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
[ 47, 14, 55, 63 ]
49
[ "55-47=8", "14*8=112", "112-63=49" ]
Current State: 49:[47, 14, 55, 63], Operations: [] Exploring Operation: 55-47=8, Resulting Numbers: [14, 63, 8] Generated Node #2: [14, 63, 8] from Operation: 55-47=8 Current State: 49:[14, 63, 8], Operations: ['55-47=8'] Exploring Operation: 14*8=112, Resulting Numbers: [63, 112] Generated Node #3: [63, 112] from Operation: 14*8=112 Current State: 49:[63, 112], Operations: ['55-47=8', '14*8=112'] Exploring Operation: 112-63=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[47, 14, 55, 63], Operations: [] Exploring Operation: 63-47=16, Resulting Numbers: [14, 55, 16] Generated Node #0,0: 49:[14, 55, 16] Operation: 63-47=16 Exploring Operation: 63-14=49, Resulting Numbers: [47, 55, 49] Generated Node #0,1: 49:[47, 55, 49] Operation: 63-14=49 Exploring Operation: 63-55=8, Resulting Numbers: [47, 14, 8] Generated Node #0,2: 49:[47, 14, 8] Operation: 63-55=8 Exploring Operation: 55-47=8, Resulting Numbers: [14, 63, 8] Generated Node #0,3: 49:[14, 63, 8] Operation: 55-47=8 Moving to Node #0,1 Current State: 49:[47, 55, 49], Operations: ['63-14=49'] Exploring Operation: 47+55=102, Resulting Numbers: [49, 102] Generated Node #0,1,0: 49:[49, 102] Operation: 47+55=102 Exploring Operation: 55-49=6, Resulting Numbers: [47, 6] Generated Node #0,1,1: 49:[47, 6] Operation: 55-49=6 Exploring Operation: 55-47=8, Resulting Numbers: [49, 8] Generated Node #0,1,2: 49:[49, 8] Operation: 55-47=8 Exploring Operation: 49-47=2, Resulting Numbers: [55, 2] Generated Node #0,1,3: 49:[55, 2] Operation: 49-47=2 Moving to Node #0,2 Current State: 49:[47, 14, 8], Operations: ['63-55=8'] Exploring Operation: 47+14=61, Resulting Numbers: [8, 61] Generated Node #0,2,0: 49:[8, 61] Operation: 47+14=61 Exploring Operation: 47+8=55, Resulting Numbers: [14, 55] Generated Node #0,2,1: 49:[14, 55] Operation: 47+8=55 Exploring Operation: 47-14=33, Resulting Numbers: [8, 33] Generated Node #0,2,2: 49:[8, 33] Operation: 47-14=33 Exploring Operation: 14-8=6, Resulting Numbers: [47, 6] Generated Node #0,2,3: 49:[47, 6] Operation: 14-8=6 Moving to Node #0,3 Current State: 49:[14, 63, 8], Operations: ['55-47=8'] Exploring Operation: 63-14=49, Resulting Numbers: [8, 49] Generated Node #0,3,0: 49:[8, 49] Operation: 63-14=49 Exploring Operation: 14-8=6, Resulting Numbers: [63, 6] Generated Node #0,3,1: 49:[63, 6] Operation: 14-8=6 Exploring Operation: 14+63=77, Resulting Numbers: [8, 77] Generated Node #0,3,2: 49:[8, 77] Operation: 14+63=77 Exploring Operation: 63-8=55, Resulting Numbers: [14, 55] Generated Node #0,3,3: 49:[14, 55] Operation: 63-8=55 Moving to Node #0,0 Current State: 49:[14, 55, 16], Operations: ['63-47=16'] Exploring Operation: 16-14=2, Resulting Numbers: [55, 2] Generated Node #0,0,0: 49:[55, 2] Operation: 16-14=2 Exploring Operation: 55-16=39, Resulting Numbers: [14, 39] Generated Node #0,0,1: 49:[14, 39] Operation: 55-16=39 Exploring Operation: 14+16=30, Resulting Numbers: [55, 30] Generated Node #0,0,2: 49:[55, 30] Operation: 14+16=30 Exploring Operation: 55-14=41, Resulting Numbers: [16, 41] Generated Node #0,0,3: 49:[16, 41] Operation: 55-14=41 Moving to Node #0,1,2 Current State: 49:[49, 8], Operations: ['63-14=49', '55-47=8'] Exploring Operation: 49*8=392, Resulting Numbers: [392] 392,49 unequal: No Solution Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,49 unequal: No Solution Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,49 unequal: No Solution Moving to Node #0,3,0 Current State: 49:[8, 49], Operations: ['55-47=8', '63-14=49'] Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,49 unequal: No Solution Exploring Operation: 8*49=392, Resulting Numbers: [392] 392,49 unequal: No Solution Exploring Operation: 8+49=57, Resulting Numbers: [57] 57,49 unequal: No Solution Moving to Node #0,2,3 Current State: 49:[47, 6], Operations: ['63-55=8', '14-8=6'] Exploring Operation: 47*6=282, Resulting Numbers: [282] 282,49 unequal: No Solution Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,49 unequal: No Solution Moving to Node #0,1,1 Current State: 49:[47, 6], Operations: ['63-14=49', '55-49=6'] Exploring Operation: 47*6=282, Resulting Numbers: [282] 282,49 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,49 unequal: No Solution Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,49 unequal: No Solution Moving to Node #0,1,3 Current State: 49:[55, 2], Operations: ['63-14=49', '49-47=2'] Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,49 unequal: No Solution Exploring Operation: 55*2=110, Resulting Numbers: [110] 110,49 unequal: No Solution Moving to Node #0,0,0 Current State: 49:[55, 2], Operations: ['63-47=16', '16-14=2'] Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,49 unequal: No Solution Exploring Operation: 55*2=110, Resulting Numbers: [110] 110,49 unequal: No Solution Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[14, 55], Operations: ['63-55=8', '47+8=55'] Exploring Operation: 55-14=41, Resulting Numbers: [41] 41,49 unequal: No Solution Exploring Operation: 14+55=69, Resulting Numbers: [69] 69,49 unequal: No Solution Exploring Operation: 14*55=770, Resulting Numbers: [770] 770,49 unequal: No Solution Moving to Node #0,2,0 Current State: 49:[8, 61], Operations: ['63-55=8', '47+14=61'] Exploring Operation: 8*61=488, Resulting Numbers: [488] 488,49 unequal: No Solution Exploring Operation: 8+61=69, Resulting Numbers: [69] 69,49 unequal: No Solution Exploring Operation: 61-8=53, Resulting Numbers: [53] 53,49 unequal: No Solution Moving to Node #0,3,3 Current State: 49:[14, 55], Operations: ['55-47=8', '63-8=55'] Exploring Operation: 14*55=770, Resulting Numbers: [770] 770,49 unequal: No Solution Exploring Operation: 55-14=41, Resulting Numbers: [41] 41,49 unequal: No Solution Exploring Operation: 14+55=69, Resulting Numbers: [69] 69,49 unequal: No Solution Moving to Node #0,3,1 Current State: 49:[63, 6], Operations: ['55-47=8', '14-8=6'] Exploring Operation: 63*6=378, Resulting Numbers: [378] 378,49 unequal: No Solution Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,49 unequal: No Solution Exploring Operation: 63+6=69, Resulting Numbers: [69] 69,49 unequal: No Solution Moving to Node #0,0,1 Current State: 49:[14, 39], Operations: ['63-47=16', '55-16=39'] Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,49 unequal: No Solution Exploring Operation: 14*39=546, Resulting Numbers: [546] 546,49 unequal: No Solution Exploring Operation: 14+39=53, Resulting Numbers: [53] 53,49 unequal: No Solution Moving to Node #0,0,3 Current State: 49:[16, 41], Operations: ['63-47=16', '55-14=41'] Exploring Operation: 16*41=656, Resulting Numbers: [656] 656,49 unequal: No Solution Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,49 unequal: No Solution Exploring Operation: 16+41=57, Resulting Numbers: [57] 57,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[8, 33], Operations: ['63-55=8', '47-14=33'] Exploring Operation: 8+33=41, Resulting Numbers: [41] 41,49 unequal: No Solution Exploring Operation: 8*33=264, Resulting Numbers: [264] 264,49 unequal: No Solution Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,49 unequal: No Solution Moving to Node #0,0,2 Current State: 49:[55, 30], Operations: ['63-47=16', '14+16=30'] Exploring Operation: 55+30=85, Resulting Numbers: [85] 85,49 unequal: No Solution Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,49 unequal: No Solution Exploring Operation: 55*30=1650, Resulting Numbers: [1650] 1650,49 unequal: No Solution Moving to Node #0,3,2 Current State: 49:[8, 77], Operations: ['55-47=8', '14+63=77'] Exploring Operation: 8*77=616, Resulting Numbers: [616] 616,49 unequal: No Solution Exploring Operation: 8+77=85, Resulting Numbers: [85] 85,49 unequal: No Solution Exploring Operation: 77-8=69, Resulting Numbers: [69] 69,49 unequal: No Solution Moving to Node #0,1,0 Current State: 49:[49, 102], Operations: ['63-14=49', '47+55=102'] Exploring Operation: 102-49=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 49+102=151, Resulting Numbers: [151] 151,49 unequal: No Solution Exploring Operation: 49*102=4998, Resulting Numbers: [4998] 4998,49 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 53, 61, 79, 64 ]
23
[ "61-53=8", "79-64=15", "8+15=23" ]
Current State: 23:[53, 61, 79, 64], Operations: [] Exploring Operation: 61-53=8, Resulting Numbers: [79, 64, 8] Generated Node #2: [79, 64, 8] from Operation: 61-53=8 Current State: 23:[79, 64, 8], Operations: ['61-53=8'] Exploring Operation: 79-64=15, Resulting Numbers: [8, 15] Generated Node #3: [8, 15] from Operation: 79-64=15 Current State: 23:[8, 15], Operations: ['61-53=8', '79-64=15'] Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[53, 61, 79, 64], Operations: [] Exploring Operation: 79-61=18, Resulting Numbers: [53, 64, 18] Generated Node #0,0: 23:[53, 64, 18] Operation: 79-61=18 Exploring Operation: 79-64=15, Resulting Numbers: [53, 61, 15] Generated Node #0,1: 23:[53, 61, 15] Operation: 79-64=15 Exploring Operation: 79-53=26, Resulting Numbers: [61, 64, 26] Generated Node #0,2: 23:[61, 64, 26] Operation: 79-53=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[53, 64, 18], Operations: ['79-61=18'] Exploring Operation: 64-53=11, Resulting Numbers: [18, 11] Generated Node #0,0,0: 23:[18, 11] Operation: 64-53=11 Exploring Operation: 53-18=35, Resulting Numbers: [64, 35] Generated Node #0,0,1: 23:[64, 35] Operation: 53-18=35 Exploring Operation: 64-18=46, Resulting Numbers: [53, 46] Generated Node #0,0,2: 23:[53, 46] Operation: 64-18=46 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[18, 11], Operations: ['79-61=18', '64-53=11'] Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 18*11=198, Resulting Numbers: [198] 198,23 unequal: No Solution Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 23:[64, 35], Operations: ['79-61=18', '53-18=35'] Exploring Operation: 64+35=99, Resulting Numbers: [99] 99,23 unequal: No Solution Exploring Operation: 64*35=2240, Resulting Numbers: [2240] 2240,23 unequal: No Solution Exploring Operation: 64-35=29, Resulting Numbers: [29] 29,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 23:[53, 46], Operations: ['79-61=18', '64-18=46'] Exploring Operation: 53+46=99, Resulting Numbers: [99] 99,23 unequal: No Solution Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 53*46=2438, Resulting Numbers: [2438] 2438,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[53, 61, 15], Operations: ['79-64=15'] Exploring Operation: 61-15=46, Resulting Numbers: [53, 46] Generated Node #0,1,0: 23:[53, 46] Operation: 61-15=46 Exploring Operation: 53-15=38, Resulting Numbers: [61, 38] Generated Node #0,1,1: 23:[61, 38] Operation: 53-15=38 Exploring Operation: 61-53=8, Resulting Numbers: [15, 8] Generated Node #0,1,2: 23:[15, 8] Operation: 61-53=8 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 23:[15, 8], Operations: ['79-64=15', '61-53=8'] Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[53, 61, 79, 64], Operations: [] Exploring Operation: 79-64=15, Resulting Numbers: [53, 61, 15] Generated Node #0,1: 23:[53, 61, 15] Operation: 79-64=15 Moving to Node #0,1 Current State: 23:[53, 61, 15], Operations: ['79-64=15'] Exploring Operation: 61-53=8, Resulting Numbers: [15, 8] Generated Node #0,1,2: 23:[15, 8] Operation: 61-53=8 Moving to Node #0,1,2 Current State: 23:[15, 8], Operations: ['79-64=15', '61-53=8'] Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 23, 80, 91, 70 ]
82
[ "23+80=103", "91-70=21", "103-21=82" ]
Current State: 82:[23, 80, 91, 70], Operations: [] Exploring Operation: 23+80=103, Resulting Numbers: [91, 70, 103] Generated Node #2: [91, 70, 103] from Operation: 23+80=103 Current State: 82:[91, 70, 103], Operations: ['23+80=103'] Exploring Operation: 91-70=21, Resulting Numbers: [103, 21] Generated Node #3: [103, 21] from Operation: 91-70=21 Current State: 82:[103, 21], Operations: ['23+80=103', '91-70=21'] Exploring Operation: 103-21=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[23, 80, 91, 70], Operations: [] Exploring Operation: 91-23=68, Resulting Numbers: [80, 70, 68] Generated Node #0,0: 82:[80, 70, 68] Operation: 91-23=68 Exploring Operation: 70-23=47, Resulting Numbers: [80, 91, 47] Generated Node #0,1: 82:[80, 91, 47] Operation: 70-23=47 Exploring Operation: 23+70=93, Resulting Numbers: [80, 91, 93] Generated Node #0,2: 82:[80, 91, 93] Operation: 23+70=93 Exploring Operation: 80-70=10, Resulting Numbers: [23, 91, 10] Generated Node #0,3: 82:[23, 91, 10] Operation: 80-70=10 Moving to Node #0,1 Current State: 82:[80, 91, 47], Operations: ['70-23=47'] Exploring Operation: 91-47=44, Resulting Numbers: [80, 44] Generated Node #0,1,0: 82:[80, 44] Operation: 91-47=44 Exploring Operation: 80-47=33, Resulting Numbers: [91, 33] Generated Node #0,1,1: 82:[91, 33] Operation: 80-47=33 Exploring Operation: 91-80=11, Resulting Numbers: [47, 11] Generated Node #0,1,2: 82:[47, 11] Operation: 91-80=11 Exploring Operation: 80+47=127, Resulting Numbers: [91, 127] Generated Node #0,1,3: 82:[91, 127] Operation: 80+47=127 Moving to Node #0,2 Current State: 82:[80, 91, 93], Operations: ['23+70=93'] Exploring Operation: 91-80=11, Resulting Numbers: [93, 11] Generated Node #0,2,0: 82:[93, 11] Operation: 91-80=11 Exploring Operation: 80+91=171, Resulting Numbers: [93, 171] Generated Node #0,2,1: 82:[93, 171] Operation: 80+91=171 Exploring Operation: 93-80=13, Resulting Numbers: [91, 13] Generated Node #0,2,2: 82:[91, 13] Operation: 93-80=13 Exploring Operation: 93-91=2, Resulting Numbers: [80, 2] Generated Node #0,2,3: 82:[80, 2] Operation: 93-91=2 Moving to Node #0,0 Current State: 82:[80, 70, 68], Operations: ['91-23=68'] Exploring Operation: 70+68=138, Resulting Numbers: [80, 138] Generated Node #0,0,0: 82:[80, 138] Operation: 70+68=138 Exploring Operation: 70-68=2, Resulting Numbers: [80, 2] Generated Node #0,0,1: 82:[80, 2] Operation: 70-68=2 Exploring Operation: 80-68=12, Resulting Numbers: [70, 12] Generated Node #0,0,2: 82:[70, 12] Operation: 80-68=12 Exploring Operation: 80-70=10, Resulting Numbers: [68, 10] Generated Node #0,0,3: 82:[68, 10] Operation: 80-70=10 Moving to Node #0,3 Current State: 82:[23, 91, 10], Operations: ['80-70=10'] Exploring Operation: 23+10=33, Resulting Numbers: [91, 33] Generated Node #0,3,0: 82:[91, 33] Operation: 23+10=33 Exploring Operation: 91-23=68, Resulting Numbers: [10, 68] Generated Node #0,3,1: 82:[10, 68] Operation: 91-23=68 Exploring Operation: 23-10=13, Resulting Numbers: [91, 13] Generated Node #0,3,2: 82:[91, 13] Operation: 23-10=13 Exploring Operation: 91-10=81, Resulting Numbers: [23, 81] Generated Node #0,3,3: 82:[23, 81] Operation: 91-10=81 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 82:[91, 33], Operations: ['80-70=10', '23+10=33'] Exploring Operation: 91+33=124, Resulting Numbers: [124] 124,82 unequal: No Solution Exploring Operation: 91*33=3003, Resulting Numbers: [3003] 3003,82 unequal: No Solution Exploring Operation: 91-33=58, Resulting Numbers: [58] 58,82 unequal: No Solution No 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: 82:[23, 81], Operations: ['80-70=10', '91-10=81'] Exploring Operation: 81-23=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 23+81=104, Resulting Numbers: [104] 104,82 unequal: No Solution Exploring Operation: 23*81=1863, Resulting Numbers: [1863] 1863,82 unequal: No Solution No 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: 82:[91, 13], Operations: ['80-70=10', '23-10=13'] Exploring Operation: 91/13=7, Resulting Numbers: [7] 7,82 unequal: No Solution Exploring Operation: 91+13=104, Resulting Numbers: [104] 104,82 unequal: No Solution Exploring Operation: 91*13=1183, Resulting Numbers: [1183] 1183,82 unequal: No Solution Exploring Operation: 91-13=78, Resulting Numbers: [78] 78,82 unequal: No Solution No 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: 82:[10, 68], Operations: ['80-70=10', '91-23=68'] Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 10*68=680, Resulting Numbers: [680] 680,82 unequal: No Solution Exploring Operation: 10+68=78, Resulting Numbers: [78] 78,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,3 Current State: 82:[80, 2], Operations: ['23+70=93', '93-91=2'] Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,82 unequal: No Solution Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[23, 80, 91, 70], Operations: [] Exploring Operation: 23+70=93, Resulting Numbers: [80, 91, 93] Generated Node #0,2: 82:[80, 91, 93] Operation: 23+70=93 Moving to Node #0,2 Current State: 82:[80, 91, 93], Operations: ['23+70=93'] Exploring Operation: 93-91=2, Resulting Numbers: [80, 2] Generated Node #0,2,3: 82:[80, 2] Operation: 93-91=2 Moving to Node #0,2,3 Current State: 82:[80, 2], Operations: ['23+70=93', '93-91=2'] Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.966146
hs_4
mult_heuristic
[ 69, 4, 2, 38 ]
39
[ "69-38=31", "4*2=8", "31+8=39" ]
Current State: 39:[69, 4, 2, 38], Operations: [] Exploring Operation: 69-38=31, Resulting Numbers: [4, 2, 31] Generated Node #2: [4, 2, 31] from Operation: 69-38=31 Current State: 39:[4, 2, 31], Operations: ['69-38=31'] Exploring Operation: 4*2=8, Resulting Numbers: [31, 8] Generated Node #3: [31, 8] from Operation: 4*2=8 Current State: 39:[31, 8], Operations: ['69-38=31', '4*2=8'] Exploring Operation: 31+8=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[69, 4, 2, 38], Operations: [] Exploring Operation: 69-38=31, Resulting Numbers: [4, 2, 31] Generated Node #0,0: 39:[4, 2, 31] Operation: 69-38=31 Exploring Operation: 69-4=65, Resulting Numbers: [2, 38, 65] Generated Node #0,1: 39:[2, 38, 65] Operation: 69-4=65 Moving to Node #0,0 Current State: 39:[4, 2, 31], Operations: ['69-38=31'] Exploring Operation: 2+31=33, Resulting Numbers: [4, 33] Generated Node #0,0,0: 39:[4, 33] Operation: 2+31=33 Exploring Operation: 4+31=35, Resulting Numbers: [2, 35] Generated Node #0,0,1: 39:[2, 35] Operation: 4+31=35 Moving to Node #0,1 Current State: 39:[2, 38, 65], Operations: ['69-4=65'] Exploring Operation: 65-38=27, Resulting Numbers: [2, 27] Generated Node #0,1,0: 39:[2, 27] Operation: 65-38=27 Exploring Operation: 65-2=63, Resulting Numbers: [38, 63] Generated Node #0,1,1: 39:[38, 63] Operation: 65-2=63 Moving to Node #0,0,1 Current State: 39:[2, 35], Operations: ['69-38=31', '4+31=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[4, 33], Operations: ['69-38=31', '2+31=33'] Exploring Operation: 4+33=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[2, 27], Operations: ['69-4=65', '65-38=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[38, 63], Operations: ['69-4=65', '65-2=63'] Exploring Operation: 38+63=101, Resulting Numbers: [101] 101,39 unequal: No Solution Exploring Operation: 63-38=25, Resulting Numbers: [25] 25,39 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 15, 32, 11, 84 ]
11
[ "15-11=4", "84/4=21", "32-21=11" ]
Current State: 11:[15, 32, 11, 84], Operations: [] Exploring Operation: 15-11=4, Resulting Numbers: [32, 84, 4] Generated Node #2: [32, 84, 4] from Operation: 15-11=4 Current State: 11:[32, 84, 4], Operations: ['15-11=4'] Exploring Operation: 84/4=21, Resulting Numbers: [32, 21] Generated Node #3: [32, 21] from Operation: 84/4=21 Current State: 11:[32, 21], Operations: ['15-11=4', '84/4=21'] Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[15, 32, 11, 84], Operations: [] Exploring Operation: 32-15=17, Resulting Numbers: [11, 84, 17] Generated Node #0,0: 11:[11, 84, 17] Operation: 32-15=17 Exploring Operation: 84-32=52, Resulting Numbers: [15, 11, 52] Generated Node #0,1: 11:[15, 11, 52] Operation: 84-32=52 Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[15, 11, 52], Operations: ['84-32=52'] Exploring Operation: 52-15=37, Resulting Numbers: [11, 37] Generated Node #0,1,0: 11:[11, 37] Operation: 52-15=37 Exploring Operation: 52-11=41, Resulting Numbers: [15, 41] Generated Node #0,1,1: 11:[15, 41] Operation: 52-11=41 Moving to Node #0,1,0 Current State: 11:[11, 37], Operations: ['84-32=52', '52-15=37'] Exploring Operation: 11+37=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[15, 41], Operations: ['84-32=52', '52-11=41'] Exploring Operation: 15+41=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[11, 84, 17], Operations: ['32-15=17'] Exploring Operation: 84-11=73, Resulting Numbers: [17, 73] Generated Node #0,0,0: 11:[17, 73] Operation: 84-11=73 Exploring Operation: 84-17=67, Resulting Numbers: [11, 67] Generated Node #0,0,1: 11:[11, 67] Operation: 84-17=67 Moving to Node #0,0,1 Current State: 11:[11, 67], Operations: ['32-15=17', '84-17=67'] Exploring Operation: 11+67=78, Resulting Numbers: [78] 78,11 unequal: No Solution Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,11 unequal: No Solution Moving to Node #0,0,0 Current State: 11:[17, 73], Operations: ['32-15=17', '84-11=73'] Exploring Operation: 73-17=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 17+73=90, Resulting Numbers: [90] 90,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 44, 22, 65, 7 ]
89
[ "44-22=22", "7*22=154", "154-65=89" ]
Current State: 89:[44, 22, 65, 7], Operations: [] Exploring Operation: 44-22=22, Resulting Numbers: [65, 7, 22] Generated Node #2: [65, 7, 22] from Operation: 44-22=22 Current State: 89:[65, 7, 22], Operations: ['44-22=22'] Exploring Operation: 7*22=154, Resulting Numbers: [65, 154] Generated Node #3: [65, 154] from Operation: 7*22=154 Current State: 89:[65, 154], Operations: ['44-22=22', '7*22=154'] Exploring Operation: 154-65=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[44, 22, 65, 7], Operations: [] Exploring Operation: 22+7=29, Resulting Numbers: [44, 65, 29] Generated Node #0,0: 89:[44, 65, 29] Operation: 22+7=29 Exploring Operation: 44+7=51, Resulting Numbers: [22, 65, 51] Generated Node #0,1: 89:[22, 65, 51] Operation: 44+7=51 Exploring Operation: 22+65=87, Resulting Numbers: [44, 7, 87] Generated Node #0,2: 89:[44, 7, 87] Operation: 22+65=87 Exploring Operation: 65+7=72, Resulting Numbers: [44, 22, 72] Generated Node #0,3: 89:[44, 22, 72] Operation: 65+7=72 Exploring Operation: 44+22=66, Resulting Numbers: [65, 7, 66] Generated Node #0,4: 89:[65, 7, 66] Operation: 44+22=66 Moving to Node #0,0 Current State: 89:[44, 65, 29], Operations: ['22+7=29'] Exploring Operation: 44+29=73, Resulting Numbers: [65, 73] Generated Node #0,0,0: 89:[65, 73] Operation: 44+29=73 Exploring Operation: 65+29=94, Resulting Numbers: [44, 94] Generated Node #0,0,1: 89:[44, 94] Operation: 65+29=94 Exploring Operation: 44-29=15, Resulting Numbers: [65, 15] Generated Node #0,0,2: 89:[65, 15] Operation: 44-29=15 Exploring Operation: 65-29=36, Resulting Numbers: [44, 36] Generated Node #0,0,3: 89:[44, 36] Operation: 65-29=36 Exploring Operation: 44+65=109, Resulting Numbers: [29, 109] Generated Node #0,0,4: 89:[29, 109] Operation: 44+65=109 Moving to Node #0,2 Current State: 89:[44, 7, 87], Operations: ['22+65=87'] Exploring Operation: 7+87=94, Resulting Numbers: [44, 94] Generated Node #0,2,0: 89:[44, 94] Operation: 7+87=94 Exploring Operation: 87-7=80, Resulting Numbers: [44, 80] Generated Node #0,2,1: 89:[44, 80] Operation: 87-7=80 Exploring Operation: 44+87=131, Resulting Numbers: [7, 131] Generated Node #0,2,2: 89:[7, 131] Operation: 44+87=131 Exploring Operation: 44-7=37, Resulting Numbers: [87, 37] Generated Node #0,2,3: 89:[87, 37] Operation: 44-7=37 Exploring Operation: 44+7=51, Resulting Numbers: [87, 51] Generated Node #0,2,4: 89:[87, 51] Operation: 44+7=51 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 89:[87, 51], Operations: ['22+65=87', '44+7=51'] Exploring Operation: 87-51=36, Resulting Numbers: [36] 36,89 unequal: No Solution Exploring Operation: 87+51=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 87*51=4437, Resulting Numbers: [4437] 4437,89 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 #0,2,0 Current State: 89:[44, 94], Operations: ['22+65=87', '7+87=94'] Exploring Operation: 44+94=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 94-44=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 44*94=4136, Resulting Numbers: [4136] 4136,89 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 #0,2,1 Current State: 89:[44, 80], Operations: ['22+65=87', '87-7=80'] Exploring Operation: 44+80=124, Resulting Numbers: [124] 124,89 unequal: No Solution Exploring Operation: 44*80=3520, Resulting Numbers: [3520] 3520,89 unequal: No Solution Exploring Operation: 80-44=36, Resulting Numbers: [36] 36,89 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 #0,2,3 Current State: 89:[87, 37], Operations: ['22+65=87', '44-7=37'] Exploring Operation: 87*37=3219, Resulting Numbers: [3219] 3219,89 unequal: No Solution Exploring Operation: 87+37=124, Resulting Numbers: [124] 124,89 unequal: No Solution Exploring Operation: 87-37=50, Resulting Numbers: [50] 50,89 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 #0,2,2 Current State: 89:[7, 131], Operations: ['22+65=87', '44+87=131'] Exploring Operation: 7*131=917, Resulting Numbers: [917] 917,89 unequal: No Solution Exploring Operation: 7+131=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 131-7=124, Resulting Numbers: [124] 124,89 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: 89:[65, 7, 66], Operations: ['44+22=66'] Exploring Operation: 7+66=73, Resulting Numbers: [65, 73] Generated Node #0,4,0: 89:[65, 73] Operation: 7+66=73 Exploring Operation: 65-7=58, Resulting Numbers: [66, 58] Generated Node #0,4,1: 89:[66, 58] Operation: 65-7=58 Exploring Operation: 65+66=131, Resulting Numbers: [7, 131] Generated Node #0,4,2: 89:[7, 131] Operation: 65+66=131 Exploring Operation: 66-7=59, Resulting Numbers: [65, 59] Generated Node #0,4,3: 89:[65, 59] Operation: 66-7=59 Exploring Operation: 65+7=72, Resulting Numbers: [66, 72] Generated Node #0,4,4: 89:[66, 72] Operation: 65+7=72 Moving to Node #0,1 Current State: 89:[22, 65, 51], Operations: ['44+7=51'] Exploring Operation: 51-22=29, Resulting Numbers: [65, 29] Generated Node #0,1,0: 89:[65, 29] Operation: 51-22=29 Exploring Operation: 22+65=87, Resulting Numbers: [51, 87] Generated Node #0,1,1: 89:[51, 87] Operation: 22+65=87 Exploring Operation: 65-22=43, Resulting Numbers: [51, 43] Generated Node #0,1,2: 89:[51, 43] Operation: 65-22=43 Exploring Operation: 22+51=73, Resulting Numbers: [65, 73] Generated Node #0,1,3: 89:[65, 73] Operation: 22+51=73 Exploring Operation: 65+51=116, Resulting Numbers: [22, 116] Generated Node #0,1,4: 89:[22, 116] Operation: 65+51=116 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[51, 87], Operations: ['44+7=51', '22+65=87'] Exploring Operation: 51+87=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 87-51=36, Resulting Numbers: [36] 36,89 unequal: No Solution Exploring Operation: 51*87=4437, Resulting Numbers: [4437] 4437,89 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 #0,1,3 Current State: 89:[65, 73], Operations: ['44+7=51', '22+51=73'] Exploring Operation: 65+73=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 73-65=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 65*73=4745, Resulting Numbers: [4745] 4745,89 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 #0,1,0 Current State: 89:[65, 29], Operations: ['44+7=51', '51-22=29'] Exploring Operation: 65-29=36, Resulting Numbers: [36] 36,89 unequal: No Solution Exploring Operation: 65+29=94, Resulting Numbers: [94] 94,89 unequal: No Solution Exploring Operation: 65*29=1885, Resulting Numbers: [1885] 1885,89 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 #0,1,2 Current State: 89:[51, 43], Operations: ['44+7=51', '65-22=43'] Exploring Operation: 51*43=2193, Resulting Numbers: [2193] 2193,89 unequal: No Solution Exploring Operation: 51+43=94, Resulting Numbers: [94] 94,89 unequal: No Solution Exploring Operation: 51-43=8, Resulting Numbers: [8] 8,89 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 #0,1,4 Current State: 89:[22, 116], Operations: ['44+7=51', '65+51=116'] Exploring Operation: 116-22=94, Resulting Numbers: [94] 94,89 unequal: No Solution Exploring Operation: 22+116=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 22*116=2552, Resulting Numbers: [2552] 2552,89 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: 89:[44, 22, 72], Operations: ['65+7=72'] Exploring Operation: 44-22=22, Resulting Numbers: [72, 22] Generated Node #0,3,0: 89:[72, 22] Operation: 44-22=22 Exploring Operation: 44+72=116, Resulting Numbers: [22, 116] Generated Node #0,3,1: 89:[22, 116] Operation: 44+72=116 Exploring Operation: 22+72=94, Resulting Numbers: [44, 94] Generated Node #0,3,2: 89:[44, 94] Operation: 22+72=94 Exploring Operation: 44+22=66, Resulting Numbers: [72, 66] Generated Node #0,3,3: 89:[72, 66] Operation: 44+22=66 Exploring Operation: 72-22=50, Resulting Numbers: [44, 50] Generated Node #0,3,4: 89:[44, 50] Operation: 72-22=50 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 89:[72, 66], Operations: ['65+7=72', '44+22=66'] Exploring Operation: 72*66=4752, Resulting Numbers: [4752] 4752,89 unequal: No Solution Exploring Operation: 72+66=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 72-66=6, Resulting Numbers: [6] 6,89 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 #0,3,2 Current State: 89:[44, 94], Operations: ['65+7=72', '22+72=94'] Exploring Operation: 44+94=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 44*94=4136, Resulting Numbers: [4136] 4136,89 unequal: No Solution Exploring Operation: 94-44=50, Resulting Numbers: [50] 50,89 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 #0,3,0 Current State: 89:[72, 22], Operations: ['65+7=72', '44-22=22'] Exploring Operation: 72*22=1584, Resulting Numbers: [1584] 1584,89 unequal: No Solution Exploring Operation: 72-22=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 72+22=94, Resulting Numbers: [94] 94,89 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 #0,3,4 Current State: 89:[44, 50], Operations: ['65+7=72', '72-22=50'] Exploring Operation: 44+50=94, Resulting Numbers: [94] 94,89 unequal: No Solution Exploring Operation: 50-44=6, Resulting Numbers: [6] 6,89 unequal: No Solution Exploring Operation: 44*50=2200, Resulting Numbers: [2200] 2200,89 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 #0,3,1 Current State: 89:[22, 116], Operations: ['65+7=72', '44+72=116'] Exploring Operation: 22*116=2552, Resulting Numbers: [2552] 2552,89 unequal: No Solution Exploring Operation: 22+116=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 116-22=94, Resulting Numbers: [94] 94,89 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: 89:[65, 73], Operations: ['22+7=29', '44+29=73'] Exploring Operation: 73-65=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 65*73=4745, Resulting Numbers: [4745] 4745,89 unequal: No Solution Exploring Operation: 65+73=138, Resulting Numbers: [138] 138,89 unequal: No Solution Moving to Node #0,4,0 Current State: 89:[65, 73], Operations: ['44+22=66', '7+66=73'] Exploring Operation: 65+73=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 65*73=4745, Resulting Numbers: [4745] 4745,89 unequal: No Solution Exploring Operation: 73-65=8, Resulting Numbers: [8] 8,89 unequal: No Solution Moving to Node #0,4,4 Current State: 89:[66, 72], Operations: ['44+22=66', '65+7=72'] Exploring Operation: 72-66=6, Resulting Numbers: [6] 6,89 unequal: No Solution Exploring Operation: 66*72=4752, Resulting Numbers: [4752] 4752,89 unequal: No Solution Exploring Operation: 66+72=138, Resulting Numbers: [138] 138,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[44, 94], Operations: ['22+7=29', '65+29=94'] Exploring Operation: 44+94=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 44*94=4136, Resulting Numbers: [4136] 4136,89 unequal: No Solution Exploring Operation: 94-44=50, Resulting Numbers: [50] 50,89 unequal: No Solution Moving to Node #0,4,3 Current State: 89:[65, 59], Operations: ['44+22=66', '66-7=59'] Exploring Operation: 65+59=124, Resulting Numbers: [124] 124,89 unequal: No Solution Exploring Operation: 65*59=3835, Resulting Numbers: [3835] 3835,89 unequal: No Solution Exploring Operation: 65-59=6, Resulting Numbers: [6] 6,89 unequal: No Solution Moving to Node #0,4,1 Current State: 89:[66, 58], Operations: ['44+22=66', '65-7=58'] Exploring Operation: 66-58=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 66+58=124, Resulting Numbers: [124] 124,89 unequal: No Solution Exploring Operation: 66*58=3828, Resulting Numbers: [3828] 3828,89 unequal: No Solution Moving to Node #0,0,4 Current State: 89:[29, 109], Operations: ['22+7=29', '44+65=109'] Exploring Operation: 29+109=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 109-29=80, Resulting Numbers: [80] 80,89 unequal: No Solution Exploring Operation: 29*109=3161, Resulting Numbers: [3161] 3161,89 unequal: No Solution Moving to Node #0,0,3 Current State: 89:[44, 36], Operations: ['22+7=29', '65-29=36'] Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 44+36=80, Resulting Numbers: [80] 80,89 unequal: No Solution Exploring Operation: 44*36=1584, Resulting Numbers: [1584] 1584,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[65, 15], Operations: ['22+7=29', '44-29=15'] Exploring Operation: 65+15=80, Resulting Numbers: [80] 80,89 unequal: No Solution Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 65*15=975, Resulting Numbers: [975] 975,89 unequal: No Solution Moving to Node #0,4,2 Current State: 89:[7, 131], Operations: ['44+22=66', '65+66=131'] Exploring Operation: 7+131=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 131-7=124, Resulting Numbers: [124] 124,89 unequal: No Solution Exploring Operation: 7*131=917, Resulting Numbers: [917] 917,89 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 33, 8, 75, 2 ]
32
[ "33+8=41", "75-2=73", "73-41=32" ]
Current State: 32:[33, 8, 75, 2], Operations: [] Exploring Operation: 33+8=41, Resulting Numbers: [75, 2, 41] Generated Node #2: [75, 2, 41] from Operation: 33+8=41 Current State: 32:[75, 2, 41], Operations: ['33+8=41'] Exploring Operation: 75-2=73, Resulting Numbers: [41, 73] Generated Node #3: [41, 73] from Operation: 75-2=73 Current State: 32:[41, 73], Operations: ['33+8=41', '75-2=73'] Exploring Operation: 73-41=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[33, 8, 75, 2], Operations: [] Exploring Operation: 75-33=42, Resulting Numbers: [8, 2, 42] Generated Node #0,0: 32:[8, 2, 42] Operation: 75-33=42 Moving to Node #0,0 Current State: 32:[8, 2, 42], Operations: ['75-33=42'] Exploring Operation: 42-8=34, Resulting Numbers: [2, 34] Generated Node #0,0,0: 32:[2, 34] Operation: 42-8=34 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[2, 34], Operations: ['75-33=42', '42-8=34'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[33, 8, 75, 2], Operations: [] Exploring Operation: 75-33=42, Resulting Numbers: [8, 2, 42] Generated Node #0,0: 32:[8, 2, 42] Operation: 75-33=42 Moving to Node #0,0 Current State: 32:[8, 2, 42], Operations: ['75-33=42'] Exploring Operation: 42-8=34, Resulting Numbers: [2, 34] Generated Node #0,0,0: 32:[2, 34] Operation: 42-8=34 Moving to Node #0,0,0 Current State: 32:[2, 34], Operations: ['75-33=42', '42-8=34'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 97, 31, 23, 73 ]
16
[ "97-31=66", "73-23=50", "66-50=16" ]
Current State: 16:[97, 31, 23, 73], Operations: [] Exploring Operation: 97-31=66, Resulting Numbers: [23, 73, 66] Generated Node #2: [23, 73, 66] from Operation: 97-31=66 Current State: 16:[23, 73, 66], Operations: ['97-31=66'] Exploring Operation: 73-23=50, Resulting Numbers: [66, 50] Generated Node #3: [66, 50] from Operation: 73-23=50 Current State: 16:[66, 50], Operations: ['97-31=66', '73-23=50'] Exploring Operation: 66-50=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[97, 31, 23, 73], Operations: [] Exploring Operation: 97-73=24, Resulting Numbers: [31, 23, 24] Generated Node #0,0: 16:[31, 23, 24] Operation: 97-73=24 Exploring Operation: 97-23=74, Resulting Numbers: [31, 73, 74] Generated Node #0,1: 16:[31, 73, 74] Operation: 97-23=74 Exploring Operation: 97-31=66, Resulting Numbers: [23, 73, 66] Generated Node #0,2: 16:[23, 73, 66] Operation: 97-31=66 Exploring Operation: 73-31=42, Resulting Numbers: [97, 23, 42] Generated Node #0,3: 16:[97, 23, 42] Operation: 73-31=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[31, 23, 24], Operations: ['97-73=24'] Exploring Operation: 31-24=7, Resulting Numbers: [23, 7] Generated Node #0,0,0: 16:[23, 7] Operation: 31-24=7 Exploring Operation: 31-23=8, Resulting Numbers: [24, 8] Generated Node #0,0,1: 16:[24, 8] Operation: 31-23=8 Exploring Operation: 31+23=54, Resulting Numbers: [24, 54] Generated Node #0,0,2: 16:[24, 54] Operation: 31+23=54 Exploring Operation: 24-23=1, Resulting Numbers: [31, 1] Generated Node #0,0,3: 16:[31, 1] Operation: 24-23=1 Moving to Node #0,0,0 Current State: 16:[23, 7], Operations: ['97-73=24', '31-24=7'] Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,16 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[97, 31, 23, 73], Operations: [] Exploring Operation: 97-73=24, Resulting Numbers: [31, 23, 24] Generated Node #0,0: 16:[31, 23, 24] Operation: 97-73=24 Moving to Node #0,0 Current State: 16:[31, 23, 24], Operations: ['97-73=24'] Exploring Operation: 31-24=7, Resulting Numbers: [23, 7] Generated Node #0,0,0: 16:[23, 7] Operation: 31-24=7 Moving to Node #0,0,0 Current State: 16:[23, 7], Operations: ['97-73=24', '31-24=7'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 4, 45, 2, 51 ]
32
[ "45-2=43", "51-43=8", "4*8=32" ]
Current State: 32:[4, 45, 2, 51], Operations: [] Exploring Operation: 45-2=43, Resulting Numbers: [4, 51, 43] Generated Node #2: [4, 51, 43] from Operation: 45-2=43 Current State: 32:[4, 51, 43], Operations: ['45-2=43'] Exploring Operation: 51-43=8, Resulting Numbers: [4, 8] Generated Node #3: [4, 8] from Operation: 51-43=8 Current State: 32:[4, 8], Operations: ['45-2=43', '51-43=8'] Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[4, 45, 2, 51], Operations: [] Exploring Operation: 45-2=43, Resulting Numbers: [4, 51, 43] Generated Node #0,0: 32:[4, 51, 43] Operation: 45-2=43 Exploring Operation: 51-4=47, Resulting Numbers: [45, 2, 47] Generated Node #0,1: 32:[45, 2, 47] Operation: 51-4=47 Exploring Operation: 45-4=41, Resulting Numbers: [2, 51, 41] Generated Node #0,2: 32:[2, 51, 41] Operation: 45-4=41 Exploring Operation: 51-2=49, Resulting Numbers: [4, 45, 49] Generated Node #0,3: 32:[4, 45, 49] Operation: 51-2=49 Exploring Operation: 51-45=6, Resulting Numbers: [4, 2, 6] Generated Node #0,4: 32:[4, 2, 6] Operation: 51-45=6 Start Sub Search at level 1: Moving to Node #0,4 Current State: 32:[4, 2, 6], Operations: ['51-45=6'] Exploring Operation: 6/2=3, Resulting Numbers: [4, 3] Generated Node #0,4,0: 32:[4, 3] Operation: 6/2=3 Exploring Operation: 2+6=8, Resulting Numbers: [4, 8] Generated Node #0,4,1: 32:[4, 8] Operation: 2+6=8 Exploring Operation: 6-4=2, Resulting Numbers: [2, 2] Generated Node #0,4,2: 32:[2, 2] Operation: 6-4=2 Exploring Operation: 4*2=8, Resulting Numbers: [6, 8] Generated Node #0,4,3: 32:[6, 8] Operation: 4*2=8 Exploring Operation: 6-2=4, Resulting Numbers: [4, 4] Generated Node #0,4,4: 32:[4, 4] Operation: 6-2=4 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 32:[4, 8], Operations: ['51-45=6', '2+6=8'] Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[4, 45, 2, 51], Operations: [] Exploring Operation: 51-45=6, Resulting Numbers: [4, 2, 6] Generated Node #0,4: 32:[4, 2, 6] Operation: 51-45=6 Moving to Node #0,4 Current State: 32:[4, 2, 6], Operations: ['51-45=6'] Exploring Operation: 2+6=8, Resulting Numbers: [4, 8] Generated Node #0,4,1: 32:[4, 8] Operation: 2+6=8 Moving to Node #0,4,1 Current State: 32:[4, 8], Operations: ['51-45=6', '2+6=8'] Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 6, 97, 18, 6 ]
78
[ "6/6=1", "97-18=79", "79-1=78" ]
Current State: 78:[6, 97, 18, 6], Operations: [] Exploring Operation: 6/6=1, Resulting Numbers: [97, 18, 1] Generated Node #2: [97, 18, 1] from Operation: 6/6=1 Current State: 78:[97, 18, 1], Operations: ['6/6=1'] Exploring Operation: 97-18=79, Resulting Numbers: [1, 79] Generated Node #3: [1, 79] from Operation: 97-18=79 Current State: 78:[1, 79], Operations: ['6/6=1', '97-18=79'] Exploring Operation: 79-1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[6, 97, 18, 6], Operations: [] Exploring Operation: 97-18=79, Resulting Numbers: [6, 6, 79] Generated Node #0,0: 78:[6, 6, 79] Operation: 97-18=79 Exploring Operation: 97-6=91, Resulting Numbers: [6, 18, 91] Generated Node #0,1: 78:[6, 18, 91] Operation: 97-6=91 Exploring Operation: 97-6=91, Resulting Numbers: [18, 6, 91] Generated Node #0,2: 78:[18, 6, 91] Operation: 97-6=91 Moving to Node #0,0 Current State: 78:[6, 6, 79], Operations: ['97-18=79'] Exploring Operation: 6-6=0, Resulting Numbers: [79, 0] Generated Node #0,0,0: 78:[79, 0] Operation: 6-6=0 Exploring Operation: 6/6=1, Resulting Numbers: [79, 1] Generated Node #0,0,1: 78:[79, 1] Operation: 6/6=1 Exploring Operation: 6+6=12, Resulting Numbers: [79, 12] Generated Node #0,0,2: 78:[79, 12] Operation: 6+6=12 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[79, 1], Operations: ['97-18=79', '6/6=1'] Exploring Operation: 79*1=79, Resulting Numbers: [79] 79,78 unequal: No Solution Exploring Operation: 79/1=79, Resulting Numbers: [79] 79,78 unequal: No Solution Exploring Operation: 79-1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[6, 97, 18, 6], Operations: [] Exploring Operation: 97-18=79, Resulting Numbers: [6, 6, 79] Generated Node #0,0: 78:[6, 6, 79] Operation: 97-18=79 Moving to Node #0,0 Current State: 78:[6, 6, 79], Operations: ['97-18=79'] Exploring Operation: 6/6=1, Resulting Numbers: [79, 1] Generated Node #0,0,1: 78:[79, 1] Operation: 6/6=1 Moving to Node #0,0,1 Current State: 78:[79, 1], Operations: ['97-18=79', '6/6=1'] Exploring Operation: 79-1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 11, 95, 2, 7 ]
75
[ "95-11=84", "2+7=9", "84-9=75" ]
Current State: 75:[11, 95, 2, 7], Operations: [] Exploring Operation: 95-11=84, Resulting Numbers: [2, 7, 84] Generated Node #2: [2, 7, 84] from Operation: 95-11=84 Current State: 75:[2, 7, 84], Operations: ['95-11=84'] Exploring Operation: 2+7=9, Resulting Numbers: [84, 9] Generated Node #3: [84, 9] from Operation: 2+7=9 Current State: 75:[84, 9], Operations: ['95-11=84', '2+7=9'] Exploring Operation: 84-9=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[11, 95, 2, 7], Operations: [] Exploring Operation: 95-7=88, Resulting Numbers: [11, 2, 88] Generated Node #0,0: 75:[11, 2, 88] Operation: 95-7=88 Exploring Operation: 95-11=84, Resulting Numbers: [2, 7, 84] Generated Node #0,1: 75:[2, 7, 84] Operation: 95-11=84 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[2, 7, 84], Operations: ['95-11=84'] Exploring Operation: 84-7=77, Resulting Numbers: [2, 77] Generated Node #0,1,0: 75:[2, 77] Operation: 84-7=77 Exploring Operation: 84/7=12, Resulting Numbers: [2, 12] Generated Node #0,1,1: 75:[2, 12] Operation: 84/7=12 Moving to Node #0,1,0 Current State: 75:[2, 77], Operations: ['95-11=84', '84-7=77'] Exploring Operation: 2+77=79, Resulting Numbers: [79] 79,75 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[11, 95, 2, 7], Operations: [] Exploring Operation: 95-11=84, Resulting Numbers: [2, 7, 84] Generated Node #0,1: 75:[2, 7, 84] Operation: 95-11=84 Moving to Node #0,1 Current State: 75:[2, 7, 84], Operations: ['95-11=84'] Exploring Operation: 84-7=77, Resulting Numbers: [2, 77] Generated Node #0,1,0: 75:[2, 77] Operation: 84-7=77 Moving to Node #0,1,0 Current State: 75:[2, 77], Operations: ['95-11=84', '84-7=77'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 92, 87, 38, 87 ]
55
[ "92-38=54", "87/87=1", "54+1=55" ]
Current State: 55:[92, 87, 38, 87], Operations: [] Exploring Operation: 92-38=54, Resulting Numbers: [87, 87, 54] Generated Node #2: [87, 87, 54] from Operation: 92-38=54 Current State: 55:[87, 87, 54], Operations: ['92-38=54'] Exploring Operation: 87/87=1, Resulting Numbers: [54, 1] Generated Node #3: [54, 1] from Operation: 87/87=1 Current State: 55:[54, 1], Operations: ['92-38=54', '87/87=1'] Exploring Operation: 54+1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[92, 87, 38, 87], Operations: [] Exploring Operation: 92-87=5, Resulting Numbers: [87, 38, 5] Generated Node #0,0: 55:[87, 38, 5] Operation: 92-87=5 Exploring Operation: 92-87=5, Resulting Numbers: [38, 87, 5] Generated Node #0,1: 55:[38, 87, 5] Operation: 92-87=5 Exploring Operation: 92-38=54, Resulting Numbers: [87, 87, 54] Generated Node #0,2: 55:[87, 87, 54] Operation: 92-38=54 Exploring Operation: 87/87=1, Resulting Numbers: [92, 38, 1] Generated Node #0,3: 55:[92, 38, 1] Operation: 87/87=1 Exploring Operation: 87-87=0, Resulting Numbers: [92, 38, 0] Generated Node #0,4: 55:[92, 38, 0] Operation: 87-87=0 Moving to Node #0,0 Current State: 55:[87, 38, 5], Operations: ['92-87=5'] Exploring Operation: 87-5=82, Resulting Numbers: [38, 82] Generated Node #0,0,0: 55:[38, 82] Operation: 87-5=82 Exploring Operation: 87-38=49, Resulting Numbers: [5, 49] Generated Node #0,0,1: 55:[5, 49] Operation: 87-38=49 Exploring Operation: 38+5=43, Resulting Numbers: [87, 43] Generated Node #0,0,2: 55:[87, 43] Operation: 38+5=43 Exploring Operation: 87+5=92, Resulting Numbers: [38, 92] Generated Node #0,0,3: 55:[38, 92] Operation: 87+5=92 Exploring Operation: 38-5=33, Resulting Numbers: [87, 33] Generated Node #0,0,4: 55:[87, 33] Operation: 38-5=33 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 55:[5, 49], Operations: ['92-87=5', '87-38=49'] Exploring Operation: 5*49=245, Resulting Numbers: [245] 245,55 unequal: No Solution Exploring Operation: 49-5=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 5+49=54, Resulting Numbers: [54] 54,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 55:[38, 82], Operations: ['92-87=5', '87-5=82'] Exploring Operation: 38*82=3116, Resulting Numbers: [3116] 3116,55 unequal: No Solution Exploring Operation: 82-38=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 38+82=120, Resulting Numbers: [120] 120,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 55:[87, 43], Operations: ['92-87=5', '38+5=43'] Exploring Operation: 87*43=3741, Resulting Numbers: [3741] 3741,55 unequal: No Solution Exploring Operation: 87+43=130, Resulting Numbers: [130] 130,55 unequal: No Solution Exploring Operation: 87-43=44, Resulting Numbers: [44] 44,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 55:[38, 92], Operations: ['92-87=5', '87+5=92'] Exploring Operation: 38+92=130, Resulting Numbers: [130] 130,55 unequal: No Solution Exploring Operation: 92-38=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 38*92=3496, Resulting Numbers: [3496] 3496,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 55:[87, 33], Operations: ['92-87=5', '38-5=33'] Exploring Operation: 87*33=2871, Resulting Numbers: [2871] 2871,55 unequal: No Solution Exploring Operation: 87+33=120, Resulting Numbers: [120] 120,55 unequal: No Solution Exploring Operation: 87-33=54, Resulting Numbers: [54] 54,55 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: 55:[38, 87, 5], Operations: ['92-87=5'] Exploring Operation: 38+5=43, Resulting Numbers: [87, 43] Generated Node #0,1,0: 55:[87, 43] Operation: 38+5=43 Exploring Operation: 87+5=92, Resulting Numbers: [38, 92] Generated Node #0,1,1: 55:[38, 92] Operation: 87+5=92 Exploring Operation: 38-5=33, Resulting Numbers: [87, 33] Generated Node #0,1,2: 55:[87, 33] Operation: 38-5=33 Exploring Operation: 87-5=82, Resulting Numbers: [38, 82] Generated Node #0,1,3: 55:[38, 82] Operation: 87-5=82 Exploring Operation: 87-38=49, Resulting Numbers: [5, 49] Generated Node #0,1,4: 55:[5, 49] Operation: 87-38=49 Moving to Node #0,3 Current State: 55:[92, 38, 1], Operations: ['87/87=1'] Exploring Operation: 38+1=39, Resulting Numbers: [92, 39] Generated Node #0,3,0: 55:[92, 39] Operation: 38+1=39 Exploring Operation: 92/1=92, Resulting Numbers: [38, 92] Generated Node #0,3,1: 55:[38, 92] Operation: 92/1=92 Exploring Operation: 92-1=91, Resulting Numbers: [38, 91] Generated Node #0,3,2: 55:[38, 91] Operation: 92-1=91 Exploring Operation: 92*1=92, Resulting Numbers: [38, 92] Generated Node #0,3,3: 55:[38, 92] Operation: 92*1=92 Exploring Operation: 92-38=54, Resulting Numbers: [1, 54] Generated Node #0,3,4: 55:[1, 54] Operation: 92-38=54 Moving to Node #0,4 Current State: 55:[92, 38, 0], Operations: ['87-87=0'] Exploring Operation: 38*0=0, Resulting Numbers: [92, 0] Generated Node #0,4,0: 55:[92, 0] Operation: 38*0=0 Exploring Operation: 92-38=54, Resulting Numbers: [0, 54] Generated Node #0,4,1: 55:[0, 54] Operation: 92-38=54 Exploring Operation: 92+0=92, Resulting Numbers: [38, 92] Generated Node #0,4,2: 55:[38, 92] Operation: 92+0=92 Exploring Operation: 92*0=0, Resulting Numbers: [38, 0] Generated Node #0,4,3: 55:[38, 0] Operation: 92*0=0 Exploring Operation: 92-0=92, Resulting Numbers: [38, 92] Generated Node #0,4,4: 55:[38, 92] Operation: 92-0=92 Moving to Node #0,2 Current State: 55:[87, 87, 54], Operations: ['92-38=54'] Exploring Operation: 87/87=1, Resulting Numbers: [54, 1] Generated Node #0,2,0: 55:[54, 1] Operation: 87/87=1 Exploring Operation: 87-54=33, Resulting Numbers: [87, 33] Generated Node #0,2,1: 55:[87, 33] Operation: 87-54=33 Exploring Operation: 87-87=0, Resulting Numbers: [54, 0] Generated Node #0,2,2: 55:[54, 0] Operation: 87-87=0 Exploring Operation: 87-54=33, Resulting Numbers: [87, 33] Generated Node #0,2,3: 55:[87, 33] Operation: 87-54=33 Exploring Operation: 87+54=141, Resulting Numbers: [87, 141] Generated Node #0,2,4: 55:[87, 141] Operation: 87+54=141 Moving to Node #0,3,4 Current State: 55:[1, 54], Operations: ['87/87=1', '92-38=54'] Exploring Operation: 54/1=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 1*54=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 1+54=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[92, 87, 38, 87], Operations: [] Exploring Operation: 87/87=1, Resulting Numbers: [92, 38, 1] Generated Node #0,3: 55:[92, 38, 1] Operation: 87/87=1 Moving to Node #0,3 Current State: 55:[92, 38, 1], Operations: ['87/87=1'] Exploring Operation: 92-38=54, Resulting Numbers: [1, 54] Generated Node #0,3,4: 55:[1, 54] Operation: 92-38=54 Moving to Node #0,3,4 Current State: 55:[1, 54], Operations: ['87/87=1', '92-38=54'] Exploring Operation: 1+54=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
0.954861
hs_5
sum_heuristic
[ 12, 33, 16, 27 ]
56
[ "12+33=45", "27-16=11", "45+11=56" ]
Current State: 56:[12, 33, 16, 27], Operations: [] Exploring Operation: 12+33=45, Resulting Numbers: [16, 27, 45] Generated Node #2: [16, 27, 45] from Operation: 12+33=45 Current State: 56:[16, 27, 45], Operations: ['12+33=45'] Exploring Operation: 27-16=11, Resulting Numbers: [45, 11] Generated Node #3: [45, 11] from Operation: 27-16=11 Current State: 56:[45, 11], Operations: ['12+33=45', '27-16=11'] Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[12, 33, 16, 27], Operations: [] Exploring Operation: 12+16=28, Resulting Numbers: [33, 27, 28] Generated Node #0,0: 56:[33, 27, 28] Operation: 12+16=28 Exploring Operation: 33-27=6, Resulting Numbers: [12, 16, 6] Generated Node #0,1: 56:[12, 16, 6] Operation: 33-27=6 Moving to Node #0,1 Current State: 56:[12, 16, 6], Operations: ['33-27=6'] Exploring Operation: 12+16=28, Resulting Numbers: [6, 28] Generated Node #0,1,0: 56:[6, 28] Operation: 12+16=28 Exploring Operation: 16-12=4, Resulting Numbers: [6, 4] Generated Node #0,1,1: 56:[6, 4] Operation: 16-12=4 Moving to Node #0,0 Current State: 56:[33, 27, 28], Operations: ['12+16=28'] Exploring Operation: 33-28=5, Resulting Numbers: [27, 5] Generated Node #0,0,0: 56:[27, 5] Operation: 33-28=5 Exploring Operation: 33-27=6, Resulting Numbers: [28, 6] Generated Node #0,0,1: 56:[28, 6] Operation: 33-27=6 Moving to Node #0,1,0 Current State: 56:[6, 28], Operations: ['33-27=6', '12+16=28'] Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 6+28=34, Resulting Numbers: [34] 34,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[28, 6], Operations: ['12+16=28', '33-27=6'] Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 28+6=34, Resulting Numbers: [34] 34,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[6, 4], Operations: ['33-27=6', '16-12=4'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,56 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[27, 5], Operations: ['12+16=28', '33-28=5'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,56 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 42, 66, 70, 57 ]
95
[ "42+66=108", "70-57=13", "108-13=95" ]
Current State: 95:[42, 66, 70, 57], Operations: [] Exploring Operation: 42+66=108, Resulting Numbers: [70, 57, 108] Generated Node #2: [70, 57, 108] from Operation: 42+66=108 Current State: 95:[70, 57, 108], Operations: ['42+66=108'] Exploring Operation: 70-57=13, Resulting Numbers: [108, 13] Generated Node #3: [108, 13] from Operation: 70-57=13 Current State: 95:[108, 13], Operations: ['42+66=108', '70-57=13'] Exploring Operation: 108-13=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[42, 66, 70, 57], Operations: [] Exploring Operation: 42+57=99, Resulting Numbers: [66, 70, 99] Generated Node #0,0: 95:[66, 70, 99] Operation: 42+57=99 Exploring Operation: 70-66=4, Resulting Numbers: [42, 57, 4] Generated Node #0,1: 95:[42, 57, 4] Operation: 70-66=4 Exploring Operation: 66-57=9, Resulting Numbers: [42, 70, 9] Generated Node #0,2: 95:[42, 70, 9] Operation: 66-57=9 Exploring Operation: 70-57=13, Resulting Numbers: [42, 66, 13] Generated Node #0,3: 95:[42, 66, 13] Operation: 70-57=13 Exploring Operation: 57-42=15, Resulting Numbers: [66, 70, 15] Generated Node #0,4: 95:[66, 70, 15] Operation: 57-42=15 Moving to Node #0,2 Current State: 95:[42, 70, 9], Operations: ['66-57=9'] Exploring Operation: 70+9=79, Resulting Numbers: [42, 79] Generated Node #0,2,0: 95:[42, 79] Operation: 70+9=79 Exploring Operation: 42-9=33, Resulting Numbers: [70, 33] Generated Node #0,2,1: 95:[70, 33] Operation: 42-9=33 Exploring Operation: 42+9=51, Resulting Numbers: [70, 51] Generated Node #0,2,2: 95:[70, 51] Operation: 42+9=51 Exploring Operation: 42+70=112, Resulting Numbers: [9, 112] Generated Node #0,2,3: 95:[9, 112] Operation: 42+70=112 Exploring Operation: 70-42=28, Resulting Numbers: [9, 28] Generated Node #0,2,4: 95:[9, 28] Operation: 70-42=28 Moving to Node #0,3 Current State: 95:[42, 66, 13], Operations: ['70-57=13'] Exploring Operation: 66-13=53, Resulting Numbers: [42, 53] Generated Node #0,3,0: 95:[42, 53] Operation: 66-13=53 Exploring Operation: 42+66=108, Resulting Numbers: [13, 108] Generated Node #0,3,1: 95:[13, 108] Operation: 42+66=108 Exploring Operation: 66-42=24, Resulting Numbers: [13, 24] Generated Node #0,3,2: 95:[13, 24] Operation: 66-42=24 Exploring Operation: 66+13=79, Resulting Numbers: [42, 79] Generated Node #0,3,3: 95:[42, 79] Operation: 66+13=79 Exploring Operation: 42-13=29, Resulting Numbers: [66, 29] Generated Node #0,3,4: 95:[66, 29] Operation: 42-13=29 Moving to Node #0,0 Current State: 95:[66, 70, 99], Operations: ['42+57=99'] Exploring Operation: 70-66=4, Resulting Numbers: [99, 4] Generated Node #0,0,0: 95:[99, 4] Operation: 70-66=4 Exploring Operation: 66+70=136, Resulting Numbers: [99, 136] Generated Node #0,0,1: 95:[99, 136] Operation: 66+70=136 Exploring Operation: 99-66=33, Resulting Numbers: [70, 33] Generated Node #0,0,2: 95:[70, 33] Operation: 99-66=33 Exploring Operation: 66+99=165, Resulting Numbers: [70, 165] Generated Node #0,0,3: 95:[70, 165] Operation: 66+99=165 Exploring Operation: 99-70=29, Resulting Numbers: [66, 29] Generated Node #0,0,4: 95:[66, 29] Operation: 99-70=29 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[99, 4], Operations: ['42+57=99', '70-66=4'] Exploring Operation: 99*4=396, Resulting Numbers: [396] 396,95 unequal: No Solution Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[42, 66, 70, 57], Operations: [] Exploring Operation: 42+57=99, Resulting Numbers: [66, 70, 99] Generated Node #0,0: 95:[66, 70, 99] Operation: 42+57=99 Moving to Node #0,0 Current State: 95:[66, 70, 99], Operations: ['42+57=99'] Exploring Operation: 70-66=4, Resulting Numbers: [99, 4] Generated Node #0,0,0: 95:[99, 4] Operation: 70-66=4 Moving to Node #0,0,0 Current State: 95:[99, 4], Operations: ['42+57=99', '70-66=4'] Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
mult_heuristic
[ 80, 66, 21, 42 ]
70
[ "80*21=1680", "66-42=24", "1680/24=70" ]
Current State: 70:[80, 66, 21, 42], Operations: [] Exploring Operation: 80*21=1680, Resulting Numbers: [66, 42, 1680] Generated Node #2: [66, 42, 1680] from Operation: 80*21=1680 Current State: 70:[66, 42, 1680], Operations: ['80*21=1680'] Exploring Operation: 66-42=24, Resulting Numbers: [1680, 24] Generated Node #3: [1680, 24] from Operation: 66-42=24 Current State: 70:[1680, 24], Operations: ['80*21=1680', '66-42=24'] Exploring Operation: 1680/24=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[80, 66, 21, 42], Operations: [] Exploring Operation: 42/21=2, Resulting Numbers: [80, 66, 2] Generated Node #0,0: 70:[80, 66, 2] Operation: 42/21=2 Exploring Operation: 42-21=21, Resulting Numbers: [80, 66, 21] Generated Node #0,1: 70:[80, 66, 21] Operation: 42-21=21 Exploring Operation: 80-42=38, Resulting Numbers: [66, 21, 38] Generated Node #0,2: 70:[66, 21, 38] Operation: 80-42=38 Exploring Operation: 21+42=63, Resulting Numbers: [80, 66, 63] Generated Node #0,3: 70:[80, 66, 63] Operation: 21+42=63 Exploring Operation: 80-66=14, Resulting Numbers: [21, 42, 14] Generated Node #0,4: 70:[21, 42, 14] Operation: 80-66=14 Moving to Node #0,0 Current State: 70:[80, 66, 2], Operations: ['42/21=2'] Exploring Operation: 66/2=33, Resulting Numbers: [80, 33] Generated Node #0,0,0: 70:[80, 33] Operation: 66/2=33 Exploring Operation: 66+2=68, Resulting Numbers: [80, 68] Generated Node #0,0,1: 70:[80, 68] Operation: 66+2=68 Exploring Operation: 80-2=78, Resulting Numbers: [66, 78] Generated Node #0,0,2: 70:[66, 78] Operation: 80-2=78 Exploring Operation: 80/2=40, Resulting Numbers: [66, 40] Generated Node #0,0,3: 70:[66, 40] Operation: 80/2=40 Exploring Operation: 80-66=14, Resulting Numbers: [2, 14] Generated Node #0,0,4: 70:[2, 14] Operation: 80-66=14 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 70:[2, 14], Operations: ['42/21=2', '80-66=14'] Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,70 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,70 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 #0,0,3 Current State: 70:[66, 40], Operations: ['42/21=2', '80/2=40'] Exploring Operation: 66-40=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 66+40=106, Resulting Numbers: [106] 106,70 unequal: No Solution Exploring Operation: 66*40=2640, Resulting Numbers: [2640] 2640,70 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 #0,0,0 Current State: 70:[80, 33], Operations: ['42/21=2', '66/2=33'] Exploring Operation: 80*33=2640, Resulting Numbers: [2640] 2640,70 unequal: No Solution Exploring Operation: 80+33=113, Resulting Numbers: [113] 113,70 unequal: No Solution Exploring Operation: 80-33=47, Resulting Numbers: [47] 47,70 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 #0,0,1 Current State: 70:[80, 68], Operations: ['42/21=2', '66+2=68'] Exploring Operation: 80*68=5440, Resulting Numbers: [5440] 5440,70 unequal: No Solution Exploring Operation: 80+68=148, Resulting Numbers: [148] 148,70 unequal: No Solution Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,70 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 #0,0,2 Current State: 70:[66, 78], Operations: ['42/21=2', '80-2=78'] Exploring Operation: 78-66=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 66*78=5148, Resulting Numbers: [5148] 5148,70 unequal: No Solution Exploring Operation: 66+78=144, Resulting Numbers: [144] 144,70 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: 70:[21, 42, 14], Operations: ['80-66=14'] Exploring Operation: 21-14=7, Resulting Numbers: [42, 7] Generated Node #0,4,0: 70:[42, 7] Operation: 21-14=7 Exploring Operation: 21+14=35, Resulting Numbers: [42, 35] Generated Node #0,4,1: 70:[42, 35] Operation: 21+14=35 Exploring Operation: 42-21=21, Resulting Numbers: [14, 21] Generated Node #0,4,2: 70:[14, 21] Operation: 42-21=21 Exploring Operation: 21+42=63, Resulting Numbers: [14, 63] Generated Node #0,4,3: 70:[14, 63] Operation: 21+42=63 Exploring Operation: 42/21=2, Resulting Numbers: [14, 2] Generated Node #0,4,4: 70:[14, 2] Operation: 42/21=2 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 70:[14, 2], Operations: ['80-66=14', '42/21=2'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,70 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,70 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 #0,4,0 Current State: 70:[42, 7], Operations: ['80-66=14', '21-14=7'] Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 42*7=294, Resulting Numbers: [294] 294,70 unequal: No Solution Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,70 unequal: No Solution Exploring Operation: 42+7=49, Resulting Numbers: [49] 49,70 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 #0,4,1 Current State: 70:[42, 35], Operations: ['80-66=14', '21+14=35'] Exploring Operation: 42-35=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 42+35=77, Resulting Numbers: [77] 77,70 unequal: No Solution Exploring Operation: 42*35=1470, Resulting Numbers: [1470] 1470,70 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 #0,4,2 Current State: 70:[14, 21], Operations: ['80-66=14', '42-21=21'] Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 14*21=294, Resulting Numbers: [294] 294,70 unequal: No Solution Exploring Operation: 14+21=35, Resulting Numbers: [35] 35,70 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 #0,4,3 Current State: 70:[14, 63], Operations: ['80-66=14', '21+42=63'] Exploring Operation: 63-14=49, Resulting Numbers: [49] 49,70 unequal: No Solution Exploring Operation: 14*63=882, Resulting Numbers: [882] 882,70 unequal: No Solution Exploring Operation: 14+63=77, Resulting Numbers: [77] 77,70 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: 70:[66, 21, 38], Operations: ['80-42=38'] Exploring Operation: 21+38=59, Resulting Numbers: [66, 59] Generated Node #0,2,0: 70:[66, 59] Operation: 21+38=59 Exploring Operation: 66-21=45, Resulting Numbers: [38, 45] Generated Node #0,2,1: 70:[38, 45] Operation: 66-21=45 Exploring Operation: 66-38=28, Resulting Numbers: [21, 28] Generated Node #0,2,2: 70:[21, 28] Operation: 66-38=28 Exploring Operation: 66+21=87, Resulting Numbers: [38, 87] Generated Node #0,2,3: 70:[38, 87] Operation: 66+21=87 Exploring Operation: 38-21=17, Resulting Numbers: [66, 17] Generated Node #0,2,4: 70:[66, 17] Operation: 38-21=17 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 70:[66, 17], Operations: ['80-42=38', '38-21=17'] Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,70 unequal: No Solution Exploring Operation: 66*17=1122, Resulting Numbers: [1122] 1122,70 unequal: No Solution Exploring Operation: 66+17=83, Resulting Numbers: [83] 83,70 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 #0,2,1 Current State: 70:[38, 45], Operations: ['80-42=38', '66-21=45'] Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,70 unequal: No Solution Exploring Operation: 38*45=1710, Resulting Numbers: [1710] 1710,70 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 #0,2,2 Current State: 70:[21, 28], Operations: ['80-42=38', '66-38=28'] Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,70 unequal: No Solution Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,70 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 #0,2,0 Current State: 70:[66, 59], Operations: ['80-42=38', '21+38=59'] Exploring Operation: 66+59=125, Resulting Numbers: [125] 125,70 unequal: No Solution Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 66*59=3894, Resulting Numbers: [3894] 3894,70 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 #0,2,3 Current State: 70:[38, 87], Operations: ['80-42=38', '66+21=87'] Exploring Operation: 38+87=125, Resulting Numbers: [125] 125,70 unequal: No Solution Exploring Operation: 38*87=3306, Resulting Numbers: [3306] 3306,70 unequal: No Solution Exploring Operation: 87-38=49, Resulting Numbers: [49] 49,70 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: 70:[80, 66, 21], Operations: ['42-21=21'] Exploring Operation: 80+21=101, Resulting Numbers: [66, 101] Generated Node #0,1,0: 70:[66, 101] Operation: 80+21=101 Exploring Operation: 80-66=14, Resulting Numbers: [21, 14] Generated Node #0,1,1: 70:[21, 14] Operation: 80-66=14 Exploring Operation: 66+21=87, Resulting Numbers: [80, 87] Generated Node #0,1,2: 70:[80, 87] Operation: 66+21=87 Exploring Operation: 80-21=59, Resulting Numbers: [66, 59] Generated Node #0,1,3: 70:[66, 59] Operation: 80-21=59 Exploring Operation: 66-21=45, Resulting Numbers: [80, 45] Generated Node #0,1,4: 70:[80, 45] Operation: 66-21=45 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 70:[21, 14], Operations: ['42-21=21', '80-66=14'] Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,70 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,70 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 #0,1,3 Current State: 70:[66, 59], Operations: ['42-21=21', '80-21=59'] Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 66+59=125, Resulting Numbers: [125] 125,70 unequal: No Solution Exploring Operation: 66*59=3894, Resulting Numbers: [3894] 3894,70 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 #0,1,4 Current State: 70:[80, 45], Operations: ['42-21=21', '66-21=45'] Exploring Operation: 80*45=3600, Resulting Numbers: [3600] 3600,70 unequal: No Solution Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,70 unequal: No Solution Exploring Operation: 80+45=125, Resulting Numbers: [125] 125,70 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 #0,1,2 Current State: 70:[80, 87], Operations: ['42-21=21', '66+21=87'] Exploring Operation: 87-80=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 80*87=6960, Resulting Numbers: [6960] 6960,70 unequal: No Solution Exploring Operation: 80+87=167, Resulting Numbers: [167] 167,70 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 #0,1,0 Current State: 70:[66, 101], Operations: ['42-21=21', '80+21=101'] Exploring Operation: 66*101=6666, Resulting Numbers: [6666] 6666,70 unequal: No Solution Exploring Operation: 66+101=167, Resulting Numbers: [167] 167,70 unequal: No Solution Exploring Operation: 101-66=35, Resulting Numbers: [35] 35,70 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: 70:[80, 66, 63], Operations: ['21+42=63'] Exploring Operation: 80-66=14, Resulting Numbers: [63, 14] Generated Node #0,3,0: 70:[63, 14] Operation: 80-66=14 Exploring Operation: 80-63=17, Resulting Numbers: [66, 17] Generated Node #0,3,1: 70:[66, 17] Operation: 80-63=17 Exploring Operation: 80+63=143, Resulting Numbers: [66, 143] Generated Node #0,3,2: 70:[66, 143] Operation: 80+63=143 Exploring Operation: 66-63=3, Resulting Numbers: [80, 3] Generated Node #0,3,3: 70:[80, 3] Operation: 66-63=3 Exploring Operation: 66+63=129, Resulting Numbers: [80, 129] Generated Node #0,3,4: 70:[80, 129] Operation: 66+63=129 Moving to Node #0,3,0 Current State: 70:[63, 14], Operations: ['21+42=63', '80-66=14'] Exploring Operation: 63-14=49, Resulting Numbers: [49] 49,70 unequal: No Solution Exploring Operation: 63+14=77, Resulting Numbers: [77] 77,70 unequal: No Solution Exploring Operation: 63*14=882, Resulting Numbers: [882] 882,70 unequal: No Solution Moving to Node #0,3,1 Current State: 70:[66, 17], Operations: ['21+42=63', '80-63=17'] Exploring Operation: 66*17=1122, Resulting Numbers: [1122] 1122,70 unequal: No Solution Exploring Operation: 66+17=83, Resulting Numbers: [83] 83,70 unequal: No Solution Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,70 unequal: No Solution Moving to Node #0,3,3 Current State: 70:[80, 3], Operations: ['21+42=63', '66-63=3'] Exploring Operation: 80*3=240, Resulting Numbers: [240] 240,70 unequal: No Solution Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,70 unequal: No Solution Exploring Operation: 80+3=83, Resulting Numbers: [83] 83,70 unequal: No Solution Moving to Node #0,3,4 Current State: 70:[80, 129], Operations: ['21+42=63', '66+63=129'] Exploring Operation: 80+129=209, Resulting Numbers: [209] 209,70 unequal: No Solution Exploring Operation: 80*129=10320, Resulting Numbers: [10320] 10320,70 unequal: No Solution Exploring Operation: 129-80=49, Resulting Numbers: [49] 49,70 unequal: No Solution Moving to Node #0,3,2 Current State: 70:[66, 143], Operations: ['21+42=63', '80+63=143'] Exploring Operation: 66*143=9438, Resulting Numbers: [9438] 9438,70 unequal: No Solution Exploring Operation: 66+143=209, Resulting Numbers: [209] 209,70 unequal: No Solution Exploring Operation: 143-66=77, Resulting Numbers: [77] 77,70 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 97, 33, 82, 18 ]
30
[ "97+33=130", "82+18=100", "130-100=30" ]
Current State: 30:[97, 33, 82, 18], Operations: [] Exploring Operation: 97+33=130, Resulting Numbers: [82, 18, 130] Generated Node #2: [82, 18, 130] from Operation: 97+33=130 Current State: 30:[82, 18, 130], Operations: ['97+33=130'] Exploring Operation: 82+18=100, Resulting Numbers: [130, 100] Generated Node #3: [130, 100] from Operation: 82+18=100 Current State: 30:[130, 100], Operations: ['97+33=130', '82+18=100'] Exploring Operation: 130-100=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[97, 33, 82, 18], Operations: [] Exploring Operation: 82-33=49, Resulting Numbers: [97, 18, 49] Generated Node #0,0: 30:[97, 18, 49] Operation: 82-33=49 Exploring Operation: 97-82=15, Resulting Numbers: [33, 18, 15] Generated Node #0,1: 30:[33, 18, 15] Operation: 97-82=15 Exploring Operation: 97-18=79, Resulting Numbers: [33, 82, 79] Generated Node #0,2: 30:[33, 82, 79] Operation: 97-18=79 Exploring Operation: 97-33=64, Resulting Numbers: [82, 18, 64] Generated Node #0,3: 30:[82, 18, 64] Operation: 97-33=64 Moving to Node #0,1 Current State: 30:[33, 18, 15], Operations: ['97-82=15'] Exploring Operation: 18-15=3, Resulting Numbers: [33, 3] Generated Node #0,1,0: 30:[33, 3] Operation: 18-15=3 Exploring Operation: 33-15=18, Resulting Numbers: [18, 18] Generated Node #0,1,1: 30:[18, 18] Operation: 33-15=18 Exploring Operation: 18+15=33, Resulting Numbers: [33, 33] Generated Node #0,1,2: 30:[33, 33] Operation: 18+15=33 Exploring Operation: 33-18=15, Resulting Numbers: [15, 15] Generated Node #0,1,3: 30:[15, 15] Operation: 33-18=15 Moving to Node #0,3 Current State: 30:[82, 18, 64], Operations: ['97-33=64'] Exploring Operation: 64-18=46, Resulting Numbers: [82, 46] Generated Node #0,3,0: 30:[82, 46] Operation: 64-18=46 Exploring Operation: 82+18=100, Resulting Numbers: [64, 100] Generated Node #0,3,1: 30:[64, 100] Operation: 82+18=100 Exploring Operation: 82-64=18, Resulting Numbers: [18, 18] Generated Node #0,3,2: 30:[18, 18] Operation: 82-64=18 Exploring Operation: 82-18=64, Resulting Numbers: [64, 64] Generated Node #0,3,3: 30:[64, 64] Operation: 82-18=64 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 30:[18, 18], Operations: ['97-33=64', '82-64=18'] Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,30 unequal: No Solution Exploring Operation: 18*18=324, Resulting Numbers: [324] 324,30 unequal: No Solution Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 18-18=0, Resulting Numbers: [0] 0,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 30:[82, 46], Operations: ['97-33=64', '64-18=46'] Exploring Operation: 82-46=36, Resulting Numbers: [36] 36,30 unequal: No Solution Exploring Operation: 82+46=128, Resulting Numbers: [128] 128,30 unequal: No Solution Exploring Operation: 82*46=3772, Resulting Numbers: [3772] 3772,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 30:[64, 64], Operations: ['97-33=64', '82-18=64'] Exploring Operation: 64*64=4096, Resulting Numbers: [4096] 4096,30 unequal: No Solution Exploring Operation: 64+64=128, Resulting Numbers: [128] 128,30 unequal: No Solution Exploring Operation: 64-64=0, Resulting Numbers: [0] 0,30 unequal: No Solution Exploring Operation: 64/64=1, Resulting Numbers: [1] 1,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 30:[64, 100], Operations: ['97-33=64', '82+18=100'] Exploring Operation: 100-64=36, Resulting Numbers: [36] 36,30 unequal: No Solution Exploring Operation: 64*100=6400, Resulting Numbers: [6400] 6400,30 unequal: No Solution Exploring Operation: 64+100=164, Resulting Numbers: [164] 164,30 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: 30:[97, 18, 49], Operations: ['82-33=49'] Exploring Operation: 97-18=79, Resulting Numbers: [49, 79] Generated Node #0,0,0: 30:[49, 79] Operation: 97-18=79 Exploring Operation: 49-18=31, Resulting Numbers: [97, 31] Generated Node #0,0,1: 30:[97, 31] Operation: 49-18=31 Exploring Operation: 97-49=48, Resulting Numbers: [18, 48] Generated Node #0,0,2: 30:[18, 48] Operation: 97-49=48 Exploring Operation: 97+18=115, Resulting Numbers: [49, 115] Generated Node #0,0,3: 30:[49, 115] Operation: 97+18=115 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 30:[18, 48], Operations: ['82-33=49', '97-49=48'] Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,30 unequal: No Solution Exploring Operation: 18+48=66, Resulting Numbers: [66] 66,30 unequal: No Solution Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[97, 33, 82, 18], Operations: [] Exploring Operation: 82-33=49, Resulting Numbers: [97, 18, 49] Generated Node #0,0: 30:[97, 18, 49] Operation: 82-33=49 Moving to Node #0,0 Current State: 30:[97, 18, 49], Operations: ['82-33=49'] Exploring Operation: 97-49=48, Resulting Numbers: [18, 48] Generated Node #0,0,2: 30:[18, 48] Operation: 97-49=48 Moving to Node #0,0,2 Current State: 30:[18, 48], Operations: ['82-33=49', '97-49=48'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_4
mult_heuristic
[ 55, 64, 54, 1 ]
65
[ "55+64=119", "54*1=54", "119-54=65" ]
Current State: 65:[55, 64, 54, 1], Operations: [] Exploring Operation: 55+64=119, Resulting Numbers: [54, 1, 119] Generated Node #2: [54, 1, 119] from Operation: 55+64=119 Current State: 65:[54, 1, 119], Operations: ['55+64=119'] Exploring Operation: 54*1=54, Resulting Numbers: [119, 54] Generated Node #3: [119, 54] from Operation: 54*1=54 Current State: 65:[119, 54], Operations: ['55+64=119', '54*1=54'] Exploring Operation: 119-54=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[55, 64, 54, 1], Operations: [] Exploring Operation: 64-55=9, Resulting Numbers: [54, 1, 9] Generated Node #0,0: 65:[54, 1, 9] Operation: 64-55=9 Exploring Operation: 55-54=1, Resulting Numbers: [64, 1, 1] Generated Node #0,1: 65:[64, 1, 1] Operation: 55-54=1 Exploring Operation: 64-54=10, Resulting Numbers: [55, 1, 10] Generated Node #0,2: 65:[55, 1, 10] Operation: 64-54=10 Moving to Node #0,1 Current State: 65:[64, 1, 1], Operations: ['55-54=1'] Exploring Operation: 64+1=65, Resulting Numbers: [1, 65] Generated Node #0,1,0: 65:[1, 65] Operation: 64+1=65 Exploring Operation: 64+1=65, Resulting Numbers: [1, 65] Generated Node #0,1,1: 65:[1, 65] Operation: 64+1=65 Exploring Operation: 1+1=2, Resulting Numbers: [64, 2] Generated Node #0,1,2: 65:[64, 2] Operation: 1+1=2 Moving to Node #0,2 Current State: 65:[55, 1, 10], Operations: ['64-54=10'] Exploring Operation: 55+1=56, Resulting Numbers: [10, 56] Generated Node #0,2,0: 65:[10, 56] Operation: 55+1=56 Exploring Operation: 1+10=11, Resulting Numbers: [55, 11] Generated Node #0,2,1: 65:[55, 11] Operation: 1+10=11 Exploring Operation: 55+10=65, Resulting Numbers: [1, 65] Generated Node #0,2,2: 65:[1, 65] Operation: 55+10=65 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 65:[1, 65], Operations: ['64-54=10', '55+10=65'] Exploring Operation: 1+65=66, Resulting Numbers: [66] 66,65 unequal: No Solution Exploring Operation: 1*65=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[55, 64, 54, 1], Operations: [] Exploring Operation: 64-54=10, Resulting Numbers: [55, 1, 10] Generated Node #0,2: 65:[55, 1, 10] Operation: 64-54=10 Moving to Node #0,2 Current State: 65:[55, 1, 10], Operations: ['64-54=10'] Exploring Operation: 55+10=65, Resulting Numbers: [1, 65] Generated Node #0,2,2: 65:[1, 65] Operation: 55+10=65 Moving to Node #0,2,2 Current State: 65:[1, 65], Operations: ['64-54=10', '55+10=65'] Exploring Operation: 1*65=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 40, 3, 7, 64 ]
24
[ "7-3=4", "64/4=16", "40-16=24" ]
Current State: 24:[40, 3, 7, 64], Operations: [] Exploring Operation: 7-3=4, Resulting Numbers: [40, 64, 4] Generated Node #2: [40, 64, 4] from Operation: 7-3=4 Current State: 24:[40, 64, 4], Operations: ['7-3=4'] Exploring Operation: 64/4=16, Resulting Numbers: [40, 16] Generated Node #3: [40, 16] from Operation: 64/4=16 Current State: 24:[40, 16], Operations: ['7-3=4', '64/4=16'] Exploring Operation: 40-16=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[40, 3, 7, 64], Operations: [] Exploring Operation: 40-7=33, Resulting Numbers: [3, 64, 33] Generated Node #0,0: 24:[3, 64, 33] Operation: 40-7=33 Exploring Operation: 64-7=57, Resulting Numbers: [40, 3, 57] Generated Node #0,1: 24:[40, 3, 57] Operation: 64-7=57 Exploring Operation: 40-3=37, Resulting Numbers: [7, 64, 37] Generated Node #0,2: 24:[7, 64, 37] Operation: 40-3=37 Exploring Operation: 64-40=24, Resulting Numbers: [3, 7, 24] Generated Node #0,3: 24:[3, 7, 24] Operation: 64-40=24 Start Sub Search at level 1: Moving to Node #0,3 Current State: 24:[3, 7, 24], Operations: ['64-40=24'] Exploring Operation: 3+7=10, Resulting Numbers: [24, 10] Generated Node #0,3,0: 24:[24, 10] Operation: 3+7=10 Exploring Operation: 3*7=21, Resulting Numbers: [24, 21] Generated Node #0,3,1: 24:[24, 21] Operation: 3*7=21 Exploring Operation: 24/3=8, Resulting Numbers: [7, 8] Generated Node #0,3,2: 24:[7, 8] Operation: 24/3=8 Exploring Operation: 7-3=4, Resulting Numbers: [24, 4] Generated Node #0,3,3: 24:[24, 4] Operation: 7-3=4 Moving to Node #0,3,3 Current State: 24:[24, 4], Operations: ['64-40=24', '7-3=4'] Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,24 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,24 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[7, 8], Operations: ['64-40=24', '24/3=8'] Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,24 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,24 unequal: No Solution Moving to Node #0,3,0 Current State: 24:[24, 10], Operations: ['64-40=24', '3+7=10'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 24*10=240, Resulting Numbers: [240] 240,24 unequal: No Solution Moving to Node #0,3,1 Current State: 24:[24, 21], Operations: ['64-40=24', '3*7=21'] Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,24 unequal: No Solution Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[3, 64, 33], Operations: ['40-7=33'] Exploring Operation: 33-3=30, Resulting Numbers: [64, 30] Generated Node #0,0,0: 24:[64, 30] Operation: 33-3=30 Exploring Operation: 64-33=31, Resulting Numbers: [3, 31] Generated Node #0,0,1: 24:[3, 31] Operation: 64-33=31 Exploring Operation: 33/3=11, Resulting Numbers: [64, 11] Generated Node #0,0,2: 24:[64, 11] Operation: 33/3=11 Exploring Operation: 64-3=61, Resulting Numbers: [33, 61] Generated Node #0,0,3: 24:[33, 61] Operation: 64-3=61 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 24:[3, 31], Operations: ['40-7=33', '64-33=31'] Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,24 unequal: No Solution Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,24 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:[64, 11], Operations: ['40-7=33', '33/3=11'] Exploring Operation: 64-11=53, Resulting Numbers: [53] 53,24 unequal: No Solution Exploring Operation: 64*11=704, Resulting Numbers: [704] 704,24 unequal: No Solution Exploring Operation: 64+11=75, Resulting Numbers: [75] 75,24 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 #0,0,0 Current State: 24:[64, 30], Operations: ['40-7=33', '33-3=30'] Exploring Operation: 64*30=1920, Resulting Numbers: [1920] 1920,24 unequal: No Solution Exploring Operation: 64+30=94, Resulting Numbers: [94] 94,24 unequal: No Solution Exploring Operation: 64-30=34, Resulting Numbers: [34] 34,24 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:[33, 61], Operations: ['40-7=33', '64-3=61'] Exploring Operation: 61-33=28, Resulting Numbers: [28] 28,24 unequal: No Solution Exploring Operation: 33*61=2013, Resulting Numbers: [2013] 2013,24 unequal: No Solution Exploring Operation: 33+61=94, Resulting Numbers: [94] 94,24 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 #0,1 Current State: 24:[40, 3, 57], Operations: ['64-7=57'] Exploring Operation: 40-3=37, Resulting Numbers: [57, 37] Generated Node #0,1,0: 24:[57, 37] Operation: 40-3=37 Exploring Operation: 57/3=19, Resulting Numbers: [40, 19] Generated Node #0,1,1: 24:[40, 19] Operation: 57/3=19 Exploring Operation: 57-40=17, Resulting Numbers: [3, 17] Generated Node #0,1,2: 24:[3, 17] Operation: 57-40=17 Exploring Operation: 57-3=54, Resulting Numbers: [40, 54] Generated Node #0,1,3: 24:[40, 54] Operation: 57-3=54 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 24:[3, 17], Operations: ['64-7=57', '57-40=17'] Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,24 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 #0,1,1 Current State: 24:[40, 19], Operations: ['64-7=57', '57/3=19'] Exploring Operation: 40+19=59, Resulting Numbers: [59] 59,24 unequal: No Solution Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,24 unequal: No Solution Exploring Operation: 40*19=760, Resulting Numbers: [760] 760,24 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 #0,1,0 Current State: 24:[57, 37], Operations: ['64-7=57', '40-3=37'] Exploring Operation: 57-37=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 57*37=2109, Resulting Numbers: [2109] 2109,24 unequal: No Solution Exploring Operation: 57+37=94, Resulting Numbers: [94] 94,24 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 #0,1,3 Current State: 24:[40, 54], Operations: ['64-7=57', '57-3=54'] Exploring Operation: 40+54=94, Resulting Numbers: [94] 94,24 unequal: No Solution Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 40*54=2160, Resulting Numbers: [2160] 2160,24 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 #0,2 Current State: 24:[7, 64, 37], Operations: ['40-3=37'] Exploring Operation: 37-7=30, Resulting Numbers: [64, 30] Generated Node #0,2,0: 24:[64, 30] Operation: 37-7=30 Exploring Operation: 7+64=71, Resulting Numbers: [37, 71] Generated Node #0,2,1: 24:[37, 71] Operation: 7+64=71 Exploring Operation: 64-37=27, Resulting Numbers: [7, 27] Generated Node #0,2,2: 24:[7, 27] Operation: 64-37=27 Exploring Operation: 64-7=57, Resulting Numbers: [37, 57] Generated Node #0,2,3: 24:[37, 57] Operation: 64-7=57 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 24:[7, 27], Operations: ['40-3=37', '64-37=27'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 7*27=189, Resulting Numbers: [189] 189,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 24:[64, 30], Operations: ['40-3=37', '37-7=30'] Exploring Operation: 64-30=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 64*30=1920, Resulting Numbers: [1920] 1920,24 unequal: No Solution Exploring Operation: 64+30=94, Resulting Numbers: [94] 94,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 24:[37, 57], Operations: ['40-3=37', '64-7=57'] Exploring Operation: 57-37=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 37+57=94, Resulting Numbers: [94] 94,24 unequal: No Solution Exploring Operation: 37*57=2109, Resulting Numbers: [2109] 2109,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 24:[37, 71], Operations: ['40-3=37', '7+64=71'] Exploring Operation: 71-37=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 37+71=108, Resulting Numbers: [108] 108,24 unequal: No Solution Exploring Operation: 37*71=2627, Resulting Numbers: [2627] 2627,24 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 No solution found.
0
hs_4
mult_heuristic
[ 77, 80, 44, 42 ]
83
[ "80-77=3", "44+42=86", "86-3=83" ]
Current State: 83:[77, 80, 44, 42], Operations: [] Exploring Operation: 80-77=3, Resulting Numbers: [44, 42, 3] Generated Node #2: [44, 42, 3] from Operation: 80-77=3 Current State: 83:[44, 42, 3], Operations: ['80-77=3'] Exploring Operation: 44+42=86, Resulting Numbers: [3, 86] Generated Node #3: [3, 86] from Operation: 44+42=86 Current State: 83:[3, 86], Operations: ['80-77=3', '44+42=86'] Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[77, 80, 44, 42], Operations: [] Exploring Operation: 44+42=86, Resulting Numbers: [77, 80, 86] Generated Node #0,0: 83:[77, 80, 86] Operation: 44+42=86 Exploring Operation: 77+42=119, Resulting Numbers: [80, 44, 119] Generated Node #0,1: 83:[80, 44, 119] Operation: 77+42=119 Exploring Operation: 77+44=121, Resulting Numbers: [80, 42, 121] Generated Node #0,2: 83:[80, 42, 121] Operation: 77+44=121 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[77, 80, 86], Operations: ['44+42=86'] Exploring Operation: 77+80=157, Resulting Numbers: [86, 157] Generated Node #0,0,0: 83:[86, 157] Operation: 77+80=157 Exploring Operation: 80-77=3, Resulting Numbers: [86, 3] Generated Node #0,0,1: 83:[86, 3] Operation: 80-77=3 Exploring Operation: 86-77=9, Resulting Numbers: [80, 9] Generated Node #0,0,2: 83:[80, 9] Operation: 86-77=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[86, 157], Operations: ['44+42=86', '77+80=157'] Exploring Operation: 86+157=243, Resulting Numbers: [243] 243,83 unequal: No Solution Exploring Operation: 157-86=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 86*157=13502, Resulting Numbers: [13502] 13502,83 unequal: No Solution No 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: 83:[80, 9], Operations: ['44+42=86', '86-77=9'] Exploring Operation: 80*9=720, Resulting Numbers: [720] 720,83 unequal: No Solution Exploring Operation: 80+9=89, Resulting Numbers: [89] 89,83 unequal: No Solution Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,83 unequal: No Solution No 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: 83:[86, 3], Operations: ['44+42=86', '80-77=3'] Exploring Operation: 86*3=258, Resulting Numbers: [258] 258,83 unequal: No Solution Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,83 unequal: No Solution Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[77, 80, 44, 42], Operations: [] Exploring Operation: 44+42=86, Resulting Numbers: [77, 80, 86] Generated Node #0,0: 83:[77, 80, 86] Operation: 44+42=86 Moving to Node #0,0 Current State: 83:[77, 80, 86], Operations: ['44+42=86'] Exploring Operation: 80-77=3, Resulting Numbers: [86, 3] Generated Node #0,0,1: 83:[86, 3] Operation: 80-77=3 Moving to Node #0,0,1 Current State: 83:[86, 3], Operations: ['44+42=86', '80-77=3'] Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 8, 24, 80, 3 ]
82
[ "80/8=10", "24*3=72", "10+72=82" ]
Current State: 82:[8, 24, 80, 3], Operations: [] Exploring Operation: 80/8=10, Resulting Numbers: [24, 3, 10] Generated Node #2: [24, 3, 10] from Operation: 80/8=10 Current State: 82:[24, 3, 10], Operations: ['80/8=10'] Exploring Operation: 24*3=72, Resulting Numbers: [10, 72] Generated Node #3: [10, 72] from Operation: 24*3=72 Current State: 82:[10, 72], Operations: ['80/8=10', '24*3=72'] Exploring Operation: 10+72=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[8, 24, 80, 3], Operations: [] Exploring Operation: 24/3=8, Resulting Numbers: [8, 80, 8] Generated Node #0,0: 82:[8, 80, 8] Operation: 24/3=8 Exploring Operation: 24/8=3, Resulting Numbers: [80, 3, 3] Generated Node #0,1: 82:[80, 3, 3] Operation: 24/8=3 Exploring Operation: 8+24=32, Resulting Numbers: [80, 3, 32] Generated Node #0,2: 82:[80, 3, 32] Operation: 8+24=32 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[80, 3, 3], Operations: ['24/8=3'] Exploring Operation: 80+3=83, Resulting Numbers: [3, 83] Generated Node #0,1,0: 82:[3, 83] Operation: 80+3=83 Exploring Operation: 80+3=83, Resulting Numbers: [3, 83] Generated Node #0,1,1: 82:[3, 83] Operation: 80+3=83 Exploring Operation: 3/3=1, Resulting Numbers: [80, 1] Generated Node #0,1,2: 82:[80, 1] Operation: 3/3=1 Moving to Node #0,1,0 Current State: 82:[3, 83], Operations: ['24/8=3', '80+3=83'] Exploring Operation: 83-3=80, Resulting Numbers: [80] 80,82 unequal: No Solution Exploring Operation: 3+83=86, Resulting Numbers: [86] 86,82 unequal: No Solution Exploring Operation: 3*83=249, Resulting Numbers: [249] 249,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[3, 83], Operations: ['24/8=3', '80+3=83'] Exploring Operation: 3+83=86, Resulting Numbers: [86] 86,82 unequal: No Solution Exploring Operation: 3*83=249, Resulting Numbers: [249] 249,82 unequal: No Solution Exploring Operation: 83-3=80, Resulting Numbers: [80] 80,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[80, 1], Operations: ['24/8=3', '3/3=1'] Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,82 unequal: No Solution Exploring Operation: 80*1=80, Resulting Numbers: [80] 80,82 unequal: No Solution Exploring Operation: 80/1=80, Resulting Numbers: [80] 80,82 unequal: No Solution No 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: 82:[80, 3, 32], Operations: ['8+24=32'] Exploring Operation: 80+3=83, Resulting Numbers: [32, 83] Generated Node #0,2,0: 82:[32, 83] Operation: 80+3=83 Exploring Operation: 3+32=35, Resulting Numbers: [80, 35] Generated Node #0,2,1: 82:[80, 35] Operation: 3+32=35 Exploring Operation: 80-32=48, Resulting Numbers: [3, 48] Generated Node #0,2,2: 82:[3, 48] Operation: 80-32=48 Moving to Node #0,2,1 Current State: 82:[80, 35], Operations: ['8+24=32', '3+32=35'] Exploring Operation: 80*35=2800, Resulting Numbers: [2800] 2800,82 unequal: No Solution Exploring Operation: 80-35=45, Resulting Numbers: [45] 45,82 unequal: No Solution Exploring Operation: 80+35=115, Resulting Numbers: [115] 115,82 unequal: No Solution Moving to Node #0,2,2 Current State: 82:[3, 48], Operations: ['8+24=32', '80-32=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,82 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,82 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,82 unequal: No Solution Moving to Node #0,2,0 Current State: 82:[32, 83], Operations: ['8+24=32', '80+3=83'] Exploring Operation: 83-32=51, Resulting Numbers: [51] 51,82 unequal: No Solution Exploring Operation: 32*83=2656, Resulting Numbers: [2656] 2656,82 unequal: No Solution Exploring Operation: 32+83=115, Resulting Numbers: [115] 115,82 unequal: No Solution No 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: 82:[8, 80, 8], Operations: ['24/3=8'] Exploring Operation: 8-8=0, Resulting Numbers: [80, 0] Generated Node #0,0,0: 82:[80, 0] Operation: 8-8=0 Exploring Operation: 8+80=88, Resulting Numbers: [8, 88] Generated Node #0,0,1: 82:[8, 88] Operation: 8+80=88 Exploring Operation: 8/8=1, Resulting Numbers: [80, 1] Generated Node #0,0,2: 82:[80, 1] Operation: 8/8=1 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[80, 1], Operations: ['24/3=8', '8/8=1'] Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,82 unequal: No Solution Exploring Operation: 80*1=80, Resulting Numbers: [80] 80,82 unequal: No Solution Exploring Operation: 80/1=80, Resulting Numbers: [80] 80,82 unequal: No Solution No 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: 82:[80, 0], Operations: ['24/3=8', '8-8=0'] Exploring Operation: 80-0=80, Resulting Numbers: [80] 80,82 unequal: No Solution Exploring Operation: 80*0=0, Resulting Numbers: [0] 0,82 unequal: No Solution Exploring Operation: 80+0=80, Resulting Numbers: [80] 80,82 unequal: No Solution No 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: 82:[8, 88], Operations: ['24/3=8', '8+80=88'] Exploring Operation: 8+88=96, Resulting Numbers: [96] 96,82 unequal: No Solution Exploring Operation: 88-8=80, Resulting Numbers: [80] 80,82 unequal: No Solution Exploring Operation: 88/8=11, Resulting Numbers: [11] 11,82 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
[ 36, 75, 18, 31 ]
62
[ "36+75=111", "18+31=49", "111-49=62" ]
Current State: 62:[36, 75, 18, 31], Operations: [] Exploring Operation: 36+75=111, Resulting Numbers: [18, 31, 111] Generated Node #2: [18, 31, 111] from Operation: 36+75=111 Current State: 62:[18, 31, 111], Operations: ['36+75=111'] Exploring Operation: 18+31=49, Resulting Numbers: [111, 49] Generated Node #3: [111, 49] from Operation: 18+31=49 Current State: 62:[111, 49], Operations: ['36+75=111', '18+31=49'] Exploring Operation: 111-49=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[36, 75, 18, 31], Operations: [] Exploring Operation: 75-18=57, Resulting Numbers: [36, 31, 57] Generated Node #0,0: 62:[36, 31, 57] Operation: 75-18=57 Exploring Operation: 75-36=39, Resulting Numbers: [18, 31, 39] Generated Node #0,1: 62:[18, 31, 39] Operation: 75-36=39 Exploring Operation: 36/18=2, Resulting Numbers: [75, 31, 2] Generated Node #0,2: 62:[75, 31, 2] Operation: 36/18=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[36, 31, 57], Operations: ['75-18=57'] Exploring Operation: 57-36=21, Resulting Numbers: [31, 21] Generated Node #0,0,0: 62:[31, 21] Operation: 57-36=21 Exploring Operation: 36+31=67, Resulting Numbers: [57, 67] Generated Node #0,0,1: 62:[57, 67] Operation: 36+31=67 Exploring Operation: 36-31=5, Resulting Numbers: [57, 5] Generated Node #0,0,2: 62:[57, 5] Operation: 36-31=5 Moving to Node #0,0,2 Current State: 62:[57, 5], Operations: ['75-18=57', '36-31=5'] Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,62 unequal: No Solution Exploring Operation: 57+5=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[36, 75, 18, 31], Operations: [] Exploring Operation: 75-18=57, Resulting Numbers: [36, 31, 57] Generated Node #0,0: 62:[36, 31, 57] Operation: 75-18=57 Moving to Node #0,0 Current State: 62:[36, 31, 57], Operations: ['75-18=57'] Exploring Operation: 36-31=5, Resulting Numbers: [57, 5] Generated Node #0,0,2: 62:[57, 5] Operation: 36-31=5 Moving to Node #0,0,2 Current State: 62:[57, 5], Operations: ['75-18=57', '36-31=5'] Exploring Operation: 57+5=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 25, 12, 8, 80 ]
31
[ "80-8=72", "72/12=6", "25+6=31" ]
Current State: 31:[25, 12, 8, 80], Operations: [] Exploring Operation: 80-8=72, Resulting Numbers: [25, 12, 72] Generated Node #2: [25, 12, 72] from Operation: 80-8=72 Current State: 31:[25, 12, 72], Operations: ['80-8=72'] Exploring Operation: 72/12=6, Resulting Numbers: [25, 6] Generated Node #3: [25, 6] from Operation: 72/12=6 Current State: 31:[25, 6], Operations: ['80-8=72', '72/12=6'] Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[25, 12, 8, 80], Operations: [] Exploring Operation: 80-25=55, Resulting Numbers: [12, 8, 55] Generated Node #0,0: 31:[12, 8, 55] Operation: 80-25=55 Exploring Operation: 12+8=20, Resulting Numbers: [25, 80, 20] Generated Node #0,1: 31:[25, 80, 20] Operation: 12+8=20 Exploring Operation: 80/8=10, Resulting Numbers: [25, 12, 10] Generated Node #0,2: 31:[25, 12, 10] Operation: 80/8=10 Exploring Operation: 80-12=68, Resulting Numbers: [25, 8, 68] Generated Node #0,3: 31:[25, 8, 68] Operation: 80-12=68 Moving to Node #0,2 Current State: 31:[25, 12, 10], Operations: ['80/8=10'] Exploring Operation: 25+12=37, Resulting Numbers: [10, 37] Generated Node #0,2,0: 31:[10, 37] Operation: 25+12=37 Exploring Operation: 25+10=35, Resulting Numbers: [12, 35] Generated Node #0,2,1: 31:[12, 35] Operation: 25+10=35 Exploring Operation: 12+10=22, Resulting Numbers: [25, 22] Generated Node #0,2,2: 31:[25, 22] Operation: 12+10=22 Exploring Operation: 25-10=15, Resulting Numbers: [12, 15] Generated Node #0,2,3: 31:[12, 15] Operation: 25-10=15 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 31:[25, 22], Operations: ['80/8=10', '12+10=22'] Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,31 unequal: No Solution Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 25*22=550, Resulting Numbers: [550] 550,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 31:[12, 35], Operations: ['80/8=10', '25+10=35'] Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,31 unequal: No Solution Exploring Operation: 12+35=47, Resulting Numbers: [47] 47,31 unequal: No Solution Exploring Operation: 12*35=420, Resulting Numbers: [420] 420,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[10, 37], Operations: ['80/8=10', '25+12=37'] Exploring Operation: 10*37=370, Resulting Numbers: [370] 370,31 unequal: No Solution Exploring Operation: 37-10=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 10+37=47, Resulting Numbers: [47] 47,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 31:[12, 15], Operations: ['80/8=10', '25-10=15'] Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,31 unequal: No Solution Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,31 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: 31:[25, 80, 20], Operations: ['12+8=20'] Exploring Operation: 25+20=45, Resulting Numbers: [80, 45] Generated Node #0,1,0: 31:[80, 45] Operation: 25+20=45 Exploring Operation: 80/20=4, Resulting Numbers: [25, 4] Generated Node #0,1,1: 31:[25, 4] Operation: 80/20=4 Exploring Operation: 80-25=55, Resulting Numbers: [20, 55] Generated Node #0,1,2: 31:[20, 55] Operation: 80-25=55 Exploring Operation: 80-20=60, Resulting Numbers: [25, 60] Generated Node #0,1,3: 31:[25, 60] Operation: 80-20=60 Moving to Node #0,0 Current State: 31:[12, 8, 55], Operations: ['80-25=55'] Exploring Operation: 55-12=43, Resulting Numbers: [8, 43] Generated Node #0,0,0: 31:[8, 43] Operation: 55-12=43 Exploring Operation: 55-8=47, Resulting Numbers: [12, 47] Generated Node #0,0,1: 31:[12, 47] Operation: 55-8=47 Exploring Operation: 12+8=20, Resulting Numbers: [55, 20] Generated Node #0,0,2: 31:[55, 20] Operation: 12+8=20 Exploring Operation: 12-8=4, Resulting Numbers: [55, 4] Generated Node #0,0,3: 31:[55, 4] Operation: 12-8=4 Moving to Node #0,3 Current State: 31:[25, 8, 68], Operations: ['80-12=68'] Exploring Operation: 25-8=17, Resulting Numbers: [68, 17] Generated Node #0,3,0: 31:[68, 17] Operation: 25-8=17 Exploring Operation: 68-8=60, Resulting Numbers: [25, 60] Generated Node #0,3,1: 31:[25, 60] Operation: 68-8=60 Exploring Operation: 25+8=33, Resulting Numbers: [68, 33] Generated Node #0,3,2: 31:[68, 33] Operation: 25+8=33 Exploring Operation: 68-25=43, Resulting Numbers: [8, 43] Generated Node #0,3,3: 31:[8, 43] Operation: 68-25=43 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 31:[25, 60], Operations: ['80-12=68', '68-8=60'] Exploring Operation: 25+60=85, Resulting Numbers: [85] 85,31 unequal: No Solution Exploring Operation: 25*60=1500, Resulting Numbers: [1500] 1500,31 unequal: No Solution Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 31:[8, 43], Operations: ['80-12=68', '68-25=43'] Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,31 unequal: No Solution Exploring Operation: 8*43=344, Resulting Numbers: [344] 344,31 unequal: No Solution Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 31:[68, 33], Operations: ['80-12=68', '25+8=33'] Exploring Operation: 68-33=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 68*33=2244, Resulting Numbers: [2244] 2244,31 unequal: No Solution Exploring Operation: 68+33=101, Resulting Numbers: [101] 101,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 31:[68, 17], Operations: ['80-12=68', '25-8=17'] Exploring Operation: 68-17=51, Resulting Numbers: [51] 51,31 unequal: No Solution Exploring Operation: 68*17=1156, Resulting Numbers: [1156] 1156,31 unequal: No Solution Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 68+17=85, Resulting Numbers: [85] 85,31 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: 31:[25, 4], Operations: ['12+8=20', '80/20=4'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,31 unequal: No Solution Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,31 unequal: No Solution Moving to Node #0,1,3 Current State: 31:[25, 60], Operations: ['12+8=20', '80-20=60'] Exploring Operation: 25*60=1500, Resulting Numbers: [1500] 1500,31 unequal: No Solution Exploring Operation: 25+60=85, Resulting Numbers: [85] 85,31 unequal: No Solution Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[55, 20], Operations: ['80-25=55', '12+8=20'] Exploring Operation: 55*20=1100, Resulting Numbers: [1100] 1100,31 unequal: No Solution Exploring Operation: 55+20=75, Resulting Numbers: [75] 75,31 unequal: No Solution Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[12, 47], Operations: ['80-25=55', '55-8=47'] Exploring Operation: 12*47=564, Resulting Numbers: [564] 564,31 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 12+47=59, Resulting Numbers: [59] 59,31 unequal: No Solution Moving to Node #0,1,2 Current State: 31:[20, 55], Operations: ['12+8=20', '80-25=55'] Exploring Operation: 20*55=1100, Resulting Numbers: [1100] 1100,31 unequal: No Solution Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 20+55=75, Resulting Numbers: [75] 75,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[8, 43], Operations: ['80-25=55', '55-12=43'] Exploring Operation: 8*43=344, Resulting Numbers: [344] 344,31 unequal: No Solution Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[55, 4], Operations: ['80-25=55', '12-8=4'] Exploring Operation: 55+4=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,31 unequal: No Solution Exploring Operation: 55*4=220, Resulting Numbers: [220] 220,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[80, 45], Operations: ['12+8=20', '25+20=45'] Exploring Operation: 80+45=125, Resulting Numbers: [125] 125,31 unequal: No Solution Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 80*45=3600, Resulting Numbers: [3600] 3600,31 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 18, 1, 45, 89 ]
27
[ "18-1=17", "89-45=44", "44-17=27" ]
Current State: 27:[18, 1, 45, 89], Operations: [] Exploring Operation: 18-1=17, Resulting Numbers: [45, 89, 17] Generated Node #2: [45, 89, 17] from Operation: 18-1=17 Current State: 27:[45, 89, 17], Operations: ['18-1=17'] Exploring Operation: 89-45=44, Resulting Numbers: [17, 44] Generated Node #3: [17, 44] from Operation: 89-45=44 Current State: 27:[17, 44], Operations: ['18-1=17', '89-45=44'] Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[18, 1, 45, 89], Operations: [] Exploring Operation: 89-18=71, Resulting Numbers: [1, 45, 71] Generated Node #0,0: 27:[1, 45, 71] Operation: 89-18=71 Exploring Operation: 45-18=27, Resulting Numbers: [1, 89, 27] Generated Node #0,1: 27:[1, 89, 27] Operation: 45-18=27 Exploring Operation: 89-45=44, Resulting Numbers: [18, 1, 44] Generated Node #0,2: 27:[18, 1, 44] Operation: 89-45=44 Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[18, 1, 44], Operations: ['89-45=44'] Exploring Operation: 18-1=17, Resulting Numbers: [44, 17] Generated Node #0,2,0: 27:[44, 17] Operation: 18-1=17 Exploring Operation: 18+1=19, Resulting Numbers: [44, 19] Generated Node #0,2,1: 27:[44, 19] Operation: 18+1=19 Exploring Operation: 44-18=26, Resulting Numbers: [1, 26] Generated Node #0,2,2: 27:[1, 26] Operation: 44-18=26 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 27:[1, 26], Operations: ['89-45=44', '44-18=26'] Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,27 unequal: No Solution Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[18, 1, 45, 89], Operations: [] Exploring Operation: 89-45=44, Resulting Numbers: [18, 1, 44] Generated Node #0,2: 27:[18, 1, 44] Operation: 89-45=44 Moving to Node #0,2 Current State: 27:[18, 1, 44], Operations: ['89-45=44'] Exploring Operation: 44-18=26, Resulting Numbers: [1, 26] Generated Node #0,2,2: 27:[1, 26] Operation: 44-18=26 Moving to Node #0,2,2 Current State: 27:[1, 26], Operations: ['89-45=44', '44-18=26'] Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 13, 63, 6, 62 ]
65
[ "63-6=57", "62-57=5", "13*5=65" ]
Current State: 65:[13, 63, 6, 62], Operations: [] Exploring Operation: 63-6=57, Resulting Numbers: [13, 62, 57] Generated Node #2: [13, 62, 57] from Operation: 63-6=57 Current State: 65:[13, 62, 57], Operations: ['63-6=57'] Exploring Operation: 62-57=5, Resulting Numbers: [13, 5] Generated Node #3: [13, 5] from Operation: 62-57=5 Current State: 65:[13, 5], Operations: ['63-6=57', '62-57=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[13, 63, 6, 62], Operations: [] Exploring Operation: 63+6=69, Resulting Numbers: [13, 62, 69] Generated Node #0,0: 65:[13, 62, 69] Operation: 63+6=69 Exploring Operation: 13-6=7, Resulting Numbers: [63, 62, 7] Generated Node #0,1: 65:[63, 62, 7] Operation: 13-6=7 Exploring Operation: 6+62=68, Resulting Numbers: [13, 63, 68] Generated Node #0,2: 65:[13, 63, 68] Operation: 6+62=68 Exploring Operation: 63-62=1, Resulting Numbers: [13, 6, 1] Generated Node #0,3: 65:[13, 6, 1] Operation: 63-62=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[13, 63, 68], Operations: ['6+62=68'] Exploring Operation: 68-13=55, Resulting Numbers: [63, 55] Generated Node #0,2,0: 65:[63, 55] Operation: 68-13=55 Exploring Operation: 63-13=50, Resulting Numbers: [68, 50] Generated Node #0,2,1: 65:[68, 50] Operation: 63-13=50 Exploring Operation: 13+63=76, Resulting Numbers: [68, 76] Generated Node #0,2,2: 65:[68, 76] Operation: 13+63=76 Exploring Operation: 68-63=5, Resulting Numbers: [13, 5] Generated Node #0,2,3: 65:[13, 5] Operation: 68-63=5 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 65:[13, 5], Operations: ['6+62=68', '68-63=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[13, 63, 6, 62], Operations: [] Exploring Operation: 6+62=68, Resulting Numbers: [13, 63, 68] Generated Node #0,2: 65:[13, 63, 68] Operation: 6+62=68 Moving to Node #0,2 Current State: 65:[13, 63, 68], Operations: ['6+62=68'] Exploring Operation: 68-63=5, Resulting Numbers: [13, 5] Generated Node #0,2,3: 65:[13, 5] Operation: 68-63=5 Moving to Node #0,2,3 Current State: 65:[13, 5], Operations: ['6+62=68', '68-63=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 70, 64, 13, 27 ]
34
[ "70-64=6", "13+27=40", "40-6=34" ]
Current State: 34:[70, 64, 13, 27], Operations: [] Exploring Operation: 70-64=6, Resulting Numbers: [13, 27, 6] Generated Node #2: [13, 27, 6] from Operation: 70-64=6 Current State: 34:[13, 27, 6], Operations: ['70-64=6'] Exploring Operation: 13+27=40, Resulting Numbers: [6, 40] Generated Node #3: [6, 40] from Operation: 13+27=40 Current State: 34:[6, 40], Operations: ['70-64=6', '13+27=40'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[70, 64, 13, 27], Operations: [] Exploring Operation: 64-27=37, Resulting Numbers: [70, 13, 37] Generated Node #0,0: 34:[70, 13, 37] Operation: 64-27=37 Exploring Operation: 70-64=6, Resulting Numbers: [13, 27, 6] Generated Node #0,1: 34:[13, 27, 6] Operation: 70-64=6 Exploring Operation: 70-27=43, Resulting Numbers: [64, 13, 43] Generated Node #0,2: 34:[64, 13, 43] Operation: 70-27=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[13, 27, 6], Operations: ['70-64=6'] Exploring Operation: 27-6=21, Resulting Numbers: [13, 21] Generated Node #0,1,0: 34:[13, 21] Operation: 27-6=21 Exploring Operation: 27+6=33, Resulting Numbers: [13, 33] Generated Node #0,1,1: 34:[13, 33] Operation: 27+6=33 Exploring Operation: 27-13=14, Resulting Numbers: [6, 14] Generated Node #0,1,2: 34:[6, 14] Operation: 27-13=14 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 34:[13, 33], Operations: ['70-64=6', '27+6=33'] Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,34 unequal: No Solution Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,34 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,34 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:[6, 14], Operations: ['70-64=6', '27-13=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,34 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,34 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 #0,1,0 Current State: 34:[13, 21], Operations: ['70-64=6', '27-6=21'] Exploring Operation: 13*21=273, Resulting Numbers: [273] 273,34 unequal: No Solution Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,34 unequal: No Solution Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[70, 64, 13, 27], Operations: [] Exploring Operation: 70-64=6, Resulting Numbers: [13, 27, 6] Generated Node #0,1: 34:[13, 27, 6] Operation: 70-64=6 Moving to Node #0,1 Current State: 34:[13, 27, 6], Operations: ['70-64=6'] Exploring Operation: 27-6=21, Resulting Numbers: [13, 21] Generated Node #0,1,0: 34:[13, 21] Operation: 27-6=21 Moving to Node #0,1,0 Current State: 34:[13, 21], Operations: ['70-64=6', '27-6=21'] Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 29, 67, 36, 25 ]
35
[ "29+67=96", "36+25=61", "96-61=35" ]
Current State: 35:[29, 67, 36, 25], Operations: [] Exploring Operation: 29+67=96, Resulting Numbers: [36, 25, 96] Generated Node #2: [36, 25, 96] from Operation: 29+67=96 Current State: 35:[36, 25, 96], Operations: ['29+67=96'] Exploring Operation: 36+25=61, Resulting Numbers: [96, 61] Generated Node #3: [96, 61] from Operation: 36+25=61 Current State: 35:[96, 61], Operations: ['29+67=96', '36+25=61'] Exploring Operation: 96-61=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[29, 67, 36, 25], Operations: [] Exploring Operation: 67-29=38, Resulting Numbers: [36, 25, 38] Generated Node #0,0: 35:[36, 25, 38] Operation: 67-29=38 Exploring Operation: 29-25=4, Resulting Numbers: [67, 36, 4] Generated Node #0,1: 35:[67, 36, 4] Operation: 29-25=4 Exploring Operation: 67-25=42, Resulting Numbers: [29, 36, 42] Generated Node #0,2: 35:[29, 36, 42] Operation: 67-25=42 Exploring Operation: 67-36=31, Resulting Numbers: [29, 25, 31] Generated Node #0,3: 35:[29, 25, 31] Operation: 67-36=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[36, 25, 38], Operations: ['67-29=38'] Exploring Operation: 36-25=11, Resulting Numbers: [38, 11] Generated Node #0,0,0: 35:[38, 11] Operation: 36-25=11 Exploring Operation: 36+25=61, Resulting Numbers: [38, 61] Generated Node #0,0,1: 35:[38, 61] Operation: 36+25=61 Exploring Operation: 38-25=13, Resulting Numbers: [36, 13] Generated Node #0,0,2: 35:[36, 13] Operation: 38-25=13 Exploring Operation: 38-36=2, Resulting Numbers: [25, 2] Generated Node #0,0,3: 35:[25, 2] Operation: 38-36=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[38, 11], Operations: ['67-29=38', '36-25=11'] Exploring Operation: 38+11=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 38*11=418, Resulting Numbers: [418] 418,35 unequal: No Solution Exploring Operation: 38-11=27, Resulting Numbers: [27] 27,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 35:[36, 13], Operations: ['67-29=38', '38-25=13'] Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,35 unequal: No Solution Exploring Operation: 36*13=468, Resulting Numbers: [468] 468,35 unequal: No Solution Exploring Operation: 36+13=49, Resulting Numbers: [49] 49,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 35:[25, 2], Operations: ['67-29=38', '38-36=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,35 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 35:[38, 61], Operations: ['67-29=38', '36+25=61'] Exploring Operation: 38+61=99, Resulting Numbers: [99] 99,35 unequal: No Solution Exploring Operation: 61-38=23, Resulting Numbers: [23] 23,35 unequal: No Solution Exploring Operation: 38*61=2318, Resulting Numbers: [2318] 2318,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[29, 36, 42], Operations: ['67-25=42'] Exploring Operation: 36-29=7, Resulting Numbers: [42, 7] Generated Node #0,2,0: 35:[42, 7] Operation: 36-29=7 Exploring Operation: 42-36=6, Resulting Numbers: [29, 6] Generated Node #0,2,1: 35:[29, 6] Operation: 42-36=6 Exploring Operation: 29+36=65, Resulting Numbers: [42, 65] Generated Node #0,2,2: 35:[42, 65] Operation: 29+36=65 Exploring Operation: 42-29=13, Resulting Numbers: [36, 13] Generated Node #0,2,3: 35:[36, 13] Operation: 42-29=13 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 35:[42, 7], Operations: ['67-25=42', '36-29=7'] Exploring Operation: 42*7=294, Resulting Numbers: [294] 294,35 unequal: No Solution Exploring Operation: 42+7=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[29, 67, 36, 25], Operations: [] Exploring Operation: 67-25=42, Resulting Numbers: [29, 36, 42] Generated Node #0,2: 35:[29, 36, 42] Operation: 67-25=42 Moving to Node #0,2 Current State: 35:[29, 36, 42], Operations: ['67-25=42'] Exploring Operation: 36-29=7, Resulting Numbers: [42, 7] Generated Node #0,2,0: 35:[42, 7] Operation: 36-29=7 Moving to Node #0,2,0 Current State: 35:[42, 7], Operations: ['67-25=42', '36-29=7'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 48, 85, 51, 99 ]
11
[ "85-48=37", "99-51=48", "48-37=11" ]
Current State: 11:[48, 85, 51, 99], Operations: [] Exploring Operation: 85-48=37, Resulting Numbers: [51, 99, 37] Generated Node #2: [51, 99, 37] from Operation: 85-48=37 Current State: 11:[51, 99, 37], Operations: ['85-48=37'] Exploring Operation: 99-51=48, Resulting Numbers: [37, 48] Generated Node #3: [37, 48] from Operation: 99-51=48 Current State: 11:[37, 48], Operations: ['85-48=37', '99-51=48'] Exploring Operation: 48-37=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[48, 85, 51, 99], Operations: [] Exploring Operation: 99-85=14, Resulting Numbers: [48, 51, 14] Generated Node #0,0: 11:[48, 51, 14] Operation: 99-85=14 Exploring Operation: 85-48=37, Resulting Numbers: [51, 99, 37] Generated Node #0,1: 11:[51, 99, 37] Operation: 85-48=37 Exploring Operation: 85-51=34, Resulting Numbers: [48, 99, 34] Generated Node #0,2: 11:[48, 99, 34] Operation: 85-51=34 Exploring Operation: 99-51=48, Resulting Numbers: [48, 85, 48] Generated Node #0,3: 11:[48, 85, 48] Operation: 99-51=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[48, 51, 14], Operations: ['99-85=14'] Exploring Operation: 51-48=3, Resulting Numbers: [14, 3] Generated Node #0,0,0: 11:[14, 3] Operation: 51-48=3 Exploring Operation: 51-14=37, Resulting Numbers: [48, 37] Generated Node #0,0,1: 11:[48, 37] Operation: 51-14=37 Exploring Operation: 48+51=99, Resulting Numbers: [14, 99] Generated Node #0,0,2: 11:[14, 99] Operation: 48+51=99 Exploring Operation: 48-14=34, Resulting Numbers: [51, 34] Generated Node #0,0,3: 11:[51, 34] Operation: 48-14=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[14, 3], Operations: ['99-85=14', '51-48=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,11 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[48, 85, 51, 99], Operations: [] Exploring Operation: 99-85=14, Resulting Numbers: [48, 51, 14] Generated Node #0,0: 11:[48, 51, 14] Operation: 99-85=14 Moving to Node #0,0 Current State: 11:[48, 51, 14], Operations: ['99-85=14'] Exploring Operation: 51-48=3, Resulting Numbers: [14, 3] Generated Node #0,0,0: 11:[14, 3] Operation: 51-48=3 Moving to Node #0,0,0 Current State: 11:[14, 3], Operations: ['99-85=14', '51-48=3'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 17, 14, 89, 8 ]
65
[ "17-14=3", "8*3=24", "89-24=65" ]
Current State: 65:[17, 14, 89, 8], Operations: [] Exploring Operation: 17-14=3, Resulting Numbers: [89, 8, 3] Generated Node #2: [89, 8, 3] from Operation: 17-14=3 Current State: 65:[89, 8, 3], Operations: ['17-14=3'] Exploring Operation: 8*3=24, Resulting Numbers: [89, 24] Generated Node #3: [89, 24] from Operation: 8*3=24 Current State: 65:[89, 24], Operations: ['17-14=3', '8*3=24'] Exploring Operation: 89-24=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[17, 14, 89, 8], Operations: [] Exploring Operation: 89-14=75, Resulting Numbers: [17, 8, 75] Generated Node #0,0: 65:[17, 8, 75] Operation: 89-14=75 Exploring Operation: 89-8=81, Resulting Numbers: [17, 14, 81] Generated Node #0,1: 65:[17, 14, 81] Operation: 89-8=81 Exploring Operation: 89-17=72, Resulting Numbers: [14, 8, 72] Generated Node #0,2: 65:[14, 8, 72] Operation: 89-17=72 Moving to Node #0,2 Current State: 65:[14, 8, 72], Operations: ['89-17=72'] Exploring Operation: 14-8=6, Resulting Numbers: [72, 6] Generated Node #0,2,0: 65:[72, 6] Operation: 14-8=6 Exploring Operation: 72/8=9, Resulting Numbers: [14, 9] Generated Node #0,2,1: 65:[14, 9] Operation: 72/8=9 Exploring Operation: 72-8=64, Resulting Numbers: [14, 64] Generated Node #0,2,2: 65:[14, 64] Operation: 72-8=64 Moving to Node #0,0 Current State: 65:[17, 8, 75], Operations: ['89-14=75'] Exploring Operation: 75-17=58, Resulting Numbers: [8, 58] Generated Node #0,0,0: 65:[8, 58] Operation: 75-17=58 Exploring Operation: 75-8=67, Resulting Numbers: [17, 67] Generated Node #0,0,1: 65:[17, 67] Operation: 75-8=67 Exploring Operation: 17-8=9, Resulting Numbers: [75, 9] Generated Node #0,0,2: 65:[75, 9] Operation: 17-8=9 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 65:[17, 67], Operations: ['89-14=75', '75-8=67'] Exploring Operation: 17+67=84, Resulting Numbers: [84] 84,65 unequal: No Solution Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,65 unequal: No Solution Exploring Operation: 17*67=1139, Resulting Numbers: [1139] 1139,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[8, 58], Operations: ['89-14=75', '75-17=58'] Exploring Operation: 8*58=464, Resulting Numbers: [464] 464,65 unequal: No Solution Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,65 unequal: No Solution Exploring Operation: 8+58=66, Resulting Numbers: [66] 66,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 65:[75, 9], Operations: ['89-14=75', '17-8=9'] Exploring Operation: 75+9=84, Resulting Numbers: [84] 84,65 unequal: No Solution Exploring Operation: 75-9=66, Resulting Numbers: [66] 66,65 unequal: No Solution Exploring Operation: 75*9=675, Resulting Numbers: [675] 675,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 65:[17, 14, 81], Operations: ['89-8=81'] Exploring Operation: 17-14=3, Resulting Numbers: [81, 3] Generated Node #0,1,0: 65:[81, 3] Operation: 17-14=3 Exploring Operation: 81-17=64, Resulting Numbers: [14, 64] Generated Node #0,1,1: 65:[14, 64] Operation: 81-17=64 Exploring Operation: 81-14=67, Resulting Numbers: [17, 67] Generated Node #0,1,2: 65:[17, 67] Operation: 81-14=67 Moving to Node #0,2,2 Current State: 65:[14, 64], Operations: ['89-17=72', '72-8=64'] Exploring Operation: 14+64=78, Resulting Numbers: [78] 78,65 unequal: No Solution Exploring Operation: 64-14=50, Resulting Numbers: [50] 50,65 unequal: No Solution Exploring Operation: 14*64=896, Resulting Numbers: [896] 896,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[14, 64], Operations: ['89-8=81', '81-17=64'] Exploring Operation: 14*64=896, Resulting Numbers: [896] 896,65 unequal: No Solution Exploring Operation: 64-14=50, Resulting Numbers: [50] 50,65 unequal: No Solution Exploring Operation: 14+64=78, Resulting Numbers: [78] 78,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[14, 9], Operations: ['89-17=72', '72/8=9'] Exploring Operation: 14*9=126, Resulting Numbers: [126] 126,65 unequal: No Solution Exploring Operation: 14+9=23, Resulting Numbers: [23] 23,65 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,65 unequal: No Solution Moving to Node #0,1,2 Current State: 65:[17, 67], Operations: ['89-8=81', '81-14=67'] Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,65 unequal: No Solution Exploring Operation: 17*67=1139, Resulting Numbers: [1139] 1139,65 unequal: No Solution Exploring Operation: 17+67=84, Resulting Numbers: [84] 84,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[72, 6], Operations: ['89-17=72', '14-8=6'] Exploring Operation: 72-6=66, Resulting Numbers: [66] 66,65 unequal: No Solution Exploring Operation: 72+6=78, Resulting Numbers: [78] 78,65 unequal: No Solution Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,65 unequal: No Solution Moving to Node #0,1,0 Current State: 65:[81, 3], Operations: ['89-8=81', '17-14=3'] Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,65 unequal: No Solution Exploring Operation: 81+3=84, Resulting Numbers: [84] 84,65 unequal: No Solution Exploring Operation: 81/3=27, Resulting Numbers: [27] 27,65 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 59, 28, 98, 77 ]
81
[ "28*77=2156", "2156/98=22", "59+22=81" ]
Current State: 81:[59, 28, 98, 77], Operations: [] Exploring Operation: 28*77=2156, Resulting Numbers: [59, 98, 2156] Generated Node #2: [59, 98, 2156] from Operation: 28*77=2156 Current State: 81:[59, 98, 2156], Operations: ['28*77=2156'] Exploring Operation: 2156/98=22, Resulting Numbers: [59, 22] Generated Node #3: [59, 22] from Operation: 2156/98=22 Current State: 81:[59, 22], Operations: ['28*77=2156', '2156/98=22'] Exploring Operation: 59+22=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[59, 28, 98, 77], Operations: [] Exploring Operation: 98-59=39, Resulting Numbers: [28, 77, 39] Generated Node #0,0: 81:[28, 77, 39] Operation: 98-59=39 Exploring Operation: 59+28=87, Resulting Numbers: [98, 77, 87] Generated Node #0,1: 81:[98, 77, 87] Operation: 59+28=87 Exploring Operation: 59-28=31, Resulting Numbers: [98, 77, 31] Generated Node #0,2: 81:[98, 77, 31] Operation: 59-28=31 Moving to Node #0,0 Current State: 81:[28, 77, 39], Operations: ['98-59=39'] Exploring Operation: 28+39=67, Resulting Numbers: [77, 67] Generated Node #0,0,0: 81:[77, 67] Operation: 28+39=67 Exploring Operation: 77-39=38, Resulting Numbers: [28, 38] Generated Node #0,0,1: 81:[28, 38] Operation: 77-39=38 Exploring Operation: 39-28=11, Resulting Numbers: [77, 11] Generated Node #0,0,2: 81:[77, 11] Operation: 39-28=11 Moving to Node #0,2 Current State: 81:[98, 77, 31], Operations: ['59-28=31'] Exploring Operation: 98-77=21, Resulting Numbers: [31, 21] Generated Node #0,2,0: 81:[31, 21] Operation: 98-77=21 Exploring Operation: 77-31=46, Resulting Numbers: [98, 46] Generated Node #0,2,1: 81:[98, 46] Operation: 77-31=46 Exploring Operation: 98-31=67, Resulting Numbers: [77, 67] Generated Node #0,2,2: 81:[77, 67] Operation: 98-31=67 Moving to Node #0,1 Current State: 81:[98, 77, 87], Operations: ['59+28=87'] Exploring Operation: 87-77=10, Resulting Numbers: [98, 10] Generated Node #0,1,0: 81:[98, 10] Operation: 87-77=10 Exploring Operation: 98-77=21, Resulting Numbers: [87, 21] Generated Node #0,1,1: 81:[87, 21] Operation: 98-77=21 Exploring Operation: 98-87=11, Resulting Numbers: [77, 11] Generated Node #0,1,2: 81:[77, 11] Operation: 98-87=11 Moving to Node #0,0,2 Current State: 81:[77, 11], Operations: ['98-59=39', '39-28=11'] Exploring Operation: 77-11=66, Resulting Numbers: [66] 66,81 unequal: No Solution Exploring Operation: 77/11=7, Resulting Numbers: [7] 7,81 unequal: No Solution Exploring Operation: 77+11=88, Resulting Numbers: [88] 88,81 unequal: No Solution Moving to Node #0,1,2 Current State: 81:[77, 11], Operations: ['59+28=87', '98-87=11'] Exploring Operation: 77+11=88, Resulting Numbers: [88] 88,81 unequal: No Solution Exploring Operation: 77-11=66, Resulting Numbers: [66] 66,81 unequal: No Solution Exploring Operation: 77/11=7, Resulting Numbers: [7] 7,81 unequal: No Solution Moving to Node #0,2,0 Current State: 81:[31, 21], Operations: ['59-28=31', '98-77=21'] Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,81 unequal: No Solution Exploring Operation: 31*21=651, Resulting Numbers: [651] 651,81 unequal: No Solution Exploring Operation: 31+21=52, Resulting Numbers: [52] 52,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[28, 38], Operations: ['98-59=39', '77-39=38'] Exploring Operation: 38-28=10, Resulting Numbers: [10] 10,81 unequal: No Solution Exploring Operation: 28*38=1064, Resulting Numbers: [1064] 1064,81 unequal: No Solution Exploring Operation: 28+38=66, Resulting Numbers: [66] 66,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[87, 21], Operations: ['59+28=87', '98-77=21'] Exploring Operation: 87-21=66, Resulting Numbers: [66] 66,81 unequal: No Solution Exploring Operation: 87*21=1827, Resulting Numbers: [1827] 1827,81 unequal: No Solution Exploring Operation: 87+21=108, Resulting Numbers: [108] 108,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[77, 67], Operations: ['98-59=39', '28+39=67'] Exploring Operation: 77+67=144, Resulting Numbers: [144] 144,81 unequal: No Solution Exploring Operation: 77*67=5159, Resulting Numbers: [5159] 5159,81 unequal: No Solution Exploring Operation: 77-67=10, Resulting Numbers: [10] 10,81 unequal: No Solution Moving to Node #0,2,2 Current State: 81:[77, 67], Operations: ['59-28=31', '98-31=67'] Exploring Operation: 77-67=10, Resulting Numbers: [10] 10,81 unequal: No Solution Exploring Operation: 77*67=5159, Resulting Numbers: [5159] 5159,81 unequal: No Solution Exploring Operation: 77+67=144, Resulting Numbers: [144] 144,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[98, 10], Operations: ['59+28=87', '87-77=10'] Exploring Operation: 98-10=88, Resulting Numbers: [88] 88,81 unequal: No Solution Exploring Operation: 98+10=108, Resulting Numbers: [108] 108,81 unequal: No Solution Exploring Operation: 98*10=980, Resulting Numbers: [980] 980,81 unequal: No Solution Moving to Node #0,2,1 Current State: 81:[98, 46], Operations: ['59-28=31', '77-31=46'] Exploring Operation: 98*46=4508, Resulting Numbers: [4508] 4508,81 unequal: No Solution Exploring Operation: 98+46=144, Resulting Numbers: [144] 144,81 unequal: No Solution Exploring Operation: 98-46=52, Resulting Numbers: [52] 52,81 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 91, 24, 77, 8 ]
45
[ "91+77=168", "168/8=21", "24+21=45" ]
Current State: 45:[91, 24, 77, 8], Operations: [] Exploring Operation: 91+77=168, Resulting Numbers: [24, 8, 168] Generated Node #2: [24, 8, 168] from Operation: 91+77=168 Current State: 45:[24, 8, 168], Operations: ['91+77=168'] Exploring Operation: 168/8=21, Resulting Numbers: [24, 21] Generated Node #3: [24, 21] from Operation: 168/8=21 Current State: 45:[24, 21], Operations: ['91+77=168', '168/8=21'] Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[91, 24, 77, 8], Operations: [] Exploring Operation: 91-24=67, Resulting Numbers: [77, 8, 67] Generated Node #0,0: 45:[77, 8, 67] Operation: 91-24=67 Exploring Operation: 91-77=14, Resulting Numbers: [24, 8, 14] Generated Node #0,1: 45:[24, 8, 14] Operation: 91-77=14 Moving to Node #0,1 Current State: 45:[24, 8, 14], Operations: ['91-77=14'] Exploring Operation: 24-8=16, Resulting Numbers: [14, 16] Generated Node #0,1,0: 45:[14, 16] Operation: 24-8=16 Exploring Operation: 24/8=3, Resulting Numbers: [14, 3] Generated Node #0,1,1: 45:[14, 3] Operation: 24/8=3 Moving to Node #0,0 Current State: 45:[77, 8, 67], Operations: ['91-24=67'] Exploring Operation: 77-67=10, Resulting Numbers: [8, 10] Generated Node #0,0,0: 45:[8, 10] Operation: 77-67=10 Exploring Operation: 77-8=69, Resulting Numbers: [67, 69] Generated Node #0,0,1: 45:[67, 69] Operation: 77-8=69 Moving to Node #0,1,1 Current State: 45:[14, 3], Operations: ['91-77=14', '24/8=3'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,45 unequal: No Solution Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[8, 10], Operations: ['91-24=67', '77-67=10'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[14, 16], Operations: ['91-77=14', '24-8=16'] Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[67, 69], Operations: ['91-24=67', '77-8=69'] Exploring Operation: 67+69=136, Resulting Numbers: [136] 136,45 unequal: No Solution Exploring Operation: 69-67=2, Resulting Numbers: [2] 2,45 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 30, 22, 81, 68 ]
78
[ "22+68=90", "90/30=3", "81-3=78" ]
Current State: 78:[30, 22, 81, 68], Operations: [] Exploring Operation: 22+68=90, Resulting Numbers: [30, 81, 90] Generated Node #2: [30, 81, 90] from Operation: 22+68=90 Current State: 78:[30, 81, 90], Operations: ['22+68=90'] Exploring Operation: 90/30=3, Resulting Numbers: [81, 3] Generated Node #3: [81, 3] from Operation: 90/30=3 Current State: 78:[81, 3], Operations: ['22+68=90', '90/30=3'] Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[30, 22, 81, 68], Operations: [] Exploring Operation: 68-30=38, Resulting Numbers: [22, 81, 38] Generated Node #0,0: 78:[22, 81, 38] Operation: 68-30=38 Moving to Node #0,0 Current State: 78:[22, 81, 38], Operations: ['68-30=38'] Exploring Operation: 38-22=16, Resulting Numbers: [81, 16] Generated Node #0,0,0: 78:[81, 16] Operation: 38-22=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[81, 16], Operations: ['68-30=38', '38-22=16'] Exploring Operation: 81-16=65, Resulting Numbers: [65] 65,78 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
[ 4, 82, 25, 81 ]
20
[ "4+82=86", "25+81=106", "106-86=20" ]
Current State: 20:[4, 82, 25, 81], Operations: [] Exploring Operation: 4+82=86, Resulting Numbers: [25, 81, 86] Generated Node #2: [25, 81, 86] from Operation: 4+82=86 Current State: 20:[25, 81, 86], Operations: ['4+82=86'] Exploring Operation: 25+81=106, Resulting Numbers: [86, 106] Generated Node #3: [86, 106] from Operation: 25+81=106 Current State: 20:[86, 106], Operations: ['4+82=86', '25+81=106'] Exploring Operation: 106-86=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[4, 82, 25, 81], Operations: [] Exploring Operation: 82-81=1, Resulting Numbers: [4, 25, 1] Generated Node #0,0: 20:[4, 25, 1] Operation: 82-81=1 Exploring Operation: 82-25=57, Resulting Numbers: [4, 81, 57] Generated Node #0,1: 20:[4, 81, 57] Operation: 82-25=57 Exploring Operation: 82-4=78, Resulting Numbers: [25, 81, 78] Generated Node #0,2: 20:[25, 81, 78] Operation: 82-4=78 Exploring Operation: 25-4=21, Resulting Numbers: [82, 81, 21] Generated Node #0,3: 20:[82, 81, 21] Operation: 25-4=21 Exploring Operation: 81-25=56, Resulting Numbers: [4, 82, 56] Generated Node #0,4: 20:[4, 82, 56] Operation: 81-25=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[4, 25, 1], Operations: ['82-81=1'] Exploring Operation: 4+1=5, Resulting Numbers: [25, 5] Generated Node #0,0,0: 20:[25, 5] Operation: 4+1=5 Exploring Operation: 4/1=4, Resulting Numbers: [25, 4] Generated Node #0,0,1: 20:[25, 4] Operation: 4/1=4 Exploring Operation: 25-1=24, Resulting Numbers: [4, 24] Generated Node #0,0,2: 20:[4, 24] Operation: 25-1=24 Exploring Operation: 4*1=4, Resulting Numbers: [25, 4] Generated Node #0,0,3: 20:[25, 4] Operation: 4*1=4 Exploring Operation: 25-4=21, Resulting Numbers: [1, 21] Generated Node #0,0,4: 20:[1, 21] Operation: 25-4=21 Moving to Node #0,0,4 Current State: 20:[1, 21], Operations: ['82-81=1', '25-4=21'] Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,20 unequal: No Solution Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[4, 82, 25, 81], Operations: [] Exploring Operation: 82-81=1, Resulting Numbers: [4, 25, 1] Generated Node #0,0: 20:[4, 25, 1] Operation: 82-81=1 Moving to Node #0,0 Current State: 20:[4, 25, 1], Operations: ['82-81=1'] Exploring Operation: 25-4=21, Resulting Numbers: [1, 21] Generated Node #0,0,4: 20:[1, 21] Operation: 25-4=21 Moving to Node #0,0,4 Current State: 20:[1, 21], Operations: ['82-81=1', '25-4=21'] Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 3, 29, 29, 6 ]
52
[ "3*29=87", "29+6=35", "87-35=52" ]
Current State: 52:[3, 29, 29, 6], Operations: [] Exploring Operation: 3*29=87, Resulting Numbers: [6, 87] Generated Node #2: [6, 87] from Operation: 3*29=87 Current State: 52:[6, 87], Operations: ['3*29=87'] Exploring Operation: 29+6=35, Resulting Numbers: [87, 35] Generated Node #3: [87, 35] from Operation: 29+6=35 Current State: 52:[87, 35], Operations: ['3*29=87', '29+6=35'] Exploring Operation: 87-35=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[3, 29, 29, 6], Operations: [] Exploring Operation: 29-3=26, Resulting Numbers: [29, 6, 26] Generated Node #0,0: 52:[29, 6, 26] Operation: 29-3=26 Exploring Operation: 29-3=26, Resulting Numbers: [29, 6, 26] Generated Node #0,1: 52:[29, 6, 26] Operation: 29-3=26 Exploring Operation: 29/29=1, Resulting Numbers: [3, 6, 1] Generated Node #0,2: 52:[3, 6, 1] Operation: 29/29=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[3, 6, 1], Operations: ['29/29=1'] Exploring Operation: 6/3=2, Resulting Numbers: [1, 2] Generated Node #0,2,0: 52:[1, 2] Operation: 6/3=2 Exploring Operation: 6-3=3, Resulting Numbers: [1, 3] Generated Node #0,2,1: 52:[1, 3] Operation: 6-3=3 Exploring Operation: 3+1=4, Resulting Numbers: [6, 4] Generated Node #0,2,2: 52:[6, 4] Operation: 3+1=4 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 52:[1, 2], Operations: ['29/29=1', '6/3=2'] Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,52 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,52 unequal: No Solution No 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: 52:[1, 3], Operations: ['29/29=1', '6-3=3'] Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,52 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,52 unequal: No Solution No 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: 52:[6, 4], Operations: ['29/29=1', '3+1=4'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,52 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: 52:[29, 6, 26], Operations: ['29-3=26'] Exploring Operation: 29-6=23, Resulting Numbers: [26, 23] Generated Node #0,0,0: 52:[26, 23] Operation: 29-6=23 Exploring Operation: 29+26=55, Resulting Numbers: [6, 55] Generated Node #0,0,1: 52:[6, 55] Operation: 29+26=55 Exploring Operation: 29-26=3, Resulting Numbers: [6, 3] Generated Node #0,0,2: 52:[6, 3] Operation: 29-26=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[26, 23], Operations: ['29-3=26', '29-6=23'] Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,52 unequal: No Solution Exploring Operation: 26+23=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 26*23=598, Resulting Numbers: [598] 598,52 unequal: No Solution No 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: 52:[6, 3], Operations: ['29-3=26', '29-26=3'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,52 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,52 unequal: No Solution No 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: 52:[6, 55], Operations: ['29-3=26', '29+26=55'] Exploring Operation: 6*55=330, Resulting Numbers: [330] 330,52 unequal: No Solution Exploring Operation: 55-6=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 6+55=61, Resulting Numbers: [61] 61,52 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: 52:[29, 6, 26], Operations: ['29-3=26'] Exploring Operation: 29-6=23, Resulting Numbers: [26, 23] Generated Node #0,1,0: 52:[26, 23] Operation: 29-6=23 Exploring Operation: 29+26=55, Resulting Numbers: [6, 55] Generated Node #0,1,1: 52:[6, 55] Operation: 29+26=55 Exploring Operation: 29-26=3, Resulting Numbers: [6, 3] Generated Node #0,1,2: 52:[6, 3] Operation: 29-26=3 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[26, 23], Operations: ['29-3=26', '29-6=23'] Exploring Operation: 26+23=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 26*23=598, Resulting Numbers: [598] 598,52 unequal: No Solution Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,52 unequal: No Solution No 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: 52:[6, 3], Operations: ['29-3=26', '29-26=3'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,52 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,52 unequal: No Solution No 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: 52:[6, 55], Operations: ['29-3=26', '29+26=55'] Exploring Operation: 55-6=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 6+55=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 6*55=330, Resulting Numbers: [330] 330,52 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
[ 37, 49, 2, 69 ]
75
[ "49-37=12", "12/2=6", "69+6=75" ]
Current State: 75:[37, 49, 2, 69], Operations: [] Exploring Operation: 49-37=12, Resulting Numbers: [2, 69, 12] Generated Node #2: [2, 69, 12] from Operation: 49-37=12 Current State: 75:[2, 69, 12], Operations: ['49-37=12'] Exploring Operation: 12/2=6, Resulting Numbers: [69, 6] Generated Node #3: [69, 6] from Operation: 12/2=6 Current State: 75:[69, 6], Operations: ['49-37=12', '12/2=6'] Exploring Operation: 69+6=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[37, 49, 2, 69], Operations: [] Exploring Operation: 49-37=12, Resulting Numbers: [2, 69, 12] Generated Node #0,0: 75:[2, 69, 12] Operation: 49-37=12 Exploring Operation: 37+49=86, Resulting Numbers: [2, 69, 86] Generated Node #0,1: 75:[2, 69, 86] Operation: 37+49=86 Moving to Node #0,0 Current State: 75:[2, 69, 12], Operations: ['49-37=12'] Exploring Operation: 2+69=71, Resulting Numbers: [12, 71] Generated Node #0,0,0: 75:[12, 71] Operation: 2+69=71 Exploring Operation: 2+12=14, Resulting Numbers: [69, 14] Generated Node #0,0,1: 75:[69, 14] Operation: 2+12=14 Moving to Node #0,1 Current State: 75:[2, 69, 86], Operations: ['37+49=86'] Exploring Operation: 2+69=71, Resulting Numbers: [86, 71] Generated Node #0,1,0: 75:[86, 71] Operation: 2+69=71 Exploring Operation: 86-69=17, Resulting Numbers: [2, 17] Generated Node #0,1,1: 75:[2, 17] Operation: 86-69=17 Moving to Node #0,1,1 Current State: 75:[2, 17], Operations: ['37+49=86', '86-69=17'] Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[12, 71], Operations: ['49-37=12', '2+69=71'] Exploring Operation: 12+71=83, Resulting Numbers: [83] 83,75 unequal: No Solution Exploring Operation: 71-12=59, Resulting Numbers: [59] 59,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[69, 14], Operations: ['49-37=12', '2+12=14'] Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,75 unequal: No Solution Exploring Operation: 69+14=83, Resulting Numbers: [83] 83,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[86, 71], Operations: ['37+49=86', '2+69=71'] Exploring Operation: 86-71=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 86+71=157, Resulting Numbers: [157] 157,75 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 72, 13, 72, 90 ]
90
[ "72-72=0", "13*0=0", "90+0=90" ]
Current State: 90:[72, 13, 72, 90], Operations: [] Exploring Operation: 72-72=0, Resulting Numbers: [13, 90, 0] Generated Node #2: [13, 90, 0] from Operation: 72-72=0 Current State: 90:[13, 90, 0], Operations: ['72-72=0'] Exploring Operation: 13*0=0, Resulting Numbers: [90, 0] Generated Node #3: [90, 0] from Operation: 13*0=0 Current State: 90:[90, 0], Operations: ['72-72=0', '13*0=0'] Exploring Operation: 90+0=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[72, 13, 72, 90], Operations: [] Exploring Operation: 72-72=0, Resulting Numbers: [13, 90, 0] Generated Node #0,0: 90:[13, 90, 0] Operation: 72-72=0 Exploring Operation: 90-72=18, Resulting Numbers: [13, 72, 18] Generated Node #0,1: 90:[13, 72, 18] Operation: 90-72=18 Exploring Operation: 90-72=18, Resulting Numbers: [72, 13, 18] Generated Node #0,2: 90:[72, 13, 18] Operation: 90-72=18 Exploring Operation: 72/72=1, Resulting Numbers: [13, 90, 1] Generated Node #0,3: 90:[13, 90, 1] Operation: 72/72=1 Exploring Operation: 72+13=85, Resulting Numbers: [72, 90, 85] Generated Node #0,4: 90:[72, 90, 85] Operation: 72+13=85 Moving to Node #0,3 Current State: 90:[13, 90, 1], Operations: ['72/72=1'] Exploring Operation: 13/1=13, Resulting Numbers: [90, 13] Generated Node #0,3,0: 90:[90, 13] Operation: 13/1=13 Exploring Operation: 90*1=90, Resulting Numbers: [13, 90] Generated Node #0,3,1: 90:[13, 90] Operation: 90*1=90 Exploring Operation: 13+1=14, Resulting Numbers: [90, 14] Generated Node #0,3,2: 90:[90, 14] Operation: 13+1=14 Exploring Operation: 13*1=13, Resulting Numbers: [90, 13] Generated Node #0,3,3: 90:[90, 13] Operation: 13*1=13 Exploring Operation: 13-1=12, Resulting Numbers: [90, 12] Generated Node #0,3,4: 90:[90, 12] Operation: 13-1=12 Moving to Node #0,0 Current State: 90:[13, 90, 0], Operations: ['72-72=0'] Exploring Operation: 13+0=13, Resulting Numbers: [90, 13] Generated Node #0,0,0: 90:[90, 13] Operation: 13+0=13 Exploring Operation: 90-0=90, Resulting Numbers: [13, 90] Generated Node #0,0,1: 90:[13, 90] Operation: 90-0=90 Exploring Operation: 13*0=0, Resulting Numbers: [90, 0] Generated Node #0,0,2: 90:[90, 0] Operation: 13*0=0 Exploring Operation: 90+0=90, Resulting Numbers: [13, 90] Generated Node #0,0,3: 90:[13, 90] Operation: 90+0=90 Exploring Operation: 13-0=13, Resulting Numbers: [90, 13] Generated Node #0,0,4: 90:[90, 13] Operation: 13-0=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[90, 13], Operations: ['72-72=0', '13+0=13'] Exploring Operation: 90*13=1170, Resulting Numbers: [1170] 1170,90 unequal: No Solution Exploring Operation: 90+13=103, Resulting Numbers: [103] 103,90 unequal: No Solution Exploring Operation: 90-13=77, Resulting Numbers: [77] 77,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[13, 90], Operations: ['72-72=0', '90-0=90'] Exploring Operation: 90-13=77, Resulting Numbers: [77] 77,90 unequal: No Solution Exploring Operation: 13+90=103, Resulting Numbers: [103] 103,90 unequal: No Solution Exploring Operation: 13*90=1170, Resulting Numbers: [1170] 1170,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[90, 0], Operations: ['72-72=0', '13*0=0'] Exploring Operation: 90+0=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[72, 13, 72, 90], Operations: [] Exploring Operation: 72-72=0, Resulting Numbers: [13, 90, 0] Generated Node #0,0: 90:[13, 90, 0] Operation: 72-72=0 Moving to Node #0,0 Current State: 90:[13, 90, 0], Operations: ['72-72=0'] Exploring Operation: 13*0=0, Resulting Numbers: [90, 0] Generated Node #0,0,2: 90:[90, 0] Operation: 13*0=0 Moving to Node #0,0,2 Current State: 90:[90, 0], Operations: ['72-72=0', '13*0=0'] Exploring Operation: 90+0=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
mult_heuristic
[ 56, 92, 84, 98 ]
42
[ "92-56=36", "98*36=3528", "3528/84=42" ]
Current State: 42:[56, 92, 84, 98], Operations: [] Exploring Operation: 92-56=36, Resulting Numbers: [84, 98, 36] Generated Node #2: [84, 98, 36] from Operation: 92-56=36 Current State: 42:[84, 98, 36], Operations: ['92-56=36'] Exploring Operation: 98*36=3528, Resulting Numbers: [84, 3528] Generated Node #3: [84, 3528] from Operation: 98*36=3528 Current State: 42:[84, 3528], Operations: ['92-56=36', '98*36=3528'] Exploring Operation: 3528/84=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[56, 92, 84, 98], Operations: [] Exploring Operation: 98-84=14, Resulting Numbers: [56, 92, 14] Generated Node #0,0: 42:[56, 92, 14] Operation: 98-84=14 Exploring Operation: 98-92=6, Resulting Numbers: [56, 84, 6] Generated Node #0,1: 42:[56, 84, 6] Operation: 98-92=6 Exploring Operation: 92-84=8, Resulting Numbers: [56, 98, 8] Generated Node #0,2: 42:[56, 98, 8] Operation: 92-84=8 Exploring Operation: 98-56=42, Resulting Numbers: [92, 84, 42] Generated Node #0,3: 42:[92, 84, 42] Operation: 98-56=42 Moving to Node #0,1 Current State: 42:[56, 84, 6], Operations: ['98-92=6'] Exploring Operation: 56-6=50, Resulting Numbers: [84, 50] Generated Node #0,1,0: 42:[84, 50] Operation: 56-6=50 Exploring Operation: 84/6=14, Resulting Numbers: [56, 14] Generated Node #0,1,1: 42:[56, 14] Operation: 84/6=14 Exploring Operation: 84-56=28, Resulting Numbers: [6, 28] Generated Node #0,1,2: 42:[6, 28] Operation: 84-56=28 Exploring Operation: 84-6=78, Resulting Numbers: [56, 78] Generated Node #0,1,3: 42:[56, 78] Operation: 84-6=78 Moving to Node #0,0 Current State: 42:[56, 92, 14], Operations: ['98-84=14'] Exploring Operation: 92-14=78, Resulting Numbers: [56, 78] Generated Node #0,0,0: 42:[56, 78] Operation: 92-14=78 Exploring Operation: 56/14=4, Resulting Numbers: [92, 4] Generated Node #0,0,1: 42:[92, 4] Operation: 56/14=4 Exploring Operation: 92-56=36, Resulting Numbers: [14, 36] Generated Node #0,0,2: 42:[14, 36] Operation: 92-56=36 Exploring Operation: 56-14=42, Resulting Numbers: [92, 42] Generated Node #0,0,3: 42:[92, 42] Operation: 56-14=42 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 42:[14, 36], Operations: ['98-84=14', '92-56=36'] Exploring Operation: 14+36=50, Resulting Numbers: [50] 50,42 unequal: No Solution Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 14*36=504, Resulting Numbers: [504] 504,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[56, 78], Operations: ['98-84=14', '92-14=78'] Exploring Operation: 78-56=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 56+78=134, Resulting Numbers: [134] 134,42 unequal: No Solution Exploring Operation: 56*78=4368, Resulting Numbers: [4368] 4368,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 42:[92, 42], Operations: ['98-84=14', '56-14=42'] Exploring Operation: 92-42=50, Resulting Numbers: [50] 50,42 unequal: No Solution Exploring Operation: 92+42=134, Resulting Numbers: [134] 134,42 unequal: No Solution Exploring Operation: 92*42=3864, Resulting Numbers: [3864] 3864,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 42:[92, 4], Operations: ['98-84=14', '56/14=4'] Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,42 unequal: No Solution Exploring Operation: 92*4=368, Resulting Numbers: [368] 368,42 unequal: No Solution Exploring Operation: 92/4=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 92+4=96, Resulting Numbers: [96] 96,42 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: 42:[56, 98, 8], Operations: ['92-84=8'] Exploring Operation: 98-56=42, Resulting Numbers: [8, 42] Generated Node #0,2,0: 42:[8, 42] Operation: 98-56=42 Exploring Operation: 56/8=7, Resulting Numbers: [98, 7] Generated Node #0,2,1: 42:[98, 7] Operation: 56/8=7 Exploring Operation: 98-8=90, Resulting Numbers: [56, 90] Generated Node #0,2,2: 42:[56, 90] Operation: 98-8=90 Exploring Operation: 56-8=48, Resulting Numbers: [98, 48] Generated Node #0,2,3: 42:[98, 48] Operation: 56-8=48 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 42:[8, 42], Operations: ['92-84=8', '98-56=42'] Exploring Operation: 8+42=50, Resulting Numbers: [50] 50,42 unequal: No Solution Exploring Operation: 8*42=336, Resulting Numbers: [336] 336,42 unequal: No Solution Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 42:[98, 7], Operations: ['92-84=8', '56/8=7'] Exploring Operation: 98/7=14, Resulting Numbers: [14] 14,42 unequal: No Solution Exploring Operation: 98-7=91, Resulting Numbers: [91] 91,42 unequal: No Solution Exploring Operation: 98*7=686, Resulting Numbers: [686] 686,42 unequal: No Solution Exploring Operation: 98+7=105, Resulting Numbers: [105] 105,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 42:[56, 90], Operations: ['92-84=8', '98-8=90'] Exploring Operation: 90-56=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 56*90=5040, Resulting Numbers: [5040] 5040,42 unequal: No Solution Exploring Operation: 56+90=146, Resulting Numbers: [146] 146,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 42:[98, 48], Operations: ['92-84=8', '56-8=48'] Exploring Operation: 98-48=50, Resulting Numbers: [50] 50,42 unequal: No Solution Exploring Operation: 98*48=4704, Resulting Numbers: [4704] 4704,42 unequal: No Solution Exploring Operation: 98+48=146, Resulting Numbers: [146] 146,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 42:[92, 84, 42], Operations: ['98-56=42'] Exploring Operation: 84/42=2, Resulting Numbers: [92, 2] Generated Node #0,3,0: 42:[92, 2] Operation: 84/42=2 Exploring Operation: 92-42=50, Resulting Numbers: [84, 50] Generated Node #0,3,1: 42:[84, 50] Operation: 92-42=50 Exploring Operation: 84-42=42, Resulting Numbers: [92, 42] Generated Node #0,3,2: 42:[92, 42] Operation: 84-42=42 Exploring Operation: 92-84=8, Resulting Numbers: [42, 8] Generated Node #0,3,3: 42:[42, 8] Operation: 92-84=8 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 42:[42, 8], Operations: ['98-56=42', '92-84=8'] Exploring Operation: 42*8=336, Resulting Numbers: [336] 336,42 unequal: No Solution Exploring Operation: 42+8=50, Resulting Numbers: [50] 50,42 unequal: No Solution Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 42:[92, 2], Operations: ['98-56=42', '84/42=2'] Exploring Operation: 92+2=94, Resulting Numbers: [94] 94,42 unequal: No Solution Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,42 unequal: No Solution Exploring Operation: 92*2=184, Resulting Numbers: [184] 184,42 unequal: No Solution Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 42:[84, 50], Operations: ['98-56=42', '92-42=50'] Exploring Operation: 84+50=134, Resulting Numbers: [134] 134,42 unequal: No Solution Exploring Operation: 84-50=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 84*50=4200, Resulting Numbers: [4200] 4200,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 42:[92, 42], Operations: ['98-56=42', '84-42=42'] Exploring Operation: 92*42=3864, Resulting Numbers: [3864] 3864,42 unequal: No Solution Exploring Operation: 92+42=134, Resulting Numbers: [134] 134,42 unequal: No Solution Exploring Operation: 92-42=50, Resulting Numbers: [50] 50,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 42:[6, 28], Operations: ['98-92=6', '84-56=28'] Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 6+28=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 6*28=168, Resulting Numbers: [168] 168,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[56, 14], Operations: ['98-92=6', '84/6=14'] Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[56, 92, 84, 98], Operations: [] Exploring Operation: 98-92=6, Resulting Numbers: [56, 84, 6] Generated Node #0,1: 42:[56, 84, 6] Operation: 98-92=6 Moving to Node #0,1 Current State: 42:[56, 84, 6], Operations: ['98-92=6'] Exploring Operation: 84/6=14, Resulting Numbers: [56, 14] Generated Node #0,1,1: 42:[56, 14] Operation: 84/6=14 Moving to Node #0,1,1 Current State: 42:[56, 14], Operations: ['98-92=6', '84/6=14'] Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
0.94184
hs_4
sum_heuristic
[ 61, 25, 55, 65 ]
85
[ "61-55=6", "25*6=150", "150-65=85" ]
Current State: 85:[61, 25, 55, 65], Operations: [] Exploring Operation: 61-55=6, Resulting Numbers: [25, 65, 6] Generated Node #2: [25, 65, 6] from Operation: 61-55=6 Current State: 85:[25, 65, 6], Operations: ['61-55=6'] Exploring Operation: 25*6=150, Resulting Numbers: [65, 150] Generated Node #3: [65, 150] from Operation: 25*6=150 Current State: 85:[65, 150], Operations: ['61-55=6', '25*6=150'] Exploring Operation: 150-65=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[61, 25, 55, 65], Operations: [] Exploring Operation: 61-55=6, Resulting Numbers: [25, 65, 6] Generated Node #0,0: 85:[25, 65, 6] Operation: 61-55=6 Moving to Node #0,0 Current State: 85:[25, 65, 6], Operations: ['61-55=6'] Exploring Operation: 25+65=90, Resulting Numbers: [6, 90] Generated Node #0,0,0: 85:[6, 90] Operation: 25+65=90 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[6, 90], Operations: ['61-55=6', '25+65=90'] Exploring Operation: 90-6=84, Resulting Numbers: [84] 84,85 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
[ 58, 19, 35, 47 ]
27
[ "58-19=39", "47-35=12", "39-12=27" ]
Current State: 27:[58, 19, 35, 47], Operations: [] Exploring Operation: 58-19=39, Resulting Numbers: [35, 47, 39] Generated Node #2: [35, 47, 39] from Operation: 58-19=39 Current State: 27:[35, 47, 39], Operations: ['58-19=39'] Exploring Operation: 47-35=12, Resulting Numbers: [39, 12] Generated Node #3: [39, 12] from Operation: 47-35=12 Current State: 27:[39, 12], Operations: ['58-19=39', '47-35=12'] Exploring Operation: 39-12=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[58, 19, 35, 47], Operations: [] Exploring Operation: 58-47=11, Resulting Numbers: [19, 35, 11] Generated Node #0,0: 27:[19, 35, 11] Operation: 58-47=11 Exploring Operation: 58-35=23, Resulting Numbers: [19, 47, 23] Generated Node #0,1: 27:[19, 47, 23] Operation: 58-35=23 Exploring Operation: 58-19=39, Resulting Numbers: [35, 47, 39] Generated Node #0,2: 27:[35, 47, 39] Operation: 58-19=39 Moving to Node #0,0 Current State: 27:[19, 35, 11], Operations: ['58-47=11'] Exploring Operation: 19-11=8, Resulting Numbers: [35, 8] Generated Node #0,0,0: 27:[35, 8] Operation: 19-11=8 Exploring Operation: 19+11=30, Resulting Numbers: [35, 30] Generated Node #0,0,1: 27:[35, 30] Operation: 19+11=30 Exploring Operation: 35-19=16, Resulting Numbers: [11, 16] Generated Node #0,0,2: 27:[11, 16] Operation: 35-19=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[35, 8], Operations: ['58-47=11', '19-11=8'] Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,27 unequal: No Solution Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,27 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[58, 19, 35, 47], Operations: [] Exploring Operation: 58-47=11, Resulting Numbers: [19, 35, 11] Generated Node #0,0: 27:[19, 35, 11] Operation: 58-47=11 Moving to Node #0,0 Current State: 27:[19, 35, 11], Operations: ['58-47=11'] Exploring Operation: 19-11=8, Resulting Numbers: [35, 8] Generated Node #0,0,0: 27:[35, 8] Operation: 19-11=8 Moving to Node #0,0,0 Current State: 27:[35, 8], Operations: ['58-47=11', '19-11=8'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 33, 57, 4, 42 ]
27
[ "57-42=15", "4*15=60", "60-33=27" ]
Current State: 27:[33, 57, 4, 42], Operations: [] Exploring Operation: 57-42=15, Resulting Numbers: [33, 4, 15] Generated Node #2: [33, 4, 15] from Operation: 57-42=15 Current State: 27:[33, 4, 15], Operations: ['57-42=15'] Exploring Operation: 4*15=60, Resulting Numbers: [33, 60] Generated Node #3: [33, 60] from Operation: 4*15=60 Current State: 27:[33, 60], Operations: ['57-42=15', '4*15=60'] Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[33, 57, 4, 42], Operations: [] Exploring Operation: 57-42=15, Resulting Numbers: [33, 4, 15] Generated Node #0,0: 27:[33, 4, 15] Operation: 57-42=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[33, 4, 15], Operations: ['57-42=15'] Exploring Operation: 33-4=29, Resulting Numbers: [15, 29] Generated Node #0,0,0: 27:[15, 29] Operation: 33-4=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[15, 29], Operations: ['57-42=15', '33-4=29'] Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,27 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
[ 22, 24, 64, 21 ]
34
[ "64*21=1344", "1344/24=56", "56-22=34" ]
Current State: 34:[22, 24, 64, 21], Operations: [] Exploring Operation: 64*21=1344, Resulting Numbers: [22, 24, 1344] Generated Node #2: [22, 24, 1344] from Operation: 64*21=1344 Current State: 34:[22, 24, 1344], Operations: ['64*21=1344'] Exploring Operation: 1344/24=56, Resulting Numbers: [22, 56] Generated Node #3: [22, 56] from Operation: 1344/24=56 Current State: 34:[22, 56], Operations: ['64*21=1344', '1344/24=56'] Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[22, 24, 64, 21], Operations: [] Exploring Operation: 64-22=42, Resulting Numbers: [24, 21, 42] Generated Node #0,0: 34:[24, 21, 42] Operation: 64-22=42 Exploring Operation: 64-24=40, Resulting Numbers: [22, 21, 40] Generated Node #0,1: 34:[22, 21, 40] Operation: 64-24=40 Exploring Operation: 64-21=43, Resulting Numbers: [22, 24, 43] Generated Node #0,2: 34:[22, 24, 43] Operation: 64-21=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[22, 21, 40], Operations: ['64-24=40'] Exploring Operation: 40-22=18, Resulting Numbers: [21, 18] Generated Node #0,1,0: 34:[21, 18] Operation: 40-22=18 Exploring Operation: 40-21=19, Resulting Numbers: [22, 19] Generated Node #0,1,1: 34:[22, 19] Operation: 40-21=19 Exploring Operation: 22-21=1, Resulting Numbers: [40, 1] Generated Node #0,1,2: 34:[40, 1] Operation: 22-21=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 34:[21, 18], Operations: ['64-24=40', '40-22=18'] Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,34 unequal: No Solution Exploring Operation: 21+18=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:[22, 19], Operations: ['64-24=40', '40-21=19'] Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,34 unequal: No Solution Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,34 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:[40, 1], Operations: ['64-24=40', '22-21=1'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,34 unequal: No Solution Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,34 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 #0,0 Current State: 34:[24, 21, 42], Operations: ['64-22=42'] Exploring Operation: 24-21=3, Resulting Numbers: [42, 3] Generated Node #0,0,0: 34:[42, 3] Operation: 24-21=3 Exploring Operation: 42/21=2, Resulting Numbers: [24, 2] Generated Node #0,0,1: 34:[24, 2] Operation: 42/21=2 Exploring Operation: 42-24=18, Resulting Numbers: [21, 18] Generated Node #0,0,2: 34:[21, 18] Operation: 42-24=18 Moving to Node #0,0,2 Current State: 34:[21, 18], Operations: ['64-22=42', '42-24=18'] Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,34 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 21+18=39, Resulting Numbers: [39] 39,34 unequal: No Solution Moving to Node #0,0,1 Current State: 34:[24, 2], Operations: ['64-22=42', '42/21=2'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,34 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,34 unequal: No Solution Moving to Node #0,0,0 Current State: 34:[42, 3], Operations: ['64-22=42', '24-21=3'] Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,34 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,34 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[22, 24, 43], Operations: ['64-21=43'] Exploring Operation: 43-22=21, Resulting Numbers: [24, 21] Generated Node #0,2,0: 34:[24, 21] Operation: 43-22=21 Exploring Operation: 43-24=19, Resulting Numbers: [22, 19] Generated Node #0,2,1: 34:[22, 19] Operation: 43-24=19 Exploring Operation: 24-22=2, Resulting Numbers: [43, 2] Generated Node #0,2,2: 34:[43, 2] Operation: 24-22=2 Moving to Node #0,2,1 Current State: 34:[22, 19], Operations: ['64-21=43', '43-24=19'] Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,34 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[43, 2], Operations: ['64-21=43', '24-22=2'] Exploring Operation: 43*2=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,34 unequal: No Solution Exploring Operation: 43+2=45, Resulting Numbers: [45] 45,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[24, 21], Operations: ['64-21=43', '43-22=21'] Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,34 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,34 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
[ 42, 9, 45, 35 ]
61
[ "42+9=51", "45-35=10", "51+10=61" ]
Current State: 61:[42, 9, 45, 35], Operations: [] Exploring Operation: 42+9=51, Resulting Numbers: [45, 35, 51] Generated Node #2: [45, 35, 51] from Operation: 42+9=51 Current State: 61:[45, 35, 51], Operations: ['42+9=51'] Exploring Operation: 45-35=10, Resulting Numbers: [51, 10] Generated Node #3: [51, 10] from Operation: 45-35=10 Current State: 61:[51, 10], Operations: ['42+9=51', '45-35=10'] Exploring Operation: 51+10=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[42, 9, 45, 35], Operations: [] Exploring Operation: 9+35=44, Resulting Numbers: [42, 45, 44] Generated Node #0,0: 61:[42, 45, 44] Operation: 9+35=44 Exploring Operation: 9+45=54, Resulting Numbers: [42, 35, 54] Generated Node #0,1: 61:[42, 35, 54] Operation: 9+45=54 Exploring Operation: 42+9=51, Resulting Numbers: [45, 35, 51] Generated Node #0,2: 61:[45, 35, 51] Operation: 42+9=51 Exploring Operation: 42-9=33, Resulting Numbers: [45, 35, 33] Generated Node #0,3: 61:[45, 35, 33] Operation: 42-9=33 Moving to Node #0,0 Current State: 61:[42, 45, 44], Operations: ['9+35=44'] Exploring Operation: 45+44=89, Resulting Numbers: [42, 89] Generated Node #0,0,0: 61:[42, 89] Operation: 45+44=89 Exploring Operation: 45-42=3, Resulting Numbers: [44, 3] Generated Node #0,0,1: 61:[44, 3] Operation: 45-42=3 Exploring Operation: 42+44=86, Resulting Numbers: [45, 86] Generated Node #0,0,2: 61:[45, 86] Operation: 42+44=86 Exploring Operation: 42+45=87, Resulting Numbers: [44, 87] Generated Node #0,0,3: 61:[44, 87] Operation: 42+45=87 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 61:[45, 86], Operations: ['9+35=44', '42+44=86'] Exploring Operation: 86-45=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 45*86=3870, Resulting Numbers: [3870] 3870,61 unequal: No Solution Exploring Operation: 45+86=131, Resulting Numbers: [131] 131,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 61:[44, 87], Operations: ['9+35=44', '42+45=87'] Exploring Operation: 44*87=3828, Resulting Numbers: [3828] 3828,61 unequal: No Solution Exploring Operation: 44+87=131, Resulting Numbers: [131] 131,61 unequal: No Solution Exploring Operation: 87-44=43, Resulting Numbers: [43] 43,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[42, 89], Operations: ['9+35=44', '45+44=89'] Exploring Operation: 89-42=47, Resulting Numbers: [47] 47,61 unequal: No Solution Exploring Operation: 42+89=131, Resulting Numbers: [131] 131,61 unequal: No Solution Exploring Operation: 42*89=3738, Resulting Numbers: [3738] 3738,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[44, 3], Operations: ['9+35=44', '45-42=3'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 44*3=132, Resulting Numbers: [132] 132,61 unequal: No Solution Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,61 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: 61:[45, 35, 51], Operations: ['42+9=51'] Exploring Operation: 45+51=96, Resulting Numbers: [35, 96] Generated Node #0,2,0: 61:[35, 96] Operation: 45+51=96 Exploring Operation: 45+35=80, Resulting Numbers: [51, 80] Generated Node #0,2,1: 61:[51, 80] Operation: 45+35=80 Exploring Operation: 45-35=10, Resulting Numbers: [51, 10] Generated Node #0,2,2: 61:[51, 10] Operation: 45-35=10 Exploring Operation: 35+51=86, Resulting Numbers: [45, 86] Generated Node #0,2,3: 61:[45, 86] Operation: 35+51=86 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 61:[51, 80], Operations: ['42+9=51', '45+35=80'] Exploring Operation: 51+80=131, Resulting Numbers: [131] 131,61 unequal: No Solution Exploring Operation: 80-51=29, Resulting Numbers: [29] 29,61 unequal: No Solution Exploring Operation: 51*80=4080, Resulting Numbers: [4080] 4080,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 61:[45, 86], Operations: ['42+9=51', '35+51=86'] Exploring Operation: 45+86=131, Resulting Numbers: [131] 131,61 unequal: No Solution Exploring Operation: 86-45=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 45*86=3870, Resulting Numbers: [3870] 3870,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[35, 96], Operations: ['42+9=51', '45+51=96'] Exploring Operation: 96-35=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[42, 9, 45, 35], Operations: [] Exploring Operation: 42+9=51, Resulting Numbers: [45, 35, 51] Generated Node #0,2: 61:[45, 35, 51] Operation: 42+9=51 Moving to Node #0,2 Current State: 61:[45, 35, 51], Operations: ['42+9=51'] Exploring Operation: 45+51=96, Resulting Numbers: [35, 96] Generated Node #0,2,0: 61:[35, 96] Operation: 45+51=96 Moving to Node #0,2,0 Current State: 61:[35, 96], Operations: ['42+9=51', '45+51=96'] Exploring Operation: 96-35=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_4
sum_heuristic
[ 57, 80, 56, 57 ]
23
[ "80-57=23", "57-56=1", "23*1=23" ]
Current State: 23:[57, 80, 56, 57], Operations: [] Exploring Operation: 80-57=23, Resulting Numbers: [56, 23] Generated Node #2: [56, 23] from Operation: 80-57=23 Current State: 23:[56, 23], Operations: ['80-57=23'] Exploring Operation: 57-56=1, Resulting Numbers: [23, 1] Generated Node #3: [23, 1] from Operation: 57-56=1 Current State: 23:[23, 1], Operations: ['80-57=23', '57-56=1'] Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[57, 80, 56, 57], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [57, 57, 24] Generated Node #0,0: 23:[57, 57, 24] Operation: 80-56=24 Exploring Operation: 80-57=23, Resulting Numbers: [56, 57, 23] Generated Node #0,1: 23:[56, 57, 23] Operation: 80-57=23 Exploring Operation: 80-57=23, Resulting Numbers: [57, 56, 23] Generated Node #0,2: 23:[57, 56, 23] Operation: 80-57=23 Exploring Operation: 57/57=1, Resulting Numbers: [80, 56, 1] Generated Node #0,3: 23:[80, 56, 1] Operation: 57/57=1 Moving to Node #0,1 Current State: 23:[56, 57, 23], Operations: ['80-57=23'] Exploring Operation: 57-56=1, Resulting Numbers: [23, 1] Generated Node #0,1,0: 23:[23, 1] Operation: 57-56=1 Exploring Operation: 56+57=113, Resulting Numbers: [23, 113] Generated Node #0,1,1: 23:[23, 113] Operation: 56+57=113 Exploring Operation: 57-23=34, Resulting Numbers: [56, 34] Generated Node #0,1,2: 23:[56, 34] Operation: 57-23=34 Exploring Operation: 56-23=33, Resulting Numbers: [57, 33] Generated Node #0,1,3: 23:[57, 33] Operation: 56-23=33 Moving to Node #0,2 Current State: 23:[57, 56, 23], Operations: ['80-57=23'] Exploring Operation: 57+56=113, Resulting Numbers: [23, 113] Generated Node #0,2,0: 23:[23, 113] Operation: 57+56=113 Exploring Operation: 56-23=33, Resulting Numbers: [57, 33] Generated Node #0,2,1: 23:[57, 33] Operation: 56-23=33 Exploring Operation: 57-23=34, Resulting Numbers: [56, 34] Generated Node #0,2,2: 23:[56, 34] Operation: 57-23=34 Exploring Operation: 57-56=1, Resulting Numbers: [23, 1] Generated Node #0,2,3: 23:[23, 1] Operation: 57-56=1 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 23:[23, 1], Operations: ['80-57=23', '57-56=1'] Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[57, 80, 56, 57], Operations: [] Exploring Operation: 80-57=23, Resulting Numbers: [57, 56, 23] Generated Node #0,2: 23:[57, 56, 23] Operation: 80-57=23 Moving to Node #0,2 Current State: 23:[57, 56, 23], Operations: ['80-57=23'] Exploring Operation: 57-56=1, Resulting Numbers: [23, 1] Generated Node #0,2,3: 23:[23, 1] Operation: 57-56=1 Moving to Node #0,2,3 Current State: 23:[23, 1], Operations: ['80-57=23', '57-56=1'] Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 98, 7, 38, 97 ]
73
[ "98/7=14", "97-38=59", "14+59=73" ]
Current State: 73:[98, 7, 38, 97], Operations: [] Exploring Operation: 98/7=14, Resulting Numbers: [38, 97, 14] Generated Node #2: [38, 97, 14] from Operation: 98/7=14 Current State: 73:[38, 97, 14], Operations: ['98/7=14'] Exploring Operation: 97-38=59, Resulting Numbers: [14, 59] Generated Node #3: [14, 59] from Operation: 97-38=59 Current State: 73:[14, 59], Operations: ['98/7=14', '97-38=59'] Exploring Operation: 14+59=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[98, 7, 38, 97], Operations: [] Exploring Operation: 98-7=91, Resulting Numbers: [38, 97, 91] Generated Node #0,0: 73:[38, 97, 91] Operation: 98-7=91 Exploring Operation: 97-7=90, Resulting Numbers: [98, 38, 90] Generated Node #0,1: 73:[98, 38, 90] Operation: 97-7=90 Exploring Operation: 7+38=45, Resulting Numbers: [98, 97, 45] Generated Node #0,2: 73:[98, 97, 45] Operation: 7+38=45 Exploring Operation: 98+7=105, Resulting Numbers: [38, 97, 105] Generated Node #0,3: 73:[38, 97, 105] Operation: 98+7=105 Moving to Node #0,0 Current State: 73:[38, 97, 91], Operations: ['98-7=91'] Exploring Operation: 38+97=135, Resulting Numbers: [91, 135] Generated Node #0,0,0: 73:[91, 135] Operation: 38+97=135 Exploring Operation: 97-38=59, Resulting Numbers: [91, 59] Generated Node #0,0,1: 73:[91, 59] Operation: 97-38=59 Exploring Operation: 91-38=53, Resulting Numbers: [97, 53] Generated Node #0,0,2: 73:[97, 53] Operation: 91-38=53 Exploring Operation: 38+91=129, Resulting Numbers: [97, 129] Generated Node #0,0,3: 73:[97, 129] Operation: 38+91=129 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[91, 59], Operations: ['98-7=91', '97-38=59'] Exploring Operation: 91+59=150, Resulting Numbers: [150] 150,73 unequal: No Solution Exploring Operation: 91-59=32, Resulting Numbers: [32] 32,73 unequal: No Solution Exploring Operation: 91*59=5369, Resulting Numbers: [5369] 5369,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 73:[97, 53], Operations: ['98-7=91', '91-38=53'] Exploring Operation: 97*53=5141, Resulting Numbers: [5141] 5141,73 unequal: No Solution Exploring Operation: 97+53=150, Resulting Numbers: [150] 150,73 unequal: No Solution Exploring Operation: 97-53=44, Resulting Numbers: [44] 44,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[91, 135], Operations: ['98-7=91', '38+97=135'] Exploring Operation: 91*135=12285, Resulting Numbers: [12285] 12285,73 unequal: No Solution Exploring Operation: 135-91=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 91+135=226, Resulting Numbers: [226] 226,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 73:[97, 129], Operations: ['98-7=91', '38+91=129'] Exploring Operation: 97*129=12513, Resulting Numbers: [12513] 12513,73 unequal: No Solution Exploring Operation: 97+129=226, Resulting Numbers: [226] 226,73 unequal: No Solution Exploring Operation: 129-97=32, Resulting Numbers: [32] 32,73 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: 73:[98, 97, 45], Operations: ['7+38=45'] Exploring Operation: 97+45=142, Resulting Numbers: [98, 142] Generated Node #0,2,0: 73:[98, 142] Operation: 97+45=142 Exploring Operation: 98+45=143, Resulting Numbers: [97, 143] Generated Node #0,2,1: 73:[97, 143] Operation: 98+45=143 Exploring Operation: 98-45=53, Resulting Numbers: [97, 53] Generated Node #0,2,2: 73:[97, 53] Operation: 98-45=53 Exploring Operation: 97-45=52, Resulting Numbers: [98, 52] Generated Node #0,2,3: 73:[98, 52] Operation: 97-45=52 Moving to Node #0,1 Current State: 73:[98, 38, 90], Operations: ['97-7=90'] Exploring Operation: 98-38=60, Resulting Numbers: [90, 60] Generated Node #0,1,0: 73:[90, 60] Operation: 98-38=60 Exploring Operation: 38+90=128, Resulting Numbers: [98, 128] Generated Node #0,1,1: 73:[98, 128] Operation: 38+90=128 Exploring Operation: 98+38=136, Resulting Numbers: [90, 136] Generated Node #0,1,2: 73:[90, 136] Operation: 98+38=136 Exploring Operation: 90-38=52, Resulting Numbers: [98, 52] Generated Node #0,1,3: 73:[98, 52] Operation: 90-38=52 Moving to Node #0,3 Current State: 73:[38, 97, 105], Operations: ['98+7=105'] Exploring Operation: 38+105=143, Resulting Numbers: [97, 143] Generated Node #0,3,0: 73:[97, 143] Operation: 38+105=143 Exploring Operation: 105-38=67, Resulting Numbers: [97, 67] Generated Node #0,3,1: 73:[97, 67] Operation: 105-38=67 Exploring Operation: 97-38=59, Resulting Numbers: [105, 59] Generated Node #0,3,2: 73:[105, 59] Operation: 97-38=59 Exploring Operation: 38+97=135, Resulting Numbers: [105, 135] Generated Node #0,3,3: 73:[105, 135] Operation: 38+97=135 Moving to Node #0,1,0 Current State: 73:[90, 60], Operations: ['97-7=90', '98-38=60'] Exploring Operation: 90+60=150, Resulting Numbers: [150] 150,73 unequal: No Solution Exploring Operation: 90*60=5400, Resulting Numbers: [5400] 5400,73 unequal: No Solution Exploring Operation: 90-60=30, Resulting Numbers: [30] 30,73 unequal: No Solution Moving to Node #0,3,1 Current State: 73:[97, 67], Operations: ['98+7=105', '105-38=67'] Exploring Operation: 97+67=164, Resulting Numbers: [164] 164,73 unequal: No Solution Exploring Operation: 97*67=6499, Resulting Numbers: [6499] 6499,73 unequal: No Solution Exploring Operation: 97-67=30, Resulting Numbers: [30] 30,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[97, 53], Operations: ['7+38=45', '98-45=53'] Exploring Operation: 97*53=5141, Resulting Numbers: [5141] 5141,73 unequal: No Solution Exploring Operation: 97-53=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 97+53=150, Resulting Numbers: [150] 150,73 unequal: No Solution Moving to Node #0,1,3 Current State: 73:[98, 52], Operations: ['97-7=90', '90-38=52'] Exploring Operation: 98-52=46, Resulting Numbers: [46] 46,73 unequal: No Solution Exploring Operation: 98*52=5096, Resulting Numbers: [5096] 5096,73 unequal: No Solution Exploring Operation: 98+52=150, Resulting Numbers: [150] 150,73 unequal: No Solution Moving to Node #0,2,3 Current State: 73:[98, 52], Operations: ['7+38=45', '97-45=52'] Exploring Operation: 98+52=150, Resulting Numbers: [150] 150,73 unequal: No Solution Exploring Operation: 98-52=46, Resulting Numbers: [46] 46,73 unequal: No Solution Exploring Operation: 98*52=5096, Resulting Numbers: [5096] 5096,73 unequal: No Solution Moving to Node #0,3,2 Current State: 73:[105, 59], Operations: ['98+7=105', '97-38=59'] Exploring Operation: 105*59=6195, Resulting Numbers: [6195] 6195,73 unequal: No Solution Exploring Operation: 105-59=46, Resulting Numbers: [46] 46,73 unequal: No Solution Exploring Operation: 105+59=164, Resulting Numbers: [164] 164,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[98, 128], Operations: ['97-7=90', '38+90=128'] Exploring Operation: 98+128=226, Resulting Numbers: [226] 226,73 unequal: No Solution Exploring Operation: 98*128=12544, Resulting Numbers: [12544] 12544,73 unequal: No Solution Exploring Operation: 128-98=30, Resulting Numbers: [30] 30,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[90, 136], Operations: ['97-7=90', '98+38=136'] Exploring Operation: 90+136=226, Resulting Numbers: [226] 226,73 unequal: No Solution Exploring Operation: 136-90=46, Resulting Numbers: [46] 46,73 unequal: No Solution Exploring Operation: 90*136=12240, Resulting Numbers: [12240] 12240,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[98, 142], Operations: ['7+38=45', '97+45=142'] Exploring Operation: 98+142=240, Resulting Numbers: [240] 240,73 unequal: No Solution Exploring Operation: 142-98=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 98*142=13916, Resulting Numbers: [13916] 13916,73 unequal: No Solution Moving to Node #0,3,0 Current State: 73:[97, 143], Operations: ['98+7=105', '38+105=143'] Exploring Operation: 97*143=13871, Resulting Numbers: [13871] 13871,73 unequal: No Solution Exploring Operation: 97+143=240, Resulting Numbers: [240] 240,73 unequal: No Solution Exploring Operation: 143-97=46, Resulting Numbers: [46] 46,73 unequal: No Solution Moving to Node #0,3,3 Current State: 73:[105, 135], Operations: ['98+7=105', '38+97=135'] Exploring Operation: 105*135=14175, Resulting Numbers: [14175] 14175,73 unequal: No Solution Exploring Operation: 135-105=30, Resulting Numbers: [30] 30,73 unequal: No Solution Exploring Operation: 105+135=240, Resulting Numbers: [240] 240,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[97, 143], Operations: ['7+38=45', '98+45=143'] Exploring Operation: 97*143=13871, Resulting Numbers: [13871] 13871,73 unequal: No Solution Exploring Operation: 143-97=46, Resulting Numbers: [46] 46,73 unequal: No Solution Exploring Operation: 97+143=240, Resulting Numbers: [240] 240,73 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 75, 3, 67, 72 ]
86
[ "75*3=225", "67+72=139", "225-139=86" ]
Current State: 86:[75, 3, 67, 72], Operations: [] Exploring Operation: 75*3=225, Resulting Numbers: [67, 72, 225] Generated Node #2: [67, 72, 225] from Operation: 75*3=225 Current State: 86:[67, 72, 225], Operations: ['75*3=225'] Exploring Operation: 67+72=139, Resulting Numbers: [225, 139] Generated Node #3: [225, 139] from Operation: 67+72=139 Current State: 86:[225, 139], Operations: ['75*3=225', '67+72=139'] Exploring Operation: 225-139=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[75, 3, 67, 72], Operations: [] Exploring Operation: 72-67=5, Resulting Numbers: [75, 3, 5] Generated Node #0,0: 86:[75, 3, 5] Operation: 72-67=5 Exploring Operation: 75-67=8, Resulting Numbers: [3, 72, 8] Generated Node #0,1: 86:[3, 72, 8] Operation: 75-67=8 Moving to Node #0,0 Current State: 86:[75, 3, 5], Operations: ['72-67=5'] Exploring Operation: 75+5=80, Resulting Numbers: [3, 80] Generated Node #0,0,0: 86:[3, 80] Operation: 75+5=80 Exploring Operation: 75+3=78, Resulting Numbers: [5, 78] Generated Node #0,0,1: 86:[5, 78] Operation: 75+3=78 Moving to Node #0,1 Current State: 86:[3, 72, 8], Operations: ['75-67=8'] Exploring Operation: 72/8=9, Resulting Numbers: [3, 9] Generated Node #0,1,0: 86:[3, 9] Operation: 72/8=9 Exploring Operation: 72+8=80, Resulting Numbers: [3, 80] Generated Node #0,1,1: 86:[3, 80] Operation: 72+8=80 Moving to Node #0,0,0 Current State: 86:[3, 80], Operations: ['72-67=5', '75+5=80'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,86 unequal: No Solution Exploring Operation: 3+80=83, Resulting Numbers: [83] 83,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[3, 80], Operations: ['75-67=8', '72+8=80'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,86 unequal: No Solution Exploring Operation: 3+80=83, Resulting Numbers: [83] 83,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[3, 9], Operations: ['75-67=8', '72/8=9'] Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,86 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[5, 78], Operations: ['72-67=5', '75+3=78'] Exploring Operation: 5+78=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 78-5=73, Resulting Numbers: [73] 73,86 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 59, 46, 17, 1 ]
87
[ "59+46=105", "17+1=18", "105-18=87" ]
Current State: 87:[59, 46, 17, 1], Operations: [] Exploring Operation: 59+46=105, Resulting Numbers: [17, 1, 105] Generated Node #2: [17, 1, 105] from Operation: 59+46=105 Current State: 87:[17, 1, 105], Operations: ['59+46=105'] Exploring Operation: 17+1=18, Resulting Numbers: [105, 18] Generated Node #3: [105, 18] from Operation: 17+1=18 Current State: 87:[105, 18], Operations: ['59+46=105', '17+1=18'] Exploring Operation: 105-18=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[59, 46, 17, 1], Operations: [] Exploring Operation: 59-46=13, Resulting Numbers: [17, 1, 13] Generated Node #0,0: 87:[17, 1, 13] Operation: 59-46=13 Moving to Node #0,0 Current State: 87:[17, 1, 13], Operations: ['59-46=13'] Exploring Operation: 17+13=30, Resulting Numbers: [1, 30] Generated Node #0,0,0: 87:[1, 30] Operation: 17+13=30 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[1, 30], Operations: ['59-46=13', '17+13=30'] Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 35, 11, 1, 17 ]
62
[ "35+11=46", "17-1=16", "46+16=62" ]
Current State: 62:[35, 11, 1, 17], Operations: [] Exploring Operation: 35+11=46, Resulting Numbers: [1, 17, 46] Generated Node #2: [1, 17, 46] from Operation: 35+11=46 Current State: 62:[1, 17, 46], Operations: ['35+11=46'] Exploring Operation: 17-1=16, Resulting Numbers: [46, 16] Generated Node #3: [46, 16] from Operation: 17-1=16 Current State: 62:[46, 16], Operations: ['35+11=46', '17-1=16'] Exploring Operation: 46+16=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[35, 11, 1, 17], Operations: [] Exploring Operation: 17-11=6, Resulting Numbers: [35, 1, 6] Generated Node #0,0: 62:[35, 1, 6] Operation: 17-11=6 Exploring Operation: 35+17=52, Resulting Numbers: [11, 1, 52] Generated Node #0,1: 62:[11, 1, 52] Operation: 35+17=52 Exploring Operation: 11+17=28, Resulting Numbers: [35, 1, 28] Generated Node #0,2: 62:[35, 1, 28] Operation: 11+17=28 Exploring Operation: 35-11=24, Resulting Numbers: [1, 17, 24] Generated Node #0,3: 62:[1, 17, 24] Operation: 35-11=24 Exploring Operation: 35-17=18, Resulting Numbers: [11, 1, 18] Generated Node #0,4: 62:[11, 1, 18] Operation: 35-17=18 Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[35, 1, 28], Operations: ['11+17=28'] Exploring Operation: 35*1=35, Resulting Numbers: [28, 35] Generated Node #0,2,0: 62:[28, 35] Operation: 35*1=35 Exploring Operation: 35+28=63, Resulting Numbers: [1, 63] Generated Node #0,2,1: 62:[1, 63] Operation: 35+28=63 Exploring Operation: 35-28=7, Resulting Numbers: [1, 7] Generated Node #0,2,2: 62:[1, 7] Operation: 35-28=7 Exploring Operation: 1+28=29, Resulting Numbers: [35, 29] Generated Node #0,2,3: 62:[35, 29] Operation: 1+28=29 Exploring Operation: 35-1=34, Resulting Numbers: [28, 34] Generated Node #0,2,4: 62:[28, 34] Operation: 35-1=34 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 62:[1, 63], Operations: ['11+17=28', '35+28=63'] Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,62 unequal: No Solution Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[35, 11, 1, 17], Operations: [] Exploring Operation: 11+17=28, Resulting Numbers: [35, 1, 28] Generated Node #0,2: 62:[35, 1, 28] Operation: 11+17=28 Moving to Node #0,2 Current State: 62:[35, 1, 28], Operations: ['11+17=28'] Exploring Operation: 35+28=63, Resulting Numbers: [1, 63] Generated Node #0,2,1: 62:[1, 63] Operation: 35+28=63 Moving to Node #0,2,1 Current State: 62:[1, 63], Operations: ['11+17=28', '35+28=63'] Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 55, 6, 99, 80 ]
24
[ "55*6=330", "99*80=7920", "7920/330=24" ]
Current State: 24:[55, 6, 99, 80], Operations: [] Exploring Operation: 55*6=330, Resulting Numbers: [99, 80, 330] Generated Node #2: [99, 80, 330] from Operation: 55*6=330 Current State: 24:[99, 80, 330], Operations: ['55*6=330'] Exploring Operation: 99*80=7920, Resulting Numbers: [330, 7920] Generated Node #3: [330, 7920] from Operation: 99*80=7920 Current State: 24:[330, 7920], Operations: ['55*6=330', '99*80=7920'] Exploring Operation: 7920/330=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[55, 6, 99, 80], Operations: [] Exploring Operation: 55-6=49, Resulting Numbers: [99, 80, 49] Generated Node #0,0: 24:[99, 80, 49] Operation: 55-6=49 Exploring Operation: 99-80=19, Resulting Numbers: [55, 6, 19] Generated Node #0,1: 24:[55, 6, 19] Operation: 99-80=19 Exploring Operation: 99-55=44, Resulting Numbers: [6, 80, 44] Generated Node #0,2: 24:[6, 80, 44] Operation: 99-55=44 Exploring Operation: 80-55=25, Resulting Numbers: [6, 99, 25] Generated Node #0,3: 24:[6, 99, 25] Operation: 80-55=25 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[55, 6, 19], Operations: ['99-80=19'] Exploring Operation: 19-6=13, Resulting Numbers: [55, 13] Generated Node #0,1,0: 24:[55, 13] Operation: 19-6=13 Exploring Operation: 55-6=49, Resulting Numbers: [19, 49] Generated Node #0,1,1: 24:[19, 49] Operation: 55-6=49 Exploring Operation: 55-19=36, Resulting Numbers: [6, 36] Generated Node #0,1,2: 24:[6, 36] Operation: 55-19=36 Exploring Operation: 6+19=25, Resulting Numbers: [55, 25] Generated Node #0,1,3: 24:[55, 25] Operation: 6+19=25 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 24:[6, 36], Operations: ['99-80=19', '55-19=36'] Exploring Operation: 6+36=42, Resulting Numbers: [42] 42,24 unequal: No Solution Exploring Operation: 6*36=216, Resulting Numbers: [216] 216,24 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,24 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,24 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 #0,1,1 Current State: 24:[19, 49], Operations: ['99-80=19', '55-6=49'] Exploring Operation: 19*49=931, Resulting Numbers: [931] 931,24 unequal: No Solution Exploring Operation: 19+49=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 49-19=30, Resulting Numbers: [30] 30,24 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 #0,1,0 Current State: 24:[55, 13], Operations: ['99-80=19', '19-6=13'] Exploring Operation: 55-13=42, Resulting Numbers: [42] 42,24 unequal: No Solution Exploring Operation: 55+13=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 55*13=715, Resulting Numbers: [715] 715,24 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 #0,1,3 Current State: 24:[55, 25], Operations: ['99-80=19', '6+19=25'] Exploring Operation: 55*25=1375, Resulting Numbers: [1375] 1375,24 unequal: No Solution Exploring Operation: 55+25=80, Resulting Numbers: [80] 80,24 unequal: No Solution Exploring Operation: 55-25=30, Resulting Numbers: [30] 30,24 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 #0,2 Current State: 24:[6, 80, 44], Operations: ['99-55=44'] Exploring Operation: 80-6=74, Resulting Numbers: [44, 74] Generated Node #0,2,0: 24:[44, 74] Operation: 80-6=74 Exploring Operation: 80-44=36, Resulting Numbers: [6, 36] Generated Node #0,2,1: 24:[6, 36] Operation: 80-44=36 Exploring Operation: 44-6=38, Resulting Numbers: [80, 38] Generated Node #0,2,2: 24:[80, 38] Operation: 44-6=38 Exploring Operation: 6+80=86, Resulting Numbers: [44, 86] Generated Node #0,2,3: 24:[44, 86] Operation: 6+80=86 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 24:[6, 36], Operations: ['99-55=44', '80-44=36'] Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,24 unequal: No Solution Exploring Operation: 6+36=42, Resulting Numbers: [42] 42,24 unequal: No Solution Exploring Operation: 6*36=216, Resulting Numbers: [216] 216,24 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 24:[44, 74], Operations: ['99-55=44', '80-6=74'] Exploring Operation: 44+74=118, Resulting Numbers: [118] 118,24 unequal: No Solution Exploring Operation: 74-44=30, Resulting Numbers: [30] 30,24 unequal: No Solution Exploring Operation: 44*74=3256, Resulting Numbers: [3256] 3256,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 24:[80, 38], Operations: ['99-55=44', '44-6=38'] Exploring Operation: 80-38=42, Resulting Numbers: [42] 42,24 unequal: No Solution Exploring Operation: 80+38=118, Resulting Numbers: [118] 118,24 unequal: No Solution Exploring Operation: 80*38=3040, Resulting Numbers: [3040] 3040,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 24:[44, 86], Operations: ['99-55=44', '6+80=86'] Exploring Operation: 44*86=3784, Resulting Numbers: [3784] 3784,24 unequal: No Solution Exploring Operation: 86-44=42, Resulting Numbers: [42] 42,24 unequal: No Solution Exploring Operation: 44+86=130, Resulting Numbers: [130] 130,24 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 #0,3 Current State: 24:[6, 99, 25], Operations: ['80-55=25'] Exploring Operation: 25-6=19, Resulting Numbers: [99, 19] Generated Node #0,3,0: 24:[99, 19] Operation: 25-6=19 Exploring Operation: 99-25=74, Resulting Numbers: [6, 74] Generated Node #0,3,1: 24:[6, 74] Operation: 99-25=74 Exploring Operation: 6+99=105, Resulting Numbers: [25, 105] Generated Node #0,3,2: 24:[25, 105] Operation: 6+99=105 Exploring Operation: 99-6=93, Resulting Numbers: [25, 93] Generated Node #0,3,3: 24:[25, 93] Operation: 99-6=93 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 24:[6, 74], Operations: ['80-55=25', '99-25=74'] Exploring Operation: 6+74=80, Resulting Numbers: [80] 80,24 unequal: No Solution Exploring Operation: 6*74=444, Resulting Numbers: [444] 444,24 unequal: No Solution Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,24 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 #0,3,3 Current State: 24:[25, 93], Operations: ['80-55=25', '99-6=93'] Exploring Operation: 25+93=118, Resulting Numbers: [118] 118,24 unequal: No Solution Exploring Operation: 25*93=2325, Resulting Numbers: [2325] 2325,24 unequal: No Solution Exploring Operation: 93-25=68, Resulting Numbers: [68] 68,24 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 #0,3,0 Current State: 24:[99, 19], Operations: ['80-55=25', '25-6=19'] Exploring Operation: 99+19=118, Resulting Numbers: [118] 118,24 unequal: No Solution Exploring Operation: 99*19=1881, Resulting Numbers: [1881] 1881,24 unequal: No Solution Exploring Operation: 99-19=80, Resulting Numbers: [80] 80,24 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 #0,3,2 Current State: 24:[25, 105], Operations: ['80-55=25', '6+99=105'] Exploring Operation: 25+105=130, Resulting Numbers: [130] 130,24 unequal: No Solution Exploring Operation: 25*105=2625, Resulting Numbers: [2625] 2625,24 unequal: No Solution Exploring Operation: 105-25=80, Resulting Numbers: [80] 80,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[99, 80, 49], Operations: ['55-6=49'] Exploring Operation: 99+80=179, Resulting Numbers: [49, 179] Generated Node #0,0,0: 24:[49, 179] Operation: 99+80=179 Exploring Operation: 99-80=19, Resulting Numbers: [49, 19] Generated Node #0,0,1: 24:[49, 19] Operation: 99-80=19 Exploring Operation: 99-49=50, Resulting Numbers: [80, 50] Generated Node #0,0,2: 24:[80, 50] Operation: 99-49=50 Exploring Operation: 80-49=31, Resulting Numbers: [99, 31] Generated Node #0,0,3: 24:[99, 31] Operation: 80-49=31 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 24:[49, 19], Operations: ['55-6=49', '99-80=19'] Exploring Operation: 49+19=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 49-19=30, Resulting Numbers: [30] 30,24 unequal: No Solution Exploring Operation: 49*19=931, Resulting Numbers: [931] 931,24 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:[80, 50], Operations: ['55-6=49', '99-49=50'] Exploring Operation: 80*50=4000, Resulting Numbers: [4000] 4000,24 unequal: No Solution Exploring Operation: 80+50=130, Resulting Numbers: [130] 130,24 unequal: No Solution Exploring Operation: 80-50=30, Resulting Numbers: [30] 30,24 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:[99, 31], Operations: ['55-6=49', '80-49=31'] Exploring Operation: 99*31=3069, Resulting Numbers: [3069] 3069,24 unequal: No Solution Exploring Operation: 99+31=130, Resulting Numbers: [130] 130,24 unequal: No Solution Exploring Operation: 99-31=68, Resulting Numbers: [68] 68,24 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 #0,0,0 Current State: 24:[49, 179], Operations: ['55-6=49', '99+80=179'] Exploring Operation: 49*179=8771, Resulting Numbers: [8771] 8771,24 unequal: No Solution Exploring Operation: 179-49=130, Resulting Numbers: [130] 130,24 unequal: No Solution Exploring Operation: 49+179=228, Resulting Numbers: [228] 228,24 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 No solution found.
0
hs_4
sum_heuristic
[ 61, 2, 32, 78 ]
25
[ "61*32=1952", "1952-2=1950", "1950/78=25" ]
Current State: 25:[61, 2, 32, 78], Operations: [] Exploring Operation: 61*32=1952, Resulting Numbers: [2, 78, 1952] Generated Node #2: [2, 78, 1952] from Operation: 61*32=1952 Current State: 25:[2, 78, 1952], Operations: ['61*32=1952'] Exploring Operation: 1952-2=1950, Resulting Numbers: [78, 1950] Generated Node #3: [78, 1950] from Operation: 1952-2=1950 Current State: 25:[78, 1950], Operations: ['61*32=1952', '1952-2=1950'] Exploring Operation: 1950/78=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[61, 2, 32, 78], Operations: [] Exploring Operation: 61-32=29, Resulting Numbers: [2, 78, 29] Generated Node #0,0: 25:[2, 78, 29] Operation: 61-32=29 Exploring Operation: 78/2=39, Resulting Numbers: [61, 32, 39] Generated Node #0,1: 25:[61, 32, 39] Operation: 78/2=39 Exploring Operation: 78-61=17, Resulting Numbers: [2, 32, 17] Generated Node #0,2: 25:[2, 32, 17] Operation: 78-61=17 Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[2, 32, 17], Operations: ['78-61=17'] Exploring Operation: 2+17=19, Resulting Numbers: [32, 19] Generated Node #0,2,0: 25:[32, 19] Operation: 2+17=19 Exploring Operation: 32-17=15, Resulting Numbers: [2, 15] Generated Node #0,2,1: 25:[2, 15] Operation: 32-17=15 Exploring Operation: 32-2=30, Resulting Numbers: [17, 30] Generated Node #0,2,2: 25:[17, 30] Operation: 32-2=30 Moving to Node #0,2,0 Current State: 25:[32, 19], Operations: ['78-61=17', '2+17=19'] Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 32*19=608, Resulting Numbers: [608] 608,25 unequal: No Solution Exploring Operation: 32+19=51, Resulting Numbers: [51] 51,25 unequal: No Solution Moving to Node #0,2,1 Current State: 25:[2, 15], Operations: ['78-61=17', '32-17=15'] Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,25 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,25 unequal: No Solution Moving to Node #0,2,2 Current State: 25:[17, 30], Operations: ['78-61=17', '32-2=30'] Exploring Operation: 17*30=510, Resulting Numbers: [510] 510,25 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 17+30=47, Resulting Numbers: [47] 47,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[61, 32, 39], Operations: ['78/2=39'] Exploring Operation: 61-32=29, Resulting Numbers: [39, 29] Generated Node #0,1,0: 25:[39, 29] Operation: 61-32=29 Exploring Operation: 61-39=22, Resulting Numbers: [32, 22] Generated Node #0,1,1: 25:[32, 22] Operation: 61-39=22 Exploring Operation: 39-32=7, Resulting Numbers: [61, 7] Generated Node #0,1,2: 25:[61, 7] Operation: 39-32=7 Moving to Node #0,1,1 Current State: 25:[32, 22], Operations: ['78/2=39', '61-39=22'] Exploring Operation: 32*22=704, Resulting Numbers: [704] 704,25 unequal: No Solution Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 32+22=54, Resulting Numbers: [54] 54,25 unequal: No Solution Moving to Node #0,1,0 Current State: 25:[39, 29], Operations: ['78/2=39', '61-32=29'] Exploring Operation: 39+29=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 39-29=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 39*29=1131, Resulting Numbers: [1131] 1131,25 unequal: No Solution Moving to Node #0,1,2 Current State: 25:[61, 7], Operations: ['78/2=39', '39-32=7'] Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,25 unequal: No Solution Exploring Operation: 61+7=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 61*7=427, Resulting Numbers: [427] 427,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[2, 78, 29], Operations: ['61-32=29'] Exploring Operation: 78-29=49, Resulting Numbers: [2, 49] Generated Node #0,0,0: 25:[2, 49] Operation: 78-29=49 Exploring Operation: 78-2=76, Resulting Numbers: [29, 76] Generated Node #0,0,1: 25:[29, 76] Operation: 78-2=76 Exploring Operation: 78/2=39, Resulting Numbers: [29, 39] Generated Node #0,0,2: 25:[29, 39] Operation: 78/2=39 Moving to Node #0,0,2 Current State: 25:[29, 39], Operations: ['61-32=29', '78/2=39'] Exploring Operation: 29*39=1131, Resulting Numbers: [1131] 1131,25 unequal: No Solution Exploring Operation: 39-29=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 29+39=68, Resulting Numbers: [68] 68,25 unequal: No Solution Moving to Node #0,0,0 Current State: 25:[2, 49], Operations: ['61-32=29', '78-29=49'] Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,25 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,25 unequal: No Solution Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[29, 76], Operations: ['61-32=29', '78-2=76'] Exploring Operation: 76-29=47, Resulting Numbers: [47] 47,25 unequal: No Solution Exploring Operation: 29*76=2204, Resulting Numbers: [2204] 2204,25 unequal: No Solution Exploring Operation: 29+76=105, Resulting Numbers: [105] 105,25 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
[ 57, 4, 99, 52 ]
77
[ "57*4=228", "99+52=151", "228-151=77" ]
Current State: 77:[57, 4, 99, 52], Operations: [] Exploring Operation: 57*4=228, Resulting Numbers: [99, 52, 228] Generated Node #2: [99, 52, 228] from Operation: 57*4=228 Current State: 77:[99, 52, 228], Operations: ['57*4=228'] Exploring Operation: 99+52=151, Resulting Numbers: [228, 151] Generated Node #3: [228, 151] from Operation: 99+52=151 Current State: 77:[228, 151], Operations: ['57*4=228', '99+52=151'] Exploring Operation: 228-151=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[57, 4, 99, 52], Operations: [] Exploring Operation: 57-52=5, Resulting Numbers: [4, 99, 5] Generated Node #0,0: 77:[4, 99, 5] Operation: 57-52=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[4, 99, 5], Operations: ['57-52=5'] Exploring Operation: 99-4=95, Resulting Numbers: [5, 95] Generated Node #0,0,0: 77:[5, 95] Operation: 99-4=95 Moving to Node #0,0,0 Current State: 77:[5, 95], Operations: ['57-52=5', '99-4=95'] Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 71, 86, 51, 57 ]
49
[ "71+86=157", "51+57=108", "157-108=49" ]
Current State: 49:[71, 86, 51, 57], Operations: [] Exploring Operation: 71+86=157, Resulting Numbers: [51, 57, 157] Generated Node #2: [51, 57, 157] from Operation: 71+86=157 Current State: 49:[51, 57, 157], Operations: ['71+86=157'] Exploring Operation: 51+57=108, Resulting Numbers: [157, 108] Generated Node #3: [157, 108] from Operation: 51+57=108 Current State: 49:[157, 108], Operations: ['71+86=157', '51+57=108'] Exploring Operation: 157-108=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[71, 86, 51, 57], Operations: [] Exploring Operation: 86-57=29, Resulting Numbers: [71, 51, 29] Generated Node #0,0: 49:[71, 51, 29] Operation: 86-57=29 Exploring Operation: 86-51=35, Resulting Numbers: [71, 57, 35] Generated Node #0,1: 49:[71, 57, 35] Operation: 86-51=35 Exploring Operation: 86-71=15, Resulting Numbers: [51, 57, 15] Generated Node #0,2: 49:[51, 57, 15] Operation: 86-71=15 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[51, 57, 15], Operations: ['86-71=15'] Exploring Operation: 51-15=36, Resulting Numbers: [57, 36] Generated Node #0,2,0: 49:[57, 36] Operation: 51-15=36 Exploring Operation: 57-15=42, Resulting Numbers: [51, 42] Generated Node #0,2,1: 49:[51, 42] Operation: 57-15=42 Exploring Operation: 57-51=6, Resulting Numbers: [15, 6] Generated Node #0,2,2: 49:[15, 6] Operation: 57-51=6 Moving to Node #0,2,1 Current State: 49:[51, 42], Operations: ['86-71=15', '57-15=42'] Exploring Operation: 51+42=93, Resulting Numbers: [93] 93,49 unequal: No Solution Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 51*42=2142, Resulting Numbers: [2142] 2142,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[15, 6], Operations: ['86-71=15', '57-51=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,49 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,49 unequal: No Solution Moving to Node #0,2,0 Current State: 49:[57, 36], Operations: ['86-71=15', '51-15=36'] Exploring Operation: 57*36=2052, Resulting Numbers: [2052] 2052,49 unequal: No Solution Exploring Operation: 57-36=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 57+36=93, Resulting Numbers: [93] 93,49 unequal: No Solution No 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: 49:[71, 51, 29], Operations: ['86-57=29'] Exploring Operation: 71-29=42, Resulting Numbers: [51, 42] Generated Node #0,0,0: 49:[51, 42] Operation: 71-29=42 Exploring Operation: 51-29=22, Resulting Numbers: [71, 22] Generated Node #0,0,1: 49:[71, 22] Operation: 51-29=22 Exploring Operation: 71-51=20, Resulting Numbers: [29, 20] Generated Node #0,0,2: 49:[29, 20] Operation: 71-51=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[51, 42], Operations: ['86-57=29', '71-29=42'] Exploring Operation: 51*42=2142, Resulting Numbers: [2142] 2142,49 unequal: No Solution Exploring Operation: 51+42=93, Resulting Numbers: [93] 93,49 unequal: No Solution Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,49 unequal: No Solution No 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: 49:[29, 20], Operations: ['86-57=29', '71-51=20'] Exploring Operation: 29*20=580, Resulting Numbers: [580] 580,49 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 29+20=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[71, 86, 51, 57], Operations: [] Exploring Operation: 86-57=29, Resulting Numbers: [71, 51, 29] Generated Node #0,0: 49:[71, 51, 29] Operation: 86-57=29 Moving to Node #0,0 Current State: 49:[71, 51, 29], Operations: ['86-57=29'] Exploring Operation: 71-51=20, Resulting Numbers: [29, 20] Generated Node #0,0,2: 49:[29, 20] Operation: 71-51=20 Moving to Node #0,0,2 Current State: 49:[29, 20], Operations: ['86-57=29', '71-51=20'] Exploring Operation: 29+20=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.975694
hs_3
sum_heuristic
[ 30, 90, 88, 92 ]
84
[ "88+92=180", "180/30=6", "90-6=84" ]
Current State: 84:[30, 90, 88, 92], Operations: [] Exploring Operation: 88+92=180, Resulting Numbers: [30, 90, 180] Generated Node #2: [30, 90, 180] from Operation: 88+92=180 Current State: 84:[30, 90, 180], Operations: ['88+92=180'] Exploring Operation: 180/30=6, Resulting Numbers: [90, 6] Generated Node #3: [90, 6] from Operation: 180/30=6 Current State: 84:[90, 6], Operations: ['88+92=180', '180/30=6'] Exploring Operation: 90-6=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[30, 90, 88, 92], Operations: [] Exploring Operation: 92-90=2, Resulting Numbers: [30, 88, 2] Generated Node #0,0: 84:[30, 88, 2] Operation: 92-90=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[30, 88, 2], Operations: ['92-90=2'] Exploring Operation: 30-2=28, Resulting Numbers: [88, 28] Generated Node #0,0,0: 84:[88, 28] Operation: 30-2=28 Moving to Node #0,0,0 Current State: 84:[88, 28], Operations: ['92-90=2', '30-2=28'] Exploring Operation: 88-28=60, Resulting Numbers: [60] 60,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 53, 17, 9, 92 ]
47
[ "53-17=36", "92-9=83", "83-36=47" ]
Current State: 47:[53, 17, 9, 92], Operations: [] Exploring Operation: 53-17=36, Resulting Numbers: [9, 92, 36] Generated Node #2: [9, 92, 36] from Operation: 53-17=36 Current State: 47:[9, 92, 36], Operations: ['53-17=36'] Exploring Operation: 92-9=83, Resulting Numbers: [36, 83] Generated Node #3: [36, 83] from Operation: 92-9=83 Current State: 47:[36, 83], Operations: ['53-17=36', '92-9=83'] Exploring Operation: 83-36=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[53, 17, 9, 92], Operations: [] Exploring Operation: 17+9=26, Resulting Numbers: [53, 92, 26] Generated Node #0,0: 47:[53, 92, 26] Operation: 17+9=26 Exploring Operation: 53-9=44, Resulting Numbers: [17, 92, 44] Generated Node #0,1: 47:[17, 92, 44] Operation: 53-9=44 Exploring Operation: 92-53=39, Resulting Numbers: [17, 9, 39] Generated Node #0,2: 47:[17, 9, 39] Operation: 92-53=39 Exploring Operation: 92-9=83, Resulting Numbers: [53, 17, 83] Generated Node #0,3: 47:[53, 17, 83] Operation: 92-9=83 Exploring Operation: 92-17=75, Resulting Numbers: [53, 9, 75] Generated Node #0,4: 47:[53, 9, 75] Operation: 92-17=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[53, 92, 26], Operations: ['17+9=26'] Exploring Operation: 92+26=118, Resulting Numbers: [53, 118] Generated Node #0,0,0: 47:[53, 118] Operation: 92+26=118 Exploring Operation: 53+26=79, Resulting Numbers: [92, 79] Generated Node #0,0,1: 47:[92, 79] Operation: 53+26=79 Exploring Operation: 92-53=39, Resulting Numbers: [26, 39] Generated Node #0,0,2: 47:[26, 39] Operation: 92-53=39 Exploring Operation: 92-26=66, Resulting Numbers: [53, 66] Generated Node #0,0,3: 47:[53, 66] Operation: 92-26=66 Exploring Operation: 53-26=27, Resulting Numbers: [92, 27] Generated Node #0,0,4: 47:[92, 27] Operation: 53-26=27 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 47:[53, 66], Operations: ['17+9=26', '92-26=66'] Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,47 unequal: No Solution Exploring Operation: 53*66=3498, Resulting Numbers: [3498] 3498,47 unequal: No Solution Exploring Operation: 53+66=119, Resulting Numbers: [119] 119,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 47:[26, 39], Operations: ['17+9=26', '92-53=39'] Exploring Operation: 26*39=1014, Resulting Numbers: [1014] 1014,47 unequal: No Solution Exploring Operation: 26+39=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 39-26=13, Resulting Numbers: [13] 13,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 47:[92, 27], Operations: ['17+9=26', '53-26=27'] Exploring Operation: 92-27=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 92*27=2484, Resulting Numbers: [2484] 2484,47 unequal: No Solution Exploring Operation: 92+27=119, Resulting Numbers: [119] 119,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[53, 118], Operations: ['17+9=26', '92+26=118'] Exploring Operation: 118-53=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 53*118=6254, Resulting Numbers: [6254] 6254,47 unequal: No Solution Exploring Operation: 53+118=171, Resulting Numbers: [171] 171,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 47:[92, 79], Operations: ['17+9=26', '53+26=79'] Exploring Operation: 92-79=13, Resulting Numbers: [13] 13,47 unequal: No Solution Exploring Operation: 92+79=171, Resulting Numbers: [171] 171,47 unequal: No Solution Exploring Operation: 92*79=7268, Resulting Numbers: [7268] 7268,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 47:[53, 17, 83], Operations: ['92-9=83'] Exploring Operation: 17+83=100, Resulting Numbers: [53, 100] Generated Node #0,3,0: 47:[53, 100] Operation: 17+83=100 Exploring Operation: 83-53=30, Resulting Numbers: [17, 30] Generated Node #0,3,1: 47:[17, 30] Operation: 83-53=30 Exploring Operation: 53-17=36, Resulting Numbers: [83, 36] Generated Node #0,3,2: 47:[83, 36] Operation: 53-17=36 Exploring Operation: 53+17=70, Resulting Numbers: [83, 70] Generated Node #0,3,3: 47:[83, 70] Operation: 53+17=70 Exploring Operation: 83-17=66, Resulting Numbers: [53, 66] Generated Node #0,3,4: 47:[53, 66] Operation: 83-17=66 Moving to Node #0,3,4 Current State: 47:[53, 66], Operations: ['92-9=83', '83-17=66'] Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,47 unequal: No Solution Exploring Operation: 53+66=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 53*66=3498, Resulting Numbers: [3498] 3498,47 unequal: No Solution Moving to Node #0,3,2 Current State: 47:[83, 36], Operations: ['92-9=83', '53-17=36'] Exploring Operation: 83+36=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 83*36=2988, Resulting Numbers: [2988] 2988,47 unequal: No Solution Exploring Operation: 83-36=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[53, 17, 9, 92], Operations: [] Exploring Operation: 92-9=83, Resulting Numbers: [53, 17, 83] Generated Node #0,3: 47:[53, 17, 83] Operation: 92-9=83 Moving to Node #0,3 Current State: 47:[53, 17, 83], Operations: ['92-9=83'] Exploring Operation: 53-17=36, Resulting Numbers: [83, 36] Generated Node #0,3,2: 47:[83, 36] Operation: 53-17=36 Moving to Node #0,3,2 Current State: 47:[83, 36], Operations: ['92-9=83', '53-17=36'] Exploring Operation: 83-36=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_5
mult_heuristic
[ 16, 18, 78, 59 ]
17
[ "18-16=2", "78-59=19", "19-2=17" ]
Current State: 17:[16, 18, 78, 59], Operations: [] Exploring Operation: 18-16=2, Resulting Numbers: [78, 59, 2] Generated Node #2: [78, 59, 2] from Operation: 18-16=2 Current State: 17:[78, 59, 2], Operations: ['18-16=2'] Exploring Operation: 78-59=19, Resulting Numbers: [2, 19] Generated Node #3: [2, 19] from Operation: 78-59=19 Current State: 17:[2, 19], Operations: ['18-16=2', '78-59=19'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[16, 18, 78, 59], Operations: [] Exploring Operation: 59-18=41, Resulting Numbers: [16, 78, 41] Generated Node #0,0: 17:[16, 78, 41] Operation: 59-18=41 Exploring Operation: 59-16=43, Resulting Numbers: [18, 78, 43] Generated Node #0,1: 17:[18, 78, 43] Operation: 59-16=43 Exploring Operation: 78-16=62, Resulting Numbers: [18, 59, 62] Generated Node #0,2: 17:[18, 59, 62] Operation: 78-16=62 Exploring Operation: 78-59=19, Resulting Numbers: [16, 18, 19] Generated Node #0,3: 17:[16, 18, 19] Operation: 78-59=19 Exploring Operation: 78-18=60, Resulting Numbers: [16, 59, 60] Generated Node #0,4: 17:[16, 59, 60] Operation: 78-18=60 Start Sub Search at level 1: Moving to Node #0,3 Current State: 17:[16, 18, 19], Operations: ['78-59=19'] Exploring Operation: 19-18=1, Resulting Numbers: [16, 1] Generated Node #0,3,0: 17:[16, 1] Operation: 19-18=1 Exploring Operation: 16+19=35, Resulting Numbers: [18, 35] Generated Node #0,3,1: 17:[18, 35] Operation: 16+19=35 Exploring Operation: 16+18=34, Resulting Numbers: [19, 34] Generated Node #0,3,2: 17:[19, 34] Operation: 16+18=34 Exploring Operation: 18-16=2, Resulting Numbers: [19, 2] Generated Node #0,3,3: 17:[19, 2] Operation: 18-16=2 Exploring Operation: 19-16=3, Resulting Numbers: [18, 3] Generated Node #0,3,4: 17:[18, 3] Operation: 19-16=3 Moving to Node #0,3,4 Current State: 17:[18, 3], Operations: ['78-59=19', '19-16=3'] Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,17 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,17 unequal: No Solution Moving to Node #0,3,3 Current State: 17:[19, 2], Operations: ['78-59=19', '18-16=2'] Exploring Operation: 19+2=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,17 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[16, 18, 78, 59], Operations: [] Exploring Operation: 78-59=19, Resulting Numbers: [16, 18, 19] Generated Node #0,3: 17:[16, 18, 19] Operation: 78-59=19 Moving to Node #0,3 Current State: 17:[16, 18, 19], Operations: ['78-59=19'] Exploring Operation: 18-16=2, Resulting Numbers: [19, 2] Generated Node #0,3,3: 17:[19, 2] Operation: 18-16=2 Moving to Node #0,3,3 Current State: 17:[19, 2], Operations: ['78-59=19', '18-16=2'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 84, 44, 50, 33 ]
47
[ "50-44=6", "84/6=14", "33+14=47" ]
Current State: 47:[84, 44, 50, 33], Operations: [] Exploring Operation: 50-44=6, Resulting Numbers: [84, 33, 6] Generated Node #2: [84, 33, 6] from Operation: 50-44=6 Current State: 47:[84, 33, 6], Operations: ['50-44=6'] Exploring Operation: 84/6=14, Resulting Numbers: [33, 14] Generated Node #3: [33, 14] from Operation: 84/6=14 Current State: 47:[33, 14], Operations: ['50-44=6', '84/6=14'] Exploring Operation: 33+14=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[84, 44, 50, 33], Operations: [] Exploring Operation: 84-33=51, Resulting Numbers: [44, 50, 51] Generated Node #0,0: 47:[44, 50, 51] Operation: 84-33=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[44, 50, 51], Operations: ['84-33=51'] Exploring Operation: 51-44=7, Resulting Numbers: [50, 7] Generated Node #0,0,0: 47:[50, 7] Operation: 51-44=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[50, 7], Operations: ['84-33=51', '51-44=7'] Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 56, 71, 91, 96 ]
20
[ "71-56=15", "96-91=5", "15+5=20" ]
Current State: 20:[56, 71, 91, 96], Operations: [] Exploring Operation: 71-56=15, Resulting Numbers: [91, 96, 15] Generated Node #2: [91, 96, 15] from Operation: 71-56=15 Current State: 20:[91, 96, 15], Operations: ['71-56=15'] Exploring Operation: 96-91=5, Resulting Numbers: [15, 5] Generated Node #3: [15, 5] from Operation: 96-91=5 Current State: 20:[15, 5], Operations: ['71-56=15', '96-91=5'] Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[56, 71, 91, 96], Operations: [] Exploring Operation: 91-71=20, Resulting Numbers: [56, 96, 20] Generated Node #0,0: 20:[56, 96, 20] Operation: 91-71=20 Exploring Operation: 96-91=5, Resulting Numbers: [56, 71, 5] Generated Node #0,1: 20:[56, 71, 5] Operation: 96-91=5 Moving to Node #0,1 Current State: 20:[56, 71, 5], Operations: ['96-91=5'] Exploring Operation: 71-56=15, Resulting Numbers: [5, 15] Generated Node #0,1,0: 20:[5, 15] Operation: 71-56=15 Exploring Operation: 56-5=51, Resulting Numbers: [71, 51] Generated Node #0,1,1: 20:[71, 51] Operation: 56-5=51 Moving to Node #0,0 Current State: 20:[56, 96, 20], Operations: ['91-71=20'] Exploring Operation: 56-20=36, Resulting Numbers: [96, 36] Generated Node #0,0,0: 20:[96, 36] Operation: 56-20=36 Exploring Operation: 96-56=40, Resulting Numbers: [20, 40] Generated Node #0,0,1: 20:[20, 40] Operation: 96-56=40 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 20:[20, 40], Operations: ['91-71=20', '96-56=40'] Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[56, 71, 91, 96], Operations: [] Exploring Operation: 91-71=20, Resulting Numbers: [56, 96, 20] Generated Node #0,0: 20:[56, 96, 20] Operation: 91-71=20 Moving to Node #0,0 Current State: 20:[56, 96, 20], Operations: ['91-71=20'] Exploring Operation: 96-56=40, Resulting Numbers: [20, 40] Generated Node #0,0,1: 20:[20, 40] Operation: 96-56=40 Moving to Node #0,0,1 Current State: 20:[20, 40], Operations: ['91-71=20', '96-56=40'] Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 5, 20, 75, 10 ]
60
[ "5+20=25", "75+10=85", "85-25=60" ]
Current State: 60:[5, 20, 75, 10], Operations: [] Exploring Operation: 5+20=25, Resulting Numbers: [75, 10, 25] Generated Node #2: [75, 10, 25] from Operation: 5+20=25 Current State: 60:[75, 10, 25], Operations: ['5+20=25'] Exploring Operation: 75+10=85, Resulting Numbers: [25, 85] Generated Node #3: [25, 85] from Operation: 75+10=85 Current State: 60:[25, 85], Operations: ['5+20=25', '75+10=85'] Exploring Operation: 85-25=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[5, 20, 75, 10], Operations: [] Exploring Operation: 75/5=15, Resulting Numbers: [20, 10, 15] Generated Node #0,0: 60:[20, 10, 15] Operation: 75/5=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[20, 10, 15], Operations: ['75/5=15'] Exploring Operation: 20+10=30, Resulting Numbers: [15, 30] Generated Node #0,0,0: 60:[15, 30] Operation: 20+10=30 Moving to Node #0,0,0 Current State: 60:[15, 30], Operations: ['75/5=15', '20+10=30'] Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,60 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
[ 9, 12, 4, 32 ]
14
[ "32-12=20", "20/4=5", "9+5=14" ]
Current State: 14:[9, 12, 4, 32], Operations: [] Exploring Operation: 32-12=20, Resulting Numbers: [9, 4, 20] Generated Node #2: [9, 4, 20] from Operation: 32-12=20 Current State: 14:[9, 4, 20], Operations: ['32-12=20'] Exploring Operation: 20/4=5, Resulting Numbers: [9, 5] Generated Node #3: [9, 5] from Operation: 20/4=5 Current State: 14:[9, 5], Operations: ['32-12=20', '20/4=5'] Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[9, 12, 4, 32], Operations: [] Exploring Operation: 32/4=8, Resulting Numbers: [9, 12, 8] Generated Node #0,0: 14:[9, 12, 8] Operation: 32/4=8 Exploring Operation: 32-9=23, Resulting Numbers: [12, 4, 23] Generated Node #0,1: 14:[12, 4, 23] Operation: 32-9=23 Exploring Operation: 32-4=28, Resulting Numbers: [9, 12, 28] Generated Node #0,2: 14:[9, 12, 28] Operation: 32-4=28 Exploring Operation: 32-12=20, Resulting Numbers: [9, 4, 20] Generated Node #0,3: 14:[9, 4, 20] Operation: 32-12=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[9, 12, 8], Operations: ['32/4=8'] Exploring Operation: 12-9=3, Resulting Numbers: [8, 3] Generated Node #0,0,0: 14:[8, 3] Operation: 12-9=3 Exploring Operation: 12-8=4, Resulting Numbers: [9, 4] Generated Node #0,0,1: 14:[9, 4] Operation: 12-8=4 Exploring Operation: 9+8=17, Resulting Numbers: [12, 17] Generated Node #0,0,2: 14:[12, 17] Operation: 9+8=17 Exploring Operation: 9-8=1, Resulting Numbers: [12, 1] Generated Node #0,0,3: 14:[12, 1] Operation: 9-8=1 Moving to Node #0,0,0 Current State: 14:[8, 3], Operations: ['32/4=8', '12-9=3'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,14 unequal: No Solution Moving to Node #0,0,3 Current State: 14:[12, 1], Operations: ['32/4=8', '9-8=1'] Exploring Operation: 12*1=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 12+1=13, Resulting Numbers: [13] 13,14 unequal: No Solution Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[9, 4], Operations: ['32/4=8', '12-8=4'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,14 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,14 unequal: No Solution Moving to Node #0,0,2 Current State: 14:[12, 17], Operations: ['32/4=8', '9+8=17'] Exploring Operation: 12+17=29, Resulting Numbers: [29] 29,14 unequal: No Solution Exploring Operation: 12*17=204, Resulting Numbers: [204] 204,14 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 14:[9, 4, 20], Operations: ['32-12=20'] Exploring Operation: 20-9=11, Resulting Numbers: [4, 11] Generated Node #0,3,0: 14:[4, 11] Operation: 20-9=11 Exploring Operation: 20/4=5, Resulting Numbers: [9, 5] Generated Node #0,3,1: 14:[9, 5] Operation: 20/4=5 Exploring Operation: 20-4=16, Resulting Numbers: [9, 16] Generated Node #0,3,2: 14:[9, 16] Operation: 20-4=16 Exploring Operation: 9+4=13, Resulting Numbers: [20, 13] Generated Node #0,3,3: 14:[20, 13] Operation: 9+4=13 Moving to Node #0,3,1 Current State: 14:[9, 5], Operations: ['32-12=20', '20/4=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,14 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[9, 12, 4, 32], Operations: [] Exploring Operation: 32-12=20, Resulting Numbers: [9, 4, 20] Generated Node #0,3: 14:[9, 4, 20] Operation: 32-12=20 Moving to Node #0,3 Current State: 14:[9, 4, 20], Operations: ['32-12=20'] Exploring Operation: 20/4=5, Resulting Numbers: [9, 5] Generated Node #0,3,1: 14:[9, 5] Operation: 20/4=5 Moving to Node #0,3,1 Current State: 14:[9, 5], Operations: ['32-12=20', '20/4=5'] Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 38, 29, 74, 66 ]
17
[ "38-29=9", "74-66=8", "9+8=17" ]
Current State: 17:[38, 29, 74, 66], Operations: [] Exploring Operation: 38-29=9, Resulting Numbers: [74, 66, 9] Generated Node #2: [74, 66, 9] from Operation: 38-29=9 Current State: 17:[74, 66, 9], Operations: ['38-29=9'] Exploring Operation: 74-66=8, Resulting Numbers: [9, 8] Generated Node #3: [9, 8] from Operation: 74-66=8 Current State: 17:[9, 8], Operations: ['38-29=9', '74-66=8'] Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[38, 29, 74, 66], Operations: [] Exploring Operation: 74-38=36, Resulting Numbers: [29, 66, 36] Generated Node #0,0: 17:[29, 66, 36] Operation: 74-38=36 Exploring Operation: 74-66=8, Resulting Numbers: [38, 29, 8] Generated Node #0,1: 17:[38, 29, 8] Operation: 74-66=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[38, 29, 8], Operations: ['74-66=8'] Exploring Operation: 38-8=30, Resulting Numbers: [29, 30] Generated Node #0,1,0: 17:[29, 30] Operation: 38-8=30 Exploring Operation: 38-29=9, Resulting Numbers: [8, 9] Generated Node #0,1,1: 17:[8, 9] Operation: 38-29=9 Moving to Node #0,1,1 Current State: 17:[8, 9], Operations: ['74-66=8', '38-29=9'] Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[38, 29, 74, 66], Operations: [] Exploring Operation: 74-66=8, Resulting Numbers: [38, 29, 8] Generated Node #0,1: 17:[38, 29, 8] Operation: 74-66=8 Moving to Node #0,1 Current State: 17:[38, 29, 8], Operations: ['74-66=8'] Exploring Operation: 38-29=9, Resulting Numbers: [8, 9] Generated Node #0,1,1: 17:[8, 9] Operation: 38-29=9 Moving to Node #0,1,1 Current State: 17:[8, 9], Operations: ['74-66=8', '38-29=9'] Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 42, 49, 17, 12 ]
67
[ "49-42=7", "12*7=84", "84-17=67" ]
Current State: 67:[42, 49, 17, 12], Operations: [] Exploring Operation: 49-42=7, Resulting Numbers: [17, 12, 7] Generated Node #2: [17, 12, 7] from Operation: 49-42=7 Current State: 67:[17, 12, 7], Operations: ['49-42=7'] Exploring Operation: 12*7=84, Resulting Numbers: [17, 84] Generated Node #3: [17, 84] from Operation: 12*7=84 Current State: 67:[17, 84], Operations: ['49-42=7', '12*7=84'] Exploring Operation: 84-17=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[42, 49, 17, 12], Operations: [] Exploring Operation: 42+12=54, Resulting Numbers: [49, 17, 54] Generated Node #0,0: 67:[49, 17, 54] Operation: 42+12=54 Exploring Operation: 42+17=59, Resulting Numbers: [49, 12, 59] Generated Node #0,1: 67:[49, 12, 59] Operation: 42+17=59 Moving to Node #0,0 Current State: 67:[49, 17, 54], Operations: ['42+12=54'] Exploring Operation: 17+54=71, Resulting Numbers: [49, 71] Generated Node #0,0,0: 67:[49, 71] Operation: 17+54=71 Exploring Operation: 49+17=66, Resulting Numbers: [54, 66] Generated Node #0,0,1: 67:[54, 66] Operation: 49+17=66 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[54, 66], Operations: ['42+12=54', '49+17=66'] Exploring Operation: 54+66=120, Resulting Numbers: [120] 120,67 unequal: No Solution Exploring Operation: 66-54=12, Resulting Numbers: [12] 12,67 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:[49, 71], Operations: ['42+12=54', '17+54=71'] Exploring Operation: 49+71=120, Resulting Numbers: [120] 120,67 unequal: No Solution Exploring Operation: 71-49=22, Resulting Numbers: [22] 22,67 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: 67:[49, 12, 59], Operations: ['42+17=59'] Exploring Operation: 49+12=61, Resulting Numbers: [59, 61] Generated Node #0,1,0: 67:[59, 61] Operation: 49+12=61 Exploring Operation: 12+59=71, Resulting Numbers: [49, 71] Generated Node #0,1,1: 67:[49, 71] Operation: 12+59=71 Moving to Node #0,1,0 Current State: 67:[59, 61], Operations: ['42+17=59', '49+12=61'] Exploring Operation: 59+61=120, Resulting Numbers: [120] 120,67 unequal: No Solution Exploring Operation: 61-59=2, Resulting Numbers: [2] 2,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[49, 71], Operations: ['42+17=59', '12+59=71'] Exploring Operation: 71-49=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 49+71=120, Resulting Numbers: [120] 120,67 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 54, 3, 5, 27 ]
89
[ "54+3=57", "5+27=32", "57+32=89" ]
Current State: 89:[54, 3, 5, 27], Operations: [] Exploring Operation: 54+3=57, Resulting Numbers: [5, 27, 57] Generated Node #2: [5, 27, 57] from Operation: 54+3=57 Current State: 89:[5, 27, 57], Operations: ['54+3=57'] Exploring Operation: 5+27=32, Resulting Numbers: [57, 32] Generated Node #3: [57, 32] from Operation: 5+27=32 Current State: 89:[57, 32], Operations: ['54+3=57', '5+27=32'] Exploring Operation: 57+32=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[54, 3, 5, 27], Operations: [] Exploring Operation: 5*27=135, Resulting Numbers: [54, 3, 135] Generated Node #0,0: 89:[54, 3, 135] Operation: 5*27=135 Exploring Operation: 3*5=15, Resulting Numbers: [54, 27, 15] Generated Node #0,1: 89:[54, 27, 15] Operation: 3*5=15 Exploring Operation: 3*27=81, Resulting Numbers: [54, 5, 81] Generated Node #0,2: 89:[54, 5, 81] Operation: 3*27=81 Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[54, 5, 81], Operations: ['3*27=81'] Exploring Operation: 54+5=59, Resulting Numbers: [81, 59] Generated Node #0,2,0: 89:[81, 59] Operation: 54+5=59 Exploring Operation: 54-5=49, Resulting Numbers: [81, 49] Generated Node #0,2,1: 89:[81, 49] Operation: 54-5=49 Exploring Operation: 5+81=86, Resulting Numbers: [54, 86] Generated Node #0,2,2: 89:[54, 86] Operation: 5+81=86 Moving to Node #0,2,0 Current State: 89:[81, 59], Operations: ['3*27=81', '54+5=59'] Exploring Operation: 81*59=4779, Resulting Numbers: [4779] 4779,89 unequal: No Solution Exploring Operation: 81+59=140, Resulting Numbers: [140] 140,89 unequal: No Solution Exploring Operation: 81-59=22, Resulting Numbers: [22] 22,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[54, 86], Operations: ['3*27=81', '5+81=86'] Exploring Operation: 86-54=32, Resulting Numbers: [32] 32,89 unequal: No Solution Exploring Operation: 54+86=140, Resulting Numbers: [140] 140,89 unequal: No Solution Exploring Operation: 54*86=4644, Resulting Numbers: [4644] 4644,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[81, 49], Operations: ['3*27=81', '54-5=49'] Exploring Operation: 81-49=32, Resulting Numbers: [32] 32,89 unequal: No Solution Exploring Operation: 81+49=130, Resulting Numbers: [130] 130,89 unequal: No Solution Exploring Operation: 81*49=3969, Resulting Numbers: [3969] 3969,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[54, 3, 135], Operations: ['5*27=135'] Exploring Operation: 54+3=57, Resulting Numbers: [135, 57] Generated Node #0,0,0: 89:[135, 57] Operation: 54+3=57 Exploring Operation: 135-3=132, Resulting Numbers: [54, 132] Generated Node #0,0,1: 89:[54, 132] Operation: 135-3=132 Exploring Operation: 135/3=45, Resulting Numbers: [54, 45] Generated Node #0,0,2: 89:[54, 45] Operation: 135/3=45 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[135, 57], Operations: ['5*27=135', '54+3=57'] Exploring Operation: 135+57=192, Resulting Numbers: [192] 192,89 unequal: No Solution Exploring Operation: 135*57=7695, Resulting Numbers: [7695] 7695,89 unequal: No Solution Exploring Operation: 135-57=78, Resulting Numbers: [78] 78,89 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 #0,0,1 Current State: 89:[54, 132], Operations: ['5*27=135', '135-3=132'] Exploring Operation: 132-54=78, Resulting Numbers: [78] 78,89 unequal: No Solution Exploring Operation: 54*132=7128, Resulting Numbers: [7128] 7128,89 unequal: No Solution Exploring Operation: 54+132=186, Resulting Numbers: [186] 186,89 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 #0,0,2 Current State: 89:[54, 45], Operations: ['5*27=135', '135/3=45'] Exploring Operation: 54+45=99, Resulting Numbers: [99] 99,89 unequal: No Solution Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,89 unequal: No Solution Exploring Operation: 54*45=2430, Resulting Numbers: [2430] 2430,89 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 #0,1 Current State: 89:[54, 27, 15], Operations: ['3*5=15'] Exploring Operation: 54+15=69, Resulting Numbers: [27, 69] Generated Node #0,1,0: 89:[27, 69] Operation: 54+15=69 Exploring Operation: 27+15=42, Resulting Numbers: [54, 42] Generated Node #0,1,1: 89:[54, 42] Operation: 27+15=42 Exploring Operation: 54+27=81, Resulting Numbers: [15, 81] Generated Node #0,1,2: 89:[15, 81] Operation: 54+27=81 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[27, 69], Operations: ['3*5=15', '54+15=69'] Exploring Operation: 27*69=1863, Resulting Numbers: [1863] 1863,89 unequal: No Solution Exploring Operation: 69-27=42, Resulting Numbers: [42] 42,89 unequal: No Solution Exploring Operation: 27+69=96, Resulting Numbers: [96] 96,89 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:[54, 42], Operations: ['3*5=15', '27+15=42'] Exploring Operation: 54*42=2268, Resulting Numbers: [2268] 2268,89 unequal: No Solution Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,89 unequal: No Solution Exploring Operation: 54+42=96, Resulting Numbers: [96] 96,89 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 #0,1,2 Current State: 89:[15, 81], Operations: ['3*5=15', '54+27=81'] Exploring Operation: 15+81=96, Resulting Numbers: [96] 96,89 unequal: No Solution Exploring Operation: 15*81=1215, Resulting Numbers: [1215] 1215,89 unequal: No Solution Exploring Operation: 81-15=66, Resulting Numbers: [66] 66,89 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_3
sum_heuristic
[ 5, 24, 9, 46 ]
78
[ "9*46=414", "414-24=390", "390/5=78" ]
Current State: 78:[5, 24, 9, 46], Operations: [] Exploring Operation: 9*46=414, Resulting Numbers: [5, 24, 414] Generated Node #2: [5, 24, 414] from Operation: 9*46=414 Current State: 78:[5, 24, 414], Operations: ['9*46=414'] Exploring Operation: 414-24=390, Resulting Numbers: [5, 390] Generated Node #3: [5, 390] from Operation: 414-24=390 Current State: 78:[5, 390], Operations: ['9*46=414', '414-24=390'] Exploring Operation: 390/5=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[5, 24, 9, 46], Operations: [] Exploring Operation: 46-9=37, Resulting Numbers: [5, 24, 37] Generated Node #0,0: 78:[5, 24, 37] Operation: 46-9=37 Moving to Node #0,0 Current State: 78:[5, 24, 37], Operations: ['46-9=37'] Exploring Operation: 37-24=13, Resulting Numbers: [5, 13] Generated Node #0,0,0: 78:[5, 13] Operation: 37-24=13 Moving to Node #0,0,0 Current State: 78:[5, 13], Operations: ['46-9=37', '37-24=13'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,78 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 2, 91, 2, 13 ]
53
[ "2+91=93", "13+93=106", "106/2=53" ]
Current State: 53:[2, 91, 2, 13], Operations: [] Exploring Operation: 2+91=93, Resulting Numbers: [13, 93] Generated Node #2: [13, 93] from Operation: 2+91=93 Current State: 53:[13, 93], Operations: ['2+91=93'] Exploring Operation: 13+93=106, Resulting Numbers: [106] 106,53 equal: Goal Reached Exploring Operation: 106/2=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[2, 91, 2, 13], Operations: [] Exploring Operation: 2*13=26, Resulting Numbers: [91, 2, 26] Generated Node #0,0: 53:[91, 2, 26] Operation: 2*13=26 Exploring Operation: 2*13=26, Resulting Numbers: [2, 91, 26] Generated Node #0,1: 53:[2, 91, 26] Operation: 2*13=26 Exploring Operation: 91-2=89, Resulting Numbers: [2, 13, 89] Generated Node #0,2: 53:[2, 13, 89] Operation: 91-2=89 Exploring Operation: 2+2=4, Resulting Numbers: [91, 13, 4] Generated Node #0,3: 53:[91, 13, 4] Operation: 2+2=4 Moving to Node #0,0 Current State: 53:[91, 2, 26], Operations: ['2*13=26'] Exploring Operation: 2+26=28, Resulting Numbers: [91, 28] Generated Node #0,0,0: 53:[91, 28] Operation: 2+26=28 Exploring Operation: 91-2=89, Resulting Numbers: [26, 89] Generated Node #0,0,1: 53:[26, 89] Operation: 91-2=89 Exploring Operation: 91-26=65, Resulting Numbers: [2, 65] Generated Node #0,0,2: 53:[2, 65] Operation: 91-26=65 Exploring Operation: 2*26=52, Resulting Numbers: [91, 52] Generated Node #0,0,3: 53:[91, 52] Operation: 2*26=52 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 53:[91, 52], Operations: ['2*13=26', '2*26=52'] Exploring Operation: 91*52=4732, Resulting Numbers: [4732] 4732,53 unequal: No Solution Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,53 unequal: No Solution Exploring Operation: 91+52=143, Resulting Numbers: [143] 143,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[91, 28], Operations: ['2*13=26', '2+26=28'] Exploring Operation: 91*28=2548, Resulting Numbers: [2548] 2548,53 unequal: No Solution Exploring Operation: 91+28=119, Resulting Numbers: [119] 119,53 unequal: No Solution Exploring Operation: 91-28=63, Resulting Numbers: [63] 63,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[26, 89], Operations: ['2*13=26', '91-2=89'] Exploring Operation: 26+89=115, Resulting Numbers: [115] 115,53 unequal: No Solution Exploring Operation: 89-26=63, Resulting Numbers: [63] 63,53 unequal: No Solution Exploring Operation: 26*89=2314, Resulting Numbers: [2314] 2314,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 53:[2, 65], Operations: ['2*13=26', '91-26=65'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,53 unequal: No Solution Exploring Operation: 2+65=67, Resulting Numbers: [67] 67,53 unequal: No Solution Exploring Operation: 2*65=130, Resulting Numbers: [130] 130,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 53:[2, 91, 26], Operations: ['2*13=26'] Exploring Operation: 2+26=28, Resulting Numbers: [91, 28] Generated Node #0,1,0: 53:[91, 28] Operation: 2+26=28 Exploring Operation: 2*26=52, Resulting Numbers: [91, 52] Generated Node #0,1,1: 53:[91, 52] Operation: 2*26=52 Exploring Operation: 91-26=65, Resulting Numbers: [2, 65] Generated Node #0,1,2: 53:[2, 65] Operation: 91-26=65 Exploring Operation: 91-2=89, Resulting Numbers: [26, 89] Generated Node #0,1,3: 53:[26, 89] Operation: 91-2=89 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 53:[91, 52], Operations: ['2*13=26', '2*26=52'] Exploring Operation: 91+52=143, Resulting Numbers: [143] 143,53 unequal: No Solution Exploring Operation: 91*52=4732, Resulting Numbers: [4732] 4732,53 unequal: No Solution Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[91, 28], Operations: ['2*13=26', '2+26=28'] Exploring Operation: 91+28=119, Resulting Numbers: [119] 119,53 unequal: No Solution Exploring Operation: 91-28=63, Resulting Numbers: [63] 63,53 unequal: No Solution Exploring Operation: 91*28=2548, Resulting Numbers: [2548] 2548,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 53:[2, 65], Operations: ['2*13=26', '91-26=65'] Exploring Operation: 2+65=67, Resulting Numbers: [67] 67,53 unequal: No Solution Exploring Operation: 2*65=130, Resulting Numbers: [130] 130,53 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 53:[26, 89], Operations: ['2*13=26', '91-2=89'] Exploring Operation: 26*89=2314, Resulting Numbers: [2314] 2314,53 unequal: No Solution Exploring Operation: 26+89=115, Resulting Numbers: [115] 115,53 unequal: No Solution Exploring Operation: 89-26=63, Resulting Numbers: [63] 63,53 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: 53:[91, 13, 4], Operations: ['2+2=4'] Exploring Operation: 91-13=78, Resulting Numbers: [4, 78] Generated Node #0,3,0: 53:[4, 78] Operation: 91-13=78 Exploring Operation: 13*4=52, Resulting Numbers: [91, 52] Generated Node #0,3,1: 53:[91, 52] Operation: 13*4=52 Exploring Operation: 13+4=17, Resulting Numbers: [91, 17] Generated Node #0,3,2: 53:[91, 17] Operation: 13+4=17 Exploring Operation: 91-4=87, Resulting Numbers: [13, 87] Generated Node #0,3,3: 53:[13, 87] Operation: 91-4=87 Moving to Node #0,2 Current State: 53:[2, 13, 89], Operations: ['91-2=89'] Exploring Operation: 2*13=26, Resulting Numbers: [89, 26] Generated Node #0,2,0: 53:[89, 26] Operation: 2*13=26 Exploring Operation: 2+13=15, Resulting Numbers: [89, 15] Generated Node #0,2,1: 53:[89, 15] Operation: 2+13=15 Exploring Operation: 89-2=87, Resulting Numbers: [13, 87] Generated Node #0,2,2: 53:[13, 87] Operation: 89-2=87 Exploring Operation: 89-13=76, Resulting Numbers: [2, 76] Generated Node #0,2,3: 53:[2, 76] Operation: 89-13=76 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 53:[89, 26], Operations: ['91-2=89', '2*13=26'] Exploring Operation: 89*26=2314, Resulting Numbers: [2314] 2314,53 unequal: No Solution Exploring Operation: 89+26=115, Resulting Numbers: [115] 115,53 unequal: No Solution Exploring Operation: 89-26=63, Resulting Numbers: [63] 63,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 53:[89, 15], Operations: ['91-2=89', '2+13=15'] Exploring Operation: 89-15=74, Resulting Numbers: [74] 74,53 unequal: No Solution Exploring Operation: 89+15=104, Resulting Numbers: [104] 104,53 unequal: No Solution Exploring Operation: 89*15=1335, Resulting Numbers: [1335] 1335,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 53:[13, 87], Operations: ['91-2=89', '89-2=87'] Exploring Operation: 13*87=1131, Resulting Numbers: [1131] 1131,53 unequal: No Solution Exploring Operation: 87-13=74, Resulting Numbers: [74] 74,53 unequal: No Solution Exploring Operation: 13+87=100, Resulting Numbers: [100] 100,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 53:[2, 76], Operations: ['91-2=89', '89-13=76'] Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,53 unequal: No Solution Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 2+76=78, Resulting Numbers: [78] 78,53 unequal: No Solution Exploring Operation: 2*76=152, Resulting Numbers: [152] 152,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 53:[91, 52], Operations: ['2+2=4', '13*4=52'] Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,53 unequal: No Solution Exploring Operation: 91+52=143, Resulting Numbers: [143] 143,53 unequal: No Solution Exploring Operation: 91*52=4732, Resulting Numbers: [4732] 4732,53 unequal: No Solution Moving to Node #0,3,2 Current State: 53:[91, 17], Operations: ['2+2=4', '13+4=17'] Exploring Operation: 91*17=1547, Resulting Numbers: [1547] 1547,53 unequal: No Solution Exploring Operation: 91-17=74, Resulting Numbers: [74] 74,53 unequal: No Solution Exploring Operation: 91+17=108, Resulting Numbers: [108] 108,53 unequal: No Solution Moving to Node #0,3,0 Current State: 53:[4, 78], Operations: ['2+2=4', '91-13=78'] Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,53 unequal: No Solution Exploring Operation: 4+78=82, Resulting Numbers: [82] 82,53 unequal: No Solution Exploring Operation: 4*78=312, Resulting Numbers: [312] 312,53 unequal: No Solution Moving to Node #0,3,3 Current State: 53:[13, 87], Operations: ['2+2=4', '91-4=87'] Exploring Operation: 13+87=100, Resulting Numbers: [100] 100,53 unequal: No Solution Exploring Operation: 13*87=1131, Resulting Numbers: [1131] 1131,53 unequal: No Solution Exploring Operation: 87-13=74, Resulting Numbers: [74] 74,53 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 87, 23, 51, 74 ]
44
[ "87+74=161", "161/23=7", "51-7=44" ]
Current State: 44:[87, 23, 51, 74], Operations: [] Exploring Operation: 87+74=161, Resulting Numbers: [23, 51, 161] Generated Node #2: [23, 51, 161] from Operation: 87+74=161 Current State: 44:[23, 51, 161], Operations: ['87+74=161'] Exploring Operation: 161/23=7, Resulting Numbers: [51, 7] Generated Node #3: [51, 7] from Operation: 161/23=7 Current State: 44:[51, 7], Operations: ['87+74=161', '161/23=7'] Exploring Operation: 51-7=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[87, 23, 51, 74], Operations: [] Exploring Operation: 87-74=13, Resulting Numbers: [23, 51, 13] Generated Node #0,0: 44:[23, 51, 13] Operation: 87-74=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[23, 51, 13], Operations: ['87-74=13'] Exploring Operation: 51-13=38, Resulting Numbers: [23, 38] Generated Node #0,0,0: 44:[23, 38] Operation: 51-13=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[23, 38], Operations: ['87-74=13', '51-13=38'] Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 29, 34, 29, 28 ]
34
[ "29-29=0", "28*0=0", "34+0=34" ]
Current State: 34:[29, 34, 29, 28], Operations: [] Exploring Operation: 29-29=0, Resulting Numbers: [34, 28, 0] Generated Node #2: [34, 28, 0] from Operation: 29-29=0 Current State: 34:[34, 28, 0], Operations: ['29-29=0'] Exploring Operation: 28*0=0, Resulting Numbers: [34, 0] Generated Node #3: [34, 0] from Operation: 28*0=0 Current State: 34:[34, 0], Operations: ['29-29=0', '28*0=0'] Exploring Operation: 34+0=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[29, 34, 29, 28], Operations: [] Exploring Operation: 29-28=1, Resulting Numbers: [29, 34, 1] Generated Node #0,0: 34:[29, 34, 1] Operation: 29-28=1 Exploring Operation: 29-28=1, Resulting Numbers: [34, 29, 1] Generated Node #0,1: 34:[34, 29, 1] Operation: 29-28=1 Exploring Operation: 29/29=1, Resulting Numbers: [34, 28, 1] Generated Node #0,2: 34:[34, 28, 1] Operation: 29/29=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[29, 34, 1], Operations: ['29-28=1'] Exploring Operation: 29+1=30, Resulting Numbers: [34, 30] Generated Node #0,0,0: 34:[34, 30] Operation: 29+1=30 Exploring Operation: 34-29=5, Resulting Numbers: [1, 5] Generated Node #0,0,1: 34:[1, 5] Operation: 34-29=5 Exploring Operation: 29*1=29, Resulting Numbers: [34, 29] Generated Node #0,0,2: 34:[34, 29] Operation: 29*1=29 Moving to Node #0,0,0 Current State: 34:[34, 30], Operations: ['29-28=1', '29+1=30'] Exploring Operation: 34*30=1020, Resulting Numbers: [1020] 1020,34 unequal: No Solution Exploring Operation: 34-30=4, Resulting Numbers: [4] 4,34 unequal: No Solution Exploring Operation: 34+30=64, Resulting Numbers: [64] 64,34 unequal: No Solution Moving to Node #0,0,1 Current State: 34:[1, 5], Operations: ['29-28=1', '34-29=5'] Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,34 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,34 unequal: No Solution Moving to Node #0,0,2 Current State: 34:[34, 29], Operations: ['29-28=1', '29*1=29'] Exploring Operation: 34*29=986, Resulting Numbers: [986] 986,34 unequal: No Solution Exploring Operation: 34+29=63, Resulting Numbers: [63] 63,34 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,34 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:[34, 29, 1], Operations: ['29-28=1'] Exploring Operation: 34*1=34, Resulting Numbers: [29, 34] Generated Node #0,1,0: 34:[29, 34] Operation: 34*1=34 Exploring Operation: 29+1=30, Resulting Numbers: [34, 30] Generated Node #0,1,1: 34:[34, 30] Operation: 29+1=30 Exploring Operation: 34-29=5, Resulting Numbers: [1, 5] Generated Node #0,1,2: 34:[1, 5] Operation: 34-29=5 Moving to Node #0,1,1 Current State: 34:[34, 30], Operations: ['29-28=1', '29+1=30'] Exploring Operation: 34+30=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 34*30=1020, Resulting Numbers: [1020] 1020,34 unequal: No Solution Exploring Operation: 34-30=4, Resulting Numbers: [4] 4,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[1, 5], Operations: ['29-28=1', '34-29=5'] Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,34 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,34 unequal: No Solution Moving to Node #0,1,0 Current State: 34:[29, 34], Operations: ['29-28=1', '34*1=34'] Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 29+34=63, Resulting Numbers: [63] 63,34 unequal: No Solution Exploring Operation: 29*34=986, Resulting Numbers: [986] 986,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[34, 28, 1], Operations: ['29/29=1'] Exploring Operation: 34*1=34, Resulting Numbers: [28, 34] Generated Node #0,2,0: 34:[28, 34] Operation: 34*1=34 Exploring Operation: 28+1=29, Resulting Numbers: [34, 29] Generated Node #0,2,1: 34:[34, 29] Operation: 28+1=29 Exploring Operation: 34-28=6, Resulting Numbers: [1, 6] Generated Node #0,2,2: 34:[1, 6] Operation: 34-28=6 Moving to Node #0,2,1 Current State: 34:[34, 29], Operations: ['29/29=1', '28+1=29'] Exploring Operation: 34*29=986, Resulting Numbers: [986] 986,34 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 34+29=63, Resulting Numbers: [63] 63,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[1, 6], Operations: ['29/29=1', '34-28=6'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[28, 34], Operations: ['29/29=1', '34*1=34'] Exploring Operation: 28+34=62, Resulting Numbers: [62] 62,34 unequal: No Solution Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 28*34=952, Resulting Numbers: [952] 952,34 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
[ 86, 17, 69, 48 ]
47
[ "86-17=69", "69/69=1", "48-1=47" ]
Current State: 47:[86, 17, 69, 48], Operations: [] Exploring Operation: 86-17=69, Resulting Numbers: [69, 48, 69] Generated Node #2: [69, 48, 69] from Operation: 86-17=69 Current State: 47:[69, 48, 69], Operations: ['86-17=69'] Exploring Operation: 69/69=1, Resulting Numbers: [48, 1] Generated Node #3: [48, 1] from Operation: 69/69=1 Current State: 47:[48, 1], Operations: ['86-17=69', '69/69=1'] Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[86, 17, 69, 48], Operations: [] Exploring Operation: 69-17=52, Resulting Numbers: [86, 48, 52] Generated Node #0,0: 47:[86, 48, 52] Operation: 69-17=52 Exploring Operation: 86-17=69, Resulting Numbers: [69, 48, 69] Generated Node #0,1: 47:[69, 48, 69] Operation: 86-17=69 Exploring Operation: 86-48=38, Resulting Numbers: [17, 69, 38] Generated Node #0,2: 47:[17, 69, 38] Operation: 86-48=38 Exploring Operation: 86-69=17, Resulting Numbers: [17, 48, 17] Generated Node #0,3: 47:[17, 48, 17] Operation: 86-69=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[86, 48, 52], Operations: ['69-17=52'] Exploring Operation: 86+48=134, Resulting Numbers: [52, 134] Generated Node #0,0,0: 47:[52, 134] Operation: 86+48=134 Exploring Operation: 86-48=38, Resulting Numbers: [52, 38] Generated Node #0,0,1: 47:[52, 38] Operation: 86-48=38 Exploring Operation: 86-52=34, Resulting Numbers: [48, 34] Generated Node #0,0,2: 47:[48, 34] Operation: 86-52=34 Exploring Operation: 52-48=4, Resulting Numbers: [86, 4] Generated Node #0,0,3: 47:[86, 4] Operation: 52-48=4 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 47:[52, 38], Operations: ['69-17=52', '86-48=38'] Exploring Operation: 52+38=90, Resulting Numbers: [90] 90,47 unequal: No Solution Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 52*38=1976, Resulting Numbers: [1976] 1976,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 47:[48, 34], Operations: ['69-17=52', '86-52=34'] Exploring Operation: 48*34=1632, Resulting Numbers: [1632] 1632,47 unequal: No Solution Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 48+34=82, Resulting Numbers: [82] 82,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 47:[86, 4], Operations: ['69-17=52', '52-48=4'] Exploring Operation: 86+4=90, Resulting Numbers: [90] 90,47 unequal: No Solution Exploring Operation: 86-4=82, Resulting Numbers: [82] 82,47 unequal: No Solution Exploring Operation: 86*4=344, Resulting Numbers: [344] 344,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[52, 134], Operations: ['69-17=52', '86+48=134'] Exploring Operation: 134-52=82, Resulting Numbers: [82] 82,47 unequal: No Solution Exploring Operation: 52*134=6968, Resulting Numbers: [6968] 6968,47 unequal: No Solution Exploring Operation: 52+134=186, Resulting Numbers: [186] 186,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[69, 48, 69], Operations: ['86-17=69'] Exploring Operation: 69/69=1, Resulting Numbers: [48, 1] Generated Node #0,1,0: 47:[48, 1] Operation: 69/69=1 Exploring Operation: 69-48=21, Resulting Numbers: [69, 21] Generated Node #0,1,1: 47:[69, 21] Operation: 69-48=21 Exploring Operation: 69-69=0, Resulting Numbers: [48, 0] Generated Node #0,1,2: 47:[48, 0] Operation: 69-69=0 Exploring Operation: 69-48=21, Resulting Numbers: [69, 21] Generated Node #0,1,3: 47:[69, 21] Operation: 69-48=21 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 47:[48, 1], Operations: ['86-17=69', '69/69=1'] Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[86, 17, 69, 48], Operations: [] Exploring Operation: 86-17=69, Resulting Numbers: [69, 48, 69] Generated Node #0,1: 47:[69, 48, 69] Operation: 86-17=69 Moving to Node #0,1 Current State: 47:[69, 48, 69], Operations: ['86-17=69'] Exploring Operation: 69/69=1, Resulting Numbers: [48, 1] Generated Node #0,1,0: 47:[48, 1] Operation: 69/69=1 Moving to Node #0,1,0 Current State: 47:[48, 1], Operations: ['86-17=69', '69/69=1'] Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 83, 71, 62, 84 ]
55
[ "83-71=12", "84/12=7", "62-7=55" ]
Current State: 55:[83, 71, 62, 84], Operations: [] Exploring Operation: 83-71=12, Resulting Numbers: [62, 84, 12] Generated Node #2: [62, 84, 12] from Operation: 83-71=12 Current State: 55:[62, 84, 12], Operations: ['83-71=12'] Exploring Operation: 84/12=7, Resulting Numbers: [62, 7] Generated Node #3: [62, 7] from Operation: 84/12=7 Current State: 55:[62, 7], Operations: ['83-71=12', '84/12=7'] Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[83, 71, 62, 84], Operations: [] Exploring Operation: 83-62=21, Resulting Numbers: [71, 84, 21] Generated Node #0,0: 55:[71, 84, 21] Operation: 83-62=21 Exploring Operation: 84-83=1, Resulting Numbers: [71, 62, 1] Generated Node #0,1: 55:[71, 62, 1] Operation: 84-83=1 Exploring Operation: 84-62=22, Resulting Numbers: [83, 71, 22] Generated Node #0,2: 55:[83, 71, 22] Operation: 84-62=22 Exploring Operation: 84-71=13, Resulting Numbers: [83, 62, 13] Generated Node #0,3: 55:[83, 62, 13] Operation: 84-71=13 Exploring Operation: 83-71=12, Resulting Numbers: [62, 84, 12] Generated Node #0,4: 55:[62, 84, 12] Operation: 83-71=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[71, 62, 1], Operations: ['84-83=1'] Exploring Operation: 71-1=70, Resulting Numbers: [62, 70] Generated Node #0,1,0: 55:[62, 70] Operation: 71-1=70 Exploring Operation: 62-1=61, Resulting Numbers: [71, 61] Generated Node #0,1,1: 55:[71, 61] Operation: 62-1=61 Exploring Operation: 71/1=71, Resulting Numbers: [62, 71] Generated Node #0,1,2: 55:[62, 71] Operation: 71/1=71 Exploring Operation: 71-62=9, Resulting Numbers: [1, 9] Generated Node #0,1,3: 55:[1, 9] Operation: 71-62=9 Exploring Operation: 71*1=71, Resulting Numbers: [62, 71] Generated Node #0,1,4: 55:[62, 71] Operation: 71*1=71 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 55:[1, 9], Operations: ['84-83=1', '71-62=9'] Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 1*9=9, Resulting Numbers: [9] 9,55 unequal: No Solution Exploring Operation: 1+9=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 9/1=9, Resulting Numbers: [9] 9,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[62, 70], Operations: ['84-83=1', '71-1=70'] Exploring Operation: 62*70=4340, Resulting Numbers: [4340] 4340,55 unequal: No Solution Exploring Operation: 70-62=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 62+70=132, Resulting Numbers: [132] 132,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 55:[71, 61], Operations: ['84-83=1', '62-1=61'] Exploring Operation: 71+61=132, Resulting Numbers: [132] 132,55 unequal: No Solution Exploring Operation: 71-61=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 71*61=4331, Resulting Numbers: [4331] 4331,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 55:[62, 71], Operations: ['84-83=1', '71/1=71'] Exploring Operation: 62+71=133, Resulting Numbers: [133] 133,55 unequal: No Solution Exploring Operation: 71-62=9, Resulting Numbers: [9] 9,55 unequal: No Solution Exploring Operation: 62*71=4402, Resulting Numbers: [4402] 4402,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 55:[62, 71], Operations: ['84-83=1', '71*1=71'] Exploring Operation: 62+71=133, Resulting Numbers: [133] 133,55 unequal: No Solution Exploring Operation: 62*71=4402, Resulting Numbers: [4402] 4402,55 unequal: No Solution Exploring Operation: 71-62=9, Resulting Numbers: [9] 9,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 55:[83, 62, 13], Operations: ['84-71=13'] Exploring Operation: 62-13=49, Resulting Numbers: [83, 49] Generated Node #0,3,0: 55:[83, 49] Operation: 62-13=49 Exploring Operation: 83-62=21, Resulting Numbers: [13, 21] Generated Node #0,3,1: 55:[13, 21] Operation: 83-62=21 Exploring Operation: 83+13=96, Resulting Numbers: [62, 96] Generated Node #0,3,2: 55:[62, 96] Operation: 83+13=96 Exploring Operation: 62+13=75, Resulting Numbers: [83, 75] Generated Node #0,3,3: 55:[83, 75] Operation: 62+13=75 Exploring Operation: 83-13=70, Resulting Numbers: [62, 70] Generated Node #0,3,4: 55:[62, 70] Operation: 83-13=70 Moving to Node #0,3,1 Current State: 55:[13, 21], Operations: ['84-71=13', '83-62=21'] Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,55 unequal: No Solution Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 13*21=273, Resulting Numbers: [273] 273,55 unequal: No Solution Moving to Node #0,3,4 Current State: 55:[62, 70], Operations: ['84-71=13', '83-13=70'] Exploring Operation: 62*70=4340, Resulting Numbers: [4340] 4340,55 unequal: No Solution Exploring Operation: 70-62=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 62+70=132, Resulting Numbers: [132] 132,55 unequal: No Solution Moving to Node #0,3,0 Current State: 55:[83, 49], Operations: ['84-71=13', '62-13=49'] Exploring Operation: 83*49=4067, Resulting Numbers: [4067] 4067,55 unequal: No Solution Exploring Operation: 83+49=132, Resulting Numbers: [132] 132,55 unequal: No Solution Exploring Operation: 83-49=34, Resulting Numbers: [34] 34,55 unequal: No Solution Moving to Node #0,3,2 Current State: 55:[62, 96], Operations: ['84-71=13', '83+13=96'] Exploring Operation: 62+96=158, Resulting Numbers: [158] 158,55 unequal: No Solution Exploring Operation: 62*96=5952, Resulting Numbers: [5952] 5952,55 unequal: No Solution Exploring Operation: 96-62=34, Resulting Numbers: [34] 34,55 unequal: No Solution Moving to Node #0,3,3 Current State: 55:[83, 75], Operations: ['84-71=13', '62+13=75'] Exploring Operation: 83-75=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 83+75=158, Resulting Numbers: [158] 158,55 unequal: No Solution Exploring Operation: 83*75=6225, Resulting Numbers: [6225] 6225,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 55:[62, 84, 12], Operations: ['83-71=12'] Exploring Operation: 62-12=50, Resulting Numbers: [84, 50] Generated Node #0,4,0: 55:[84, 50] Operation: 62-12=50 Exploring Operation: 62+12=74, Resulting Numbers: [84, 74] Generated Node #0,4,1: 55:[84, 74] Operation: 62+12=74 Exploring Operation: 84-12=72, Resulting Numbers: [62, 72] Generated Node #0,4,2: 55:[62, 72] Operation: 84-12=72 Exploring Operation: 84/12=7, Resulting Numbers: [62, 7] Generated Node #0,4,3: 55:[62, 7] Operation: 84/12=7 Exploring Operation: 84-62=22, Resulting Numbers: [12, 22] Generated Node #0,4,4: 55:[12, 22] Operation: 84-62=22 Moving to Node #0,4,3 Current State: 55:[62, 7], Operations: ['83-71=12', '84/12=7'] Exploring Operation: 62*7=434, Resulting Numbers: [434] 434,55 unequal: No Solution Exploring Operation: 62+7=69, Resulting Numbers: [69] 69,55 unequal: No Solution Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[83, 71, 62, 84], Operations: [] Exploring Operation: 83-71=12, Resulting Numbers: [62, 84, 12] Generated Node #0,4: 55:[62, 84, 12] Operation: 83-71=12 Moving to Node #0,4 Current State: 55:[62, 84, 12], Operations: ['83-71=12'] Exploring Operation: 84/12=7, Resulting Numbers: [62, 7] Generated Node #0,4,3: 55:[62, 7] Operation: 84/12=7 Moving to Node #0,4,3 Current State: 55:[62, 7], Operations: ['83-71=12', '84/12=7'] Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.949653
hs_5
mult_heuristic
[ 87, 37, 7, 85 ]
15
[ "87-85=2", "37-7=30", "30/2=15" ]
Current State: 15:[87, 37, 7, 85], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [37, 7, 2] Generated Node #2: [37, 7, 2] from Operation: 87-85=2 Current State: 15:[37, 7, 2], Operations: ['87-85=2'] Exploring Operation: 37-7=30, Resulting Numbers: [2, 30] Generated Node #3: [2, 30] from Operation: 37-7=30 Current State: 15:[2, 30], Operations: ['87-85=2', '37-7=30'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[87, 37, 7, 85], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [37, 7, 2] Generated Node #0,0: 15:[37, 7, 2] Operation: 87-85=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[37, 7, 2], Operations: ['87-85=2'] Exploring Operation: 37-7=30, Resulting Numbers: [2, 30] Generated Node #0,0,0: 15:[2, 30] Operation: 37-7=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[2, 30], Operations: ['87-85=2', '37-7=30'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[87, 37, 7, 85], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [37, 7, 2] Generated Node #0,0: 15:[37, 7, 2] Operation: 87-85=2 Moving to Node #0,0 Current State: 15:[37, 7, 2], Operations: ['87-85=2'] Exploring Operation: 37-7=30, Resulting Numbers: [2, 30] Generated Node #0,0,0: 15:[2, 30] Operation: 37-7=30 Moving to Node #0,0,0 Current State: 15:[2, 30], Operations: ['87-85=2', '37-7=30'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 22, 96, 56, 12 ]
15
[ "96/12=8", "56/8=7", "22-7=15" ]
Current State: 15:[22, 96, 56, 12], Operations: [] Exploring Operation: 96/12=8, Resulting Numbers: [22, 56, 8] Generated Node #2: [22, 56, 8] from Operation: 96/12=8 Current State: 15:[22, 56, 8], Operations: ['96/12=8'] Exploring Operation: 56/8=7, Resulting Numbers: [22, 7] Generated Node #3: [22, 7] from Operation: 56/8=7 Current State: 15:[22, 7], Operations: ['96/12=8', '56/8=7'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[22, 96, 56, 12], Operations: [] Exploring Operation: 96-12=84, Resulting Numbers: [22, 56, 84] Generated Node #0,0: 15:[22, 56, 84] Operation: 96-12=84 Exploring Operation: 96-22=74, Resulting Numbers: [56, 12, 74] Generated Node #0,1: 15:[56, 12, 74] Operation: 96-22=74 Exploring Operation: 96-56=40, Resulting Numbers: [22, 12, 40] Generated Node #0,2: 15:[22, 12, 40] Operation: 96-56=40 Exploring Operation: 56-22=34, Resulting Numbers: [96, 12, 34] Generated Node #0,3: 15:[96, 12, 34] Operation: 56-22=34 Exploring Operation: 96/12=8, Resulting Numbers: [22, 56, 8] Generated Node #0,4: 15:[22, 56, 8] Operation: 96/12=8 Moving to Node #0,2 Current State: 15:[22, 12, 40], Operations: ['96-56=40'] Exploring Operation: 40-22=18, Resulting Numbers: [12, 18] Generated Node #0,2,0: 15:[12, 18] Operation: 40-22=18 Exploring Operation: 40-12=28, Resulting Numbers: [22, 28] Generated Node #0,2,1: 15:[22, 28] Operation: 40-12=28 Exploring Operation: 22+12=34, Resulting Numbers: [40, 34] Generated Node #0,2,2: 15:[40, 34] Operation: 22+12=34 Exploring Operation: 12+40=52, Resulting Numbers: [22, 52] Generated Node #0,2,3: 15:[22, 52] Operation: 12+40=52 Exploring Operation: 22-12=10, Resulting Numbers: [40, 10] Generated Node #0,2,4: 15:[40, 10] Operation: 22-12=10 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 15:[12, 18], Operations: ['96-56=40', '40-22=18'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,15 unequal: No Solution Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 15:[22, 28], Operations: ['96-56=40', '40-12=28'] Exploring Operation: 22+28=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 22*28=616, Resulting Numbers: [616] 616,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 15:[40, 10], Operations: ['96-56=40', '22-12=10'] Exploring Operation: 40*10=400, Resulting Numbers: [400] 400,15 unequal: No Solution Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 40+10=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 15:[40, 34], Operations: ['96-56=40', '22+12=34'] Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 40*34=1360, Resulting Numbers: [1360] 1360,15 unequal: No Solution Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 15:[22, 52], Operations: ['96-56=40', '12+40=52'] Exploring Operation: 22*52=1144, Resulting Numbers: [1144] 1144,15 unequal: No Solution Exploring Operation: 22+52=74, Resulting Numbers: [74] 74,15 unequal: No Solution Exploring Operation: 52-22=30, Resulting Numbers: [30] 30,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 15:[22, 56, 8], Operations: ['96/12=8'] Exploring Operation: 22-8=14, Resulting Numbers: [56, 14] Generated Node #0,4,0: 15:[56, 14] Operation: 22-8=14 Exploring Operation: 56-8=48, Resulting Numbers: [22, 48] Generated Node #0,4,1: 15:[22, 48] Operation: 56-8=48 Exploring Operation: 22+8=30, Resulting Numbers: [56, 30] Generated Node #0,4,2: 15:[56, 30] Operation: 22+8=30 Exploring Operation: 56-22=34, Resulting Numbers: [8, 34] Generated Node #0,4,3: 15:[8, 34] Operation: 56-22=34 Exploring Operation: 56/8=7, Resulting Numbers: [22, 7] Generated Node #0,4,4: 15:[22, 7] Operation: 56/8=7 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 15:[22, 7], Operations: ['96/12=8', '56/8=7'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[22, 96, 56, 12], Operations: [] Exploring Operation: 96/12=8, Resulting Numbers: [22, 56, 8] Generated Node #0,4: 15:[22, 56, 8] Operation: 96/12=8 Moving to Node #0,4 Current State: 15:[22, 56, 8], Operations: ['96/12=8'] Exploring Operation: 56/8=7, Resulting Numbers: [22, 7] Generated Node #0,4,4: 15:[22, 7] Operation: 56/8=7 Moving to Node #0,4,4 Current State: 15:[22, 7], Operations: ['96/12=8', '56/8=7'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 62, 32, 60, 84 ]
50
[ "62+32=94", "60+84=144", "144-94=50" ]
Current State: 50:[62, 32, 60, 84], Operations: [] Exploring Operation: 62+32=94, Resulting Numbers: [60, 84, 94] Generated Node #2: [60, 84, 94] from Operation: 62+32=94 Current State: 50:[60, 84, 94], Operations: ['62+32=94'] Exploring Operation: 60+84=144, Resulting Numbers: [94, 144] Generated Node #3: [94, 144] from Operation: 60+84=144 Current State: 50:[94, 144], Operations: ['62+32=94', '60+84=144'] Exploring Operation: 144-94=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[62, 32, 60, 84], Operations: [] Exploring Operation: 84-62=22, Resulting Numbers: [32, 60, 22] Generated Node #0,0: 50:[32, 60, 22] Operation: 84-62=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[32, 60, 22], Operations: ['84-62=22'] Exploring Operation: 60-32=28, Resulting Numbers: [22, 28] Generated Node #0,0,0: 50:[22, 28] Operation: 60-32=28 Moving to Node #0,0,0 Current State: 50:[22, 28], Operations: ['84-62=22', '60-32=28'] Exploring Operation: 22+28=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[62, 32, 60, 84], Operations: [] Exploring Operation: 84-62=22, Resulting Numbers: [32, 60, 22] Generated Node #0,0: 50:[32, 60, 22] Operation: 84-62=22 Moving to Node #0,0 Current State: 50:[32, 60, 22], Operations: ['84-62=22'] Exploring Operation: 60-32=28, Resulting Numbers: [22, 28] Generated Node #0,0,0: 50:[22, 28] Operation: 60-32=28 Moving to Node #0,0,0 Current State: 50:[22, 28], Operations: ['84-62=22', '60-32=28'] Exploring Operation: 22+28=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 69, 34, 71, 43 ]
60
[ "71-69=2", "34/2=17", "43+17=60" ]
Current State: 60:[69, 34, 71, 43], Operations: [] Exploring Operation: 71-69=2, Resulting Numbers: [34, 43, 2] Generated Node #2: [34, 43, 2] from Operation: 71-69=2 Current State: 60:[34, 43, 2], Operations: ['71-69=2'] Exploring Operation: 34/2=17, Resulting Numbers: [43, 17] Generated Node #3: [43, 17] from Operation: 34/2=17 Current State: 60:[43, 17], Operations: ['71-69=2', '34/2=17'] Exploring Operation: 43+17=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[69, 34, 71, 43], Operations: [] Exploring Operation: 69-43=26, Resulting Numbers: [34, 71, 26] Generated Node #0,0: 60:[34, 71, 26] Operation: 69-43=26 Exploring Operation: 43-34=9, Resulting Numbers: [69, 71, 9] Generated Node #0,1: 60:[69, 71, 9] Operation: 43-34=9 Exploring Operation: 71-69=2, Resulting Numbers: [34, 43, 2] Generated Node #0,2: 60:[34, 43, 2] Operation: 71-69=2 Exploring Operation: 71-43=28, Resulting Numbers: [69, 34, 28] Generated Node #0,3: 60:[69, 34, 28] Operation: 71-43=28 Moving to Node #0,3 Current State: 60:[69, 34, 28], Operations: ['71-43=28'] Exploring Operation: 34-28=6, Resulting Numbers: [69, 6] Generated Node #0,3,0: 60:[69, 6] Operation: 34-28=6 Exploring Operation: 69-34=35, Resulting Numbers: [28, 35] Generated Node #0,3,1: 60:[28, 35] Operation: 69-34=35 Exploring Operation: 69-28=41, Resulting Numbers: [34, 41] Generated Node #0,3,2: 60:[34, 41] Operation: 69-28=41 Exploring Operation: 34+28=62, Resulting Numbers: [69, 62] Generated Node #0,3,3: 60:[69, 62] Operation: 34+28=62 Moving to Node #0,2 Current State: 60:[34, 43, 2], Operations: ['71-69=2'] Exploring Operation: 43-2=41, Resulting Numbers: [34, 41] Generated Node #0,2,0: 60:[34, 41] Operation: 43-2=41 Exploring Operation: 34-2=32, Resulting Numbers: [43, 32] Generated Node #0,2,1: 60:[43, 32] Operation: 34-2=32 Exploring Operation: 43-34=9, Resulting Numbers: [2, 9] Generated Node #0,2,2: 60:[2, 9] Operation: 43-34=9 Exploring Operation: 34/2=17, Resulting Numbers: [43, 17] Generated Node #0,2,3: 60:[43, 17] Operation: 34/2=17 Moving to Node #0,0 Current State: 60:[34, 71, 26], Operations: ['69-43=26'] Exploring Operation: 71-34=37, Resulting Numbers: [26, 37] Generated Node #0,0,0: 60:[26, 37] Operation: 71-34=37 Exploring Operation: 71-26=45, Resulting Numbers: [34, 45] Generated Node #0,0,1: 60:[34, 45] Operation: 71-26=45 Exploring Operation: 34+26=60, Resulting Numbers: [71, 60] Generated Node #0,0,2: 60:[71, 60] Operation: 34+26=60 Exploring Operation: 34-26=8, Resulting Numbers: [71, 8] Generated Node #0,0,3: 60:[71, 8] Operation: 34-26=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[26, 37], Operations: ['69-43=26', '71-34=37'] Exploring Operation: 26+37=63, Resulting Numbers: [63] 63,60 unequal: No Solution Exploring Operation: 37-26=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 26*37=962, Resulting Numbers: [962] 962,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[71, 60], Operations: ['69-43=26', '34+26=60'] Exploring Operation: 71-60=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 71+60=131, Resulting Numbers: [131] 131,60 unequal: No Solution Exploring Operation: 71*60=4260, Resulting Numbers: [4260] 4260,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 60:[71, 8], Operations: ['69-43=26', '34-26=8'] Exploring Operation: 71-8=63, Resulting Numbers: [63] 63,60 unequal: No Solution Exploring Operation: 71+8=79, Resulting Numbers: [79] 79,60 unequal: No Solution Exploring Operation: 71*8=568, Resulting Numbers: [568] 568,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[34, 45], Operations: ['69-43=26', '71-26=45'] Exploring Operation: 34+45=79, Resulting Numbers: [79] 79,60 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 34*45=1530, Resulting Numbers: [1530] 1530,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 60:[69, 71, 9], Operations: ['43-34=9'] Exploring Operation: 69+9=78, Resulting Numbers: [71, 78] Generated Node #0,1,0: 60:[71, 78] Operation: 69+9=78 Exploring Operation: 71-69=2, Resulting Numbers: [9, 2] Generated Node #0,1,1: 60:[9, 2] Operation: 71-69=2 Exploring Operation: 69-9=60, Resulting Numbers: [71, 60] Generated Node #0,1,2: 60:[71, 60] Operation: 69-9=60 Exploring Operation: 71-9=62, Resulting Numbers: [69, 62] Generated Node #0,1,3: 60:[69, 62] Operation: 71-9=62 Moving to Node #0,2,2 Current State: 60:[2, 9], Operations: ['71-69=2', '43-34=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[9, 2], Operations: ['43-34=9', '71-69=2'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,60 unequal: No Solution Moving to Node #0,3,1 Current State: 60:[28, 35], Operations: ['71-43=28', '69-34=35'] Exploring Operation: 28+35=63, Resulting Numbers: [63] 63,60 unequal: No Solution Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 28*35=980, Resulting Numbers: [980] 980,60 unequal: No Solution Moving to Node #0,3,0 Current State: 60:[69, 6], Operations: ['71-43=28', '34-28=6'] Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,60 unequal: No Solution Exploring Operation: 69*6=414, Resulting Numbers: [414] 414,60 unequal: No Solution Exploring Operation: 69+6=75, Resulting Numbers: [75] 75,60 unequal: No Solution Moving to Node #0,3,3 Current State: 60:[69, 62], Operations: ['71-43=28', '34+28=62'] Exploring Operation: 69+62=131, Resulting Numbers: [131] 131,60 unequal: No Solution Exploring Operation: 69-62=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 69*62=4278, Resulting Numbers: [4278] 4278,60 unequal: No Solution Moving to Node #0,1,2 Current State: 60:[71, 60], Operations: ['43-34=9', '69-9=60'] Exploring Operation: 71-60=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 71*60=4260, Resulting Numbers: [4260] 4260,60 unequal: No Solution Exploring Operation: 71+60=131, Resulting Numbers: [131] 131,60 unequal: No Solution Moving to Node #0,1,3 Current State: 60:[69, 62], Operations: ['43-34=9', '71-9=62'] Exploring Operation: 69-62=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 69+62=131, Resulting Numbers: [131] 131,60 unequal: No Solution Exploring Operation: 69*62=4278, Resulting Numbers: [4278] 4278,60 unequal: No Solution Moving to Node #0,2,1 Current State: 60:[43, 32], Operations: ['71-69=2', '34-2=32'] Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,60 unequal: No Solution Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,60 unequal: No Solution Moving to Node #0,2,0 Current State: 60:[34, 41], Operations: ['71-69=2', '43-2=41'] Exploring Operation: 34*41=1394, Resulting Numbers: [1394] 1394,60 unequal: No Solution Exploring Operation: 34+41=75, Resulting Numbers: [75] 75,60 unequal: No Solution Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,2,3 Current State: 60:[43, 17], Operations: ['71-69=2', '34/2=17'] Exploring Operation: 43+17=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[69, 34, 71, 43], Operations: [] Exploring Operation: 71-69=2, Resulting Numbers: [34, 43, 2] Generated Node #0,2: 60:[34, 43, 2] Operation: 71-69=2 Moving to Node #0,2 Current State: 60:[34, 43, 2], Operations: ['71-69=2'] Exploring Operation: 34/2=17, Resulting Numbers: [43, 17] Generated Node #0,2,3: 60:[43, 17] Operation: 34/2=17 Moving to Node #0,2,3 Current State: 60:[43, 17], Operations: ['71-69=2', '34/2=17'] Exploring Operation: 43+17=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
0.944444
hs_4
sum_heuristic
[ 68, 64, 40, 34 ]
22
[ "68+64=132", "40-34=6", "132/6=22" ]
Current State: 22:[68, 64, 40, 34], Operations: [] Exploring Operation: 68+64=132, Resulting Numbers: [40, 34, 132] Generated Node #2: [40, 34, 132] from Operation: 68+64=132 Current State: 22:[40, 34, 132], Operations: ['68+64=132'] Exploring Operation: 40-34=6, Resulting Numbers: [132, 6] Generated Node #3: [132, 6] from Operation: 40-34=6 Current State: 22:[132, 6], Operations: ['68+64=132', '40-34=6'] Exploring Operation: 132/6=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[68, 64, 40, 34], Operations: [] Exploring Operation: 68-40=28, Resulting Numbers: [64, 34, 28] Generated Node #0,0: 22:[64, 34, 28] Operation: 68-40=28 Exploring Operation: 64-40=24, Resulting Numbers: [68, 34, 24] Generated Node #0,1: 22:[68, 34, 24] Operation: 64-40=24 Exploring Operation: 68-64=4, Resulting Numbers: [40, 34, 4] Generated Node #0,2: 22:[40, 34, 4] Operation: 68-64=4 Exploring Operation: 68/34=2, Resulting Numbers: [64, 40, 2] Generated Node #0,3: 22:[64, 40, 2] Operation: 68/34=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[40, 34, 4], Operations: ['68-64=4'] Exploring Operation: 40-4=36, Resulting Numbers: [34, 36] Generated Node #0,2,0: 22:[34, 36] Operation: 40-4=36 Exploring Operation: 34-4=30, Resulting Numbers: [40, 30] Generated Node #0,2,1: 22:[40, 30] Operation: 34-4=30 Exploring Operation: 40-34=6, Resulting Numbers: [4, 6] Generated Node #0,2,2: 22:[4, 6] Operation: 40-34=6 Exploring Operation: 40/4=10, Resulting Numbers: [34, 10] Generated Node #0,2,3: 22:[34, 10] Operation: 40/4=10 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 22:[4, 6], Operations: ['68-64=4', '40-34=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,22 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,22 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 22:[34, 10], Operations: ['68-64=4', '40/4=10'] Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,22 unequal: No Solution Exploring Operation: 34+10=44, Resulting Numbers: [44] 44,22 unequal: No Solution Exploring Operation: 34*10=340, Resulting Numbers: [340] 340,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 22:[34, 36], Operations: ['68-64=4', '40-4=36'] Exploring Operation: 34+36=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 34*36=1224, Resulting Numbers: [1224] 1224,22 unequal: No Solution Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 22:[40, 30], Operations: ['68-64=4', '34-4=30'] Exploring Operation: 40*30=1200, Resulting Numbers: [1200] 1200,22 unequal: No Solution Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[64, 34, 28], Operations: ['68-40=28'] Exploring Operation: 34-28=6, Resulting Numbers: [64, 6] Generated Node #0,0,0: 22:[64, 6] Operation: 34-28=6 Exploring Operation: 64+34=98, Resulting Numbers: [28, 98] Generated Node #0,0,1: 22:[28, 98] Operation: 64+34=98 Exploring Operation: 64-28=36, Resulting Numbers: [34, 36] Generated Node #0,0,2: 22:[34, 36] Operation: 64-28=36 Exploring Operation: 64-34=30, Resulting Numbers: [28, 30] Generated Node #0,0,3: 22:[28, 30] Operation: 64-34=30 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 22:[28, 30], Operations: ['68-40=28', '64-34=30'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 28*30=840, Resulting Numbers: [840] 840,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 22:[34, 36], Operations: ['68-40=28', '64-28=36'] Exploring Operation: 34+36=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 34*36=1224, Resulting Numbers: [1224] 1224,22 unequal: No Solution Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 22:[64, 6], Operations: ['68-40=28', '34-28=6'] Exploring Operation: 64*6=384, Resulting Numbers: [384] 384,22 unequal: No Solution Exploring Operation: 64-6=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 64+6=70, Resulting Numbers: [70] 70,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 22:[28, 98], Operations: ['68-40=28', '64+34=98'] Exploring Operation: 28*98=2744, Resulting Numbers: [2744] 2744,22 unequal: No Solution Exploring Operation: 28+98=126, Resulting Numbers: [126] 126,22 unequal: No Solution Exploring Operation: 98-28=70, Resulting Numbers: [70] 70,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[68, 34, 24], Operations: ['64-40=24'] Exploring Operation: 34-24=10, Resulting Numbers: [68, 10] Generated Node #0,1,0: 22:[68, 10] Operation: 34-24=10 Exploring Operation: 68-34=34, Resulting Numbers: [24, 34] Generated Node #0,1,1: 22:[24, 34] Operation: 68-34=34 Exploring Operation: 68/34=2, Resulting Numbers: [24, 2] Generated Node #0,1,2: 22:[24, 2] Operation: 68/34=2 Exploring Operation: 68-24=44, Resulting Numbers: [34, 44] Generated Node #0,1,3: 22:[34, 44] Operation: 68-24=44 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 22:[24, 2], Operations: ['64-40=24', '68/34=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,22 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,22 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[68, 64, 40, 34], Operations: [] Exploring Operation: 64-40=24, Resulting Numbers: [68, 34, 24] Generated Node #0,1: 22:[68, 34, 24] Operation: 64-40=24 Moving to Node #0,1 Current State: 22:[68, 34, 24], Operations: ['64-40=24'] Exploring Operation: 68/34=2, Resulting Numbers: [24, 2] Generated Node #0,1,2: 22:[24, 2] Operation: 68/34=2 Moving to Node #0,1,2 Current State: 22:[24, 2], Operations: ['64-40=24', '68/34=2'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.959201
hs_4
sum_heuristic
[ 36, 44, 32, 73 ]
76
[ "44-32=12", "36/12=3", "73+3=76" ]
Current State: 76:[36, 44, 32, 73], Operations: [] Exploring Operation: 44-32=12, Resulting Numbers: [36, 73, 12] Generated Node #2: [36, 73, 12] from Operation: 44-32=12 Current State: 76:[36, 73, 12], Operations: ['44-32=12'] Exploring Operation: 36/12=3, Resulting Numbers: [73, 3] Generated Node #3: [73, 3] from Operation: 36/12=3 Current State: 76:[73, 3], Operations: ['44-32=12', '36/12=3'] Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[36, 44, 32, 73], Operations: [] Exploring Operation: 44+32=76, Resulting Numbers: [36, 73, 76] Generated Node #0,0: 76:[36, 73, 76] Operation: 44+32=76 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[36, 73, 76], Operations: ['44+32=76'] Exploring Operation: 73-36=37, Resulting Numbers: [76, 37] Generated Node #0,0,0: 76:[76, 37] Operation: 73-36=37 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 76:[76, 37], Operations: ['44+32=76', '73-36=37'] Exploring Operation: 76-37=39, Resulting Numbers: [39] 39,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 93, 28, 24, 39 ]
25
[ "93+24=117", "117/39=3", "28-3=25" ]
Current State: 25:[93, 28, 24, 39], Operations: [] Exploring Operation: 93+24=117, Resulting Numbers: [28, 39, 117] Generated Node #2: [28, 39, 117] from Operation: 93+24=117 Current State: 25:[28, 39, 117], Operations: ['93+24=117'] Exploring Operation: 117/39=3, Resulting Numbers: [28, 3] Generated Node #3: [28, 3] from Operation: 117/39=3 Current State: 25:[28, 3], Operations: ['93+24=117', '117/39=3'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[93, 28, 24, 39], Operations: [] Exploring Operation: 93-28=65, Resulting Numbers: [24, 39, 65] Generated Node #0,0: 25:[24, 39, 65] Operation: 93-28=65 Exploring Operation: 93-39=54, Resulting Numbers: [28, 24, 54] Generated Node #0,1: 25:[28, 24, 54] Operation: 93-39=54 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[28, 24, 54], Operations: ['93-39=54'] Exploring Operation: 54-28=26, Resulting Numbers: [24, 26] Generated Node #0,1,0: 25:[24, 26] Operation: 54-28=26 Exploring Operation: 54-24=30, Resulting Numbers: [28, 30] Generated Node #0,1,1: 25:[28, 30] Operation: 54-24=30 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[24, 26], Operations: ['93-39=54', '54-28=26'] Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,25 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 #0,1,1 Current State: 25:[28, 30], Operations: ['93-39=54', '54-24=30'] Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,25 unequal: No Solution Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,25 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: 25:[24, 39, 65], Operations: ['93-28=65'] Exploring Operation: 65-39=26, Resulting Numbers: [24, 26] Generated Node #0,0,0: 25:[24, 26] Operation: 65-39=26 Exploring Operation: 65-24=41, Resulting Numbers: [39, 41] Generated Node #0,0,1: 25:[39, 41] Operation: 65-24=41 Moving to Node #0,0,0 Current State: 25:[24, 26], Operations: ['93-28=65', '65-39=26'] Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[39, 41], Operations: ['93-28=65', '65-24=41'] Exploring Operation: 39+41=80, Resulting Numbers: [80] 80,25 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 52, 24, 13, 47 ]
67
[ "52/13=4", "24+47=71", "71-4=67" ]
Current State: 67:[52, 24, 13, 47], Operations: [] Exploring Operation: 52/13=4, Resulting Numbers: [24, 47, 4] Generated Node #2: [24, 47, 4] from Operation: 52/13=4 Current State: 67:[24, 47, 4], Operations: ['52/13=4'] Exploring Operation: 24+47=71, Resulting Numbers: [4, 71] Generated Node #3: [4, 71] from Operation: 24+47=71 Current State: 67:[4, 71], Operations: ['52/13=4', '24+47=71'] Exploring Operation: 71-4=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[52, 24, 13, 47], Operations: [] Exploring Operation: 52+13=65, Resulting Numbers: [24, 47, 65] Generated Node #0,0: 67:[24, 47, 65] Operation: 52+13=65 Exploring Operation: 24+13=37, Resulting Numbers: [52, 47, 37] Generated Node #0,1: 67:[52, 47, 37] Operation: 24+13=37 Moving to Node #0,0 Current State: 67:[24, 47, 65], Operations: ['52+13=65'] Exploring Operation: 24+47=71, Resulting Numbers: [65, 71] Generated Node #0,0,0: 67:[65, 71] Operation: 24+47=71 Exploring Operation: 24+65=89, Resulting Numbers: [47, 89] Generated Node #0,0,1: 67:[47, 89] Operation: 24+65=89 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[65, 71], Operations: ['52+13=65', '24+47=71'] Exploring Operation: 65+71=136, Resulting Numbers: [136] 136,67 unequal: No Solution Exploring Operation: 71-65=6, Resulting Numbers: [6] 6,67 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 #0,0,1 Current State: 67:[47, 89], Operations: ['52+13=65', '24+65=89'] Exploring Operation: 47+89=136, Resulting Numbers: [136] 136,67 unequal: No Solution Exploring Operation: 89-47=42, Resulting Numbers: [42] 42,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 67:[52, 47, 37], Operations: ['24+13=37'] Exploring Operation: 52+37=89, Resulting Numbers: [47, 89] Generated Node #0,1,0: 67:[47, 89] Operation: 52+37=89 Exploring Operation: 47+37=84, Resulting Numbers: [52, 84] Generated Node #0,1,1: 67:[52, 84] Operation: 47+37=84 Moving to Node #0,1,1 Current State: 67:[52, 84], Operations: ['24+13=37', '47+37=84'] Exploring Operation: 84-52=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 52+84=136, Resulting Numbers: [136] 136,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[47, 89], Operations: ['24+13=37', '52+37=89'] Exploring Operation: 47+89=136, Resulting Numbers: [136] 136,67 unequal: No Solution Exploring Operation: 89-47=42, Resulting Numbers: [42] 42,67 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 57, 14, 62, 63 ]
42
[ "57-14=43", "63-62=1", "43-1=42" ]
Current State: 42:[57, 14, 62, 63], Operations: [] Exploring Operation: 57-14=43, Resulting Numbers: [62, 63, 43] Generated Node #2: [62, 63, 43] from Operation: 57-14=43 Current State: 42:[62, 63, 43], Operations: ['57-14=43'] Exploring Operation: 63-62=1, Resulting Numbers: [43, 1] Generated Node #3: [43, 1] from Operation: 63-62=1 Current State: 42:[43, 1], Operations: ['57-14=43', '63-62=1'] Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[57, 14, 62, 63], Operations: [] Exploring Operation: 62-14=48, Resulting Numbers: [57, 63, 48] Generated Node #0,0: 42:[57, 63, 48] Operation: 62-14=48 Exploring Operation: 63-62=1, Resulting Numbers: [57, 14, 1] Generated Node #0,1: 42:[57, 14, 1] Operation: 63-62=1 Exploring Operation: 57-14=43, Resulting Numbers: [62, 63, 43] Generated Node #0,2: 42:[62, 63, 43] Operation: 57-14=43 Exploring Operation: 62-57=5, Resulting Numbers: [14, 63, 5] Generated Node #0,3: 42:[14, 63, 5] Operation: 62-57=5 Exploring Operation: 63-57=6, Resulting Numbers: [14, 62, 6] Generated Node #0,4: 42:[14, 62, 6] Operation: 63-57=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[57, 14, 1], Operations: ['63-62=1'] Exploring Operation: 57-14=43, Resulting Numbers: [1, 43] Generated Node #0,1,0: 42:[1, 43] Operation: 57-14=43 Exploring Operation: 14*1=14, Resulting Numbers: [57, 14] Generated Node #0,1,1: 42:[57, 14] Operation: 14*1=14 Exploring Operation: 57/1=57, Resulting Numbers: [14, 57] Generated Node #0,1,2: 42:[14, 57] Operation: 57/1=57 Exploring Operation: 57*1=57, Resulting Numbers: [14, 57] Generated Node #0,1,3: 42:[14, 57] Operation: 57*1=57 Exploring Operation: 57-1=56, Resulting Numbers: [14, 56] Generated Node #0,1,4: 42:[14, 56] Operation: 57-1=56 Moving to Node #0,1,0 Current State: 42:[1, 43], Operations: ['63-62=1', '57-14=43'] Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[57, 14, 62, 63], Operations: [] Exploring Operation: 63-62=1, Resulting Numbers: [57, 14, 1] Generated Node #0,1: 42:[57, 14, 1] Operation: 63-62=1 Moving to Node #0,1 Current State: 42:[57, 14, 1], Operations: ['63-62=1'] Exploring Operation: 57-14=43, Resulting Numbers: [1, 43] Generated Node #0,1,0: 42:[1, 43] Operation: 57-14=43 Moving to Node #0,1,0 Current State: 42:[1, 43], Operations: ['63-62=1', '57-14=43'] Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 36, 5, 20, 12 ]
18
[ "36/12=3", "20-5=15", "3+15=18" ]
Current State: 18:[36, 5, 20, 12], Operations: [] Exploring Operation: 36/12=3, Resulting Numbers: [5, 20, 3] Generated Node #2: [5, 20, 3] from Operation: 36/12=3 Current State: 18:[5, 20, 3], Operations: ['36/12=3'] Exploring Operation: 20-5=15, Resulting Numbers: [3, 15] Generated Node #3: [3, 15] from Operation: 20-5=15 Current State: 18:[3, 15], Operations: ['36/12=3', '20-5=15'] Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[36, 5, 20, 12], Operations: [] Exploring Operation: 36-12=24, Resulting Numbers: [5, 20, 24] Generated Node #0,0: 18:[5, 20, 24] Operation: 36-12=24 Exploring Operation: 36-20=16, Resulting Numbers: [5, 12, 16] Generated Node #0,1: 18:[5, 12, 16] Operation: 36-20=16 Exploring Operation: 36/12=3, Resulting Numbers: [5, 20, 3] Generated Node #0,2: 18:[5, 20, 3] Operation: 36/12=3 Moving to Node #0,2 Current State: 18:[5, 20, 3], Operations: ['36/12=3'] Exploring Operation: 5-3=2, Resulting Numbers: [20, 2] Generated Node #0,2,0: 18:[20, 2] Operation: 5-3=2 Exploring Operation: 20/5=4, Resulting Numbers: [3, 4] Generated Node #0,2,1: 18:[3, 4] Operation: 20/5=4 Exploring Operation: 20-3=17, Resulting Numbers: [5, 17] Generated Node #0,2,2: 18:[5, 17] Operation: 20-3=17 Moving to Node #0,1 Current State: 18:[5, 12, 16], Operations: ['36-20=16'] Exploring Operation: 5+12=17, Resulting Numbers: [16, 17] Generated Node #0,1,0: 18:[16, 17] Operation: 5+12=17 Exploring Operation: 16-12=4, Resulting Numbers: [5, 4] Generated Node #0,1,1: 18:[5, 4] Operation: 16-12=4 Exploring Operation: 12-5=7, Resulting Numbers: [16, 7] Generated Node #0,1,2: 18:[16, 7] Operation: 12-5=7 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[5, 4], Operations: ['36-20=16', '16-12=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 5+4=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 #0,1,0 Current State: 18:[16, 17], Operations: ['36-20=16', '5+12=17'] Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,18 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 16+17=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 #0,1,2 Current State: 18:[16, 7], Operations: ['36-20=16', '12-5=7'] Exploring Operation: 16*7=112, Resulting Numbers: [112] 112,18 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,18 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:[5, 20, 24], Operations: ['36-12=24'] Exploring Operation: 24-20=4, Resulting Numbers: [5, 4] Generated Node #0,0,0: 18:[5, 4] Operation: 24-20=4 Exploring Operation: 24-5=19, Resulting Numbers: [20, 19] Generated Node #0,0,1: 18:[20, 19] Operation: 24-5=19 Exploring Operation: 20/5=4, Resulting Numbers: [24, 4] Generated Node #0,0,2: 18:[24, 4] Operation: 20/5=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[5, 4], Operations: ['36-12=24', '24-20=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 5+4=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 #0,0,1 Current State: 18:[20, 19], Operations: ['36-12=24', '24-5=19'] Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 20+19=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 20*19=380, Resulting Numbers: [380] 380,18 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:[24, 4], Operations: ['36-12=24', '20/5=4'] Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 18:[3, 4], Operations: ['36/12=3', '20/5=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[20, 2], Operations: ['36/12=3', '5-3=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[36, 5, 20, 12], Operations: [] Exploring Operation: 36/12=3, Resulting Numbers: [5, 20, 3] Generated Node #0,2: 18:[5, 20, 3] Operation: 36/12=3 Moving to Node #0,2 Current State: 18:[5, 20, 3], Operations: ['36/12=3'] Exploring Operation: 5-3=2, Resulting Numbers: [20, 2] Generated Node #0,2,0: 18:[20, 2] Operation: 5-3=2 Moving to Node #0,2,0 Current State: 18:[20, 2], Operations: ['36/12=3', '5-3=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.966146
hs_3
sum_heuristic
[ 92, 65, 79, 52 ]
26
[ "92+65=157", "79+52=131", "157-131=26" ]
Current State: 26:[92, 65, 79, 52], Operations: [] Exploring Operation: 92+65=157, Resulting Numbers: [79, 52, 157] Generated Node #2: [79, 52, 157] from Operation: 92+65=157 Current State: 26:[79, 52, 157], Operations: ['92+65=157'] Exploring Operation: 79+52=131, Resulting Numbers: [157, 131] Generated Node #3: [157, 131] from Operation: 79+52=131 Current State: 26:[157, 131], Operations: ['92+65=157', '79+52=131'] Exploring Operation: 157-131=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[92, 65, 79, 52], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [65, 52, 13] Generated Node #0,0: 26:[65, 52, 13] Operation: 92-79=13 Exploring Operation: 79-65=14, Resulting Numbers: [92, 52, 14] Generated Node #0,1: 26:[92, 52, 14] Operation: 79-65=14 Exploring Operation: 92-65=27, Resulting Numbers: [79, 52, 27] Generated Node #0,2: 26:[79, 52, 27] Operation: 92-65=27 Moving to Node #0,0 Current State: 26:[65, 52, 13], Operations: ['92-79=13'] Exploring Operation: 65/13=5, Resulting Numbers: [52, 5] Generated Node #0,0,0: 26:[52, 5] Operation: 65/13=5 Exploring Operation: 52/13=4, Resulting Numbers: [65, 4] Generated Node #0,0,1: 26:[65, 4] Operation: 52/13=4 Exploring Operation: 65-52=13, Resulting Numbers: [13, 13] Generated Node #0,0,2: 26:[13, 13] Operation: 65-52=13 Moving to Node #0,2 Current State: 26:[79, 52, 27], Operations: ['92-65=27'] Exploring Operation: 79-27=52, Resulting Numbers: [52, 52] Generated Node #0,2,0: 26:[52, 52] Operation: 79-27=52 Exploring Operation: 79-52=27, Resulting Numbers: [27, 27] Generated Node #0,2,1: 26:[27, 27] Operation: 79-52=27 Exploring Operation: 52-27=25, Resulting Numbers: [79, 25] Generated Node #0,2,2: 26:[79, 25] Operation: 52-27=25 Moving to Node #0,1 Current State: 26:[92, 52, 14], Operations: ['79-65=14'] Exploring Operation: 92-14=78, Resulting Numbers: [52, 78] Generated Node #0,1,0: 26:[52, 78] Operation: 92-14=78 Exploring Operation: 92-52=40, Resulting Numbers: [14, 40] Generated Node #0,1,1: 26:[14, 40] Operation: 92-52=40 Exploring Operation: 52-14=38, Resulting Numbers: [92, 38] Generated Node #0,1,2: 26:[92, 38] Operation: 52-14=38 Moving to Node #0,0,2 Current State: 26:[13, 13], Operations: ['92-79=13', '65-52=13'] Exploring Operation: 13+13=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[92, 65, 79, 52], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [65, 52, 13] Generated Node #0,0: 26:[65, 52, 13] Operation: 92-79=13 Moving to Node #0,0 Current State: 26:[65, 52, 13], Operations: ['92-79=13'] Exploring Operation: 65-52=13, Resulting Numbers: [13, 13] Generated Node #0,0,2: 26:[13, 13] Operation: 65-52=13 Moving to Node #0,0,2 Current State: 26:[13, 13], Operations: ['92-79=13', '65-52=13'] Exploring Operation: 13+13=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
0.985243
hs_3
mult_heuristic
[ 69, 1, 57, 71 ]
83
[ "69*1=69", "71-57=14", "69+14=83" ]
Current State: 83:[69, 1, 57, 71], Operations: [] Exploring Operation: 69*1=69, Resulting Numbers: [57, 71, 69] Generated Node #2: [57, 71, 69] from Operation: 69*1=69 Current State: 83:[57, 71, 69], Operations: ['69*1=69'] Exploring Operation: 71-57=14, Resulting Numbers: [69, 14] Generated Node #3: [69, 14] from Operation: 71-57=14 Current State: 83:[69, 14], Operations: ['69*1=69', '71-57=14'] Exploring Operation: 69+14=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[69, 1, 57, 71], Operations: [] Exploring Operation: 69+1=70, Resulting Numbers: [57, 71, 70] Generated Node #0,0: 83:[57, 71, 70] Operation: 69+1=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[57, 71, 70], Operations: ['69+1=70'] Exploring Operation: 57+70=127, Resulting Numbers: [71, 127] Generated Node #0,0,0: 83:[71, 127] Operation: 57+70=127 Moving to Node #0,0,0 Current State: 83:[71, 127], Operations: ['69+1=70', '57+70=127'] Exploring Operation: 127-71=56, Resulting Numbers: [56] 56,83 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
[ 50, 31, 65, 29 ]
17
[ "50-31=19", "65-29=36", "36-19=17" ]
Current State: 17:[50, 31, 65, 29], Operations: [] Exploring Operation: 50-31=19, Resulting Numbers: [65, 29, 19] Generated Node #2: [65, 29, 19] from Operation: 50-31=19 Current State: 17:[65, 29, 19], Operations: ['50-31=19'] Exploring Operation: 65-29=36, Resulting Numbers: [19, 36] Generated Node #3: [19, 36] from Operation: 65-29=36 Current State: 17:[19, 36], Operations: ['50-31=19', '65-29=36'] Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[50, 31, 65, 29], Operations: [] Exploring Operation: 65-50=15, Resulting Numbers: [31, 29, 15] Generated Node #0,0: 17:[31, 29, 15] Operation: 65-50=15 Moving to Node #0,0 Current State: 17:[31, 29, 15], Operations: ['65-50=15'] Exploring Operation: 31-15=16, Resulting Numbers: [29, 16] Generated Node #0,0,0: 17:[29, 16] Operation: 31-15=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 17:[29, 16], Operations: ['65-50=15', '31-15=16'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,17 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
[ 77, 68, 80, 39 ]
44
[ "77*68=5236", "80+39=119", "5236/119=44" ]
Current State: 44:[77, 68, 80, 39], Operations: [] Exploring Operation: 77*68=5236, Resulting Numbers: [80, 39, 5236] Generated Node #2: [80, 39, 5236] from Operation: 77*68=5236 Current State: 44:[80, 39, 5236], Operations: ['77*68=5236'] Exploring Operation: 80+39=119, Resulting Numbers: [5236, 119] Generated Node #3: [5236, 119] from Operation: 80+39=119 Current State: 44:[5236, 119], Operations: ['77*68=5236', '80+39=119'] Exploring Operation: 5236/119=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[77, 68, 80, 39], Operations: [] Exploring Operation: 80-68=12, Resulting Numbers: [77, 39, 12] Generated Node #0,0: 44:[77, 39, 12] Operation: 80-68=12 Exploring Operation: 77-68=9, Resulting Numbers: [80, 39, 9] Generated Node #0,1: 44:[80, 39, 9] Operation: 77-68=9 Exploring Operation: 80-77=3, Resulting Numbers: [68, 39, 3] Generated Node #0,2: 44:[68, 39, 3] Operation: 80-77=3 Exploring Operation: 80-39=41, Resulting Numbers: [77, 68, 41] Generated Node #0,3: 44:[77, 68, 41] Operation: 80-39=41 Moving to Node #0,2 Current State: 44:[68, 39, 3], Operations: ['80-77=3'] Exploring Operation: 39+3=42, Resulting Numbers: [68, 42] Generated Node #0,2,0: 44:[68, 42] Operation: 39+3=42 Exploring Operation: 68-39=29, Resulting Numbers: [3, 29] Generated Node #0,2,1: 44:[3, 29] Operation: 68-39=29 Exploring Operation: 68-3=65, Resulting Numbers: [39, 65] Generated Node #0,2,2: 44:[39, 65] Operation: 68-3=65 Exploring Operation: 39/3=13, Resulting Numbers: [68, 13] Generated Node #0,2,3: 44:[68, 13] Operation: 39/3=13 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 44:[3, 29], Operations: ['80-77=3', '68-39=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,44 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,44 unequal: No Solution No 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: 44:[68, 42], Operations: ['80-77=3', '39+3=42'] Exploring Operation: 68-42=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 68*42=2856, Resulting Numbers: [2856] 2856,44 unequal: No Solution Exploring Operation: 68+42=110, Resulting Numbers: [110] 110,44 unequal: No Solution No 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: 44:[39, 65], Operations: ['80-77=3', '68-3=65'] Exploring Operation: 65-39=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 39+65=104, Resulting Numbers: [104] 104,44 unequal: No Solution Exploring Operation: 39*65=2535, Resulting Numbers: [2535] 2535,44 unequal: No Solution No 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: 44:[68, 13], Operations: ['80-77=3', '39/3=13'] Exploring Operation: 68+13=81, Resulting Numbers: [81] 81,44 unequal: No Solution Exploring Operation: 68*13=884, Resulting Numbers: [884] 884,44 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,44 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: 44:[77, 39, 12], Operations: ['80-68=12'] Exploring Operation: 77-39=38, Resulting Numbers: [12, 38] Generated Node #0,0,0: 44:[12, 38] Operation: 77-39=38 Exploring Operation: 39+12=51, Resulting Numbers: [77, 51] Generated Node #0,0,1: 44:[77, 51] Operation: 39+12=51 Exploring Operation: 77-12=65, Resulting Numbers: [39, 65] Generated Node #0,0,2: 44:[39, 65] Operation: 77-12=65 Exploring Operation: 39-12=27, Resulting Numbers: [77, 27] Generated Node #0,0,3: 44:[77, 27] Operation: 39-12=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[12, 38], Operations: ['80-68=12', '77-39=38'] Exploring Operation: 12*38=456, Resulting Numbers: [456] 456,44 unequal: No Solution Exploring Operation: 38-12=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 12+38=50, Resulting Numbers: [50] 50,44 unequal: No Solution No 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: 44:[39, 65], Operations: ['80-68=12', '77-12=65'] Exploring Operation: 39+65=104, Resulting Numbers: [104] 104,44 unequal: No Solution Exploring Operation: 65-39=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 39*65=2535, Resulting Numbers: [2535] 2535,44 unequal: No Solution No 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: 44:[77, 27], Operations: ['80-68=12', '39-12=27'] Exploring Operation: 77*27=2079, Resulting Numbers: [2079] 2079,44 unequal: No Solution Exploring Operation: 77-27=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 77+27=104, Resulting Numbers: [104] 104,44 unequal: No Solution No 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: 44:[77, 51], Operations: ['80-68=12', '39+12=51'] Exploring Operation: 77*51=3927, Resulting Numbers: [3927] 3927,44 unequal: No Solution Exploring Operation: 77-51=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 77+51=128, Resulting Numbers: [128] 128,44 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: 44:[80, 39, 9], Operations: ['77-68=9'] Exploring Operation: 39-9=30, Resulting Numbers: [80, 30] Generated Node #0,1,0: 44:[80, 30] Operation: 39-9=30 Exploring Operation: 39+9=48, Resulting Numbers: [80, 48] Generated Node #0,1,1: 44:[80, 48] Operation: 39+9=48 Exploring Operation: 80-39=41, Resulting Numbers: [9, 41] Generated Node #0,1,2: 44:[9, 41] Operation: 80-39=41 Exploring Operation: 80-9=71, Resulting Numbers: [39, 71] Generated Node #0,1,3: 44:[39, 71] Operation: 80-9=71 Moving to Node #0,3 Current State: 44:[77, 68, 41], Operations: ['80-39=41'] Exploring Operation: 68-41=27, Resulting Numbers: [77, 27] Generated Node #0,3,0: 44:[77, 27] Operation: 68-41=27 Exploring Operation: 77-68=9, Resulting Numbers: [41, 9] Generated Node #0,3,1: 44:[41, 9] Operation: 77-68=9 Exploring Operation: 77-41=36, Resulting Numbers: [68, 36] Generated Node #0,3,2: 44:[68, 36] Operation: 77-41=36 Exploring Operation: 77+41=118, Resulting Numbers: [68, 118] Generated Node #0,3,3: 44:[68, 118] Operation: 77+41=118 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 44:[41, 9], Operations: ['80-39=41', '77-68=9'] Exploring Operation: 41*9=369, Resulting Numbers: [369] 369,44 unequal: No Solution Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,44 unequal: No Solution Exploring Operation: 41+9=50, Resulting Numbers: [50] 50,44 unequal: No Solution No 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: 44:[68, 36], Operations: ['80-39=41', '77-41=36'] Exploring Operation: 68+36=104, Resulting Numbers: [104] 104,44 unequal: No Solution Exploring Operation: 68*36=2448, Resulting Numbers: [2448] 2448,44 unequal: No Solution Exploring Operation: 68-36=32, Resulting Numbers: [32] 32,44 unequal: No Solution No 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: 44:[77, 27], Operations: ['80-39=41', '68-41=27'] Exploring Operation: 77*27=2079, Resulting Numbers: [2079] 2079,44 unequal: No Solution Exploring Operation: 77-27=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 77+27=104, Resulting Numbers: [104] 104,44 unequal: No Solution No 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: 44:[68, 118], Operations: ['80-39=41', '77+41=118'] Exploring Operation: 118-68=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 68*118=8024, Resulting Numbers: [8024] 8024,44 unequal: No Solution Exploring Operation: 68+118=186, Resulting Numbers: [186] 186,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 44:[9, 41], Operations: ['77-68=9', '80-39=41'] Exploring Operation: 9+41=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,44 unequal: No Solution Exploring Operation: 9*41=369, Resulting Numbers: [369] 369,44 unequal: No Solution Moving to Node #0,1,3 Current State: 44:[39, 71], Operations: ['77-68=9', '80-9=71'] Exploring Operation: 39*71=2769, Resulting Numbers: [2769] 2769,44 unequal: No Solution Exploring Operation: 39+71=110, Resulting Numbers: [110] 110,44 unequal: No Solution Exploring Operation: 71-39=32, Resulting Numbers: [32] 32,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[80, 48], Operations: ['77-68=9', '39+9=48'] Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,44 unequal: No Solution Exploring Operation: 80*48=3840, Resulting Numbers: [3840] 3840,44 unequal: No Solution Exploring Operation: 80+48=128, Resulting Numbers: [128] 128,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[80, 30], Operations: ['77-68=9', '39-9=30'] Exploring Operation: 80+30=110, Resulting Numbers: [110] 110,44 unequal: No Solution Exploring Operation: 80*30=2400, Resulting Numbers: [2400] 2400,44 unequal: No Solution Exploring Operation: 80-30=50, Resulting Numbers: [50] 50,44 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 81, 30, 88, 19 ]
56
[ "81-30=51", "88+19=107", "107-51=56" ]
Current State: 56:[81, 30, 88, 19], Operations: [] Exploring Operation: 81-30=51, Resulting Numbers: [88, 19, 51] Generated Node #2: [88, 19, 51] from Operation: 81-30=51 Current State: 56:[88, 19, 51], Operations: ['81-30=51'] Exploring Operation: 88+19=107, Resulting Numbers: [51, 107] Generated Node #3: [51, 107] from Operation: 88+19=107 Current State: 56:[51, 107], Operations: ['81-30=51', '88+19=107'] Exploring Operation: 107-51=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[81, 30, 88, 19], Operations: [] Exploring Operation: 88-30=58, Resulting Numbers: [81, 19, 58] Generated Node #0,0: 56:[81, 19, 58] Operation: 88-30=58 Exploring Operation: 88-81=7, Resulting Numbers: [30, 19, 7] Generated Node #0,1: 56:[30, 19, 7] Operation: 88-81=7 Exploring Operation: 88-19=69, Resulting Numbers: [81, 30, 69] Generated Node #0,2: 56:[81, 30, 69] Operation: 88-19=69 Exploring Operation: 81-30=51, Resulting Numbers: [88, 19, 51] Generated Node #0,3: 56:[88, 19, 51] Operation: 81-30=51 Exploring Operation: 81-19=62, Resulting Numbers: [30, 88, 62] Generated Node #0,4: 56:[30, 88, 62] Operation: 81-19=62 Moving to Node #0,1 Current State: 56:[30, 19, 7], Operations: ['88-81=7'] Exploring Operation: 30-7=23, Resulting Numbers: [19, 23] Generated Node #0,1,0: 56:[19, 23] Operation: 30-7=23 Exploring Operation: 30-19=11, Resulting Numbers: [7, 11] Generated Node #0,1,1: 56:[7, 11] Operation: 30-19=11 Exploring Operation: 19+7=26, Resulting Numbers: [30, 26] Generated Node #0,1,2: 56:[30, 26] Operation: 19+7=26 Exploring Operation: 30+19=49, Resulting Numbers: [7, 49] Generated Node #0,1,3: 56:[7, 49] Operation: 30+19=49 Exploring Operation: 19-7=12, Resulting Numbers: [30, 12] Generated Node #0,1,4: 56:[30, 12] Operation: 19-7=12 Moving to Node #0,0 Current State: 56:[81, 19, 58], Operations: ['88-30=58'] Exploring Operation: 58-19=39, Resulting Numbers: [81, 39] Generated Node #0,0,0: 56:[81, 39] Operation: 58-19=39 Exploring Operation: 19+58=77, Resulting Numbers: [81, 77] Generated Node #0,0,1: 56:[81, 77] Operation: 19+58=77 Exploring Operation: 81-58=23, Resulting Numbers: [19, 23] Generated Node #0,0,2: 56:[19, 23] Operation: 81-58=23 Exploring Operation: 81-19=62, Resulting Numbers: [58, 62] Generated Node #0,0,3: 56:[58, 62] Operation: 81-19=62 Exploring Operation: 81+19=100, Resulting Numbers: [58, 100] Generated Node #0,0,4: 56:[58, 100] Operation: 81+19=100 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 56:[58, 62], Operations: ['88-30=58', '81-19=62'] Exploring Operation: 58+62=120, Resulting Numbers: [120] 120,56 unequal: No Solution Exploring Operation: 58*62=3596, Resulting Numbers: [3596] 3596,56 unequal: No Solution Exploring Operation: 62-58=4, Resulting Numbers: [4] 4,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 56:[19, 23], Operations: ['88-30=58', '81-58=23'] Exploring Operation: 19+23=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 23-19=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 19*23=437, Resulting Numbers: [437] 437,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[81, 39], Operations: ['88-30=58', '58-19=39'] Exploring Operation: 81+39=120, Resulting Numbers: [120] 120,56 unequal: No Solution Exploring Operation: 81*39=3159, Resulting Numbers: [3159] 3159,56 unequal: No Solution Exploring Operation: 81-39=42, Resulting Numbers: [42] 42,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 56:[81, 77], Operations: ['88-30=58', '19+58=77'] Exploring Operation: 81*77=6237, Resulting Numbers: [6237] 6237,56 unequal: No Solution Exploring Operation: 81-77=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 81+77=158, Resulting Numbers: [158] 158,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 56:[58, 100], Operations: ['88-30=58', '81+19=100'] Exploring Operation: 58*100=5800, Resulting Numbers: [5800] 5800,56 unequal: No Solution Exploring Operation: 100-58=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 58+100=158, Resulting Numbers: [158] 158,56 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: 56:[81, 30, 69], Operations: ['88-19=69'] Exploring Operation: 30+69=99, Resulting Numbers: [81, 99] Generated Node #0,2,0: 56:[81, 99] Operation: 30+69=99 Exploring Operation: 69-30=39, Resulting Numbers: [81, 39] Generated Node #0,2,1: 56:[81, 39] Operation: 69-30=39 Exploring Operation: 81-69=12, Resulting Numbers: [30, 12] Generated Node #0,2,2: 56:[30, 12] Operation: 81-69=12 Exploring Operation: 81+30=111, Resulting Numbers: [69, 111] Generated Node #0,2,3: 56:[69, 111] Operation: 81+30=111 Exploring Operation: 81-30=51, Resulting Numbers: [69, 51] Generated Node #0,2,4: 56:[69, 51] Operation: 81-30=51 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 56:[30, 12], Operations: ['88-19=69', '81-69=12'] Exploring Operation: 30*12=360, Resulting Numbers: [360] 360,56 unequal: No Solution Exploring Operation: 30+12=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 56:[69, 51], Operations: ['88-19=69', '81-30=51'] Exploring Operation: 69+51=120, Resulting Numbers: [120] 120,56 unequal: No Solution Exploring Operation: 69*51=3519, Resulting Numbers: [3519] 3519,56 unequal: No Solution Exploring Operation: 69-51=18, Resulting Numbers: [18] 18,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 56:[81, 39], Operations: ['88-19=69', '69-30=39'] Exploring Operation: 81*39=3159, Resulting Numbers: [3159] 3159,56 unequal: No Solution Exploring Operation: 81+39=120, Resulting Numbers: [120] 120,56 unequal: No Solution Exploring Operation: 81-39=42, Resulting Numbers: [42] 42,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 56:[81, 99], Operations: ['88-19=69', '30+69=99'] Exploring Operation: 81*99=8019, Resulting Numbers: [8019] 8019,56 unequal: No Solution Exploring Operation: 81+99=180, Resulting Numbers: [180] 180,56 unequal: No Solution Exploring Operation: 99-81=18, Resulting Numbers: [18] 18,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 56:[69, 111], Operations: ['88-19=69', '81+30=111'] Exploring Operation: 111-69=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 69+111=180, Resulting Numbers: [180] 180,56 unequal: No Solution Exploring Operation: 69*111=7659, Resulting Numbers: [7659] 7659,56 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: 56:[30, 88, 62], Operations: ['81-19=62'] Exploring Operation: 62-30=32, Resulting Numbers: [88, 32] Generated Node #0,4,0: 56:[88, 32] Operation: 62-30=32 Exploring Operation: 30+62=92, Resulting Numbers: [88, 92] Generated Node #0,4,1: 56:[88, 92] Operation: 30+62=92 Exploring Operation: 88-30=58, Resulting Numbers: [62, 58] Generated Node #0,4,2: 56:[62, 58] Operation: 88-30=58 Exploring Operation: 30+88=118, Resulting Numbers: [62, 118] Generated Node #0,4,3: 56:[62, 118] Operation: 30+88=118 Exploring Operation: 88-62=26, Resulting Numbers: [30, 26] Generated Node #0,4,4: 56:[30, 26] Operation: 88-62=26 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 56:[30, 26], Operations: ['81-19=62', '88-62=26'] Exploring Operation: 30+26=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[81, 30, 88, 19], Operations: [] Exploring Operation: 81-19=62, Resulting Numbers: [30, 88, 62] Generated Node #0,4: 56:[30, 88, 62] Operation: 81-19=62 Moving to Node #0,4 Current State: 56:[30, 88, 62], Operations: ['81-19=62'] Exploring Operation: 88-62=26, Resulting Numbers: [30, 26] Generated Node #0,4,4: 56:[30, 26] Operation: 88-62=26 Moving to Node #0,4,4 Current State: 56:[30, 26], Operations: ['81-19=62', '88-62=26'] Exploring Operation: 30+26=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.947917
hs_5
mult_heuristic
[ 1, 77, 6, 2 ]
44
[ "77-1=76", "76/2=38", "6+38=44" ]
Current State: 44:[1, 77, 6, 2], Operations: [] Exploring Operation: 77-1=76, Resulting Numbers: [6, 2, 76] Generated Node #2: [6, 2, 76] from Operation: 77-1=76 Current State: 44:[6, 2, 76], Operations: ['77-1=76'] Exploring Operation: 76/2=38, Resulting Numbers: [6, 38] Generated Node #3: [6, 38] from Operation: 76/2=38 Current State: 44:[6, 38], Operations: ['77-1=76', '76/2=38'] Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[1, 77, 6, 2], Operations: [] Exploring Operation: 77-6=71, Resulting Numbers: [1, 2, 71] Generated Node #0,0: 44:[1, 2, 71] Operation: 77-6=71 Exploring Operation: 77-1=76, Resulting Numbers: [6, 2, 76] Generated Node #0,1: 44:[6, 2, 76] Operation: 77-1=76 Exploring Operation: 6-1=5, Resulting Numbers: [77, 2, 5] Generated Node #0,2: 44:[77, 2, 5] Operation: 6-1=5 Moving to Node #0,0 Current State: 44:[1, 2, 71], Operations: ['77-6=71'] Exploring Operation: 71-1=70, Resulting Numbers: [2, 70] Generated Node #0,0,0: 44:[2, 70] Operation: 71-1=70 Exploring Operation: 71-2=69, Resulting Numbers: [1, 69] Generated Node #0,0,1: 44:[1, 69] Operation: 71-2=69 Exploring Operation: 1*2=2, Resulting Numbers: [71, 2] Generated Node #0,0,2: 44:[71, 2] Operation: 1*2=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[2, 70], Operations: ['77-6=71', '71-1=70'] Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,44 unequal: No Solution Exploring Operation: 2+70=72, Resulting Numbers: [72] 72,44 unequal: No Solution No 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: 44:[1, 69], Operations: ['77-6=71', '71-2=69'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 1*69=69, Resulting Numbers: [69] 69,44 unequal: No Solution Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,44 unequal: No Solution No 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: 44:[71, 2], Operations: ['77-6=71', '1*2=2'] Exploring Operation: 71*2=142, Resulting Numbers: [142] 142,44 unequal: No Solution Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,44 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,44 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: 44:[6, 2, 76], Operations: ['77-1=76'] Exploring Operation: 76/2=38, Resulting Numbers: [6, 38] Generated Node #0,1,0: 44:[6, 38] Operation: 76/2=38 Exploring Operation: 76-6=70, Resulting Numbers: [2, 70] Generated Node #0,1,1: 44:[2, 70] Operation: 76-6=70 Exploring Operation: 6-2=4, Resulting Numbers: [76, 4] Generated Node #0,1,2: 44:[76, 4] Operation: 6-2=4 Moving to Node #0,2 Current State: 44:[77, 2, 5], Operations: ['6-1=5'] Exploring Operation: 77-5=72, Resulting Numbers: [2, 72] Generated Node #0,2,0: 44:[2, 72] Operation: 77-5=72 Exploring Operation: 2*5=10, Resulting Numbers: [77, 10] Generated Node #0,2,1: 44:[77, 10] Operation: 2*5=10 Exploring Operation: 77-2=75, Resulting Numbers: [5, 75] Generated Node #0,2,2: 44:[5, 75] Operation: 77-2=75 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 44:[2, 72], Operations: ['6-1=5', '77-5=72'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,44 unequal: No Solution Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,44 unequal: No Solution No 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: 44:[5, 75], Operations: ['6-1=5', '77-2=75'] Exploring Operation: 75/5=15, Resulting Numbers: [15] 15,44 unequal: No Solution Exploring Operation: 75-5=70, Resulting Numbers: [70] 70,44 unequal: No Solution Exploring Operation: 5+75=80, Resulting Numbers: [80] 80,44 unequal: No Solution No 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: 44:[77, 10], Operations: ['6-1=5', '2*5=10'] Exploring Operation: 77+10=87, Resulting Numbers: [87] 87,44 unequal: No Solution Exploring Operation: 77-10=67, Resulting Numbers: [67] 67,44 unequal: No Solution Exploring Operation: 77*10=770, Resulting Numbers: [770] 770,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 44:[6, 38], Operations: ['77-1=76', '76/2=38'] Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,44 unequal: No Solution Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[1, 77, 6, 2], Operations: [] Exploring Operation: 77-1=76, Resulting Numbers: [6, 2, 76] Generated Node #0,1: 44:[6, 2, 76] Operation: 77-1=76 Moving to Node #0,1 Current State: 44:[6, 2, 76], Operations: ['77-1=76'] Exploring Operation: 76/2=38, Resulting Numbers: [6, 38] Generated Node #0,1,0: 44:[6, 38] Operation: 76/2=38 Moving to Node #0,1,0 Current State: 44:[6, 38], Operations: ['77-1=76', '76/2=38'] Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
0.96875
hs_3
mult_heuristic
[ 23, 78, 76, 39 ]
85
[ "78-76=2", "23*2=46", "39+46=85" ]
Current State: 85:[23, 78, 76, 39], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [23, 39, 2] Generated Node #2: [23, 39, 2] from Operation: 78-76=2 Current State: 85:[23, 39, 2], Operations: ['78-76=2'] Exploring Operation: 23*2=46, Resulting Numbers: [39, 46] Generated Node #3: [39, 46] from Operation: 23*2=46 Current State: 85:[39, 46], Operations: ['78-76=2', '23*2=46'] Exploring Operation: 39+46=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[23, 78, 76, 39], Operations: [] Exploring Operation: 78-39=39, Resulting Numbers: [23, 76, 39] Generated Node #0,0: 85:[23, 76, 39] Operation: 78-39=39 Exploring Operation: 78-76=2, Resulting Numbers: [23, 39, 2] Generated Node #0,1: 85:[23, 39, 2] Operation: 78-76=2 Exploring Operation: 39-23=16, Resulting Numbers: [78, 76, 16] Generated Node #0,2: 85:[78, 76, 16] Operation: 39-23=16 Exploring Operation: 78/39=2, Resulting Numbers: [23, 76, 2] Generated Node #0,3: 85:[23, 76, 2] Operation: 78/39=2 Exploring Operation: 76-39=37, Resulting Numbers: [23, 78, 37] Generated Node #0,4: 85:[23, 78, 37] Operation: 76-39=37 Moving to Node #0,2 Current State: 85:[78, 76, 16], Operations: ['39-23=16'] Exploring Operation: 78-16=62, Resulting Numbers: [76, 62] Generated Node #0,2,0: 85:[76, 62] Operation: 78-16=62 Exploring Operation: 78+16=94, Resulting Numbers: [76, 94] Generated Node #0,2,1: 85:[76, 94] Operation: 78+16=94 Exploring Operation: 78-76=2, Resulting Numbers: [16, 2] Generated Node #0,2,2: 85:[16, 2] Operation: 78-76=2 Exploring Operation: 76+16=92, Resulting Numbers: [78, 92] Generated Node #0,2,3: 85:[78, 92] Operation: 76+16=92 Exploring Operation: 76-16=60, Resulting Numbers: [78, 60] Generated Node #0,2,4: 85:[78, 60] Operation: 76-16=60 Moving to Node #0,3 Current State: 85:[23, 76, 2], Operations: ['78/39=2'] Exploring Operation: 23-2=21, Resulting Numbers: [76, 21] Generated Node #0,3,0: 85:[76, 21] Operation: 23-2=21 Exploring Operation: 23+2=25, Resulting Numbers: [76, 25] Generated Node #0,3,1: 85:[76, 25] Operation: 23+2=25 Exploring Operation: 76+2=78, Resulting Numbers: [23, 78] Generated Node #0,3,2: 85:[23, 78] Operation: 76+2=78 Exploring Operation: 23+76=99, Resulting Numbers: [2, 99] Generated Node #0,3,3: 85:[2, 99] Operation: 23+76=99 Exploring Operation: 76-2=74, Resulting Numbers: [23, 74] Generated Node #0,3,4: 85:[23, 74] Operation: 76-2=74 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 85:[76, 21], Operations: ['78/39=2', '23-2=21'] Exploring Operation: 76-21=55, Resulting Numbers: [55] 55,85 unequal: No Solution Exploring Operation: 76+21=97, Resulting Numbers: [97] 97,85 unequal: No Solution Exploring Operation: 76*21=1596, Resulting Numbers: [1596] 1596,85 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 #0,3,2 Current State: 85:[23, 78], Operations: ['78/39=2', '76+2=78'] Exploring Operation: 23*78=1794, Resulting Numbers: [1794] 1794,85 unequal: No Solution Exploring Operation: 78-23=55, Resulting Numbers: [55] 55,85 unequal: No Solution Exploring Operation: 23+78=101, Resulting Numbers: [101] 101,85 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 #0,3,1 Current State: 85:[76, 25], Operations: ['78/39=2', '23+2=25'] Exploring Operation: 76+25=101, Resulting Numbers: [101] 101,85 unequal: No Solution Exploring Operation: 76*25=1900, Resulting Numbers: [1900] 1900,85 unequal: No Solution Exploring Operation: 76-25=51, Resulting Numbers: [51] 51,85 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 #0,3,3 Current State: 85:[2, 99], Operations: ['78/39=2', '23+76=99'] Exploring Operation: 99-2=97, Resulting Numbers: [97] 97,85 unequal: No Solution Exploring Operation: 2+99=101, Resulting Numbers: [101] 101,85 unequal: No Solution Exploring Operation: 2*99=198, Resulting Numbers: [198] 198,85 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 #0,3,4 Current State: 85:[23, 74], Operations: ['78/39=2', '76-2=74'] Exploring Operation: 23*74=1702, Resulting Numbers: [1702] 1702,85 unequal: No Solution Exploring Operation: 74-23=51, Resulting Numbers: [51] 51,85 unequal: No Solution Exploring Operation: 23+74=97, Resulting Numbers: [97] 97,85 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: 85:[23, 39, 2], Operations: ['78-76=2'] Exploring Operation: 39*2=78, Resulting Numbers: [23, 78] Generated Node #0,1,0: 85:[23, 78] Operation: 39*2=78 Exploring Operation: 23-2=21, Resulting Numbers: [39, 21] Generated Node #0,1,1: 85:[39, 21] Operation: 23-2=21 Exploring Operation: 39-2=37, Resulting Numbers: [23, 37] Generated Node #0,1,2: 85:[23, 37] Operation: 39-2=37 Exploring Operation: 39-23=16, Resulting Numbers: [2, 16] Generated Node #0,1,3: 85:[2, 16] Operation: 39-23=16 Exploring Operation: 23+39=62, Resulting Numbers: [2, 62] Generated Node #0,1,4: 85:[2, 62] Operation: 23+39=62 Moving to Node #0,4 Current State: 85:[23, 78, 37], Operations: ['76-39=37'] Exploring Operation: 78-37=41, Resulting Numbers: [23, 41] Generated Node #0,4,0: 85:[23, 41] Operation: 78-37=41 Exploring Operation: 23+37=60, Resulting Numbers: [78, 60] Generated Node #0,4,1: 85:[78, 60] Operation: 23+37=60 Exploring Operation: 23+78=101, Resulting Numbers: [37, 101] Generated Node #0,4,2: 85:[37, 101] Operation: 23+78=101 Exploring Operation: 37-23=14, Resulting Numbers: [78, 14] Generated Node #0,4,3: 85:[78, 14] Operation: 37-23=14 Exploring Operation: 78+37=115, Resulting Numbers: [23, 115] Generated Node #0,4,4: 85:[23, 115] Operation: 78+37=115 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 85:[78, 14], Operations: ['76-39=37', '37-23=14'] Exploring Operation: 78+14=92, Resulting Numbers: [92] 92,85 unequal: No Solution Exploring Operation: 78*14=1092, Resulting Numbers: [1092] 1092,85 unequal: No Solution Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,85 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 #0,4,0 Current State: 85:[23, 41], Operations: ['76-39=37', '78-37=41'] Exploring Operation: 23*41=943, Resulting Numbers: [943] 943,85 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 23+41=64, Resulting Numbers: [64] 64,85 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 #0,4,1 Current State: 85:[78, 60], Operations: ['76-39=37', '23+37=60'] Exploring Operation: 78+60=138, Resulting Numbers: [138] 138,85 unequal: No Solution Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 78*60=4680, Resulting Numbers: [4680] 4680,85 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 #0,4,2 Current State: 85:[37, 101], Operations: ['76-39=37', '23+78=101'] Exploring Operation: 37+101=138, Resulting Numbers: [138] 138,85 unequal: No Solution Exploring Operation: 101-37=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 37*101=3737, Resulting Numbers: [3737] 3737,85 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 #0,4,4 Current State: 85:[23, 115], Operations: ['76-39=37', '78+37=115'] Exploring Operation: 115-23=92, Resulting Numbers: [92] 92,85 unequal: No Solution Exploring Operation: 23+115=138, Resulting Numbers: [138] 138,85 unequal: No Solution Exploring Operation: 23*115=2645, Resulting Numbers: [2645] 2645,85 unequal: No Solution Exploring Operation: 115/23=5, Resulting Numbers: [5] 5,85 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: 85:[23, 76, 39], Operations: ['78-39=39'] Exploring Operation: 76+39=115, Resulting Numbers: [23, 115] Generated Node #0,0,0: 85:[23, 115] Operation: 76+39=115 Exploring Operation: 76-39=37, Resulting Numbers: [23, 37] Generated Node #0,0,1: 85:[23, 37] Operation: 76-39=37 Exploring Operation: 23+76=99, Resulting Numbers: [39, 99] Generated Node #0,0,2: 85:[39, 99] Operation: 23+76=99 Exploring Operation: 39-23=16, Resulting Numbers: [76, 16] Generated Node #0,0,3: 85:[76, 16] Operation: 39-23=16 Exploring Operation: 23+39=62, Resulting Numbers: [76, 62] Generated Node #0,0,4: 85:[76, 62] Operation: 23+39=62 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 85:[76, 16], Operations: ['78-39=39', '39-23=16'] Exploring Operation: 76*16=1216, Resulting Numbers: [1216] 1216,85 unequal: No Solution Exploring Operation: 76-16=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 76+16=92, Resulting Numbers: [92] 92,85 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 #0,0,1 Current State: 85:[23, 37], Operations: ['78-39=39', '76-39=37'] Exploring Operation: 23*37=851, Resulting Numbers: [851] 851,85 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 23+37=60, Resulting Numbers: [60] 60,85 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 #0,0,4 Current State: 85:[76, 62], Operations: ['78-39=39', '23+39=62'] Exploring Operation: 76-62=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 76*62=4712, Resulting Numbers: [4712] 4712,85 unequal: No Solution Exploring Operation: 76+62=138, Resulting Numbers: [138] 138,85 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 #0,0,0 Current State: 85:[23, 115], Operations: ['78-39=39', '76+39=115'] Exploring Operation: 115-23=92, Resulting Numbers: [92] 92,85 unequal: No Solution Exploring Operation: 23+115=138, Resulting Numbers: [138] 138,85 unequal: No Solution Exploring Operation: 115/23=5, Resulting Numbers: [5] 5,85 unequal: No Solution Exploring Operation: 23*115=2645, Resulting Numbers: [2645] 2645,85 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 #0,0,2 Current State: 85:[39, 99], Operations: ['78-39=39', '23+76=99'] Exploring Operation: 99-39=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 39*99=3861, Resulting Numbers: [3861] 3861,85 unequal: No Solution Exploring Operation: 39+99=138, Resulting Numbers: [138] 138,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 85:[16, 2], Operations: ['39-23=16', '78-76=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,85 unequal: No Solution Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,85 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,85 unequal: No Solution Moving to Node #0,1,3 Current State: 85:[2, 16], Operations: ['78-76=2', '39-23=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,85 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[23, 78], Operations: ['78-76=2', '39*2=78'] Exploring Operation: 23+78=101, Resulting Numbers: [101] 101,85 unequal: No Solution Exploring Operation: 23*78=1794, Resulting Numbers: [1794] 1794,85 unequal: No Solution Exploring Operation: 78-23=55, Resulting Numbers: [55] 55,85 unequal: No Solution Moving to Node #0,2,3 Current State: 85:[78, 92], Operations: ['39-23=16', '76+16=92'] Exploring Operation: 92-78=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 78*92=7176, Resulting Numbers: [7176] 7176,85 unequal: No Solution Exploring Operation: 78+92=170, Resulting Numbers: [170] 170,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[76, 94], Operations: ['39-23=16', '78+16=94'] Exploring Operation: 76+94=170, Resulting Numbers: [170] 170,85 unequal: No Solution Exploring Operation: 76*94=7144, Resulting Numbers: [7144] 7144,85 unequal: No Solution Exploring Operation: 94-76=18, Resulting Numbers: [18] 18,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[23, 37], Operations: ['78-76=2', '39-2=37'] Exploring Operation: 23+37=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 23*37=851, Resulting Numbers: [851] 851,85 unequal: No Solution Moving to Node #0,1,4 Current State: 85:[2, 62], Operations: ['78-76=2', '23+39=62'] Exploring Operation: 2*62=124, Resulting Numbers: [124] 124,85 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,85 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[39, 21], Operations: ['78-76=2', '23-2=21'] Exploring Operation: 39+21=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 39*21=819, Resulting Numbers: [819] 819,85 unequal: No Solution Moving to Node #0,2,0 Current State: 85:[76, 62], Operations: ['39-23=16', '78-16=62'] Exploring Operation: 76+62=138, Resulting Numbers: [138] 138,85 unequal: No Solution Exploring Operation: 76*62=4712, Resulting Numbers: [4712] 4712,85 unequal: No Solution Exploring Operation: 76-62=14, Resulting Numbers: [14] 14,85 unequal: No Solution Moving to Node #0,2,4 Current State: 85:[78, 60], Operations: ['39-23=16', '76-16=60'] Exploring Operation: 78+60=138, Resulting Numbers: [138] 138,85 unequal: No Solution Exploring Operation: 78*60=4680, Resulting Numbers: [4680] 4680,85 unequal: No Solution Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,85 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 36, 15, 52, 64 ]
64
[ "36+15=51", "52-51=1", "64*1=64" ]
Current State: 64:[36, 15, 52, 64], Operations: [] Exploring Operation: 36+15=51, Resulting Numbers: [52, 64, 51] Generated Node #2: [52, 64, 51] from Operation: 36+15=51 Current State: 64:[52, 64, 51], Operations: ['36+15=51'] Exploring Operation: 52-51=1, Resulting Numbers: [64, 1] Generated Node #3: [64, 1] from Operation: 52-51=1 Current State: 64:[64, 1], Operations: ['36+15=51', '52-51=1'] Exploring Operation: 64*1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[36, 15, 52, 64], Operations: [] Exploring Operation: 15+52=67, Resulting Numbers: [36, 64, 67] Generated Node #0,0: 64:[36, 64, 67] Operation: 15+52=67 Exploring Operation: 52-36=16, Resulting Numbers: [15, 64, 16] Generated Node #0,1: 64:[15, 64, 16] Operation: 52-36=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[15, 64, 16], Operations: ['52-36=16'] Exploring Operation: 15+16=31, Resulting Numbers: [64, 31] Generated Node #0,1,0: 64:[64, 31] Operation: 15+16=31 Exploring Operation: 16-15=1, Resulting Numbers: [64, 1] Generated Node #0,1,1: 64:[64, 1] Operation: 16-15=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 64:[64, 31], Operations: ['52-36=16', '15+16=31'] Exploring Operation: 64+31=95, Resulting Numbers: [95] 95,64 unequal: No Solution Exploring Operation: 64-31=33, Resulting Numbers: [33] 33,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 64:[64, 1], Operations: ['52-36=16', '16-15=1'] Exploring Operation: 64*1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[36, 15, 52, 64], Operations: [] Exploring Operation: 52-36=16, Resulting Numbers: [15, 64, 16] Generated Node #0,1: 64:[15, 64, 16] Operation: 52-36=16 Moving to Node #0,1 Current State: 64:[15, 64, 16], Operations: ['52-36=16'] Exploring Operation: 16-15=1, Resulting Numbers: [64, 1] Generated Node #0,1,1: 64:[64, 1] Operation: 16-15=1 Moving to Node #0,1,1 Current State: 64:[64, 1], Operations: ['52-36=16', '16-15=1'] Exploring Operation: 64*1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 50, 79, 96, 8 ]
86
[ "96-79=17", "8*17=136", "136-50=86" ]
Current State: 86:[50, 79, 96, 8], Operations: [] Exploring Operation: 96-79=17, Resulting Numbers: [50, 8, 17] Generated Node #2: [50, 8, 17] from Operation: 96-79=17 Current State: 86:[50, 8, 17], Operations: ['96-79=17'] Exploring Operation: 8*17=136, Resulting Numbers: [50, 136] Generated Node #3: [50, 136] from Operation: 8*17=136 Current State: 86:[50, 136], Operations: ['96-79=17', '8*17=136'] Exploring Operation: 136-50=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[50, 79, 96, 8], Operations: [] Exploring Operation: 96-50=46, Resulting Numbers: [79, 8, 46] Generated Node #0,0: 86:[79, 8, 46] Operation: 96-50=46 Exploring Operation: 50-8=42, Resulting Numbers: [79, 96, 42] Generated Node #0,1: 86:[79, 96, 42] Operation: 50-8=42 Exploring Operation: 96-8=88, Resulting Numbers: [50, 79, 88] Generated Node #0,2: 86:[50, 79, 88] Operation: 96-8=88 Moving to Node #0,0 Current State: 86:[79, 8, 46], Operations: ['96-50=46'] Exploring Operation: 79-46=33, Resulting Numbers: [8, 33] Generated Node #0,0,0: 86:[8, 33] Operation: 79-46=33 Exploring Operation: 46-8=38, Resulting Numbers: [79, 38] Generated Node #0,0,1: 86:[79, 38] Operation: 46-8=38 Exploring Operation: 79+8=87, Resulting Numbers: [46, 87] Generated Node #0,0,2: 86:[46, 87] Operation: 79+8=87 Moving to Node #0,2 Current State: 86:[50, 79, 88], Operations: ['96-8=88'] Exploring Operation: 88-79=9, Resulting Numbers: [50, 9] Generated Node #0,2,0: 86:[50, 9] Operation: 88-79=9 Exploring Operation: 79-50=29, Resulting Numbers: [88, 29] Generated Node #0,2,1: 86:[88, 29] Operation: 79-50=29 Exploring Operation: 88-50=38, Resulting Numbers: [79, 38] Generated Node #0,2,2: 86:[79, 38] Operation: 88-50=38 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 86:[79, 38], Operations: ['96-8=88', '88-50=38'] Exploring Operation: 79*38=3002, Resulting Numbers: [3002] 3002,86 unequal: No Solution Exploring Operation: 79+38=117, Resulting Numbers: [117] 117,86 unequal: No Solution Exploring Operation: 79-38=41, Resulting Numbers: [41] 41,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 86:[50, 9], Operations: ['96-8=88', '88-79=9'] Exploring Operation: 50+9=59, Resulting Numbers: [59] 59,86 unequal: No Solution Exploring Operation: 50-9=41, Resulting Numbers: [41] 41,86 unequal: No Solution Exploring Operation: 50*9=450, Resulting Numbers: [450] 450,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 86:[88, 29], Operations: ['96-8=88', '79-50=29'] Exploring Operation: 88-29=59, Resulting Numbers: [59] 59,86 unequal: No Solution Exploring Operation: 88*29=2552, Resulting Numbers: [2552] 2552,86 unequal: No Solution Exploring Operation: 88+29=117, Resulting Numbers: [117] 117,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 86:[79, 96, 42], Operations: ['50-8=42'] Exploring Operation: 96-79=17, Resulting Numbers: [42, 17] Generated Node #0,1,0: 86:[42, 17] Operation: 96-79=17 Exploring Operation: 96-42=54, Resulting Numbers: [79, 54] Generated Node #0,1,1: 86:[79, 54] Operation: 96-42=54 Exploring Operation: 79-42=37, Resulting Numbers: [96, 37] Generated Node #0,1,2: 86:[96, 37] Operation: 79-42=37 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[42, 17], Operations: ['50-8=42', '96-79=17'] Exploring Operation: 42*17=714, Resulting Numbers: [714] 714,86 unequal: No Solution Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,86 unequal: No Solution Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[96, 37], Operations: ['50-8=42', '79-42=37'] Exploring Operation: 96*37=3552, Resulting Numbers: [3552] 3552,86 unequal: No Solution Exploring Operation: 96+37=133, Resulting Numbers: [133] 133,86 unequal: No Solution Exploring Operation: 96-37=59, Resulting Numbers: [59] 59,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[79, 54], Operations: ['50-8=42', '96-42=54'] Exploring Operation: 79-54=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 79*54=4266, Resulting Numbers: [4266] 4266,86 unequal: No Solution Exploring Operation: 79+54=133, Resulting Numbers: [133] 133,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 86:[46, 87], Operations: ['96-50=46', '79+8=87'] Exploring Operation: 87-46=41, Resulting Numbers: [41] 41,86 unequal: No Solution Exploring Operation: 46+87=133, Resulting Numbers: [133] 133,86 unequal: No Solution Exploring Operation: 46*87=4002, Resulting Numbers: [4002] 4002,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[79, 38], Operations: ['96-50=46', '46-8=38'] Exploring Operation: 79+38=117, Resulting Numbers: [117] 117,86 unequal: No Solution Exploring Operation: 79-38=41, Resulting Numbers: [41] 41,86 unequal: No Solution Exploring Operation: 79*38=3002, Resulting Numbers: [3002] 3002,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[8, 33], Operations: ['96-50=46', '79-46=33'] Exploring Operation: 8+33=41, Resulting Numbers: [41] 41,86 unequal: No Solution Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 8*33=264, Resulting Numbers: [264] 264,86 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 70, 5, 46, 16 ]
76
[ "70/5=14", "46+16=62", "14+62=76" ]
Current State: 76:[70, 5, 46, 16], Operations: [] Exploring Operation: 70/5=14, Resulting Numbers: [46, 16, 14] Generated Node #2: [46, 16, 14] from Operation: 70/5=14 Current State: 76:[46, 16, 14], Operations: ['70/5=14'] Exploring Operation: 46+16=62, Resulting Numbers: [14, 62] Generated Node #3: [14, 62] from Operation: 46+16=62 Current State: 76:[14, 62], Operations: ['70/5=14', '46+16=62'] Exploring Operation: 14+62=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[70, 5, 46, 16], Operations: [] Exploring Operation: 46-5=41, Resulting Numbers: [70, 16, 41] Generated Node #0,0: 76:[70, 16, 41] Operation: 46-5=41 Exploring Operation: 70-46=24, Resulting Numbers: [5, 16, 24] Generated Node #0,1: 76:[5, 16, 24] Operation: 70-46=24 Exploring Operation: 46-16=30, Resulting Numbers: [70, 5, 30] Generated Node #0,2: 76:[70, 5, 30] Operation: 46-16=30 Exploring Operation: 70+5=75, Resulting Numbers: [46, 16, 75] Generated Node #0,3: 76:[46, 16, 75] Operation: 70+5=75 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[5, 16, 24], Operations: ['70-46=24'] Exploring Operation: 5+16=21, Resulting Numbers: [24, 21] Generated Node #0,1,0: 76:[24, 21] Operation: 5+16=21 Exploring Operation: 24-5=19, Resulting Numbers: [16, 19] Generated Node #0,1,1: 76:[16, 19] Operation: 24-5=19 Exploring Operation: 24-16=8, Resulting Numbers: [5, 8] Generated Node #0,1,2: 76:[5, 8] Operation: 24-16=8 Exploring Operation: 16+24=40, Resulting Numbers: [5, 40] Generated Node #0,1,3: 76:[5, 40] Operation: 16+24=40 Moving to Node #0,1,1 Current State: 76:[16, 19], Operations: ['70-46=24', '24-5=19'] Exploring Operation: 16*19=304, Resulting Numbers: [304] 304,76 unequal: No Solution Exploring Operation: 16+19=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,76 unequal: No Solution Moving to Node #0,1,3 Current State: 76:[5, 40], Operations: ['70-46=24', '16+24=40'] Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,76 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 5*40=200, Resulting Numbers: [200] 200,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[5, 8], Operations: ['70-46=24', '24-16=8'] Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,76 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[24, 21], Operations: ['70-46=24', '5+16=21'] Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,76 unequal: No Solution Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[70, 16, 41], Operations: ['46-5=41'] Exploring Operation: 70+16=86, Resulting Numbers: [41, 86] Generated Node #0,0,0: 76:[41, 86] Operation: 70+16=86 Exploring Operation: 41-16=25, Resulting Numbers: [70, 25] Generated Node #0,0,1: 76:[70, 25] Operation: 41-16=25 Exploring Operation: 70-41=29, Resulting Numbers: [16, 29] Generated Node #0,0,2: 76:[16, 29] Operation: 70-41=29 Exploring Operation: 70-16=54, Resulting Numbers: [41, 54] Generated Node #0,0,3: 76:[41, 54] Operation: 70-16=54 Moving to Node #0,0,1 Current State: 76:[70, 25], Operations: ['46-5=41', '41-16=25'] Exploring Operation: 70+25=95, Resulting Numbers: [95] 95,76 unequal: No Solution Exploring Operation: 70-25=45, Resulting Numbers: [45] 45,76 unequal: No Solution Exploring Operation: 70*25=1750, Resulting Numbers: [1750] 1750,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[16, 29], Operations: ['46-5=41', '70-41=29'] Exploring Operation: 16*29=464, Resulting Numbers: [464] 464,76 unequal: No Solution Exploring Operation: 16+29=45, Resulting Numbers: [45] 45,76 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[41, 86], Operations: ['46-5=41', '70+16=86'] Exploring Operation: 86-41=45, Resulting Numbers: [45] 45,76 unequal: No Solution Exploring Operation: 41*86=3526, Resulting Numbers: [3526] 3526,76 unequal: No Solution Exploring Operation: 41+86=127, Resulting Numbers: [127] 127,76 unequal: No Solution Moving to Node #0,0,3 Current State: 76:[41, 54], Operations: ['46-5=41', '70-16=54'] Exploring Operation: 54-41=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 41+54=95, Resulting Numbers: [95] 95,76 unequal: No Solution Exploring Operation: 41*54=2214, Resulting Numbers: [2214] 2214,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 76:[46, 16, 75], Operations: ['70+5=75'] Exploring Operation: 16+75=91, Resulting Numbers: [46, 91] Generated Node #0,3,0: 76:[46, 91] Operation: 16+75=91 Exploring Operation: 75-46=29, Resulting Numbers: [16, 29] Generated Node #0,3,1: 76:[16, 29] Operation: 75-46=29 Exploring Operation: 46+16=62, Resulting Numbers: [75, 62] Generated Node #0,3,2: 76:[75, 62] Operation: 46+16=62 Exploring Operation: 46-16=30, Resulting Numbers: [75, 30] Generated Node #0,3,3: 76:[75, 30] Operation: 46-16=30 Moving to Node #0,3,3 Current State: 76:[75, 30], Operations: ['70+5=75', '46-16=30'] Exploring Operation: 75-30=45, Resulting Numbers: [45] 45,76 unequal: No Solution Exploring Operation: 75+30=105, Resulting Numbers: [105] 105,76 unequal: No Solution Exploring Operation: 75*30=2250, Resulting Numbers: [2250] 2250,76 unequal: No Solution Moving to Node #0,3,1 Current State: 76:[16, 29], Operations: ['70+5=75', '75-46=29'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 16*29=464, Resulting Numbers: [464] 464,76 unequal: No Solution Exploring Operation: 16+29=45, Resulting Numbers: [45] 45,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[75, 62], Operations: ['70+5=75', '46+16=62'] Exploring Operation: 75*62=4650, Resulting Numbers: [4650] 4650,76 unequal: No Solution Exploring Operation: 75+62=137, Resulting Numbers: [137] 137,76 unequal: No Solution Exploring Operation: 75-62=13, Resulting Numbers: [13] 13,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[46, 91], Operations: ['70+5=75', '16+75=91'] Exploring Operation: 46+91=137, Resulting Numbers: [137] 137,76 unequal: No Solution Exploring Operation: 46*91=4186, Resulting Numbers: [4186] 4186,76 unequal: No Solution Exploring Operation: 91-46=45, Resulting Numbers: [45] 45,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[70, 5, 30], Operations: ['46-16=30'] Exploring Operation: 5+30=35, Resulting Numbers: [70, 35] Generated Node #0,2,0: 76:[70, 35] Operation: 5+30=35 Exploring Operation: 70+5=75, Resulting Numbers: [30, 75] Generated Node #0,2,1: 76:[30, 75] Operation: 70+5=75 Exploring Operation: 30/5=6, Resulting Numbers: [70, 6] Generated Node #0,2,2: 76:[70, 6] Operation: 30/5=6 Exploring Operation: 70-30=40, Resulting Numbers: [5, 40] Generated Node #0,2,3: 76:[5, 40] Operation: 70-30=40 Moving to Node #0,2,3 Current State: 76:[5, 40], Operations: ['46-16=30', '70-30=40'] Exploring Operation: 5*40=200, Resulting Numbers: [200] 200,76 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[70, 6], Operations: ['46-16=30', '30/5=6'] Exploring Operation: 70+6=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[70, 5, 46, 16], Operations: [] Exploring Operation: 46-16=30, Resulting Numbers: [70, 5, 30] Generated Node #0,2: 76:[70, 5, 30] Operation: 46-16=30 Moving to Node #0,2 Current State: 76:[70, 5, 30], Operations: ['46-16=30'] Exploring Operation: 30/5=6, Resulting Numbers: [70, 6] Generated Node #0,2,2: 76:[70, 6] Operation: 30/5=6 Moving to Node #0,2,2 Current State: 76:[70, 6], Operations: ['46-16=30', '30/5=6'] Exploring Operation: 70+6=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.942708
hs_4
sum_heuristic
[ 61, 12, 23, 92 ]
69
[ "61+12=73", "92/23=4", "73-4=69" ]
Current State: 69:[61, 12, 23, 92], Operations: [] Exploring Operation: 61+12=73, Resulting Numbers: [23, 92, 73] Generated Node #2: [23, 92, 73] from Operation: 61+12=73 Current State: 69:[23, 92, 73], Operations: ['61+12=73'] Exploring Operation: 92/23=4, Resulting Numbers: [73, 4] Generated Node #3: [73, 4] from Operation: 92/23=4 Current State: 69:[73, 4], Operations: ['61+12=73', '92/23=4'] Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[61, 12, 23, 92], Operations: [] Exploring Operation: 92-23=69, Resulting Numbers: [61, 12, 69] Generated Node #0,0: 69:[61, 12, 69] Operation: 92-23=69 Exploring Operation: 92-61=31, Resulting Numbers: [12, 23, 31] Generated Node #0,1: 69:[12, 23, 31] Operation: 92-61=31 Exploring Operation: 92/23=4, Resulting Numbers: [61, 12, 4] Generated Node #0,2: 69:[61, 12, 4] Operation: 92/23=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[61, 12, 69], Operations: ['92-23=69'] Exploring Operation: 69-61=8, Resulting Numbers: [12, 8] Generated Node #0,0,0: 69:[12, 8] Operation: 69-61=8 Exploring Operation: 61+12=73, Resulting Numbers: [69, 73] Generated Node #0,0,1: 69:[69, 73] Operation: 61+12=73 Exploring Operation: 61-12=49, Resulting Numbers: [69, 49] Generated Node #0,0,2: 69:[69, 49] Operation: 61-12=49 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 69:[69, 73], Operations: ['92-23=69', '61+12=73'] Exploring Operation: 69*73=5037, Resulting Numbers: [5037] 5037,69 unequal: No Solution Exploring Operation: 73-69=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 69+73=142, Resulting Numbers: [142] 142,69 unequal: No Solution No 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: 69:[12, 8], Operations: ['92-23=69', '69-61=8'] Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,69 unequal: No Solution No 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: 69:[69, 49], Operations: ['92-23=69', '61-12=49'] Exploring Operation: 69+49=118, Resulting Numbers: [118] 118,69 unequal: No Solution Exploring Operation: 69-49=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 69*49=3381, Resulting Numbers: [3381] 3381,69 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: 69:[12, 23, 31], Operations: ['92-61=31'] Exploring Operation: 23-12=11, Resulting Numbers: [31, 11] Generated Node #0,1,0: 69:[31, 11] Operation: 23-12=11 Exploring Operation: 31-23=8, Resulting Numbers: [12, 8] Generated Node #0,1,1: 69:[12, 8] Operation: 31-23=8 Exploring Operation: 31-12=19, Resulting Numbers: [23, 19] Generated Node #0,1,2: 69:[23, 19] Operation: 31-12=19 Moving to Node #0,1,2 Current State: 69:[23, 19], Operations: ['92-61=31', '31-12=19'] Exploring Operation: 23-19=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 23*19=437, Resulting Numbers: [437] 437,69 unequal: No Solution Exploring Operation: 23+19=42, Resulting Numbers: [42] 42,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[12, 8], Operations: ['92-61=31', '31-23=8'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,69 unequal: No Solution Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,69 unequal: No Solution Moving to Node #0,1,0 Current State: 69:[31, 11], Operations: ['92-61=31', '23-12=11'] Exploring Operation: 31*11=341, Resulting Numbers: [341] 341,69 unequal: No Solution Exploring Operation: 31+11=42, Resulting Numbers: [42] 42,69 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,69 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 #0,2 Current State: 69:[61, 12, 4], Operations: ['92/23=4'] Exploring Operation: 61+12=73, Resulting Numbers: [4, 73] Generated Node #0,2,0: 69:[4, 73] Operation: 61+12=73 Exploring Operation: 61+4=65, Resulting Numbers: [12, 65] Generated Node #0,2,1: 69:[12, 65] Operation: 61+4=65 Exploring Operation: 12/4=3, Resulting Numbers: [61, 3] Generated Node #0,2,2: 69:[61, 3] Operation: 12/4=3 Moving to Node #0,2,0 Current State: 69:[4, 73], Operations: ['92/23=4', '61+12=73'] Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[61, 12, 23, 92], Operations: [] Exploring Operation: 92/23=4, Resulting Numbers: [61, 12, 4] Generated Node #0,2: 69:[61, 12, 4] Operation: 92/23=4 Moving to Node #0,2 Current State: 69:[61, 12, 4], Operations: ['92/23=4'] Exploring Operation: 61+12=73, Resulting Numbers: [4, 73] Generated Node #0,2,0: 69:[4, 73] Operation: 61+12=73 Moving to Node #0,2,0 Current State: 69:[4, 73], Operations: ['92/23=4', '61+12=73'] Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_3
sum_heuristic
[ 90, 71, 11, 74 ]
41
[ "74-71=3", "90/3=30", "11+30=41" ]
Current State: 41:[90, 71, 11, 74], Operations: [] Exploring Operation: 74-71=3, Resulting Numbers: [90, 11, 3] Generated Node #2: [90, 11, 3] from Operation: 74-71=3 Current State: 41:[90, 11, 3], Operations: ['74-71=3'] Exploring Operation: 90/3=30, Resulting Numbers: [11, 30] Generated Node #3: [11, 30] from Operation: 90/3=30 Current State: 41:[11, 30], Operations: ['74-71=3', '90/3=30'] Exploring Operation: 11+30=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[90, 71, 11, 74], Operations: [] Exploring Operation: 90-71=19, Resulting Numbers: [11, 74, 19] Generated Node #0,0: 41:[11, 74, 19] Operation: 90-71=19 Exploring Operation: 90-11=79, Resulting Numbers: [71, 74, 79] Generated Node #0,1: 41:[71, 74, 79] Operation: 90-11=79 Exploring Operation: 90-74=16, Resulting Numbers: [71, 11, 16] Generated Node #0,2: 41:[71, 11, 16] Operation: 90-74=16 Moving to Node #0,0 Current State: 41:[11, 74, 19], Operations: ['90-71=19'] Exploring Operation: 74-19=55, Resulting Numbers: [11, 55] Generated Node #0,0,0: 41:[11, 55] Operation: 74-19=55 Exploring Operation: 11+19=30, Resulting Numbers: [74, 30] Generated Node #0,0,1: 41:[74, 30] Operation: 11+19=30 Exploring Operation: 74-11=63, Resulting Numbers: [19, 63] Generated Node #0,0,2: 41:[19, 63] Operation: 74-11=63 Moving to Node #0,2 Current State: 41:[71, 11, 16], Operations: ['90-74=16'] Exploring Operation: 71-11=60, Resulting Numbers: [16, 60] Generated Node #0,2,0: 41:[16, 60] Operation: 71-11=60 Exploring Operation: 71-16=55, Resulting Numbers: [11, 55] Generated Node #0,2,1: 41:[11, 55] Operation: 71-16=55 Exploring Operation: 11+16=27, Resulting Numbers: [71, 27] Generated Node #0,2,2: 41:[71, 27] Operation: 11+16=27 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 41:[16, 60], Operations: ['90-74=16', '71-11=60'] Exploring Operation: 16*60=960, Resulting Numbers: [960] 960,41 unequal: No Solution Exploring Operation: 60-16=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 16+60=76, Resulting Numbers: [76] 76,41 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 #0,2,1 Current State: 41:[11, 55], Operations: ['90-74=16', '71-16=55'] Exploring Operation: 11+55=66, Resulting Numbers: [66] 66,41 unequal: No Solution Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,41 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 #0,2,2 Current State: 41:[71, 27], Operations: ['90-74=16', '11+16=27'] Exploring Operation: 71*27=1917, Resulting Numbers: [1917] 1917,41 unequal: No Solution Exploring Operation: 71+27=98, Resulting Numbers: [98] 98,41 unequal: No Solution Exploring Operation: 71-27=44, Resulting Numbers: [44] 44,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 41:[71, 74, 79], Operations: ['90-11=79'] Exploring Operation: 79-71=8, Resulting Numbers: [74, 8] Generated Node #0,1,0: 41:[74, 8] Operation: 79-71=8 Exploring Operation: 79-74=5, Resulting Numbers: [71, 5] Generated Node #0,1,1: 41:[71, 5] Operation: 79-74=5 Exploring Operation: 74-71=3, Resulting Numbers: [79, 3] Generated Node #0,1,2: 41:[79, 3] Operation: 74-71=3 Moving to Node #0,0,0 Current State: 41:[11, 55], Operations: ['90-71=19', '74-19=55'] Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 11+55=66, Resulting Numbers: [66] 66,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[19, 63], Operations: ['90-71=19', '74-11=63'] Exploring Operation: 63-19=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 19*63=1197, Resulting Numbers: [1197] 1197,41 unequal: No Solution Exploring Operation: 19+63=82, Resulting Numbers: [82] 82,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[74, 30], Operations: ['90-71=19', '11+19=30'] Exploring Operation: 74-30=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 74+30=104, Resulting Numbers: [104] 104,41 unequal: No Solution Exploring Operation: 74*30=2220, Resulting Numbers: [2220] 2220,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[74, 8], Operations: ['90-11=79', '79-71=8'] Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,41 unequal: No Solution Exploring Operation: 74+8=82, Resulting Numbers: [82] 82,41 unequal: No Solution Exploring Operation: 74*8=592, Resulting Numbers: [592] 592,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[71, 5], Operations: ['90-11=79', '79-74=5'] Exploring Operation: 71+5=76, Resulting Numbers: [76] 76,41 unequal: No Solution Exploring Operation: 71-5=66, Resulting Numbers: [66] 66,41 unequal: No Solution Exploring Operation: 71*5=355, Resulting Numbers: [355] 355,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[79, 3], Operations: ['90-11=79', '74-71=3'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,41 unequal: No Solution Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,41 unequal: No Solution Exploring Operation: 79*3=237, Resulting Numbers: [237] 237,41 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 58, 64, 34, 6 ]
16
[ "58-34=24", "64*6=384", "384/24=16" ]
Current State: 16:[58, 64, 34, 6], Operations: [] Exploring Operation: 58-34=24, Resulting Numbers: [64, 6, 24] Generated Node #2: [64, 6, 24] from Operation: 58-34=24 Current State: 16:[64, 6, 24], Operations: ['58-34=24'] Exploring Operation: 64*6=384, Resulting Numbers: [24, 384] Generated Node #3: [24, 384] from Operation: 64*6=384 Current State: 16:[24, 384], Operations: ['58-34=24', '64*6=384'] Exploring Operation: 384/24=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[58, 64, 34, 6], Operations: [] Exploring Operation: 58-34=24, Resulting Numbers: [64, 6, 24] Generated Node #0,0: 16:[64, 6, 24] Operation: 58-34=24 Exploring Operation: 64-34=30, Resulting Numbers: [58, 6, 30] Generated Node #0,1: 16:[58, 6, 30] Operation: 64-34=30 Exploring Operation: 64-58=6, Resulting Numbers: [34, 6, 6] Generated Node #0,2: 16:[34, 6, 6] Operation: 64-58=6 Exploring Operation: 58-6=52, Resulting Numbers: [64, 34, 52] Generated Node #0,3: 16:[64, 34, 52] Operation: 58-6=52 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[34, 6, 6], Operations: ['64-58=6'] Exploring Operation: 6-6=0, Resulting Numbers: [34, 0] Generated Node #0,2,0: 16:[34, 0] Operation: 6-6=0 Exploring Operation: 34-6=28, Resulting Numbers: [6, 28] Generated Node #0,2,1: 16:[6, 28] Operation: 34-6=28 Exploring Operation: 34-6=28, Resulting Numbers: [6, 28] Generated Node #0,2,2: 16:[6, 28] Operation: 34-6=28 Exploring Operation: 6/6=1, Resulting Numbers: [34, 1] Generated Node #0,2,3: 16:[34, 1] Operation: 6/6=1 Moving to Node #0,2,1 Current State: 16:[6, 28], Operations: ['64-58=6', '34-6=28'] Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 6+28=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 6*28=168, Resulting Numbers: [168] 168,16 unequal: No Solution Moving to Node #0,2,2 Current State: 16:[6, 28], Operations: ['64-58=6', '34-6=28'] Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 6+28=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 6*28=168, Resulting Numbers: [168] 168,16 unequal: No Solution Moving to Node #0,2,3 Current State: 16:[34, 1], Operations: ['64-58=6', '6/6=1'] Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,16 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[34, 0], Operations: ['64-58=6', '6-6=0'] Exploring Operation: 34+0=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 34-0=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 34*0=0, Resulting Numbers: [0] 0,16 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 #0,0 Current State: 16:[64, 6, 24], Operations: ['58-34=24'] Exploring Operation: 24/6=4, Resulting Numbers: [64, 4] Generated Node #0,0,0: 16:[64, 4] Operation: 24/6=4 Exploring Operation: 24-6=18, Resulting Numbers: [64, 18] Generated Node #0,0,1: 16:[64, 18] Operation: 24-6=18 Exploring Operation: 64-24=40, Resulting Numbers: [6, 40] Generated Node #0,0,2: 16:[6, 40] Operation: 64-24=40 Exploring Operation: 64-6=58, Resulting Numbers: [24, 58] Generated Node #0,0,3: 16:[24, 58] Operation: 64-6=58 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 16:[6, 40], Operations: ['58-34=24', '64-24=40'] Exploring Operation: 6*40=240, Resulting Numbers: [240] 240,16 unequal: No Solution Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 6+40=46, Resulting Numbers: [46] 46,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 16:[64, 4], Operations: ['58-34=24', '24/6=4'] Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,16 unequal: No Solution Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 64*4=256, Resulting Numbers: [256] 256,16 unequal: No Solution Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[58, 64, 34, 6], Operations: [] Exploring Operation: 58-34=24, Resulting Numbers: [64, 6, 24] Generated Node #0,0: 16:[64, 6, 24] Operation: 58-34=24 Moving to Node #0,0 Current State: 16:[64, 6, 24], Operations: ['58-34=24'] Exploring Operation: 24/6=4, Resulting Numbers: [64, 4] Generated Node #0,0,0: 16:[64, 4] Operation: 24/6=4 Moving to Node #0,0,0 Current State: 16:[64, 4], Operations: ['58-34=24', '24/6=4'] Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_4
sum_heuristic
[ 65, 12, 20, 14 ]
85
[ "65-14=51", "20*51=1020", "1020/12=85" ]
Current State: 85:[65, 12, 20, 14], Operations: [] Exploring Operation: 65-14=51, Resulting Numbers: [12, 20, 51] Generated Node #2: [12, 20, 51] from Operation: 65-14=51 Current State: 85:[12, 20, 51], Operations: ['65-14=51'] Exploring Operation: 20*51=1020, Resulting Numbers: [12, 1020] Generated Node #3: [12, 1020] from Operation: 20*51=1020 Current State: 85:[12, 1020], Operations: ['65-14=51', '20*51=1020'] Exploring Operation: 1020/12=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[65, 12, 20, 14], Operations: [] Exploring Operation: 65+12=77, Resulting Numbers: [20, 14, 77] Generated Node #0,0: 85:[20, 14, 77] Operation: 65+12=77 Exploring Operation: 65+20=85, Resulting Numbers: [12, 14, 85] Generated Node #0,1: 85:[12, 14, 85] Operation: 65+20=85 Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[12, 14, 85], Operations: ['65+20=85'] Exploring Operation: 12+14=26, Resulting Numbers: [85, 26] Generated Node #0,1,0: 85:[85, 26] Operation: 12+14=26 Exploring Operation: 14-12=2, Resulting Numbers: [85, 2] Generated Node #0,1,1: 85:[85, 2] Operation: 14-12=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 85:[85, 2], Operations: ['65+20=85', '14-12=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,85 unequal: No Solution Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,85 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 #0,1,0 Current State: 85:[85, 26], Operations: ['65+20=85', '12+14=26'] Exploring Operation: 85-26=59, Resulting Numbers: [59] 59,85 unequal: No Solution Exploring Operation: 85+26=111, Resulting Numbers: [111] 111,85 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 #0,0 Current State: 85:[20, 14, 77], Operations: ['65+12=77'] Exploring Operation: 14+77=91, Resulting Numbers: [20, 91] Generated Node #0,0,0: 85:[20, 91] Operation: 14+77=91 Exploring Operation: 20-14=6, Resulting Numbers: [77, 6] Generated Node #0,0,1: 85:[77, 6] Operation: 20-14=6 Moving to Node #0,0,0 Current State: 85:[20, 91], Operations: ['65+12=77', '14+77=91'] Exploring Operation: 20+91=111, Resulting Numbers: [111] 111,85 unequal: No Solution Exploring Operation: 91-20=71, Resulting Numbers: [71] 71,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[77, 6], Operations: ['65+12=77', '20-14=6'] Exploring Operation: 77-6=71, Resulting Numbers: [71] 71,85 unequal: No Solution Exploring Operation: 77+6=83, Resulting Numbers: [83] 83,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 55, 63, 94, 40 ]
16
[ "55+63=118", "94+40=134", "134-118=16" ]
Current State: 16:[55, 63, 94, 40], Operations: [] Exploring Operation: 55+63=118, Resulting Numbers: [94, 40, 118] Generated Node #2: [94, 40, 118] from Operation: 55+63=118 Current State: 16:[94, 40, 118], Operations: ['55+63=118'] Exploring Operation: 94+40=134, Resulting Numbers: [118, 134] Generated Node #3: [118, 134] from Operation: 94+40=134 Current State: 16:[118, 134], Operations: ['55+63=118', '94+40=134'] Exploring Operation: 134-118=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[55, 63, 94, 40], Operations: [] Exploring Operation: 94-55=39, Resulting Numbers: [63, 40, 39] Generated Node #0,0: 16:[63, 40, 39] Operation: 94-55=39 Exploring Operation: 63-55=8, Resulting Numbers: [94, 40, 8] Generated Node #0,1: 16:[94, 40, 8] Operation: 63-55=8 Exploring Operation: 94-63=31, Resulting Numbers: [55, 40, 31] Generated Node #0,2: 16:[55, 40, 31] Operation: 94-63=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[55, 40, 31], Operations: ['94-63=31'] Exploring Operation: 40-31=9, Resulting Numbers: [55, 9] Generated Node #0,2,0: 16:[55, 9] Operation: 40-31=9 Exploring Operation: 55-40=15, Resulting Numbers: [31, 15] Generated Node #0,2,1: 16:[31, 15] Operation: 55-40=15 Exploring Operation: 55-31=24, Resulting Numbers: [40, 24] Generated Node #0,2,2: 16:[40, 24] Operation: 55-31=24 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 16:[31, 15], Operations: ['94-63=31', '55-40=15'] Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,16 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[55, 63, 94, 40], Operations: [] Exploring Operation: 94-63=31, Resulting Numbers: [55, 40, 31] Generated Node #0,2: 16:[55, 40, 31] Operation: 94-63=31 Moving to Node #0,2 Current State: 16:[55, 40, 31], Operations: ['94-63=31'] Exploring Operation: 55-40=15, Resulting Numbers: [31, 15] Generated Node #0,2,1: 16:[31, 15] Operation: 55-40=15 Moving to Node #0,2,1 Current State: 16:[31, 15], Operations: ['94-63=31', '55-40=15'] Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 12, 87, 3, 94 ]
87
[ "87-3=84", "84/12=7", "94-7=87" ]
Current State: 87:[12, 87, 3, 94], Operations: [] Exploring Operation: 87-3=84, Resulting Numbers: [12, 94, 84] Generated Node #2: [12, 94, 84] from Operation: 87-3=84 Current State: 87:[12, 94, 84], Operations: ['87-3=84'] Exploring Operation: 84/12=7, Resulting Numbers: [94, 7] Generated Node #3: [94, 7] from Operation: 84/12=7 Current State: 87:[94, 7], Operations: ['87-3=84', '84/12=7'] Exploring Operation: 94-7=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[12, 87, 3, 94], Operations: [] Exploring Operation: 94-12=82, Resulting Numbers: [87, 3, 82] Generated Node #0,0: 87:[87, 3, 82] Operation: 94-12=82 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[87, 3, 82], Operations: ['94-12=82'] Exploring Operation: 87-82=5, Resulting Numbers: [3, 5] Generated Node #0,0,0: 87:[3, 5] Operation: 87-82=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[3, 5], Operations: ['94-12=82', '87-82=5'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,87 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_1
sum_heuristic
[ 18, 33, 45, 27 ]
63
[ "18*45=810", "810/27=30", "33+30=63" ]
Current State: 63:[18, 33, 45, 27], Operations: [] Exploring Operation: 18*45=810, Resulting Numbers: [33, 27, 810] Generated Node #2: [33, 27, 810] from Operation: 18*45=810 Current State: 63:[33, 27, 810], Operations: ['18*45=810'] Exploring Operation: 810/27=30, Resulting Numbers: [33, 30] Generated Node #3: [33, 30] from Operation: 810/27=30 Current State: 63:[33, 30], Operations: ['18*45=810', '810/27=30'] Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[18, 33, 45, 27], Operations: [] Exploring Operation: 18+45=63, Resulting Numbers: [33, 27, 63] Generated Node #0,0: 63:[33, 27, 63] Operation: 18+45=63 Exploring Operation: 45-33=12, Resulting Numbers: [18, 27, 12] Generated Node #0,1: 63:[18, 27, 12] Operation: 45-33=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[18, 27, 12], Operations: ['45-33=12'] Exploring Operation: 18-12=6, Resulting Numbers: [27, 6] Generated Node #0,1,0: 63:[27, 6] Operation: 18-12=6 Exploring Operation: 27-18=9, Resulting Numbers: [12, 9] Generated Node #0,1,1: 63:[12, 9] Operation: 27-18=9 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 63:[12, 9], Operations: ['45-33=12', '27-18=9'] Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 63:[27, 6], Operations: ['45-33=12', '18-12=6'] Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[33, 27, 63], Operations: ['18+45=63'] Exploring Operation: 33-27=6, Resulting Numbers: [63, 6] Generated Node #0,0,0: 63:[63, 6] Operation: 33-27=6 Exploring Operation: 33+27=60, Resulting Numbers: [63, 60] Generated Node #0,0,1: 63:[63, 60] Operation: 33+27=60 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[63, 6], Operations: ['18+45=63', '33-27=6'] Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,63 unequal: No Solution Exploring Operation: 63+6=69, Resulting Numbers: [69] 69,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 63:[63, 60], Operations: ['18+45=63', '33+27=60'] Exploring Operation: 63+60=123, Resulting Numbers: [123] 123,63 unequal: No Solution Exploring Operation: 63-60=3, Resulting Numbers: [3] 3,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 8, 26, 56, 67 ]
100
[ "56/8=7", "26+67=93", "7+93=100" ]
Current State: 100:[8, 26, 56, 67], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [26, 67, 7] Generated Node #2: [26, 67, 7] from Operation: 56/8=7 Current State: 100:[26, 67, 7], Operations: ['56/8=7'] Exploring Operation: 26+67=93, Resulting Numbers: [7, 93] Generated Node #3: [7, 93] from Operation: 26+67=93 Current State: 100:[7, 93], Operations: ['56/8=7', '26+67=93'] Exploring Operation: 7+93=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[8, 26, 56, 67], Operations: [] Exploring Operation: 67-56=11, Resulting Numbers: [8, 26, 11] Generated Node #0,0: 100:[8, 26, 11] Operation: 67-56=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[8, 26, 11], Operations: ['67-56=11'] Exploring Operation: 8+11=19, Resulting Numbers: [26, 19] Generated Node #0,0,0: 100:[26, 19] Operation: 8+11=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 100:[26, 19], Operations: ['67-56=11', '8+11=19'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,100 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
[ 31, 24, 21, 2 ]
99
[ "31+2=33", "24-21=3", "33*3=99" ]
Current State: 99:[31, 24, 21, 2], Operations: [] Exploring Operation: 31+2=33, Resulting Numbers: [24, 21, 33] Generated Node #2: [24, 21, 33] from Operation: 31+2=33 Current State: 99:[24, 21, 33], Operations: ['31+2=33'] Exploring Operation: 24-21=3, Resulting Numbers: [33, 3] Generated Node #3: [33, 3] from Operation: 24-21=3 Current State: 99:[33, 3], Operations: ['31+2=33', '24-21=3'] Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[31, 24, 21, 2], Operations: [] Exploring Operation: 24-21=3, Resulting Numbers: [31, 2, 3] Generated Node #0,0: 99:[31, 2, 3] Operation: 24-21=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[31, 2, 3], Operations: ['24-21=3'] Exploring Operation: 31+2=33, Resulting Numbers: [3, 33] Generated Node #0,0,0: 99:[3, 33] Operation: 31+2=33 Moving to Node #0,0,0 Current State: 99:[3, 33], Operations: ['24-21=3', '31+2=33'] Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[31, 24, 21, 2], Operations: [] Exploring Operation: 24-21=3, Resulting Numbers: [31, 2, 3] Generated Node #0,0: 99:[31, 2, 3] Operation: 24-21=3 Moving to Node #0,0 Current State: 99:[31, 2, 3], Operations: ['24-21=3'] Exploring Operation: 31+2=33, Resulting Numbers: [3, 33] Generated Node #0,0,0: 99:[3, 33] Operation: 31+2=33 Moving to Node #0,0,0 Current State: 99:[3, 33], Operations: ['24-21=3', '31+2=33'] Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 7, 64, 43, 81 ]
95
[ "64-7=57", "81-43=38", "57+38=95" ]
Current State: 95:[7, 64, 43, 81], Operations: [] Exploring Operation: 64-7=57, Resulting Numbers: [43, 81, 57] Generated Node #2: [43, 81, 57] from Operation: 64-7=57 Current State: 95:[43, 81, 57], Operations: ['64-7=57'] Exploring Operation: 81-43=38, Resulting Numbers: [57, 38] Generated Node #3: [57, 38] from Operation: 81-43=38 Current State: 95:[57, 38], Operations: ['64-7=57', '81-43=38'] Exploring Operation: 57+38=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[7, 64, 43, 81], Operations: [] Exploring Operation: 64+43=107, Resulting Numbers: [7, 81, 107] Generated Node #0,0: 95:[7, 81, 107] Operation: 64+43=107 Exploring Operation: 64-43=21, Resulting Numbers: [7, 81, 21] Generated Node #0,1: 95:[7, 81, 21] Operation: 64-43=21 Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[7, 81, 21], Operations: ['64-43=21'] Exploring Operation: 7+81=88, Resulting Numbers: [21, 88] Generated Node #0,1,0: 95:[21, 88] Operation: 7+81=88 Exploring Operation: 81+21=102, Resulting Numbers: [7, 102] Generated Node #0,1,1: 95:[7, 102] Operation: 81+21=102 Moving to Node #0,1,0 Current State: 95:[21, 88], Operations: ['64-43=21', '7+81=88'] Exploring Operation: 88-21=67, Resulting Numbers: [67] 67,95 unequal: No Solution Exploring Operation: 21+88=109, Resulting Numbers: [109] 109,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[7, 102], Operations: ['64-43=21', '81+21=102'] Exploring Operation: 7+102=109, Resulting Numbers: [109] 109,95 unequal: No Solution Exploring Operation: 102-7=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[7, 64, 43, 81], Operations: [] Exploring Operation: 64-43=21, Resulting Numbers: [7, 81, 21] Generated Node #0,1: 95:[7, 81, 21] Operation: 64-43=21 Moving to Node #0,1 Current State: 95:[7, 81, 21], Operations: ['64-43=21'] Exploring Operation: 81+21=102, Resulting Numbers: [7, 102] Generated Node #0,1,1: 95:[7, 102] Operation: 81+21=102 Moving to Node #0,1,1 Current State: 95:[7, 102], Operations: ['64-43=21', '81+21=102'] Exploring Operation: 102-7=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 57, 66, 56, 30 ]
35
[ "66-57=9", "56-30=26", "9+26=35" ]
Current State: 35:[57, 66, 56, 30], Operations: [] Exploring Operation: 66-57=9, Resulting Numbers: [56, 30, 9] Generated Node #2: [56, 30, 9] from Operation: 66-57=9 Current State: 35:[56, 30, 9], Operations: ['66-57=9'] Exploring Operation: 56-30=26, Resulting Numbers: [9, 26] Generated Node #3: [9, 26] from Operation: 56-30=26 Current State: 35:[9, 26], Operations: ['66-57=9', '56-30=26'] Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[57, 66, 56, 30], Operations: [] Exploring Operation: 66-57=9, Resulting Numbers: [56, 30, 9] Generated Node #0,0: 35:[56, 30, 9] Operation: 66-57=9 Exploring Operation: 66-56=10, Resulting Numbers: [57, 30, 10] Generated Node #0,1: 35:[57, 30, 10] Operation: 66-56=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[56, 30, 9], Operations: ['66-57=9'] Exploring Operation: 56-9=47, Resulting Numbers: [30, 47] Generated Node #0,0,0: 35:[30, 47] Operation: 56-9=47 Exploring Operation: 56-30=26, Resulting Numbers: [9, 26] Generated Node #0,0,1: 35:[9, 26] Operation: 56-30=26 Moving to Node #0,0,1 Current State: 35:[9, 26], Operations: ['66-57=9', '56-30=26'] Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[57, 66, 56, 30], Operations: [] Exploring Operation: 66-57=9, Resulting Numbers: [56, 30, 9] Generated Node #0,0: 35:[56, 30, 9] Operation: 66-57=9 Moving to Node #0,0 Current State: 35:[56, 30, 9], Operations: ['66-57=9'] Exploring Operation: 56-30=26, Resulting Numbers: [9, 26] Generated Node #0,0,1: 35:[9, 26] Operation: 56-30=26 Moving to Node #0,0,1 Current State: 35:[9, 26], Operations: ['66-57=9', '56-30=26'] Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 4, 11, 48, 13 ]
48
[ "11+13=24", "4*24=96", "96-48=48" ]
Current State: 48:[4, 11, 48, 13], Operations: [] Exploring Operation: 11+13=24, Resulting Numbers: [4, 48, 24] Generated Node #2: [4, 48, 24] from Operation: 11+13=24 Current State: 48:[4, 48, 24], Operations: ['11+13=24'] Exploring Operation: 4*24=96, Resulting Numbers: [48, 96] Generated Node #3: [48, 96] from Operation: 4*24=96 Current State: 48:[48, 96], Operations: ['11+13=24', '4*24=96'] Exploring Operation: 96-48=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[4, 11, 48, 13], Operations: [] Exploring Operation: 11+13=24, Resulting Numbers: [4, 48, 24] Generated Node #0,0: 48:[4, 48, 24] Operation: 11+13=24 Exploring Operation: 4+11=15, Resulting Numbers: [48, 13, 15] Generated Node #0,1: 48:[48, 13, 15] Operation: 4+11=15 Exploring Operation: 13-11=2, Resulting Numbers: [4, 48, 2] Generated Node #0,2: 48:[4, 48, 2] Operation: 13-11=2 Moving to Node #0,0 Current State: 48:[4, 48, 24], Operations: ['11+13=24'] Exploring Operation: 48-24=24, Resulting Numbers: [4, 24] Generated Node #0,0,0: 48:[4, 24] Operation: 48-24=24 Exploring Operation: 48/4=12, Resulting Numbers: [24, 12] Generated Node #0,0,1: 48:[24, 12] Operation: 48/4=12 Exploring Operation: 24/4=6, Resulting Numbers: [48, 6] Generated Node #0,0,2: 48:[48, 6] Operation: 24/4=6 Moving to Node #0,2 Current State: 48:[4, 48, 2], Operations: ['13-11=2'] Exploring Operation: 48/4=12, Resulting Numbers: [2, 12] Generated Node #0,2,0: 48:[2, 12] Operation: 48/4=12 Exploring Operation: 4+2=6, Resulting Numbers: [48, 6] Generated Node #0,2,1: 48:[48, 6] Operation: 4+2=6 Exploring Operation: 4*2=8, Resulting Numbers: [48, 8] Generated Node #0,2,2: 48:[48, 8] Operation: 4*2=8 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 48:[2, 12], Operations: ['13-11=2', '48/4=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,48 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,48 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 48:[48, 6], Operations: ['13-11=2', '4+2=6'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,48 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 48:[48, 8], Operations: ['13-11=2', '4*2=8'] Exploring Operation: 48+8=56, Resulting Numbers: [56] 56,48 unequal: No Solution Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,48 unequal: No Solution Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 48:[48, 13, 15], Operations: ['4+11=15'] Exploring Operation: 15-13=2, Resulting Numbers: [48, 2] Generated Node #0,1,0: 48:[48, 2] Operation: 15-13=2 Exploring Operation: 13+15=28, Resulting Numbers: [48, 28] Generated Node #0,1,1: 48:[48, 28] Operation: 13+15=28 Exploring Operation: 48-15=33, Resulting Numbers: [13, 33] Generated Node #0,1,2: 48:[13, 33] Operation: 48-15=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[48, 2], Operations: ['4+11=15', '15-13=2'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,48 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,48 unequal: No Solution Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 48:[48, 28], Operations: ['4+11=15', '13+15=28'] Exploring Operation: 48+28=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 48-28=20, Resulting Numbers: [20] 20,48 unequal: No Solution Exploring Operation: 48*28=1344, Resulting Numbers: [1344] 1344,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 48:[13, 33], Operations: ['4+11=15', '48-15=33'] Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,48 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,48 unequal: No Solution Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,48 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: 48:[4, 24], Operations: ['11+13=24', '48-24=24'] Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,48 unequal: No Solution Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[24, 12], Operations: ['11+13=24', '48/4=12'] Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,48 unequal: No Solution Exploring Operation: 24+12=36, Resulting Numbers: [36] 36,48 unequal: No Solution Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,48 unequal: No Solution Moving to Node #0,0,2 Current State: 48:[48, 6], Operations: ['11+13=24', '24/4=6'] Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,48 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,48 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 64, 12, 68, 76 ]
20
[ "76-68=8", "64/8=8", "12+8=20" ]
Current State: 20:[64, 12, 68, 76], Operations: [] Exploring Operation: 76-68=8, Resulting Numbers: [64, 12, 8] Generated Node #2: [64, 12, 8] from Operation: 76-68=8 Current State: 20:[64, 12, 8], Operations: ['76-68=8'] Exploring Operation: 64/8=8, Resulting Numbers: [12, 8] Generated Node #3: [12, 8] from Operation: 64/8=8 Current State: 20:[12, 8], Operations: ['76-68=8', '64/8=8'] Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[64, 12, 68, 76], Operations: [] Exploring Operation: 76-64=12, Resulting Numbers: [12, 68, 12] Generated Node #0,0: 20:[12, 68, 12] Operation: 76-64=12 Exploring Operation: 76-68=8, Resulting Numbers: [64, 12, 8] Generated Node #0,1: 20:[64, 12, 8] Operation: 76-68=8 Exploring Operation: 68-64=4, Resulting Numbers: [12, 76, 4] Generated Node #0,2: 20:[12, 76, 4] Operation: 68-64=4 Exploring Operation: 68-12=56, Resulting Numbers: [64, 76, 56] Generated Node #0,3: 20:[64, 76, 56] Operation: 68-12=56 Exploring Operation: 64-12=52, Resulting Numbers: [68, 76, 52] Generated Node #0,4: 20:[68, 76, 52] Operation: 64-12=52 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[64, 12, 8], Operations: ['76-68=8'] Exploring Operation: 12-8=4, Resulting Numbers: [64, 4] Generated Node #0,1,0: 20:[64, 4] Operation: 12-8=4 Exploring Operation: 12+8=20, Resulting Numbers: [64, 20] Generated Node #0,1,1: 20:[64, 20] Operation: 12+8=20 Exploring Operation: 64-12=52, Resulting Numbers: [8, 52] Generated Node #0,1,2: 20:[8, 52] Operation: 64-12=52 Exploring Operation: 64/8=8, Resulting Numbers: [12, 8] Generated Node #0,1,3: 20:[12, 8] Operation: 64/8=8 Exploring Operation: 64-8=56, Resulting Numbers: [12, 56] Generated Node #0,1,4: 20:[12, 56] Operation: 64-8=56 Moving to Node #0,1,3 Current State: 20:[12, 8], Operations: ['76-68=8', '64/8=8'] Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,20 unequal: No Solution Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[64, 12, 68, 76], Operations: [] Exploring Operation: 76-68=8, Resulting Numbers: [64, 12, 8] Generated Node #0,1: 20:[64, 12, 8] Operation: 76-68=8 Moving to Node #0,1 Current State: 20:[64, 12, 8], Operations: ['76-68=8'] Exploring Operation: 64/8=8, Resulting Numbers: [12, 8] Generated Node #0,1,3: 20:[12, 8] Operation: 64/8=8 Moving to Node #0,1,3 Current State: 20:[12, 8], Operations: ['76-68=8', '64/8=8'] Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 6, 7, 4, 22 ]
66
[ "7-6=1", "4-1=3", "22*3=66" ]
Current State: 66:[6, 7, 4, 22], Operations: [] Exploring Operation: 7-6=1, Resulting Numbers: [4, 22, 1] Generated Node #2: [4, 22, 1] from Operation: 7-6=1 Current State: 66:[4, 22, 1], Operations: ['7-6=1'] Exploring Operation: 4-1=3, Resulting Numbers: [22, 3] Generated Node #3: [22, 3] from Operation: 4-1=3 Current State: 66:[22, 3], Operations: ['7-6=1', '4-1=3'] Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[6, 7, 4, 22], Operations: [] Exploring Operation: 7+4=11, Resulting Numbers: [6, 22, 11] Generated Node #0,0: 66:[6, 22, 11] Operation: 7+4=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[6, 22, 11], Operations: ['7+4=11'] Exploring Operation: 6*11=66, Resulting Numbers: [22, 66] Generated Node #0,0,0: 66:[22, 66] Operation: 6*11=66 Moving to Node #0,0,0 Current State: 66:[22, 66], Operations: ['7+4=11', '6*11=66'] Exploring Operation: 66/22=3, Resulting Numbers: [3] 3,66 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