, 31, 21] Operation: 25-4=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[25, 4, 20], Operations: ['51-31=20'] Exploring Operation: 25-20=5, Resulting Numbers: [4, 5] Generated Node #0,2,0: 12:[4, 5] Operation: 25-20=5 Exploring Operation: 20-4=16, Resulting Numbers: [25, 16] Generated Node #0,2,1: 12:[25, 16] Operation: 20-4=16 Exploring Operation: 25+4=29, Resulting Numbers: [20, 29] Generated Node #0,2,2: 12:[20, 29] Operation: 25+4=29 Exploring Operation: 20/4=5, Resulting Numbers: [25, 5] Generated Node #0,2,3: 12:[25, 5] Operation: 20/4=5 Exploring Operation: 25-4=21, Resulting Numbers: [20, 21] Generated Node #0,2,4: 12:[20, 21] Operation: 25-4=21 Moving to Node #0,2,0 Current State: 12:[4, 5], Operations: ['51-31=20', '25-20=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[25, 5], Operations: ['51-31=20', '20/4=5'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,12 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[25, 16], Operations: ['51-31=20', '20-4=16'] Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,12 unequal: No Solution Exploring Operation: 25*16=400, Resulting Numbers: [400] 400,12 unequal: No Solution Moving to Node #0,2,4 Current State: 12:[20, 21], Operations: ['51-31=20', '25-4=21'] Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 20*21=420, Resulting Numbers: [420] 420,12 unequal: No Solution Exploring Operation: 20+21=41, Resulting Numbers: [41] 41,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[20, 29], Operations: ['51-31=20', '25+4=29'] Exploring Operation: 20+29=49, Resulting Numbers: [49] 49,12 unequal: No Solution Exploring Operation: 20*29=580, Resulting Numbers: [580] 580,12 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,12 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 Current State: 12:[31, 4, 26], Operations: ['51-25=26'] Exploring Operation: 31+4=35, Resulting Numbers: [26, 35] Generated Node #0,0,0: 12:[26, 35] Operation: 31+4=35 Exploring Operation: 31-4=27, Resulting Numbers: [26, 27] Generated Node #0,0,1: 12:[26, 27] Operation: 31-4=27 Exploring Operation: 31-26=5, Resulting Numbers: [4, 5] Generated Node #0,0,2: 12:[4, 5] Operation: 31-26=5 Exploring Operation: 26-4=22, Resulting Numbers: [31, 22] Generated Node #0,0,3: 12:[31, 22] Operation: 26-4=22 Exploring Operation: 4+26=30, Resulting Numbers: [31, 30] Generated Node #0,0,4: 12:[31, 30] Operation: 4+26=30 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 12:[4, 5], Operations: ['51-25=26', '31-26=5'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 12:[26, 27], Operations: ['51-25=26', '31-4=27'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 26*27=702, Resulting Numbers: [702] 702,12 unequal: No Solution Exploring Operation: 26+27=53, Resulting Numbers: [53] 53,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 12:[31, 22], Operations: ['51-25=26', '26-4=22'] Exploring Operation: 31+22=53, Resulting Numbers: [53] 53,12 unequal: No Solution Exploring Operation: 31*22=682, Resulting Numbers: [682] 682,12 unequal: No Solution Exploring Operation: 31-22=9, Resulting Numbers: [9] 9,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[26, 35], Operations: ['51-25=26', '31+4=35'] Exploring Operation: 26+35=61, Resulting Numbers: [61] 61,12 unequal: No Solution Exploring Operation: 35-26=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 26*35=910, Resulting Numbers: [910] 910,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 12:[31, 30], Operations: ['51-25=26', '4+26=30'] Exploring Operation: 31*30=930, Resulting Numbers: [930] 930,12 unequal: No Solution Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 31+30=61, Resulting Numbers: [61] 61,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[51, 4, 6], Operations: ['31-25=6'] Exploring Operation: 51-6=45, Resulting Numbers: [4, 45] Generated Node #0,3,0: 12:[4, 45] Operation: 51-6=45 Exploring Operation: 51+4=55, Resulting Numbers: [6, 55] Generated Node #0,3,1: 12:[6, 55] Operation: 51+4=55 Exploring Operation: 51-4=47, Resulting Numbers: [6, 47] Generated Node #0,3,2: 12:[6, 47] Operation: 51-4=47 Exploring Operation: 6-4=2, Resulting Numbers: [51, 2] Generated Node #0,3,3: 12:[51, 2] Operation: 6-4=2 Exploring Operation: 4+6=10, Resulting Numbers: [51, 10] Generated Node #0,3,4: 12:[51, 10] Operation: 4+6=10 Moving to Node #0,3,0 Current State: 12:[4, 45], Operations: ['31-25=6', '51-6=45'] Exploring Operation: 4*45=180, Resulting Numbers: [180] 180,12 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,12 unequal: No Solution Exploring Operation: 4+45=49, Resulting Numbers: [49] 49,12 unequal: No Solution Moving to Node #0,3,2 Current State: 12:[6, 47], Operations: ['31-25=6', '51-4=47'] Exploring Operation: 6*47=282, Resulting Numbers: [282] 282,12 unequal: No Solution Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,12 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,12 unequal: No Solution Moving to Node #0,3,3 Current State: 12:[51, 2], Operations: ['31-25=6', '6-4=2'] Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,12 unequal: No Solution Exploring Operation: 51*2=102, Resulting Numbers: [102] 102,12 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,12 unequal: No Solution Moving to Node #0,3,4 Current State: 12:[51, 10], Operations: ['31-25=6', '4+6=10'] Exploring Operation: 51*10=510, Resulting Numbers: [510] 510,12 unequal: No Solution Exploring Operation: 51+10=61, Resulting Numbers: [61] 61,12 unequal: No Solution Exploring Operation: 51-10=41, Resulting Numbers: [41] 41,12 unequal: No Solution Moving to Node #0,3,1 Current State: 12:[6, 55], Operations: ['31-25=6', '51+4=55'] Exploring Operation: 6+55=61, Resulting Numbers: [61] 61,12 unequal: No Solution Exploring Operation: 6*55=330, Resulting Numbers: [330] 330,12 unequal: No Solution Exploring Operation: 55-6=49, Resulting Numbers: [49] 49,12 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 Current State: 12:[25, 31, 47], Operations: ['51-4=47'] Exploring Operation: 25+47=72, Resulting Numbers: [31, 72] Generated Node #0,1,0: 12:[31, 72] Operation: 25+47=72 Exploring Operation: 47-25=22, Resulting Numbers: [31, 22] Generated Node #0,1,1: 12:[31, 22] Operation: 47-25=22 Exploring Operation: 47-31=16, Resulting Numbers: [25, 16] Generated Node #0,1,2: 12:[25, 16] Operation: 47-31=16 Exploring Operation: 31-25=6, Resulting Numbers: [47, 6] Generated Node #0,1,3: 12:[47, 6] Operation: 31-25=6 Exploring Operation: 25+31=56, Resulting Numbers: [47, 56] Generated Node #0,1,4: 12:[47, 56] Operation: 25+31=56 Moving to Node #0,1,2 Current State: 12:[25, 16], Operations: ['51-4=47', '47-31=16'] Exploring Operation: 25*16=400, Resulting Numbers: [400] 400,12 unequal: No Solution Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[31, 22], Operations: ['51-4=47', '47-25=22'] Exploring Operation: 31+22=53, Resulting Numbers: [53] 53,12 unequal: No Solution Exploring Operation: 31-22=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 31*22=682, Resulting Numbers: [682] 682,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[47, 6], Operations: ['51-4=47', '31-25=6'] Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,12 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,12 unequal: No Solution Exploring Operation: 47*6=282, Resulting Numbers: [282] 282,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[31, 72], Operations: ['51-4=47', '25+47=72'] Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,12 unequal: No Solution Exploring Operation: 31*72=2232, Resulting Numbers: [2232] 2232,12 unequal: No Solution Exploring Operation: 31+72=103, Resulting Numbers: [103] 103,12 unequal: No Solution Moving to Node #0,1,4 Current State: 12:[47, 56], Operations: ['51-4=47', '25+31=56'] Exploring Operation: 47*56=2632, Resulting Numbers: [2632] 2632,12 unequal: No Solution Exploring Operation: 47+56=103, Resulting Numbers: [103] 103,12 unequal: No Solution Exploring Operation: 56-47=9, Resulting Numbers: [9] 9,12 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 #0,4 Current State: 12:[51, 31, 21], Operations: ['25-4=21'] Exploring Operation: 51-21=30, Resulting Numbers: [31, 30] Generated Node #0,4,0: 12:[31, 30] Operation: 51-21=30 Exploring Operation: 51+21=72, Resulting Numbers: [31, 72] Generated Node #0,4,1: 12:[31, 72] Operation: 51+21=72 Exploring Operation: 51-31=20, Resulting Numbers: [21, 20] Generated Node #0,4,2: 12:[21, 20] Operation: 51-31=20 Exploring Operation: 31-21=10, Resulting Numbers: [51, 10] Generated Node #0,4,3: 12:[51, 10] Operation: 31-21=10 Exploring Operation: 51+31=82, Resulting Numbers: [21, 82] Generated Node #0,4,4: 12:[21, 82] Operation: 51+31=82 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 12:[21, 20], Operations: ['25-4=21', '51-31=20'] Exploring Operation: 21*20=420, Resulting Numbers: [420] 420,12 unequal: No Solution Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,12 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 12:[31, 30], Operations: ['25-4=21', '51-21=30'] Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 31+30=61, Resulting Numbers: [61] 61,12 unequal: No Solution Exploring Operation: 31*30=930, Resulting Numbers: [930] 930,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 12:[51, 10], Operations: ['25-4=21', '31-21=10'] Exploring Operation: 51+10=61, Resulting Numbers: [61] 61,12 unequal: No Solution Exploring Operation: 51*10=510, Resulting Numbers: [510] 510,12 unequal: No Solution Exploring Operation: 51-10=41, Resulting Numbers: [41] 41,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 12:[31, 72], Operations: ['25-4=21', '51+21=72'] Exploring Operation: 31*72=2232, Resulting Numbers: [2232] 2232,12 unequal: No Solution Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,12 unequal: No Solution Exploring Operation: 31+72=103, Resulting Numbers: [103] 103,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 12:[21, 82], Operations: ['25-4=21', '51+31=82'] Exploring Operation: 21*82=1722, Resulting Numbers: [1722] 1722,12 unequal: No Solution Exploring Operation: 82-21=61, Resulting Numbers: [61] 61,12 unequal: No Solution Exploring Operation: 21+82=103, Resulting Numbers: [103] 103,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 63, 29, 26, 5 ]
32
[ "26-5=21", "63/21=3", "29+3=32" ]
Current State: 32:[63, 29, 26, 5], Operations: [] Exploring Operation: 26-5=21, Resulting Numbers: [63, 29, 21] Generated Node #2: [63, 29, 21] from Operation: 26-5=21 Current State: 32:[63, 29, 21], Operations: ['26-5=21'] Exploring Operation: 63/21=3, Resulting Numbers: [29, 3] Generated Node #3: [29, 3] from Operation: 63/21=3 Current State: 32:[29, 3], Operations: ['26-5=21', '63/21=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[63, 29, 26, 5], Operations: [] Exploring Operation: 63-5=58, Resulting Numbers: [29, 26, 58] Generated Node #0,0: 32:[29, 26, 58] Operation: 63-5=58 Exploring Operation: 63-26=37, Resulting Numbers: [29, 5, 37] Generated Node #0,1: 32:[29, 5, 37] Operation: 63-26=37 Exploring Operation: 29-26=3, Resulting Numbers: [63, 5, 3] Generated Node #0,2: 32:[63, 5, 3] Operation: 29-26=3 Exploring Operation: 63-29=34, Resulting Numbers: [26, 5, 34] Generated Node #0,3: 32:[26, 5, 34] Operation: 63-29=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[29, 5, 37], Operations: ['63-26=37'] Exploring Operation: 37-5=32, Resulting Numbers: [29, 32] Generated Node #0,1,0: 32:[29, 32] Operation: 37-5=32 Exploring Operation: 29+5=34, Resulting Numbers: [37, 34] Generated Node #0,1,1: 32:[37, 34] Operation: 29+5=34 Exploring Operation: 29-5=24, Resulting Numbers: [37, 24] Generated Node #0,1,2: 32:[37, 24] Operation: 29-5=24 Exploring Operation: 37-29=8, Resulting Numbers: [5, 8] Generated Node #0,1,3: 32:[5, 8] Operation: 37-29=8 Moving to Node #0,1,3 Current State: 32:[5, 8], Operations: ['63-26=37', '37-29=8'] Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,32 unequal: No Solution Moving to Node #0,1,0 Current State: 32:[29, 32], Operations: ['63-26=37', '37-5=32'] Exploring Operation: 32-29=3, Resulting Numbers: [3] 3,32 unequal: No Solution Exploring Operation: 29*32=928, Resulting Numbers: [928] 928,32 unequal: No Solution Exploring Operation: 29+32=61, Resulting Numbers: [61] 61,32 unequal: No Solution Moving to Node #0,1,1 Current State: 32:[37, 34], Operations: ['63-26=37', '29+5=34'] Exploring Operation: 37+34=71, Resulting Numbers: [71] 71,32 unequal: No Solution Exploring Operation: 37-34=3, Resulting Numbers: [3] 3,32 unequal: No Solution Exploring Operation: 37*34=1258, Resulting Numbers: [1258] 1258,32 unequal: No Solution Moving to Node #0,1,2 Current State: 32:[37, 24], Operations: ['63-26=37', '29-5=24'] Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,32 unequal: No Solution Exploring Operation: 37*24=888, Resulting Numbers: [888] 888,32 unequal: No Solution Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,32 unequal: No Solution No 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: 32:[26, 5, 34], Operations: ['63-29=34'] Exploring Operation: 26-5=21, Resulting Numbers: [34, 21] Generated Node #0,3,0: 32:[34, 21] Operation: 26-5=21 Exploring Operation: 26+5=31, Resulting Numbers: [34, 31] Generated Node #0,3,1: 32:[34, 31] Operation: 26+5=31 Exploring Operation: 34-5=29, Resulting Numbers: [26, 29] Generated Node #0,3,2: 32:[26, 29] Operation: 34-5=29 Exploring Operation: 34-26=8, Resulting Numbers: [5, 8] Generated Node #0,3,3: 32:[5, 8] Operation: 34-26=8 Moving to Node #0,3,3 Current State: 32:[5, 8], Operations: ['63-29=34', '34-26=8'] Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,32 unequal: No Solution Moving to Node #0,3,1 Current State: 32:[34, 31], Operations: ['63-29=34', '26+5=31'] Exploring Operation: 34*31=1054, Resulting Numbers: [1054] 1054,32 unequal: No Solution Exploring Operation: 34+31=65, Resulting Numbers: [65] 65,32 unequal: No Solution Exploring Operation: 34-31=3, Resulting Numbers: [3] 3,32 unequal: No Solution Moving to Node #0,3,0 Current State: 32:[34, 21], Operations: ['63-29=34', '26-5=21'] Exploring Operation: 34-21=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 34+21=55, Resulting Numbers: [55] 55,32 unequal: No Solution Exploring Operation: 34*21=714, Resulting Numbers: [714] 714,32 unequal: No Solution Moving to Node #0,3,2 Current State: 32:[26, 29], Operations: ['63-29=34', '34-5=29'] Exploring Operation: 26*29=754, Resulting Numbers: [754] 754,32 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,32 unequal: No Solution Exploring Operation: 26+29=55, Resulting Numbers: [55] 55,32 unequal: No Solution No 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: 32:[63, 5, 3], Operations: ['29-26=3'] Exploring Operation: 63-3=60, Resulting Numbers: [5, 60] Generated Node #0,2,0: 32:[5, 60] Operation: 63-3=60 Exploring Operation: 5+3=8, Resulting Numbers: [63, 8] Generated Node #0,2,1: 32:[63, 8] Operation: 5+3=8 Exploring Operation: 63/3=21, Resulting Numbers: [5, 21] Generated Node #0,2,2: 32:[5, 21] Operation: 63/3=21 Exploring Operation: 63-5=58, Resulting Numbers: [3, 58] Generated Node #0,2,3: 32:[3, 58] Operation: 63-5=58 Moving to Node #0,2,2 Current State: 32:[5, 21], Operations: ['29-26=3', '63/3=21'] Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,32 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,32 unequal: No Solution Moving to Node #0,2,3 Current State: 32:[3, 58], Operations: ['29-26=3', '63-5=58'] Exploring Operation: 3*58=174, Resulting Numbers: [174] 174,32 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,32 unequal: No Solution Exploring Operation: 3+58=61, Resulting Numbers: [61] 61,32 unequal: No Solution Moving to Node #0,2,0 Current State: 32:[5, 60], Operations: ['29-26=3', '63-3=60'] Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,32 unequal: No Solution Exploring Operation: 5+60=65, Resulting Numbers: [65] 65,32 unequal: No Solution Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,32 unequal: No Solution Exploring Operation: 5*60=300, Resulting Numbers: [300] 300,32 unequal: No Solution Moving to Node #0,2,1 Current State: 32:[63, 8], Operations: ['29-26=3', '5+3=8'] Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,32 unequal: No Solution Exploring Operation: 63+8=71, Resulting Numbers: [71] 71,32 unequal: No Solution Exploring Operation: 63*8=504, Resulting Numbers: [504] 504,32 unequal: No Solution No 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: 32:[29, 26, 58], Operations: ['63-5=58'] Exploring Operation: 58-26=32, Resulting Numbers: [29, 32] Generated Node #0,0,0: 32:[29, 32] Operation: 58-26=32 Exploring Operation: 58/29=2, Resulting Numbers: [26, 2] Generated Node #0,0,1: 32:[26, 2] Operation: 58/29=2 Exploring Operation: 58-29=29, Resulting Numbers: [26, 29] Generated Node #0,0,2: 32:[26, 29] Operation: 58-29=29 Exploring Operation: 29-26=3, Resulting Numbers: [58, 3] Generated Node #0,0,3: 32:[58, 3] Operation: 29-26=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[29, 32], Operations: ['63-5=58', '58-26=32'] Exploring Operation: 29+32=61, Resulting Numbers: [61] 61,32 unequal: No Solution Exploring Operation: 29*32=928, Resulting Numbers: [928] 928,32 unequal: No Solution Exploring Operation: 32-29=3, Resulting Numbers: [3] 3,32 unequal: No Solution No 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: 32:[26, 2], Operations: ['63-5=58', '58/29=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,32 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,32 unequal: No Solution No 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: 32:[26, 29], Operations: ['63-5=58', '58-29=29'] Exploring Operation: 26*29=754, Resulting Numbers: [754] 754,32 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,32 unequal: No Solution Exploring Operation: 26+29=55, Resulting Numbers: [55] 55,32 unequal: No Solution No 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: 32:[58, 3], Operations: ['63-5=58', '29-26=3'] Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,32 unequal: No Solution Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,32 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 32, 69, 23, 62 ]
91
[ "32+62=94", "69/23=3", "94-3=91" ]
Current State: 91:[32, 69, 23, 62], Operations: [] Exploring Operation: 32+62=94, Resulting Numbers: [69, 23, 94] Generated Node #2: [69, 23, 94] from Operation: 32+62=94 Current State: 91:[69, 23, 94], Operations: ['32+62=94'] Exploring Operation: 69/23=3, Resulting Numbers: [94, 3] Generated Node #3: [94, 3] from Operation: 69/23=3 Current State: 91:[94, 3], Operations: ['32+62=94', '69/23=3'] Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[32, 69, 23, 62], Operations: [] Exploring Operation: 69-62=7, Resulting Numbers: [32, 23, 7] Generated Node #0,0: 91:[32, 23, 7] Operation: 69-62=7 Exploring Operation: 32+69=101, Resulting Numbers: [23, 62, 101] Generated Node #0,1: 91:[23, 62, 101] Operation: 32+69=101 Exploring Operation: 32+62=94, Resulting Numbers: [69, 23, 94] Generated Node #0,2: 91:[69, 23, 94] Operation: 32+62=94 Exploring Operation: 23+62=85, Resulting Numbers: [32, 69, 85] Generated Node #0,3: 91:[32, 69, 85] Operation: 23+62=85 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[32, 23, 7], Operations: ['69-62=7'] Exploring Operation: 32-7=25, Resulting Numbers: [23, 25] Generated Node #0,0,0: 91:[23, 25] Operation: 32-7=25 Exploring Operation: 32-23=9, Resulting Numbers: [7, 9] Generated Node #0,0,1: 91:[7, 9] Operation: 32-23=9 Exploring Operation: 23-7=16, Resulting Numbers: [32, 16] Generated Node #0,0,2: 91:[32, 16] Operation: 23-7=16 Exploring Operation: 32+23=55, Resulting Numbers: [7, 55] Generated Node #0,0,3: 91:[7, 55] Operation: 32+23=55 Moving to Node #0,0,1 Current State: 91:[7, 9], Operations: ['69-62=7', '32-23=9'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,91 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[32, 16], Operations: ['69-62=7', '23-7=16'] Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,91 unequal: No Solution Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 32+16=48, Resulting Numbers: [48] 48,91 unequal: No Solution Exploring Operation: 32*16=512, Resulting Numbers: [512] 512,91 unequal: No Solution Moving to Node #0,0,0 Current State: 91:[23, 25], Operations: ['69-62=7', '32-7=25'] Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,91 unequal: No Solution Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 23*25=575, Resulting Numbers: [575] 575,91 unequal: No Solution Moving to Node #0,0,3 Current State: 91:[7, 55], Operations: ['69-62=7', '32+23=55'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,91 unequal: No Solution Exploring Operation: 7*55=385, Resulting Numbers: [385] 385,91 unequal: No Solution Exploring Operation: 7+55=62, Resulting Numbers: [62] 62,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[69, 23, 94], Operations: ['32+62=94'] Exploring Operation: 69+23=92, Resulting Numbers: [94, 92] Generated Node #0,2,0: 91:[94, 92] Operation: 69+23=92 Exploring Operation: 94-69=25, Resulting Numbers: [23, 25] Generated Node #0,2,1: 91:[23, 25] Operation: 94-69=25 Exploring Operation: 69/23=3, Resulting Numbers: [94, 3] Generated Node #0,2,2: 91:[94, 3] Operation: 69/23=3 Exploring Operation: 69-23=46, Resulting Numbers: [94, 46] Generated Node #0,2,3: 91:[94, 46] Operation: 69-23=46 Moving to Node #0,2,0 Current State: 91:[94, 92], Operations: ['32+62=94', '69+23=92'] Exploring Operation: 94+92=186, Resulting Numbers: [186] 186,91 unequal: No Solution Exploring Operation: 94*92=8648, Resulting Numbers: [8648] 8648,91 unequal: No Solution Exploring Operation: 94-92=2, Resulting Numbers: [2] 2,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[94, 3], Operations: ['32+62=94', '69/23=3'] Exploring Operation: 94+3=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 94*3=282, Resulting Numbers: [282] 282,91 unequal: No Solution Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[32, 69, 23, 62], Operations: [] Exploring Operation: 32+62=94, Resulting Numbers: [69, 23, 94] Generated Node #0,2: 91:[69, 23, 94] Operation: 32+62=94 Moving to Node #0,2 Current State: 91:[69, 23, 94], Operations: ['32+62=94'] Exploring Operation: 69/23=3, Resulting Numbers: [94, 3] Generated Node #0,2,2: 91:[94, 3] Operation: 69/23=3 Moving to Node #0,2,2 Current State: 91:[94, 3], Operations: ['32+62=94', '69/23=3'] Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_4
sum_heuristic
[ 73, 1, 28, 34 ]
80
[ "73+1=74", "34-28=6", "74+6=80" ]
Current State: 80:[73, 1, 28, 34], Operations: [] Exploring Operation: 73+1=74, Resulting Numbers: [28, 34, 74] Generated Node #2: [28, 34, 74] from Operation: 73+1=74 Current State: 80:[28, 34, 74], Operations: ['73+1=74'] Exploring Operation: 34-28=6, Resulting Numbers: [74, 6] Generated Node #3: [74, 6] from Operation: 34-28=6 Current State: 80:[74, 6], Operations: ['73+1=74', '34-28=6'] Exploring Operation: 74+6=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[73, 1, 28, 34], Operations: [] Exploring Operation: 34-28=6, Resulting Numbers: [73, 1, 6] Generated Node #0,0: 80:[73, 1, 6] Operation: 34-28=6 Moving to Node #0,0 Current State: 80:[73, 1, 6], Operations: ['34-28=6'] Exploring Operation: 73+6=79, Resulting Numbers: [1, 79] Generated Node #0,0,0: 80:[1, 79] Operation: 73+6=79 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[1, 79], Operations: ['34-28=6', '73+6=79'] Exploring Operation: 1+79=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[73, 1, 28, 34], Operations: [] Exploring Operation: 34-28=6, Resulting Numbers: [73, 1, 6] Generated Node #0,0: 80:[73, 1, 6] Operation: 34-28=6 Moving to Node #0,0 Current State: 80:[73, 1, 6], Operations: ['34-28=6'] Exploring Operation: 73+6=79, Resulting Numbers: [1, 79] Generated Node #0,0,0: 80:[1, 79] Operation: 73+6=79 Moving to Node #0,0,0 Current State: 80:[1, 79], Operations: ['34-28=6', '73+6=79'] Exploring Operation: 1+79=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 2, 70, 6, 66 ]
24
[ "70/2=35", "66/6=11", "35-11=24" ]
Current State: 24:[2, 70, 6, 66], Operations: [] Exploring Operation: 70/2=35, Resulting Numbers: [6, 66, 35] Generated Node #2: [6, 66, 35] from Operation: 70/2=35 Current State: 24:[6, 66, 35], Operations: ['70/2=35'] Exploring Operation: 66/6=11, Resulting Numbers: [35, 11] Generated Node #3: [35, 11] from Operation: 66/6=11 Current State: 24:[35, 11], Operations: ['70/2=35', '66/6=11'] Exploring Operation: 35-11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[2, 70, 6, 66], Operations: [] Exploring Operation: 70-66=4, Resulting Numbers: [2, 6, 4] Generated Node #0,0: 24:[2, 6, 4] Operation: 70-66=4 Exploring Operation: 66/2=33, Resulting Numbers: [70, 6, 33] Generated Node #0,1: 24:[70, 6, 33] Operation: 66/2=33 Exploring Operation: 70-6=64, Resulting Numbers: [2, 66, 64] Generated Node #0,2: 24:[2, 66, 64] Operation: 70-6=64 Exploring Operation: 70/2=35, Resulting Numbers: [6, 66, 35] Generated Node #0,3: 24:[6, 66, 35] Operation: 70/2=35 Exploring Operation: 66/6=11, Resulting Numbers: [2, 70, 11] Generated Node #0,4: 24:[2, 70, 11] Operation: 66/6=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[2, 6, 4], Operations: ['70-66=4'] Exploring Operation: 2+6=8, Resulting Numbers: [4, 8] Generated Node #0,0,0: 24:[4, 8] Operation: 2+6=8 Exploring Operation: 2+4=6, Resulting Numbers: [6, 6] Generated Node #0,0,1: 24:[6, 6] Operation: 2+4=6 Exploring Operation: 6/2=3, Resulting Numbers: [4, 3] Generated Node #0,0,2: 24:[4, 3] Operation: 6/2=3 Exploring Operation: 6-2=4, Resulting Numbers: [4, 4] Generated Node #0,0,3: 24:[4, 4] Operation: 6-2=4 Exploring Operation: 2*6=12, Resulting Numbers: [4, 12] Generated Node #0,0,4: 24:[4, 12] Operation: 2*6=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[4, 8], Operations: ['70-66=4', '2+6=8'] Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 24:[6, 6], Operations: ['70-66=4', '2+4=6'] Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,24 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,24 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 24:[4, 3], Operations: ['70-66=4', '6/2=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,24 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 24:[4, 4], Operations: ['70-66=4', '6-2=4'] Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,24 unequal: No Solution Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,24 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 24:[4, 12], Operations: ['70-66=4', '2*6=12'] Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,24 unequal: No Solution Exploring Operation: 4*12=48, Resulting Numbers: [48] 48,24 unequal: No Solution Exploring Operation: 4+12=16, Resulting Numbers: [16] 16,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 24:[2, 70, 11], Operations: ['66/6=11'] Exploring Operation: 2+11=13, Resulting Numbers: [70, 13] Generated Node #0,4,0: 24:[70, 13] Operation: 2+11=13 Exploring Operation: 70-11=59, Resulting Numbers: [2, 59] Generated Node #0,4,1: 24:[2, 59] Operation: 70-11=59 Exploring Operation: 70-2=68, Resulting Numbers: [11, 68] Generated Node #0,4,2: 24:[11, 68] Operation: 70-2=68 Exploring Operation: 70/2=35, Resulting Numbers: [11, 35] Generated Node #0,4,3: 24:[11, 35] Operation: 70/2=35 Exploring Operation: 11-2=9, Resulting Numbers: [70, 9] Generated Node #0,4,4: 24:[70, 9] Operation: 11-2=9 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 24:[11, 35], Operations: ['66/6=11', '70/2=35'] Exploring Operation: 11*35=385, Resulting Numbers: [385] 385,24 unequal: No Solution Exploring Operation: 35-11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[2, 70, 6, 66], Operations: [] Exploring Operation: 66/6=11, Resulting Numbers: [2, 70, 11] Generated Node #0,4: 24:[2, 70, 11] Operation: 66/6=11 Moving to Node #0,4 Current State: 24:[2, 70, 11], Operations: ['66/6=11'] Exploring Operation: 70/2=35, Resulting Numbers: [11, 35] Generated Node #0,4,3: 24:[11, 35] Operation: 70/2=35 Moving to Node #0,4,3 Current State: 24:[11, 35], Operations: ['66/6=11', '70/2=35'] Exploring Operation: 35-11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_5
sum_heuristic
[ 45, 73, 40, 34 ]
45
[ "73-40=33", "34-33=1", "45*1=45" ]
Current State: 45:[45, 73, 40, 34], Operations: [] Exploring Operation: 73-40=33, Resulting Numbers: [45, 34, 33] Generated Node #2: [45, 34, 33] from Operation: 73-40=33 Current State: 45:[45, 34, 33], Operations: ['73-40=33'] Exploring Operation: 34-33=1, Resulting Numbers: [45, 1] Generated Node #3: [45, 1] from Operation: 34-33=1 Current State: 45:[45, 1], Operations: ['73-40=33', '34-33=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[45, 73, 40, 34], Operations: [] Exploring Operation: 73-34=39, Resulting Numbers: [45, 40, 39] Generated Node #0,0: 45:[45, 40, 39] Operation: 73-34=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[45, 40, 39], Operations: ['73-34=39'] Exploring Operation: 40-39=1, Resulting Numbers: [45, 1] Generated Node #0,0,0: 45:[45, 1] Operation: 40-39=1 Moving to Node #0,0,0 Current State: 45:[45, 1], Operations: ['73-34=39', '40-39=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[45, 73, 40, 34], Operations: [] Exploring Operation: 73-34=39, Resulting Numbers: [45, 40, 39] Generated Node #0,0: 45:[45, 40, 39] Operation: 73-34=39 Moving to Node #0,0 Current State: 45:[45, 40, 39], Operations: ['73-34=39'] Exploring Operation: 40-39=1, Resulting Numbers: [45, 1] Generated Node #0,0,0: 45:[45, 1] Operation: 40-39=1 Moving to Node #0,0,0 Current State: 45:[45, 1], Operations: ['73-34=39', '40-39=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 64, 4, 62, 32 ]
78
[ "64/4=16", "62+32=94", "94-16=78" ]
Current State: 78:[64, 4, 62, 32], Operations: [] Exploring Operation: 64/4=16, Resulting Numbers: [62, 32, 16] Generated Node #2: [62, 32, 16] from Operation: 64/4=16 Current State: 78:[62, 32, 16], Operations: ['64/4=16'] Exploring Operation: 62+32=94, Resulting Numbers: [16, 94] Generated Node #3: [16, 94] from Operation: 62+32=94 Current State: 78:[16, 94], Operations: ['64/4=16', '62+32=94'] Exploring Operation: 94-16=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[64, 4, 62, 32], Operations: [] Exploring Operation: 64-62=2, Resulting Numbers: [4, 32, 2] Generated Node #0,0: 78:[4, 32, 2] Operation: 64-62=2 Exploring Operation: 64/32=2, Resulting Numbers: [4, 62, 2] Generated Node #0,1: 78:[4, 62, 2] Operation: 64/32=2 Moving to Node #0,0 Current State: 78:[4, 32, 2], Operations: ['64-62=2'] Exploring Operation: 32/4=8, Resulting Numbers: [2, 8] Generated Node #0,0,0: 78:[2, 8] Operation: 32/4=8 Exploring Operation: 32-4=28, Resulting Numbers: [2, 28] Generated Node #0,0,1: 78:[2, 28] Operation: 32-4=28 Moving to Node #0,1 Current State: 78:[4, 62, 2], Operations: ['64/32=2'] Exploring Operation: 62/2=31, Resulting Numbers: [4, 31] Generated Node #0,1,0: 78:[4, 31] Operation: 62/2=31 Exploring Operation: 4+62=66, Resulting Numbers: [2, 66] Generated Node #0,1,1: 78:[2, 66] Operation: 4+62=66 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[4, 31], Operations: ['64/32=2', '62/2=31'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[2, 66], Operations: ['64/32=2', '4+62=66'] Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,78 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 78:[2, 8], Operations: ['64-62=2', '32/4=8'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,78 unequal: No Solution Moving to Node #0,0,1 Current State: 78:[2, 28], Operations: ['64-62=2', '32-4=28'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,78 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 52, 56, 2, 38 ]
99
[ "56+38=94", "94/2=47", "52+47=99" ]
Current State: 99:[52, 56, 2, 38], Operations: [] Exploring Operation: 56+38=94, Resulting Numbers: [52, 2, 94] Generated Node #2: [52, 2, 94] from Operation: 56+38=94 Current State: 99:[52, 2, 94], Operations: ['56+38=94'] Exploring Operation: 94/2=47, Resulting Numbers: [52, 47] Generated Node #3: [52, 47] from Operation: 94/2=47 Current State: 99:[52, 47], Operations: ['56+38=94', '94/2=47'] Exploring Operation: 52+47=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[52, 56, 2, 38], Operations: [] Exploring Operation: 56-52=4, Resulting Numbers: [2, 38, 4] Generated Node #0,0: 99:[2, 38, 4] Operation: 56-52=4 Exploring Operation: 52+56=108, Resulting Numbers: [2, 38, 108] Generated Node #0,1: 99:[2, 38, 108] Operation: 52+56=108 Exploring Operation: 56+38=94, Resulting Numbers: [52, 2, 94] Generated Node #0,2: 99:[52, 2, 94] Operation: 56+38=94 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[2, 38, 4], Operations: ['56-52=4'] Exploring Operation: 38-2=36, Resulting Numbers: [4, 36] Generated Node #0,0,0: 99:[4, 36] Operation: 38-2=36 Exploring Operation: 38-4=34, Resulting Numbers: [2, 34] Generated Node #0,0,1: 99:[2, 34] Operation: 38-4=34 Exploring Operation: 2*4=8, Resulting Numbers: [38, 8] Generated Node #0,0,2: 99:[38, 8] Operation: 2*4=8 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 99:[2, 34], Operations: ['56-52=4', '38-4=34'] Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,99 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[4, 36], Operations: ['56-52=4', '38-2=36'] Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,99 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 99:[38, 8], Operations: ['56-52=4', '2*4=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 38*8=304, Resulting Numbers: [304] 304,99 unequal: No Solution Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[2, 38, 108], Operations: ['52+56=108'] Exploring Operation: 108-2=106, Resulting Numbers: [38, 106] Generated Node #0,1,0: 99:[38, 106] Operation: 108-2=106 Exploring Operation: 38-2=36, Resulting Numbers: [108, 36] Generated Node #0,1,1: 99:[108, 36] Operation: 38-2=36 Exploring Operation: 2+38=40, Resulting Numbers: [108, 40] Generated Node #0,1,2: 99:[108, 40] Operation: 2+38=40 Moving to Node #0,1,0 Current State: 99:[38, 106], Operations: ['52+56=108', '108-2=106'] Exploring Operation: 38+106=144, Resulting Numbers: [144] 144,99 unequal: No Solution Exploring Operation: 106-38=68, Resulting Numbers: [68] 68,99 unequal: No Solution Exploring Operation: 38*106=4028, Resulting Numbers: [4028] 4028,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[108, 36], Operations: ['52+56=108', '38-2=36'] Exploring Operation: 108+36=144, Resulting Numbers: [144] 144,99 unequal: No Solution Exploring Operation: 108-36=72, Resulting Numbers: [72] 72,99 unequal: No Solution Exploring Operation: 108/36=3, Resulting Numbers: [3] 3,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[108, 40], Operations: ['52+56=108', '2+38=40'] Exploring Operation: 108+40=148, Resulting Numbers: [148] 148,99 unequal: No Solution Exploring Operation: 108*40=4320, Resulting Numbers: [4320] 4320,99 unequal: No Solution Exploring Operation: 108-40=68, Resulting Numbers: [68] 68,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[52, 2, 94], Operations: ['56+38=94'] Exploring Operation: 52*2=104, Resulting Numbers: [94, 104] Generated Node #0,2,0: 99:[94, 104] Operation: 52*2=104 Exploring Operation: 52/2=26, Resulting Numbers: [94, 26] Generated Node #0,2,1: 99:[94, 26] Operation: 52/2=26 Exploring Operation: 94-52=42, Resulting Numbers: [2, 42] Generated Node #0,2,2: 99:[2, 42] Operation: 94-52=42 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 99:[94, 104], Operations: ['56+38=94', '52*2=104'] Exploring Operation: 104-94=10, Resulting Numbers: [10] 10,99 unequal: No Solution Exploring Operation: 94+104=198, Resulting Numbers: [198] 198,99 unequal: No Solution Exploring Operation: 94*104=9776, Resulting Numbers: [9776] 9776,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 99:[2, 42], Operations: ['56+38=94', '94-52=42'] Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,99 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 99:[94, 26], Operations: ['56+38=94', '52/2=26'] Exploring Operation: 94-26=68, Resulting Numbers: [68] 68,99 unequal: No Solution Exploring Operation: 94+26=120, Resulting Numbers: [120] 120,99 unequal: No Solution Exploring Operation: 94*26=2444, Resulting Numbers: [2444] 2444,99 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_3
sum_heuristic
[ 4, 21, 34, 42 ]
42
[ "4*42=168", "168/21=8", "34+8=42" ]
Current State: 42:[4, 21, 34, 42], Operations: [] Exploring Operation: 4*42=168, Resulting Numbers: [21, 34, 168] Generated Node #2: [21, 34, 168] from Operation: 4*42=168 Current State: 42:[21, 34, 168], Operations: ['4*42=168'] Exploring Operation: 168/21=8, Resulting Numbers: [34, 8] Generated Node #3: [34, 8] from Operation: 168/21=8 Current State: 42:[34, 8], Operations: ['4*42=168', '168/21=8'] Exploring Operation: 34+8=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[4, 21, 34, 42], Operations: [] Exploring Operation: 34-21=13, Resulting Numbers: [4, 42, 13] Generated Node #0,0: 42:[4, 42, 13] Operation: 34-21=13 Exploring Operation: 42-34=8, Resulting Numbers: [4, 21, 8] Generated Node #0,1: 42:[4, 21, 8] Operation: 42-34=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[4, 42, 13], Operations: ['34-21=13'] Exploring Operation: 4+13=17, Resulting Numbers: [42, 17] Generated Node #0,0,0: 42:[42, 17] Operation: 4+13=17 Exploring Operation: 13-4=9, Resulting Numbers: [42, 9] Generated Node #0,0,1: 42:[42, 9] Operation: 13-4=9 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 42:[42, 9], Operations: ['34-21=13', '13-4=9'] Exploring Operation: 42+9=51, Resulting Numbers: [51] 51,42 unequal: No Solution Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[42, 17], Operations: ['34-21=13', '4+13=17'] Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,42 unequal: No Solution Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[4, 21, 8], Operations: ['42-34=8'] Exploring Operation: 8-4=4, Resulting Numbers: [21, 4] Generated Node #0,1,0: 42:[21, 4] Operation: 8-4=4 Exploring Operation: 8/4=2, Resulting Numbers: [21, 2] Generated Node #0,1,1: 42:[21, 2] Operation: 8/4=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 42:[21, 2], Operations: ['42-34=8', '8/4=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[4, 21, 34, 42], Operations: [] Exploring Operation: 42-34=8, Resulting Numbers: [4, 21, 8] Generated Node #0,1: 42:[4, 21, 8] Operation: 42-34=8 Moving to Node #0,1 Current State: 42:[4, 21, 8], Operations: ['42-34=8'] Exploring Operation: 8/4=2, Resulting Numbers: [21, 2] Generated Node #0,1,1: 42:[21, 2] Operation: 8/4=2 Moving to Node #0,1,1 Current State: 42:[21, 2], Operations: ['42-34=8', '8/4=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 95, 20, 42, 30 ]
63
[ "95-20=75", "42-30=12", "75-12=63" ]
Current State: 63:[95, 20, 42, 30], Operations: [] Exploring Operation: 95-20=75, Resulting Numbers: [42, 30, 75] Generated Node #2: [42, 30, 75] from Operation: 95-20=75 Current State: 63:[42, 30, 75], Operations: ['95-20=75'] Exploring Operation: 42-30=12, Resulting Numbers: [75, 12] Generated Node #3: [75, 12] from Operation: 42-30=12 Current State: 63:[75, 12], Operations: ['95-20=75', '42-30=12'] Exploring Operation: 75-12=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[95, 20, 42, 30], Operations: [] Exploring Operation: 95-42=53, Resulting Numbers: [20, 30, 53] Generated Node #0,0: 63:[20, 30, 53] Operation: 95-42=53 Moving to Node #0,0 Current State: 63:[20, 30, 53], Operations: ['95-42=53'] Exploring Operation: 53-30=23, Resulting Numbers: [20, 23] Generated Node #0,0,0: 63:[20, 23] Operation: 53-30=23 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[20, 23], Operations: ['95-42=53', '53-30=23'] Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 96, 76, 43, 4 ]
38
[ "96-76=20", "20/4=5", "43-5=38" ]
Current State: 38:[96, 76, 43, 4], Operations: [] Exploring Operation: 96-76=20, Resulting Numbers: [43, 4, 20] Generated Node #2: [43, 4, 20] from Operation: 96-76=20 Current State: 38:[43, 4, 20], Operations: ['96-76=20'] Exploring Operation: 20/4=5, Resulting Numbers: [43, 5] Generated Node #3: [43, 5] from Operation: 20/4=5 Current State: 38:[43, 5], Operations: ['96-76=20', '20/4=5'] Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[96, 76, 43, 4], Operations: [] Exploring Operation: 96-76=20, Resulting Numbers: [43, 4, 20] Generated Node #0,0: 38:[43, 4, 20] Operation: 96-76=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[43, 4, 20], Operations: ['96-76=20'] Exploring Operation: 43-4=39, Resulting Numbers: [20, 39] Generated Node #0,0,0: 38:[20, 39] Operation: 43-4=39 Moving to Node #0,0,0 Current State: 38:[20, 39], Operations: ['96-76=20', '43-4=39'] Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 38, 7, 62, 10 ]
46
[ "62-38=24", "7*10=70", "70-24=46" ]
Current State: 46:[38, 7, 62, 10], Operations: [] Exploring Operation: 62-38=24, Resulting Numbers: [7, 10, 24] Generated Node #2: [7, 10, 24] from Operation: 62-38=24 Current State: 46:[7, 10, 24], Operations: ['62-38=24'] Exploring Operation: 7*10=70, Resulting Numbers: [24, 70] Generated Node #3: [24, 70] from Operation: 7*10=70 Current State: 46:[24, 70], Operations: ['62-38=24', '7*10=70'] Exploring Operation: 70-24=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[38, 7, 62, 10], Operations: [] Exploring Operation: 62-38=24, Resulting Numbers: [7, 10, 24] Generated Node #0,0: 46:[7, 10, 24] Operation: 62-38=24 Exploring Operation: 62-10=52, Resulting Numbers: [38, 7, 52] Generated Node #0,1: 46:[38, 7, 52] Operation: 62-10=52 Moving to Node #0,0 Current State: 46:[7, 10, 24], Operations: ['62-38=24'] Exploring Operation: 10-7=3, Resulting Numbers: [24, 3] Generated Node #0,0,0: 46:[24, 3] Operation: 10-7=3 Exploring Operation: 7+10=17, Resulting Numbers: [24, 17] Generated Node #0,0,1: 46:[24, 17] Operation: 7+10=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 46:[24, 3], Operations: ['62-38=24', '10-7=3'] Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,46 unequal: No Solution No 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: 46:[24, 17], Operations: ['62-38=24', '7+10=17'] Exploring Operation: 24-17=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 24+17=41, Resulting Numbers: [41] 41,46 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: 46:[38, 7, 52], Operations: ['62-10=52'] Exploring Operation: 38+7=45, Resulting Numbers: [52, 45] Generated Node #0,1,0: 46:[52, 45] Operation: 38+7=45 Exploring Operation: 52-7=45, Resulting Numbers: [38, 45] Generated Node #0,1,1: 46:[38, 45] Operation: 52-7=45 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 46:[52, 45], Operations: ['62-10=52', '38+7=45'] Exploring Operation: 52+45=97, Resulting Numbers: [97] 97,46 unequal: No Solution Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,46 unequal: No Solution No 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: 46:[38, 45], Operations: ['62-10=52', '52-7=45'] Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,46 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,46 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
[ 61, 15, 63, 6 ]
54
[ "15-6=9", "63/9=7", "61-7=54" ]
Current State: 54:[61, 15, 63, 6], Operations: [] Exploring Operation: 15-6=9, Resulting Numbers: [61, 63, 9] Generated Node #2: [61, 63, 9] from Operation: 15-6=9 Current State: 54:[61, 63, 9], Operations: ['15-6=9'] Exploring Operation: 63/9=7, Resulting Numbers: [61, 7] Generated Node #3: [61, 7] from Operation: 63/9=7 Current State: 54:[61, 7], Operations: ['15-6=9', '63/9=7'] Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[61, 15, 63, 6], Operations: [] Exploring Operation: 63-61=2, Resulting Numbers: [15, 6, 2] Generated Node #0,0: 54:[15, 6, 2] Operation: 63-61=2 Moving to Node #0,0 Current State: 54:[15, 6, 2], Operations: ['63-61=2'] Exploring Operation: 15-6=9, Resulting Numbers: [2, 9] Generated Node #0,0,0: 54:[2, 9] Operation: 15-6=9 Moving to Node #0,0,0 Current State: 54:[2, 9], Operations: ['63-61=2', '15-6=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,54 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 45, 85, 73, 80 ]
75
[ "85-45=40", "80/40=2", "73+2=75" ]
Current State: 75:[45, 85, 73, 80], Operations: [] Exploring Operation: 85-45=40, Resulting Numbers: [73, 80, 40] Generated Node #2: [73, 80, 40] from Operation: 85-45=40 Current State: 75:[73, 80, 40], Operations: ['85-45=40'] Exploring Operation: 80/40=2, Resulting Numbers: [73, 2] Generated Node #3: [73, 2] from Operation: 80/40=2 Current State: 75:[73, 2], Operations: ['85-45=40', '80/40=2'] Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[45, 85, 73, 80], Operations: [] Exploring Operation: 73-45=28, Resulting Numbers: [85, 80, 28] Generated Node #0,0: 75:[85, 80, 28] Operation: 73-45=28 Moving to Node #0,0 Current State: 75:[85, 80, 28], Operations: ['73-45=28'] Exploring Operation: 85-80=5, Resulting Numbers: [28, 5] Generated Node #0,0,0: 75:[28, 5] Operation: 85-80=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[28, 5], Operations: ['73-45=28', '85-80=5'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,75 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
[ 96, 56, 93, 46 ]
82
[ "96-93=3", "46*3=138", "138-56=82" ]
Current State: 82:[96, 56, 93, 46], Operations: [] Exploring Operation: 96-93=3, Resulting Numbers: [56, 46, 3] Generated Node #2: [56, 46, 3] from Operation: 96-93=3 Current State: 82:[56, 46, 3], Operations: ['96-93=3'] Exploring Operation: 46*3=138, Resulting Numbers: [56, 138] Generated Node #3: [56, 138] from Operation: 46*3=138 Current State: 82:[56, 138], Operations: ['96-93=3', '46*3=138'] Exploring Operation: 138-56=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[96, 56, 93, 46], Operations: [] Exploring Operation: 96-56=40, Resulting Numbers: [93, 46, 40] Generated Node #0,0: 82:[93, 46, 40] Operation: 96-56=40 Moving to Node #0,0 Current State: 82:[93, 46, 40], Operations: ['96-56=40'] Exploring Operation: 93-46=47, Resulting Numbers: [40, 47] Generated Node #0,0,0: 82:[40, 47] Operation: 93-46=47 Moving to Node #0,0,0 Current State: 82:[40, 47], Operations: ['96-56=40', '93-46=47'] Exploring Operation: 40+47=87, Resulting Numbers: [87] 87,82 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 14, 29, 1, 35 ]
85
[ "35-29=6", "14*6=84", "1+84=85" ]
Current State: 85:[14, 29, 1, 35], Operations: [] Exploring Operation: 35-29=6, Resulting Numbers: [14, 1, 6] Generated Node #2: [14, 1, 6] from Operation: 35-29=6 Current State: 85:[14, 1, 6], Operations: ['35-29=6'] Exploring Operation: 14*6=84, Resulting Numbers: [1, 84] Generated Node #3: [1, 84] from Operation: 14*6=84 Current State: 85:[1, 84], Operations: ['35-29=6', '14*6=84'] Exploring Operation: 1+84=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[14, 29, 1, 35], Operations: [] Exploring Operation: 35-14=21, Resulting Numbers: [29, 1, 21] Generated Node #0,0: 85:[29, 1, 21] Operation: 35-14=21 Exploring Operation: 35-29=6, Resulting Numbers: [14, 1, 6] Generated Node #0,1: 85:[14, 1, 6] Operation: 35-29=6 Exploring Operation: 29-14=15, Resulting Numbers: [1, 35, 15] Generated Node #0,2: 85:[1, 35, 15] Operation: 29-14=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[14, 1, 6], Operations: ['35-29=6'] Exploring Operation: 6-1=5, Resulting Numbers: [14, 5] Generated Node #0,1,0: 85:[14, 5] Operation: 6-1=5 Exploring Operation: 14+1=15, Resulting Numbers: [6, 15] Generated Node #0,1,1: 85:[6, 15] Operation: 14+1=15 Exploring Operation: 14*1=14, Resulting Numbers: [6, 14] Generated Node #0,1,2: 85:[6, 14] Operation: 14*1=14 Moving to Node #0,1,0 Current State: 85:[14, 5], Operations: ['35-29=6', '6-1=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,85 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,85 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[6, 15], Operations: ['35-29=6', '14+1=15'] Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,85 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,85 unequal: No Solution Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[6, 14], Operations: ['35-29=6', '14*1=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,85 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[29, 1, 21], Operations: ['35-14=21'] Exploring Operation: 29-1=28, Resulting Numbers: [21, 28] Generated Node #0,0,0: 85:[21, 28] Operation: 29-1=28 Exploring Operation: 21-1=20, Resulting Numbers: [29, 20] Generated Node #0,0,1: 85:[29, 20] Operation: 21-1=20 Exploring Operation: 29-21=8, Resulting Numbers: [1, 8] Generated Node #0,0,2: 85:[1, 8] Operation: 29-21=8 Moving to Node #0,0,2 Current State: 85:[1, 8], Operations: ['35-14=21', '29-21=8'] Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,85 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,85 unequal: No Solution Exploring Operation: 1*8=8, Resulting Numbers: [8] 8,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[21, 28], Operations: ['35-14=21', '29-1=28'] Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,85 unequal: No Solution Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,85 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[29, 20], Operations: ['35-14=21', '21-1=20'] Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,85 unequal: No Solution Exploring Operation: 29+20=49, Resulting Numbers: [49] 49,85 unequal: No Solution Exploring Operation: 29*20=580, Resulting Numbers: [580] 580,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 85:[1, 35, 15], Operations: ['29-14=15'] Exploring Operation: 35-15=20, Resulting Numbers: [1, 20] Generated Node #0,2,0: 85:[1, 20] Operation: 35-15=20 Exploring Operation: 1+15=16, Resulting Numbers: [35, 16] Generated Node #0,2,1: 85:[35, 16] Operation: 1+15=16 Exploring Operation: 35-1=34, Resulting Numbers: [15, 34] Generated Node #0,2,2: 85:[15, 34] Operation: 35-1=34 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 85:[1, 20], Operations: ['29-14=15', '35-15=20'] Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 1*20=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 85:[35, 16], Operations: ['29-14=15', '1+15=16'] Exploring Operation: 35*16=560, Resulting Numbers: [560] 560,85 unequal: No Solution Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,85 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 85:[15, 34], Operations: ['29-14=15', '35-1=34'] Exploring Operation: 15+34=49, Resulting Numbers: [49] 49,85 unequal: No Solution Exploring Operation: 15*34=510, Resulting Numbers: [510] 510,85 unequal: No Solution Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 31, 25, 4, 38 ]
53
[ "38-31=7", "4*7=28", "25+28=53" ]
Current State: 53:[31, 25, 4, 38], Operations: [] Exploring Operation: 38-31=7, Resulting Numbers: [25, 4, 7] Generated Node #2: [25, 4, 7] from Operation: 38-31=7 Current State: 53:[25, 4, 7], Operations: ['38-31=7'] Exploring Operation: 4*7=28, Resulting Numbers: [25, 28] Generated Node #3: [25, 28] from Operation: 4*7=28 Current State: 53:[25, 28], Operations: ['38-31=7', '4*7=28'] Exploring Operation: 25+28=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[31, 25, 4, 38], Operations: [] Exploring Operation: 31+4=35, Resulting Numbers: [25, 38, 35] Generated Node #0,0: 53:[25, 38, 35] Operation: 31+4=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[25, 38, 35], Operations: ['31+4=35'] Exploring Operation: 25+35=60, Resulting Numbers: [38, 60] Generated Node #0,0,0: 53:[38, 60] Operation: 25+35=60 Moving to Node #0,0,0 Current State: 53:[38, 60], Operations: ['31+4=35', '25+35=60'] Exploring Operation: 60-38=22, Resulting Numbers: [22] 22,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 6, 85, 38, 76 ]
35
[ "85-6=79", "38+76=114", "114-79=35" ]
Current State: 35:[6, 85, 38, 76], Operations: [] Exploring Operation: 85-6=79, Resulting Numbers: [38, 76, 79] Generated Node #2: [38, 76, 79] from Operation: 85-6=79 Current State: 35:[38, 76, 79], Operations: ['85-6=79'] Exploring Operation: 38+76=114, Resulting Numbers: [79, 114] Generated Node #3: [79, 114] from Operation: 38+76=114 Current State: 35:[79, 114], Operations: ['85-6=79', '38+76=114'] Exploring Operation: 114-79=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[6, 85, 38, 76], Operations: [] Exploring Operation: 85-76=9, Resulting Numbers: [6, 38, 9] Generated Node #0,0: 35:[6, 38, 9] Operation: 85-76=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[6, 38, 9], Operations: ['85-76=9'] Exploring Operation: 38-6=32, Resulting Numbers: [9, 32] Generated Node #0,0,0: 35:[9, 32] Operation: 38-6=32 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[9, 32], Operations: ['85-76=9', '38-6=32'] Exploring Operation: 9+32=41, Resulting Numbers: [41] 41,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 99, 86, 59, 90 ]
18
[ "99-86=13", "90-59=31", "31-13=18" ]
Current State: 18:[99, 86, 59, 90], Operations: [] Exploring Operation: 99-86=13, Resulting Numbers: [59, 90, 13] Generated Node #2: [59, 90, 13] from Operation: 99-86=13 Current State: 18:[59, 90, 13], Operations: ['99-86=13'] Exploring Operation: 90-59=31, Resulting Numbers: [13, 31] Generated Node #3: [13, 31] from Operation: 90-59=31 Current State: 18:[13, 31], Operations: ['99-86=13', '90-59=31'] Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[99, 86, 59, 90], Operations: [] Exploring Operation: 99-59=40, Resulting Numbers: [86, 90, 40] Generated Node #0,0: 18:[86, 90, 40] Operation: 99-59=40 Exploring Operation: 90-86=4, Resulting Numbers: [99, 59, 4] Generated Node #0,1: 18:[99, 59, 4] Operation: 90-86=4 Exploring Operation: 99-90=9, Resulting Numbers: [86, 59, 9] Generated Node #0,2: 18:[86, 59, 9] Operation: 99-90=9 Exploring Operation: 86-59=27, Resulting Numbers: [99, 90, 27] Generated Node #0,3: 18:[99, 90, 27] Operation: 86-59=27 Exploring Operation: 99-86=13, Resulting Numbers: [59, 90, 13] Generated Node #0,4: 18:[59, 90, 13] Operation: 99-86=13 Moving to Node #0,2 Current State: 18:[86, 59, 9], Operations: ['99-90=9'] Exploring Operation: 86-59=27, Resulting Numbers: [9, 27] Generated Node #0,2,0: 18:[9, 27] Operation: 86-59=27 Exploring Operation: 86+9=95, Resulting Numbers: [59, 95] Generated Node #0,2,1: 18:[59, 95] Operation: 86+9=95 Exploring Operation: 59-9=50, Resulting Numbers: [86, 50] Generated Node #0,2,2: 18:[86, 50] Operation: 59-9=50 Exploring Operation: 86-9=77, Resulting Numbers: [59, 77] Generated Node #0,2,3: 18:[59, 77] Operation: 86-9=77 Exploring Operation: 59+9=68, Resulting Numbers: [86, 68] Generated Node #0,2,4: 18:[86, 68] Operation: 59+9=68 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[9, 27], Operations: ['99-90=9', '86-59=27'] Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[99, 86, 59, 90], Operations: [] Exploring Operation: 99-90=9, Resulting Numbers: [86, 59, 9] Generated Node #0,2: 18:[86, 59, 9] Operation: 99-90=9 Moving to Node #0,2 Current State: 18:[86, 59, 9], Operations: ['99-90=9'] Exploring Operation: 86-59=27, Resulting Numbers: [9, 27] Generated Node #0,2,0: 18:[9, 27] Operation: 86-59=27 Moving to Node #0,2,0 Current State: 18:[9, 27], Operations: ['99-90=9', '86-59=27'] Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 7, 5, 5, 5 ]
57
[ "5+5=10", "5*10=50", "7+50=57" ]
Current State: 57:[7, 5, 5, 5], Operations: [] Exploring Operation: 5+5=10, Resulting Numbers: [7, 10] Generated Node #2: [7, 10] from Operation: 5+5=10 Current State: 57:[7, 10], Operations: ['5+5=10'] Exploring Operation: 5*10=50, Resulting Numbers: [7, 50] Generated Node #3: [7, 50] from Operation: 5*10=50 Current State: 57:[7, 50], Operations: ['5+5=10', '5*10=50'] Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[7, 5, 5, 5], Operations: [] Exploring Operation: 7-5=2, Resulting Numbers: [5, 5, 2] Generated Node #0,0: 57:[5, 5, 2] Operation: 7-5=2 Exploring Operation: 7-5=2, Resulting Numbers: [5, 5, 2] Generated Node #0,1: 57:[5, 5, 2] Operation: 7-5=2 Moving to Node #0,0 Current State: 57:[5, 5, 2], Operations: ['7-5=2'] Exploring Operation: 5-2=3, Resulting Numbers: [5, 3] Generated Node #0,0,0: 57:[5, 3] Operation: 5-2=3 Exploring Operation: 5-2=3, Resulting Numbers: [5, 3] Generated Node #0,0,1: 57:[5, 3] Operation: 5-2=3 Moving to Node #0,1 Current State: 57:[5, 5, 2], Operations: ['7-5=2'] Exploring Operation: 5-2=3, Resulting Numbers: [5, 3] Generated Node #0,1,0: 57:[5, 3] Operation: 5-2=3 Exploring Operation: 5-2=3, Resulting Numbers: [5, 3] Generated Node #0,1,1: 57:[5, 3] Operation: 5-2=3 Moving to Node #0,0,0 Current State: 57:[5, 3], Operations: ['7-5=2', '5-2=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,57 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[5, 3], Operations: ['7-5=2', '5-2=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,57 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[5, 3], Operations: ['7-5=2', '5-2=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,57 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[5, 3], Operations: ['7-5=2', '5-2=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,57 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,57 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 30, 33, 51, 29 ]
83
[ "33-30=3", "51+29=80", "3+80=83" ]
Current State: 83:[30, 33, 51, 29], Operations: [] Exploring Operation: 33-30=3, Resulting Numbers: [51, 29, 3] Generated Node #2: [51, 29, 3] from Operation: 33-30=3 Current State: 83:[51, 29, 3], Operations: ['33-30=3'] Exploring Operation: 51+29=80, Resulting Numbers: [3, 80] Generated Node #3: [3, 80] from Operation: 51+29=80 Current State: 83:[3, 80], Operations: ['33-30=3', '51+29=80'] Exploring Operation: 3+80=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[30, 33, 51, 29], Operations: [] Exploring Operation: 30+51=81, Resulting Numbers: [33, 29, 81] Generated Node #0,0: 83:[33, 29, 81] Operation: 30+51=81 Exploring Operation: 30+29=59, Resulting Numbers: [33, 51, 59] Generated Node #0,1: 83:[33, 51, 59] Operation: 30+29=59 Exploring Operation: 33+29=62, Resulting Numbers: [30, 51, 62] Generated Node #0,2: 83:[30, 51, 62] Operation: 33+29=62 Exploring Operation: 30+33=63, Resulting Numbers: [51, 29, 63] Generated Node #0,3: 83:[51, 29, 63] Operation: 30+33=63 Exploring Operation: 51+29=80, Resulting Numbers: [30, 33, 80] Generated Node #0,4: 83:[30, 33, 80] Operation: 51+29=80 Moving to Node #0,0 Current State: 83:[33, 29, 81], Operations: ['30+51=81'] Exploring Operation: 33+81=114, Resulting Numbers: [29, 114] Generated Node #0,0,0: 83:[29, 114] Operation: 33+81=114 Exploring Operation: 33+29=62, Resulting Numbers: [81, 62] Generated Node #0,0,1: 83:[81, 62] Operation: 33+29=62 Exploring Operation: 81-29=52, Resulting Numbers: [33, 52] Generated Node #0,0,2: 83:[33, 52] Operation: 81-29=52 Exploring Operation: 29+81=110, Resulting Numbers: [33, 110] Generated Node #0,0,3: 83:[33, 110] Operation: 29+81=110 Exploring Operation: 33-29=4, Resulting Numbers: [81, 4] Generated Node #0,0,4: 83:[81, 4] Operation: 33-29=4 Moving to Node #0,2 Current State: 83:[30, 51, 62], Operations: ['33+29=62'] Exploring Operation: 62-30=32, Resulting Numbers: [51, 32] Generated Node #0,2,0: 83:[51, 32] Operation: 62-30=32 Exploring Operation: 51-30=21, Resulting Numbers: [62, 21] Generated Node #0,2,1: 83:[62, 21] Operation: 51-30=21 Exploring Operation: 30+51=81, Resulting Numbers: [62, 81] Generated Node #0,2,2: 83:[62, 81] Operation: 30+51=81 Exploring Operation: 51+62=113, Resulting Numbers: [30, 113] Generated Node #0,2,3: 83:[30, 113] Operation: 51+62=113 Exploring Operation: 30+62=92, Resulting Numbers: [51, 92] Generated Node #0,2,4: 83:[51, 92] Operation: 30+62=92 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 83:[62, 81], Operations: ['33+29=62', '30+51=81'] Exploring Operation: 62+81=143, Resulting Numbers: [143] 143,83 unequal: No Solution Exploring Operation: 62*81=5022, Resulting Numbers: [5022] 5022,83 unequal: No Solution Exploring Operation: 81-62=19, Resulting Numbers: [19] 19,83 unequal: No Solution No 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: 83:[51, 92], Operations: ['33+29=62', '30+62=92'] Exploring Operation: 92-51=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 51*92=4692, Resulting Numbers: [4692] 4692,83 unequal: No Solution Exploring Operation: 51+92=143, Resulting Numbers: [143] 143,83 unequal: No Solution No 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: 83:[51, 32], Operations: ['33+29=62', '62-30=32'] Exploring Operation: 51*32=1632, Resulting Numbers: [1632] 1632,83 unequal: No Solution Exploring Operation: 51+32=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[30, 33, 51, 29], Operations: [] Exploring Operation: 33+29=62, Resulting Numbers: [30, 51, 62] Generated Node #0,2: 83:[30, 51, 62] Operation: 33+29=62 Moving to Node #0,2 Current State: 83:[30, 51, 62], Operations: ['33+29=62'] Exploring Operation: 62-30=32, Resulting Numbers: [51, 32] Generated Node #0,2,0: 83:[51, 32] Operation: 62-30=32 Moving to Node #0,2,0 Current State: 83:[51, 32], Operations: ['33+29=62', '62-30=32'] Exploring Operation: 51+32=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_5
sum_heuristic
[ 4, 93, 60, 13 ]
17
[ "13-4=9", "93+60=153", "153/9=17" ]
Current State: 17:[4, 93, 60, 13], Operations: [] Exploring Operation: 13-4=9, Resulting Numbers: [93, 60, 9] Generated Node #2: [93, 60, 9] from Operation: 13-4=9 Current State: 17:[93, 60, 9], Operations: ['13-4=9'] Exploring Operation: 93+60=153, Resulting Numbers: [9, 153] Generated Node #3: [9, 153] from Operation: 93+60=153 Current State: 17:[9, 153], Operations: ['13-4=9', '93+60=153'] Exploring Operation: 153/9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[4, 93, 60, 13], Operations: [] Exploring Operation: 60/4=15, Resulting Numbers: [93, 13, 15] Generated Node #0,0: 17:[93, 13, 15] Operation: 60/4=15 Exploring Operation: 93-4=89, Resulting Numbers: [60, 13, 89] Generated Node #0,1: 17:[60, 13, 89] Operation: 93-4=89 Exploring Operation: 93-60=33, Resulting Numbers: [4, 13, 33] Generated Node #0,2: 17:[4, 13, 33] Operation: 93-60=33 Moving to Node #0,2 Current State: 17:[4, 13, 33], Operations: ['93-60=33'] Exploring Operation: 4+13=17, Resulting Numbers: [33, 17] Generated Node #0,2,0: 17:[33, 17] Operation: 4+13=17 Exploring Operation: 33-4=29, Resulting Numbers: [13, 29] Generated Node #0,2,1: 17:[13, 29] Operation: 33-4=29 Exploring Operation: 33-13=20, Resulting Numbers: [4, 20] Generated Node #0,2,2: 17:[4, 20] Operation: 33-13=20 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 17:[33, 17], Operations: ['93-60=33', '4+13=17'] Exploring Operation: 33+17=50, Resulting Numbers: [50] 50,17 unequal: No Solution Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 33*17=561, Resulting Numbers: [561] 561,17 unequal: No Solution No 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: 17:[13, 29], Operations: ['93-60=33', '33-4=29'] Exploring Operation: 13*29=377, Resulting Numbers: [377] 377,17 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,17 unequal: No Solution No 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: 17:[4, 20], Operations: ['93-60=33', '33-13=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,17 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: 17:[93, 13, 15], Operations: ['60/4=15'] Exploring Operation: 93-15=78, Resulting Numbers: [13, 78] Generated Node #0,0,0: 17:[13, 78] Operation: 93-15=78 Exploring Operation: 13+15=28, Resulting Numbers: [93, 28] Generated Node #0,0,1: 17:[93, 28] Operation: 13+15=28 Exploring Operation: 93-13=80, Resulting Numbers: [15, 80] Generated Node #0,0,2: 17:[15, 80] Operation: 93-13=80 Moving to Node #0,1 Current State: 17:[60, 13, 89], Operations: ['93-4=89'] Exploring Operation: 60-13=47, Resulting Numbers: [89, 47] Generated Node #0,1,0: 17:[89, 47] Operation: 60-13=47 Exploring Operation: 89-60=29, Resulting Numbers: [13, 29] Generated Node #0,1,1: 17:[13, 29] Operation: 89-60=29 Exploring Operation: 89-13=76, Resulting Numbers: [60, 76] Generated Node #0,1,2: 17:[60, 76] Operation: 89-13=76 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 17:[13, 29], Operations: ['93-4=89', '89-60=29'] Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 13*29=377, Resulting Numbers: [377] 377,17 unequal: No Solution Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,17 unequal: No Solution No 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: 17:[89, 47], Operations: ['93-4=89', '60-13=47'] Exploring Operation: 89*47=4183, Resulting Numbers: [4183] 4183,17 unequal: No Solution Exploring Operation: 89+47=136, Resulting Numbers: [136] 136,17 unequal: No Solution Exploring Operation: 89-47=42, Resulting Numbers: [42] 42,17 unequal: No Solution No 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: 17:[60, 76], Operations: ['93-4=89', '89-13=76'] Exploring Operation: 60+76=136, Resulting Numbers: [136] 136,17 unequal: No Solution Exploring Operation: 60*76=4560, Resulting Numbers: [4560] 4560,17 unequal: No Solution Exploring Operation: 76-60=16, Resulting Numbers: [16] 16,17 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: 17:[13, 78], Operations: ['60/4=15', '93-15=78'] Exploring Operation: 78-13=65, Resulting Numbers: [65] 65,17 unequal: No Solution Exploring Operation: 13+78=91, Resulting Numbers: [91] 91,17 unequal: No Solution Exploring Operation: 78/13=6, Resulting Numbers: [6] 6,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[15, 80], Operations: ['60/4=15', '93-13=80'] Exploring Operation: 15+80=95, Resulting Numbers: [95] 95,17 unequal: No Solution Exploring Operation: 80-15=65, Resulting Numbers: [65] 65,17 unequal: No Solution Exploring Operation: 15*80=1200, Resulting Numbers: [1200] 1200,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[93, 28], Operations: ['60/4=15', '13+15=28'] Exploring Operation: 93-28=65, Resulting Numbers: [65] 65,17 unequal: No Solution Exploring Operation: 93*28=2604, Resulting Numbers: [2604] 2604,17 unequal: No Solution Exploring Operation: 93+28=121, Resulting Numbers: [121] 121,17 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 71, 30, 96, 17 ]
22
[ "71+30=101", "96-17=79", "101-79=22" ]
Current State: 22:[71, 30, 96, 17], Operations: [] Exploring Operation: 71+30=101, Resulting Numbers: [96, 17, 101] Generated Node #2: [96, 17, 101] from Operation: 71+30=101 Current State: 22:[96, 17, 101], Operations: ['71+30=101'] Exploring Operation: 96-17=79, Resulting Numbers: [101, 79] Generated Node #3: [101, 79] from Operation: 96-17=79 Current State: 22:[101, 79], Operations: ['71+30=101', '96-17=79'] Exploring Operation: 101-79=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[71, 30, 96, 17], Operations: [] Exploring Operation: 96-71=25, Resulting Numbers: [30, 17, 25] Generated Node #0,0: 22:[30, 17, 25] Operation: 96-71=25 Exploring Operation: 96-30=66, Resulting Numbers: [71, 17, 66] Generated Node #0,1: 22:[71, 17, 66] Operation: 96-30=66 Exploring Operation: 71-30=41, Resulting Numbers: [96, 17, 41] Generated Node #0,2: 22:[96, 17, 41] Operation: 71-30=41 Moving to Node #0,0 Current State: 22:[30, 17, 25], Operations: ['96-71=25'] Exploring Operation: 30-17=13, Resulting Numbers: [25, 13] Generated Node #0,0,0: 22:[25, 13] Operation: 30-17=13 Exploring Operation: 30-25=5, Resulting Numbers: [17, 5] Generated Node #0,0,1: 22:[17, 5] Operation: 30-25=5 Exploring Operation: 25-17=8, Resulting Numbers: [30, 8] Generated Node #0,0,2: 22:[30, 8] Operation: 25-17=8 Moving to Node #0,1 Current State: 22:[71, 17, 66], Operations: ['96-30=66'] Exploring Operation: 71-66=5, Resulting Numbers: [17, 5] Generated Node #0,1,0: 22:[17, 5] Operation: 71-66=5 Exploring Operation: 66-17=49, Resulting Numbers: [71, 49] Generated Node #0,1,1: 22:[71, 49] Operation: 66-17=49 Exploring Operation: 71-17=54, Resulting Numbers: [66, 54] Generated Node #0,1,2: 22:[66, 54] Operation: 71-17=54 Moving to Node #0,2 Current State: 22:[96, 17, 41], Operations: ['71-30=41'] Exploring Operation: 96-17=79, Resulting Numbers: [41, 79] Generated Node #0,2,0: 22:[41, 79] Operation: 96-17=79 Exploring Operation: 41-17=24, Resulting Numbers: [96, 24] Generated Node #0,2,1: 22:[96, 24] Operation: 41-17=24 Exploring Operation: 96-41=55, Resulting Numbers: [17, 55] Generated Node #0,2,2: 22:[17, 55] Operation: 96-41=55 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 22:[17, 55], Operations: ['71-30=41', '96-41=55'] Exploring Operation: 17+55=72, Resulting Numbers: [72] 72,22 unequal: No Solution Exploring Operation: 17*55=935, Resulting Numbers: [935] 935,22 unequal: No Solution Exploring Operation: 55-17=38, Resulting Numbers: [38] 38,22 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 #0,2,0 Current State: 22:[41, 79], Operations: ['71-30=41', '96-17=79'] Exploring Operation: 79-41=38, Resulting Numbers: [38] 38,22 unequal: No Solution Exploring Operation: 41+79=120, Resulting Numbers: [120] 120,22 unequal: No Solution Exploring Operation: 41*79=3239, Resulting Numbers: [3239] 3239,22 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 #0,2,1 Current State: 22:[96, 24], Operations: ['71-30=41', '41-17=24'] Exploring Operation: 96-24=72, Resulting Numbers: [72] 72,22 unequal: No Solution Exploring Operation: 96+24=120, Resulting Numbers: [120] 120,22 unequal: No Solution Exploring Operation: 96/24=4, Resulting Numbers: [4] 4,22 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: 22:[25, 13], Operations: ['96-71=25', '30-17=13'] Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,22 unequal: No Solution Exploring Operation: 25+13=38, Resulting Numbers: [38] 38,22 unequal: No Solution Exploring Operation: 25*13=325, Resulting Numbers: [325] 325,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[17, 5], Operations: ['96-71=25', '30-25=5'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,22 unequal: No Solution Exploring Operation: 17*5=85, Resulting Numbers: [85] 85,22 unequal: No Solution Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[71, 30, 96, 17], Operations: [] Exploring Operation: 96-71=25, Resulting Numbers: [30, 17, 25] Generated Node #0,0: 22:[30, 17, 25] Operation: 96-71=25 Moving to Node #0,0 Current State: 22:[30, 17, 25], Operations: ['96-71=25'] Exploring Operation: 30-25=5, Resulting Numbers: [17, 5] Generated Node #0,0,1: 22:[17, 5] Operation: 30-25=5 Moving to Node #0,0,1 Current State: 22:[17, 5], Operations: ['96-71=25', '30-25=5'] Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.97309
hs_3
sum_heuristic
[ 41, 13, 56, 84 ]
28
[ "13*84=1092", "56+1092=1148", "1148/41=28" ]
Current State: 28:[41, 13, 56, 84], Operations: [] Exploring Operation: 13*84=1092, Resulting Numbers: [41, 56, 1092] Generated Node #2: [41, 56, 1092] from Operation: 13*84=1092 Current State: 28:[41, 56, 1092], Operations: ['13*84=1092'] Exploring Operation: 56+1092=1148, Resulting Numbers: [41, 1148] Generated Node #3: [41, 1148] from Operation: 56+1092=1148 Current State: 28:[41, 1148], Operations: ['13*84=1092', '56+1092=1148'] Exploring Operation: 1148/41=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[41, 13, 56, 84], Operations: [] Exploring Operation: 84-41=43, Resulting Numbers: [13, 56, 43] Generated Node #0,0: 28:[13, 56, 43] Operation: 84-41=43 Exploring Operation: 41-13=28, Resulting Numbers: [56, 84, 28] Generated Node #0,1: 28:[56, 84, 28] Operation: 41-13=28 Exploring Operation: 56-13=43, Resulting Numbers: [41, 84, 43] Generated Node #0,2: 28:[41, 84, 43] Operation: 56-13=43 Exploring Operation: 56-41=15, Resulting Numbers: [13, 84, 15] Generated Node #0,3: 28:[13, 84, 15] Operation: 56-41=15 Exploring Operation: 84-56=28, Resulting Numbers: [41, 13, 28] Generated Node #0,4: 28:[41, 13, 28] Operation: 84-56=28 Moving to Node #0,4 Current State: 28:[41, 13, 28], Operations: ['84-56=28'] Exploring Operation: 13+28=41, Resulting Numbers: [41, 41] Generated Node #0,4,0: 28:[41, 41] Operation: 13+28=41 Exploring Operation: 41-13=28, Resulting Numbers: [28, 28] Generated Node #0,4,1: 28:[28, 28] Operation: 41-13=28 Exploring Operation: 28-13=15, Resulting Numbers: [41, 15] Generated Node #0,4,2: 28:[41, 15] Operation: 28-13=15 Exploring Operation: 41+13=54, Resulting Numbers: [28, 54] Generated Node #0,4,3: 28:[28, 54] Operation: 41+13=54 Exploring Operation: 41-28=13, Resulting Numbers: [13, 13] Generated Node #0,4,4: 28:[13, 13] Operation: 41-28=13 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 28:[28, 28], Operations: ['84-56=28', '41-13=28'] Exploring Operation: 28/28=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 28-28=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 28*28=784, Resulting Numbers: [784] 784,28 unequal: No Solution Exploring Operation: 28+28=56, Resulting Numbers: [56] 56,28 unequal: No Solution No 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: 28:[13, 13], Operations: ['84-56=28', '41-28=13'] Exploring Operation: 13/13=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 13+13=26, Resulting Numbers: [26] 26,28 unequal: No Solution Exploring Operation: 13*13=169, Resulting Numbers: [169] 169,28 unequal: No Solution Exploring Operation: 13-13=0, Resulting Numbers: [0] 0,28 unequal: No Solution No 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: 28:[41, 15], Operations: ['84-56=28', '28-13=15'] Exploring Operation: 41*15=615, Resulting Numbers: [615] 615,28 unequal: No Solution Exploring Operation: 41+15=56, Resulting Numbers: [56] 56,28 unequal: No Solution Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,28 unequal: No Solution No 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: 28:[41, 41], Operations: ['84-56=28', '13+28=41'] Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,28 unequal: No Solution Exploring Operation: 41*41=1681, Resulting Numbers: [1681] 1681,28 unequal: No Solution Exploring Operation: 41-41=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 41/41=1, Resulting Numbers: [1] 1,28 unequal: No Solution No 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: 28:[28, 54], Operations: ['84-56=28', '41+13=54'] Exploring Operation: 28*54=1512, Resulting Numbers: [1512] 1512,28 unequal: No Solution Exploring Operation: 28+54=82, Resulting Numbers: [82] 82,28 unequal: No Solution Exploring Operation: 54-28=26, Resulting Numbers: [26] 26,28 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: 28:[13, 56, 43], Operations: ['84-41=43'] Exploring Operation: 43-13=30, Resulting Numbers: [56, 30] Generated Node #0,0,0: 28:[56, 30] Operation: 43-13=30 Exploring Operation: 56-43=13, Resulting Numbers: [13, 13] Generated Node #0,0,1: 28:[13, 13] Operation: 56-43=13 Exploring Operation: 13+56=69, Resulting Numbers: [43, 69] Generated Node #0,0,2: 28:[43, 69] Operation: 13+56=69 Exploring Operation: 13+43=56, Resulting Numbers: [56, 56] Generated Node #0,0,3: 28:[56, 56] Operation: 13+43=56 Exploring Operation: 56-13=43, Resulting Numbers: [43, 43] Generated Node #0,0,4: 28:[43, 43] Operation: 56-13=43 Moving to Node #0,3 Current State: 28:[13, 84, 15], Operations: ['56-41=15'] Exploring Operation: 13+84=97, Resulting Numbers: [15, 97] Generated Node #0,3,0: 28:[15, 97] Operation: 13+84=97 Exploring Operation: 13+15=28, Resulting Numbers: [84, 28] Generated Node #0,3,1: 28:[84, 28] Operation: 13+15=28 Exploring Operation: 15-13=2, Resulting Numbers: [84, 2] Generated Node #0,3,2: 28:[84, 2] Operation: 15-13=2 Exploring Operation: 84-13=71, Resulting Numbers: [15, 71] Generated Node #0,3,3: 28:[15, 71] Operation: 84-13=71 Exploring Operation: 84-15=69, Resulting Numbers: [13, 69] Generated Node #0,3,4: 28:[13, 69] Operation: 84-15=69 Moving to Node #0,1 Current State: 28:[56, 84, 28], Operations: ['41-13=28'] Exploring Operation: 84-28=56, Resulting Numbers: [56, 56] Generated Node #0,1,0: 28:[56, 56] Operation: 84-28=56 Exploring Operation: 56-28=28, Resulting Numbers: [84, 28] Generated Node #0,1,1: 28:[84, 28] Operation: 56-28=28 Exploring Operation: 84-56=28, Resulting Numbers: [28, 28] Generated Node #0,1,2: 28:[28, 28] Operation: 84-56=28 Exploring Operation: 56/28=2, Resulting Numbers: [84, 2] Generated Node #0,1,3: 28:[84, 2] Operation: 56/28=2 Exploring Operation: 84/28=3, Resulting Numbers: [56, 3] Generated Node #0,1,4: 28:[56, 3] Operation: 84/28=3 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 28:[28, 28], Operations: ['41-13=28', '84-56=28'] Exploring Operation: 28-28=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 28+28=56, Resulting Numbers: [56] 56,28 unequal: No Solution Exploring Operation: 28*28=784, Resulting Numbers: [784] 784,28 unequal: No Solution Exploring Operation: 28/28=1, Resulting Numbers: [1] 1,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 28:[56, 3], Operations: ['41-13=28', '84/28=3'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,28 unequal: No Solution Exploring Operation: 56+3=59, Resulting Numbers: [59] 59,28 unequal: No Solution Exploring Operation: 56*3=168, Resulting Numbers: [168] 168,28 unequal: No Solution No 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: 28:[56, 56], Operations: ['41-13=28', '84-28=56'] Exploring Operation: 56+56=112, Resulting Numbers: [112] 112,28 unequal: No Solution Exploring Operation: 56*56=3136, Resulting Numbers: [3136] 3136,28 unequal: No Solution Exploring Operation: 56/56=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 56-56=0, Resulting Numbers: [0] 0,28 unequal: No Solution No 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: 28:[84, 28], Operations: ['41-13=28', '56-28=28'] Exploring Operation: 84*28=2352, Resulting Numbers: [2352] 2352,28 unequal: No Solution Exploring Operation: 84-28=56, Resulting Numbers: [56] 56,28 unequal: No Solution Exploring Operation: 84+28=112, Resulting Numbers: [112] 112,28 unequal: No Solution Exploring Operation: 84/28=3, Resulting Numbers: [3] 3,28 unequal: No Solution No 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: 28:[84, 2], Operations: ['41-13=28', '56/28=2'] Exploring Operation: 84*2=168, Resulting Numbers: [168] 168,28 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,28 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,28 unequal: No Solution Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,28 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: 28:[41, 84, 43], Operations: ['56-13=43'] Exploring Operation: 43-41=2, Resulting Numbers: [84, 2] Generated Node #0,2,0: 28:[84, 2] Operation: 43-41=2 Exploring Operation: 84-41=43, Resulting Numbers: [43, 43] Generated Node #0,2,1: 28:[43, 43] Operation: 84-41=43 Exploring Operation: 41+84=125, Resulting Numbers: [43, 125] Generated Node #0,2,2: 28:[43, 125] Operation: 41+84=125 Exploring Operation: 41+43=84, Resulting Numbers: [84, 84] Generated Node #0,2,3: 28:[84, 84] Operation: 41+43=84 Exploring Operation: 84-43=41, Resulting Numbers: [41, 41] Generated Node #0,2,4: 28:[41, 41] Operation: 84-43=41 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 28:[41, 41], Operations: ['56-13=43', '84-43=41'] Exploring Operation: 41/41=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 41*41=1681, Resulting Numbers: [1681] 1681,28 unequal: No Solution Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,28 unequal: No Solution Exploring Operation: 41-41=0, Resulting Numbers: [0] 0,28 unequal: No Solution No 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: 28:[43, 43], Operations: ['56-13=43', '84-41=43'] Exploring Operation: 43*43=1849, Resulting Numbers: [1849] 1849,28 unequal: No Solution Exploring Operation: 43+43=86, Resulting Numbers: [86] 86,28 unequal: No Solution Exploring Operation: 43-43=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 43/43=1, Resulting Numbers: [1] 1,28 unequal: No Solution No 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: 28:[84, 2], Operations: ['56-13=43', '43-41=2'] Exploring Operation: 84*2=168, Resulting Numbers: [168] 168,28 unequal: No Solution Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,28 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,28 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,28 unequal: No Solution No 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: 28:[43, 125], Operations: ['56-13=43', '41+84=125'] Exploring Operation: 43*125=5375, Resulting Numbers: [5375] 5375,28 unequal: No Solution Exploring Operation: 43+125=168, Resulting Numbers: [168] 168,28 unequal: No Solution Exploring Operation: 125-43=82, Resulting Numbers: [82] 82,28 unequal: No Solution No 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: 28:[84, 84], Operations: ['56-13=43', '41+43=84'] Exploring Operation: 84-84=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 84/84=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 84*84=7056, Resulting Numbers: [7056] 7056,28 unequal: No Solution Exploring Operation: 84+84=168, Resulting Numbers: [168] 168,28 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: 28:[13, 13], Operations: ['84-41=43', '56-43=13'] Exploring Operation: 13/13=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 13*13=169, Resulting Numbers: [169] 169,28 unequal: No Solution Exploring Operation: 13-13=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 13+13=26, Resulting Numbers: [26] 26,28 unequal: No Solution Moving to Node #0,0,4 Current State: 28:[43, 43], Operations: ['84-41=43', '56-13=43'] Exploring Operation: 43-43=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 43*43=1849, Resulting Numbers: [1849] 1849,28 unequal: No Solution Exploring Operation: 43+43=86, Resulting Numbers: [86] 86,28 unequal: No Solution Exploring Operation: 43/43=1, Resulting Numbers: [1] 1,28 unequal: No Solution Moving to Node #0,0,0 Current State: 28:[56, 30], Operations: ['84-41=43', '43-13=30'] Exploring Operation: 56+30=86, Resulting Numbers: [86] 86,28 unequal: No Solution Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,28 unequal: No Solution Exploring Operation: 56*30=1680, Resulting Numbers: [1680] 1680,28 unequal: No Solution Moving to Node #0,3,4 Current State: 28:[13, 69], Operations: ['56-41=15', '84-15=69'] Exploring Operation: 69-13=56, Resulting Numbers: [56] 56,28 unequal: No Solution Exploring Operation: 13*69=897, Resulting Numbers: [897] 897,28 unequal: No Solution Exploring Operation: 13+69=82, Resulting Numbers: [82] 82,28 unequal: No Solution Moving to Node #0,3,3 Current State: 28:[15, 71], Operations: ['56-41=15', '84-13=71'] Exploring Operation: 71-15=56, Resulting Numbers: [56] 56,28 unequal: No Solution Exploring Operation: 15+71=86, Resulting Numbers: [86] 86,28 unequal: No Solution Exploring Operation: 15*71=1065, Resulting Numbers: [1065] 1065,28 unequal: No Solution Moving to Node #0,3,1 Current State: 28:[84, 28], Operations: ['56-41=15', '13+15=28'] Exploring Operation: 84-28=56, Resulting Numbers: [56] 56,28 unequal: No Solution Exploring Operation: 84*28=2352, Resulting Numbers: [2352] 2352,28 unequal: No Solution Exploring Operation: 84/28=3, Resulting Numbers: [3] 3,28 unequal: No Solution Exploring Operation: 84+28=112, Resulting Numbers: [112] 112,28 unequal: No Solution Moving to Node #0,0,3 Current State: 28:[56, 56], Operations: ['84-41=43', '13+43=56'] Exploring Operation: 56-56=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 56*56=3136, Resulting Numbers: [3136] 3136,28 unequal: No Solution Exploring Operation: 56/56=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 56+56=112, Resulting Numbers: [112] 112,28 unequal: No Solution Moving to Node #0,0,2 Current State: 28:[43, 69], Operations: ['84-41=43', '13+56=69'] Exploring Operation: 69-43=26, Resulting Numbers: [26] 26,28 unequal: No Solution Exploring Operation: 43+69=112, Resulting Numbers: [112] 112,28 unequal: No Solution Exploring Operation: 43*69=2967, Resulting Numbers: [2967] 2967,28 unequal: No Solution Moving to Node #0,3,2 Current State: 28:[84, 2], Operations: ['56-41=15', '15-13=2'] Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,28 unequal: No Solution Exploring Operation: 84*2=168, Resulting Numbers: [168] 168,28 unequal: No Solution Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,28 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,28 unequal: No Solution Moving to Node #0,3,0 Current State: 28:[15, 97], Operations: ['56-41=15', '13+84=97'] Exploring Operation: 15*97=1455, Resulting Numbers: [1455] 1455,28 unequal: No Solution Exploring Operation: 15+97=112, Resulting Numbers: [112] 112,28 unequal: No Solution Exploring Operation: 97-15=82, Resulting Numbers: [82] 82,28 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 42, 34, 17, 49 ]
35
[ "42*34=1428", "1428/17=84", "84-49=35" ]
Current State: 35:[42, 34, 17, 49], Operations: [] Exploring Operation: 42*34=1428, Resulting Numbers: [17, 49, 1428] Generated Node #2: [17, 49, 1428] from Operation: 42*34=1428 Current State: 35:[17, 49, 1428], Operations: ['42*34=1428'] Exploring Operation: 1428/17=84, Resulting Numbers: [49, 84] Generated Node #3: [49, 84] from Operation: 1428/17=84 Current State: 35:[49, 84], Operations: ['42*34=1428', '1428/17=84'] Exploring Operation: 84-49=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[42, 34, 17, 49], Operations: [] Exploring Operation: 42-34=8, Resulting Numbers: [17, 49, 8] Generated Node #0,0: 35:[17, 49, 8] Operation: 42-34=8 Exploring Operation: 34/17=2, Resulting Numbers: [42, 49, 2] Generated Node #0,1: 35:[42, 49, 2] Operation: 34/17=2 Exploring Operation: 42-17=25, Resulting Numbers: [34, 49, 25] Generated Node #0,2: 35:[34, 49, 25] Operation: 42-17=25 Exploring Operation: 49-42=7, Resulting Numbers: [34, 17, 7] Generated Node #0,3: 35:[34, 17, 7] Operation: 49-42=7 Exploring Operation: 49-17=32, Resulting Numbers: [42, 34, 32] Generated Node #0,4: 35:[42, 34, 32] Operation: 49-17=32 Moving to Node #0,3 Current State: 35:[34, 17, 7], Operations: ['49-42=7'] Exploring Operation: 34/17=2, Resulting Numbers: [7, 2] Generated Node #0,3,0: 35:[7, 2] Operation: 34/17=2 Exploring Operation: 17-7=10, Resulting Numbers: [34, 10] Generated Node #0,3,1: 35:[34, 10] Operation: 17-7=10 Exploring Operation: 34-17=17, Resulting Numbers: [7, 17] Generated Node #0,3,2: 35:[7, 17] Operation: 34-17=17 Exploring Operation: 34+17=51, Resulting Numbers: [7, 51] Generated Node #0,3,3: 35:[7, 51] Operation: 34+17=51 Exploring Operation: 17+7=24, Resulting Numbers: [34, 24] Generated Node #0,3,4: 35:[34, 24] Operation: 17+7=24 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 35:[7, 2], Operations: ['49-42=7', '34/17=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,35 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 35:[34, 10], Operations: ['49-42=7', '17-7=10'] Exploring Operation: 34*10=340, Resulting Numbers: [340] 340,35 unequal: No Solution Exploring Operation: 34+10=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 35:[7, 17], Operations: ['49-42=7', '34-17=17'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,35 unequal: No Solution Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 35:[34, 24], Operations: ['49-42=7', '17+7=24'] Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,35 unequal: No Solution Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,35 unequal: No Solution Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 35:[7, 51], Operations: ['49-42=7', '34+17=51'] Exploring Operation: 7*51=357, Resulting Numbers: [357] 357,35 unequal: No Solution Exploring Operation: 51-7=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 7+51=58, Resulting Numbers: [58] 58,35 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: 35:[42, 34, 32], Operations: ['49-17=32'] Exploring Operation: 34+32=66, Resulting Numbers: [42, 66] Generated Node #0,4,0: 35:[42, 66] Operation: 34+32=66 Exploring Operation: 42+32=74, Resulting Numbers: [34, 74] Generated Node #0,4,1: 35:[34, 74] Operation: 42+32=74 Exploring Operation: 34-32=2, Resulting Numbers: [42, 2] Generated Node #0,4,2: 35:[42, 2] Operation: 34-32=2 Exploring Operation: 42-32=10, Resulting Numbers: [34, 10] Generated Node #0,4,3: 35:[34, 10] Operation: 42-32=10 Exploring Operation: 42-34=8, Resulting Numbers: [32, 8] Generated Node #0,4,4: 35:[32, 8] Operation: 42-34=8 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 35:[34, 10], Operations: ['49-17=32', '42-32=10'] Exploring Operation: 34+10=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,35 unequal: No Solution Exploring Operation: 34*10=340, Resulting Numbers: [340] 340,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 35:[32, 8], Operations: ['49-17=32', '42-34=8'] Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,35 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,35 unequal: No Solution Exploring Operation: 32*8=256, Resulting Numbers: [256] 256,35 unequal: No Solution Exploring Operation: 32+8=40, Resulting Numbers: [40] 40,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 35:[42, 2], Operations: ['49-17=32', '34-32=2'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,35 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 35:[42, 66], Operations: ['49-17=32', '34+32=66'] Exploring Operation: 42*66=2772, Resulting Numbers: [2772] 2772,35 unequal: No Solution Exploring Operation: 66-42=24, Resulting Numbers: [24] 24,35 unequal: No Solution Exploring Operation: 42+66=108, Resulting Numbers: [108] 108,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 35:[34, 74], Operations: ['49-17=32', '42+32=74'] Exploring Operation: 74-34=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 34*74=2516, Resulting Numbers: [2516] 2516,35 unequal: No Solution Exploring Operation: 34+74=108, Resulting Numbers: [108] 108,35 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: 35:[42, 49, 2], Operations: ['34/17=2'] Exploring Operation: 49-2=47, Resulting Numbers: [42, 47] Generated Node #0,1,0: 35:[42, 47] Operation: 49-2=47 Exploring Operation: 42+2=44, Resulting Numbers: [49, 44] Generated Node #0,1,1: 35:[49, 44] Operation: 42+2=44 Exploring Operation: 49+2=51, Resulting Numbers: [42, 51] Generated Node #0,1,2: 35:[42, 51] Operation: 49+2=51 Exploring Operation: 49-42=7, Resulting Numbers: [2, 7] Generated Node #0,1,3: 35:[2, 7] Operation: 49-42=7 Exploring Operation: 42-2=40, Resulting Numbers: [49, 40] Generated Node #0,1,4: 35:[49, 40] Operation: 42-2=40 Moving to Node #0,0 Current State: 35:[17, 49, 8], Operations: ['42-34=8'] Exploring Operation: 49-8=41, Resulting Numbers: [17, 41] Generated Node #0,0,0: 35:[17, 41] Operation: 49-8=41 Exploring Operation: 17-8=9, Resulting Numbers: [49, 9] Generated Node #0,0,1: 35:[49, 9] Operation: 17-8=9 Exploring Operation: 17+49=66, Resulting Numbers: [8, 66] Generated Node #0,0,2: 35:[8, 66] Operation: 17+49=66 Exploring Operation: 17+8=25, Resulting Numbers: [49, 25] Generated Node #0,0,3: 35:[49, 25] Operation: 17+8=25 Exploring Operation: 49-17=32, Resulting Numbers: [8, 32] Generated Node #0,0,4: 35:[8, 32] Operation: 49-17=32 Moving to Node #0,2 Current State: 35:[34, 49, 25], Operations: ['42-17=25'] Exploring Operation: 34+25=59, Resulting Numbers: [49, 59] Generated Node #0,2,0: 35:[49, 59] Operation: 34+25=59 Exploring Operation: 49-25=24, Resulting Numbers: [34, 24] Generated Node #0,2,1: 35:[34, 24] Operation: 49-25=24 Exploring Operation: 34-25=9, Resulting Numbers: [49, 9] Generated Node #0,2,2: 35:[49, 9] Operation: 34-25=9 Exploring Operation: 49-34=15, Resulting Numbers: [25, 15] Generated Node #0,2,3: 35:[25, 15] Operation: 49-34=15 Exploring Operation: 49+25=74, Resulting Numbers: [34, 74] Generated Node #0,2,4: 35:[34, 74] Operation: 49+25=74 Moving to Node #0,1,3 Current State: 35:[2, 7], Operations: ['34/17=2', '49-42=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,35 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,35 unequal: No Solution Moving to Node #0,0,4 Current State: 35:[8, 32], Operations: ['42-34=8', '49-17=32'] Exploring Operation: 8+32=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,35 unequal: No Solution Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,35 unequal: No Solution Exploring Operation: 8*32=256, Resulting Numbers: [256] 256,35 unequal: No Solution Moving to Node #0,2,1 Current State: 35:[34, 24], Operations: ['42-17=25', '49-25=24'] Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,35 unequal: No Solution Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[17, 41], Operations: ['42-34=8', '49-8=41'] Exploring Operation: 17+41=58, Resulting Numbers: [58] 58,35 unequal: No Solution Exploring Operation: 17*41=697, Resulting Numbers: [697] 697,35 unequal: No Solution Exploring Operation: 41-17=24, Resulting Numbers: [24] 24,35 unequal: No Solution Moving to Node #0,2,2 Current State: 35:[49, 9], Operations: ['42-17=25', '34-25=9'] Exploring Operation: 49*9=441, Resulting Numbers: [441] 441,35 unequal: No Solution Exploring Operation: 49+9=58, Resulting Numbers: [58] 58,35 unequal: No Solution Exploring Operation: 49-9=40, Resulting Numbers: [40] 40,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[49, 9], Operations: ['42-34=8', '17-8=9'] Exploring Operation: 49*9=441, Resulting Numbers: [441] 441,35 unequal: No Solution Exploring Operation: 49+9=58, Resulting Numbers: [58] 58,35 unequal: No Solution Exploring Operation: 49-9=40, Resulting Numbers: [40] 40,35 unequal: No Solution Moving to Node #0,2,3 Current State: 35:[25, 15], Operations: ['42-17=25', '49-34=15'] Exploring Operation: 25+15=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 25*15=375, Resulting Numbers: [375] 375,35 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,35 unequal: No Solution Moving to Node #0,1,4 Current State: 35:[49, 40], Operations: ['34/17=2', '42-2=40'] Exploring Operation: 49-40=9, Resulting Numbers: [9] 9,35 unequal: No Solution Exploring Operation: 49+40=89, Resulting Numbers: [89] 89,35 unequal: No Solution Exploring Operation: 49*40=1960, Resulting Numbers: [1960] 1960,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[42, 47], Operations: ['34/17=2', '49-2=47'] Exploring Operation: 47-42=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 42+47=89, Resulting Numbers: [89] 89,35 unequal: No Solution Exploring Operation: 42*47=1974, Resulting Numbers: [1974] 1974,35 unequal: No Solution Moving to Node #0,1,2 Current State: 35:[42, 51], Operations: ['34/17=2', '49+2=51'] Exploring Operation: 42*51=2142, Resulting Numbers: [2142] 2142,35 unequal: No Solution Exploring Operation: 42+51=93, Resulting Numbers: [93] 93,35 unequal: No Solution Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[49, 44], Operations: ['34/17=2', '42+2=44'] Exploring Operation: 49*44=2156, Resulting Numbers: [2156] 2156,35 unequal: No Solution Exploring Operation: 49+44=93, Resulting Numbers: [93] 93,35 unequal: No Solution Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,35 unequal: No Solution Moving to Node #0,0,3 Current State: 35:[49, 25], Operations: ['42-34=8', '17+8=25'] Exploring Operation: 49+25=74, Resulting Numbers: [74] 74,35 unequal: No Solution Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,35 unequal: No Solution Exploring Operation: 49*25=1225, Resulting Numbers: [1225] 1225,35 unequal: No Solution Moving to Node #0,0,2 Current State: 35:[8, 66], Operations: ['42-34=8', '17+49=66'] Exploring Operation: 8*66=528, Resulting Numbers: [528] 528,35 unequal: No Solution Exploring Operation: 8+66=74, Resulting Numbers: [74] 74,35 unequal: No Solution Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[49, 59], Operations: ['42-17=25', '34+25=59'] Exploring Operation: 49*59=2891, Resulting Numbers: [2891] 2891,35 unequal: No Solution Exploring Operation: 59-49=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 49+59=108, Resulting Numbers: [108] 108,35 unequal: No Solution Moving to Node #0,2,4 Current State: 35:[34, 74], Operations: ['42-17=25', '49+25=74'] Exploring Operation: 34+74=108, Resulting Numbers: [108] 108,35 unequal: No Solution Exploring Operation: 74-34=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 34*74=2516, Resulting Numbers: [2516] 2516,35 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 2, 9, 18, 66 ]
35
[ "66/2=33", "18/9=2", "33+2=35" ]
Current State: 35:[2, 9, 18, 66], Operations: [] Exploring Operation: 66/2=33, Resulting Numbers: [9, 18, 33] Generated Node #2: [9, 18, 33] from Operation: 66/2=33 Current State: 35:[9, 18, 33], Operations: ['66/2=33'] Exploring Operation: 18/9=2, Resulting Numbers: [33, 2] Generated Node #3: [33, 2] from Operation: 18/9=2 Current State: 35:[33, 2], Operations: ['66/2=33', '18/9=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[2, 9, 18, 66], Operations: [] Exploring Operation: 66-18=48, Resulting Numbers: [2, 9, 48] Generated Node #0,0: 35:[2, 9, 48] Operation: 66-18=48 Exploring Operation: 66/2=33, Resulting Numbers: [9, 18, 33] Generated Node #0,1: 35:[9, 18, 33] Operation: 66/2=33 Exploring Operation: 2*18=36, Resulting Numbers: [9, 66, 36] Generated Node #0,2: 35:[9, 66, 36] Operation: 2*18=36 Moving to Node #0,1 Current State: 35:[9, 18, 33], Operations: ['66/2=33'] Exploring Operation: 18/9=2, Resulting Numbers: [33, 2] Generated Node #0,1,0: 35:[33, 2] Operation: 18/9=2 Exploring Operation: 18-9=9, Resulting Numbers: [33, 9] Generated Node #0,1,1: 35:[33, 9] Operation: 18-9=9 Exploring Operation: 9+18=27, Resulting Numbers: [33, 27] Generated Node #0,1,2: 35:[33, 27] Operation: 9+18=27 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[33, 9], Operations: ['66/2=33', '18-9=9'] Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,35 unequal: No Solution Exploring Operation: 33*9=297, Resulting Numbers: [297] 297,35 unequal: No Solution Exploring Operation: 33+9=42, Resulting Numbers: [42] 42,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[33, 2], Operations: ['66/2=33', '18/9=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[2, 9, 18, 66], Operations: [] Exploring Operation: 66/2=33, Resulting Numbers: [9, 18, 33] Generated Node #0,1: 35:[9, 18, 33] Operation: 66/2=33 Moving to Node #0,1 Current State: 35:[9, 18, 33], Operations: ['66/2=33'] Exploring Operation: 18/9=2, Resulting Numbers: [33, 2] Generated Node #0,1,0: 35:[33, 2] Operation: 18/9=2 Moving to Node #0,1,0 Current State: 35:[33, 2], Operations: ['66/2=33', '18/9=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 82, 35, 84, 26 ]
63
[ "82-35=47", "84+26=110", "110-47=63" ]
Current State: 63:[82, 35, 84, 26], Operations: [] Exploring Operation: 82-35=47, Resulting Numbers: [84, 26, 47] Generated Node #2: [84, 26, 47] from Operation: 82-35=47 Current State: 63:[84, 26, 47], Operations: ['82-35=47'] Exploring Operation: 84+26=110, Resulting Numbers: [47, 110] Generated Node #3: [47, 110] from Operation: 84+26=110 Current State: 63:[47, 110], Operations: ['82-35=47', '84+26=110'] Exploring Operation: 110-47=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[82, 35, 84, 26], Operations: [] Exploring Operation: 84-35=49, Resulting Numbers: [82, 26, 49] Generated Node #0,0: 63:[82, 26, 49] Operation: 84-35=49 Exploring Operation: 84-82=2, Resulting Numbers: [35, 26, 2] Generated Node #0,1: 63:[35, 26, 2] Operation: 84-82=2 Moving to Node #0,1 Current State: 63:[35, 26, 2], Operations: ['84-82=2'] Exploring Operation: 35-26=9, Resulting Numbers: [2, 9] Generated Node #0,1,0: 63:[2, 9] Operation: 35-26=9 Exploring Operation: 35+26=61, Resulting Numbers: [2, 61] Generated Node #0,1,1: 63:[2, 61] Operation: 35+26=61 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 63:[2, 9], Operations: ['84-82=2', '35-26=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 No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 63:[2, 61], Operations: ['84-82=2', '35+26=61'] Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[82, 35, 84, 26], Operations: [] Exploring Operation: 84-82=2, Resulting Numbers: [35, 26, 2] Generated Node #0,1: 63:[35, 26, 2] Operation: 84-82=2 Moving to Node #0,1 Current State: 63:[35, 26, 2], Operations: ['84-82=2'] Exploring Operation: 35+26=61, Resulting Numbers: [2, 61] Generated Node #0,1,1: 63:[2, 61] Operation: 35+26=61 Moving to Node #0,1,1 Current State: 63:[2, 61], Operations: ['84-82=2', '35+26=61'] Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 39, 67, 76, 18 ]
41
[ "76-67=9", "18/9=2", "39+2=41" ]
Current State: 41:[39, 67, 76, 18], Operations: [] Exploring Operation: 76-67=9, Resulting Numbers: [39, 18, 9] Generated Node #2: [39, 18, 9] from Operation: 76-67=9 Current State: 41:[39, 18, 9], Operations: ['76-67=9'] Exploring Operation: 18/9=2, Resulting Numbers: [39, 2] Generated Node #3: [39, 2] from Operation: 18/9=2 Current State: 41:[39, 2], Operations: ['76-67=9', '18/9=2'] Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[39, 67, 76, 18], Operations: [] Exploring Operation: 76-39=37, Resulting Numbers: [67, 18, 37] Generated Node #0,0: 41:[67, 18, 37] Operation: 76-39=37 Exploring Operation: 76-67=9, Resulting Numbers: [39, 18, 9] Generated Node #0,1: 41:[39, 18, 9] Operation: 76-67=9 Exploring Operation: 76-18=58, Resulting Numbers: [39, 67, 58] Generated Node #0,2: 41:[39, 67, 58] Operation: 76-18=58 Exploring Operation: 67-18=49, Resulting Numbers: [39, 76, 49] Generated Node #0,3: 41:[39, 76, 49] Operation: 67-18=49 Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[39, 67, 58], Operations: ['76-18=58'] Exploring Operation: 58-39=19, Resulting Numbers: [67, 19] Generated Node #0,2,0: 41:[67, 19] Operation: 58-39=19 Exploring Operation: 67-39=28, Resulting Numbers: [58, 28] Generated Node #0,2,1: 41:[58, 28] Operation: 67-39=28 Exploring Operation: 39+67=106, Resulting Numbers: [58, 106] Generated Node #0,2,2: 41:[58, 106] Operation: 39+67=106 Exploring Operation: 67-58=9, Resulting Numbers: [39, 9] Generated Node #0,2,3: 41:[39, 9] Operation: 67-58=9 Moving to Node #0,2,1 Current State: 41:[58, 28], Operations: ['76-18=58', '67-39=28'] Exploring Operation: 58*28=1624, Resulting Numbers: [1624] 1624,41 unequal: No Solution Exploring Operation: 58-28=30, Resulting Numbers: [30] 30,41 unequal: No Solution Exploring Operation: 58+28=86, Resulting Numbers: [86] 86,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[39, 9], Operations: ['76-18=58', '67-58=9'] Exploring Operation: 39*9=351, Resulting Numbers: [351] 351,41 unequal: No Solution Exploring Operation: 39-9=30, Resulting Numbers: [30] 30,41 unequal: No Solution Exploring Operation: 39+9=48, Resulting Numbers: [48] 48,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[67, 19], Operations: ['76-18=58', '58-39=19'] Exploring Operation: 67+19=86, Resulting Numbers: [86] 86,41 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 67*19=1273, Resulting Numbers: [1273] 1273,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[58, 106], Operations: ['76-18=58', '39+67=106'] Exploring Operation: 106-58=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 58*106=6148, Resulting Numbers: [6148] 6148,41 unequal: No Solution Exploring Operation: 58+106=164, Resulting Numbers: [164] 164,41 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 #0,3 Current State: 41:[39, 76, 49], Operations: ['67-18=49'] Exploring Operation: 49-39=10, Resulting Numbers: [76, 10] Generated Node #0,3,0: 41:[76, 10] Operation: 49-39=10 Exploring Operation: 39+76=115, Resulting Numbers: [49, 115] Generated Node #0,3,1: 41:[49, 115] Operation: 39+76=115 Exploring Operation: 76-49=27, Resulting Numbers: [39, 27] Generated Node #0,3,2: 41:[39, 27] Operation: 76-49=27 Exploring Operation: 76-39=37, Resulting Numbers: [49, 37] Generated Node #0,3,3: 41:[49, 37] Operation: 76-39=37 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 41:[49, 37], Operations: ['67-18=49', '76-39=37'] Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 49*37=1813, Resulting Numbers: [1813] 1813,41 unequal: No Solution Exploring Operation: 49+37=86, Resulting Numbers: [86] 86,41 unequal: No Solution No 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: 41:[39, 27], Operations: ['67-18=49', '76-49=27'] Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,41 unequal: No Solution Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 39*27=1053, Resulting Numbers: [1053] 1053,41 unequal: No Solution No 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: 41:[76, 10], Operations: ['67-18=49', '49-39=10'] Exploring Operation: 76-10=66, Resulting Numbers: [66] 66,41 unequal: No Solution Exploring Operation: 76*10=760, Resulting Numbers: [760] 760,41 unequal: No Solution Exploring Operation: 76+10=86, Resulting Numbers: [86] 86,41 unequal: No Solution No 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: 41:[49, 115], Operations: ['67-18=49', '39+76=115'] Exploring Operation: 49+115=164, Resulting Numbers: [164] 164,41 unequal: No Solution Exploring Operation: 49*115=5635, Resulting Numbers: [5635] 5635,41 unequal: No Solution Exploring Operation: 115-49=66, Resulting Numbers: [66] 66,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[67, 18, 37], Operations: ['76-39=37'] Exploring Operation: 67-18=49, Resulting Numbers: [37, 49] Generated Node #0,0,0: 41:[37, 49] Operation: 67-18=49 Exploring Operation: 67-37=30, Resulting Numbers: [18, 30] Generated Node #0,0,1: 41:[18, 30] Operation: 67-37=30 Exploring Operation: 18+37=55, Resulting Numbers: [67, 55] Generated Node #0,0,2: 41:[67, 55] Operation: 18+37=55 Exploring Operation: 67+18=85, Resulting Numbers: [37, 85] Generated Node #0,0,3: 41:[37, 85] Operation: 67+18=85 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[37, 49], Operations: ['76-39=37', '67-18=49'] Exploring Operation: 37*49=1813, Resulting Numbers: [1813] 1813,41 unequal: No Solution Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 37+49=86, Resulting Numbers: [86] 86,41 unequal: No Solution No 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: 41:[18, 30], Operations: ['76-39=37', '67-37=30'] Exploring Operation: 18*30=540, Resulting Numbers: [540] 540,41 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 18+30=48, Resulting Numbers: [48] 48,41 unequal: No Solution No 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: 41:[67, 55], Operations: ['76-39=37', '18+37=55'] Exploring Operation: 67+55=122, Resulting Numbers: [122] 122,41 unequal: No Solution Exploring Operation: 67-55=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 67*55=3685, Resulting Numbers: [3685] 3685,41 unequal: No Solution No 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: 41:[37, 85], Operations: ['76-39=37', '67+18=85'] Exploring Operation: 37*85=3145, Resulting Numbers: [3145] 3145,41 unequal: No Solution Exploring Operation: 85-37=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 37+85=122, Resulting Numbers: [122] 122,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[39, 18, 9], Operations: ['76-67=9'] Exploring Operation: 39+9=48, Resulting Numbers: [18, 48] Generated Node #0,1,0: 41:[18, 48] Operation: 39+9=48 Exploring Operation: 18+9=27, Resulting Numbers: [39, 27] Generated Node #0,1,1: 41:[39, 27] Operation: 18+9=27 Exploring Operation: 39-9=30, Resulting Numbers: [18, 30] Generated Node #0,1,2: 41:[18, 30] Operation: 39-9=30 Exploring Operation: 18-9=9, Resulting Numbers: [39, 9] Generated Node #0,1,3: 41:[39, 9] Operation: 18-9=9 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 41:[39, 27], Operations: ['76-67=9', '18+9=27'] Exploring Operation: 39*27=1053, Resulting Numbers: [1053] 1053,41 unequal: No Solution Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,41 unequal: No Solution No 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: 41:[18, 48], Operations: ['76-67=9', '39+9=48'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,41 unequal: No Solution Exploring Operation: 18+48=66, Resulting Numbers: [66] 66,41 unequal: No Solution Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,41 unequal: No Solution No 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: 41:[18, 30], Operations: ['76-67=9', '39-9=30'] Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 18*30=540, Resulting Numbers: [540] 540,41 unequal: No Solution Exploring Operation: 18+30=48, Resulting Numbers: [48] 48,41 unequal: No Solution No 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: 41:[39, 9], Operations: ['76-67=9', '18-9=9'] Exploring Operation: 39+9=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 39-9=30, Resulting Numbers: [30] 30,41 unequal: No Solution Exploring Operation: 39*9=351, Resulting Numbers: [351] 351,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 9, 69, 46, 46 ]
69
[ "46-46=0", "9*0=0", "69+0=69" ]
Current State: 69:[9, 69, 46, 46], Operations: [] Exploring Operation: 46-46=0, Resulting Numbers: [9, 69, 0] Generated Node #2: [9, 69, 0] from Operation: 46-46=0 Current State: 69:[9, 69, 0], Operations: ['46-46=0'] Exploring Operation: 9*0=0, Resulting Numbers: [69, 0] Generated Node #3: [69, 0] from Operation: 9*0=0 Current State: 69:[69, 0], Operations: ['46-46=0', '9*0=0'] Exploring Operation: 69+0=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[9, 69, 46, 46], Operations: [] Exploring Operation: 46/46=1, Resulting Numbers: [9, 69, 1] Generated Node #0,0: 69:[9, 69, 1] Operation: 46/46=1 Exploring Operation: 46-46=0, Resulting Numbers: [9, 69, 0] Generated Node #0,1: 69:[9, 69, 0] Operation: 46-46=0 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[9, 69, 1], Operations: ['46/46=1'] Exploring Operation: 9*1=9, Resulting Numbers: [69, 9] Generated Node #0,0,0: 69:[69, 9] Operation: 9*1=9 Exploring Operation: 9-1=8, Resulting Numbers: [69, 8] Generated Node #0,0,1: 69:[69, 8] Operation: 9-1=8 Moving to Node #0,0,1 Current State: 69:[69, 8], Operations: ['46/46=1', '9-1=8'] Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,69 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[69, 9], Operations: ['46/46=1', '9*1=9'] Exploring Operation: 69-9=60, Resulting Numbers: [60] 60,69 unequal: No Solution Exploring Operation: 69+9=78, Resulting Numbers: [78] 78,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[9, 69, 0], Operations: ['46-46=0'] Exploring Operation: 9*0=0, Resulting Numbers: [69, 0] Generated Node #0,1,0: 69:[69, 0] Operation: 9*0=0 Exploring Operation: 9+0=9, Resulting Numbers: [69, 9] Generated Node #0,1,1: 69:[69, 9] Operation: 9+0=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 69:[69, 0], Operations: ['46-46=0', '9*0=0'] Exploring Operation: 69+0=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[9, 69, 46, 46], Operations: [] Exploring Operation: 46-46=0, Resulting Numbers: [9, 69, 0] Generated Node #0,1: 69:[9, 69, 0] Operation: 46-46=0 Moving to Node #0,1 Current State: 69:[9, 69, 0], Operations: ['46-46=0'] Exploring Operation: 9*0=0, Resulting Numbers: [69, 0] Generated Node #0,1,0: 69:[69, 0] Operation: 9*0=0 Moving to Node #0,1,0 Current State: 69:[69, 0], Operations: ['46-46=0', '9*0=0'] Exploring Operation: 69+0=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 39, 20, 80, 40 ]
61
[ "39+20=59", "80+40=120", "120-59=61" ]
Current State: 61:[39, 20, 80, 40], Operations: [] Exploring Operation: 39+20=59, Resulting Numbers: [80, 40, 59] Generated Node #2: [80, 40, 59] from Operation: 39+20=59 Current State: 61:[80, 40, 59], Operations: ['39+20=59'] Exploring Operation: 80+40=120, Resulting Numbers: [59, 120] Generated Node #3: [59, 120] from Operation: 80+40=120 Current State: 61:[59, 120], Operations: ['39+20=59', '80+40=120'] Exploring Operation: 120-59=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[39, 20, 80, 40], Operations: [] Exploring Operation: 39+20=59, Resulting Numbers: [80, 40, 59] Generated Node #0,0: 61:[80, 40, 59] Operation: 39+20=59 Moving to Node #0,0 Current State: 61:[80, 40, 59], Operations: ['39+20=59'] Exploring Operation: 80-40=40, Resulting Numbers: [59, 40] Generated Node #0,0,0: 61:[59, 40] Operation: 80-40=40 Moving to Node #0,0,0 Current State: 61:[59, 40], Operations: ['39+20=59', '80-40=40'] Exploring Operation: 59+40=99, Resulting Numbers: [99] 99,61 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 95, 15, 24, 18 ]
97
[ "24-15=9", "18/9=2", "95+2=97" ]
Current State: 97:[95, 15, 24, 18], Operations: [] Exploring Operation: 24-15=9, Resulting Numbers: [95, 18, 9] Generated Node #2: [95, 18, 9] from Operation: 24-15=9 Current State: 97:[95, 18, 9], Operations: ['24-15=9'] Exploring Operation: 18/9=2, Resulting Numbers: [95, 2] Generated Node #3: [95, 2] from Operation: 18/9=2 Current State: 97:[95, 2], Operations: ['24-15=9', '18/9=2'] Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[95, 15, 24, 18], Operations: [] Exploring Operation: 15+18=33, Resulting Numbers: [95, 24, 33] Generated Node #0,0: 97:[95, 24, 33] Operation: 15+18=33 Exploring Operation: 15+24=39, Resulting Numbers: [95, 18, 39] Generated Node #0,1: 97:[95, 18, 39] Operation: 15+24=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[95, 24, 33], Operations: ['15+18=33'] Exploring Operation: 24+33=57, Resulting Numbers: [95, 57] Generated Node #0,0,0: 97:[95, 57] Operation: 24+33=57 Exploring Operation: 95+24=119, Resulting Numbers: [33, 119] Generated Node #0,0,1: 97:[33, 119] Operation: 95+24=119 Moving to Node #0,0,0 Current State: 97:[95, 57], Operations: ['15+18=33', '24+33=57'] Exploring Operation: 95-57=38, Resulting Numbers: [38] 38,97 unequal: No Solution Exploring Operation: 95+57=152, Resulting Numbers: [152] 152,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[33, 119], Operations: ['15+18=33', '95+24=119'] Exploring Operation: 33+119=152, Resulting Numbers: [152] 152,97 unequal: No Solution Exploring Operation: 119-33=86, Resulting Numbers: [86] 86,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[95, 18, 39], Operations: ['15+24=39'] Exploring Operation: 95+18=113, Resulting Numbers: [39, 113] Generated Node #0,1,0: 97:[39, 113] Operation: 95+18=113 Exploring Operation: 18+39=57, Resulting Numbers: [95, 57] Generated Node #0,1,1: 97:[95, 57] Operation: 18+39=57 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 97:[95, 57], Operations: ['15+24=39', '18+39=57'] Exploring Operation: 95+57=152, Resulting Numbers: [152] 152,97 unequal: No Solution Exploring Operation: 95-57=38, Resulting Numbers: [38] 38,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[39, 113], Operations: ['15+24=39', '95+18=113'] Exploring Operation: 113-39=74, Resulting Numbers: [74] 74,97 unequal: No Solution Exploring Operation: 39+113=152, Resulting Numbers: [152] 152,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 98, 86, 5, 43 ]
60
[ "98-86=12", "5+43=48", "12+48=60" ]
Current State: 60:[98, 86, 5, 43], Operations: [] Exploring Operation: 98-86=12, Resulting Numbers: [5, 43, 12] Generated Node #2: [5, 43, 12] from Operation: 98-86=12 Current State: 60:[5, 43, 12], Operations: ['98-86=12'] Exploring Operation: 5+43=48, Resulting Numbers: [12, 48] Generated Node #3: [12, 48] from Operation: 5+43=48 Current State: 60:[12, 48], Operations: ['98-86=12', '5+43=48'] Exploring Operation: 12+48=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[98, 86, 5, 43], Operations: [] Exploring Operation: 98-5=93, Resulting Numbers: [86, 43, 93] Generated Node #0,0: 60:[86, 43, 93] Operation: 98-5=93 Exploring Operation: 86/43=2, Resulting Numbers: [98, 5, 2] Generated Node #0,1: 60:[98, 5, 2] Operation: 86/43=2 Exploring Operation: 98-86=12, Resulting Numbers: [5, 43, 12] Generated Node #0,2: 60:[5, 43, 12] Operation: 98-86=12 Exploring Operation: 98-43=55, Resulting Numbers: [86, 5, 55] Generated Node #0,3: 60:[86, 5, 55] Operation: 98-43=55 Exploring Operation: 86-43=43, Resulting Numbers: [98, 5, 43] Generated Node #0,4: 60:[98, 5, 43] Operation: 86-43=43 Moving to Node #0,2 Current State: 60:[5, 43, 12], Operations: ['98-86=12'] Exploring Operation: 5+43=48, Resulting Numbers: [12, 48] Generated Node #0,2,0: 60:[12, 48] Operation: 5+43=48 Exploring Operation: 43+12=55, Resulting Numbers: [5, 55] Generated Node #0,2,1: 60:[5, 55] Operation: 43+12=55 Exploring Operation: 43-12=31, Resulting Numbers: [5, 31] Generated Node #0,2,2: 60:[5, 31] Operation: 43-12=31 Exploring Operation: 43-5=38, Resulting Numbers: [12, 38] Generated Node #0,2,3: 60:[12, 38] Operation: 43-5=38 Exploring Operation: 5*12=60, Resulting Numbers: [43, 60] Generated Node #0,2,4: 60:[43, 60] Operation: 5*12=60 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 60:[5, 31], Operations: ['98-86=12', '43-12=31'] Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,60 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,60 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 60:[5, 55], Operations: ['98-86=12', '43+12=55'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[98, 86, 5, 43], Operations: [] Exploring Operation: 98-86=12, Resulting Numbers: [5, 43, 12] Generated Node #0,2: 60:[5, 43, 12] Operation: 98-86=12 Moving to Node #0,2 Current State: 60:[5, 43, 12], Operations: ['98-86=12'] Exploring Operation: 43+12=55, Resulting Numbers: [5, 55] Generated Node #0,2,1: 60:[5, 55] Operation: 43+12=55 Moving to Node #0,2,1 Current State: 60:[5, 55], Operations: ['98-86=12', '43+12=55'] Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 63, 20, 30, 72 ]
90
[ "63+72=135", "20*135=2700", "2700/30=90" ]
Current State: 90:[63, 20, 30, 72], Operations: [] Exploring Operation: 63+72=135, Resulting Numbers: [20, 30, 135] Generated Node #2: [20, 30, 135] from Operation: 63+72=135 Current State: 90:[20, 30, 135], Operations: ['63+72=135'] Exploring Operation: 20*135=2700, Resulting Numbers: [30, 2700] Generated Node #3: [30, 2700] from Operation: 20*135=2700 Current State: 90:[30, 2700], Operations: ['63+72=135', '20*135=2700'] Exploring Operation: 2700/30=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[63, 20, 30, 72], Operations: [] Exploring Operation: 72-63=9, Resulting Numbers: [20, 30, 9] Generated Node #0,0: 90:[20, 30, 9] Operation: 72-63=9 Exploring Operation: 20+72=92, Resulting Numbers: [63, 30, 92] Generated Node #0,1: 90:[63, 30, 92] Operation: 20+72=92 Exploring Operation: 63-20=43, Resulting Numbers: [30, 72, 43] Generated Node #0,2: 90:[30, 72, 43] Operation: 63-20=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[20, 30, 9], Operations: ['72-63=9'] Exploring Operation: 30-20=10, Resulting Numbers: [9, 10] Generated Node #0,0,0: 90:[9, 10] Operation: 30-20=10 Exploring Operation: 20+9=29, Resulting Numbers: [30, 29] Generated Node #0,0,1: 90:[30, 29] Operation: 20+9=29 Exploring Operation: 20-9=11, Resulting Numbers: [30, 11] Generated Node #0,0,2: 90:[30, 11] Operation: 20-9=11 Moving to Node #0,0,0 Current State: 90:[9, 10], Operations: ['72-63=9', '30-20=10'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[63, 20, 30, 72], Operations: [] Exploring Operation: 72-63=9, Resulting Numbers: [20, 30, 9] Generated Node #0,0: 90:[20, 30, 9] Operation: 72-63=9 Moving to Node #0,0 Current State: 90:[20, 30, 9], Operations: ['72-63=9'] Exploring Operation: 30-20=10, Resulting Numbers: [9, 10] Generated Node #0,0,0: 90:[9, 10] Operation: 30-20=10 Moving to Node #0,0,0 Current State: 90:[9, 10], Operations: ['72-63=9', '30-20=10'] Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic