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
[ 15, 4, 20, 7 ]
21
[ "15*4=60", "60/20=3", "7*3=21" ]
Current State: 21:[15, 4, 20, 7], Operations: [] Exploring Operation: 15*4=60, Resulting Numbers: [20, 7, 60] Generated Node #2: [20, 7, 60] from Operation: 15*4=60 Current State: 21:[20, 7, 60], Operations: ['15*4=60'] Exploring Operation: 60/20=3, Resulting Numbers: [7, 3] Generated Node #3: [7, 3] from Operation: 60/20=3 Current State: 21:[7, 3], Operations: ['15*4=60', '60/20=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[15, 4, 20, 7], Operations: [] Exploring Operation: 20-15=5, Resulting Numbers: [4, 7, 5] Generated Node #0,0: 21:[4, 7, 5] Operation: 20-15=5 Exploring Operation: 15-7=8, Resulting Numbers: [4, 20, 8] Generated Node #0,1: 21:[4, 20, 8] Operation: 15-7=8 Exploring Operation: 15+4=19, Resulting Numbers: [20, 7, 19] Generated Node #0,2: 21:[20, 7, 19] Operation: 15+4=19 Exploring Operation: 15+7=22, Resulting Numbers: [4, 20, 22] Generated Node #0,3: 21:[4, 20, 22] Operation: 15+7=22 Moving to Node #0,0 Current State: 21:[4, 7, 5], Operations: ['20-15=5'] Exploring Operation: 5-4=1, Resulting Numbers: [7, 1] Generated Node #0,0,0: 21:[7, 1] Operation: 5-4=1 Exploring Operation: 4+5=9, Resulting Numbers: [7, 9] Generated Node #0,0,1: 21:[7, 9] Operation: 4+5=9 Exploring Operation: 4*5=20, Resulting Numbers: [7, 20] Generated Node #0,0,2: 21:[7, 20] Operation: 4*5=20 Exploring Operation: 7-4=3, Resulting Numbers: [5, 3] Generated Node #0,0,3: 21:[5, 3] Operation: 7-4=3 Moving to Node #0,2 Current State: 21:[20, 7, 19], Operations: ['15+4=19'] Exploring Operation: 20-19=1, Resulting Numbers: [7, 1] Generated Node #0,2,0: 21:[7, 1] Operation: 20-19=1 Exploring Operation: 7+19=26, Resulting Numbers: [20, 26] Generated Node #0,2,1: 21:[20, 26] Operation: 7+19=26 Exploring Operation: 19-7=12, Resulting Numbers: [20, 12] Generated Node #0,2,2: 21:[20, 12] Operation: 19-7=12 Exploring Operation: 20+7=27, Resulting Numbers: [19, 27] Generated Node #0,2,3: 21:[19, 27] Operation: 20+7=27 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 21:[7, 1], Operations: ['15+4=19', '20-19=1'] Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,21 unequal: No Solution No 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: 21:[20, 26], Operations: ['15+4=19', '7+19=26'] Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,21 unequal: No Solution No 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: 21:[20, 12], Operations: ['15+4=19', '19-7=12'] Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 20*12=240, Resulting Numbers: [240] 240,21 unequal: No Solution Exploring Operation: 20+12=32, Resulting Numbers: [32] 32,21 unequal: No Solution No 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: 21:[19, 27], Operations: ['15+4=19', '20+7=27'] Exploring Operation: 27-19=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 19+27=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 19*27=513, Resulting Numbers: [513] 513,21 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: 21:[4, 20, 8], Operations: ['15-7=8'] Exploring Operation: 8-4=4, Resulting Numbers: [20, 4] Generated Node #0,1,0: 21:[20, 4] Operation: 8-4=4 Exploring Operation: 4+20=24, Resulting Numbers: [8, 24] Generated Node #0,1,1: 21:[8, 24] Operation: 4+20=24 Exploring Operation: 20/4=5, Resulting Numbers: [8, 5] Generated Node #0,1,2: 21:[8, 5] Operation: 20/4=5 Exploring Operation: 8/4=2, Resulting Numbers: [20, 2] Generated Node #0,1,3: 21:[20, 2] Operation: 8/4=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 21:[20, 4], Operations: ['15-7=8', '8-4=4'] Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,21 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,21 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,21 unequal: No Solution No 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: 21:[20, 2], Operations: ['15-7=8', '8/4=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,21 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,21 unequal: No Solution No 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: 21:[8, 5], Operations: ['15-7=8', '20/4=5'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,21 unequal: No Solution No 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: 21:[8, 24], Operations: ['15-7=8', '4+20=24'] Exploring Operation: 8*24=192, Resulting Numbers: [192] 192,21 unequal: No Solution Exploring Operation: 8+24=32, Resulting Numbers: [32] 32,21 unequal: No Solution Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,21 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: 21:[4, 20, 22], Operations: ['15+7=22'] Exploring Operation: 20/4=5, Resulting Numbers: [22, 5] Generated Node #0,3,0: 21:[22, 5] Operation: 20/4=5 Exploring Operation: 22-4=18, Resulting Numbers: [20, 18] Generated Node #0,3,1: 21:[20, 18] Operation: 22-4=18 Exploring Operation: 22-20=2, Resulting Numbers: [4, 2] Generated Node #0,3,2: 21:[4, 2] Operation: 22-20=2 Exploring Operation: 4+20=24, Resulting Numbers: [22, 24] Generated Node #0,3,3: 21:[22, 24] Operation: 4+20=24 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 21:[4, 2], Operations: ['15+7=22', '22-20=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,21 unequal: No Solution No 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: 21:[22, 5], Operations: ['15+7=22', '20/4=5'] Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,21 unequal: No Solution Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,21 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,21 unequal: No Solution No 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: 21:[20, 18], Operations: ['15+7=22', '22-4=18'] Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,21 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,21 unequal: No Solution No 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: 21:[22, 24], Operations: ['15+7=22', '4+20=24'] Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 22*24=528, Resulting Numbers: [528] 528,21 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: 21:[7, 20], Operations: ['20-15=5', '4*5=20'] Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,21 unequal: No Solution Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,21 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[7, 9], Operations: ['20-15=5', '4+5=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,21 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[7, 1], Operations: ['20-15=5', '5-4=1'] Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,21 unequal: No Solution Moving to Node #0,0,3 Current State: 21:[5, 3], Operations: ['20-15=5', '7-4=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,21 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 4, 82, 25, 88 ]
35
[ "82-4=78", "25+88=113", "113-78=35" ]
Current State: 35:[4, 82, 25, 88], Operations: [] Exploring Operation: 82-4=78, Resulting Numbers: [25, 88, 78] Generated Node #2: [25, 88, 78] from Operation: 82-4=78 Current State: 35:[25, 88, 78], Operations: ['82-4=78'] Exploring Operation: 25+88=113, Resulting Numbers: [78, 113] Generated Node #3: [78, 113] from Operation: 25+88=113 Current State: 35:[78, 113], Operations: ['82-4=78', '25+88=113'] Exploring Operation: 113-78=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[4, 82, 25, 88], Operations: [] Exploring Operation: 88-82=6, Resulting Numbers: [4, 25, 6] Generated Node #0,0: 35:[4, 25, 6] Operation: 88-82=6 Exploring Operation: 82-25=57, Resulting Numbers: [4, 88, 57] Generated Node #0,1: 35:[4, 88, 57] Operation: 82-25=57 Exploring Operation: 88-25=63, Resulting Numbers: [4, 82, 63] Generated Node #0,2: 35:[4, 82, 63] Operation: 88-25=63 Exploring Operation: 88/4=22, Resulting Numbers: [82, 25, 22] Generated Node #0,3: 35:[82, 25, 22] Operation: 88/4=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[4, 25, 6], Operations: ['88-82=6'] Exploring Operation: 6-4=2, Resulting Numbers: [25, 2] Generated Node #0,0,0: 35:[25, 2] Operation: 6-4=2 Exploring Operation: 4+6=10, Resulting Numbers: [25, 10] Generated Node #0,0,1: 35:[25, 10] Operation: 4+6=10 Exploring Operation: 4+25=29, Resulting Numbers: [6, 29] Generated Node #0,0,2: 35:[6, 29] Operation: 4+25=29 Exploring Operation: 25+6=31, Resulting Numbers: [4, 31] Generated Node #0,0,3: 35:[4, 31] Operation: 25+6=31 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 35:[4, 31], Operations: ['88-82=6', '25+6=31'] Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[4, 82, 25, 88], Operations: [] Exploring Operation: 88-82=6, Resulting Numbers: [4, 25, 6] Generated Node #0,0: 35:[4, 25, 6] Operation: 88-82=6 Moving to Node #0,0 Current State: 35:[4, 25, 6], Operations: ['88-82=6'] Exploring Operation: 25+6=31, Resulting Numbers: [4, 31] Generated Node #0,0,3: 35:[4, 31] Operation: 25+6=31 Moving to Node #0,0,3 Current State: 35:[4, 31], Operations: ['88-82=6', '25+6=31'] Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 8, 5, 71, 24 ]
98
[ "8-5=3", "71+24=95", "3+95=98" ]
Current State: 98:[8, 5, 71, 24], Operations: [] Exploring Operation: 8-5=3, Resulting Numbers: [71, 24, 3] Generated Node #2: [71, 24, 3] from Operation: 8-5=3 Current State: 98:[71, 24, 3], Operations: ['8-5=3'] Exploring Operation: 71+24=95, Resulting Numbers: [3, 95] Generated Node #3: [3, 95] from Operation: 71+24=95 Current State: 98:[3, 95], Operations: ['8-5=3', '71+24=95'] Exploring Operation: 3+95=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[8, 5, 71, 24], Operations: [] Exploring Operation: 71-24=47, Resulting Numbers: [8, 5, 47] Generated Node #0,0: 98:[8, 5, 47] Operation: 71-24=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[8, 5, 47], Operations: ['71-24=47'] Exploring Operation: 8+5=13, Resulting Numbers: [47, 13] Generated Node #0,0,0: 98:[47, 13] Operation: 8+5=13 Moving to Node #0,0,0 Current State: 98:[47, 13], Operations: ['71-24=47', '8+5=13'] Exploring Operation: 47+13=60, Resulting Numbers: [60] 60,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 33, 32, 73, 49 ]
71
[ "49-33=16", "32/16=2", "73-2=71" ]
Current State: 71:[33, 32, 73, 49], Operations: [] Exploring Operation: 49-33=16, Resulting Numbers: [32, 73, 16] Generated Node #2: [32, 73, 16] from Operation: 49-33=16 Current State: 71:[32, 73, 16], Operations: ['49-33=16'] Exploring Operation: 32/16=2, Resulting Numbers: [73, 2] Generated Node #3: [73, 2] from Operation: 32/16=2 Current State: 71:[73, 2], Operations: ['49-33=16', '32/16=2'] Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[33, 32, 73, 49], Operations: [] Exploring Operation: 73-32=41, Resulting Numbers: [33, 49, 41] Generated Node #0,0: 71:[33, 49, 41] Operation: 73-32=41 Exploring Operation: 73-33=40, Resulting Numbers: [32, 49, 40] Generated Node #0,1: 71:[32, 49, 40] Operation: 73-33=40 Exploring Operation: 33+32=65, Resulting Numbers: [73, 49, 65] Generated Node #0,2: 71:[73, 49, 65] Operation: 33+32=65 Exploring Operation: 32+49=81, Resulting Numbers: [33, 73, 81] Generated Node #0,3: 71:[33, 73, 81] Operation: 32+49=81 Exploring Operation: 33+49=82, Resulting Numbers: [32, 73, 82] Generated Node #0,4: 71:[32, 73, 82] Operation: 33+49=82 Moving to Node #0,2 Current State: 71:[73, 49, 65], Operations: ['33+32=65'] Exploring Operation: 73+49=122, Resulting Numbers: [65, 122] Generated Node #0,2,0: 71:[65, 122] Operation: 73+49=122 Exploring Operation: 73-49=24, Resulting Numbers: [65, 24] Generated Node #0,2,1: 71:[65, 24] Operation: 73-49=24 Exploring Operation: 65-49=16, Resulting Numbers: [73, 16] Generated Node #0,2,2: 71:[73, 16] Operation: 65-49=16 Exploring Operation: 73-65=8, Resulting Numbers: [49, 8] Generated Node #0,2,3: 71:[49, 8] Operation: 73-65=8 Exploring Operation: 49+65=114, Resulting Numbers: [73, 114] Generated Node #0,2,4: 71:[73, 114] Operation: 49+65=114 Moving to Node #0,3 Current State: 71:[33, 73, 81], Operations: ['32+49=81'] Exploring Operation: 33+73=106, Resulting Numbers: [81, 106] Generated Node #0,3,0: 71:[81, 106] Operation: 33+73=106 Exploring Operation: 81-73=8, Resulting Numbers: [33, 8] Generated Node #0,3,1: 71:[33, 8] Operation: 81-73=8 Exploring Operation: 73-33=40, Resulting Numbers: [81, 40] Generated Node #0,3,2: 71:[81, 40] Operation: 73-33=40 Exploring Operation: 33+81=114, Resulting Numbers: [73, 114] Generated Node #0,3,3: 71:[73, 114] Operation: 33+81=114 Exploring Operation: 81-33=48, Resulting Numbers: [73, 48] Generated Node #0,3,4: 71:[73, 48] Operation: 81-33=48 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 71:[73, 48], Operations: ['32+49=81', '81-33=48'] Exploring Operation: 73+48=121, Resulting Numbers: [121] 121,71 unequal: No Solution Exploring Operation: 73*48=3504, Resulting Numbers: [3504] 3504,71 unequal: No Solution Exploring Operation: 73-48=25, Resulting Numbers: [25] 25,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 71:[81, 40], Operations: ['32+49=81', '73-33=40'] Exploring Operation: 81-40=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 81+40=121, Resulting Numbers: [121] 121,71 unequal: No Solution Exploring Operation: 81*40=3240, Resulting Numbers: [3240] 3240,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 71:[81, 106], Operations: ['32+49=81', '33+73=106'] Exploring Operation: 106-81=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 81*106=8586, Resulting Numbers: [8586] 8586,71 unequal: No Solution Exploring Operation: 81+106=187, Resulting Numbers: [187] 187,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 71:[73, 114], Operations: ['32+49=81', '33+81=114'] Exploring Operation: 73*114=8322, Resulting Numbers: [8322] 8322,71 unequal: No Solution Exploring Operation: 114-73=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 73+114=187, Resulting Numbers: [187] 187,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 71:[33, 8], Operations: ['32+49=81', '81-73=8'] Exploring Operation: 33+8=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 33*8=264, Resulting Numbers: [264] 264,71 unequal: No Solution Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,71 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: 71:[32, 73, 82], Operations: ['33+49=82'] Exploring Operation: 73-32=41, Resulting Numbers: [82, 41] Generated Node #0,4,0: 71:[82, 41] Operation: 73-32=41 Exploring Operation: 32+82=114, Resulting Numbers: [73, 114] Generated Node #0,4,1: 71:[73, 114] Operation: 32+82=114 Exploring Operation: 82-32=50, Resulting Numbers: [73, 50] Generated Node #0,4,2: 71:[73, 50] Operation: 82-32=50 Exploring Operation: 82-73=9, Resulting Numbers: [32, 9] Generated Node #0,4,3: 71:[32, 9] Operation: 82-73=9 Exploring Operation: 32+73=105, Resulting Numbers: [82, 105] Generated Node #0,4,4: 71:[82, 105] Operation: 32+73=105 Moving to Node #0,0 Current State: 71:[33, 49, 41], Operations: ['73-32=41'] Exploring Operation: 41-33=8, Resulting Numbers: [49, 8] Generated Node #0,0,0: 71:[49, 8] Operation: 41-33=8 Exploring Operation: 33+49=82, Resulting Numbers: [41, 82] Generated Node #0,0,1: 71:[41, 82] Operation: 33+49=82 Exploring Operation: 33+41=74, Resulting Numbers: [49, 74] Generated Node #0,0,2: 71:[49, 74] Operation: 33+41=74 Exploring Operation: 49+41=90, Resulting Numbers: [33, 90] Generated Node #0,0,3: 71:[33, 90] Operation: 49+41=90 Exploring Operation: 49-33=16, Resulting Numbers: [41, 16] Generated Node #0,0,4: 71:[41, 16] Operation: 49-33=16 Moving to Node #0,1 Current State: 71:[32, 49, 40], Operations: ['73-33=40'] Exploring Operation: 49+40=89, Resulting Numbers: [32, 89] Generated Node #0,1,0: 71:[32, 89] Operation: 49+40=89 Exploring Operation: 49-32=17, Resulting Numbers: [40, 17] Generated Node #0,1,1: 71:[40, 17] Operation: 49-32=17 Exploring Operation: 32+40=72, Resulting Numbers: [49, 72] Generated Node #0,1,2: 71:[49, 72] Operation: 32+40=72 Exploring Operation: 40-32=8, Resulting Numbers: [49, 8] Generated Node #0,1,3: 71:[49, 8] Operation: 40-32=8 Exploring Operation: 32+49=81, Resulting Numbers: [40, 81] Generated Node #0,1,4: 71:[40, 81] Operation: 32+49=81 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 71:[49, 72], Operations: ['73-33=40', '32+40=72'] Exploring Operation: 49+72=121, Resulting Numbers: [121] 121,71 unequal: No Solution Exploring Operation: 49*72=3528, Resulting Numbers: [3528] 3528,71 unequal: No Solution Exploring Operation: 72-49=23, Resulting Numbers: [23] 23,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 71:[40, 81], Operations: ['73-33=40', '32+49=81'] Exploring Operation: 40*81=3240, Resulting Numbers: [3240] 3240,71 unequal: No Solution Exploring Operation: 40+81=121, Resulting Numbers: [121] 121,71 unequal: No Solution Exploring Operation: 81-40=41, Resulting Numbers: [41] 41,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 71:[32, 89], Operations: ['73-33=40', '49+40=89'] Exploring Operation: 32*89=2848, Resulting Numbers: [2848] 2848,71 unequal: No Solution Exploring Operation: 89-32=57, Resulting Numbers: [57] 57,71 unequal: No Solution Exploring Operation: 32+89=121, Resulting Numbers: [121] 121,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 71:[40, 17], Operations: ['73-33=40', '49-32=17'] Exploring Operation: 40*17=680, Resulting Numbers: [680] 680,71 unequal: No Solution Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,71 unequal: No Solution Exploring Operation: 40+17=57, Resulting Numbers: [57] 57,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 71:[49, 8], Operations: ['73-33=40', '40-32=8'] Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,71 unequal: No Solution Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 49*8=392, Resulting Numbers: [392] 392,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,2 Current State: 71:[73, 50], Operations: ['33+49=82', '82-32=50'] Exploring Operation: 73*50=3650, Resulting Numbers: [3650] 3650,71 unequal: No Solution Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,71 unequal: No Solution Exploring Operation: 73+50=123, Resulting Numbers: [123] 123,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[49, 74], Operations: ['73-32=41', '33+41=74'] Exploring Operation: 49*74=3626, Resulting Numbers: [3626] 3626,71 unequal: No Solution Exploring Operation: 49+74=123, Resulting Numbers: [123] 123,71 unequal: No Solution Exploring Operation: 74-49=25, Resulting Numbers: [25] 25,71 unequal: No Solution Moving to Node #0,4,0 Current State: 71:[82, 41], Operations: ['33+49=82', '73-32=41'] Exploring Operation: 82*41=3362, Resulting Numbers: [3362] 3362,71 unequal: No Solution Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,71 unequal: No Solution Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 82+41=123, Resulting Numbers: [123] 123,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[41, 82], Operations: ['73-32=41', '33+49=82'] Exploring Operation: 41*82=3362, Resulting Numbers: [3362] 3362,71 unequal: No Solution Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,71 unequal: No Solution Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 41+82=123, Resulting Numbers: [123] 123,71 unequal: No Solution Moving to Node #0,2,4 Current State: 71:[73, 114], Operations: ['33+32=65', '49+65=114'] Exploring Operation: 114-73=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 73*114=8322, Resulting Numbers: [8322] 8322,71 unequal: No Solution Exploring Operation: 73+114=187, Resulting Numbers: [187] 187,71 unequal: No Solution Moving to Node #0,4,1 Current State: 71:[73, 114], Operations: ['33+49=82', '32+82=114'] Exploring Operation: 73*114=8322, Resulting Numbers: [8322] 8322,71 unequal: No Solution Exploring Operation: 114-73=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 73+114=187, Resulting Numbers: [187] 187,71 unequal: No Solution Moving to Node #0,4,4 Current State: 71:[82, 105], Operations: ['33+49=82', '32+73=105'] Exploring Operation: 82*105=8610, Resulting Numbers: [8610] 8610,71 unequal: No Solution Exploring Operation: 105-82=23, Resulting Numbers: [23] 23,71 unequal: No Solution Exploring Operation: 82+105=187, Resulting Numbers: [187] 187,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[65, 24], Operations: ['33+32=65', '73-49=24'] Exploring Operation: 65+24=89, Resulting Numbers: [89] 89,71 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 65*24=1560, Resulting Numbers: [1560] 1560,71 unequal: No Solution Moving to Node #0,0,3 Current State: 71:[33, 90], Operations: ['73-32=41', '49+41=90'] Exploring Operation: 33+90=123, Resulting Numbers: [123] 123,71 unequal: No Solution Exploring Operation: 90-33=57, Resulting Numbers: [57] 57,71 unequal: No Solution Exploring Operation: 33*90=2970, Resulting Numbers: [2970] 2970,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[65, 122], Operations: ['33+32=65', '73+49=122'] Exploring Operation: 65*122=7930, Resulting Numbers: [7930] 7930,71 unequal: No Solution Exploring Operation: 65+122=187, Resulting Numbers: [187] 187,71 unequal: No Solution Exploring Operation: 122-65=57, Resulting Numbers: [57] 57,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[73, 16], Operations: ['33+32=65', '65-49=16'] Exploring Operation: 73+16=89, Resulting Numbers: [89] 89,71 unequal: No Solution Exploring Operation: 73-16=57, Resulting Numbers: [57] 57,71 unequal: No Solution Exploring Operation: 73*16=1168, Resulting Numbers: [1168] 1168,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[49, 8], Operations: ['73-32=41', '41-33=8'] Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,71 unequal: No Solution Exploring Operation: 49*8=392, Resulting Numbers: [392] 392,71 unequal: No Solution Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[49, 8], Operations: ['33+32=65', '73-65=8'] Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,71 unequal: No Solution Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 49*8=392, Resulting Numbers: [392] 392,71 unequal: No Solution Moving to Node #0,0,4 Current State: 71:[41, 16], Operations: ['73-32=41', '49-33=16'] Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 41+16=57, Resulting Numbers: [57] 57,71 unequal: No Solution Exploring Operation: 41*16=656, Resulting Numbers: [656] 656,71 unequal: No Solution Moving to Node #0,4,3 Current State: 71:[32, 9], Operations: ['33+49=82', '82-73=9'] Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,71 unequal: No Solution Exploring Operation: 32*9=288, Resulting Numbers: [288] 288,71 unequal: No Solution Exploring Operation: 32+9=41, Resulting Numbers: [41] 41,71 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 96, 61, 65, 67 ]
97
[ "96-61=35", "65+67=132", "132-35=97" ]
Current State: 97:[96, 61, 65, 67], Operations: [] Exploring Operation: 96-61=35, Resulting Numbers: [65, 67, 35] Generated Node #2: [65, 67, 35] from Operation: 96-61=35 Current State: 97:[65, 67, 35], Operations: ['96-61=35'] Exploring Operation: 65+67=132, Resulting Numbers: [35, 132] Generated Node #3: [35, 132] from Operation: 65+67=132 Current State: 97:[35, 132], Operations: ['96-61=35', '65+67=132'] Exploring Operation: 132-35=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[96, 61, 65, 67], Operations: [] Exploring Operation: 61+65=126, Resulting Numbers: [96, 67, 126] Generated Node #0,0: 97:[96, 67, 126] Operation: 61+65=126 Exploring Operation: 65+67=132, Resulting Numbers: [96, 61, 132] Generated Node #0,1: 97:[96, 61, 132] Operation: 65+67=132 Exploring Operation: 61+67=128, Resulting Numbers: [96, 65, 128] Generated Node #0,2: 97:[96, 65, 128] Operation: 61+67=128 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[96, 67, 126], Operations: ['61+65=126'] Exploring Operation: 96-67=29, Resulting Numbers: [126, 29] Generated Node #0,0,0: 97:[126, 29] Operation: 96-67=29 Exploring Operation: 126-67=59, Resulting Numbers: [96, 59] Generated Node #0,0,1: 97:[96, 59] Operation: 126-67=59 Exploring Operation: 96+67=163, Resulting Numbers: [126, 163] Generated Node #0,0,2: 97:[126, 163] Operation: 96+67=163 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 97:[96, 59], Operations: ['61+65=126', '126-67=59'] Exploring Operation: 96-59=37, Resulting Numbers: [37] 37,97 unequal: No Solution Exploring Operation: 96+59=155, Resulting Numbers: [155] 155,97 unequal: No Solution Exploring Operation: 96*59=5664, Resulting Numbers: [5664] 5664,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 97:[126, 163], Operations: ['61+65=126', '96+67=163'] Exploring Operation: 163-126=37, Resulting Numbers: [37] 37,97 unequal: No Solution Exploring Operation: 126+163=289, Resulting Numbers: [289] 289,97 unequal: No Solution Exploring Operation: 126*163=20538, Resulting Numbers: [20538] 20538,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[126, 29], Operations: ['61+65=126', '96-67=29'] Exploring Operation: 126-29=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[96, 61, 65, 67], Operations: [] Exploring Operation: 61+65=126, Resulting Numbers: [96, 67, 126] Generated Node #0,0: 97:[96, 67, 126] Operation: 61+65=126 Moving to Node #0,0 Current State: 97:[96, 67, 126], Operations: ['61+65=126'] Exploring Operation: 96-67=29, Resulting Numbers: [126, 29] Generated Node #0,0,0: 97:[126, 29] Operation: 96-67=29 Moving to Node #0,0,0 Current State: 97:[126, 29], Operations: ['61+65=126', '96-67=29'] Exploring Operation: 126-29=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 45, 28, 83, 23 ]
21
[ "45*28=1260", "83-23=60", "1260/60=21" ]
Current State: 21:[45, 28, 83, 23], Operations: [] Exploring Operation: 45*28=1260, Resulting Numbers: [83, 23, 1260] Generated Node #2: [83, 23, 1260] from Operation: 45*28=1260 Current State: 21:[83, 23, 1260], Operations: ['45*28=1260'] Exploring Operation: 83-23=60, Resulting Numbers: [1260, 60] Generated Node #3: [1260, 60] from Operation: 83-23=60 Current State: 21:[1260, 60], Operations: ['45*28=1260', '83-23=60'] Exploring Operation: 1260/60=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[45, 28, 83, 23], Operations: [] Exploring Operation: 83-45=38, Resulting Numbers: [28, 23, 38] Generated Node #0,0: 21:[28, 23, 38] Operation: 83-45=38 Exploring Operation: 45-28=17, Resulting Numbers: [83, 23, 17] Generated Node #0,1: 21:[83, 23, 17] Operation: 45-28=17 Exploring Operation: 83-28=55, Resulting Numbers: [45, 23, 55] Generated Node #0,2: 21:[45, 23, 55] Operation: 83-28=55 Moving to Node #0,0 Current State: 21:[28, 23, 38], Operations: ['83-45=38'] Exploring Operation: 28-23=5, Resulting Numbers: [38, 5] Generated Node #0,0,0: 21:[38, 5] Operation: 28-23=5 Exploring Operation: 38-28=10, Resulting Numbers: [23, 10] Generated Node #0,0,1: 21:[23, 10] Operation: 38-28=10 Exploring Operation: 38-23=15, Resulting Numbers: [28, 15] Generated Node #0,0,2: 21:[28, 15] Operation: 38-23=15 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[23, 10], Operations: ['83-45=38', '38-28=10'] Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,21 unequal: No Solution Exploring Operation: 23*10=230, Resulting Numbers: [230] 230,21 unequal: No Solution Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,21 unequal: No Solution No 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: 21:[28, 15], Operations: ['83-45=38', '38-23=15'] Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,21 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,21 unequal: No Solution Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,21 unequal: No Solution No 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: 21:[38, 5], Operations: ['83-45=38', '28-23=5'] Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 38*5=190, Resulting Numbers: [190] 190,21 unequal: No Solution Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,21 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: 21:[45, 23, 55], Operations: ['83-28=55'] Exploring Operation: 55-23=32, Resulting Numbers: [45, 32] Generated Node #0,2,0: 21:[45, 32] Operation: 55-23=32 Exploring Operation: 55-45=10, Resulting Numbers: [23, 10] Generated Node #0,2,1: 21:[23, 10] Operation: 55-45=10 Exploring Operation: 45-23=22, Resulting Numbers: [55, 22] Generated Node #0,2,2: 21:[55, 22] Operation: 45-23=22 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 21:[23, 10], Operations: ['83-28=55', '55-45=10'] Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,21 unequal: No Solution Exploring Operation: 23*10=230, Resulting Numbers: [230] 230,21 unequal: No Solution No 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: 21:[45, 32], Operations: ['83-28=55', '55-23=32'] Exploring Operation: 45+32=77, Resulting Numbers: [77] 77,21 unequal: No Solution Exploring Operation: 45-32=13, Resulting Numbers: [13] 13,21 unequal: No Solution Exploring Operation: 45*32=1440, Resulting Numbers: [1440] 1440,21 unequal: No Solution No 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: 21:[55, 22], Operations: ['83-28=55', '45-23=22'] Exploring Operation: 55+22=77, Resulting Numbers: [77] 77,21 unequal: No Solution Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 55*22=1210, Resulting Numbers: [1210] 1210,21 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: 21:[83, 23, 17], Operations: ['45-28=17'] Exploring Operation: 83-17=66, Resulting Numbers: [23, 66] Generated Node #0,1,0: 21:[23, 66] Operation: 83-17=66 Exploring Operation: 83-23=60, Resulting Numbers: [17, 60] Generated Node #0,1,1: 21:[17, 60] Operation: 83-23=60 Exploring Operation: 23-17=6, Resulting Numbers: [83, 6] Generated Node #0,1,2: 21:[83, 6] Operation: 23-17=6 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 21:[17, 60], Operations: ['45-28=17', '83-23=60'] Exploring Operation: 17+60=77, Resulting Numbers: [77] 77,21 unequal: No Solution Exploring Operation: 60-17=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 17*60=1020, Resulting Numbers: [1020] 1020,21 unequal: No Solution No 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: 21:[23, 66], Operations: ['45-28=17', '83-17=66'] Exploring Operation: 23+66=89, Resulting Numbers: [89] 89,21 unequal: No Solution Exploring Operation: 66-23=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 23*66=1518, Resulting Numbers: [1518] 1518,21 unequal: No Solution No 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: 21:[83, 6], Operations: ['45-28=17', '23-17=6'] Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,21 unequal: No Solution Exploring Operation: 83*6=498, Resulting Numbers: [498] 498,21 unequal: No Solution Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,21 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
[ 16, 85, 48, 16 ]
87
[ "48-16=32", "32/16=2", "85+2=87" ]
Current State: 87:[16, 85, 48, 16], Operations: [] Exploring Operation: 48-16=32, Resulting Numbers: [85, 32] Generated Node #2: [85, 32] from Operation: 48-16=32 Current State: 87:[85, 32], Operations: ['48-16=32'] Exploring Operation: 32/16=2, Resulting Numbers: [85, 2] Generated Node #3: [85, 2] from Operation: 32/16=2 Current State: 87:[85, 2], Operations: ['48-16=32', '32/16=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[16, 85, 48, 16], Operations: [] Exploring Operation: 48-16=32, Resulting Numbers: [85, 16, 32] Generated Node #0,0: 87:[85, 16, 32] Operation: 48-16=32 Exploring Operation: 16/16=1, Resulting Numbers: [85, 48, 1] Generated Node #0,1: 87:[85, 48, 1] Operation: 16/16=1 Exploring Operation: 48/16=3, Resulting Numbers: [85, 16, 3] Generated Node #0,2: 87:[85, 16, 3] Operation: 48/16=3 Exploring Operation: 48/16=3, Resulting Numbers: [16, 85, 3] Generated Node #0,3: 87:[16, 85, 3] Operation: 48/16=3 Exploring Operation: 48-16=32, Resulting Numbers: [16, 85, 32] Generated Node #0,4: 87:[16, 85, 32] Operation: 48-16=32 Moving to Node #0,2 Current State: 87:[85, 16, 3], Operations: ['48/16=3'] Exploring Operation: 85+3=88, Resulting Numbers: [16, 88] Generated Node #0,2,0: 87:[16, 88] Operation: 85+3=88 Exploring Operation: 85-16=69, Resulting Numbers: [3, 69] Generated Node #0,2,1: 87:[3, 69] Operation: 85-16=69 Exploring Operation: 16+3=19, Resulting Numbers: [85, 19] Generated Node #0,2,2: 87:[85, 19] Operation: 16+3=19 Exploring Operation: 16-3=13, Resulting Numbers: [85, 13] Generated Node #0,2,3: 87:[85, 13] Operation: 16-3=13 Exploring Operation: 85+16=101, Resulting Numbers: [3, 101] Generated Node #0,2,4: 87:[3, 101] Operation: 85+16=101 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 87:[85, 19], Operations: ['48/16=3', '16+3=19'] Exploring Operation: 85*19=1615, Resulting Numbers: [1615] 1615,87 unequal: No Solution Exploring Operation: 85-19=66, Resulting Numbers: [66] 66,87 unequal: No Solution Exploring Operation: 85+19=104, Resulting Numbers: [104] 104,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 87:[85, 13], Operations: ['48/16=3', '16-3=13'] Exploring Operation: 85+13=98, Resulting Numbers: [98] 98,87 unequal: No Solution Exploring Operation: 85-13=72, Resulting Numbers: [72] 72,87 unequal: No Solution Exploring Operation: 85*13=1105, Resulting Numbers: [1105] 1105,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 87:[16, 88], Operations: ['48/16=3', '85+3=88'] Exploring Operation: 16+88=104, Resulting Numbers: [104] 104,87 unequal: No Solution Exploring Operation: 16*88=1408, Resulting Numbers: [1408] 1408,87 unequal: No Solution Exploring Operation: 88-16=72, Resulting Numbers: [72] 72,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 87:[3, 101], Operations: ['48/16=3', '85+16=101'] Exploring Operation: 101-3=98, Resulting Numbers: [98] 98,87 unequal: No Solution Exploring Operation: 3+101=104, Resulting Numbers: [104] 104,87 unequal: No Solution Exploring Operation: 3*101=303, Resulting Numbers: [303] 303,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 87:[3, 69], Operations: ['48/16=3', '85-16=69'] Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,87 unequal: No Solution Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,87 unequal: No Solution Exploring Operation: 3+69=72, Resulting Numbers: [72] 72,87 unequal: No Solution Exploring Operation: 3*69=207, Resulting Numbers: [207] 207,87 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: 87:[16, 85, 3], Operations: ['48/16=3'] Exploring Operation: 16-3=13, Resulting Numbers: [85, 13] Generated Node #0,3,0: 87:[85, 13] Operation: 16-3=13 Exploring Operation: 85+3=88, Resulting Numbers: [16, 88] Generated Node #0,3,1: 87:[16, 88] Operation: 85+3=88 Exploring Operation: 85-16=69, Resulting Numbers: [3, 69] Generated Node #0,3,2: 87:[3, 69] Operation: 85-16=69 Exploring Operation: 16+85=101, Resulting Numbers: [3, 101] Generated Node #0,3,3: 87:[3, 101] Operation: 16+85=101 Exploring Operation: 16+3=19, Resulting Numbers: [85, 19] Generated Node #0,3,4: 87:[85, 19] Operation: 16+3=19 Moving to Node #0,0 Current State: 87:[85, 16, 32], Operations: ['48-16=32'] Exploring Operation: 32-16=16, Resulting Numbers: [85, 16] Generated Node #0,0,0: 87:[85, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [85, 2] Generated Node #0,0,1: 87:[85, 2] Operation: 32/16=2 Exploring Operation: 16+32=48, Resulting Numbers: [85, 48] Generated Node #0,0,2: 87:[85, 48] Operation: 16+32=48 Exploring Operation: 85+16=101, Resulting Numbers: [32, 101] Generated Node #0,0,3: 87:[32, 101] Operation: 85+16=101 Exploring Operation: 85-16=69, Resulting Numbers: [32, 69] Generated Node #0,0,4: 87:[32, 69] Operation: 85-16=69 Moving to Node #0,4 Current State: 87:[16, 85, 32], Operations: ['48-16=32'] Exploring Operation: 16+85=101, Resulting Numbers: [32, 101] Generated Node #0,4,0: 87:[32, 101] Operation: 16+85=101 Exploring Operation: 85-16=69, Resulting Numbers: [32, 69] Generated Node #0,4,1: 87:[32, 69] Operation: 85-16=69 Exploring Operation: 32-16=16, Resulting Numbers: [85, 16] Generated Node #0,4,2: 87:[85, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [85, 2] Generated Node #0,4,3: 87:[85, 2] Operation: 32/16=2 Exploring Operation: 16+32=48, Resulting Numbers: [85, 48] Generated Node #0,4,4: 87:[85, 48] Operation: 16+32=48 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 87:[85, 2], Operations: ['48-16=32', '32/16=2'] Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,87 unequal: No Solution Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[16, 85, 48, 16], Operations: [] Exploring Operation: 48-16=32, Resulting Numbers: [16, 85, 32] Generated Node #0,4: 87:[16, 85, 32] Operation: 48-16=32 Moving to Node #0,4 Current State: 87:[16, 85, 32], Operations: ['48-16=32'] Exploring Operation: 32/16=2, Resulting Numbers: [85, 2] Generated Node #0,4,3: 87:[85, 2] Operation: 32/16=2 Moving to Node #0,4,3 Current State: 87:[85, 2], Operations: ['48-16=32', '32/16=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
mult_heuristic
[ 63, 27, 62, 65 ]
72
[ "65-62=3", "27/3=9", "63+9=72" ]
Current State: 72:[63, 27, 62, 65], Operations: [] Exploring Operation: 65-62=3, Resulting Numbers: [63, 27, 3] Generated Node #2: [63, 27, 3] from Operation: 65-62=3 Current State: 72:[63, 27, 3], Operations: ['65-62=3'] Exploring Operation: 27/3=9, Resulting Numbers: [63, 9] Generated Node #3: [63, 9] from Operation: 27/3=9 Current State: 72:[63, 9], Operations: ['65-62=3', '27/3=9'] Exploring Operation: 63+9=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[63, 27, 62, 65], Operations: [] Exploring Operation: 65-62=3, Resulting Numbers: [63, 27, 3] Generated Node #0,0: 72:[63, 27, 3] Operation: 65-62=3 Exploring Operation: 63-62=1, Resulting Numbers: [27, 65, 1] Generated Node #0,1: 72:[27, 65, 1] Operation: 63-62=1 Exploring Operation: 65-63=2, Resulting Numbers: [27, 62, 2] Generated Node #0,2: 72:[27, 62, 2] Operation: 65-63=2 Moving to Node #0,1 Current State: 72:[27, 65, 1], Operations: ['63-62=1'] Exploring Operation: 65+1=66, Resulting Numbers: [27, 66] Generated Node #0,1,0: 72:[27, 66] Operation: 65+1=66 Exploring Operation: 65-27=38, Resulting Numbers: [1, 38] Generated Node #0,1,1: 72:[1, 38] Operation: 65-27=38 Exploring Operation: 27-1=26, Resulting Numbers: [65, 26] Generated Node #0,1,2: 72:[65, 26] Operation: 27-1=26 Moving to Node #0,0 Current State: 72:[63, 27, 3], Operations: ['65-62=3'] Exploring Operation: 63-27=36, Resulting Numbers: [3, 36] Generated Node #0,0,0: 72:[3, 36] Operation: 63-27=36 Exploring Operation: 63/3=21, Resulting Numbers: [27, 21] Generated Node #0,0,1: 72:[27, 21] Operation: 63/3=21 Exploring Operation: 63+3=66, Resulting Numbers: [27, 66] Generated Node #0,0,2: 72:[27, 66] Operation: 63+3=66 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[3, 36], Operations: ['65-62=3', '63-27=36'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,72 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[27, 21], Operations: ['65-62=3', '63/3=21'] Exploring Operation: 27*21=567, Resulting Numbers: [567] 567,72 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,72 unequal: No Solution Exploring Operation: 27+21=48, Resulting Numbers: [48] 48,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 72:[27, 66], Operations: ['65-62=3', '63+3=66'] Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,72 unequal: No Solution Exploring Operation: 27*66=1782, Resulting Numbers: [1782] 1782,72 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: 72:[27, 62, 2], Operations: ['65-63=2'] Exploring Operation: 62-27=35, Resulting Numbers: [2, 35] Generated Node #0,2,0: 72:[2, 35] Operation: 62-27=35 Exploring Operation: 62/2=31, Resulting Numbers: [27, 31] Generated Node #0,2,1: 72:[27, 31] Operation: 62/2=31 Exploring Operation: 27-2=25, Resulting Numbers: [62, 25] Generated Node #0,2,2: 72:[62, 25] Operation: 27-2=25 Moving to Node #0,2,0 Current State: 72:[2, 35], Operations: ['65-63=2', '62-27=35'] Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,72 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[1, 38], Operations: ['63-62=1', '65-27=38'] Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 1*38=38, Resulting Numbers: [38] 38,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[27, 31], Operations: ['65-63=2', '62/2=31'] Exploring Operation: 27+31=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 31-27=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 27*31=837, Resulting Numbers: [837] 837,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[65, 26], Operations: ['63-62=1', '27-1=26'] Exploring Operation: 65+26=91, Resulting Numbers: [91] 91,72 unequal: No Solution Exploring Operation: 65*26=1690, Resulting Numbers: [1690] 1690,72 unequal: No Solution Exploring Operation: 65-26=39, Resulting Numbers: [39] 39,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[27, 66], Operations: ['63-62=1', '65+1=66'] Exploring Operation: 27*66=1782, Resulting Numbers: [1782] 1782,72 unequal: No Solution Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[62, 25], Operations: ['65-63=2', '27-2=25'] Exploring Operation: 62*25=1550, Resulting Numbers: [1550] 1550,72 unequal: No Solution Exploring Operation: 62+25=87, Resulting Numbers: [87] 87,72 unequal: No Solution Exploring Operation: 62-25=37, Resulting Numbers: [37] 37,72 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 93, 24, 6, 1 ]
96
[ "93-1=92", "24/6=4", "92+4=96" ]
Current State: 96:[93, 24, 6, 1], Operations: [] Exploring Operation: 93-1=92, Resulting Numbers: [24, 6, 92] Generated Node #2: [24, 6, 92] from Operation: 93-1=92 Current State: 96:[24, 6, 92], Operations: ['93-1=92'] Exploring Operation: 24/6=4, Resulting Numbers: [92, 4] Generated Node #3: [92, 4] from Operation: 24/6=4 Current State: 96:[92, 4], Operations: ['93-1=92', '24/6=4'] Exploring Operation: 92+4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[93, 24, 6, 1], Operations: [] Exploring Operation: 93*1=93, Resulting Numbers: [24, 6, 93] Generated Node #0,0: 96:[24, 6, 93] Operation: 93*1=93 Exploring Operation: 93+1=94, Resulting Numbers: [24, 6, 94] Generated Node #0,1: 96:[24, 6, 94] Operation: 93+1=94 Exploring Operation: 24*1=24, Resulting Numbers: [93, 6, 24] Generated Node #0,2: 96:[93, 6, 24] Operation: 24*1=24 Exploring Operation: 93/1=93, Resulting Numbers: [24, 6, 93] Generated Node #0,3: 96:[24, 6, 93] Operation: 93/1=93 Moving to Node #0,1 Current State: 96:[24, 6, 94], Operations: ['93+1=94'] Exploring Operation: 24+6=30, Resulting Numbers: [94, 30] Generated Node #0,1,0: 96:[94, 30] Operation: 24+6=30 Exploring Operation: 6+94=100, Resulting Numbers: [24, 100] Generated Node #0,1,1: 96:[24, 100] Operation: 6+94=100 Exploring Operation: 24/6=4, Resulting Numbers: [94, 4] Generated Node #0,1,2: 96:[94, 4] Operation: 24/6=4 Exploring Operation: 24-6=18, Resulting Numbers: [94, 18] Generated Node #0,1,3: 96:[94, 18] Operation: 24-6=18 Moving to Node #0,2 Current State: 96:[93, 6, 24], Operations: ['24*1=24'] Exploring Operation: 6+24=30, Resulting Numbers: [93, 30] Generated Node #0,2,0: 96:[93, 30] Operation: 6+24=30 Exploring Operation: 24-6=18, Resulting Numbers: [93, 18] Generated Node #0,2,1: 96:[93, 18] Operation: 24-6=18 Exploring Operation: 93+6=99, Resulting Numbers: [24, 99] Generated Node #0,2,2: 96:[24, 99] Operation: 93+6=99 Exploring Operation: 24/6=4, Resulting Numbers: [93, 4] Generated Node #0,2,3: 96:[93, 4] Operation: 24/6=4 Moving to Node #0,0 Current State: 96:[24, 6, 93], Operations: ['93*1=93'] Exploring Operation: 24-6=18, Resulting Numbers: [93, 18] Generated Node #0,0,0: 96:[93, 18] Operation: 24-6=18 Exploring Operation: 24+6=30, Resulting Numbers: [93, 30] Generated Node #0,0,1: 96:[93, 30] Operation: 24+6=30 Exploring Operation: 6+93=99, Resulting Numbers: [24, 99] Generated Node #0,0,2: 96:[24, 99] Operation: 6+93=99 Exploring Operation: 24/6=4, Resulting Numbers: [93, 4] Generated Node #0,0,3: 96:[93, 4] Operation: 24/6=4 Moving to Node #0,3 Current State: 96:[24, 6, 93], Operations: ['93/1=93'] Exploring Operation: 24/6=4, Resulting Numbers: [93, 4] Generated Node #0,3,0: 96:[93, 4] Operation: 24/6=4 Exploring Operation: 24-6=18, Resulting Numbers: [93, 18] Generated Node #0,3,1: 96:[93, 18] Operation: 24-6=18 Exploring Operation: 6+93=99, Resulting Numbers: [24, 99] Generated Node #0,3,2: 96:[24, 99] Operation: 6+93=99 Exploring Operation: 24+6=30, Resulting Numbers: [93, 30] Generated Node #0,3,3: 96:[93, 30] Operation: 24+6=30 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 96:[93, 4], Operations: ['93/1=93', '24/6=4'] Exploring Operation: 93+4=97, Resulting Numbers: [97] 97,96 unequal: No Solution Exploring Operation: 93-4=89, Resulting Numbers: [89] 89,96 unequal: No Solution Exploring Operation: 93*4=372, Resulting Numbers: [372] 372,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 96:[24, 99], Operations: ['93/1=93', '6+93=99'] Exploring Operation: 99-24=75, Resulting Numbers: [75] 75,96 unequal: No Solution Exploring Operation: 24+99=123, Resulting Numbers: [123] 123,96 unequal: No Solution Exploring Operation: 24*99=2376, Resulting Numbers: [2376] 2376,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 96:[93, 18], Operations: ['93/1=93', '24-6=18'] Exploring Operation: 93-18=75, Resulting Numbers: [75] 75,96 unequal: No Solution Exploring Operation: 93+18=111, Resulting Numbers: [111] 111,96 unequal: No Solution Exploring Operation: 93*18=1674, Resulting Numbers: [1674] 1674,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 96:[93, 30], Operations: ['93/1=93', '24+6=30'] Exploring Operation: 93-30=63, Resulting Numbers: [63] 63,96 unequal: No Solution Exploring Operation: 93*30=2790, Resulting Numbers: [2790] 2790,96 unequal: No Solution Exploring Operation: 93+30=123, Resulting Numbers: [123] 123,96 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: 96:[94, 4], Operations: ['93+1=94', '24/6=4'] Exploring Operation: 94*4=376, Resulting Numbers: [376] 376,96 unequal: No Solution Exploring Operation: 94+4=98, Resulting Numbers: [98] 98,96 unequal: No Solution Exploring Operation: 94-4=90, Resulting Numbers: [90] 90,96 unequal: No Solution Moving to Node #0,2,3 Current State: 96:[93, 4], Operations: ['24*1=24', '24/6=4'] Exploring Operation: 93-4=89, Resulting Numbers: [89] 89,96 unequal: No Solution Exploring Operation: 93*4=372, Resulting Numbers: [372] 372,96 unequal: No Solution Exploring Operation: 93+4=97, Resulting Numbers: [97] 97,96 unequal: No Solution Moving to Node #0,2,2 Current State: 96:[24, 99], Operations: ['24*1=24', '93+6=99'] Exploring Operation: 24+99=123, Resulting Numbers: [123] 123,96 unequal: No Solution Exploring Operation: 24*99=2376, Resulting Numbers: [2376] 2376,96 unequal: No Solution Exploring Operation: 99-24=75, Resulting Numbers: [75] 75,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[93, 4], Operations: ['93*1=93', '24/6=4'] Exploring Operation: 93-4=89, Resulting Numbers: [89] 89,96 unequal: No Solution Exploring Operation: 93*4=372, Resulting Numbers: [372] 372,96 unequal: No Solution Exploring Operation: 93+4=97, Resulting Numbers: [97] 97,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[24, 99], Operations: ['93*1=93', '6+93=99'] Exploring Operation: 99-24=75, Resulting Numbers: [75] 75,96 unequal: No Solution Exploring Operation: 24*99=2376, Resulting Numbers: [2376] 2376,96 unequal: No Solution Exploring Operation: 24+99=123, Resulting Numbers: [123] 123,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[24, 100], Operations: ['93+1=94', '6+94=100'] Exploring Operation: 100-24=76, Resulting Numbers: [76] 76,96 unequal: No Solution Exploring Operation: 24*100=2400, Resulting Numbers: [2400] 2400,96 unequal: No Solution Exploring Operation: 24+100=124, Resulting Numbers: [124] 124,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[94, 30], Operations: ['93+1=94', '24+6=30'] Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,96 unequal: No Solution Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,96 unequal: No Solution Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,96 unequal: No Solution Moving to Node #0,1,3 Current State: 96:[94, 18], Operations: ['93+1=94', '24-6=18'] Exploring Operation: 94-18=76, Resulting Numbers: [76] 76,96 unequal: No Solution Exploring Operation: 94+18=112, Resulting Numbers: [112] 112,96 unequal: No Solution Exploring Operation: 94*18=1692, Resulting Numbers: [1692] 1692,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[93, 30], Operations: ['24*1=24', '6+24=30'] Exploring Operation: 93*30=2790, Resulting Numbers: [2790] 2790,96 unequal: No Solution Exploring Operation: 93+30=123, Resulting Numbers: [123] 123,96 unequal: No Solution Exploring Operation: 93-30=63, Resulting Numbers: [63] 63,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[93, 30], Operations: ['93*1=93', '24+6=30'] Exploring Operation: 93*30=2790, Resulting Numbers: [2790] 2790,96 unequal: No Solution Exploring Operation: 93+30=123, Resulting Numbers: [123] 123,96 unequal: No Solution Exploring Operation: 93-30=63, Resulting Numbers: [63] 63,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[93, 18], Operations: ['93*1=93', '24-6=18'] Exploring Operation: 93+18=111, Resulting Numbers: [111] 111,96 unequal: No Solution Exploring Operation: 93*18=1674, Resulting Numbers: [1674] 1674,96 unequal: No Solution Exploring Operation: 93-18=75, Resulting Numbers: [75] 75,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[93, 18], Operations: ['24*1=24', '24-6=18'] Exploring Operation: 93*18=1674, Resulting Numbers: [1674] 1674,96 unequal: No Solution Exploring Operation: 93+18=111, Resulting Numbers: [111] 111,96 unequal: No Solution Exploring Operation: 93-18=75, Resulting Numbers: [75] 75,96 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 21, 64, 23, 47 ]
19
[ "64-21=43", "47-23=24", "43-24=19" ]
Current State: 19:[21, 64, 23, 47], Operations: [] Exploring Operation: 64-21=43, Resulting Numbers: [23, 47, 43] Generated Node #2: [23, 47, 43] from Operation: 64-21=43 Current State: 19:[23, 47, 43], Operations: ['64-21=43'] Exploring Operation: 47-23=24, Resulting Numbers: [43, 24] Generated Node #3: [43, 24] from Operation: 47-23=24 Current State: 19:[43, 24], Operations: ['64-21=43', '47-23=24'] Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[21, 64, 23, 47], Operations: [] Exploring Operation: 64-23=41, Resulting Numbers: [21, 47, 41] Generated Node #0,0: 19:[21, 47, 41] Operation: 64-23=41 Exploring Operation: 64-47=17, Resulting Numbers: [21, 23, 17] Generated Node #0,1: 19:[21, 23, 17] Operation: 64-47=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[21, 23, 17], Operations: ['64-47=17'] Exploring Operation: 23-17=6, Resulting Numbers: [21, 6] Generated Node #0,1,0: 19:[21, 6] Operation: 23-17=6 Exploring Operation: 23-21=2, Resulting Numbers: [17, 2] Generated Node #0,1,1: 19:[17, 2] Operation: 23-21=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 19:[21, 6], Operations: ['64-47=17', '23-17=6'] Exploring Operation: 21+6=27, Resulting Numbers: [27] 27,19 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 19:[17, 2], Operations: ['64-47=17', '23-21=2'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,19 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[21, 64, 23, 47], Operations: [] Exploring Operation: 64-47=17, Resulting Numbers: [21, 23, 17] Generated Node #0,1: 19:[21, 23, 17] Operation: 64-47=17 Moving to Node #0,1 Current State: 19:[21, 23, 17], Operations: ['64-47=17'] Exploring Operation: 23-21=2, Resulting Numbers: [17, 2] Generated Node #0,1,1: 19:[17, 2] Operation: 23-21=2 Moving to Node #0,1,1 Current State: 19:[17, 2], Operations: ['64-47=17', '23-21=2'] Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 48, 32, 90, 11 ]
63
[ "48-32=16", "90-11=79", "79-16=63" ]
Current State: 63:[48, 32, 90, 11], Operations: [] Exploring Operation: 48-32=16, Resulting Numbers: [90, 11, 16] Generated Node #2: [90, 11, 16] from Operation: 48-32=16 Current State: 63:[90, 11, 16], Operations: ['48-32=16'] Exploring Operation: 90-11=79, Resulting Numbers: [16, 79] Generated Node #3: [16, 79] from Operation: 90-11=79 Current State: 63:[16, 79], Operations: ['48-32=16', '90-11=79'] Exploring Operation: 79-16=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[48, 32, 90, 11], Operations: [] Exploring Operation: 48+11=59, Resulting Numbers: [32, 90, 59] Generated Node #0,0: 63:[32, 90, 59] Operation: 48+11=59 Exploring Operation: 48-32=16, Resulting Numbers: [90, 11, 16] Generated Node #0,1: 63:[90, 11, 16] Operation: 48-32=16 Exploring Operation: 90-48=42, Resulting Numbers: [32, 11, 42] Generated Node #0,2: 63:[32, 11, 42] Operation: 90-48=42 Exploring Operation: 90-32=58, Resulting Numbers: [48, 11, 58] Generated Node #0,3: 63:[48, 11, 58] Operation: 90-32=58 Exploring Operation: 32-11=21, Resulting Numbers: [48, 90, 21] Generated Node #0,4: 63:[48, 90, 21] Operation: 32-11=21 Start Sub Search at level 1: Moving to Node #0,3 Current State: 63:[48, 11, 58], Operations: ['90-32=58'] Exploring Operation: 58-48=10, Resulting Numbers: [11, 10] Generated Node #0,3,0: 63:[11, 10] Operation: 58-48=10 Exploring Operation: 11+58=69, Resulting Numbers: [48, 69] Generated Node #0,3,1: 63:[48, 69] Operation: 11+58=69 Exploring Operation: 48-11=37, Resulting Numbers: [58, 37] Generated Node #0,3,2: 63:[58, 37] Operation: 48-11=37 Exploring Operation: 48+11=59, Resulting Numbers: [58, 59] Generated Node #0,3,3: 63:[58, 59] Operation: 48+11=59 Exploring Operation: 58-11=47, Resulting Numbers: [48, 47] Generated Node #0,3,4: 63:[48, 47] Operation: 58-11=47 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 63:[11, 10], Operations: ['90-32=58', '58-48=10'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 11+10=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 11*10=110, Resulting Numbers: [110] 110,63 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 #0,3,3 Current State: 63:[58, 59], Operations: ['90-32=58', '48+11=59'] Exploring Operation: 59-58=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 58*59=3422, Resulting Numbers: [3422] 3422,63 unequal: No Solution Exploring Operation: 58+59=117, Resulting Numbers: [117] 117,63 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 #0,3,1 Current State: 63:[48, 69], Operations: ['90-32=58', '11+58=69'] Exploring Operation: 48*69=3312, Resulting Numbers: [3312] 3312,63 unequal: No Solution Exploring Operation: 69-48=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 48+69=117, Resulting Numbers: [117] 117,63 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 #0,3,2 Current State: 63:[58, 37], Operations: ['90-32=58', '48-11=37'] Exploring Operation: 58+37=95, Resulting Numbers: [95] 95,63 unequal: No Solution Exploring Operation: 58*37=2146, Resulting Numbers: [2146] 2146,63 unequal: No Solution Exploring Operation: 58-37=21, Resulting Numbers: [21] 21,63 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 #0,3,4 Current State: 63:[48, 47], Operations: ['90-32=58', '58-11=47'] Exploring Operation: 48*47=2256, Resulting Numbers: [2256] 2256,63 unequal: No Solution Exploring Operation: 48+47=95, Resulting Numbers: [95] 95,63 unequal: No Solution Exploring Operation: 48-47=1, Resulting Numbers: [1] 1,63 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 #0,1 Current State: 63:[90, 11, 16], Operations: ['48-32=16'] Exploring Operation: 11+16=27, Resulting Numbers: [90, 27] Generated Node #0,1,0: 63:[90, 27] Operation: 11+16=27 Exploring Operation: 90-11=79, Resulting Numbers: [16, 79] Generated Node #0,1,1: 63:[16, 79] Operation: 90-11=79 Exploring Operation: 90+11=101, Resulting Numbers: [16, 101] Generated Node #0,1,2: 63:[16, 101] Operation: 90+11=101 Exploring Operation: 16-11=5, Resulting Numbers: [90, 5] Generated Node #0,1,3: 63:[90, 5] Operation: 16-11=5 Exploring Operation: 90-16=74, Resulting Numbers: [11, 74] Generated Node #0,1,4: 63:[11, 74] Operation: 90-16=74 Moving to Node #0,1,4 Current State: 63:[11, 74], Operations: ['48-32=16', '90-16=74'] Exploring Operation: 11+74=85, Resulting Numbers: [85] 85,63 unequal: No Solution Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[48, 32, 90, 11], Operations: [] Exploring Operation: 48-32=16, Resulting Numbers: [90, 11, 16] Generated Node #0,1: 63:[90, 11, 16] Operation: 48-32=16 Moving to Node #0,1 Current State: 63:[90, 11, 16], Operations: ['48-32=16'] Exploring Operation: 90-16=74, Resulting Numbers: [11, 74] Generated Node #0,1,4: 63:[11, 74] Operation: 90-16=74 Moving to Node #0,1,4 Current State: 63:[11, 74], Operations: ['48-32=16', '90-16=74'] Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 83, 96, 74, 31 ]
74
[ "83+96=179", "74+31=105", "179-105=74" ]
Current State: 74:[83, 96, 74, 31], Operations: [] Exploring Operation: 83+96=179, Resulting Numbers: [74, 31, 179] Generated Node #2: [74, 31, 179] from Operation: 83+96=179 Current State: 74:[74, 31, 179], Operations: ['83+96=179'] Exploring Operation: 74+31=105, Resulting Numbers: [179, 105] Generated Node #3: [179, 105] from Operation: 74+31=105 Current State: 74:[179, 105], Operations: ['83+96=179', '74+31=105'] Exploring Operation: 179-105=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[83, 96, 74, 31], Operations: [] Exploring Operation: 96-74=22, Resulting Numbers: [83, 31, 22] Generated Node #0,0: 74:[83, 31, 22] Operation: 96-74=22 Exploring Operation: 96-83=13, Resulting Numbers: [74, 31, 13] Generated Node #0,1: 74:[74, 31, 13] Operation: 96-83=13 Exploring Operation: 96-31=65, Resulting Numbers: [83, 74, 65] Generated Node #0,2: 74:[83, 74, 65] Operation: 96-31=65 Exploring Operation: 83-31=52, Resulting Numbers: [96, 74, 52] Generated Node #0,3: 74:[96, 74, 52] Operation: 83-31=52 Exploring Operation: 83-74=9, Resulting Numbers: [96, 31, 9] Generated Node #0,4: 74:[96, 31, 9] Operation: 83-74=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[74, 31, 13], Operations: ['96-83=13'] Exploring Operation: 74-31=43, Resulting Numbers: [13, 43] Generated Node #0,1,0: 74:[13, 43] Operation: 74-31=43 Exploring Operation: 74-13=61, Resulting Numbers: [31, 61] Generated Node #0,1,1: 74:[31, 61] Operation: 74-13=61 Exploring Operation: 31+13=44, Resulting Numbers: [74, 44] Generated Node #0,1,2: 74:[74, 44] Operation: 31+13=44 Exploring Operation: 74+13=87, Resulting Numbers: [31, 87] Generated Node #0,1,3: 74:[31, 87] Operation: 74+13=87 Exploring Operation: 31-13=18, Resulting Numbers: [74, 18] Generated Node #0,1,4: 74:[74, 18] Operation: 31-13=18 Moving to Node #0,1,2 Current State: 74:[74, 44], Operations: ['96-83=13', '31+13=44'] Exploring Operation: 74-44=30, Resulting Numbers: [30] 30,74 unequal: No Solution Exploring Operation: 74+44=118, Resulting Numbers: [118] 118,74 unequal: No Solution Exploring Operation: 74*44=3256, Resulting Numbers: [3256] 3256,74 unequal: No Solution Moving to Node #0,1,4 Current State: 74:[74, 18], Operations: ['96-83=13', '31-13=18'] Exploring Operation: 74+18=92, Resulting Numbers: [92] 92,74 unequal: No Solution Exploring Operation: 74-18=56, Resulting Numbers: [56] 56,74 unequal: No Solution Exploring Operation: 74*18=1332, Resulting Numbers: [1332] 1332,74 unequal: No Solution Moving to Node #0,1,0 Current State: 74:[13, 43], Operations: ['96-83=13', '74-31=43'] Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,74 unequal: No Solution Exploring Operation: 13*43=559, Resulting Numbers: [559] 559,74 unequal: No Solution Exploring Operation: 13+43=56, Resulting Numbers: [56] 56,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[31, 61], Operations: ['96-83=13', '74-13=61'] Exploring Operation: 31+61=92, Resulting Numbers: [92] 92,74 unequal: No Solution Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,74 unequal: No Solution Exploring Operation: 31*61=1891, Resulting Numbers: [1891] 1891,74 unequal: No Solution Moving to Node #0,1,3 Current State: 74:[31, 87], Operations: ['96-83=13', '74+13=87'] Exploring Operation: 31*87=2697, Resulting Numbers: [2697] 2697,74 unequal: No Solution Exploring Operation: 31+87=118, Resulting Numbers: [118] 118,74 unequal: No Solution Exploring Operation: 87-31=56, Resulting Numbers: [56] 56,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[83, 74, 65], Operations: ['96-31=65'] Exploring Operation: 74-65=9, Resulting Numbers: [83, 9] Generated Node #0,2,0: 74:[83, 9] Operation: 74-65=9 Exploring Operation: 74+65=139, Resulting Numbers: [83, 139] Generated Node #0,2,1: 74:[83, 139] Operation: 74+65=139 Exploring Operation: 83-74=9, Resulting Numbers: [65, 9] Generated Node #0,2,2: 74:[65, 9] Operation: 83-74=9 Exploring Operation: 83+65=148, Resulting Numbers: [74, 148] Generated Node #0,2,3: 74:[74, 148] Operation: 83+65=148 Exploring Operation: 83-65=18, Resulting Numbers: [74, 18] Generated Node #0,2,4: 74:[74, 18] Operation: 83-65=18 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 74:[83, 9], Operations: ['96-31=65', '74-65=9'] Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[83, 96, 74, 31], Operations: [] Exploring Operation: 96-31=65, Resulting Numbers: [83, 74, 65] Generated Node #0,2: 74:[83, 74, 65] Operation: 96-31=65 Moving to Node #0,2 Current State: 74:[83, 74, 65], Operations: ['96-31=65'] Exploring Operation: 74-65=9, Resulting Numbers: [83, 9] Generated Node #0,2,0: 74:[83, 9] Operation: 74-65=9 Moving to Node #0,2,0 Current State: 74:[83, 9], Operations: ['96-31=65', '74-65=9'] Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_5
mult_heuristic
[ 87, 23, 19, 62 ]
100
[ "87-62=25", "23-19=4", "25*4=100" ]
Current State: 100:[87, 23, 19, 62], Operations: [] Exploring Operation: 87-62=25, Resulting Numbers: [23, 19, 25] Generated Node #2: [23, 19, 25] from Operation: 87-62=25 Current State: 100:[23, 19, 25], Operations: ['87-62=25'] Exploring Operation: 23-19=4, Resulting Numbers: [25, 4] Generated Node #3: [25, 4] from Operation: 23-19=4 Current State: 100:[25, 4], Operations: ['87-62=25', '23-19=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[87, 23, 19, 62], Operations: [] Exploring Operation: 87+23=110, Resulting Numbers: [19, 62, 110] Generated Node #0,0: 100:[19, 62, 110] Operation: 87+23=110 Exploring Operation: 23-19=4, Resulting Numbers: [87, 62, 4] Generated Node #0,1: 100:[87, 62, 4] Operation: 23-19=4 Exploring Operation: 62-19=43, Resulting Numbers: [87, 23, 43] Generated Node #0,2: 100:[87, 23, 43] Operation: 62-19=43 Exploring Operation: 87-62=25, Resulting Numbers: [23, 19, 25] Generated Node #0,3: 100:[23, 19, 25] Operation: 87-62=25 Exploring Operation: 87+19=106, Resulting Numbers: [23, 62, 106] Generated Node #0,4: 100:[23, 62, 106] Operation: 87+19=106 Moving to Node #0,3 Current State: 100:[23, 19, 25], Operations: ['87-62=25'] Exploring Operation: 25-19=6, Resulting Numbers: [23, 6] Generated Node #0,3,0: 100:[23, 6] Operation: 25-19=6 Exploring Operation: 25-23=2, Resulting Numbers: [19, 2] Generated Node #0,3,1: 100:[19, 2] Operation: 25-23=2 Exploring Operation: 23+25=48, Resulting Numbers: [19, 48] Generated Node #0,3,2: 100:[19, 48] Operation: 23+25=48 Exploring Operation: 23+19=42, Resulting Numbers: [25, 42] Generated Node #0,3,3: 100:[25, 42] Operation: 23+19=42 Exploring Operation: 23-19=4, Resulting Numbers: [25, 4] Generated Node #0,3,4: 100:[25, 4] Operation: 23-19=4 Moving to Node #0,4 Current State: 100:[23, 62, 106], Operations: ['87+19=106'] Exploring Operation: 62-23=39, Resulting Numbers: [106, 39] Generated Node #0,4,0: 100:[106, 39] Operation: 62-23=39 Exploring Operation: 106-23=83, Resulting Numbers: [62, 83] Generated Node #0,4,1: 100:[62, 83] Operation: 106-23=83 Exploring Operation: 23+106=129, Resulting Numbers: [62, 129] Generated Node #0,4,2: 100:[62, 129] Operation: 23+106=129 Exploring Operation: 106-62=44, Resulting Numbers: [23, 44] Generated Node #0,4,3: 100:[23, 44] Operation: 106-62=44 Exploring Operation: 23+62=85, Resulting Numbers: [106, 85] Generated Node #0,4,4: 100:[106, 85] Operation: 23+62=85 Moving to Node #0,2 Current State: 100:[87, 23, 43], Operations: ['62-19=43'] Exploring Operation: 87-43=44, Resulting Numbers: [23, 44] Generated Node #0,2,0: 100:[23, 44] Operation: 87-43=44 Exploring Operation: 23+43=66, Resulting Numbers: [87, 66] Generated Node #0,2,1: 100:[87, 66] Operation: 23+43=66 Exploring Operation: 87+23=110, Resulting Numbers: [43, 110] Generated Node #0,2,2: 100:[43, 110] Operation: 87+23=110 Exploring Operation: 43-23=20, Resulting Numbers: [87, 20] Generated Node #0,2,3: 100:[87, 20] Operation: 43-23=20 Exploring Operation: 87-23=64, Resulting Numbers: [43, 64] Generated Node #0,2,4: 100:[43, 64] Operation: 87-23=64 Moving to Node #0,0 Current State: 100:[19, 62, 110], Operations: ['87+23=110'] Exploring Operation: 19+110=129, Resulting Numbers: [62, 129] Generated Node #0,0,0: 100:[62, 129] Operation: 19+110=129 Exploring Operation: 110-62=48, Resulting Numbers: [19, 48] Generated Node #0,0,1: 100:[19, 48] Operation: 110-62=48 Exploring Operation: 62-19=43, Resulting Numbers: [110, 43] Generated Node #0,0,2: 100:[110, 43] Operation: 62-19=43 Exploring Operation: 19+62=81, Resulting Numbers: [110, 81] Generated Node #0,0,3: 100:[110, 81] Operation: 19+62=81 Exploring Operation: 110-19=91, Resulting Numbers: [62, 91] Generated Node #0,0,4: 100:[62, 91] Operation: 110-19=91 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[19, 48], Operations: ['87+23=110', '110-62=48'] Exploring Operation: 19+48=67, Resulting Numbers: [67] 67,100 unequal: No Solution Exploring Operation: 19*48=912, Resulting Numbers: [912] 912,100 unequal: No Solution Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 100:[110, 43], Operations: ['87+23=110', '62-19=43'] Exploring Operation: 110+43=153, Resulting Numbers: [153] 153,100 unequal: No Solution Exploring Operation: 110*43=4730, Resulting Numbers: [4730] 4730,100 unequal: No Solution Exploring Operation: 110-43=67, Resulting Numbers: [67] 67,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 100:[62, 91], Operations: ['87+23=110', '110-19=91'] Exploring Operation: 91-62=29, Resulting Numbers: [29] 29,100 unequal: No Solution Exploring Operation: 62*91=5642, Resulting Numbers: [5642] 5642,100 unequal: No Solution Exploring Operation: 62+91=153, Resulting Numbers: [153] 153,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 100:[110, 81], Operations: ['87+23=110', '19+62=81'] Exploring Operation: 110+81=191, Resulting Numbers: [191] 191,100 unequal: No Solution Exploring Operation: 110*81=8910, Resulting Numbers: [8910] 8910,100 unequal: No Solution Exploring Operation: 110-81=29, Resulting Numbers: [29] 29,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[62, 129], Operations: ['87+23=110', '19+110=129'] Exploring Operation: 62*129=7998, Resulting Numbers: [7998] 7998,100 unequal: No Solution Exploring Operation: 62+129=191, Resulting Numbers: [191] 191,100 unequal: No Solution Exploring Operation: 129-62=67, Resulting Numbers: [67] 67,100 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: 100:[87, 62, 4], Operations: ['23-19=4'] Exploring Operation: 87-4=83, Resulting Numbers: [62, 83] Generated Node #0,1,0: 100:[62, 83] Operation: 87-4=83 Exploring Operation: 62+4=66, Resulting Numbers: [87, 66] Generated Node #0,1,1: 100:[87, 66] Operation: 62+4=66 Exploring Operation: 87-62=25, Resulting Numbers: [4, 25] Generated Node #0,1,2: 100:[4, 25] Operation: 87-62=25 Exploring Operation: 62-4=58, Resulting Numbers: [87, 58] Generated Node #0,1,3: 100:[87, 58] Operation: 62-4=58 Exploring Operation: 87+4=91, Resulting Numbers: [62, 91] Generated Node #0,1,4: 100:[62, 91] Operation: 87+4=91 Moving to Node #0,3,4 Current State: 100:[25, 4], Operations: ['87-62=25', '23-19=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[87, 23, 19, 62], Operations: [] Exploring Operation: 87-62=25, Resulting Numbers: [23, 19, 25] Generated Node #0,3: 100:[23, 19, 25] Operation: 87-62=25 Moving to Node #0,3 Current State: 100:[23, 19, 25], Operations: ['87-62=25'] Exploring Operation: 23-19=4, Resulting Numbers: [25, 4] Generated Node #0,3,4: 100:[25, 4] Operation: 23-19=4 Moving to Node #0,3,4 Current State: 100:[25, 4], Operations: ['87-62=25', '23-19=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.956597
hs_5
sum_heuristic
[ 85, 45, 54, 43 ]
29
[ "85-45=40", "54-43=11", "40-11=29" ]
Current State: 29:[85, 45, 54, 43], Operations: [] Exploring Operation: 85-45=40, Resulting Numbers: [54, 43, 40] Generated Node #2: [54, 43, 40] from Operation: 85-45=40 Current State: 29:[54, 43, 40], Operations: ['85-45=40'] Exploring Operation: 54-43=11, Resulting Numbers: [40, 11] Generated Node #3: [40, 11] from Operation: 54-43=11 Current State: 29:[40, 11], Operations: ['85-45=40', '54-43=11'] Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[85, 45, 54, 43], Operations: [] Exploring Operation: 85-45=40, Resulting Numbers: [54, 43, 40] Generated Node #0,0: 29:[54, 43, 40] Operation: 85-45=40 Exploring Operation: 85-43=42, Resulting Numbers: [45, 54, 42] Generated Node #0,1: 29:[45, 54, 42] Operation: 85-43=42 Exploring Operation: 85-54=31, Resulting Numbers: [45, 43, 31] Generated Node #0,2: 29:[45, 43, 31] Operation: 85-54=31 Moving to Node #0,2 Current State: 29:[45, 43, 31], Operations: ['85-54=31'] Exploring Operation: 45-43=2, Resulting Numbers: [31, 2] Generated Node #0,2,0: 29:[31, 2] Operation: 45-43=2 Exploring Operation: 45-31=14, Resulting Numbers: [43, 14] Generated Node #0,2,1: 29:[43, 14] Operation: 45-31=14 Exploring Operation: 43-31=12, Resulting Numbers: [45, 12] Generated Node #0,2,2: 29:[45, 12] Operation: 43-31=12 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[31, 2], Operations: ['85-54=31', '45-43=2'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[85, 45, 54, 43], Operations: [] Exploring Operation: 85-54=31, Resulting Numbers: [45, 43, 31] Generated Node #0,2: 29:[45, 43, 31] Operation: 85-54=31 Moving to Node #0,2 Current State: 29:[45, 43, 31], Operations: ['85-54=31'] Exploring Operation: 45-43=2, Resulting Numbers: [31, 2] Generated Node #0,2,0: 29:[31, 2] Operation: 45-43=2 Moving to Node #0,2,0 Current State: 29:[31, 2], Operations: ['85-54=31', '45-43=2'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 47, 13, 72, 61 ]
96
[ "72-61=11", "13*11=143", "143-47=96" ]
Current State: 96:[47, 13, 72, 61], Operations: [] Exploring Operation: 72-61=11, Resulting Numbers: [47, 13, 11] Generated Node #2: [47, 13, 11] from Operation: 72-61=11 Current State: 96:[47, 13, 11], Operations: ['72-61=11'] Exploring Operation: 13*11=143, Resulting Numbers: [47, 143] Generated Node #3: [47, 143] from Operation: 13*11=143 Current State: 96:[47, 143], Operations: ['72-61=11', '13*11=143'] Exploring Operation: 143-47=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[47, 13, 72, 61], Operations: [] Exploring Operation: 61-13=48, Resulting Numbers: [47, 72, 48] Generated Node #0,0: 96:[47, 72, 48] Operation: 61-13=48 Exploring Operation: 72-61=11, Resulting Numbers: [47, 13, 11] Generated Node #0,1: 96:[47, 13, 11] Operation: 72-61=11 Exploring Operation: 72-47=25, Resulting Numbers: [13, 61, 25] Generated Node #0,2: 96:[13, 61, 25] Operation: 72-47=25 Exploring Operation: 13+72=85, Resulting Numbers: [47, 61, 85] Generated Node #0,3: 96:[47, 61, 85] Operation: 13+72=85 Exploring Operation: 72-13=59, Resulting Numbers: [47, 61, 59] Generated Node #0,4: 96:[47, 61, 59] Operation: 72-13=59 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[47, 13, 11], Operations: ['72-61=11'] Exploring Operation: 13+11=24, Resulting Numbers: [47, 24] Generated Node #0,1,0: 96:[47, 24] Operation: 13+11=24 Exploring Operation: 47-13=34, Resulting Numbers: [11, 34] Generated Node #0,1,1: 96:[11, 34] Operation: 47-13=34 Exploring Operation: 47+11=58, Resulting Numbers: [13, 58] Generated Node #0,1,2: 96:[13, 58] Operation: 47+11=58 Exploring Operation: 13-11=2, Resulting Numbers: [47, 2] Generated Node #0,1,3: 96:[47, 2] Operation: 13-11=2 Exploring Operation: 47-11=36, Resulting Numbers: [13, 36] Generated Node #0,1,4: 96:[13, 36] Operation: 47-11=36 Moving to Node #0,1,0 Current State: 96:[47, 24], Operations: ['72-61=11', '13+11=24'] Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 47*24=1128, Resulting Numbers: [1128] 1128,96 unequal: No Solution Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,96 unequal: No Solution Moving to Node #0,1,3 Current State: 96:[47, 2], Operations: ['72-61=11', '13-11=2'] Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,96 unequal: No Solution Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,96 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[11, 34], Operations: ['72-61=11', '47-13=34'] Exploring Operation: 11*34=374, Resulting Numbers: [374] 374,96 unequal: No Solution Exploring Operation: 11+34=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,96 unequal: No Solution Moving to Node #0,1,4 Current State: 96:[13, 36], Operations: ['72-61=11', '47-11=36'] Exploring Operation: 13*36=468, Resulting Numbers: [468] 468,96 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[13, 58], Operations: ['72-61=11', '47+11=58'] Exploring Operation: 13*58=754, Resulting Numbers: [754] 754,96 unequal: No Solution Exploring Operation: 13+58=71, Resulting Numbers: [71] 71,96 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[13, 61, 25], Operations: ['72-47=25'] Exploring Operation: 61+25=86, Resulting Numbers: [13, 86] Generated Node #0,2,0: 96:[13, 86] Operation: 61+25=86 Exploring Operation: 61-13=48, Resulting Numbers: [25, 48] Generated Node #0,2,1: 96:[25, 48] Operation: 61-13=48 Exploring Operation: 13+25=38, Resulting Numbers: [61, 38] Generated Node #0,2,2: 96:[61, 38] Operation: 13+25=38 Exploring Operation: 25-13=12, Resulting Numbers: [61, 12] Generated Node #0,2,3: 96:[61, 12] Operation: 25-13=12 Exploring Operation: 61-25=36, Resulting Numbers: [13, 36] Generated Node #0,2,4: 96:[13, 36] Operation: 61-25=36 Moving to Node #0,2,1 Current State: 96:[25, 48], Operations: ['72-47=25', '61-13=48'] Exploring Operation: 48-25=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 25*48=1200, Resulting Numbers: [1200] 1200,96 unequal: No Solution Exploring Operation: 25+48=73, Resulting Numbers: [73] 73,96 unequal: No Solution Moving to Node #0,2,4 Current State: 96:[13, 36], Operations: ['72-47=25', '61-25=36'] Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,96 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 13*36=468, Resulting Numbers: [468] 468,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[13, 86], Operations: ['72-47=25', '61+25=86'] Exploring Operation: 13*86=1118, Resulting Numbers: [1118] 1118,96 unequal: No Solution Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,96 unequal: No Solution Exploring Operation: 13+86=99, Resulting Numbers: [99] 99,96 unequal: No Solution Moving to Node #0,2,3 Current State: 96:[61, 12], Operations: ['72-47=25', '25-13=12'] Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,96 unequal: No Solution Exploring Operation: 61+12=73, Resulting Numbers: [73] 73,96 unequal: No Solution Exploring Operation: 61*12=732, Resulting Numbers: [732] 732,96 unequal: No Solution Moving to Node #0,2,2 Current State: 96:[61, 38], Operations: ['72-47=25', '13+25=38'] Exploring Operation: 61-38=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 61*38=2318, Resulting Numbers: [2318] 2318,96 unequal: No Solution Exploring Operation: 61+38=99, Resulting Numbers: [99] 99,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[47, 72, 48], Operations: ['61-13=48'] Exploring Operation: 48-47=1, Resulting Numbers: [72, 1] Generated Node #0,0,0: 96:[72, 1] Operation: 48-47=1 Exploring Operation: 72-48=24, Resulting Numbers: [47, 24] Generated Node #0,0,1: 96:[47, 24] Operation: 72-48=24 Exploring Operation: 47+48=95, Resulting Numbers: [72, 95] Generated Node #0,0,2: 96:[72, 95] Operation: 47+48=95 Exploring Operation: 47+72=119, Resulting Numbers: [48, 119] Generated Node #0,0,3: 96:[48, 119] Operation: 47+72=119 Exploring Operation: 72-47=25, Resulting Numbers: [48, 25] Generated Node #0,0,4: 96:[48, 25] Operation: 72-47=25 Moving to Node #0,0,1 Current State: 96:[47, 24], Operations: ['61-13=48', '72-48=24'] Exploring Operation: 47*24=1128, Resulting Numbers: [1128] 1128,96 unequal: No Solution Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,96 unequal: No Solution Moving to Node #0,0,4 Current State: 96:[48, 25], Operations: ['61-13=48', '72-47=25'] Exploring Operation: 48-25=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 48+25=73, Resulting Numbers: [73] 73,96 unequal: No Solution Exploring Operation: 48*25=1200, Resulting Numbers: [1200] 1200,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[48, 119], Operations: ['61-13=48', '47+72=119'] Exploring Operation: 119-48=71, Resulting Numbers: [71] 71,96 unequal: No Solution Exploring Operation: 48*119=5712, Resulting Numbers: [5712] 5712,96 unequal: No Solution Exploring Operation: 48+119=167, Resulting Numbers: [167] 167,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[72, 1], Operations: ['61-13=48', '48-47=1'] Exploring Operation: 72*1=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,96 unequal: No Solution Exploring Operation: 72+1=73, Resulting Numbers: [73] 73,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[72, 95], Operations: ['61-13=48', '47+48=95'] Exploring Operation: 95-72=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 72+95=167, Resulting Numbers: [167] 167,96 unequal: No Solution Exploring Operation: 72*95=6840, Resulting Numbers: [6840] 6840,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 96:[47, 61, 85], Operations: ['13+72=85'] Exploring Operation: 85-61=24, Resulting Numbers: [47, 24] Generated Node #0,3,0: 96:[47, 24] Operation: 85-61=24 Exploring Operation: 47+85=132, Resulting Numbers: [61, 132] Generated Node #0,3,1: 96:[61, 132] Operation: 47+85=132 Exploring Operation: 85-47=38, Resulting Numbers: [61, 38] Generated Node #0,3,2: 96:[61, 38] Operation: 85-47=38 Exploring Operation: 47+61=108, Resulting Numbers: [85, 108] Generated Node #0,3,3: 96:[85, 108] Operation: 47+61=108 Exploring Operation: 61-47=14, Resulting Numbers: [85, 14] Generated Node #0,3,4: 96:[85, 14] Operation: 61-47=14 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 96:[47, 24], Operations: ['13+72=85', '85-61=24'] Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,96 unequal: No Solution Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 47*24=1128, Resulting Numbers: [1128] 1128,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 96:[85, 14], Operations: ['13+72=85', '61-47=14'] Exploring Operation: 85*14=1190, Resulting Numbers: [1190] 1190,96 unequal: No Solution Exploring Operation: 85-14=71, Resulting Numbers: [71] 71,96 unequal: No Solution Exploring Operation: 85+14=99, Resulting Numbers: [99] 99,96 unequal: No Solution No 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: 96:[61, 38], Operations: ['13+72=85', '85-47=38'] Exploring Operation: 61+38=99, Resulting Numbers: [99] 99,96 unequal: No Solution Exploring Operation: 61-38=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 61*38=2318, Resulting Numbers: [2318] 2318,96 unequal: No Solution No 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: 96:[85, 108], Operations: ['13+72=85', '47+61=108'] Exploring Operation: 108-85=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 85+108=193, Resulting Numbers: [193] 193,96 unequal: No Solution Exploring Operation: 85*108=9180, Resulting Numbers: [9180] 9180,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 96:[61, 132], Operations: ['13+72=85', '47+85=132'] Exploring Operation: 61*132=8052, Resulting Numbers: [8052] 8052,96 unequal: No Solution Exploring Operation: 132-61=71, Resulting Numbers: [71] 71,96 unequal: No Solution Exploring Operation: 61+132=193, Resulting Numbers: [193] 193,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 96:[47, 61, 59], Operations: ['72-13=59'] Exploring Operation: 61-59=2, Resulting Numbers: [47, 2] Generated Node #0,4,0: 96:[47, 2] Operation: 61-59=2 Exploring Operation: 47+59=106, Resulting Numbers: [61, 106] Generated Node #0,4,1: 96:[61, 106] Operation: 47+59=106 Exploring Operation: 61-47=14, Resulting Numbers: [59, 14] Generated Node #0,4,2: 96:[59, 14] Operation: 61-47=14 Exploring Operation: 59-47=12, Resulting Numbers: [61, 12] Generated Node #0,4,3: 96:[61, 12] Operation: 59-47=12 Exploring Operation: 47+61=108, Resulting Numbers: [59, 108] Generated Node #0,4,4: 96:[59, 108] Operation: 47+61=108 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 96:[47, 2], Operations: ['72-13=59', '61-59=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,96 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 96:[59, 14], Operations: ['72-13=59', '61-47=14'] Exploring Operation: 59*14=826, Resulting Numbers: [826] 826,96 unequal: No Solution Exploring Operation: 59-14=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 59+14=73, Resulting Numbers: [73] 73,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 96:[61, 12], Operations: ['72-13=59', '59-47=12'] Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,96 unequal: No Solution Exploring Operation: 61+12=73, Resulting Numbers: [73] 73,96 unequal: No Solution Exploring Operation: 61*12=732, Resulting Numbers: [732] 732,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 96:[61, 106], Operations: ['72-13=59', '47+59=106'] Exploring Operation: 106-61=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 61+106=167, Resulting Numbers: [167] 167,96 unequal: No Solution Exploring Operation: 61*106=6466, Resulting Numbers: [6466] 6466,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 96:[59, 108], Operations: ['72-13=59', '47+61=108'] Exploring Operation: 108-59=49, Resulting Numbers: [49] 49,96 unequal: No Solution Exploring Operation: 59+108=167, Resulting Numbers: [167] 167,96 unequal: No Solution Exploring Operation: 59*108=6372, Resulting Numbers: [6372] 6372,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 5, 77, 7, 90 ]
86
[ "90-77=13", "7*13=91", "91-5=86" ]
Current State: 86:[5, 77, 7, 90], Operations: [] Exploring Operation: 90-77=13, Resulting Numbers: [5, 7, 13] Generated Node #2: [5, 7, 13] from Operation: 90-77=13 Current State: 86:[5, 7, 13], Operations: ['90-77=13'] Exploring Operation: 7*13=91, Resulting Numbers: [5, 91] Generated Node #3: [5, 91] from Operation: 7*13=91 Current State: 86:[5, 91], Operations: ['90-77=13', '7*13=91'] Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[5, 77, 7, 90], Operations: [] Exploring Operation: 77+7=84, Resulting Numbers: [5, 90, 84] Generated Node #0,0: 86:[5, 90, 84] Operation: 77+7=84 Exploring Operation: 7-5=2, Resulting Numbers: [77, 90, 2] Generated Node #0,1: 86:[77, 90, 2] Operation: 7-5=2 Exploring Operation: 5+77=82, Resulting Numbers: [7, 90, 82] Generated Node #0,2: 86:[7, 90, 82] Operation: 5+77=82 Moving to Node #0,0 Current State: 86:[5, 90, 84], Operations: ['77+7=84'] Exploring Operation: 90-84=6, Resulting Numbers: [5, 6] Generated Node #0,0,0: 86:[5, 6] Operation: 90-84=6 Exploring Operation: 5+84=89, Resulting Numbers: [90, 89] Generated Node #0,0,1: 86:[90, 89] Operation: 5+84=89 Exploring Operation: 90-5=85, Resulting Numbers: [84, 85] Generated Node #0,0,2: 86:[84, 85] Operation: 90-5=85 Moving to Node #0,1 Current State: 86:[77, 90, 2], Operations: ['7-5=2'] Exploring Operation: 90-2=88, Resulting Numbers: [77, 88] Generated Node #0,1,0: 86:[77, 88] Operation: 90-2=88 Exploring Operation: 77+2=79, Resulting Numbers: [90, 79] Generated Node #0,1,1: 86:[90, 79] Operation: 77+2=79 Exploring Operation: 90-77=13, Resulting Numbers: [2, 13] Generated Node #0,1,2: 86:[2, 13] Operation: 90-77=13 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[77, 88], Operations: ['7-5=2', '90-2=88'] Exploring Operation: 77+88=165, Resulting Numbers: [165] 165,86 unequal: No Solution Exploring Operation: 88-77=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 77*88=6776, Resulting Numbers: [6776] 6776,86 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:[90, 79], Operations: ['7-5=2', '77+2=79'] Exploring Operation: 90*79=7110, Resulting Numbers: [7110] 7110,86 unequal: No Solution Exploring Operation: 90-79=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 90+79=169, Resulting Numbers: [169] 169,86 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:[2, 13], Operations: ['7-5=2', '90-77=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,86 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,86 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: 86:[7, 90, 82], Operations: ['5+77=82'] Exploring Operation: 7+82=89, Resulting Numbers: [90, 89] Generated Node #0,2,0: 86:[90, 89] Operation: 7+82=89 Exploring Operation: 90-82=8, Resulting Numbers: [7, 8] Generated Node #0,2,1: 86:[7, 8] Operation: 90-82=8 Exploring Operation: 90-7=83, Resulting Numbers: [82, 83] Generated Node #0,2,2: 86:[82, 83] Operation: 90-7=83 Moving to Node #0,0,2 Current State: 86:[84, 85], Operations: ['77+7=84', '90-5=85'] Exploring Operation: 84*85=7140, Resulting Numbers: [7140] 7140,86 unequal: No Solution Exploring Operation: 84+85=169, Resulting Numbers: [169] 169,86 unequal: No Solution Exploring Operation: 85-84=1, Resulting Numbers: [1] 1,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[90, 89], Operations: ['77+7=84', '5+84=89'] Exploring Operation: 90-89=1, Resulting Numbers: [1] 1,86 unequal: No Solution Exploring Operation: 90+89=179, Resulting Numbers: [179] 179,86 unequal: No Solution Exploring Operation: 90*89=8010, Resulting Numbers: [8010] 8010,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[5, 6], Operations: ['77+7=84', '90-84=6'] Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,86 unequal: No Solution Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,86 unequal: No Solution Moving to Node #0,2,0 Current State: 86:[90, 89], Operations: ['5+77=82', '7+82=89'] Exploring Operation: 90-89=1, Resulting Numbers: [1] 1,86 unequal: No Solution Exploring Operation: 90*89=8010, Resulting Numbers: [8010] 8010,86 unequal: No Solution Exploring Operation: 90+89=179, Resulting Numbers: [179] 179,86 unequal: No Solution Moving to Node #0,2,2 Current State: 86:[82, 83], Operations: ['5+77=82', '90-7=83'] Exploring Operation: 82+83=165, Resulting Numbers: [165] 165,86 unequal: No Solution Exploring Operation: 82*83=6806, Resulting Numbers: [6806] 6806,86 unequal: No Solution Exploring Operation: 83-82=1, Resulting Numbers: [1] 1,86 unequal: No Solution Moving to Node #0,2,1 Current State: 86:[7, 8], Operations: ['5+77=82', '90-82=8'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,86 unequal: No Solution Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,86 unequal: No Solution Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,86 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 83, 58, 78, 49 ]
85
[ "78-49=29", "58/29=2", "83+2=85" ]
Current State: 85:[83, 58, 78, 49], Operations: [] Exploring Operation: 78-49=29, Resulting Numbers: [83, 58, 29] Generated Node #2: [83, 58, 29] from Operation: 78-49=29 Current State: 85:[83, 58, 29], Operations: ['78-49=29'] Exploring Operation: 58/29=2, Resulting Numbers: [83, 2] Generated Node #3: [83, 2] from Operation: 58/29=2 Current State: 85:[83, 2], Operations: ['78-49=29', '58/29=2'] Exploring Operation: 83+2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[83, 58, 78, 49], Operations: [] Exploring Operation: 58+49=107, Resulting Numbers: [83, 78, 107] Generated Node #0,0: 85:[83, 78, 107] Operation: 58+49=107 Exploring Operation: 78-58=20, Resulting Numbers: [83, 49, 20] Generated Node #0,1: 85:[83, 49, 20] Operation: 78-58=20 Exploring Operation: 58-49=9, Resulting Numbers: [83, 78, 9] Generated Node #0,2: 85:[83, 78, 9] Operation: 58-49=9 Moving to Node #0,2 Current State: 85:[83, 78, 9], Operations: ['58-49=9'] Exploring Operation: 83-78=5, Resulting Numbers: [9, 5] Generated Node #0,2,0: 85:[9, 5] Operation: 83-78=5 Exploring Operation: 83+9=92, Resulting Numbers: [78, 92] Generated Node #0,2,1: 85:[78, 92] Operation: 83+9=92 Exploring Operation: 78+9=87, Resulting Numbers: [83, 87] Generated Node #0,2,2: 85:[83, 87] Operation: 78+9=87 Moving to Node #0,0 Current State: 85:[83, 78, 107], Operations: ['58+49=107'] Exploring Operation: 107-83=24, Resulting Numbers: [78, 24] Generated Node #0,0,0: 85:[78, 24] Operation: 107-83=24 Exploring Operation: 83-78=5, Resulting Numbers: [107, 5] Generated Node #0,0,1: 85:[107, 5] Operation: 83-78=5 Exploring Operation: 107-78=29, Resulting Numbers: [83, 29] Generated Node #0,0,2: 85:[83, 29] Operation: 107-78=29 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[78, 24], Operations: ['58+49=107', '107-83=24'] Exploring Operation: 78*24=1872, Resulting Numbers: [1872] 1872,85 unequal: No Solution Exploring Operation: 78-24=54, Resulting Numbers: [54] 54,85 unequal: No Solution Exploring Operation: 78+24=102, Resulting Numbers: [102] 102,85 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:[83, 29], Operations: ['58+49=107', '107-78=29'] Exploring Operation: 83+29=112, Resulting Numbers: [112] 112,85 unequal: No Solution Exploring Operation: 83*29=2407, Resulting Numbers: [2407] 2407,85 unequal: No Solution Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,85 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:[107, 5], Operations: ['58+49=107', '83-78=5'] Exploring Operation: 107+5=112, Resulting Numbers: [112] 112,85 unequal: No Solution Exploring Operation: 107-5=102, Resulting Numbers: [102] 102,85 unequal: No Solution Exploring Operation: 107*5=535, Resulting Numbers: [535] 535,85 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:[83, 49, 20], Operations: ['78-58=20'] Exploring Operation: 49+20=69, Resulting Numbers: [83, 69] Generated Node #0,1,0: 85:[83, 69] Operation: 49+20=69 Exploring Operation: 49-20=29, Resulting Numbers: [83, 29] Generated Node #0,1,1: 85:[83, 29] Operation: 49-20=29 Exploring Operation: 83-49=34, Resulting Numbers: [20, 34] Generated Node #0,1,2: 85:[20, 34] Operation: 83-49=34 Moving to Node #0,2,0 Current State: 85:[9, 5], Operations: ['58-49=9', '83-78=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,85 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,85 unequal: No Solution Moving to Node #0,2,2 Current State: 85:[83, 87], Operations: ['58-49=9', '78+9=87'] Exploring Operation: 83+87=170, Resulting Numbers: [170] 170,85 unequal: No Solution Exploring Operation: 87-83=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 83*87=7221, Resulting Numbers: [7221] 7221,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[78, 92], Operations: ['58-49=9', '83+9=92'] Exploring Operation: 78*92=7176, Resulting Numbers: [7176] 7176,85 unequal: No Solution Exploring Operation: 92-78=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 78+92=170, Resulting Numbers: [170] 170,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[83, 29], Operations: ['78-58=20', '49-20=29'] Exploring Operation: 83*29=2407, Resulting Numbers: [2407] 2407,85 unequal: No Solution Exploring Operation: 83+29=112, Resulting Numbers: [112] 112,85 unequal: No Solution Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[83, 69], Operations: ['78-58=20', '49+20=69'] Exploring Operation: 83*69=5727, Resulting Numbers: [5727] 5727,85 unequal: No Solution Exploring Operation: 83+69=152, Resulting Numbers: [152] 152,85 unequal: No Solution Exploring Operation: 83-69=14, Resulting Numbers: [14] 14,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[20, 34], Operations: ['78-58=20', '83-49=34'] Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 20*34=680, Resulting Numbers: [680] 680,85 unequal: No Solution Exploring Operation: 20+34=54, Resulting Numbers: [54] 54,85 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 93, 5, 28, 10 ]
35
[ "93+5=98", "10*98=980", "980/28=35" ]
Current State: 35:[93, 5, 28, 10], Operations: [] Exploring Operation: 93+5=98, Resulting Numbers: [28, 10, 98] Generated Node #2: [28, 10, 98] from Operation: 93+5=98 Current State: 35:[28, 10, 98], Operations: ['93+5=98'] Exploring Operation: 10*98=980, Resulting Numbers: [28, 980] Generated Node #3: [28, 980] from Operation: 10*98=980 Current State: 35:[28, 980], Operations: ['93+5=98', '10*98=980'] Exploring Operation: 980/28=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[93, 5, 28, 10], Operations: [] Exploring Operation: 28+10=38, Resulting Numbers: [93, 5, 38] Generated Node #0,0: 35:[93, 5, 38] Operation: 28+10=38 Exploring Operation: 93-28=65, Resulting Numbers: [5, 10, 65] Generated Node #0,1: 35:[5, 10, 65] Operation: 93-28=65 Exploring Operation: 93-10=83, Resulting Numbers: [5, 28, 83] Generated Node #0,2: 35:[5, 28, 83] Operation: 93-10=83 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[5, 10, 65], Operations: ['93-28=65'] Exploring Operation: 65-5=60, Resulting Numbers: [10, 60] Generated Node #0,1,0: 35:[10, 60] Operation: 65-5=60 Exploring Operation: 65-10=55, Resulting Numbers: [5, 55] Generated Node #0,1,1: 35:[5, 55] Operation: 65-10=55 Exploring Operation: 65/5=13, Resulting Numbers: [10, 13] Generated Node #0,1,2: 35:[10, 13] Operation: 65/5=13 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 35:[10, 13], Operations: ['93-28=65', '65/5=13'] Exploring Operation: 10*13=130, Resulting Numbers: [130] 130,35 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 10+13=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 #0,1,1 Current State: 35:[5, 55], Operations: ['93-28=65', '65-10=55'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,35 unequal: No Solution Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,35 unequal: No Solution Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,35 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 #0,1,0 Current State: 35:[10, 60], Operations: ['93-28=65', '65-5=60'] Exploring Operation: 60-10=50, Resulting Numbers: [50] 50,35 unequal: No Solution Exploring Operation: 10+60=70, Resulting Numbers: [70] 70,35 unequal: No Solution Exploring Operation: 60/10=6, Resulting Numbers: [6] 6,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[5, 28, 83], Operations: ['93-10=83'] Exploring Operation: 83-5=78, Resulting Numbers: [28, 78] Generated Node #0,2,0: 35:[28, 78] Operation: 83-5=78 Exploring Operation: 83-28=55, Resulting Numbers: [5, 55] Generated Node #0,2,1: 35:[5, 55] Operation: 83-28=55 Exploring Operation: 5+28=33, Resulting Numbers: [83, 33] Generated Node #0,2,2: 35:[83, 33] Operation: 5+28=33 Moving to Node #0,2,1 Current State: 35:[5, 55], Operations: ['93-10=83', '83-28=55'] Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,35 unequal: No Solution Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,35 unequal: No Solution Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[28, 78], Operations: ['93-10=83', '83-5=78'] Exploring Operation: 28+78=106, Resulting Numbers: [106] 106,35 unequal: No Solution Exploring Operation: 78-28=50, Resulting Numbers: [50] 50,35 unequal: No Solution Exploring Operation: 28*78=2184, Resulting Numbers: [2184] 2184,35 unequal: No Solution Moving to Node #0,2,2 Current State: 35:[83, 33], Operations: ['93-10=83', '5+28=33'] Exploring Operation: 83*33=2739, Resulting Numbers: [2739] 2739,35 unequal: No Solution Exploring Operation: 83+33=116, Resulting Numbers: [116] 116,35 unequal: No Solution Exploring Operation: 83-33=50, Resulting Numbers: [50] 50,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[93, 5, 38], Operations: ['28+10=38'] Exploring Operation: 93-38=55, Resulting Numbers: [5, 55] Generated Node #0,0,0: 35:[5, 55] Operation: 93-38=55 Exploring Operation: 38-5=33, Resulting Numbers: [93, 33] Generated Node #0,0,1: 35:[93, 33] Operation: 38-5=33 Exploring Operation: 93-5=88, Resulting Numbers: [38, 88] Generated Node #0,0,2: 35:[38, 88] Operation: 93-5=88 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[5, 55], Operations: ['28+10=38', '93-38=55'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,35 unequal: No Solution Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,35 unequal: No Solution Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,35 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:[38, 88], Operations: ['28+10=38', '93-5=88'] Exploring Operation: 38*88=3344, Resulting Numbers: [3344] 3344,35 unequal: No Solution Exploring Operation: 88-38=50, Resulting Numbers: [50] 50,35 unequal: No Solution Exploring Operation: 38+88=126, Resulting Numbers: [126] 126,35 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:[93, 33], Operations: ['28+10=38', '38-5=33'] Exploring Operation: 93*33=3069, Resulting Numbers: [3069] 3069,35 unequal: No Solution Exploring Operation: 93+33=126, Resulting Numbers: [126] 126,35 unequal: No Solution Exploring Operation: 93-33=60, Resulting Numbers: [60] 60,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 83, 79, 46, 44 ]
87
[ "46-44=2", "83*2=166", "166-79=87" ]
Current State: 87:[83, 79, 46, 44], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [83, 79, 2] Generated Node #2: [83, 79, 2] from Operation: 46-44=2 Current State: 87:[83, 79, 2], Operations: ['46-44=2'] Exploring Operation: 83*2=166, Resulting Numbers: [79, 166] Generated Node #3: [79, 166] from Operation: 83*2=166 Current State: 87:[79, 166], Operations: ['46-44=2', '83*2=166'] Exploring Operation: 166-79=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[83, 79, 46, 44], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [83, 79, 2] Generated Node #0,0: 87:[83, 79, 2] Operation: 46-44=2 Exploring Operation: 46+44=90, Resulting Numbers: [83, 79, 90] Generated Node #0,1: 87:[83, 79, 90] Operation: 46+44=90 Moving to Node #0,0 Current State: 87:[83, 79, 2], Operations: ['46-44=2'] Exploring Operation: 83+2=85, Resulting Numbers: [79, 85] Generated Node #0,0,0: 87:[79, 85] Operation: 83+2=85 Exploring Operation: 83-79=4, Resulting Numbers: [2, 4] Generated Node #0,0,1: 87:[2, 4] Operation: 83-79=4 Moving to Node #0,1 Current State: 87:[83, 79, 90], Operations: ['46+44=90'] Exploring Operation: 90-83=7, Resulting Numbers: [79, 7] Generated Node #0,1,0: 87:[79, 7] Operation: 90-83=7 Exploring Operation: 83-79=4, Resulting Numbers: [90, 4] Generated Node #0,1,1: 87:[90, 4] Operation: 83-79=4 Moving to Node #0,0,1 Current State: 87:[2, 4], Operations: ['46-44=2', '83-79=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,87 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[90, 4], Operations: ['46+44=90', '83-79=4'] Exploring Operation: 90-4=86, Resulting Numbers: [86] 86,87 unequal: No Solution Exploring Operation: 90+4=94, Resulting Numbers: [94] 94,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[79, 85], Operations: ['46-44=2', '83+2=85'] Exploring Operation: 85-79=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 79+85=164, Resulting Numbers: [164] 164,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[79, 7], Operations: ['46+44=90', '90-83=7'] Exploring Operation: 79-7=72, Resulting Numbers: [72] 72,87 unequal: No Solution Exploring Operation: 79+7=86, Resulting Numbers: [86] 86,87 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 81, 83, 58, 84 ]
71
[ "83-81=2", "58+84=142", "142/2=71" ]
Current State: 71:[81, 83, 58, 84], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [58, 84, 2] Generated Node #2: [58, 84, 2] from Operation: 83-81=2 Current State: 71:[58, 84, 2], Operations: ['83-81=2'] Exploring Operation: 58+84=142, Resulting Numbers: [2, 142] Generated Node #3: [2, 142] from Operation: 58+84=142 Current State: 71:[2, 142], Operations: ['83-81=2', '58+84=142'] Exploring Operation: 142/2=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[81, 83, 58, 84], Operations: [] Exploring Operation: 84-58=26, Resulting Numbers: [81, 83, 26] Generated Node #0,0: 71:[81, 83, 26] Operation: 84-58=26 Exploring Operation: 81+58=139, Resulting Numbers: [83, 84, 139] Generated Node #0,1: 71:[83, 84, 139] Operation: 81+58=139 Exploring Operation: 83-58=25, Resulting Numbers: [81, 84, 25] Generated Node #0,2: 71:[81, 84, 25] Operation: 83-58=25 Exploring Operation: 81-58=23, Resulting Numbers: [83, 84, 23] Generated Node #0,3: 71:[83, 84, 23] Operation: 81-58=23 Moving to Node #0,0 Current State: 71:[81, 83, 26], Operations: ['84-58=26'] Exploring Operation: 81+26=107, Resulting Numbers: [83, 107] Generated Node #0,0,0: 71:[83, 107] Operation: 81+26=107 Exploring Operation: 81-26=55, Resulting Numbers: [83, 55] Generated Node #0,0,1: 71:[83, 55] Operation: 81-26=55 Exploring Operation: 83-26=57, Resulting Numbers: [81, 57] Generated Node #0,0,2: 71:[81, 57] Operation: 83-26=57 Exploring Operation: 83+26=109, Resulting Numbers: [81, 109] Generated Node #0,0,3: 71:[81, 109] Operation: 83+26=109 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 71:[81, 57], Operations: ['84-58=26', '83-26=57'] Exploring Operation: 81+57=138, Resulting Numbers: [138] 138,71 unequal: No Solution Exploring Operation: 81*57=4617, Resulting Numbers: [4617] 4617,71 unequal: No Solution Exploring Operation: 81-57=24, Resulting Numbers: [24] 24,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 71:[83, 55], Operations: ['84-58=26', '81-26=55'] Exploring Operation: 83-55=28, Resulting Numbers: [28] 28,71 unequal: No Solution Exploring Operation: 83*55=4565, Resulting Numbers: [4565] 4565,71 unequal: No Solution Exploring Operation: 83+55=138, Resulting Numbers: [138] 138,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[83, 107], Operations: ['84-58=26', '81+26=107'] Exploring Operation: 83*107=8881, Resulting Numbers: [8881] 8881,71 unequal: No Solution Exploring Operation: 107-83=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 83+107=190, Resulting Numbers: [190] 190,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 71:[81, 109], Operations: ['84-58=26', '83+26=109'] Exploring Operation: 81+109=190, Resulting Numbers: [190] 190,71 unequal: No Solution Exploring Operation: 81*109=8829, Resulting Numbers: [8829] 8829,71 unequal: No Solution Exploring Operation: 109-81=28, Resulting Numbers: [28] 28,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 71:[81, 84, 25], Operations: ['83-58=25'] Exploring Operation: 84-25=59, Resulting Numbers: [81, 59] Generated Node #0,2,0: 71:[81, 59] Operation: 84-25=59 Exploring Operation: 81+25=106, Resulting Numbers: [84, 106] Generated Node #0,2,1: 71:[84, 106] Operation: 81+25=106 Exploring Operation: 84+25=109, Resulting Numbers: [81, 109] Generated Node #0,2,2: 71:[81, 109] Operation: 84+25=109 Exploring Operation: 81-25=56, Resulting Numbers: [84, 56] Generated Node #0,2,3: 71:[84, 56] Operation: 81-25=56 Moving to Node #0,3 Current State: 71:[83, 84, 23], Operations: ['81-58=23'] Exploring Operation: 84-23=61, Resulting Numbers: [83, 61] Generated Node #0,3,0: 71:[83, 61] Operation: 84-23=61 Exploring Operation: 84+23=107, Resulting Numbers: [83, 107] Generated Node #0,3,1: 71:[83, 107] Operation: 84+23=107 Exploring Operation: 83-23=60, Resulting Numbers: [84, 60] Generated Node #0,3,2: 71:[84, 60] Operation: 83-23=60 Exploring Operation: 83+23=106, Resulting Numbers: [84, 106] Generated Node #0,3,3: 71:[84, 106] Operation: 83+23=106 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 71:[83, 61], Operations: ['81-58=23', '84-23=61'] Exploring Operation: 83*61=5063, Resulting Numbers: [5063] 5063,71 unequal: No Solution Exploring Operation: 83-61=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 83+61=144, Resulting Numbers: [144] 144,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 71:[84, 60], Operations: ['81-58=23', '83-23=60'] Exploring Operation: 84-60=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 84*60=5040, Resulting Numbers: [5040] 5040,71 unequal: No Solution Exploring Operation: 84+60=144, Resulting Numbers: [144] 144,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 71:[83, 107], Operations: ['81-58=23', '84+23=107'] Exploring Operation: 107-83=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 83*107=8881, Resulting Numbers: [8881] 8881,71 unequal: No Solution Exploring Operation: 83+107=190, Resulting Numbers: [190] 190,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 71:[84, 106], Operations: ['81-58=23', '83+23=106'] Exploring Operation: 106-84=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 84+106=190, Resulting Numbers: [190] 190,71 unequal: No Solution Exploring Operation: 84*106=8904, Resulting Numbers: [8904] 8904,71 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: 71:[83, 84, 139], Operations: ['81+58=139'] Exploring Operation: 83+84=167, Resulting Numbers: [139, 167] Generated Node #0,1,0: 71:[139, 167] Operation: 83+84=167 Exploring Operation: 84-83=1, Resulting Numbers: [139, 1] Generated Node #0,1,1: 71:[139, 1] Operation: 84-83=1 Exploring Operation: 139-83=56, Resulting Numbers: [84, 56] Generated Node #0,1,2: 71:[84, 56] Operation: 139-83=56 Exploring Operation: 139-84=55, Resulting Numbers: [83, 55] Generated Node #0,1,3: 71:[83, 55] Operation: 139-84=55 Moving to Node #0,2,0 Current State: 71:[81, 59], Operations: ['83-58=25', '84-25=59'] Exploring Operation: 81-59=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 81*59=4779, Resulting Numbers: [4779] 4779,71 unequal: No Solution Exploring Operation: 81+59=140, Resulting Numbers: [140] 140,71 unequal: No Solution Moving to Node #0,1,3 Current State: 71:[83, 55], Operations: ['81+58=139', '139-84=55'] Exploring Operation: 83-55=28, Resulting Numbers: [28] 28,71 unequal: No Solution Exploring Operation: 83*55=4565, Resulting Numbers: [4565] 4565,71 unequal: No Solution Exploring Operation: 83+55=138, Resulting Numbers: [138] 138,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[84, 56], Operations: ['83-58=25', '81-25=56'] Exploring Operation: 84-56=28, Resulting Numbers: [28] 28,71 unequal: No Solution Exploring Operation: 84+56=140, Resulting Numbers: [140] 140,71 unequal: No Solution Exploring Operation: 84*56=4704, Resulting Numbers: [4704] 4704,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[84, 56], Operations: ['81+58=139', '139-83=56'] Exploring Operation: 84+56=140, Resulting Numbers: [140] 140,71 unequal: No Solution Exploring Operation: 84-56=28, Resulting Numbers: [28] 28,71 unequal: No Solution Exploring Operation: 84*56=4704, Resulting Numbers: [4704] 4704,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[84, 106], Operations: ['83-58=25', '81+25=106'] Exploring Operation: 84*106=8904, Resulting Numbers: [8904] 8904,71 unequal: No Solution Exploring Operation: 84+106=190, Resulting Numbers: [190] 190,71 unequal: No Solution Exploring Operation: 106-84=22, Resulting Numbers: [22] 22,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[81, 109], Operations: ['83-58=25', '84+25=109'] Exploring Operation: 109-81=28, Resulting Numbers: [28] 28,71 unequal: No Solution Exploring Operation: 81+109=190, Resulting Numbers: [190] 190,71 unequal: No Solution Exploring Operation: 81*109=8829, Resulting Numbers: [8829] 8829,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[139, 1], Operations: ['81+58=139', '84-83=1'] Exploring Operation: 139/1=139, Resulting Numbers: [139] 139,71 unequal: No Solution Exploring Operation: 139*1=139, Resulting Numbers: [139] 139,71 unequal: No Solution Exploring Operation: 139+1=140, Resulting Numbers: [140] 140,71 unequal: No Solution Exploring Operation: 139-1=138, Resulting Numbers: [138] 138,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[139, 167], Operations: ['81+58=139', '83+84=167'] Exploring Operation: 167-139=28, Resulting Numbers: [28] 28,71 unequal: No Solution Exploring Operation: 139*167=23213, Resulting Numbers: [23213] 23213,71 unequal: No Solution Exploring Operation: 139+167=306, Resulting Numbers: [306] 306,71 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 58, 80, 46, 65 ]
90
[ "58*65=3770", "80*46=3680", "3770-3680=90" ]
Current State: 90:[58, 80, 46, 65], Operations: [] Exploring Operation: 58*65=3770, Resulting Numbers: [80, 46, 3770] Generated Node #2: [80, 46, 3770] from Operation: 58*65=3770 Current State: 90:[80, 46, 3770], Operations: ['58*65=3770'] Exploring Operation: 80*46=3680, Resulting Numbers: [3770, 3680] Generated Node #3: [3770, 3680] from Operation: 80*46=3680 Current State: 90:[3770, 3680], Operations: ['58*65=3770', '80*46=3680'] Exploring Operation: 3770-3680=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[58, 80, 46, 65], Operations: [] Exploring Operation: 65-46=19, Resulting Numbers: [58, 80, 19] Generated Node #0,0: 90:[58, 80, 19] Operation: 65-46=19 Exploring Operation: 65-58=7, Resulting Numbers: [80, 46, 7] Generated Node #0,1: 90:[80, 46, 7] Operation: 65-58=7 Exploring Operation: 80-58=22, Resulting Numbers: [46, 65, 22] Generated Node #0,2: 90:[46, 65, 22] Operation: 80-58=22 Exploring Operation: 80-65=15, Resulting Numbers: [58, 46, 15] Generated Node #0,3: 90:[58, 46, 15] Operation: 80-65=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[80, 46, 7], Operations: ['65-58=7'] Exploring Operation: 80+7=87, Resulting Numbers: [46, 87] Generated Node #0,1,0: 90:[46, 87] Operation: 80+7=87 Exploring Operation: 80-46=34, Resulting Numbers: [7, 34] Generated Node #0,1,1: 90:[7, 34] Operation: 80-46=34 Exploring Operation: 80-7=73, Resulting Numbers: [46, 73] Generated Node #0,1,2: 90:[46, 73] Operation: 80-7=73 Exploring Operation: 46-7=39, Resulting Numbers: [80, 39] Generated Node #0,1,3: 90:[80, 39] Operation: 46-7=39 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[46, 87], Operations: ['65-58=7', '80+7=87'] Exploring Operation: 46*87=4002, Resulting Numbers: [4002] 4002,90 unequal: No Solution Exploring Operation: 87-46=41, Resulting Numbers: [41] 41,90 unequal: No Solution Exploring Operation: 46+87=133, Resulting Numbers: [133] 133,90 unequal: No Solution No 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: 90:[7, 34], Operations: ['65-58=7', '80-46=34'] Exploring Operation: 7*34=238, Resulting Numbers: [238] 238,90 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,90 unequal: No Solution No 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: 90:[80, 39], Operations: ['65-58=7', '46-7=39'] Exploring Operation: 80+39=119, Resulting Numbers: [119] 119,90 unequal: No Solution Exploring Operation: 80*39=3120, Resulting Numbers: [3120] 3120,90 unequal: No Solution Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,90 unequal: No Solution No 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: 90:[46, 73], Operations: ['65-58=7', '80-7=73'] Exploring Operation: 46+73=119, Resulting Numbers: [119] 119,90 unequal: No Solution Exploring Operation: 46*73=3358, Resulting Numbers: [3358] 3358,90 unequal: No Solution Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[58, 46, 15], Operations: ['80-65=15'] Exploring Operation: 46-15=31, Resulting Numbers: [58, 31] Generated Node #0,3,0: 90:[58, 31] Operation: 46-15=31 Exploring Operation: 58+46=104, Resulting Numbers: [15, 104] Generated Node #0,3,1: 90:[15, 104] Operation: 58+46=104 Exploring Operation: 58-46=12, Resulting Numbers: [15, 12] Generated Node #0,3,2: 90:[15, 12] Operation: 58-46=12 Exploring Operation: 58-15=43, Resulting Numbers: [46, 43] Generated Node #0,3,3: 90:[46, 43] Operation: 58-15=43 Moving to Node #0,3,2 Current State: 90:[15, 12], Operations: ['80-65=15', '58-46=12'] Exploring Operation: 15+12=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 15*12=180, Resulting Numbers: [180] 180,90 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,90 unequal: No Solution Moving to Node #0,3,3 Current State: 90:[46, 43], Operations: ['80-65=15', '58-15=43'] Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 46*43=1978, Resulting Numbers: [1978] 1978,90 unequal: No Solution Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,90 unequal: No Solution Moving to Node #0,3,1 Current State: 90:[15, 104], Operations: ['80-65=15', '58+46=104'] Exploring Operation: 104-15=89, Resulting Numbers: [89] 89,90 unequal: No Solution Exploring Operation: 15*104=1560, Resulting Numbers: [1560] 1560,90 unequal: No Solution Exploring Operation: 15+104=119, Resulting Numbers: [119] 119,90 unequal: No Solution Moving to Node #0,3,0 Current State: 90:[58, 31], Operations: ['80-65=15', '46-15=31'] Exploring Operation: 58-31=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 58+31=89, Resulting Numbers: [89] 89,90 unequal: No Solution Exploring Operation: 58*31=1798, Resulting Numbers: [1798] 1798,90 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 Current State: 90:[58, 80, 19], Operations: ['65-46=19'] Exploring Operation: 80-58=22, Resulting Numbers: [19, 22] Generated Node #0,0,0: 90:[19, 22] Operation: 80-58=22 Exploring Operation: 58+19=77, Resulting Numbers: [80, 77] Generated Node #0,0,1: 90:[80, 77] Operation: 58+19=77 Exploring Operation: 58-19=39, Resulting Numbers: [80, 39] Generated Node #0,0,2: 90:[80, 39] Operation: 58-19=39 Exploring Operation: 80+19=99, Resulting Numbers: [58, 99] Generated Node #0,0,3: 90:[58, 99] Operation: 80+19=99 Moving to Node #0,0,0 Current State: 90:[19, 22], Operations: ['65-46=19', '80-58=22'] Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,90 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 19*22=418, Resulting Numbers: [418] 418,90 unequal: No Solution Moving to Node #0,0,2 Current State: 90:[80, 39], Operations: ['65-46=19', '58-19=39'] Exploring Operation: 80+39=119, Resulting Numbers: [119] 119,90 unequal: No Solution Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,90 unequal: No Solution Exploring Operation: 80*39=3120, Resulting Numbers: [3120] 3120,90 unequal: No Solution Moving to Node #0,0,3 Current State: 90:[58, 99], Operations: ['65-46=19', '80+19=99'] Exploring Operation: 99-58=41, Resulting Numbers: [41] 41,90 unequal: No Solution Exploring Operation: 58+99=157, Resulting Numbers: [157] 157,90 unequal: No Solution Exploring Operation: 58*99=5742, Resulting Numbers: [5742] 5742,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[80, 77], Operations: ['65-46=19', '58+19=77'] Exploring Operation: 80*77=6160, Resulting Numbers: [6160] 6160,90 unequal: No Solution Exploring Operation: 80+77=157, Resulting Numbers: [157] 157,90 unequal: No Solution Exploring Operation: 80-77=3, Resulting Numbers: [3] 3,90 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 #0,2 Current State: 90:[46, 65, 22], Operations: ['80-58=22'] Exploring Operation: 65-46=19, Resulting Numbers: [22, 19] Generated Node #0,2,0: 90:[22, 19] Operation: 65-46=19 Exploring Operation: 65-22=43, Resulting Numbers: [46, 43] Generated Node #0,2,1: 90:[46, 43] Operation: 65-22=43 Exploring Operation: 46+65=111, Resulting Numbers: [22, 111] Generated Node #0,2,2: 90:[22, 111] Operation: 46+65=111 Exploring Operation: 65+22=87, Resulting Numbers: [46, 87] Generated Node #0,2,3: 90:[46, 87] Operation: 65+22=87 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 90:[46, 43], Operations: ['80-58=22', '65-22=43'] Exploring Operation: 46*43=1978, Resulting Numbers: [1978] 1978,90 unequal: No Solution Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,90 unequal: No Solution Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,90 unequal: No Solution No 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: 90:[46, 87], Operations: ['80-58=22', '65+22=87'] Exploring Operation: 46+87=133, Resulting Numbers: [133] 133,90 unequal: No Solution Exploring Operation: 87-46=41, Resulting Numbers: [41] 41,90 unequal: No Solution Exploring Operation: 46*87=4002, Resulting Numbers: [4002] 4002,90 unequal: No Solution No 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: 90:[22, 19], Operations: ['80-58=22', '65-46=19'] Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,90 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,90 unequal: No Solution No 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: 90:[22, 111], Operations: ['80-58=22', '46+65=111'] Exploring Operation: 111-22=89, Resulting Numbers: [89] 89,90 unequal: No Solution Exploring Operation: 22*111=2442, Resulting Numbers: [2442] 2442,90 unequal: No Solution Exploring Operation: 22+111=133, Resulting Numbers: [133] 133,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 25, 12, 36, 31 ]
36
[ "31-25=6", "12*6=72", "72-36=36" ]
Current State: 36:[25, 12, 36, 31], Operations: [] Exploring Operation: 31-25=6, Resulting Numbers: [12, 36, 6] Generated Node #2: [12, 36, 6] from Operation: 31-25=6 Current State: 36:[12, 36, 6], Operations: ['31-25=6'] Exploring Operation: 12*6=72, Resulting Numbers: [36, 72] Generated Node #3: [36, 72] from Operation: 12*6=72 Current State: 36:[36, 72], Operations: ['31-25=6', '12*6=72'] Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[25, 12, 36, 31], Operations: [] Exploring Operation: 31-25=6, Resulting Numbers: [12, 36, 6] Generated Node #0,0: 36:[12, 36, 6] Operation: 31-25=6 Exploring Operation: 25-12=13, Resulting Numbers: [36, 31, 13] Generated Node #0,1: 36:[36, 31, 13] Operation: 25-12=13 Exploring Operation: 25+12=37, Resulting Numbers: [36, 31, 37] Generated Node #0,2: 36:[36, 31, 37] Operation: 25+12=37 Exploring Operation: 36-25=11, Resulting Numbers: [12, 31, 11] Generated Node #0,3: 36:[12, 31, 11] Operation: 36-25=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[12, 36, 6], Operations: ['31-25=6'] Exploring Operation: 12+6=18, Resulting Numbers: [36, 18] Generated Node #0,0,0: 36:[36, 18] Operation: 12+6=18 Exploring Operation: 12-6=6, Resulting Numbers: [36, 6] Generated Node #0,0,1: 36:[36, 6] Operation: 12-6=6 Exploring Operation: 12/6=2, Resulting Numbers: [36, 2] Generated Node #0,0,2: 36:[36, 2] Operation: 12/6=2 Exploring Operation: 36/12=3, Resulting Numbers: [6, 3] Generated Node #0,0,3: 36:[6, 3] Operation: 36/12=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[36, 18], Operations: ['31-25=6', '12+6=18'] Exploring Operation: 36*18=648, Resulting Numbers: [648] 648,36 unequal: No Solution Exploring Operation: 36+18=54, Resulting Numbers: [54] 54,36 unequal: No Solution Exploring Operation: 36-18=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 36/18=2, Resulting Numbers: [2] 2,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 36:[36, 6], Operations: ['31-25=6', '12-6=6'] Exploring Operation: 36*6=216, Resulting Numbers: [216] 216,36 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,36 unequal: No Solution Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 36:[36, 2], Operations: ['31-25=6', '12/6=2'] Exploring Operation: 36*2=72, Resulting Numbers: [72] 72,36 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 36:[6, 3], Operations: ['31-25=6', '36/12=3'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[36, 31, 13], Operations: ['25-12=13'] Exploring Operation: 31-13=18, Resulting Numbers: [36, 18] Generated Node #0,1,0: 36:[36, 18] Operation: 31-13=18 Exploring Operation: 36-31=5, Resulting Numbers: [13, 5] Generated Node #0,1,1: 36:[13, 5] Operation: 36-31=5 Exploring Operation: 36-13=23, Resulting Numbers: [31, 23] Generated Node #0,1,2: 36:[31, 23] Operation: 36-13=23 Exploring Operation: 31+13=44, Resulting Numbers: [36, 44] Generated Node #0,1,3: 36:[36, 44] Operation: 31+13=44 Moving to Node #0,1,0 Current State: 36:[36, 18], Operations: ['25-12=13', '31-13=18'] Exploring Operation: 36/18=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 36-18=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 36+18=54, Resulting Numbers: [54] 54,36 unequal: No Solution Exploring Operation: 36*18=648, Resulting Numbers: [648] 648,36 unequal: No Solution Moving to Node #0,1,1 Current State: 36:[13, 5], Operations: ['25-12=13', '36-31=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,36 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,36 unequal: No Solution Moving to Node #0,1,3 Current State: 36:[36, 44], Operations: ['25-12=13', '31+13=44'] Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,36 unequal: No Solution Exploring Operation: 36*44=1584, Resulting Numbers: [1584] 1584,36 unequal: No Solution Exploring Operation: 36+44=80, Resulting Numbers: [80] 80,36 unequal: No Solution Moving to Node #0,1,2 Current State: 36:[31, 23], Operations: ['25-12=13', '36-13=23'] Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,36 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,36 unequal: No Solution Exploring Operation: 31*23=713, Resulting Numbers: [713] 713,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 36:[36, 31, 37], Operations: ['25+12=37'] Exploring Operation: 37-31=6, Resulting Numbers: [36, 6] Generated Node #0,2,0: 36:[36, 6] Operation: 37-31=6 Exploring Operation: 37-36=1, Resulting Numbers: [31, 1] Generated Node #0,2,1: 36:[31, 1] Operation: 37-36=1 Exploring Operation: 36+31=67, Resulting Numbers: [37, 67] Generated Node #0,2,2: 36:[37, 67] Operation: 36+31=67 Exploring Operation: 36-31=5, Resulting Numbers: [37, 5] Generated Node #0,2,3: 36:[37, 5] Operation: 36-31=5 Moving to Node #0,2,0 Current State: 36:[36, 6], Operations: ['25+12=37', '37-31=6'] Exploring Operation: 36*6=216, Resulting Numbers: [216] 216,36 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,36 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,36 unequal: No Solution Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,36 unequal: No Solution Moving to Node #0,2,3 Current State: 36:[37, 5], Operations: ['25+12=37', '36-31=5'] Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,36 unequal: No Solution Exploring Operation: 37+5=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 37*5=185, Resulting Numbers: [185] 185,36 unequal: No Solution Moving to Node #0,2,1 Current State: 36:[31, 1], Operations: ['25+12=37', '37-36=1'] Exploring Operation: 31+1=32, Resulting Numbers: [32] 32,36 unequal: No Solution Exploring Operation: 31*1=31, Resulting Numbers: [31] 31,36 unequal: No Solution Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,36 unequal: No Solution Exploring Operation: 31-1=30, Resulting Numbers: [30] 30,36 unequal: No Solution Moving to Node #0,2,2 Current State: 36:[37, 67], Operations: ['25+12=37', '36+31=67'] Exploring Operation: 37+67=104, Resulting Numbers: [104] 104,36 unequal: No Solution Exploring Operation: 67-37=30, Resulting Numbers: [30] 30,36 unequal: No Solution Exploring Operation: 37*67=2479, Resulting Numbers: [2479] 2479,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 36:[12, 31, 11], Operations: ['36-25=11'] Exploring Operation: 31-11=20, Resulting Numbers: [12, 20] Generated Node #0,3,0: 36:[12, 20] Operation: 31-11=20 Exploring Operation: 12-11=1, Resulting Numbers: [31, 1] Generated Node #0,3,1: 36:[31, 1] Operation: 12-11=1 Exploring Operation: 31+11=42, Resulting Numbers: [12, 42] Generated Node #0,3,2: 36:[12, 42] Operation: 31+11=42 Exploring Operation: 31-12=19, Resulting Numbers: [11, 19] Generated Node #0,3,3: 36:[11, 19] Operation: 31-12=19 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 36:[12, 20], Operations: ['36-25=11', '31-11=20'] Exploring Operation: 12*20=240, Resulting Numbers: [240] 240,36 unequal: No Solution Exploring Operation: 12+20=32, Resulting Numbers: [32] 32,36 unequal: No Solution Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 36:[11, 19], Operations: ['36-25=11', '31-12=19'] Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,36 unequal: No Solution Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,36 unequal: No Solution Exploring Operation: 11*19=209, Resulting Numbers: [209] 209,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 36:[31, 1], Operations: ['36-25=11', '12-11=1'] Exploring Operation: 31+1=32, Resulting Numbers: [32] 32,36 unequal: No Solution Exploring Operation: 31-1=30, Resulting Numbers: [30] 30,36 unequal: No Solution Exploring Operation: 31*1=31, Resulting Numbers: [31] 31,36 unequal: No Solution Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 36:[12, 42], Operations: ['36-25=11', '31+11=42'] Exploring Operation: 12*42=504, Resulting Numbers: [504] 504,36 unequal: No Solution Exploring Operation: 12+42=54, Resulting Numbers: [54] 54,36 unequal: No Solution Exploring Operation: 42-12=30, Resulting Numbers: [30] 30,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 19, 82, 1, 55 ]
46
[ "19+82=101", "1*55=55", "101-55=46" ]
Current State: 46:[19, 82, 1, 55], Operations: [] Exploring Operation: 19+82=101, Resulting Numbers: [1, 55, 101] Generated Node #2: [1, 55, 101] from Operation: 19+82=101 Current State: 46:[1, 55, 101], Operations: ['19+82=101'] Exploring Operation: 1*55=55, Resulting Numbers: [101, 55] Generated Node #3: [101, 55] from Operation: 1*55=55 Current State: 46:[101, 55], Operations: ['19+82=101', '1*55=55'] Exploring Operation: 101-55=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[19, 82, 1, 55], Operations: [] Exploring Operation: 82-19=63, Resulting Numbers: [1, 55, 63] Generated Node #0,0: 46:[1, 55, 63] Operation: 82-19=63 Exploring Operation: 55-19=36, Resulting Numbers: [82, 1, 36] Generated Node #0,1: 46:[82, 1, 36] Operation: 55-19=36 Exploring Operation: 82-55=27, Resulting Numbers: [19, 1, 27] Generated Node #0,2: 46:[19, 1, 27] Operation: 82-55=27 Moving to Node #0,2 Current State: 46:[19, 1, 27], Operations: ['82-55=27'] Exploring Operation: 19+27=46, Resulting Numbers: [1, 46] Generated Node #0,2,0: 46:[1, 46] Operation: 19+27=46 Exploring Operation: 27-19=8, Resulting Numbers: [1, 8] Generated Node #0,2,1: 46:[1, 8] Operation: 27-19=8 Exploring Operation: 19+1=20, Resulting Numbers: [27, 20] Generated Node #0,2,2: 46:[27, 20] Operation: 19+1=20 Moving to Node #0,0 Current State: 46:[1, 55, 63], Operations: ['82-19=63'] Exploring Operation: 55-1=54, Resulting Numbers: [63, 54] Generated Node #0,0,0: 46:[63, 54] Operation: 55-1=54 Exploring Operation: 63-1=62, Resulting Numbers: [55, 62] Generated Node #0,0,1: 46:[55, 62] Operation: 63-1=62 Exploring Operation: 63-55=8, Resulting Numbers: [1, 8] Generated Node #0,0,2: 46:[1, 8] Operation: 63-55=8 Moving to Node #0,1 Current State: 46:[82, 1, 36], Operations: ['55-19=36'] Exploring Operation: 82-1=81, Resulting Numbers: [36, 81] Generated Node #0,1,0: 46:[36, 81] Operation: 82-1=81 Exploring Operation: 1+36=37, Resulting Numbers: [82, 37] Generated Node #0,1,1: 46:[82, 37] Operation: 1+36=37 Exploring Operation: 82-36=46, Resulting Numbers: [1, 46] Generated Node #0,1,2: 46:[1, 46] Operation: 82-36=46 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 46:[1, 46], Operations: ['55-19=36', '82-36=46'] Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[19, 82, 1, 55], Operations: [] Exploring Operation: 55-19=36, Resulting Numbers: [82, 1, 36] Generated Node #0,1: 46:[82, 1, 36] Operation: 55-19=36 Moving to Node #0,1 Current State: 46:[82, 1, 36], Operations: ['55-19=36'] Exploring Operation: 82-36=46, Resulting Numbers: [1, 46] Generated Node #0,1,2: 46:[1, 46] Operation: 82-36=46 Moving to Node #0,1,2 Current State: 46:[1, 46], Operations: ['55-19=36', '82-36=46'] Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 22, 42, 12, 24 ]
77
[ "22*42=924", "24-12=12", "924/12=77" ]
Current State: 77:[22, 42, 12, 24], Operations: [] Exploring Operation: 22*42=924, Resulting Numbers: [12, 24, 924] Generated Node #2: [12, 24, 924] from Operation: 22*42=924 Current State: 77:[12, 24, 924], Operations: ['22*42=924'] Exploring Operation: 24-12=12, Resulting Numbers: [924, 12] Generated Node #3: [924, 12] from Operation: 24-12=12 Current State: 77:[924, 12], Operations: ['22*42=924', '24-12=12'] Exploring Operation: 924/12=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[22, 42, 12, 24], Operations: [] Exploring Operation: 42-24=18, Resulting Numbers: [22, 12, 18] Generated Node #0,0: 77:[22, 12, 18] Operation: 42-24=18 Exploring Operation: 42-22=20, Resulting Numbers: [12, 24, 20] Generated Node #0,1: 77:[12, 24, 20] Operation: 42-22=20 Exploring Operation: 22+42=64, Resulting Numbers: [12, 24, 64] Generated Node #0,2: 77:[12, 24, 64] Operation: 22+42=64 Exploring Operation: 42+24=66, Resulting Numbers: [22, 12, 66] Generated Node #0,3: 77:[22, 12, 66] Operation: 42+24=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[22, 12, 18], Operations: ['42-24=18'] Exploring Operation: 22+12=34, Resulting Numbers: [18, 34] Generated Node #0,0,0: 77:[18, 34] Operation: 22+12=34 Exploring Operation: 22-18=4, Resulting Numbers: [12, 4] Generated Node #0,0,1: 77:[12, 4] Operation: 22-18=4 Exploring Operation: 22-12=10, Resulting Numbers: [18, 10] Generated Node #0,0,2: 77:[18, 10] Operation: 22-12=10 Exploring Operation: 18-12=6, Resulting Numbers: [22, 6] Generated Node #0,0,3: 77:[22, 6] Operation: 18-12=6 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 77:[12, 4], Operations: ['42-24=18', '22-18=4'] Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,77 unequal: No Solution Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 77:[18, 10], Operations: ['42-24=18', '22-12=10'] Exploring Operation: 18+10=28, Resulting Numbers: [28] 28,77 unequal: No Solution Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 18*10=180, Resulting Numbers: [180] 180,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 77:[22, 6], Operations: ['42-24=18', '18-12=6'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,77 unequal: No Solution Exploring Operation: 22*6=132, Resulting Numbers: [132] 132,77 unequal: No Solution Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[18, 34], Operations: ['42-24=18', '22+12=34'] Exploring Operation: 18*34=612, Resulting Numbers: [612] 612,77 unequal: No Solution Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,77 unequal: No Solution Exploring Operation: 18+34=52, Resulting Numbers: [52] 52,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[12, 24, 20], Operations: ['42-22=20'] Exploring Operation: 20-12=8, Resulting Numbers: [24, 8] Generated Node #0,1,0: 77:[24, 8] Operation: 20-12=8 Exploring Operation: 24-12=12, Resulting Numbers: [20, 12] Generated Node #0,1,1: 77:[20, 12] Operation: 24-12=12 Exploring Operation: 24-20=4, Resulting Numbers: [12, 4] Generated Node #0,1,2: 77:[12, 4] Operation: 24-20=4 Exploring Operation: 24/12=2, Resulting Numbers: [20, 2] Generated Node #0,1,3: 77:[20, 2] Operation: 24/12=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 77:[12, 4], Operations: ['42-22=20', '24-20=4'] Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,77 unequal: No Solution Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,77 unequal: No Solution Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 77:[20, 12], Operations: ['42-22=20', '24-12=12'] Exploring Operation: 20+12=32, Resulting Numbers: [32] 32,77 unequal: No Solution Exploring Operation: 20*12=240, Resulting Numbers: [240] 240,77 unequal: No Solution Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 77:[24, 8], Operations: ['42-22=20', '20-12=8'] Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,77 unequal: No Solution Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 24*8=192, Resulting Numbers: [192] 192,77 unequal: No Solution Exploring Operation: 24+8=32, Resulting Numbers: [32] 32,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 77:[20, 2], Operations: ['42-22=20', '24/12=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,77 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[22, 12, 66], Operations: ['42+24=66'] Exploring Operation: 66/22=3, Resulting Numbers: [12, 3] Generated Node #0,3,0: 77:[12, 3] Operation: 66/22=3 Exploring Operation: 22+66=88, Resulting Numbers: [12, 88] Generated Node #0,3,1: 77:[12, 88] Operation: 22+66=88 Exploring Operation: 22-12=10, Resulting Numbers: [66, 10] Generated Node #0,3,2: 77:[66, 10] Operation: 22-12=10 Exploring Operation: 12+66=78, Resulting Numbers: [22, 78] Generated Node #0,3,3: 77:[22, 78] Operation: 12+66=78 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 77:[12, 3], Operations: ['42+24=66', '66/22=3'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,77 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,77 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 77:[12, 88], Operations: ['42+24=66', '22+66=88'] Exploring Operation: 88-12=76, Resulting Numbers: [76] 76,77 unequal: No Solution Exploring Operation: 12*88=1056, Resulting Numbers: [1056] 1056,77 unequal: No Solution Exploring Operation: 12+88=100, Resulting Numbers: [100] 100,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 77:[66, 10], Operations: ['42+24=66', '22-12=10'] Exploring Operation: 66*10=660, Resulting Numbers: [660] 660,77 unequal: No Solution Exploring Operation: 66-10=56, Resulting Numbers: [56] 56,77 unequal: No Solution Exploring Operation: 66+10=76, Resulting Numbers: [76] 76,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 77:[22, 78], Operations: ['42+24=66', '12+66=78'] Exploring Operation: 78-22=56, Resulting Numbers: [56] 56,77 unequal: No Solution Exploring Operation: 22+78=100, Resulting Numbers: [100] 100,77 unequal: No Solution Exploring Operation: 22*78=1716, Resulting Numbers: [1716] 1716,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[12, 24, 64], Operations: ['22+42=64'] Exploring Operation: 24/12=2, Resulting Numbers: [64, 2] Generated Node #0,2,0: 77:[64, 2] Operation: 24/12=2 Exploring Operation: 24+64=88, Resulting Numbers: [12, 88] Generated Node #0,2,1: 77:[12, 88] Operation: 24+64=88 Exploring Operation: 12+64=76, Resulting Numbers: [24, 76] Generated Node #0,2,2: 77:[24, 76] Operation: 12+64=76 Exploring Operation: 24-12=12, Resulting Numbers: [64, 12] Generated Node #0,2,3: 77:[64, 12] Operation: 24-12=12 Moving to Node #0,2,1 Current State: 77:[12, 88], Operations: ['22+42=64', '24+64=88'] Exploring Operation: 12*88=1056, Resulting Numbers: [1056] 1056,77 unequal: No Solution Exploring Operation: 88-12=76, Resulting Numbers: [76] 76,77 unequal: No Solution Exploring Operation: 12+88=100, Resulting Numbers: [100] 100,77 unequal: No Solution Moving to Node #0,2,3 Current State: 77:[64, 12], Operations: ['22+42=64', '24-12=12'] Exploring Operation: 64+12=76, Resulting Numbers: [76] 76,77 unequal: No Solution Exploring Operation: 64*12=768, Resulting Numbers: [768] 768,77 unequal: No Solution Exploring Operation: 64-12=52, Resulting Numbers: [52] 52,77 unequal: No Solution Moving to Node #0,2,2 Current State: 77:[24, 76], Operations: ['22+42=64', '12+64=76'] Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,77 unequal: No Solution Exploring Operation: 24*76=1824, Resulting Numbers: [1824] 1824,77 unequal: No Solution Exploring Operation: 24+76=100, Resulting Numbers: [100] 100,77 unequal: No Solution Moving to Node #0,2,0 Current State: 77:[64, 2], Operations: ['22+42=64', '24/12=2'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,77 unequal: No Solution Exploring Operation: 64*2=128, Resulting Numbers: [128] 128,77 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,77 unequal: No Solution Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 52, 10, 5, 2 ]
54
[ "52*2=104", "10*5=50", "104-50=54" ]
Current State: 54:[52, 10, 5, 2], Operations: [] Exploring Operation: 52*2=104, Resulting Numbers: [10, 5, 104] Generated Node #2: [10, 5, 104] from Operation: 52*2=104 Current State: 54:[10, 5, 104], Operations: ['52*2=104'] Exploring Operation: 10*5=50, Resulting Numbers: [104, 50] Generated Node #3: [104, 50] from Operation: 10*5=50 Current State: 54:[104, 50], Operations: ['52*2=104', '10*5=50'] Exploring Operation: 104-50=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[52, 10, 5, 2], Operations: [] Exploring Operation: 52+2=54, Resulting Numbers: [10, 5, 54] Generated Node #0,0: 54:[10, 5, 54] Operation: 52+2=54 Moving to Node #0,0 Current State: 54:[10, 5, 54], Operations: ['52+2=54'] Exploring Operation: 10/5=2, Resulting Numbers: [54, 2] Generated Node #0,0,0: 54:[54, 2] Operation: 10/5=2 Moving to Node #0,0,0 Current State: 54:[54, 2], Operations: ['52+2=54', '10/5=2'] Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,54 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 33, 41, 10, 20 ]
89
[ "33-20=13", "10*13=130", "130-41=89" ]
Current State: 89:[33, 41, 10, 20], Operations: [] Exploring Operation: 33-20=13, Resulting Numbers: [41, 10, 13] Generated Node #2: [41, 10, 13] from Operation: 33-20=13 Current State: 89:[41, 10, 13], Operations: ['33-20=13'] Exploring Operation: 10*13=130, Resulting Numbers: [41, 130] Generated Node #3: [41, 130] from Operation: 10*13=130 Current State: 89:[41, 130], Operations: ['33-20=13', '10*13=130'] Exploring Operation: 130-41=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[33, 41, 10, 20], Operations: [] Exploring Operation: 33+10=43, Resulting Numbers: [41, 20, 43] Generated Node #0,0: 89:[41, 20, 43] Operation: 33+10=43 Exploring Operation: 33+41=74, Resulting Numbers: [10, 20, 74] Generated Node #0,1: 89:[10, 20, 74] Operation: 33+41=74 Exploring Operation: 33+20=53, Resulting Numbers: [41, 10, 53] Generated Node #0,2: 89:[41, 10, 53] Operation: 33+20=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[41, 20, 43], Operations: ['33+10=43'] Exploring Operation: 20+43=63, Resulting Numbers: [41, 63] Generated Node #0,0,0: 89:[41, 63] Operation: 20+43=63 Exploring Operation: 41+20=61, Resulting Numbers: [43, 61] Generated Node #0,0,1: 89:[43, 61] Operation: 41+20=61 Exploring Operation: 41+43=84, Resulting Numbers: [20, 84] Generated Node #0,0,2: 89:[20, 84] Operation: 41+43=84 Moving to Node #0,0,0 Current State: 89:[41, 63], Operations: ['33+10=43', '20+43=63'] Exploring Operation: 41+63=104, Resulting Numbers: [104] 104,89 unequal: No Solution Exploring Operation: 41*63=2583, Resulting Numbers: [2583] 2583,89 unequal: No Solution Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[43, 61], Operations: ['33+10=43', '41+20=61'] Exploring Operation: 43+61=104, Resulting Numbers: [104] 104,89 unequal: No Solution Exploring Operation: 43*61=2623, Resulting Numbers: [2623] 2623,89 unequal: No Solution Exploring Operation: 61-43=18, Resulting Numbers: [18] 18,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[20, 84], Operations: ['33+10=43', '41+43=84'] Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,89 unequal: No Solution Exploring Operation: 20*84=1680, Resulting Numbers: [1680] 1680,89 unequal: No Solution Exploring Operation: 20+84=104, Resulting Numbers: [104] 104,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[10, 20, 74], Operations: ['33+41=74'] Exploring Operation: 10+74=84, Resulting Numbers: [20, 84] Generated Node #0,1,0: 89:[20, 84] Operation: 10+74=84 Exploring Operation: 10+20=30, Resulting Numbers: [74, 30] Generated Node #0,1,1: 89:[74, 30] Operation: 10+20=30 Exploring Operation: 20+74=94, Resulting Numbers: [10, 94] Generated Node #0,1,2: 89:[10, 94] Operation: 20+74=94 Moving to Node #0,1,0 Current State: 89:[20, 84], Operations: ['33+41=74', '10+74=84'] Exploring Operation: 20*84=1680, Resulting Numbers: [1680] 1680,89 unequal: No Solution Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,89 unequal: No Solution Exploring Operation: 20+84=104, Resulting Numbers: [104] 104,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[74, 30], Operations: ['33+41=74', '10+20=30'] Exploring Operation: 74+30=104, Resulting Numbers: [104] 104,89 unequal: No Solution Exploring Operation: 74*30=2220, Resulting Numbers: [2220] 2220,89 unequal: No Solution Exploring Operation: 74-30=44, Resulting Numbers: [44] 44,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[10, 94], Operations: ['33+41=74', '20+74=94'] Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,89 unequal: No Solution Exploring Operation: 10*94=940, Resulting Numbers: [940] 940,89 unequal: No Solution Exploring Operation: 10+94=104, Resulting Numbers: [104] 104,89 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 Current State: 89:[41, 10, 53], Operations: ['33+20=53'] Exploring Operation: 41+10=51, Resulting Numbers: [53, 51] Generated Node #0,2,0: 89:[53, 51] Operation: 41+10=51 Exploring Operation: 10+53=63, Resulting Numbers: [41, 63] Generated Node #0,2,1: 89:[41, 63] Operation: 10+53=63 Exploring Operation: 41+53=94, Resulting Numbers: [10, 94] Generated Node #0,2,2: 89:[10, 94] Operation: 41+53=94 Moving to Node #0,2,0 Current State: 89:[53, 51], Operations: ['33+20=53', '41+10=51'] Exploring Operation: 53*51=2703, Resulting Numbers: [2703] 2703,89 unequal: No Solution Exploring Operation: 53-51=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 53+51=104, Resulting Numbers: [104] 104,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[41, 63], Operations: ['33+20=53', '10+53=63'] Exploring Operation: 41*63=2583, Resulting Numbers: [2583] 2583,89 unequal: No Solution Exploring Operation: 41+63=104, Resulting Numbers: [104] 104,89 unequal: No Solution Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[10, 94], Operations: ['33+20=53', '41+53=94'] Exploring Operation: 10+94=104, Resulting Numbers: [104] 104,89 unequal: No Solution Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,89 unequal: No Solution Exploring Operation: 10*94=940, Resulting Numbers: [940] 940,89 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
[ 11, 81, 71, 49 ]
83
[ "71-49=22", "22/11=2", "81+2=83" ]
Current State: 83:[11, 81, 71, 49], Operations: [] Exploring Operation: 71-49=22, Resulting Numbers: [11, 81, 22] Generated Node #2: [11, 81, 22] from Operation: 71-49=22 Current State: 83:[11, 81, 22], Operations: ['71-49=22'] Exploring Operation: 22/11=2, Resulting Numbers: [81, 2] Generated Node #3: [81, 2] from Operation: 22/11=2 Current State: 83:[81, 2], Operations: ['71-49=22', '22/11=2'] Exploring Operation: 81+2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[11, 81, 71, 49], Operations: [] Exploring Operation: 11+71=82, Resulting Numbers: [81, 49, 82] Generated Node #0,0: 83:[81, 49, 82] Operation: 11+71=82 Moving to Node #0,0 Current State: 83:[81, 49, 82], Operations: ['11+71=82'] Exploring Operation: 81+49=130, Resulting Numbers: [82, 130] Generated Node #0,0,0: 83:[82, 130] Operation: 81+49=130 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[82, 130], Operations: ['11+71=82', '81+49=130'] Exploring Operation: 130-82=48, Resulting Numbers: [48] 48,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 82, 46, 13, 85 ]
30
[ "82+46=128", "13+85=98", "128-98=30" ]
Current State: 30:[82, 46, 13, 85], Operations: [] Exploring Operation: 82+46=128, Resulting Numbers: [13, 85, 128] Generated Node #2: [13, 85, 128] from Operation: 82+46=128 Current State: 30:[13, 85, 128], Operations: ['82+46=128'] Exploring Operation: 13+85=98, Resulting Numbers: [128, 98] Generated Node #3: [128, 98] from Operation: 13+85=98 Current State: 30:[128, 98], Operations: ['82+46=128', '13+85=98'] Exploring Operation: 128-98=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[82, 46, 13, 85], Operations: [] Exploring Operation: 85-82=3, Resulting Numbers: [46, 13, 3] Generated Node #0,0: 30:[46, 13, 3] Operation: 85-82=3 Exploring Operation: 82-46=36, Resulting Numbers: [13, 85, 36] Generated Node #0,1: 30:[13, 85, 36] Operation: 82-46=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[46, 13, 3], Operations: ['85-82=3'] Exploring Operation: 46-3=43, Resulting Numbers: [13, 43] Generated Node #0,0,0: 30:[13, 43] Operation: 46-3=43 Exploring Operation: 46-13=33, Resulting Numbers: [3, 33] Generated Node #0,0,1: 30:[3, 33] Operation: 46-13=33 Moving to Node #0,0,1 Current State: 30:[3, 33], Operations: ['85-82=3', '46-13=33'] Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,30 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[82, 46, 13, 85], Operations: [] Exploring Operation: 85-82=3, Resulting Numbers: [46, 13, 3] Generated Node #0,0: 30:[46, 13, 3] Operation: 85-82=3 Moving to Node #0,0 Current State: 30:[46, 13, 3], Operations: ['85-82=3'] Exploring Operation: 46-13=33, Resulting Numbers: [3, 33] Generated Node #0,0,1: 30:[3, 33] Operation: 46-13=33 Moving to Node #0,0,1 Current State: 30:[3, 33], Operations: ['85-82=3', '46-13=33'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 3, 14, 40, 35 ]
27
[ "40-14=26", "35-26=9", "3*9=27" ]
Current State: 27:[3, 14, 40, 35], Operations: [] Exploring Operation: 40-14=26, Resulting Numbers: [3, 35, 26] Generated Node #2: [3, 35, 26] from Operation: 40-14=26 Current State: 27:[3, 35, 26], Operations: ['40-14=26'] Exploring Operation: 35-26=9, Resulting Numbers: [3, 9] Generated Node #3: [3, 9] from Operation: 35-26=9 Current State: 27:[3, 9], Operations: ['40-14=26', '35-26=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[3, 14, 40, 35], Operations: [] Exploring Operation: 40-14=26, Resulting Numbers: [3, 35, 26] Generated Node #0,0: 27:[3, 35, 26] Operation: 40-14=26 Exploring Operation: 40-3=37, Resulting Numbers: [14, 35, 37] Generated Node #0,1: 27:[14, 35, 37] Operation: 40-3=37 Exploring Operation: 35-14=21, Resulting Numbers: [3, 40, 21] Generated Node #0,2: 27:[3, 40, 21] Operation: 35-14=21 Exploring Operation: 14-3=11, Resulting Numbers: [40, 35, 11] Generated Node #0,3: 27:[40, 35, 11] Operation: 14-3=11 Exploring Operation: 40-35=5, Resulting Numbers: [3, 14, 5] Generated Node #0,4: 27:[3, 14, 5] Operation: 40-35=5 Start Sub Search at level 1: Moving to Node #0,4 Current State: 27:[3, 14, 5], Operations: ['40-35=5'] Exploring Operation: 3+5=8, Resulting Numbers: [14, 8] Generated Node #0,4,0: 27:[14, 8] Operation: 3+5=8 Exploring Operation: 14-3=11, Resulting Numbers: [5, 11] Generated Node #0,4,1: 27:[5, 11] Operation: 14-3=11 Exploring Operation: 14+5=19, Resulting Numbers: [3, 19] Generated Node #0,4,2: 27:[3, 19] Operation: 14+5=19 Exploring Operation: 14-5=9, Resulting Numbers: [3, 9] Generated Node #0,4,3: 27:[3, 9] Operation: 14-5=9 Exploring Operation: 5-3=2, Resulting Numbers: [14, 2] Generated Node #0,4,4: 27:[14, 2] Operation: 5-3=2 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 27:[3, 9], Operations: ['40-35=5', '14-5=9'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,27 unequal: No Solution Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[3, 14, 40, 35], Operations: [] Exploring Operation: 40-35=5, Resulting Numbers: [3, 14, 5] Generated Node #0,4: 27:[3, 14, 5] Operation: 40-35=5 Moving to Node #0,4 Current State: 27:[3, 14, 5], Operations: ['40-35=5'] Exploring Operation: 14-5=9, Resulting Numbers: [3, 9] Generated Node #0,4,3: 27:[3, 9] Operation: 14-5=9 Moving to Node #0,4,3 Current State: 27:[3, 9], Operations: ['40-35=5', '14-5=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 18, 5, 15, 57 ]
24
[ "18-15=3", "57/3=19", "5+19=24" ]
Current State: 24:[18, 5, 15, 57], Operations: [] Exploring Operation: 18-15=3, Resulting Numbers: [5, 57, 3] Generated Node #2: [5, 57, 3] from Operation: 18-15=3 Current State: 24:[5, 57, 3], Operations: ['18-15=3'] Exploring Operation: 57/3=19, Resulting Numbers: [5, 19] Generated Node #3: [5, 19] from Operation: 57/3=19 Current State: 24:[5, 19], Operations: ['18-15=3', '57/3=19'] Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[18, 5, 15, 57], Operations: [] Exploring Operation: 57-15=42, Resulting Numbers: [18, 5, 42] Generated Node #0,0: 24:[18, 5, 42] Operation: 57-15=42 Exploring Operation: 57-18=39, Resulting Numbers: [5, 15, 39] Generated Node #0,1: 24:[5, 15, 39] Operation: 57-18=39 Exploring Operation: 18-15=3, Resulting Numbers: [5, 57, 3] Generated Node #0,2: 24:[5, 57, 3] Operation: 18-15=3 Moving to Node #0,1 Current State: 24:[5, 15, 39], Operations: ['57-18=39'] Exploring Operation: 39-5=34, Resulting Numbers: [15, 34] Generated Node #0,1,0: 24:[15, 34] Operation: 39-5=34 Exploring Operation: 15/5=3, Resulting Numbers: [39, 3] Generated Node #0,1,1: 24:[39, 3] Operation: 15/5=3 Exploring Operation: 39-15=24, Resulting Numbers: [5, 24] Generated Node #0,1,2: 24:[5, 24] Operation: 39-15=24 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[5, 24], Operations: ['57-18=39', '39-15=24'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,24 unequal: No Solution Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,24 unequal: No Solution Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,24 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 #0,1,0 Current State: 24:[15, 34], Operations: ['57-18=39', '39-5=34'] Exploring Operation: 15+34=49, Resulting Numbers: [49] 49,24 unequal: No Solution Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,24 unequal: No Solution Exploring Operation: 15*34=510, Resulting Numbers: [510] 510,24 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 #0,1,1 Current State: 24:[39, 3], Operations: ['57-18=39', '15/5=3'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,24 unequal: No Solution Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,24 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,24 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: 24:[18, 5, 42], Operations: ['57-15=42'] Exploring Operation: 18-5=13, Resulting Numbers: [42, 13] Generated Node #0,0,0: 24:[42, 13] Operation: 18-5=13 Exploring Operation: 42-18=24, Resulting Numbers: [5, 24] Generated Node #0,0,1: 24:[5, 24] Operation: 42-18=24 Exploring Operation: 18+5=23, Resulting Numbers: [42, 23] Generated Node #0,0,2: 24:[42, 23] Operation: 18+5=23 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[5, 24], Operations: ['57-15=42', '42-18=24'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,24 unequal: No Solution Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,24 unequal: No Solution Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,24 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 #0,0,0 Current State: 24:[42, 13], Operations: ['57-15=42', '18-5=13'] Exploring Operation: 42*13=546, Resulting Numbers: [546] 546,24 unequal: No Solution Exploring Operation: 42-13=29, Resulting Numbers: [29] 29,24 unequal: No Solution Exploring Operation: 42+13=55, Resulting Numbers: [55] 55,24 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 #0,0,2 Current State: 24:[42, 23], Operations: ['57-15=42', '18+5=23'] Exploring Operation: 42+23=65, Resulting Numbers: [65] 65,24 unequal: No Solution Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,24 unequal: No Solution Exploring Operation: 42*23=966, Resulting Numbers: [966] 966,24 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: 24:[5, 57, 3], Operations: ['18-15=3'] Exploring Operation: 57-5=52, Resulting Numbers: [3, 52] Generated Node #0,2,0: 24:[3, 52] Operation: 57-5=52 Exploring Operation: 57-3=54, Resulting Numbers: [5, 54] Generated Node #0,2,1: 24:[5, 54] Operation: 57-3=54 Exploring Operation: 57/3=19, Resulting Numbers: [5, 19] Generated Node #0,2,2: 24:[5, 19] Operation: 57/3=19 Moving to Node #0,2,2 Current State: 24:[5, 19], Operations: ['18-15=3', '57/3=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,24 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[18, 5, 15, 57], Operations: [] Exploring Operation: 18-15=3, Resulting Numbers: [5, 57, 3] Generated Node #0,2: 24:[5, 57, 3] Operation: 18-15=3 Moving to Node #0,2 Current State: 24:[5, 57, 3], Operations: ['18-15=3'] Exploring Operation: 57/3=19, Resulting Numbers: [5, 19] Generated Node #0,2,2: 24:[5, 19] Operation: 57/3=19 Moving to Node #0,2,2 Current State: 24:[5, 19], Operations: ['18-15=3', '57/3=19'] Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
0.967882
hs_3
mult_heuristic
[ 30, 56, 82, 71 ]
54
[ "71-30=41", "82/41=2", "56-2=54" ]
Current State: 54:[30, 56, 82, 71], Operations: [] Exploring Operation: 71-30=41, Resulting Numbers: [56, 82, 41] Generated Node #2: [56, 82, 41] from Operation: 71-30=41 Current State: 54:[56, 82, 41], Operations: ['71-30=41'] Exploring Operation: 82/41=2, Resulting Numbers: [56, 2] Generated Node #3: [56, 2] from Operation: 82/41=2 Current State: 54:[56, 2], Operations: ['71-30=41', '82/41=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[30, 56, 82, 71], Operations: [] Exploring Operation: 82-30=52, Resulting Numbers: [56, 71, 52] Generated Node #0,0: 54:[56, 71, 52] Operation: 82-30=52 Exploring Operation: 82-71=11, Resulting Numbers: [30, 56, 11] Generated Node #0,1: 54:[30, 56, 11] Operation: 82-71=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[30, 56, 11], Operations: ['82-71=11'] Exploring Operation: 56-30=26, Resulting Numbers: [11, 26] Generated Node #0,1,0: 54:[11, 26] Operation: 56-30=26 Exploring Operation: 30-11=19, Resulting Numbers: [56, 19] Generated Node #0,1,1: 54:[56, 19] Operation: 30-11=19 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 54:[11, 26], Operations: ['82-71=11', '56-30=26'] Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,54 unequal: No Solution Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 54:[56, 19], Operations: ['82-71=11', '30-11=19'] Exploring Operation: 56-19=37, Resulting Numbers: [37] 37,54 unequal: No Solution Exploring Operation: 56+19=75, Resulting Numbers: [75] 75,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[56, 71, 52], Operations: ['82-30=52'] Exploring Operation: 71-56=15, Resulting Numbers: [52, 15] Generated Node #0,0,0: 54:[52, 15] Operation: 71-56=15 Exploring Operation: 71-52=19, Resulting Numbers: [56, 19] Generated Node #0,0,1: 54:[56, 19] Operation: 71-52=19 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 54:[56, 19], Operations: ['82-30=52', '71-52=19'] Exploring Operation: 56-19=37, Resulting Numbers: [37] 37,54 unequal: No Solution Exploring Operation: 56+19=75, Resulting Numbers: [75] 75,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[52, 15], Operations: ['82-30=52', '71-56=15'] Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,54 unequal: No Solution Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 2, 13, 55, 34 ]
50
[ "55-13=42", "2*42=84", "84-34=50" ]
Current State: 50:[2, 13, 55, 34], Operations: [] Exploring Operation: 55-13=42, Resulting Numbers: [2, 34, 42] Generated Node #2: [2, 34, 42] from Operation: 55-13=42 Current State: 50:[2, 34, 42], Operations: ['55-13=42'] Exploring Operation: 2*42=84, Resulting Numbers: [34, 84] Generated Node #3: [34, 84] from Operation: 2*42=84 Current State: 50:[34, 84], Operations: ['55-13=42', '2*42=84'] Exploring Operation: 84-34=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[2, 13, 55, 34], Operations: [] Exploring Operation: 55-34=21, Resulting Numbers: [2, 13, 21] Generated Node #0,0: 50:[2, 13, 21] Operation: 55-34=21 Exploring Operation: 13+34=47, Resulting Numbers: [2, 55, 47] Generated Node #0,1: 50:[2, 55, 47] Operation: 13+34=47 Exploring Operation: 2*13=26, Resulting Numbers: [55, 34, 26] Generated Node #0,2: 50:[55, 34, 26] Operation: 2*13=26 Exploring Operation: 34-13=21, Resulting Numbers: [2, 55, 21] Generated Node #0,3: 50:[2, 55, 21] Operation: 34-13=21 Exploring Operation: 13-2=11, Resulting Numbers: [55, 34, 11] Generated Node #0,4: 50:[55, 34, 11] Operation: 13-2=11 Moving to Node #0,0 Current State: 50:[2, 13, 21], Operations: ['55-34=21'] Exploring Operation: 21-13=8, Resulting Numbers: [2, 8] Generated Node #0,0,0: 50:[2, 8] Operation: 21-13=8 Exploring Operation: 2*13=26, Resulting Numbers: [21, 26] Generated Node #0,0,1: 50:[21, 26] Operation: 2*13=26 Exploring Operation: 13-2=11, Resulting Numbers: [21, 11] Generated Node #0,0,2: 50:[21, 11] Operation: 13-2=11 Exploring Operation: 2+13=15, Resulting Numbers: [21, 15] Generated Node #0,0,3: 50:[21, 15] Operation: 2+13=15 Exploring Operation: 2+21=23, Resulting Numbers: [13, 23] Generated Node #0,0,4: 50:[13, 23] Operation: 2+21=23 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[2, 8], Operations: ['55-34=21', '21-13=8'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,50 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 50:[21, 26], Operations: ['55-34=21', '2*13=26'] Exploring Operation: 21+26=47, Resulting Numbers: [47] 47,50 unequal: No Solution Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,50 unequal: No Solution Exploring Operation: 21*26=546, Resulting Numbers: [546] 546,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 50:[21, 11], Operations: ['55-34=21', '13-2=11'] Exploring Operation: 21*11=231, Resulting Numbers: [231] 231,50 unequal: No Solution Exploring Operation: 21+11=32, Resulting Numbers: [32] 32,50 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 50:[13, 23], Operations: ['55-34=21', '2+21=23'] Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 13+23=36, Resulting Numbers: [36] 36,50 unequal: No Solution Exploring Operation: 13*23=299, Resulting Numbers: [299] 299,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 50:[21, 15], Operations: ['55-34=21', '2+13=15'] Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,50 unequal: No Solution Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,50 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,50 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: 50:[2, 55, 47], Operations: ['13+34=47'] Exploring Operation: 2+55=57, Resulting Numbers: [47, 57] Generated Node #0,1,0: 50:[47, 57] Operation: 2+55=57 Exploring Operation: 47-2=45, Resulting Numbers: [55, 45] Generated Node #0,1,1: 50:[55, 45] Operation: 47-2=45 Exploring Operation: 2+47=49, Resulting Numbers: [55, 49] Generated Node #0,1,2: 50:[55, 49] Operation: 2+47=49 Exploring Operation: 55-2=53, Resulting Numbers: [47, 53] Generated Node #0,1,3: 50:[47, 53] Operation: 55-2=53 Exploring Operation: 55-47=8, Resulting Numbers: [2, 8] Generated Node #0,1,4: 50:[2, 8] Operation: 55-47=8 Moving to Node #0,3 Current State: 50:[2, 55, 21], Operations: ['34-13=21'] Exploring Operation: 55-21=34, Resulting Numbers: [2, 34] Generated Node #0,3,0: 50:[2, 34] Operation: 55-21=34 Exploring Operation: 2+55=57, Resulting Numbers: [21, 57] Generated Node #0,3,1: 50:[21, 57] Operation: 2+55=57 Exploring Operation: 55-2=53, Resulting Numbers: [21, 53] Generated Node #0,3,2: 50:[21, 53] Operation: 55-2=53 Exploring Operation: 2+21=23, Resulting Numbers: [55, 23] Generated Node #0,3,3: 50:[55, 23] Operation: 2+21=23 Exploring Operation: 21-2=19, Resulting Numbers: [55, 19] Generated Node #0,3,4: 50:[55, 19] Operation: 21-2=19 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 50:[21, 53], Operations: ['34-13=21', '55-2=53'] Exploring Operation: 21+53=74, Resulting Numbers: [74] 74,50 unequal: No Solution Exploring Operation: 53-21=32, Resulting Numbers: [32] 32,50 unequal: No Solution Exploring Operation: 21*53=1113, Resulting Numbers: [1113] 1113,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 50:[55, 23], Operations: ['34-13=21', '2+21=23'] Exploring Operation: 55-23=32, Resulting Numbers: [32] 32,50 unequal: No Solution Exploring Operation: 55*23=1265, Resulting Numbers: [1265] 1265,50 unequal: No Solution Exploring Operation: 55+23=78, Resulting Numbers: [78] 78,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 50:[2, 34], Operations: ['34-13=21', '55-21=34'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,50 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,50 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 50:[21, 57], Operations: ['34-13=21', '2+55=57'] Exploring Operation: 21+57=78, Resulting Numbers: [78] 78,50 unequal: No Solution Exploring Operation: 21*57=1197, Resulting Numbers: [1197] 1197,50 unequal: No Solution Exploring Operation: 57-21=36, Resulting Numbers: [36] 36,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 50:[55, 19], Operations: ['34-13=21', '21-2=19'] Exploring Operation: 55*19=1045, Resulting Numbers: [1045] 1045,50 unequal: No Solution Exploring Operation: 55-19=36, Resulting Numbers: [36] 36,50 unequal: No Solution Exploring Operation: 55+19=74, Resulting Numbers: [74] 74,50 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: 50:[55, 34, 26], Operations: ['2*13=26'] Exploring Operation: 55-34=21, Resulting Numbers: [26, 21] Generated Node #0,2,0: 50:[26, 21] Operation: 55-34=21 Exploring Operation: 55+34=89, Resulting Numbers: [26, 89] Generated Node #0,2,1: 50:[26, 89] Operation: 55+34=89 Exploring Operation: 34-26=8, Resulting Numbers: [55, 8] Generated Node #0,2,2: 50:[55, 8] Operation: 34-26=8 Exploring Operation: 55-26=29, Resulting Numbers: [34, 29] Generated Node #0,2,3: 50:[34, 29] Operation: 55-26=29 Exploring Operation: 34+26=60, Resulting Numbers: [55, 60] Generated Node #0,2,4: 50:[55, 60] Operation: 34+26=60 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 50:[26, 21], Operations: ['2*13=26', '55-34=21'] Exploring Operation: 26*21=546, Resulting Numbers: [546] 546,50 unequal: No Solution Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,50 unequal: No Solution Exploring Operation: 26+21=47, Resulting Numbers: [47] 47,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 50:[55, 8], Operations: ['2*13=26', '34-26=8'] Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,50 unequal: No Solution Exploring Operation: 55+8=63, Resulting Numbers: [63] 63,50 unequal: No Solution Exploring Operation: 55*8=440, Resulting Numbers: [440] 440,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 50:[34, 29], Operations: ['2*13=26', '55-26=29'] Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,50 unequal: No Solution Exploring Operation: 34*29=986, Resulting Numbers: [986] 986,50 unequal: No Solution Exploring Operation: 34+29=63, Resulting Numbers: [63] 63,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 50:[55, 60], Operations: ['2*13=26', '34+26=60'] Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,50 unequal: No Solution Exploring Operation: 55+60=115, Resulting Numbers: [115] 115,50 unequal: No Solution Exploring Operation: 55*60=3300, Resulting Numbers: [3300] 3300,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 50:[26, 89], Operations: ['2*13=26', '55+34=89'] Exploring Operation: 26+89=115, Resulting Numbers: [115] 115,50 unequal: No Solution Exploring Operation: 26*89=2314, Resulting Numbers: [2314] 2314,50 unequal: No Solution Exploring Operation: 89-26=63, Resulting Numbers: [63] 63,50 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: 50:[55, 34, 11], Operations: ['13-2=11'] Exploring Operation: 55/11=5, Resulting Numbers: [34, 5] Generated Node #0,4,0: 50:[34, 5] Operation: 55/11=5 Exploring Operation: 55-11=44, Resulting Numbers: [34, 44] Generated Node #0,4,1: 50:[34, 44] Operation: 55-11=44 Exploring Operation: 55-34=21, Resulting Numbers: [11, 21] Generated Node #0,4,2: 50:[11, 21] Operation: 55-34=21 Exploring Operation: 34+11=45, Resulting Numbers: [55, 45] Generated Node #0,4,3: 50:[55, 45] Operation: 34+11=45 Exploring Operation: 34-11=23, Resulting Numbers: [55, 23] Generated Node #0,4,4: 50:[55, 23] Operation: 34-11=23 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 50:[11, 21], Operations: ['13-2=11', '55-34=21'] Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 11*21=231, Resulting Numbers: [231] 231,50 unequal: No Solution Exploring Operation: 11+21=32, Resulting Numbers: [32] 32,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 50:[55, 23], Operations: ['13-2=11', '34-11=23'] Exploring Operation: 55-23=32, Resulting Numbers: [32] 32,50 unequal: No Solution Exploring Operation: 55*23=1265, Resulting Numbers: [1265] 1265,50 unequal: No Solution Exploring Operation: 55+23=78, Resulting Numbers: [78] 78,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 50:[34, 5], Operations: ['13-2=11', '55/11=5'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,50 unequal: No Solution Exploring Operation: 34+5=39, Resulting Numbers: [39] 39,50 unequal: No Solution Exploring Operation: 34*5=170, Resulting Numbers: [170] 170,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 50:[55, 45], Operations: ['13-2=11', '34+11=45'] Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,50 unequal: No Solution Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,50 unequal: No Solution Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 50:[34, 44], Operations: ['13-2=11', '55-11=44'] Exploring Operation: 44-34=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 34*44=1496, Resulting Numbers: [1496] 1496,50 unequal: No Solution Exploring Operation: 34+44=78, Resulting Numbers: [78] 78,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,4 Current State: 50:[2, 8], Operations: ['13+34=47', '55-47=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,50 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,50 unequal: No Solution Moving to Node #0,1,3 Current State: 50:[47, 53], Operations: ['13+34=47', '55-2=53'] Exploring Operation: 47+53=100, Resulting Numbers: [100] 100,50 unequal: No Solution Exploring Operation: 53-47=6, Resulting Numbers: [6] 6,50 unequal: No Solution Exploring Operation: 47*53=2491, Resulting Numbers: [2491] 2491,50 unequal: No Solution Moving to Node #0,1,2 Current State: 50:[55, 49], Operations: ['13+34=47', '2+47=49'] Exploring Operation: 55-49=6, Resulting Numbers: [6] 6,50 unequal: No Solution Exploring Operation: 55*49=2695, Resulting Numbers: [2695] 2695,50 unequal: No Solution Exploring Operation: 55+49=104, Resulting Numbers: [104] 104,50 unequal: No Solution Moving to Node #0,1,0 Current State: 50:[47, 57], Operations: ['13+34=47', '2+55=57'] Exploring Operation: 47*57=2679, Resulting Numbers: [2679] 2679,50 unequal: No Solution Exploring Operation: 47+57=104, Resulting Numbers: [104] 104,50 unequal: No Solution Exploring Operation: 57-47=10, Resulting Numbers: [10] 10,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[55, 45], Operations: ['13+34=47', '47-2=45'] Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,50 unequal: No Solution Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,50 unequal: No Solution Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,50 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 65, 51, 74, 75 ]
33
[ "65+51=116", "74+75=149", "149-116=33" ]
Current State: 33:[65, 51, 74, 75], Operations: [] Exploring Operation: 65+51=116, Resulting Numbers: [74, 75, 116] Generated Node #2: [74, 75, 116] from Operation: 65+51=116 Current State: 33:[74, 75, 116], Operations: ['65+51=116'] Exploring Operation: 74+75=149, Resulting Numbers: [116, 149] Generated Node #3: [116, 149] from Operation: 74+75=149 Current State: 33:[116, 149], Operations: ['65+51=116', '74+75=149'] Exploring Operation: 149-116=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[65, 51, 74, 75], Operations: [] Exploring Operation: 75-74=1, Resulting Numbers: [65, 51, 1] Generated Node #0,0: 33:[65, 51, 1] Operation: 75-74=1 Moving to Node #0,0 Current State: 33:[65, 51, 1], Operations: ['75-74=1'] Exploring Operation: 65-51=14, Resulting Numbers: [1, 14] Generated Node #0,0,0: 33:[1, 14] Operation: 65-51=14 Moving to Node #0,0,0 Current State: 33:[1, 14], Operations: ['75-74=1', '65-51=14'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,33 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 69, 72, 48, 57 ]
68
[ "69-57=12", "48/12=4", "72-4=68" ]
Current State: 68:[69, 72, 48, 57], Operations: [] Exploring Operation: 69-57=12, Resulting Numbers: [72, 48, 12] Generated Node #2: [72, 48, 12] from Operation: 69-57=12 Current State: 68:[72, 48, 12], Operations: ['69-57=12'] Exploring Operation: 48/12=4, Resulting Numbers: [72, 4] Generated Node #3: [72, 4] from Operation: 48/12=4 Current State: 68:[72, 4], Operations: ['69-57=12', '48/12=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[69, 72, 48, 57], Operations: [] Exploring Operation: 69-57=12, Resulting Numbers: [72, 48, 12] Generated Node #0,0: 68:[72, 48, 12] Operation: 69-57=12 Exploring Operation: 57-48=9, Resulting Numbers: [69, 72, 9] Generated Node #0,1: 68:[69, 72, 9] Operation: 57-48=9 Exploring Operation: 72-48=24, Resulting Numbers: [69, 57, 24] Generated Node #0,2: 68:[69, 57, 24] Operation: 72-48=24 Exploring Operation: 69-48=21, Resulting Numbers: [72, 57, 21] Generated Node #0,3: 68:[72, 57, 21] Operation: 69-48=21 Exploring Operation: 72-57=15, Resulting Numbers: [69, 48, 15] Generated Node #0,4: 68:[69, 48, 15] Operation: 72-57=15 Moving to Node #0,1 Current State: 68:[69, 72, 9], Operations: ['57-48=9'] Exploring Operation: 72-9=63, Resulting Numbers: [69, 63] Generated Node #0,1,0: 68:[69, 63] Operation: 72-9=63 Exploring Operation: 69+9=78, Resulting Numbers: [72, 78] Generated Node #0,1,1: 68:[72, 78] Operation: 69+9=78 Exploring Operation: 72-69=3, Resulting Numbers: [9, 3] Generated Node #0,1,2: 68:[9, 3] Operation: 72-69=3 Exploring Operation: 72/9=8, Resulting Numbers: [69, 8] Generated Node #0,1,3: 68:[69, 8] Operation: 72/9=8 Exploring Operation: 69-9=60, Resulting Numbers: [72, 60] Generated Node #0,1,4: 68:[72, 60] Operation: 69-9=60 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 68:[69, 8], Operations: ['57-48=9', '72/9=8'] Exploring Operation: 69*8=552, Resulting Numbers: [552] 552,68 unequal: No Solution Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 68:[69, 63], Operations: ['57-48=9', '72-9=63'] Exploring Operation: 69*63=4347, Resulting Numbers: [4347] 4347,68 unequal: No Solution Exploring Operation: 69-63=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 69+63=132, Resulting Numbers: [132] 132,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 68:[9, 3], Operations: ['57-48=9', '72-69=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,68 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,68 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 68:[72, 60], Operations: ['57-48=9', '69-9=60'] Exploring Operation: 72*60=4320, Resulting Numbers: [4320] 4320,68 unequal: No Solution Exploring Operation: 72+60=132, Resulting Numbers: [132] 132,68 unequal: No Solution Exploring Operation: 72-60=12, Resulting Numbers: [12] 12,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 68:[72, 78], Operations: ['57-48=9', '69+9=78'] Exploring Operation: 78-72=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 72*78=5616, Resulting Numbers: [5616] 5616,68 unequal: No Solution Exploring Operation: 72+78=150, Resulting Numbers: [150] 150,68 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: 68:[69, 48, 15], Operations: ['72-57=15'] Exploring Operation: 69-48=21, Resulting Numbers: [15, 21] Generated Node #0,4,0: 68:[15, 21] Operation: 69-48=21 Exploring Operation: 48+15=63, Resulting Numbers: [69, 63] Generated Node #0,4,1: 68:[69, 63] Operation: 48+15=63 Exploring Operation: 69+15=84, Resulting Numbers: [48, 84] Generated Node #0,4,2: 68:[48, 84] Operation: 69+15=84 Exploring Operation: 69-15=54, Resulting Numbers: [48, 54] Generated Node #0,4,3: 68:[48, 54] Operation: 69-15=54 Exploring Operation: 48-15=33, Resulting Numbers: [69, 33] Generated Node #0,4,4: 68:[69, 33] Operation: 48-15=33 Moving to Node #0,2 Current State: 68:[69, 57, 24], Operations: ['72-48=24'] Exploring Operation: 57-24=33, Resulting Numbers: [69, 33] Generated Node #0,2,0: 68:[69, 33] Operation: 57-24=33 Exploring Operation: 69+24=93, Resulting Numbers: [57, 93] Generated Node #0,2,1: 68:[57, 93] Operation: 69+24=93 Exploring Operation: 69-57=12, Resulting Numbers: [24, 12] Generated Node #0,2,2: 68:[24, 12] Operation: 69-57=12 Exploring Operation: 57+24=81, Resulting Numbers: [69, 81] Generated Node #0,2,3: 68:[69, 81] Operation: 57+24=81 Exploring Operation: 69-24=45, Resulting Numbers: [57, 45] Generated Node #0,2,4: 68:[57, 45] Operation: 69-24=45 Moving to Node #0,3 Current State: 68:[72, 57, 21], Operations: ['69-48=21'] Exploring Operation: 72+21=93, Resulting Numbers: [57, 93] Generated Node #0,3,0: 68:[57, 93] Operation: 72+21=93 Exploring Operation: 72-57=15, Resulting Numbers: [21, 15] Generated Node #0,3,1: 68:[21, 15] Operation: 72-57=15 Exploring Operation: 57+21=78, Resulting Numbers: [72, 78] Generated Node #0,3,2: 68:[72, 78] Operation: 57+21=78 Exploring Operation: 72-21=51, Resulting Numbers: [57, 51] Generated Node #0,3,3: 68:[57, 51] Operation: 72-21=51 Exploring Operation: 57-21=36, Resulting Numbers: [72, 36] Generated Node #0,3,4: 68:[72, 36] Operation: 57-21=36 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 68:[21, 15], Operations: ['69-48=21', '72-57=15'] Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,68 unequal: No Solution Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 68:[72, 36], Operations: ['69-48=21', '57-21=36'] Exploring Operation: 72*36=2592, Resulting Numbers: [2592] 2592,68 unequal: No Solution Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 72+36=108, Resulting Numbers: [108] 108,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 68:[72, 78], Operations: ['69-48=21', '57+21=78'] Exploring Operation: 78-72=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 72+78=150, Resulting Numbers: [150] 150,68 unequal: No Solution Exploring Operation: 72*78=5616, Resulting Numbers: [5616] 5616,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 68:[57, 51], Operations: ['69-48=21', '72-21=51'] Exploring Operation: 57+51=108, Resulting Numbers: [108] 108,68 unequal: No Solution Exploring Operation: 57*51=2907, Resulting Numbers: [2907] 2907,68 unequal: No Solution Exploring Operation: 57-51=6, Resulting Numbers: [6] 6,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 68:[57, 93], Operations: ['69-48=21', '72+21=93'] Exploring Operation: 57+93=150, Resulting Numbers: [150] 150,68 unequal: No Solution Exploring Operation: 57*93=5301, Resulting Numbers: [5301] 5301,68 unequal: No Solution Exploring Operation: 93-57=36, Resulting Numbers: [36] 36,68 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: 68:[72, 48, 12], Operations: ['69-57=12'] Exploring Operation: 72-48=24, Resulting Numbers: [12, 24] Generated Node #0,0,0: 68:[12, 24] Operation: 72-48=24 Exploring Operation: 48+12=60, Resulting Numbers: [72, 60] Generated Node #0,0,1: 68:[72, 60] Operation: 48+12=60 Exploring Operation: 48-12=36, Resulting Numbers: [72, 36] Generated Node #0,0,2: 68:[72, 36] Operation: 48-12=36 Exploring Operation: 48/12=4, Resulting Numbers: [72, 4] Generated Node #0,0,3: 68:[72, 4] Operation: 48/12=4 Exploring Operation: 72/12=6, Resulting Numbers: [48, 6] Generated Node #0,0,4: 68:[48, 6] Operation: 72/12=6 Moving to Node #0,4,4 Current State: 68:[69, 33], Operations: ['72-57=15', '48-15=33'] Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,68 unequal: No Solution Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,68 unequal: No Solution Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[69, 33], Operations: ['72-48=24', '57-24=33'] Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,68 unequal: No Solution Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,68 unequal: No Solution Moving to Node #0,0,3 Current State: 68:[72, 4], Operations: ['69-57=12', '48/12=4'] Exploring Operation: 72*4=288, Resulting Numbers: [288] 288,68 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[69, 72, 48, 57], Operations: [] Exploring Operation: 69-57=12, Resulting Numbers: [72, 48, 12] Generated Node #0,0: 68:[72, 48, 12] Operation: 69-57=12 Moving to Node #0,0 Current State: 68:[72, 48, 12], Operations: ['69-57=12'] Exploring Operation: 48/12=4, Resulting Numbers: [72, 4] Generated Node #0,0,3: 68:[72, 4] Operation: 48/12=4 Moving to Node #0,0,3 Current State: 68:[72, 4], Operations: ['69-57=12', '48/12=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
0.935764
hs_5
mult_heuristic
[ 78, 50, 36, 39 ]
84
[ "78-50=28", "39-36=3", "28*3=84" ]
Current State: 84:[78, 50, 36, 39], Operations: [] Exploring Operation: 78-50=28, Resulting Numbers: [36, 39, 28] Generated Node #2: [36, 39, 28] from Operation: 78-50=28 Current State: 84:[36, 39, 28], Operations: ['78-50=28'] Exploring Operation: 39-36=3, Resulting Numbers: [28, 3] Generated Node #3: [28, 3] from Operation: 39-36=3 Current State: 84:[28, 3], Operations: ['78-50=28', '39-36=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[78, 50, 36, 39], Operations: [] Exploring Operation: 50-36=14, Resulting Numbers: [78, 39, 14] Generated Node #0,0: 84:[78, 39, 14] Operation: 50-36=14 Exploring Operation: 78-50=28, Resulting Numbers: [36, 39, 28] Generated Node #0,1: 84:[36, 39, 28] Operation: 78-50=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[78, 39, 14], Operations: ['50-36=14'] Exploring Operation: 78-39=39, Resulting Numbers: [14, 39] Generated Node #0,0,0: 84:[14, 39] Operation: 78-39=39 Exploring Operation: 78/39=2, Resulting Numbers: [14, 2] Generated Node #0,0,1: 84:[14, 2] Operation: 78/39=2 Moving to Node #0,0,1 Current State: 84:[14, 2], Operations: ['50-36=14', '78/39=2'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[14, 39], Operations: ['50-36=14', '78-39=39'] Exploring Operation: 14+39=53, Resulting Numbers: [53] 53,84 unequal: No Solution Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[36, 39, 28], Operations: ['78-50=28'] Exploring Operation: 39-36=3, Resulting Numbers: [28, 3] Generated Node #0,1,0: 84:[28, 3] Operation: 39-36=3 Exploring Operation: 36-28=8, Resulting Numbers: [39, 8] Generated Node #0,1,1: 84:[39, 8] Operation: 36-28=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 84:[28, 3], Operations: ['78-50=28', '39-36=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[78, 50, 36, 39], Operations: [] Exploring Operation: 78-50=28, Resulting Numbers: [36, 39, 28] Generated Node #0,1: 84:[36, 39, 28] Operation: 78-50=28 Moving to Node #0,1 Current State: 84:[36, 39, 28], Operations: ['78-50=28'] Exploring Operation: 39-36=3, Resulting Numbers: [28, 3] Generated Node #0,1,0: 84:[28, 3] Operation: 39-36=3 Moving to Node #0,1,0 Current State: 84:[28, 3], Operations: ['78-50=28', '39-36=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 29, 83, 23, 12 ]
24
[ "83-23=60", "60/12=5", "29-5=24" ]
Current State: 24:[29, 83, 23, 12], Operations: [] Exploring Operation: 83-23=60, Resulting Numbers: [29, 12, 60] Generated Node #2: [29, 12, 60] from Operation: 83-23=60 Current State: 24:[29, 12, 60], Operations: ['83-23=60'] Exploring Operation: 60/12=5, Resulting Numbers: [29, 5] Generated Node #3: [29, 5] from Operation: 60/12=5 Current State: 24:[29, 5], Operations: ['83-23=60', '60/12=5'] Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[29, 83, 23, 12], Operations: [] Exploring Operation: 83-23=60, Resulting Numbers: [29, 12, 60] Generated Node #0,0: 24:[29, 12, 60] Operation: 83-23=60 Exploring Operation: 83-29=54, Resulting Numbers: [23, 12, 54] Generated Node #0,1: 24:[23, 12, 54] Operation: 83-29=54 Moving to Node #0,1 Current State: 24:[23, 12, 54], Operations: ['83-29=54'] Exploring Operation: 54-23=31, Resulting Numbers: [12, 31] Generated Node #0,1,0: 24:[12, 31] Operation: 54-23=31 Exploring Operation: 54-12=42, Resulting Numbers: [23, 42] Generated Node #0,1,1: 24:[23, 42] Operation: 54-12=42 Moving to Node #0,0 Current State: 24:[29, 12, 60], Operations: ['83-23=60'] Exploring Operation: 60-29=31, Resulting Numbers: [12, 31] Generated Node #0,0,0: 24:[12, 31] Operation: 60-29=31 Exploring Operation: 60/12=5, Resulting Numbers: [29, 5] Generated Node #0,0,1: 24:[29, 5] Operation: 60/12=5 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[29, 5], Operations: ['83-23=60', '60/12=5'] Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[29, 83, 23, 12], Operations: [] Exploring Operation: 83-23=60, Resulting Numbers: [29, 12, 60] Generated Node #0,0: 24:[29, 12, 60] Operation: 83-23=60 Moving to Node #0,0 Current State: 24:[29, 12, 60], Operations: ['83-23=60'] Exploring Operation: 60/12=5, Resulting Numbers: [29, 5] Generated Node #0,0,1: 24:[29, 5] Operation: 60/12=5 Moving to Node #0,0,1 Current State: 24:[29, 5], Operations: ['83-23=60', '60/12=5'] Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 62, 91, 7, 15 ]
64
[ "62+15=77", "91/7=13", "77-13=64" ]
Current State: 64:[62, 91, 7, 15], Operations: [] Exploring Operation: 62+15=77, Resulting Numbers: [91, 7, 77] Generated Node #2: [91, 7, 77] from Operation: 62+15=77 Current State: 64:[91, 7, 77], Operations: ['62+15=77'] Exploring Operation: 91/7=13, Resulting Numbers: [77, 13] Generated Node #3: [77, 13] from Operation: 91/7=13 Current State: 64:[77, 13], Operations: ['62+15=77', '91/7=13'] Exploring Operation: 77-13=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[62, 91, 7, 15], Operations: [] Exploring Operation: 91-7=84, Resulting Numbers: [62, 15, 84] Generated Node #0,0: 64:[62, 15, 84] Operation: 91-7=84 Exploring Operation: 15-7=8, Resulting Numbers: [62, 91, 8] Generated Node #0,1: 64:[62, 91, 8] Operation: 15-7=8 Exploring Operation: 91-62=29, Resulting Numbers: [7, 15, 29] Generated Node #0,2: 64:[7, 15, 29] Operation: 91-62=29 Exploring Operation: 91-15=76, Resulting Numbers: [62, 7, 76] Generated Node #0,3: 64:[62, 7, 76] Operation: 91-15=76 Exploring Operation: 91/7=13, Resulting Numbers: [62, 15, 13] Generated Node #0,4: 64:[62, 15, 13] Operation: 91/7=13 Moving to Node #0,2 Current State: 64:[7, 15, 29], Operations: ['91-62=29'] Exploring Operation: 29-15=14, Resulting Numbers: [7, 14] Generated Node #0,2,0: 64:[7, 14] Operation: 29-15=14 Exploring Operation: 15-7=8, Resulting Numbers: [29, 8] Generated Node #0,2,1: 64:[29, 8] Operation: 15-7=8 Exploring Operation: 7+15=22, Resulting Numbers: [29, 22] Generated Node #0,2,2: 64:[29, 22] Operation: 7+15=22 Exploring Operation: 29-7=22, Resulting Numbers: [15, 22] Generated Node #0,2,3: 64:[15, 22] Operation: 29-7=22 Exploring Operation: 7+29=36, Resulting Numbers: [15, 36] Generated Node #0,2,4: 64:[15, 36] Operation: 7+29=36 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 64:[7, 14], Operations: ['91-62=29', '29-15=14'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,64 unequal: No Solution Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,64 unequal: No Solution Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,64 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 64:[29, 8], Operations: ['91-62=29', '15-7=8'] Exploring Operation: 29+8=37, Resulting Numbers: [37] 37,64 unequal: No Solution Exploring Operation: 29*8=232, Resulting Numbers: [232] 232,64 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 64:[15, 36], Operations: ['91-62=29', '7+29=36'] Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,64 unequal: No Solution Exploring Operation: 15*36=540, Resulting Numbers: [540] 540,64 unequal: No Solution Exploring Operation: 15+36=51, Resulting Numbers: [51] 51,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 64:[15, 22], Operations: ['91-62=29', '29-7=22'] Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,64 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 64:[29, 22], Operations: ['91-62=29', '7+15=22'] Exploring Operation: 29*22=638, Resulting Numbers: [638] 638,64 unequal: No Solution Exploring Operation: 29-22=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 29+22=51, Resulting Numbers: [51] 51,64 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: 64:[62, 15, 13], Operations: ['91/7=13'] Exploring Operation: 15+13=28, Resulting Numbers: [62, 28] Generated Node #0,4,0: 64:[62, 28] Operation: 15+13=28 Exploring Operation: 62+15=77, Resulting Numbers: [13, 77] Generated Node #0,4,1: 64:[13, 77] Operation: 62+15=77 Exploring Operation: 62-13=49, Resulting Numbers: [15, 49] Generated Node #0,4,2: 64:[15, 49] Operation: 62-13=49 Exploring Operation: 62+13=75, Resulting Numbers: [15, 75] Generated Node #0,4,3: 64:[15, 75] Operation: 62+13=75 Exploring Operation: 15-13=2, Resulting Numbers: [62, 2] Generated Node #0,4,4: 64:[62, 2] Operation: 15-13=2 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 64:[62, 2], Operations: ['91/7=13', '15-13=2'] Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,64 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,64 unequal: No Solution Exploring Operation: 62*2=124, Resulting Numbers: [124] 124,64 unequal: No Solution Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[62, 91, 7, 15], Operations: [] Exploring Operation: 91/7=13, Resulting Numbers: [62, 15, 13] Generated Node #0,4: 64:[62, 15, 13] Operation: 91/7=13 Moving to Node #0,4 Current State: 64:[62, 15, 13], Operations: ['91/7=13'] Exploring Operation: 15-13=2, Resulting Numbers: [62, 2] Generated Node #0,4,4: 64:[62, 2] Operation: 15-13=2 Moving to Node #0,4,4 Current State: 64:[62, 2], Operations: ['91/7=13', '15-13=2'] Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_5
mult_heuristic
[ 13, 64, 78, 64 ]
92
[ "13+78=91", "64/64=1", "91+1=92" ]
Current State: 92:[13, 64, 78, 64], Operations: [] Exploring Operation: 13+78=91, Resulting Numbers: [64, 64, 91] Generated Node #2: [64, 64, 91] from Operation: 13+78=91 Current State: 92:[64, 64, 91], Operations: ['13+78=91'] Exploring Operation: 64/64=1, Resulting Numbers: [91, 1] Generated Node #3: [91, 1] from Operation: 64/64=1 Current State: 92:[91, 1], Operations: ['13+78=91', '64/64=1'] Exploring Operation: 91+1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[13, 64, 78, 64], Operations: [] Exploring Operation: 64/64=1, Resulting Numbers: [13, 78, 1] Generated Node #0,0: 92:[13, 78, 1] Operation: 64/64=1 Exploring Operation: 64-64=0, Resulting Numbers: [13, 78, 0] Generated Node #0,1: 92:[13, 78, 0] Operation: 64-64=0 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[13, 78, 1], Operations: ['64/64=1'] Exploring Operation: 78/13=6, Resulting Numbers: [1, 6] Generated Node #0,0,0: 92:[1, 6] Operation: 78/13=6 Exploring Operation: 13+78=91, Resulting Numbers: [1, 91] Generated Node #0,0,1: 92:[1, 91] Operation: 13+78=91 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 92:[1, 91], Operations: ['64/64=1', '13+78=91'] Exploring Operation: 1*91=91, Resulting Numbers: [91] 91,92 unequal: No Solution Exploring Operation: 1+91=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[13, 64, 78, 64], Operations: [] Exploring Operation: 64/64=1, Resulting Numbers: [13, 78, 1] Generated Node #0,0: 92:[13, 78, 1] Operation: 64/64=1 Moving to Node #0,0 Current State: 92:[13, 78, 1], Operations: ['64/64=1'] Exploring Operation: 13+78=91, Resulting Numbers: [1, 91] Generated Node #0,0,1: 92:[1, 91] Operation: 13+78=91 Moving to Node #0,0,1 Current State: 92:[1, 91], Operations: ['64/64=1', '13+78=91'] Exploring Operation: 1+91=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 36, 95, 31, 15 ]
85
[ "36+95=131", "31+15=46", "131-46=85" ]
Current State: 85:[36, 95, 31, 15], Operations: [] Exploring Operation: 36+95=131, Resulting Numbers: [31, 15, 131] Generated Node #2: [31, 15, 131] from Operation: 36+95=131 Current State: 85:[31, 15, 131], Operations: ['36+95=131'] Exploring Operation: 31+15=46, Resulting Numbers: [131, 46] Generated Node #3: [131, 46] from Operation: 31+15=46 Current State: 85:[131, 46], Operations: ['36+95=131', '31+15=46'] Exploring Operation: 131-46=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[36, 95, 31, 15], Operations: [] Exploring Operation: 31-15=16, Resulting Numbers: [36, 95, 16] Generated Node #0,0: 85:[36, 95, 16] Operation: 31-15=16 Exploring Operation: 36-31=5, Resulting Numbers: [95, 15, 5] Generated Node #0,1: 85:[95, 15, 5] Operation: 36-31=5 Exploring Operation: 36-15=21, Resulting Numbers: [95, 31, 21] Generated Node #0,2: 85:[95, 31, 21] Operation: 36-15=21 Exploring Operation: 36+31=67, Resulting Numbers: [95, 15, 67] Generated Node #0,3: 85:[95, 15, 67] Operation: 36+31=67 Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[95, 15, 5], Operations: ['36-31=5'] Exploring Operation: 95-5=90, Resulting Numbers: [15, 90] Generated Node #0,1,0: 85:[15, 90] Operation: 95-5=90 Exploring Operation: 95-15=80, Resulting Numbers: [5, 80] Generated Node #0,1,1: 85:[5, 80] Operation: 95-15=80 Exploring Operation: 15/5=3, Resulting Numbers: [95, 3] Generated Node #0,1,2: 85:[95, 3] Operation: 15/5=3 Exploring Operation: 95/5=19, Resulting Numbers: [15, 19] Generated Node #0,1,3: 85:[15, 19] Operation: 95/5=19 Moving to Node #0,1,3 Current State: 85:[15, 19], Operations: ['36-31=5', '95/5=19'] Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,85 unequal: No Solution Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[5, 80], Operations: ['36-31=5', '95-15=80'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[36, 95, 31, 15], Operations: [] Exploring Operation: 36-31=5, Resulting Numbers: [95, 15, 5] Generated Node #0,1: 85:[95, 15, 5] Operation: 36-31=5 Moving to Node #0,1 Current State: 85:[95, 15, 5], Operations: ['36-31=5'] Exploring Operation: 95-15=80, Resulting Numbers: [5, 80] Generated Node #0,1,1: 85:[5, 80] Operation: 95-15=80 Moving to Node #0,1,1 Current State: 85:[5, 80], Operations: ['36-31=5', '95-15=80'] Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 1, 54, 96, 68 ]
83
[ "1+54=55", "96-68=28", "55+28=83" ]
Current State: 83:[1, 54, 96, 68], Operations: [] Exploring Operation: 1+54=55, Resulting Numbers: [96, 68, 55] Generated Node #2: [96, 68, 55] from Operation: 1+54=55 Current State: 83:[96, 68, 55], Operations: ['1+54=55'] Exploring Operation: 96-68=28, Resulting Numbers: [55, 28] Generated Node #3: [55, 28] from Operation: 96-68=28 Current State: 83:[55, 28], Operations: ['1+54=55', '96-68=28'] Exploring Operation: 55+28=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[1, 54, 96, 68], Operations: [] Exploring Operation: 96-1=95, Resulting Numbers: [54, 68, 95] Generated Node #0,0: 83:[54, 68, 95] Operation: 96-1=95 Exploring Operation: 1+54=55, Resulting Numbers: [96, 68, 55] Generated Node #0,1: 83:[96, 68, 55] Operation: 1+54=55 Exploring Operation: 1+68=69, Resulting Numbers: [54, 96, 69] Generated Node #0,2: 83:[54, 96, 69] Operation: 1+68=69 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[54, 68, 95], Operations: ['96-1=95'] Exploring Operation: 68-54=14, Resulting Numbers: [95, 14] Generated Node #0,0,0: 83:[95, 14] Operation: 68-54=14 Exploring Operation: 54+68=122, Resulting Numbers: [95, 122] Generated Node #0,0,1: 83:[95, 122] Operation: 54+68=122 Exploring Operation: 95-54=41, Resulting Numbers: [68, 41] Generated Node #0,0,2: 83:[68, 41] Operation: 95-54=41 Moving to Node #0,0,1 Current State: 83:[95, 122], Operations: ['96-1=95', '54+68=122'] Exploring Operation: 95*122=11590, Resulting Numbers: [11590] 11590,83 unequal: No Solution Exploring Operation: 95+122=217, Resulting Numbers: [217] 217,83 unequal: No Solution Exploring Operation: 122-95=27, Resulting Numbers: [27] 27,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[68, 41], Operations: ['96-1=95', '95-54=41'] Exploring Operation: 68+41=109, Resulting Numbers: [109] 109,83 unequal: No Solution Exploring Operation: 68-41=27, Resulting Numbers: [27] 27,83 unequal: No Solution Exploring Operation: 68*41=2788, Resulting Numbers: [2788] 2788,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[95, 14], Operations: ['96-1=95', '68-54=14'] Exploring Operation: 95+14=109, Resulting Numbers: [109] 109,83 unequal: No Solution Exploring Operation: 95*14=1330, Resulting Numbers: [1330] 1330,83 unequal: No Solution Exploring Operation: 95-14=81, Resulting Numbers: [81] 81,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[96, 68, 55], Operations: ['1+54=55'] Exploring Operation: 96-68=28, Resulting Numbers: [55, 28] Generated Node #0,1,0: 83:[55, 28] Operation: 96-68=28 Exploring Operation: 68+55=123, Resulting Numbers: [96, 123] Generated Node #0,1,1: 83:[96, 123] Operation: 68+55=123 Exploring Operation: 96-55=41, Resulting Numbers: [68, 41] Generated Node #0,1,2: 83:[68, 41] Operation: 96-55=41 Moving to Node #0,1,1 Current State: 83:[96, 123], Operations: ['1+54=55', '68+55=123'] Exploring Operation: 96*123=11808, Resulting Numbers: [11808] 11808,83 unequal: No Solution Exploring Operation: 96+123=219, Resulting Numbers: [219] 219,83 unequal: No Solution Exploring Operation: 123-96=27, Resulting Numbers: [27] 27,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[68, 41], Operations: ['1+54=55', '96-55=41'] Exploring Operation: 68-41=27, Resulting Numbers: [27] 27,83 unequal: No Solution Exploring Operation: 68*41=2788, Resulting Numbers: [2788] 2788,83 unequal: No Solution Exploring Operation: 68+41=109, Resulting Numbers: [109] 109,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[55, 28], Operations: ['1+54=55', '96-68=28'] Exploring Operation: 55+28=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[1, 54, 96, 68], Operations: [] Exploring Operation: 1+54=55, Resulting Numbers: [96, 68, 55] Generated Node #0,1: 83:[96, 68, 55] Operation: 1+54=55 Moving to Node #0,1 Current State: 83:[96, 68, 55], Operations: ['1+54=55'] Exploring Operation: 96-68=28, Resulting Numbers: [55, 28] Generated Node #0,1,0: 83:[55, 28] Operation: 96-68=28 Moving to Node #0,1,0 Current State: 83:[55, 28], Operations: ['1+54=55', '96-68=28'] Exploring Operation: 55+28=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
sum_heuristic
[ 5, 39, 96, 2 ]
11
[ "96-39=57", "57-2=55", "55/5=11" ]
Current State: 11:[5, 39, 96, 2], Operations: [] Exploring Operation: 96-39=57, Resulting Numbers: [5, 2, 57] Generated Node #2: [5, 2, 57] from Operation: 96-39=57 Current State: 11:[5, 2, 57], Operations: ['96-39=57'] Exploring Operation: 57-2=55, Resulting Numbers: [5, 55] Generated Node #3: [5, 55] from Operation: 57-2=55 Current State: 11:[5, 55], Operations: ['96-39=57', '57-2=55'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[5, 39, 96, 2], Operations: [] Exploring Operation: 39-5=34, Resulting Numbers: [96, 2, 34] Generated Node #0,0: 11:[96, 2, 34] Operation: 39-5=34 Exploring Operation: 96-39=57, Resulting Numbers: [5, 2, 57] Generated Node #0,1: 11:[5, 2, 57] Operation: 96-39=57 Exploring Operation: 96/2=48, Resulting Numbers: [5, 39, 48] Generated Node #0,2: 11:[5, 39, 48] Operation: 96/2=48 Exploring Operation: 5*2=10, Resulting Numbers: [39, 96, 10] Generated Node #0,3: 11:[39, 96, 10] Operation: 5*2=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[5, 2, 57], Operations: ['96-39=57'] Exploring Operation: 57-5=52, Resulting Numbers: [2, 52] Generated Node #0,1,0: 11:[2, 52] Operation: 57-5=52 Exploring Operation: 5+2=7, Resulting Numbers: [57, 7] Generated Node #0,1,1: 11:[57, 7] Operation: 5+2=7 Exploring Operation: 57-2=55, Resulting Numbers: [5, 55] Generated Node #0,1,2: 11:[5, 55] Operation: 57-2=55 Exploring Operation: 5*2=10, Resulting Numbers: [57, 10] Generated Node #0,1,3: 11:[57, 10] Operation: 5*2=10 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 11:[57, 10], Operations: ['96-39=57', '5*2=10'] Exploring Operation: 57*10=570, Resulting Numbers: [570] 570,11 unequal: No Solution Exploring Operation: 57+10=67, Resulting Numbers: [67] 67,11 unequal: No Solution Exploring Operation: 57-10=47, Resulting Numbers: [47] 47,11 unequal: No Solution No 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: 11:[2, 52], Operations: ['96-39=57', '57-5=52'] Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 2*52=104, Resulting Numbers: [104] 104,11 unequal: No Solution No 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: 11:[57, 7], Operations: ['96-39=57', '5+2=7'] Exploring Operation: 57*7=399, Resulting Numbers: [399] 399,11 unequal: No Solution Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 57+7=64, Resulting Numbers: [64] 64,11 unequal: No Solution No 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: 11:[5, 55], Operations: ['96-39=57', '57-2=55'] Exploring Operation: 5*55=275, Resulting Numbers: [275] 275,11 unequal: No Solution Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[5, 39, 96, 2], Operations: [] Exploring Operation: 96-39=57, Resulting Numbers: [5, 2, 57] Generated Node #0,1: 11:[5, 2, 57] Operation: 96-39=57 Moving to Node #0,1 Current State: 11:[5, 2, 57], Operations: ['96-39=57'] Exploring Operation: 57-2=55, Resulting Numbers: [5, 55] Generated Node #0,1,2: 11:[5, 55] Operation: 57-2=55 Moving to Node #0,1,2 Current State: 11:[5, 55], Operations: ['96-39=57', '57-2=55'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_4
mult_heuristic
[ 13, 56, 71, 88 ]
52
[ "13+56=69", "88-71=17", "69-17=52" ]
Current State: 52:[13, 56, 71, 88], Operations: [] Exploring Operation: 13+56=69, Resulting Numbers: [71, 88, 69] Generated Node #2: [71, 88, 69] from Operation: 13+56=69 Current State: 52:[71, 88, 69], Operations: ['13+56=69'] Exploring Operation: 88-71=17, Resulting Numbers: [69, 17] Generated Node #3: [69, 17] from Operation: 88-71=17 Current State: 52:[69, 17], Operations: ['13+56=69', '88-71=17'] Exploring Operation: 69-17=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[13, 56, 71, 88], Operations: [] Exploring Operation: 88-71=17, Resulting Numbers: [13, 56, 17] Generated Node #0,0: 52:[13, 56, 17] Operation: 88-71=17 Exploring Operation: 88-13=75, Resulting Numbers: [56, 71, 75] Generated Node #0,1: 52:[56, 71, 75] Operation: 88-13=75 Exploring Operation: 88-56=32, Resulting Numbers: [13, 71, 32] Generated Node #0,2: 52:[13, 71, 32] Operation: 88-56=32 Exploring Operation: 71-56=15, Resulting Numbers: [13, 88, 15] Generated Node #0,3: 52:[13, 88, 15] Operation: 71-56=15 Exploring Operation: 71-13=58, Resulting Numbers: [56, 88, 58] Generated Node #0,4: 52:[56, 88, 58] Operation: 71-13=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[13, 56, 17], Operations: ['88-71=17'] Exploring Operation: 13+17=30, Resulting Numbers: [56, 30] Generated Node #0,0,0: 52:[56, 30] Operation: 13+17=30 Exploring Operation: 17-13=4, Resulting Numbers: [56, 4] Generated Node #0,0,1: 52:[56, 4] Operation: 17-13=4 Exploring Operation: 13+56=69, Resulting Numbers: [17, 69] Generated Node #0,0,2: 52:[17, 69] Operation: 13+56=69 Exploring Operation: 56-17=39, Resulting Numbers: [13, 39] Generated Node #0,0,3: 52:[13, 39] Operation: 56-17=39 Exploring Operation: 56-13=43, Resulting Numbers: [17, 43] Generated Node #0,0,4: 52:[17, 43] Operation: 56-13=43 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[56, 4], Operations: ['88-71=17', '17-13=4'] Exploring Operation: 56+4=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[13, 56, 71, 88], Operations: [] Exploring Operation: 88-71=17, Resulting Numbers: [13, 56, 17] Generated Node #0,0: 52:[13, 56, 17] Operation: 88-71=17 Moving to Node #0,0 Current State: 52:[13, 56, 17], Operations: ['88-71=17'] Exploring Operation: 17-13=4, Resulting Numbers: [56, 4] Generated Node #0,0,1: 52:[56, 4] Operation: 17-13=4 Moving to Node #0,0,1 Current State: 52:[56, 4], Operations: ['88-71=17', '17-13=4'] Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 3, 69, 9, 1 ]
42
[ "3*9=27", "69*1=69", "69-27=42" ]
Current State: 42:[3, 69, 9, 1], Operations: [] Exploring Operation: 3*9=27, Resulting Numbers: [69, 1, 27] Generated Node #2: [69, 1, 27] from Operation: 3*9=27 Current State: 42:[69, 1, 27], Operations: ['3*9=27'] Exploring Operation: 69*1=69, Resulting Numbers: [27, 69] Generated Node #3: [27, 69] from Operation: 69*1=69 Current State: 42:[27, 69], Operations: ['3*9=27', '69*1=69'] Exploring Operation: 69-27=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[3, 69, 9, 1], Operations: [] Exploring Operation: 69/3=23, Resulting Numbers: [9, 1, 23] Generated Node #0,0: 42:[9, 1, 23] Operation: 69/3=23 Exploring Operation: 69-9=60, Resulting Numbers: [3, 1, 60] Generated Node #0,1: 42:[3, 1, 60] Operation: 69-9=60 Moving to Node #0,0 Current State: 42:[9, 1, 23], Operations: ['69/3=23'] Exploring Operation: 23-9=14, Resulting Numbers: [1, 14] Generated Node #0,0,0: 42:[1, 14] Operation: 23-9=14 Exploring Operation: 9-1=8, Resulting Numbers: [23, 8] Generated Node #0,0,1: 42:[23, 8] Operation: 9-1=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[1, 14], Operations: ['69/3=23', '23-9=14'] Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,42 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,42 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:[23, 8], Operations: ['69/3=23', '9-1=8'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,42 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: 42:[3, 1, 60], Operations: ['69-9=60'] Exploring Operation: 60/3=20, Resulting Numbers: [1, 20] Generated Node #0,1,0: 42:[1, 20] Operation: 60/3=20 Exploring Operation: 60-3=57, Resulting Numbers: [1, 57] Generated Node #0,1,1: 42:[1, 57] Operation: 60-3=57 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 42:[1, 20], Operations: ['69-9=60', '60/3=20'] Exploring Operation: 1+20=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 1*20=20, Resulting Numbers: [20] 20,42 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 #0,1,1 Current State: 42:[1, 57], Operations: ['69-9=60', '60-3=57'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,42 unequal: No Solution Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,42 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
[ 22, 29, 11, 37 ]
45
[ "22/11=2", "37*2=74", "74-29=45" ]
Current State: 45:[22, 29, 11, 37], Operations: [] Exploring Operation: 22/11=2, Resulting Numbers: [29, 37, 2] Generated Node #2: [29, 37, 2] from Operation: 22/11=2 Current State: 45:[29, 37, 2], Operations: ['22/11=2'] Exploring Operation: 37*2=74, Resulting Numbers: [29, 74] Generated Node #3: [29, 74] from Operation: 37*2=74 Current State: 45:[29, 74], Operations: ['22/11=2', '37*2=74'] Exploring Operation: 74-29=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[22, 29, 11, 37], Operations: [] Exploring Operation: 37-29=8, Resulting Numbers: [22, 11, 8] Generated Node #0,0: 45:[22, 11, 8] Operation: 37-29=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[22, 11, 8], Operations: ['37-29=8'] Exploring Operation: 22/11=2, Resulting Numbers: [8, 2] Generated Node #0,0,0: 45:[8, 2] Operation: 22/11=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[8, 2], Operations: ['37-29=8', '22/11=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,45 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
[ 23, 38, 33, 2 ]
66
[ "23+33=56", "56/2=28", "38+28=66" ]
Current State: 66:[23, 38, 33, 2], Operations: [] Exploring Operation: 23+33=56, Resulting Numbers: [38, 2, 56] Generated Node #2: [38, 2, 56] from Operation: 23+33=56 Current State: 66:[38, 2, 56], Operations: ['23+33=56'] Exploring Operation: 56/2=28, Resulting Numbers: [38, 28] Generated Node #3: [38, 28] from Operation: 56/2=28 Current State: 66:[38, 28], Operations: ['23+33=56', '56/2=28'] Exploring Operation: 38+28=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[23, 38, 33, 2], Operations: [] Exploring Operation: 38-33=5, Resulting Numbers: [23, 2, 5] Generated Node #0,0: 66:[23, 2, 5] Operation: 38-33=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[23, 2, 5], Operations: ['38-33=5'] Exploring Operation: 5-2=3, Resulting Numbers: [23, 3] Generated Node #0,0,0: 66:[23, 3] Operation: 5-2=3 Moving to Node #0,0,0 Current State: 66:[23, 3], Operations: ['38-33=5', '5-2=3'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 44, 38, 64, 84 ]
36
[ "44+84=128", "128/64=2", "38-2=36" ]
Current State: 36:[44, 38, 64, 84], Operations: [] Exploring Operation: 44+84=128, Resulting Numbers: [38, 64, 128] Generated Node #2: [38, 64, 128] from Operation: 44+84=128 Current State: 36:[38, 64, 128], Operations: ['44+84=128'] Exploring Operation: 128/64=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 128/64=2 Current State: 36:[38, 2], Operations: ['44+84=128', '128/64=2'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[44, 38, 64, 84], Operations: [] Exploring Operation: 84-64=20, Resulting Numbers: [44, 38, 20] Generated Node #0,0: 36:[44, 38, 20] Operation: 84-64=20 Moving to Node #0,0 Current State: 36:[44, 38, 20], Operations: ['84-64=20'] Exploring Operation: 44-38=6, Resulting Numbers: [20, 6] Generated Node #0,0,0: 36:[20, 6] Operation: 44-38=6 Moving to Node #0,0,0 Current State: 36:[20, 6], Operations: ['84-64=20', '44-38=6'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,36 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 74, 44, 84, 97 ]
43
[ "74-44=30", "97-84=13", "30+13=43" ]
Current State: 43:[74, 44, 84, 97], Operations: [] Exploring Operation: 74-44=30, Resulting Numbers: [84, 97, 30] Generated Node #2: [84, 97, 30] from Operation: 74-44=30 Current State: 43:[84, 97, 30], Operations: ['74-44=30'] Exploring Operation: 97-84=13, Resulting Numbers: [30, 13] Generated Node #3: [30, 13] from Operation: 97-84=13 Current State: 43:[30, 13], Operations: ['74-44=30', '97-84=13'] Exploring Operation: 30+13=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[74, 44, 84, 97], Operations: [] Exploring Operation: 97-74=23, Resulting Numbers: [44, 84, 23] Generated Node #0,0: 43:[44, 84, 23] Operation: 97-74=23 Exploring Operation: 97-84=13, Resulting Numbers: [74, 44, 13] Generated Node #0,1: 43:[74, 44, 13] Operation: 97-84=13 Exploring Operation: 84-74=10, Resulting Numbers: [44, 97, 10] Generated Node #0,2: 43:[44, 97, 10] Operation: 84-74=10 Exploring Operation: 97-44=53, Resulting Numbers: [74, 84, 53] Generated Node #0,3: 43:[74, 84, 53] Operation: 97-44=53 Moving to Node #0,0 Current State: 43:[44, 84, 23], Operations: ['97-74=23'] Exploring Operation: 44+23=67, Resulting Numbers: [84, 67] Generated Node #0,0,0: 43:[84, 67] Operation: 44+23=67 Exploring Operation: 44-23=21, Resulting Numbers: [84, 21] Generated Node #0,0,1: 43:[84, 21] Operation: 44-23=21 Exploring Operation: 84-23=61, Resulting Numbers: [44, 61] Generated Node #0,0,2: 43:[44, 61] Operation: 84-23=61 Exploring Operation: 84-44=40, Resulting Numbers: [23, 40] Generated Node #0,0,3: 43:[23, 40] Operation: 84-44=40 Moving to Node #0,1 Current State: 43:[74, 44, 13], Operations: ['97-84=13'] Exploring Operation: 74-13=61, Resulting Numbers: [44, 61] Generated Node #0,1,0: 43:[44, 61] Operation: 74-13=61 Exploring Operation: 74-44=30, Resulting Numbers: [13, 30] Generated Node #0,1,1: 43:[13, 30] Operation: 74-44=30 Exploring Operation: 44-13=31, Resulting Numbers: [74, 31] Generated Node #0,1,2: 43:[74, 31] Operation: 44-13=31 Exploring Operation: 74+13=87, Resulting Numbers: [44, 87] Generated Node #0,1,3: 43:[44, 87] Operation: 74+13=87 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[44, 61], Operations: ['97-84=13', '74-13=61'] Exploring Operation: 61-44=17, Resulting Numbers: [17] 17,43 unequal: No Solution Exploring Operation: 44+61=105, Resulting Numbers: [105] 105,43 unequal: No Solution Exploring Operation: 44*61=2684, Resulting Numbers: [2684] 2684,43 unequal: No Solution No 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: 43:[13, 30], Operations: ['97-84=13', '74-44=30'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,43 unequal: No Solution Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[74, 44, 84, 97], Operations: [] Exploring Operation: 97-84=13, Resulting Numbers: [74, 44, 13] Generated Node #0,1: 43:[74, 44, 13] Operation: 97-84=13 Moving to Node #0,1 Current State: 43:[74, 44, 13], Operations: ['97-84=13'] Exploring Operation: 74-44=30, Resulting Numbers: [13, 30] Generated Node #0,1,1: 43:[13, 30] Operation: 74-44=30 Moving to Node #0,1,1 Current State: 43:[13, 30], Operations: ['97-84=13', '74-44=30'] Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 9, 69, 30, 10 ]
32
[ "69*10=690", "690/30=23", "9+23=32" ]
Current State: 32:[9, 69, 30, 10], Operations: [] Exploring Operation: 69*10=690, Resulting Numbers: [9, 30, 690] Generated Node #2: [9, 30, 690] from Operation: 69*10=690 Current State: 32:[9, 30, 690], Operations: ['69*10=690'] Exploring Operation: 690/30=23, Resulting Numbers: [9, 23] Generated Node #3: [9, 23] from Operation: 690/30=23 Current State: 32:[9, 23], Operations: ['69*10=690', '690/30=23'] Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[9, 69, 30, 10], Operations: [] Exploring Operation: 69-9=60, Resulting Numbers: [30, 10, 60] Generated Node #0,0: 32:[30, 10, 60] Operation: 69-9=60 Exploring Operation: 69-10=59, Resulting Numbers: [9, 30, 59] Generated Node #0,1: 32:[9, 30, 59] Operation: 69-10=59 Exploring Operation: 30/10=3, Resulting Numbers: [9, 69, 3] Generated Node #0,2: 32:[9, 69, 3] Operation: 30/10=3 Exploring Operation: 69-30=39, Resulting Numbers: [9, 10, 39] Generated Node #0,3: 32:[9, 10, 39] Operation: 69-30=39 Moving to Node #0,3 Current State: 32:[9, 10, 39], Operations: ['69-30=39'] Exploring Operation: 9+10=19, Resulting Numbers: [39, 19] Generated Node #0,3,0: 32:[39, 19] Operation: 9+10=19 Exploring Operation: 10-9=1, Resulting Numbers: [39, 1] Generated Node #0,3,1: 32:[39, 1] Operation: 10-9=1 Exploring Operation: 39-9=30, Resulting Numbers: [10, 30] Generated Node #0,3,2: 32:[10, 30] Operation: 39-9=30 Exploring Operation: 39-10=29, Resulting Numbers: [9, 29] Generated Node #0,3,3: 32:[9, 29] Operation: 39-10=29 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 32:[10, 30], Operations: ['69-30=39', '39-9=30'] Exploring Operation: 10*30=300, Resulting Numbers: [300] 300,32 unequal: No Solution Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,32 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 32:[9, 29], Operations: ['69-30=39', '39-10=29'] Exploring Operation: 9*29=261, Resulting Numbers: [261] 261,32 unequal: No Solution Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,32 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 32:[39, 1], Operations: ['69-30=39', '10-9=1'] Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 32:[39, 19], Operations: ['69-30=39', '9+10=19'] Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,32 unequal: No Solution Exploring Operation: 39+19=58, Resulting Numbers: [58] 58,32 unequal: No Solution Exploring Operation: 39*19=741, Resulting Numbers: [741] 741,32 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: 32:[9, 30, 59], Operations: ['69-10=59'] Exploring Operation: 9+30=39, Resulting Numbers: [59, 39] Generated Node #0,1,0: 32:[59, 39] Operation: 9+30=39 Exploring Operation: 30-9=21, Resulting Numbers: [59, 21] Generated Node #0,1,1: 32:[59, 21] Operation: 30-9=21 Exploring Operation: 59-30=29, Resulting Numbers: [9, 29] Generated Node #0,1,2: 32:[9, 29] Operation: 59-30=29 Exploring Operation: 59-9=50, Resulting Numbers: [30, 50] Generated Node #0,1,3: 32:[30, 50] Operation: 59-9=50 Moving to Node #0,0 Current State: 32:[30, 10, 60], Operations: ['69-9=60'] Exploring Operation: 60/30=2, Resulting Numbers: [10, 2] Generated Node #0,0,0: 32:[10, 2] Operation: 60/30=2 Exploring Operation: 60/10=6, Resulting Numbers: [30, 6] Generated Node #0,0,1: 32:[30, 6] Operation: 60/10=6 Exploring Operation: 60-30=30, Resulting Numbers: [10, 30] Generated Node #0,0,2: 32:[10, 30] Operation: 60-30=30 Exploring Operation: 60-10=50, Resulting Numbers: [30, 50] Generated Node #0,0,3: 32:[30, 50] Operation: 60-10=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[10, 2], Operations: ['69-9=60', '60/30=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,32 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,32 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,32 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[30, 6], Operations: ['69-9=60', '60/10=6'] Exploring Operation: 30*6=180, Resulting Numbers: [180] 180,32 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,32 unequal: No Solution Exploring Operation: 30+6=36, Resulting Numbers: [36] 36,32 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 32:[10, 30], Operations: ['69-9=60', '60-30=30'] Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,32 unequal: No Solution Exploring Operation: 10*30=300, Resulting Numbers: [300] 300,32 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 32:[30, 50], Operations: ['69-9=60', '60-10=50'] Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,32 unequal: No Solution Exploring Operation: 30*50=1500, Resulting Numbers: [1500] 1500,32 unequal: No Solution Exploring Operation: 30+50=80, Resulting Numbers: [80] 80,32 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: 32:[9, 69, 3], Operations: ['30/10=3'] Exploring Operation: 69-3=66, Resulting Numbers: [9, 66] Generated Node #0,2,0: 32:[9, 66] Operation: 69-3=66 Exploring Operation: 69-9=60, Resulting Numbers: [3, 60] Generated Node #0,2,1: 32:[3, 60] Operation: 69-9=60 Exploring Operation: 9/3=3, Resulting Numbers: [69, 3] Generated Node #0,2,2: 32:[69, 3] Operation: 9/3=3 Exploring Operation: 69/3=23, Resulting Numbers: [9, 23] Generated Node #0,2,3: 32:[9, 23] Operation: 69/3=23 Moving to Node #0,1,2 Current State: 32:[9, 29], Operations: ['69-10=59', '59-30=29'] Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,32 unequal: No Solution Exploring Operation: 9*29=261, Resulting Numbers: [261] 261,32 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,32 unequal: No Solution Moving to Node #0,2,3 Current State: 32:[9, 23], Operations: ['30/10=3', '69/3=23'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[9, 69, 30, 10], Operations: [] Exploring Operation: 30/10=3, Resulting Numbers: [9, 69, 3] Generated Node #0,2: 32:[9, 69, 3] Operation: 30/10=3 Moving to Node #0,2 Current State: 32:[9, 69, 3], Operations: ['30/10=3'] Exploring Operation: 69/3=23, Resulting Numbers: [9, 23] Generated Node #0,2,3: 32:[9, 23] Operation: 69/3=23 Moving to Node #0,2,3 Current State: 32:[9, 23], Operations: ['30/10=3', '69/3=23'] Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.949653
hs_4
sum_heuristic
[ 72, 35, 63, 27 ]
40
[ "72+63=135", "135/27=5", "35+5=40" ]
Current State: 40:[72, 35, 63, 27], Operations: [] Exploring Operation: 72+63=135, Resulting Numbers: [35, 27, 135] Generated Node #2: [35, 27, 135] from Operation: 72+63=135 Current State: 40:[35, 27, 135], Operations: ['72+63=135'] Exploring Operation: 135/27=5, Resulting Numbers: [35, 5] Generated Node #3: [35, 5] from Operation: 135/27=5 Current State: 40:[35, 5], Operations: ['72+63=135', '135/27=5'] Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[72, 35, 63, 27], Operations: [] Exploring Operation: 72-63=9, Resulting Numbers: [35, 27, 9] Generated Node #0,0: 40:[35, 27, 9] Operation: 72-63=9 Exploring Operation: 72-27=45, Resulting Numbers: [35, 63, 45] Generated Node #0,1: 40:[35, 63, 45] Operation: 72-27=45 Exploring Operation: 63-27=36, Resulting Numbers: [72, 35, 36] Generated Node #0,2: 40:[72, 35, 36] Operation: 63-27=36 Exploring Operation: 63-35=28, Resulting Numbers: [72, 27, 28] Generated Node #0,3: 40:[72, 27, 28] Operation: 63-35=28 Exploring Operation: 72-35=37, Resulting Numbers: [63, 27, 37] Generated Node #0,4: 40:[63, 27, 37] Operation: 72-35=37 Moving to Node #0,0 Current State: 40:[35, 27, 9], Operations: ['72-63=9'] Exploring Operation: 35-27=8, Resulting Numbers: [9, 8] Generated Node #0,0,0: 40:[9, 8] Operation: 35-27=8 Exploring Operation: 27+9=36, Resulting Numbers: [35, 36] Generated Node #0,0,1: 40:[35, 36] Operation: 27+9=36 Exploring Operation: 35+9=44, Resulting Numbers: [27, 44] Generated Node #0,0,2: 40:[27, 44] Operation: 35+9=44 Exploring Operation: 27-9=18, Resulting Numbers: [35, 18] Generated Node #0,0,3: 40:[35, 18] Operation: 27-9=18 Exploring Operation: 27/9=3, Resulting Numbers: [35, 3] Generated Node #0,0,4: 40:[35, 3] Operation: 27/9=3 Moving to Node #0,4 Current State: 40:[63, 27, 37], Operations: ['72-35=37'] Exploring Operation: 63-37=26, Resulting Numbers: [27, 26] Generated Node #0,4,0: 40:[27, 26] Operation: 63-37=26 Exploring Operation: 63-27=36, Resulting Numbers: [37, 36] Generated Node #0,4,1: 40:[37, 36] Operation: 63-27=36 Exploring Operation: 37-27=10, Resulting Numbers: [63, 10] Generated Node #0,4,2: 40:[63, 10] Operation: 37-27=10 Exploring Operation: 27+37=64, Resulting Numbers: [63, 64] Generated Node #0,4,3: 40:[63, 64] Operation: 27+37=64 Exploring Operation: 63+27=90, Resulting Numbers: [37, 90] Generated Node #0,4,4: 40:[37, 90] Operation: 63+27=90 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 40:[37, 36], Operations: ['72-35=37', '63-27=36'] Exploring Operation: 37+36=73, Resulting Numbers: [73] 73,40 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 37*36=1332, Resulting Numbers: [1332] 1332,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 40:[27, 26], Operations: ['72-35=37', '63-37=26'] Exploring Operation: 27+26=53, Resulting Numbers: [53] 53,40 unequal: No Solution Exploring Operation: 27*26=702, Resulting Numbers: [702] 702,40 unequal: No Solution Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 40:[63, 10], Operations: ['72-35=37', '37-27=10'] Exploring Operation: 63*10=630, Resulting Numbers: [630] 630,40 unequal: No Solution Exploring Operation: 63+10=73, Resulting Numbers: [73] 73,40 unequal: No Solution Exploring Operation: 63-10=53, Resulting Numbers: [53] 53,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 40:[63, 64], Operations: ['72-35=37', '27+37=64'] Exploring Operation: 64-63=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 63+64=127, Resulting Numbers: [127] 127,40 unequal: No Solution Exploring Operation: 63*64=4032, Resulting Numbers: [4032] 4032,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 40:[37, 90], Operations: ['72-35=37', '63+27=90'] Exploring Operation: 37*90=3330, Resulting Numbers: [3330] 3330,40 unequal: No Solution Exploring Operation: 37+90=127, Resulting Numbers: [127] 127,40 unequal: No Solution Exploring Operation: 90-37=53, Resulting Numbers: [53] 53,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 40:[35, 63, 45], Operations: ['72-27=45'] Exploring Operation: 45-35=10, Resulting Numbers: [63, 10] Generated Node #0,1,0: 40:[63, 10] Operation: 45-35=10 Exploring Operation: 35+45=80, Resulting Numbers: [63, 80] Generated Node #0,1,1: 40:[63, 80] Operation: 35+45=80 Exploring Operation: 63-45=18, Resulting Numbers: [35, 18] Generated Node #0,1,2: 40:[35, 18] Operation: 63-45=18 Exploring Operation: 35+63=98, Resulting Numbers: [45, 98] Generated Node #0,1,3: 40:[45, 98] Operation: 35+63=98 Exploring Operation: 63-35=28, Resulting Numbers: [45, 28] Generated Node #0,1,4: 40:[45, 28] Operation: 63-35=28 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 40:[35, 18], Operations: ['72-27=45', '63-45=18'] Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 35*18=630, Resulting Numbers: [630] 630,40 unequal: No Solution Exploring Operation: 35+18=53, Resulting Numbers: [53] 53,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 40:[45, 28], Operations: ['72-27=45', '63-35=28'] Exploring Operation: 45*28=1260, Resulting Numbers: [1260] 1260,40 unequal: No Solution Exploring Operation: 45-28=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 45+28=73, Resulting Numbers: [73] 73,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[63, 10], Operations: ['72-27=45', '45-35=10'] Exploring Operation: 63-10=53, Resulting Numbers: [53] 53,40 unequal: No Solution Exploring Operation: 63+10=73, Resulting Numbers: [73] 73,40 unequal: No Solution Exploring Operation: 63*10=630, Resulting Numbers: [630] 630,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 40:[63, 80], Operations: ['72-27=45', '35+45=80'] Exploring Operation: 63+80=143, Resulting Numbers: [143] 143,40 unequal: No Solution Exploring Operation: 63*80=5040, Resulting Numbers: [5040] 5040,40 unequal: No Solution Exploring Operation: 80-63=17, Resulting Numbers: [17] 17,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 40:[45, 98], Operations: ['72-27=45', '35+63=98'] Exploring Operation: 45+98=143, Resulting Numbers: [143] 143,40 unequal: No Solution Exploring Operation: 45*98=4410, Resulting Numbers: [4410] 4410,40 unequal: No Solution Exploring Operation: 98-45=53, Resulting Numbers: [53] 53,40 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: 40:[72, 35, 36], Operations: ['63-27=36'] Exploring Operation: 36-35=1, Resulting Numbers: [72, 1] Generated Node #0,2,0: 40:[72, 1] Operation: 36-35=1 Exploring Operation: 72/36=2, Resulting Numbers: [35, 2] Generated Node #0,2,1: 40:[35, 2] Operation: 72/36=2 Exploring Operation: 35+36=71, Resulting Numbers: [72, 71] Generated Node #0,2,2: 40:[72, 71] Operation: 35+36=71 Exploring Operation: 72-36=36, Resulting Numbers: [35, 36] Generated Node #0,2,3: 40:[35, 36] Operation: 72-36=36 Exploring Operation: 72-35=37, Resulting Numbers: [36, 37] Generated Node #0,2,4: 40:[36, 37] Operation: 72-35=37 Moving to Node #0,3 Current State: 40:[72, 27, 28], Operations: ['63-35=28'] Exploring Operation: 72-28=44, Resulting Numbers: [27, 44] Generated Node #0,3,0: 40:[27, 44] Operation: 72-28=44 Exploring Operation: 28-27=1, Resulting Numbers: [72, 1] Generated Node #0,3,1: 40:[72, 1] Operation: 28-27=1 Exploring Operation: 72+27=99, Resulting Numbers: [28, 99] Generated Node #0,3,2: 40:[28, 99] Operation: 72+27=99 Exploring Operation: 27+28=55, Resulting Numbers: [72, 55] Generated Node #0,3,3: 40:[72, 55] Operation: 27+28=55 Exploring Operation: 72-27=45, Resulting Numbers: [28, 45] Generated Node #0,3,4: 40:[28, 45] Operation: 72-27=45 Moving to Node #0,0,0 Current State: 40:[9, 8], Operations: ['72-63=9', '35-27=8'] Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,40 unequal: No Solution Moving to Node #0,2,1 Current State: 40:[35, 2], Operations: ['63-27=36', '72/36=2'] Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,40 unequal: No Solution Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,40 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,40 unequal: No Solution Moving to Node #0,0,4 Current State: 40:[35, 3], Operations: ['72-63=9', '27/9=3'] Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,40 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,40 unequal: No Solution Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,40 unequal: No Solution Moving to Node #0,2,4 Current State: 40:[36, 37], Operations: ['63-27=36', '72-35=37'] Exploring Operation: 36*37=1332, Resulting Numbers: [1332] 1332,40 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 36+37=73, Resulting Numbers: [73] 73,40 unequal: No Solution Moving to Node #0,0,3 Current State: 40:[35, 18], Operations: ['72-63=9', '27-9=18'] Exploring Operation: 35+18=53, Resulting Numbers: [53] 53,40 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 35*18=630, Resulting Numbers: [630] 630,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[35, 36], Operations: ['72-63=9', '27+9=36'] Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 35*36=1260, Resulting Numbers: [1260] 1260,40 unequal: No Solution Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,40 unequal: No Solution Moving to Node #0,2,3 Current State: 40:[35, 36], Operations: ['63-27=36', '72-36=36'] Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 35*36=1260, Resulting Numbers: [1260] 1260,40 unequal: No Solution Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,40 unequal: No Solution Moving to Node #0,0,2 Current State: 40:[27, 44], Operations: ['72-63=9', '35+9=44'] Exploring Operation: 27*44=1188, Resulting Numbers: [1188] 1188,40 unequal: No Solution Exploring Operation: 27+44=71, Resulting Numbers: [71] 71,40 unequal: No Solution Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,40 unequal: No Solution Moving to Node #0,3,0 Current State: 40:[27, 44], Operations: ['63-35=28', '72-28=44'] Exploring Operation: 27*44=1188, Resulting Numbers: [1188] 1188,40 unequal: No Solution Exploring Operation: 27+44=71, Resulting Numbers: [71] 71,40 unequal: No Solution Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,40 unequal: No Solution Moving to Node #0,3,4 Current State: 40:[28, 45], Operations: ['63-35=28', '72-27=45'] Exploring Operation: 28*45=1260, Resulting Numbers: [1260] 1260,40 unequal: No Solution Exploring Operation: 45-28=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 28+45=73, Resulting Numbers: [73] 73,40 unequal: No Solution Moving to Node #0,3,1 Current State: 40:[72, 1], Operations: ['63-35=28', '28-27=1'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,40 unequal: No Solution Exploring Operation: 72*1=72, Resulting Numbers: [72] 72,40 unequal: No Solution Exploring Operation: 72+1=73, Resulting Numbers: [73] 73,40 unequal: No Solution Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,40 unequal: No Solution Moving to Node #0,2,0 Current State: 40:[72, 1], Operations: ['63-27=36', '36-35=1'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,40 unequal: No Solution Exploring Operation: 72+1=73, Resulting Numbers: [73] 73,40 unequal: No Solution Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,40 unequal: No Solution Exploring Operation: 72*1=72, Resulting Numbers: [72] 72,40 unequal: No Solution Moving to Node #0,3,3 Current State: 40:[72, 55], Operations: ['63-35=28', '27+28=55'] Exploring Operation: 72-55=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 72+55=127, Resulting Numbers: [127] 127,40 unequal: No Solution Exploring Operation: 72*55=3960, Resulting Numbers: [3960] 3960,40 unequal: No Solution Moving to Node #0,2,2 Current State: 40:[72, 71], Operations: ['63-27=36', '35+36=71'] Exploring Operation: 72*71=5112, Resulting Numbers: [5112] 5112,40 unequal: No Solution Exploring Operation: 72-71=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 72+71=143, Resulting Numbers: [143] 143,40 unequal: No Solution Moving to Node #0,3,2 Current State: 40:[28, 99], Operations: ['63-35=28', '72+27=99'] Exploring Operation: 28+99=127, Resulting Numbers: [127] 127,40 unequal: No Solution Exploring Operation: 99-28=71, Resulting Numbers: [71] 71,40 unequal: No Solution Exploring Operation: 28*99=2772, Resulting Numbers: [2772] 2772,40 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 28, 90, 19, 92 ]
82
[ "28-19=9", "90/9=10", "92-10=82" ]
Current State: 82:[28, 90, 19, 92], Operations: [] Exploring Operation: 28-19=9, Resulting Numbers: [90, 92, 9] Generated Node #2: [90, 92, 9] from Operation: 28-19=9 Current State: 82:[90, 92, 9], Operations: ['28-19=9'] Exploring Operation: 90/9=10, Resulting Numbers: [92, 10] Generated Node #3: [92, 10] from Operation: 90/9=10 Current State: 82:[92, 10], Operations: ['28-19=9', '90/9=10'] Exploring Operation: 92-10=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[28, 90, 19, 92], Operations: [] Exploring Operation: 28-19=9, Resulting Numbers: [90, 92, 9] Generated Node #0,0: 82:[90, 92, 9] Operation: 28-19=9 Exploring Operation: 28+19=47, Resulting Numbers: [90, 92, 47] Generated Node #0,1: 82:[90, 92, 47] Operation: 28+19=47 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[90, 92, 47], Operations: ['28+19=47'] Exploring Operation: 90-47=43, Resulting Numbers: [92, 43] Generated Node #0,1,0: 82:[92, 43] Operation: 90-47=43 Exploring Operation: 92-90=2, Resulting Numbers: [47, 2] Generated Node #0,1,1: 82:[47, 2] Operation: 92-90=2 Moving to Node #0,1,1 Current State: 82:[47, 2], Operations: ['28+19=47', '92-90=2'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,82 unequal: No Solution Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[92, 43], Operations: ['28+19=47', '90-47=43'] Exploring Operation: 92-43=49, Resulting Numbers: [49] 49,82 unequal: No Solution Exploring Operation: 92+43=135, Resulting Numbers: [135] 135,82 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:[90, 92, 9], Operations: ['28-19=9'] Exploring Operation: 92-9=83, Resulting Numbers: [90, 83] Generated Node #0,0,0: 82:[90, 83] Operation: 92-9=83 Exploring Operation: 92-90=2, Resulting Numbers: [9, 2] Generated Node #0,0,1: 82:[9, 2] Operation: 92-90=2 Moving to Node #0,0,1 Current State: 82:[9, 2], Operations: ['28-19=9', '92-90=2'] Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[90, 83], Operations: ['28-19=9', '92-9=83'] Exploring Operation: 90-83=7, Resulting Numbers: [7] 7,82 unequal: No Solution Exploring Operation: 90+83=173, Resulting Numbers: [173] 173,82 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
[ 33, 74, 47, 13 ]
74
[ "47-33=14", "14-13=1", "74*1=74" ]
Current State: 74:[33, 74, 47, 13], Operations: [] Exploring Operation: 47-33=14, Resulting Numbers: [74, 13, 14] Generated Node #2: [74, 13, 14] from Operation: 47-33=14 Current State: 74:[74, 13, 14], Operations: ['47-33=14'] Exploring Operation: 14-13=1, Resulting Numbers: [74, 1] Generated Node #3: [74, 1] from Operation: 14-13=1 Current State: 74:[74, 1], Operations: ['47-33=14', '14-13=1'] Exploring Operation: 74*1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[33, 74, 47, 13], Operations: [] Exploring Operation: 33+47=80, Resulting Numbers: [74, 13, 80] Generated Node #0,0: 74:[74, 13, 80] Operation: 33+47=80 Exploring Operation: 47+13=60, Resulting Numbers: [33, 74, 60] Generated Node #0,1: 74:[33, 74, 60] Operation: 47+13=60 Exploring Operation: 47-13=34, Resulting Numbers: [33, 74, 34] Generated Node #0,2: 74:[33, 74, 34] Operation: 47-13=34 Moving to Node #0,2 Current State: 74:[33, 74, 34], Operations: ['47-13=34'] Exploring Operation: 33+34=67, Resulting Numbers: [74, 67] Generated Node #0,2,0: 74:[74, 67] Operation: 33+34=67 Exploring Operation: 74-33=41, Resulting Numbers: [34, 41] Generated Node #0,2,1: 74:[34, 41] Operation: 74-33=41 Exploring Operation: 34-33=1, Resulting Numbers: [74, 1] Generated Node #0,2,2: 74:[74, 1] Operation: 34-33=1 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 74:[74, 1], Operations: ['47-13=34', '34-33=1'] Exploring Operation: 74*1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[33, 74, 47, 13], Operations: [] Exploring Operation: 47-13=34, Resulting Numbers: [33, 74, 34] Generated Node #0,2: 74:[33, 74, 34] Operation: 47-13=34 Moving to Node #0,2 Current State: 74:[33, 74, 34], Operations: ['47-13=34'] Exploring Operation: 34-33=1, Resulting Numbers: [74, 1] Generated Node #0,2,2: 74:[74, 1] Operation: 34-33=1 Moving to Node #0,2,2 Current State: 74:[74, 1], Operations: ['47-13=34', '34-33=1'] Exploring Operation: 74*1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 54, 77, 59, 5 ]
52
[ "59-54=5", "5*5=25", "77-25=52" ]
Current State: 52:[54, 77, 59, 5], Operations: [] Exploring Operation: 59-54=5, Resulting Numbers: [77, 5, 5] Generated Node #2: [77, 5, 5] from Operation: 59-54=5 Current State: 52:[77, 5, 5], Operations: ['59-54=5'] Exploring Operation: 5*5=25, Resulting Numbers: [77, 25] Generated Node #3: [77, 25] from Operation: 5*5=25 Current State: 52:[77, 25], Operations: ['59-54=5', '5*5=25'] Exploring Operation: 77-25=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[54, 77, 59, 5], Operations: [] Exploring Operation: 59-54=5, Resulting Numbers: [77, 5, 5] Generated Node #0,0: 52:[77, 5, 5] Operation: 59-54=5 Exploring Operation: 77-5=72, Resulting Numbers: [54, 59, 72] Generated Node #0,1: 52:[54, 59, 72] Operation: 77-5=72 Exploring Operation: 77-59=18, Resulting Numbers: [54, 5, 18] Generated Node #0,2: 52:[54, 5, 18] Operation: 77-59=18 Exploring Operation: 77-54=23, Resulting Numbers: [59, 5, 23] Generated Node #0,3: 52:[59, 5, 23] Operation: 77-54=23 Moving to Node #0,2 Current State: 52:[54, 5, 18], Operations: ['77-59=18'] Exploring Operation: 54/18=3, Resulting Numbers: [5, 3] Generated Node #0,2,0: 52:[5, 3] Operation: 54/18=3 Exploring Operation: 54-5=49, Resulting Numbers: [18, 49] Generated Node #0,2,1: 52:[18, 49] Operation: 54-5=49 Exploring Operation: 18-5=13, Resulting Numbers: [54, 13] Generated Node #0,2,2: 52:[54, 13] Operation: 18-5=13 Exploring Operation: 5+18=23, Resulting Numbers: [54, 23] Generated Node #0,2,3: 52:[54, 23] Operation: 5+18=23 Moving to Node #0,3 Current State: 52:[59, 5, 23], Operations: ['77-54=23'] Exploring Operation: 23-5=18, Resulting Numbers: [59, 18] Generated Node #0,3,0: 52:[59, 18] Operation: 23-5=18 Exploring Operation: 59-23=36, Resulting Numbers: [5, 36] Generated Node #0,3,1: 52:[5, 36] Operation: 59-23=36 Exploring Operation: 59-5=54, Resulting Numbers: [23, 54] Generated Node #0,3,2: 52:[23, 54] Operation: 59-5=54 Exploring Operation: 5+23=28, Resulting Numbers: [59, 28] Generated Node #0,3,3: 52:[59, 28] Operation: 5+23=28 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 52:[23, 54], Operations: ['77-54=23', '59-5=54'] Exploring Operation: 23*54=1242, Resulting Numbers: [1242] 1242,52 unequal: No Solution Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,52 unequal: No Solution Exploring Operation: 23+54=77, Resulting Numbers: [77] 77,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 52:[59, 28], Operations: ['77-54=23', '5+23=28'] Exploring Operation: 59*28=1652, Resulting Numbers: [1652] 1652,52 unequal: No Solution Exploring Operation: 59+28=87, Resulting Numbers: [87] 87,52 unequal: No Solution Exploring Operation: 59-28=31, Resulting Numbers: [31] 31,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 52:[5, 36], Operations: ['77-54=23', '59-23=36'] Exploring Operation: 5+36=41, Resulting Numbers: [41] 41,52 unequal: No Solution Exploring Operation: 5*36=180, Resulting Numbers: [180] 180,52 unequal: No Solution Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 52:[59, 18], Operations: ['77-54=23', '23-5=18'] Exploring Operation: 59-18=41, Resulting Numbers: [41] 41,52 unequal: No Solution Exploring Operation: 59*18=1062, Resulting Numbers: [1062] 1062,52 unequal: No Solution Exploring Operation: 59+18=77, Resulting Numbers: [77] 77,52 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: 52:[77, 5, 5], Operations: ['59-54=5'] Exploring Operation: 77-5=72, Resulting Numbers: [5, 72] Generated Node #0,0,0: 52:[5, 72] Operation: 77-5=72 Exploring Operation: 5*5=25, Resulting Numbers: [77, 25] Generated Node #0,0,1: 52:[77, 25] Operation: 5*5=25 Exploring Operation: 5/5=1, Resulting Numbers: [77, 1] Generated Node #0,0,2: 52:[77, 1] Operation: 5/5=1 Exploring Operation: 77-5=72, Resulting Numbers: [5, 72] Generated Node #0,0,3: 52:[5, 72] Operation: 77-5=72 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[5, 72], Operations: ['59-54=5', '77-5=72'] Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,52 unequal: No Solution Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,52 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 52:[5, 72], Operations: ['59-54=5', '77-5=72'] Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,52 unequal: No Solution Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,52 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 52:[77, 25], Operations: ['59-54=5', '5*5=25'] Exploring Operation: 77+25=102, Resulting Numbers: [102] 102,52 unequal: No Solution Exploring Operation: 77*25=1925, Resulting Numbers: [1925] 1925,52 unequal: No Solution Exploring Operation: 77-25=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[54, 77, 59, 5], Operations: [] Exploring Operation: 59-54=5, Resulting Numbers: [77, 5, 5] Generated Node #0,0: 52:[77, 5, 5] Operation: 59-54=5 Moving to Node #0,0 Current State: 52:[77, 5, 5], Operations: ['59-54=5'] Exploring Operation: 5*5=25, Resulting Numbers: [77, 25] Generated Node #0,0,1: 52:[77, 25] Operation: 5*5=25 Moving to Node #0,0,1 Current State: 52:[77, 25], Operations: ['59-54=5', '5*5=25'] Exploring Operation: 77-25=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_4
sum_heuristic
[ 7, 27, 77, 47 ]
50
[ "27-7=20", "77-47=30", "20+30=50" ]
Current State: 50:[7, 27, 77, 47], Operations: [] Exploring Operation: 27-7=20, Resulting Numbers: [77, 47, 20] Generated Node #2: [77, 47, 20] from Operation: 27-7=20 Current State: 50:[77, 47, 20], Operations: ['27-7=20'] Exploring Operation: 77-47=30, Resulting Numbers: [20, 30] Generated Node #3: [20, 30] from Operation: 77-47=30 Current State: 50:[20, 30], Operations: ['27-7=20', '77-47=30'] Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[7, 27, 77, 47], Operations: [] Exploring Operation: 77-27=50, Resulting Numbers: [7, 47, 50] Generated Node #0,0: 50:[7, 47, 50] Operation: 77-27=50 Exploring Operation: 77/7=11, Resulting Numbers: [27, 47, 11] Generated Node #0,1: 50:[27, 47, 11] Operation: 77/7=11 Exploring Operation: 77-47=30, Resulting Numbers: [7, 27, 30] Generated Node #0,2: 50:[7, 27, 30] Operation: 77-47=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[7, 47, 50], Operations: ['77-27=50'] Exploring Operation: 50-47=3, Resulting Numbers: [7, 3] Generated Node #0,0,0: 50:[7, 3] Operation: 50-47=3 Exploring Operation: 47-7=40, Resulting Numbers: [50, 40] Generated Node #0,0,1: 50:[50, 40] Operation: 47-7=40 Exploring Operation: 7+47=54, Resulting Numbers: [50, 54] Generated Node #0,0,2: 50:[50, 54] Operation: 7+47=54 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 50:[7, 3], Operations: ['77-27=50', '50-47=3'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,50 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 50:[50, 54], Operations: ['77-27=50', '7+47=54'] Exploring Operation: 50*54=2700, Resulting Numbers: [2700] 2700,50 unequal: No Solution Exploring Operation: 54-50=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 50+54=104, Resulting Numbers: [104] 104,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 50:[50, 40], Operations: ['77-27=50', '47-7=40'] Exploring Operation: 50*40=2000, Resulting Numbers: [2000] 2000,50 unequal: No Solution Exploring Operation: 50+40=90, Resulting Numbers: [90] 90,50 unequal: No Solution Exploring Operation: 50-40=10, Resulting Numbers: [10] 10,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[27, 47, 11], Operations: ['77/7=11'] Exploring Operation: 27-11=16, Resulting Numbers: [47, 16] Generated Node #0,1,0: 50:[47, 16] Operation: 27-11=16 Exploring Operation: 47+11=58, Resulting Numbers: [27, 58] Generated Node #0,1,1: 50:[27, 58] Operation: 47+11=58 Exploring Operation: 47-27=20, Resulting Numbers: [11, 20] Generated Node #0,1,2: 50:[11, 20] Operation: 47-27=20 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 50:[11, 20], Operations: ['77/7=11', '47-27=20'] Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,50 unequal: No Solution Exploring Operation: 11+20=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 11*20=220, Resulting Numbers: [220] 220,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 50:[47, 16], Operations: ['77/7=11', '27-11=16'] Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 47+16=63, Resulting Numbers: [63] 63,50 unequal: No Solution Exploring Operation: 47*16=752, Resulting Numbers: [752] 752,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 50:[27, 58], Operations: ['77/7=11', '47+11=58'] Exploring Operation: 27*58=1566, Resulting Numbers: [1566] 1566,50 unequal: No Solution Exploring Operation: 27+58=85, Resulting Numbers: [85] 85,50 unequal: No Solution Exploring Operation: 58-27=31, Resulting Numbers: [31] 31,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 50:[7, 27, 30], Operations: ['77-47=30'] Exploring Operation: 30-27=3, Resulting Numbers: [7, 3] Generated Node #0,2,0: 50:[7, 3] Operation: 30-27=3 Exploring Operation: 30-7=23, Resulting Numbers: [27, 23] Generated Node #0,2,1: 50:[27, 23] Operation: 30-7=23 Exploring Operation: 27+30=57, Resulting Numbers: [7, 57] Generated Node #0,2,2: 50:[7, 57] Operation: 27+30=57 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 50:[7, 3], Operations: ['77-47=30', '30-27=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,50 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 50:[27, 23], Operations: ['77-47=30', '30-7=23'] Exploring Operation: 27+23=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[7, 27, 77, 47], Operations: [] Exploring Operation: 77-47=30, Resulting Numbers: [7, 27, 30] Generated Node #0,2: 50:[7, 27, 30] Operation: 77-47=30 Moving to Node #0,2 Current State: 50:[7, 27, 30], Operations: ['77-47=30'] Exploring Operation: 30-7=23, Resulting Numbers: [27, 23] Generated Node #0,2,1: 50:[27, 23] Operation: 30-7=23 Moving to Node #0,2,1 Current State: 50:[27, 23], Operations: ['77-47=30', '30-7=23'] Exploring Operation: 27+23=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_3
sum_heuristic
[ 34, 4, 33, 3 ]
10
[ "4*33=132", "132/3=44", "44-34=10" ]
Current State: 10:[34, 4, 33, 3], Operations: [] Exploring Operation: 4*33=132, Resulting Numbers: [34, 3, 132] Generated Node #2: [34, 3, 132] from Operation: 4*33=132 Current State: 10:[34, 3, 132], Operations: ['4*33=132'] Exploring Operation: 132/3=44, Resulting Numbers: [34, 44] Generated Node #3: [34, 44] from Operation: 132/3=44 Current State: 10:[34, 44], Operations: ['4*33=132', '132/3=44'] Exploring Operation: 44-34=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[34, 4, 33, 3], Operations: [] Exploring Operation: 34-4=30, Resulting Numbers: [33, 3, 30] Generated Node #0,0: 10:[33, 3, 30] Operation: 34-4=30 Exploring Operation: 34-33=1, Resulting Numbers: [4, 3, 1] Generated Node #0,1: 10:[4, 3, 1] Operation: 34-33=1 Exploring Operation: 33/3=11, Resulting Numbers: [34, 4, 11] Generated Node #0,2: 10:[34, 4, 11] Operation: 33/3=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[4, 3, 1], Operations: ['34-33=1'] Exploring Operation: 4-3=1, Resulting Numbers: [1, 1] Generated Node #0,1,0: 10:[1, 1] Operation: 4-3=1 Exploring Operation: 4+1=5, Resulting Numbers: [3, 5] Generated Node #0,1,1: 10:[3, 5] Operation: 4+1=5 Exploring Operation: 3-1=2, Resulting Numbers: [4, 2] Generated Node #0,1,2: 10:[4, 2] Operation: 3-1=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 10:[3, 5], Operations: ['34-33=1', '4+1=5'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,10 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 10:[4, 2], Operations: ['34-33=1', '3-1=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 10:[1, 1], Operations: ['34-33=1', '4-3=1'] Exploring Operation: 1/1=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 1*1=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 1+1=2, Resulting Numbers: [2] 2,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 10:[34, 4, 11], Operations: ['33/3=11'] Exploring Operation: 34-4=30, Resulting Numbers: [11, 30] Generated Node #0,2,0: 10:[11, 30] Operation: 34-4=30 Exploring Operation: 34-11=23, Resulting Numbers: [4, 23] Generated Node #0,2,1: 10:[4, 23] Operation: 34-11=23 Exploring Operation: 11-4=7, Resulting Numbers: [34, 7] Generated Node #0,2,2: 10:[34, 7] Operation: 11-4=7 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 10:[4, 23], Operations: ['33/3=11', '34-11=23'] Exploring Operation: 4*23=92, Resulting Numbers: [92] 92,10 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,10 unequal: No Solution Exploring Operation: 4+23=27, Resulting Numbers: [27] 27,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 10:[11, 30], Operations: ['33/3=11', '34-4=30'] Exploring Operation: 11*30=330, Resulting Numbers: [330] 330,10 unequal: No Solution Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,10 unequal: No Solution Exploring Operation: 11+30=41, Resulting Numbers: [41] 41,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 10:[34, 7], Operations: ['33/3=11', '11-4=7'] Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,10 unequal: No Solution Exploring Operation: 34+7=41, Resulting Numbers: [41] 41,10 unequal: No Solution Exploring Operation: 34*7=238, Resulting Numbers: [238] 238,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[33, 3, 30], Operations: ['34-4=30'] Exploring Operation: 33-30=3, Resulting Numbers: [3, 3] Generated Node #0,0,0: 10:[3, 3] Operation: 33-30=3 Exploring Operation: 30/3=10, Resulting Numbers: [33, 10] Generated Node #0,0,1: 10:[33, 10] Operation: 30/3=10 Exploring Operation: 33/3=11, Resulting Numbers: [30, 11] Generated Node #0,0,2: 10:[30, 11] Operation: 33/3=11 Moving to Node #0,0,0 Current State: 10:[3, 3], Operations: ['34-4=30', '33-30=3'] Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,10 unequal: No Solution Moving to Node #0,0,2 Current State: 10:[30, 11], Operations: ['34-4=30', '33/3=11'] Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,10 unequal: No Solution Exploring Operation: 30+11=41, Resulting Numbers: [41] 41,10 unequal: No Solution Exploring Operation: 30*11=330, Resulting Numbers: [330] 330,10 unequal: No Solution Moving to Node #0,0,1 Current State: 10:[33, 10], Operations: ['34-4=30', '30/3=10'] Exploring Operation: 33*10=330, Resulting Numbers: [330] 330,10 unequal: No Solution Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,10 unequal: No Solution Exploring Operation: 33+10=43, Resulting Numbers: [43] 43,10 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
[ 52, 7, 76, 74 ]
43
[ "52-7=45", "76-74=2", "45-2=43" ]
Current State: 43:[52, 7, 76, 74], Operations: [] Exploring Operation: 52-7=45, Resulting Numbers: [76, 74, 45] Generated Node #2: [76, 74, 45] from Operation: 52-7=45 Current State: 43:[76, 74, 45], Operations: ['52-7=45'] Exploring Operation: 76-74=2, Resulting Numbers: [45, 2] Generated Node #3: [45, 2] from Operation: 76-74=2 Current State: 43:[45, 2], Operations: ['52-7=45', '76-74=2'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[52, 7, 76, 74], Operations: [] Exploring Operation: 52-7=45, Resulting Numbers: [76, 74, 45] Generated Node #0,0: 43:[76, 74, 45] Operation: 52-7=45 Exploring Operation: 76-7=69, Resulting Numbers: [52, 74, 69] Generated Node #0,1: 43:[52, 74, 69] Operation: 76-7=69 Exploring Operation: 74-7=67, Resulting Numbers: [52, 76, 67] Generated Node #0,2: 43:[52, 76, 67] Operation: 74-7=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[76, 74, 45], Operations: ['52-7=45'] Exploring Operation: 76-74=2, Resulting Numbers: [45, 2] Generated Node #0,0,0: 43:[45, 2] Operation: 76-74=2 Exploring Operation: 76-45=31, Resulting Numbers: [74, 31] Generated Node #0,0,1: 43:[74, 31] Operation: 76-45=31 Exploring Operation: 74-45=29, Resulting Numbers: [76, 29] Generated Node #0,0,2: 43:[76, 29] Operation: 74-45=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[45, 2], Operations: ['52-7=45', '76-74=2'] Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,43 unequal: No Solution Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[52, 7, 76, 74], Operations: [] Exploring Operation: 52-7=45, Resulting Numbers: [76, 74, 45] Generated Node #0,0: 43:[76, 74, 45] Operation: 52-7=45 Moving to Node #0,0 Current State: 43:[76, 74, 45], Operations: ['52-7=45'] Exploring Operation: 76-74=2, Resulting Numbers: [45, 2] Generated Node #0,0,0: 43:[45, 2] Operation: 76-74=2 Moving to Node #0,0,0 Current State: 43:[45, 2], Operations: ['52-7=45', '76-74=2'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 18, 26, 27, 21 ]
82
[ "27-21=6", "18*6=108", "108-26=82" ]
Current State: 82:[18, 26, 27, 21], Operations: [] Exploring Operation: 27-21=6, Resulting Numbers: [18, 26, 6] Generated Node #2: [18, 26, 6] from Operation: 27-21=6 Current State: 82:[18, 26, 6], Operations: ['27-21=6'] Exploring Operation: 18*6=108, Resulting Numbers: [26, 108] Generated Node #3: [26, 108] from Operation: 18*6=108 Current State: 82:[26, 108], Operations: ['27-21=6', '18*6=108'] Exploring Operation: 108-26=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[18, 26, 27, 21], Operations: [] Exploring Operation: 21-18=3, Resulting Numbers: [26, 27, 3] Generated Node #0,0: 82:[26, 27, 3] Operation: 21-18=3 Exploring Operation: 18+21=39, Resulting Numbers: [26, 27, 39] Generated Node #0,1: 82:[26, 27, 39] Operation: 18+21=39 Moving to Node #0,0 Current State: 82:[26, 27, 3], Operations: ['21-18=3'] Exploring Operation: 26+27=53, Resulting Numbers: [3, 53] Generated Node #0,0,0: 82:[3, 53] Operation: 26+27=53 Exploring Operation: 27-26=1, Resulting Numbers: [3, 1] Generated Node #0,0,1: 82:[3, 1] Operation: 27-26=1 Moving to Node #0,1 Current State: 82:[26, 27, 39], Operations: ['18+21=39'] Exploring Operation: 26+27=53, Resulting Numbers: [39, 53] Generated Node #0,1,0: 82:[39, 53] Operation: 26+27=53 Exploring Operation: 27-26=1, Resulting Numbers: [39, 1] Generated Node #0,1,1: 82:[39, 1] Operation: 27-26=1 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 82:[39, 1], Operations: ['18+21=39', '27-26=1'] Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,82 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,82 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 #0,1,0 Current State: 82:[39, 53], Operations: ['18+21=39', '26+27=53'] Exploring Operation: 53-39=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 39+53=92, Resulting Numbers: [92] 92,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 82:[3, 1], Operations: ['21-18=3', '27-26=1'] Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[3, 53], Operations: ['21-18=3', '26+27=53'] Exploring Operation: 3+53=56, Resulting Numbers: [56] 56,82 unequal: No Solution Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,82 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 56, 68, 31, 71 ]
29
[ "56+31=87", "71-68=3", "87/3=29" ]
Current State: 29:[56, 68, 31, 71], Operations: [] Exploring Operation: 56+31=87, Resulting Numbers: [68, 71, 87] Generated Node #2: [68, 71, 87] from Operation: 56+31=87 Current State: 29:[68, 71, 87], Operations: ['56+31=87'] Exploring Operation: 71-68=3, Resulting Numbers: [87, 3] Generated Node #3: [87, 3] from Operation: 71-68=3 Current State: 29:[87, 3], Operations: ['56+31=87', '71-68=3'] Exploring Operation: 87/3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[56, 68, 31, 71], Operations: [] Exploring Operation: 71-56=15, Resulting Numbers: [68, 31, 15] Generated Node #0,0: 29:[68, 31, 15] Operation: 71-56=15 Moving to Node #0,0 Current State: 29:[68, 31, 15], Operations: ['71-56=15'] Exploring Operation: 68-31=37, Resulting Numbers: [15, 37] Generated Node #0,0,0: 29:[15, 37] Operation: 68-31=37 Moving to Node #0,0,0 Current State: 29:[15, 37], Operations: ['71-56=15', '68-31=37'] Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,29 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 34, 12, 62, 9 ]
75
[ "34-12=22", "62-9=53", "22+53=75" ]
Current State: 75:[34, 12, 62, 9], Operations: [] Exploring Operation: 34-12=22, Resulting Numbers: [62, 9, 22] Generated Node #2: [62, 9, 22] from Operation: 34-12=22 Current State: 75:[62, 9, 22], Operations: ['34-12=22'] Exploring Operation: 62-9=53, Resulting Numbers: [22, 53] Generated Node #3: [22, 53] from Operation: 62-9=53 Current State: 75:[22, 53], Operations: ['34-12=22', '62-9=53'] Exploring Operation: 22+53=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[34, 12, 62, 9], Operations: [] Exploring Operation: 12+62=74, Resulting Numbers: [34, 9, 74] Generated Node #0,0: 75:[34, 9, 74] Operation: 12+62=74 Exploring Operation: 62+9=71, Resulting Numbers: [34, 12, 71] Generated Node #0,1: 75:[34, 12, 71] Operation: 62+9=71 Exploring Operation: 34-9=25, Resulting Numbers: [12, 62, 25] Generated Node #0,2: 75:[12, 62, 25] Operation: 34-9=25 Exploring Operation: 62-34=28, Resulting Numbers: [12, 9, 28] Generated Node #0,3: 75:[12, 9, 28] Operation: 62-34=28 Start Sub Search at level 1: Moving to Node #0,3 Current State: 75:[12, 9, 28], Operations: ['62-34=28'] Exploring Operation: 28-12=16, Resulting Numbers: [9, 16] Generated Node #0,3,0: 75:[9, 16] Operation: 28-12=16 Exploring Operation: 28-9=19, Resulting Numbers: [12, 19] Generated Node #0,3,1: 75:[12, 19] Operation: 28-9=19 Exploring Operation: 12-9=3, Resulting Numbers: [28, 3] Generated Node #0,3,2: 75:[28, 3] Operation: 12-9=3 Exploring Operation: 12+9=21, Resulting Numbers: [28, 21] Generated Node #0,3,3: 75:[28, 21] Operation: 12+9=21 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 75:[28, 3], Operations: ['62-34=28', '12-9=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,75 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 75:[9, 16], Operations: ['62-34=28', '28-12=16'] Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,75 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 75:[12, 19], Operations: ['62-34=28', '28-9=19'] Exploring Operation: 12*19=228, Resulting Numbers: [228] 228,75 unequal: No Solution Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 75:[28, 21], Operations: ['62-34=28', '12+9=21'] Exploring Operation: 28*21=588, Resulting Numbers: [588] 588,75 unequal: No Solution Exploring Operation: 28+21=49, Resulting Numbers: [49] 49,75 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[34, 9, 74], Operations: ['12+62=74'] Exploring Operation: 74-34=40, Resulting Numbers: [9, 40] Generated Node #0,0,0: 75:[9, 40] Operation: 74-34=40 Exploring Operation: 9+74=83, Resulting Numbers: [34, 83] Generated Node #0,0,1: 75:[34, 83] Operation: 9+74=83 Exploring Operation: 34+9=43, Resulting Numbers: [74, 43] Generated Node #0,0,2: 75:[74, 43] Operation: 34+9=43 Exploring Operation: 34-9=25, Resulting Numbers: [74, 25] Generated Node #0,0,3: 75:[74, 25] Operation: 34-9=25 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 75:[74, 25], Operations: ['12+62=74', '34-9=25'] Exploring Operation: 74*25=1850, Resulting Numbers: [1850] 1850,75 unequal: No Solution Exploring Operation: 74-25=49, Resulting Numbers: [49] 49,75 unequal: No Solution Exploring Operation: 74+25=99, Resulting Numbers: [99] 99,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 75:[34, 83], Operations: ['12+62=74', '9+74=83'] Exploring Operation: 34*83=2822, Resulting Numbers: [2822] 2822,75 unequal: No Solution Exploring Operation: 34+83=117, Resulting Numbers: [117] 117,75 unequal: No Solution Exploring Operation: 83-34=49, Resulting Numbers: [49] 49,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[9, 40], Operations: ['12+62=74', '74-34=40'] Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 9*40=360, Resulting Numbers: [360] 360,75 unequal: No Solution Exploring Operation: 9+40=49, Resulting Numbers: [49] 49,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 75:[74, 43], Operations: ['12+62=74', '34+9=43'] Exploring Operation: 74*43=3182, Resulting Numbers: [3182] 3182,75 unequal: No Solution Exploring Operation: 74-43=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 74+43=117, Resulting Numbers: [117] 117,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[34, 12, 71], Operations: ['62+9=71'] Exploring Operation: 12+71=83, Resulting Numbers: [34, 83] Generated Node #0,1,0: 75:[34, 83] Operation: 12+71=83 Exploring Operation: 34-12=22, Resulting Numbers: [71, 22] Generated Node #0,1,1: 75:[71, 22] Operation: 34-12=22 Exploring Operation: 71-34=37, Resulting Numbers: [12, 37] Generated Node #0,1,2: 75:[12, 37] Operation: 71-34=37 Exploring Operation: 34+12=46, Resulting Numbers: [71, 46] Generated Node #0,1,3: 75:[71, 46] Operation: 34+12=46 Moving to Node #0,1,1 Current State: 75:[71, 22], Operations: ['62+9=71', '34-12=22'] Exploring Operation: 71-22=49, Resulting Numbers: [49] 49,75 unequal: No Solution Exploring Operation: 71+22=93, Resulting Numbers: [93] 93,75 unequal: No Solution Exploring Operation: 71*22=1562, Resulting Numbers: [1562] 1562,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[12, 37], Operations: ['62+9=71', '71-34=37'] Exploring Operation: 12*37=444, Resulting Numbers: [444] 444,75 unequal: No Solution Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,75 unequal: No Solution Exploring Operation: 12+37=49, Resulting Numbers: [49] 49,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[34, 83], Operations: ['62+9=71', '12+71=83'] Exploring Operation: 34+83=117, Resulting Numbers: [117] 117,75 unequal: No Solution Exploring Operation: 34*83=2822, Resulting Numbers: [2822] 2822,75 unequal: No Solution Exploring Operation: 83-34=49, Resulting Numbers: [49] 49,75 unequal: No Solution Moving to Node #0,1,3 Current State: 75:[71, 46], Operations: ['62+9=71', '34+12=46'] Exploring Operation: 71*46=3266, Resulting Numbers: [3266] 3266,75 unequal: No Solution Exploring Operation: 71+46=117, Resulting Numbers: [117] 117,75 unequal: No Solution Exploring Operation: 71-46=25, Resulting Numbers: [25] 25,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[12, 62, 25], Operations: ['34-9=25'] Exploring Operation: 62-25=37, Resulting Numbers: [12, 37] Generated Node #0,2,0: 75:[12, 37] Operation: 62-25=37 Exploring Operation: 12+62=74, Resulting Numbers: [25, 74] Generated Node #0,2,1: 75:[25, 74] Operation: 12+62=74 Exploring Operation: 62+25=87, Resulting Numbers: [12, 87] Generated Node #0,2,2: 75:[12, 87] Operation: 62+25=87 Exploring Operation: 25-12=13, Resulting Numbers: [62, 13] Generated Node #0,2,3: 75:[62, 13] Operation: 25-12=13 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 75:[25, 74], Operations: ['34-9=25', '12+62=74'] Exploring Operation: 25*74=1850, Resulting Numbers: [1850] 1850,75 unequal: No Solution Exploring Operation: 74-25=49, Resulting Numbers: [49] 49,75 unequal: No Solution Exploring Operation: 25+74=99, Resulting Numbers: [99] 99,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 75:[12, 37], Operations: ['34-9=25', '62-25=37'] Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,75 unequal: No Solution Exploring Operation: 12+37=49, Resulting Numbers: [49] 49,75 unequal: No Solution Exploring Operation: 12*37=444, Resulting Numbers: [444] 444,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 75:[12, 87], Operations: ['34-9=25', '62+25=87'] Exploring Operation: 12*87=1044, Resulting Numbers: [1044] 1044,75 unequal: No Solution Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[34, 12, 62, 9], Operations: [] Exploring Operation: 34-9=25, Resulting Numbers: [12, 62, 25] Generated Node #0,2: 75:[12, 62, 25] Operation: 34-9=25 Moving to Node #0,2 Current State: 75:[12, 62, 25], Operations: ['34-9=25'] Exploring Operation: 62+25=87, Resulting Numbers: [12, 87] Generated Node #0,2,2: 75:[12, 87] Operation: 62+25=87 Moving to Node #0,2,2 Current State: 75:[12, 87], Operations: ['34-9=25', '62+25=87'] Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.940972
hs_4
sum_heuristic
[ 63, 91, 77, 6 ]
91
[ "91-63=28", "6*28=168", "168-77=91" ]
Current State: 91:[63, 91, 77, 6], Operations: [] Exploring Operation: 91-63=28, Resulting Numbers: [77, 6, 28] Generated Node #2: [77, 6, 28] from Operation: 91-63=28 Current State: 91:[77, 6, 28], Operations: ['91-63=28'] Exploring Operation: 6*28=168, Resulting Numbers: [77, 168] Generated Node #3: [77, 168] from Operation: 6*28=168 Current State: 91:[77, 168], Operations: ['91-63=28', '6*28=168'] Exploring Operation: 168-77=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[63, 91, 77, 6], Operations: [] Exploring Operation: 77-63=14, Resulting Numbers: [91, 6, 14] Generated Node #0,0: 91:[91, 6, 14] Operation: 77-63=14 Exploring Operation: 91-63=28, Resulting Numbers: [77, 6, 28] Generated Node #0,1: 91:[77, 6, 28] Operation: 91-63=28 Exploring Operation: 91-77=14, Resulting Numbers: [63, 6, 14] Generated Node #0,2: 91:[63, 6, 14] Operation: 91-77=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[91, 6, 14], Operations: ['77-63=14'] Exploring Operation: 91-6=85, Resulting Numbers: [14, 85] Generated Node #0,0,0: 91:[14, 85] Operation: 91-6=85 Exploring Operation: 91+6=97, Resulting Numbers: [14, 97] Generated Node #0,0,1: 91:[14, 97] Operation: 91+6=97 Exploring Operation: 14-6=8, Resulting Numbers: [91, 8] Generated Node #0,0,2: 91:[91, 8] Operation: 14-6=8 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 91:[91, 8], Operations: ['77-63=14', '14-6=8'] Exploring Operation: 91+8=99, Resulting Numbers: [99] 99,91 unequal: No Solution Exploring Operation: 91*8=728, Resulting Numbers: [728] 728,91 unequal: No Solution Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[14, 85], Operations: ['77-63=14', '91-6=85'] Exploring Operation: 14*85=1190, Resulting Numbers: [1190] 1190,91 unequal: No Solution Exploring Operation: 85-14=71, Resulting Numbers: [71] 71,91 unequal: No Solution Exploring Operation: 14+85=99, Resulting Numbers: [99] 99,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[14, 97], Operations: ['77-63=14', '91+6=97'] Exploring Operation: 14*97=1358, Resulting Numbers: [1358] 1358,91 unequal: No Solution Exploring Operation: 97-14=83, Resulting Numbers: [83] 83,91 unequal: No Solution Exploring Operation: 14+97=111, Resulting Numbers: [111] 111,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[77, 6, 28], Operations: ['91-63=28'] Exploring Operation: 77+6=83, Resulting Numbers: [28, 83] Generated Node #0,1,0: 91:[28, 83] Operation: 77+6=83 Exploring Operation: 28-6=22, Resulting Numbers: [77, 22] Generated Node #0,1,1: 91:[77, 22] Operation: 28-6=22 Exploring Operation: 77+28=105, Resulting Numbers: [6, 105] Generated Node #0,1,2: 91:[6, 105] Operation: 77+28=105 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 91:[6, 105], Operations: ['91-63=28', '77+28=105'] Exploring Operation: 105-6=99, Resulting Numbers: [99] 99,91 unequal: No Solution Exploring Operation: 6+105=111, Resulting Numbers: [111] 111,91 unequal: No Solution Exploring Operation: 6*105=630, Resulting Numbers: [630] 630,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[28, 83], Operations: ['91-63=28', '77+6=83'] Exploring Operation: 28*83=2324, Resulting Numbers: [2324] 2324,91 unequal: No Solution Exploring Operation: 28+83=111, Resulting Numbers: [111] 111,91 unequal: No Solution Exploring Operation: 83-28=55, Resulting Numbers: [55] 55,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[77, 22], Operations: ['91-63=28', '28-6=22'] Exploring Operation: 77+22=99, Resulting Numbers: [99] 99,91 unequal: No Solution Exploring Operation: 77*22=1694, Resulting Numbers: [1694] 1694,91 unequal: No Solution Exploring Operation: 77-22=55, Resulting Numbers: [55] 55,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[63, 6, 14], Operations: ['91-77=14'] Exploring Operation: 63+6=69, Resulting Numbers: [14, 69] Generated Node #0,2,0: 91:[14, 69] Operation: 63+6=69 Exploring Operation: 14-6=8, Resulting Numbers: [63, 8] Generated Node #0,2,1: 91:[63, 8] Operation: 14-6=8 Exploring Operation: 63+14=77, Resulting Numbers: [6, 77] Generated Node #0,2,2: 91:[6, 77] Operation: 63+14=77 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 91:[6, 77], Operations: ['91-77=14', '63+14=77'] Exploring Operation: 6*77=462, Resulting Numbers: [462] 462,91 unequal: No Solution Exploring Operation: 6+77=83, Resulting Numbers: [83] 83,91 unequal: No Solution Exploring Operation: 77-6=71, Resulting Numbers: [71] 71,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 91:[14, 69], Operations: ['91-77=14', '63+6=69'] Exploring Operation: 14*69=966, Resulting Numbers: [966] 966,91 unequal: No Solution Exploring Operation: 14+69=83, Resulting Numbers: [83] 83,91 unequal: No Solution Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 91:[63, 8], Operations: ['91-77=14', '14-6=8'] Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,91 unequal: No Solution Exploring Operation: 63*8=504, Resulting Numbers: [504] 504,91 unequal: No Solution Exploring Operation: 63+8=71, Resulting Numbers: [71] 71,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 37, 46, 48, 54 ]
64
[ "48-46=2", "54/2=27", "37+27=64" ]
Current State: 64:[37, 46, 48, 54], Operations: [] Exploring Operation: 48-46=2, Resulting Numbers: [37, 54, 2] Generated Node #2: [37, 54, 2] from Operation: 48-46=2 Current State: 64:[37, 54, 2], Operations: ['48-46=2'] Exploring Operation: 54/2=27, Resulting Numbers: [37, 27] Generated Node #3: [37, 27] from Operation: 54/2=27 Current State: 64:[37, 27], Operations: ['48-46=2', '54/2=27'] Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[37, 46, 48, 54], Operations: [] Exploring Operation: 54-46=8, Resulting Numbers: [37, 48, 8] Generated Node #0,0: 64:[37, 48, 8] Operation: 54-46=8 Exploring Operation: 48-46=2, Resulting Numbers: [37, 54, 2] Generated Node #0,1: 64:[37, 54, 2] Operation: 48-46=2 Moving to Node #0,1 Current State: 64:[37, 54, 2], Operations: ['48-46=2'] Exploring Operation: 54-37=17, Resulting Numbers: [2, 17] Generated Node #0,1,0: 64:[2, 17] Operation: 54-37=17 Exploring Operation: 54/2=27, Resulting Numbers: [37, 27] Generated Node #0,1,1: 64:[37, 27] Operation: 54/2=27 Moving to Node #0,0 Current State: 64:[37, 48, 8], Operations: ['54-46=8'] Exploring Operation: 48/8=6, Resulting Numbers: [37, 6] Generated Node #0,0,0: 64:[37, 6] Operation: 48/8=6 Exploring Operation: 48-37=11, Resulting Numbers: [8, 11] Generated Node #0,0,1: 64:[8, 11] Operation: 48-37=11 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 64:[8, 11], Operations: ['54-46=8', '48-37=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,64 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[37, 6], Operations: ['54-46=8', '48/8=6'] Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,64 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,64 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: 64:[2, 17], Operations: ['48-46=2', '54-37=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,64 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,64 unequal: No Solution Moving to Node #0,1,1 Current State: 64:[37, 27], Operations: ['48-46=2', '54/2=27'] Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,64 unequal: No Solution Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[37, 46, 48, 54], Operations: [] Exploring Operation: 48-46=2, Resulting Numbers: [37, 54, 2] Generated Node #0,1: 64:[37, 54, 2] Operation: 48-46=2 Moving to Node #0,1 Current State: 64:[37, 54, 2], Operations: ['48-46=2'] Exploring Operation: 54/2=27, Resulting Numbers: [37, 27] Generated Node #0,1,1: 64:[37, 27] Operation: 54/2=27 Moving to Node #0,1,1 Current State: 64:[37, 27], Operations: ['48-46=2', '54/2=27'] Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
0.984375
hs_2
mult_heuristic
[ 53, 50, 41, 8 ]
18
[ "53+50=103", "41+103=144", "144/8=18" ]
Current State: 18:[53, 50, 41, 8], Operations: [] Exploring Operation: 53+50=103, Resulting Numbers: [41, 8, 103] Generated Node #2: [41, 8, 103] from Operation: 53+50=103 Current State: 18:[41, 8, 103], Operations: ['53+50=103'] Exploring Operation: 41+103=144, Resulting Numbers: [8, 144] Generated Node #3: [8, 144] from Operation: 41+103=144 Current State: 18:[8, 144], Operations: ['53+50=103', '41+103=144'] Exploring Operation: 144/8=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[53, 50, 41, 8], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [41, 8, 3] Generated Node #0,0: 18:[41, 8, 3] Operation: 53-50=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[41, 8, 3], Operations: ['53-50=3'] Exploring Operation: 41-8=33, Resulting Numbers: [3, 33] Generated Node #0,0,0: 18:[3, 33] Operation: 41-8=33 Moving to Node #0,0,0 Current State: 18:[3, 33], Operations: ['53-50=3', '41-8=33'] Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,18 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, 36, 60, 48 ]
82
[ "50*60=3000", "3000-48=2952", "2952/36=82" ]
Current State: 82:[50, 36, 60, 48], Operations: [] Exploring Operation: 50*60=3000, Resulting Numbers: [36, 48, 3000] Generated Node #2: [36, 48, 3000] from Operation: 50*60=3000 Current State: 82:[36, 48, 3000], Operations: ['50*60=3000'] Exploring Operation: 3000-48=2952, Resulting Numbers: [36, 2952] Generated Node #3: [36, 2952] from Operation: 3000-48=2952 Current State: 82:[36, 2952], Operations: ['50*60=3000', '3000-48=2952'] Exploring Operation: 2952/36=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[50, 36, 60, 48], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [36, 60, 2] Generated Node #0,0: 82:[36, 60, 2] Operation: 50-48=2 Exploring Operation: 60-50=10, Resulting Numbers: [36, 48, 10] Generated Node #0,1: 82:[36, 48, 10] Operation: 60-50=10 Moving to Node #0,1 Current State: 82:[36, 48, 10], Operations: ['60-50=10'] Exploring Operation: 48-10=38, Resulting Numbers: [36, 38] Generated Node #0,1,0: 82:[36, 38] Operation: 48-10=38 Exploring Operation: 36+48=84, Resulting Numbers: [10, 84] Generated Node #0,1,1: 82:[10, 84] Operation: 36+48=84 Moving to Node #0,0 Current State: 82:[36, 60, 2], Operations: ['50-48=2'] Exploring Operation: 60/2=30, Resulting Numbers: [36, 30] Generated Node #0,0,0: 82:[36, 30] Operation: 60/2=30 Exploring Operation: 36+60=96, Resulting Numbers: [2, 96] Generated Node #0,0,1: 82:[2, 96] Operation: 36+60=96 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 82:[2, 96], Operations: ['50-48=2', '36+60=96'] Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,82 unequal: No Solution Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,82 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 #0,0,0 Current State: 82:[36, 30], Operations: ['50-48=2', '60/2=30'] Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,82 unequal: No Solution Exploring Operation: 36+30=66, Resulting Numbers: [66] 66,82 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: 82:[36, 38], Operations: ['60-50=10', '48-10=38'] Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 36+38=74, Resulting Numbers: [74] 74,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[10, 84], Operations: ['60-50=10', '36+48=84'] Exploring Operation: 84-10=74, Resulting Numbers: [74] 74,82 unequal: No Solution Exploring Operation: 10+84=94, Resulting Numbers: [94] 94,82 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 85, 51, 12, 50 ]
72
[ "85-51=34", "50-12=38", "34+38=72" ]
Current State: 72:[85, 51, 12, 50], Operations: [] Exploring Operation: 85-51=34, Resulting Numbers: [12, 50, 34] Generated Node #2: [12, 50, 34] from Operation: 85-51=34 Current State: 72:[12, 50, 34], Operations: ['85-51=34'] Exploring Operation: 50-12=38, Resulting Numbers: [34, 38] Generated Node #3: [34, 38] from Operation: 50-12=38 Current State: 72:[34, 38], Operations: ['85-51=34', '50-12=38'] Exploring Operation: 34+38=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[85, 51, 12, 50], Operations: [] Exploring Operation: 51-50=1, Resulting Numbers: [85, 12, 1] Generated Node #0,0: 72:[85, 12, 1] Operation: 51-50=1 Exploring Operation: 85-50=35, Resulting Numbers: [51, 12, 35] Generated Node #0,1: 72:[51, 12, 35] Operation: 85-50=35 Exploring Operation: 85-51=34, Resulting Numbers: [12, 50, 34] Generated Node #0,2: 72:[12, 50, 34] Operation: 85-51=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[85, 12, 1], Operations: ['51-50=1'] Exploring Operation: 85-12=73, Resulting Numbers: [1, 73] Generated Node #0,0,0: 72:[1, 73] Operation: 85-12=73 Exploring Operation: 85*1=85, Resulting Numbers: [12, 85] Generated Node #0,0,1: 72:[12, 85] Operation: 85*1=85 Exploring Operation: 85-1=84, Resulting Numbers: [12, 84] Generated Node #0,0,2: 72:[12, 84] Operation: 85-1=84 Moving to Node #0,0,0 Current State: 72:[1, 73], Operations: ['51-50=1', '85-12=73'] Exploring Operation: 73/1=73, Resulting Numbers: [73] 73,72 unequal: No Solution Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[85, 51, 12, 50], Operations: [] Exploring Operation: 51-50=1, Resulting Numbers: [85, 12, 1] Generated Node #0,0: 72:[85, 12, 1] Operation: 51-50=1 Moving to Node #0,0 Current State: 72:[85, 12, 1], Operations: ['51-50=1'] Exploring Operation: 85-12=73, Resulting Numbers: [1, 73] Generated Node #0,0,0: 72:[1, 73] Operation: 85-12=73 Moving to Node #0,0,0 Current State: 72:[1, 73], Operations: ['51-50=1', '85-12=73'] Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 90, 10, 76, 64 ]
45
[ "76-10=66", "66-64=2", "90/2=45" ]
Current State: 45:[90, 10, 76, 64], Operations: [] Exploring Operation: 76-10=66, Resulting Numbers: [90, 64, 66] Generated Node #2: [90, 64, 66] from Operation: 76-10=66 Current State: 45:[90, 64, 66], Operations: ['76-10=66'] Exploring Operation: 66-64=2, Resulting Numbers: [90, 2] Generated Node #3: [90, 2] from Operation: 66-64=2 Current State: 45:[90, 2], Operations: ['76-10=66', '66-64=2'] Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[90, 10, 76, 64], Operations: [] Exploring Operation: 90-64=26, Resulting Numbers: [10, 76, 26] Generated Node #0,0: 45:[10, 76, 26] Operation: 90-64=26 Exploring Operation: 90-76=14, Resulting Numbers: [10, 64, 14] Generated Node #0,1: 45:[10, 64, 14] Operation: 90-76=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[10, 64, 14], Operations: ['90-76=14'] Exploring Operation: 64-10=54, Resulting Numbers: [14, 54] Generated Node #0,1,0: 45:[14, 54] Operation: 64-10=54 Exploring Operation: 64-14=50, Resulting Numbers: [10, 50] Generated Node #0,1,1: 45:[10, 50] Operation: 64-14=50 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[10, 50], Operations: ['90-76=14', '64-14=50'] Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 50/10=5, Resulting Numbers: [5] 5,45 unequal: No Solution No 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: 45:[14, 54], Operations: ['90-76=14', '64-10=54'] Exploring Operation: 14+54=68, Resulting Numbers: [68] 68,45 unequal: No Solution Exploring Operation: 54-14=40, Resulting Numbers: [40] 40,45 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: 45:[10, 76, 26], Operations: ['90-64=26'] Exploring Operation: 76-10=66, Resulting Numbers: [26, 66] Generated Node #0,0,0: 45:[26, 66] Operation: 76-10=66 Exploring Operation: 76-26=50, Resulting Numbers: [10, 50] Generated Node #0,0,1: 45:[10, 50] Operation: 76-26=50 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 45:[10, 50], Operations: ['90-64=26', '76-26=50'] Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 50/10=5, Resulting Numbers: [5] 5,45 unequal: No Solution No 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: 45:[26, 66], Operations: ['90-64=26', '76-10=66'] Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 26+66=92, Resulting Numbers: [92] 92,45 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
[ 28, 59, 94, 93 ]
31
[ "59-28=31", "94-93=1", "31*1=31" ]
Current State: 31:[28, 59, 94, 93], Operations: [] Exploring Operation: 59-28=31, Resulting Numbers: [94, 93, 31] Generated Node #2: [94, 93, 31] from Operation: 59-28=31 Current State: 31:[94, 93, 31], Operations: ['59-28=31'] Exploring Operation: 94-93=1, Resulting Numbers: [31, 1] Generated Node #3: [31, 1] from Operation: 94-93=1 Current State: 31:[31, 1], Operations: ['59-28=31', '94-93=1'] Exploring Operation: 31*1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[28, 59, 94, 93], Operations: [] Exploring Operation: 94-93=1, Resulting Numbers: [28, 59, 1] Generated Node #0,0: 31:[28, 59, 1] Operation: 94-93=1 Exploring Operation: 59-28=31, Resulting Numbers: [94, 93, 31] Generated Node #0,1: 31:[94, 93, 31] Operation: 59-28=31 Exploring Operation: 94-28=66, Resulting Numbers: [59, 93, 66] Generated Node #0,2: 31:[59, 93, 66] Operation: 94-28=66 Exploring Operation: 94-59=35, Resulting Numbers: [28, 93, 35] Generated Node #0,3: 31:[28, 93, 35] Operation: 94-59=35 Exploring Operation: 93-59=34, Resulting Numbers: [28, 94, 34] Generated Node #0,4: 31:[28, 94, 34] Operation: 93-59=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[28, 59, 1], Operations: ['94-93=1'] Exploring Operation: 59-1=58, Resulting Numbers: [28, 58] Generated Node #0,0,0: 31:[28, 58] Operation: 59-1=58 Exploring Operation: 28+1=29, Resulting Numbers: [59, 29] Generated Node #0,0,1: 31:[59, 29] Operation: 28+1=29 Exploring Operation: 59-28=31, Resulting Numbers: [1, 31] Generated Node #0,0,2: 31:[1, 31] Operation: 59-28=31 Exploring Operation: 28*1=28, Resulting Numbers: [59, 28] Generated Node #0,0,3: 31:[59, 28] Operation: 28*1=28 Exploring Operation: 28/1=28, Resulting Numbers: [59, 28] Generated Node #0,0,4: 31:[59, 28] Operation: 28/1=28 Moving to Node #0,0,0 Current State: 31:[28, 58], Operations: ['94-93=1', '59-1=58'] Exploring Operation: 58-28=30, Resulting Numbers: [30] 30,31 unequal: No Solution Exploring Operation: 28*58=1624, Resulting Numbers: [1624] 1624,31 unequal: No Solution Exploring Operation: 28+58=86, Resulting Numbers: [86] 86,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[1, 31], Operations: ['94-93=1', '59-28=31'] Exploring Operation: 1*31=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[28, 59, 94, 93], Operations: [] Exploring Operation: 94-93=1, Resulting Numbers: [28, 59, 1] Generated Node #0,0: 31:[28, 59, 1] Operation: 94-93=1 Moving to Node #0,0 Current State: 31:[28, 59, 1], Operations: ['94-93=1'] Exploring Operation: 59-28=31, Resulting Numbers: [1, 31] Generated Node #0,0,2: 31:[1, 31] Operation: 59-28=31 Moving to Node #0,0,2 Current State: 31:[1, 31], Operations: ['94-93=1', '59-28=31'] Exploring Operation: 1*31=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 75, 49, 91, 14 ]
79
[ "75-49=26", "91+14=105", "105-26=79" ]
Current State: 79:[75, 49, 91, 14], Operations: [] Exploring Operation: 75-49=26, Resulting Numbers: [91, 14, 26] Generated Node #2: [91, 14, 26] from Operation: 75-49=26 Current State: 79:[91, 14, 26], Operations: ['75-49=26'] Exploring Operation: 91+14=105, Resulting Numbers: [26, 105] Generated Node #3: [26, 105] from Operation: 91+14=105 Current State: 79:[26, 105], Operations: ['75-49=26', '91+14=105'] Exploring Operation: 105-26=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[75, 49, 91, 14], Operations: [] Exploring Operation: 91-14=77, Resulting Numbers: [75, 49, 77] Generated Node #0,0: 79:[75, 49, 77] Operation: 91-14=77 Exploring Operation: 49+14=63, Resulting Numbers: [75, 91, 63] Generated Node #0,1: 79:[75, 91, 63] Operation: 49+14=63 Moving to Node #0,1 Current State: 79:[75, 91, 63], Operations: ['49+14=63'] Exploring Operation: 91-63=28, Resulting Numbers: [75, 28] Generated Node #0,1,0: 79:[75, 28] Operation: 91-63=28 Exploring Operation: 75+63=138, Resulting Numbers: [91, 138] Generated Node #0,1,1: 79:[91, 138] Operation: 75+63=138 Moving to Node #0,0 Current State: 79:[75, 49, 77], Operations: ['91-14=77'] Exploring Operation: 49+77=126, Resulting Numbers: [75, 126] Generated Node #0,0,0: 79:[75, 126] Operation: 49+77=126 Exploring Operation: 75+49=124, Resulting Numbers: [77, 124] Generated Node #0,0,1: 79:[77, 124] Operation: 75+49=124 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[77, 124], Operations: ['91-14=77', '75+49=124'] Exploring Operation: 77+124=201, Resulting Numbers: [201] 201,79 unequal: No Solution Exploring Operation: 124-77=47, Resulting Numbers: [47] 47,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[75, 126], Operations: ['91-14=77', '49+77=126'] Exploring Operation: 126-75=51, Resulting Numbers: [51] 51,79 unequal: No Solution Exploring Operation: 75+126=201, Resulting Numbers: [201] 201,79 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: 79:[75, 28], Operations: ['49+14=63', '91-63=28'] Exploring Operation: 75+28=103, Resulting Numbers: [103] 103,79 unequal: No Solution Exploring Operation: 75-28=47, Resulting Numbers: [47] 47,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[91, 138], Operations: ['49+14=63', '75+63=138'] Exploring Operation: 91+138=229, Resulting Numbers: [229] 229,79 unequal: No Solution Exploring Operation: 138-91=47, Resulting Numbers: [47] 47,79 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 26, 57, 47, 48 ]
83
[ "26+57=83", "48-47=1", "83*1=83" ]
Current State: 83:[26, 57, 47, 48], Operations: [] Exploring Operation: 26+57=83, Resulting Numbers: [47, 48, 83] Generated Node #2: [47, 48, 83] from Operation: 26+57=83 Current State: 83:[47, 48, 83], Operations: ['26+57=83'] Exploring Operation: 48-47=1, Resulting Numbers: [83, 1] Generated Node #3: [83, 1] from Operation: 48-47=1 Current State: 83:[83, 1], Operations: ['26+57=83', '48-47=1'] Exploring Operation: 83*1=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[26, 57, 47, 48], Operations: [] Exploring Operation: 26+57=83, Resulting Numbers: [47, 48, 83] Generated Node #0,0: 83:[47, 48, 83] Operation: 26+57=83 Moving to Node #0,0 Current State: 83:[47, 48, 83], Operations: ['26+57=83'] Exploring Operation: 47+48=95, Resulting Numbers: [83, 95] Generated Node #0,0,0: 83:[83, 95] Operation: 47+48=95 Moving to Node #0,0,0 Current State: 83:[83, 95], Operations: ['26+57=83', '47+48=95'] Exploring Operation: 95-83=12, Resulting Numbers: [12] 12,83 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 32, 66, 14, 24 ]
35
[ "66-24=42", "42/14=3", "32+3=35" ]
Current State: 35:[32, 66, 14, 24], Operations: [] Exploring Operation: 66-24=42, Resulting Numbers: [32, 14, 42] Generated Node #2: [32, 14, 42] from Operation: 66-24=42 Current State: 35:[32, 14, 42], Operations: ['66-24=42'] Exploring Operation: 42/14=3, Resulting Numbers: [32, 3] Generated Node #3: [32, 3] from Operation: 42/14=3 Current State: 35:[32, 3], Operations: ['66-24=42', '42/14=3'] Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[32, 66, 14, 24], Operations: [] Exploring Operation: 66-24=42, Resulting Numbers: [32, 14, 42] Generated Node #0,0: 35:[32, 14, 42] Operation: 66-24=42 Moving to Node #0,0 Current State: 35:[32, 14, 42], Operations: ['66-24=42'] Exploring Operation: 42/14=3, Resulting Numbers: [32, 3] Generated Node #0,0,0: 35:[32, 3] Operation: 42/14=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[32, 3], Operations: ['66-24=42', '42/14=3'] Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[32, 66, 14, 24], Operations: [] Exploring Operation: 66-24=42, Resulting Numbers: [32, 14, 42] Generated Node #0,0: 35:[32, 14, 42] Operation: 66-24=42 Moving to Node #0,0 Current State: 35:[32, 14, 42], Operations: ['66-24=42'] Exploring Operation: 42/14=3, Resulting Numbers: [32, 3] Generated Node #0,0,0: 35:[32, 3] Operation: 42/14=3 Moving to Node #0,0,0 Current State: 35:[32, 3], Operations: ['66-24=42', '42/14=3'] Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 75, 26, 50, 27 ]
44
[ "50*27=1350", "1350/75=18", "26+18=44" ]
Current State: 44:[75, 26, 50, 27], Operations: [] Exploring Operation: 50*27=1350, Resulting Numbers: [75, 26, 1350] Generated Node #2: [75, 26, 1350] from Operation: 50*27=1350 Current State: 44:[75, 26, 1350], Operations: ['50*27=1350'] Exploring Operation: 1350/75=18, Resulting Numbers: [26, 18] Generated Node #3: [26, 18] from Operation: 1350/75=18 Current State: 44:[26, 18], Operations: ['50*27=1350', '1350/75=18'] Exploring Operation: 26+18=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[75, 26, 50, 27], Operations: [] Exploring Operation: 75-26=49, Resulting Numbers: [50, 27, 49] Generated Node #0,0: 44:[50, 27, 49] Operation: 75-26=49 Exploring Operation: 75-27=48, Resulting Numbers: [26, 50, 48] Generated Node #0,1: 44:[26, 50, 48] Operation: 75-27=48 Exploring Operation: 50-27=23, Resulting Numbers: [75, 26, 23] Generated Node #0,2: 44:[75, 26, 23] Operation: 50-27=23 Exploring Operation: 75-50=25, Resulting Numbers: [26, 27, 25] Generated Node #0,3: 44:[26, 27, 25] Operation: 75-50=25 Moving to Node #0,3 Current State: 44:[26, 27, 25], Operations: ['75-50=25'] Exploring Operation: 26+27=53, Resulting Numbers: [25, 53] Generated Node #0,3,0: 44:[25, 53] Operation: 26+27=53 Exploring Operation: 27-25=2, Resulting Numbers: [26, 2] Generated Node #0,3,1: 44:[26, 2] Operation: 27-25=2 Exploring Operation: 27-26=1, Resulting Numbers: [25, 1] Generated Node #0,3,2: 44:[25, 1] Operation: 27-26=1 Exploring Operation: 26-25=1, Resulting Numbers: [27, 1] Generated Node #0,3,3: 44:[27, 1] Operation: 26-25=1 Moving to Node #0,1 Current State: 44:[26, 50, 48], Operations: ['75-27=48'] Exploring Operation: 48-26=22, Resulting Numbers: [50, 22] Generated Node #0,1,0: 44:[50, 22] Operation: 48-26=22 Exploring Operation: 50-26=24, Resulting Numbers: [48, 24] Generated Node #0,1,1: 44:[48, 24] Operation: 50-26=24 Exploring Operation: 50-48=2, Resulting Numbers: [26, 2] Generated Node #0,1,2: 44:[26, 2] Operation: 50-48=2 Exploring Operation: 26+50=76, Resulting Numbers: [48, 76] Generated Node #0,1,3: 44:[48, 76] Operation: 26+50=76 Moving to Node #0,0 Current State: 44:[50, 27, 49], Operations: ['75-26=49'] Exploring Operation: 50+27=77, Resulting Numbers: [49, 77] Generated Node #0,0,0: 44:[49, 77] Operation: 50+27=77 Exploring Operation: 50-49=1, Resulting Numbers: [27, 1] Generated Node #0,0,1: 44:[27, 1] Operation: 50-49=1 Exploring Operation: 49-27=22, Resulting Numbers: [50, 22] Generated Node #0,0,2: 44:[50, 22] Operation: 49-27=22 Exploring Operation: 50-27=23, Resulting Numbers: [49, 23] Generated Node #0,0,3: 44:[49, 23] Operation: 50-27=23 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 44:[27, 1], Operations: ['75-26=49', '50-49=1'] Exploring Operation: 27+1=28, Resulting Numbers: [28] 28,44 unequal: No Solution Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,44 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,44 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:[50, 22], Operations: ['75-26=49', '49-27=22'] Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,44 unequal: No Solution Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,44 unequal: No Solution Exploring Operation: 50*22=1100, Resulting Numbers: [1100] 1100,44 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:[49, 23], Operations: ['75-26=49', '50-27=23'] Exploring Operation: 49-23=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 49+23=72, Resulting Numbers: [72] 72,44 unequal: No Solution Exploring Operation: 49*23=1127, Resulting Numbers: [1127] 1127,44 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 #0,0,0 Current State: 44:[49, 77], Operations: ['75-26=49', '50+27=77'] Exploring Operation: 49*77=3773, Resulting Numbers: [3773] 3773,44 unequal: No Solution Exploring Operation: 49+77=126, Resulting Numbers: [126] 126,44 unequal: No Solution Exploring Operation: 77-49=28, Resulting Numbers: [28] 28,44 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: 44:[75, 26, 23], Operations: ['50-27=23'] Exploring Operation: 75-26=49, Resulting Numbers: [23, 49] Generated Node #0,2,0: 44:[23, 49] Operation: 75-26=49 Exploring Operation: 26+23=49, Resulting Numbers: [75, 49] Generated Node #0,2,1: 44:[75, 49] Operation: 26+23=49 Exploring Operation: 75-23=52, Resulting Numbers: [26, 52] Generated Node #0,2,2: 44:[26, 52] Operation: 75-23=52 Exploring Operation: 26-23=3, Resulting Numbers: [75, 3] Generated Node #0,2,3: 44:[75, 3] Operation: 26-23=3 Moving to Node #0,3,1 Current State: 44:[26, 2], Operations: ['75-50=25', '27-25=2'] Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,44 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,44 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,44 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,44 unequal: No Solution Moving to Node #0,3,2 Current State: 44:[25, 1], Operations: ['75-50=25', '27-26=1'] Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,44 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,44 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,44 unequal: No Solution Moving to Node #0,1,2 Current State: 44:[26, 2], Operations: ['75-27=48', '50-48=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,44 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,44 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,44 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,44 unequal: No Solution Moving to Node #0,3,3 Current State: 44:[27, 1], Operations: ['75-50=25', '26-25=1'] Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,44 unequal: No Solution Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,44 unequal: No Solution Exploring Operation: 27+1=28, Resulting Numbers: [28] 28,44 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[48, 24], Operations: ['75-27=48', '50-26=24'] Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,44 unequal: No Solution Exploring Operation: 48+24=72, Resulting Numbers: [72] 72,44 unequal: No Solution Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 48*24=1152, Resulting Numbers: [1152] 1152,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[50, 22], Operations: ['75-27=48', '48-26=22'] Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,44 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,44 unequal: No Solution Exploring Operation: 50*22=1100, Resulting Numbers: [1100] 1100,44 unequal: No Solution Moving to Node #0,2,0 Current State: 44:[23, 49], Operations: ['50-27=23', '75-26=49'] Exploring Operation: 23+49=72, Resulting Numbers: [72] 72,44 unequal: No Solution Exploring Operation: 23*49=1127, Resulting Numbers: [1127] 1127,44 unequal: No Solution Exploring Operation: 49-23=26, Resulting Numbers: [26] 26,44 unequal: No Solution Moving to Node #0,2,2 Current State: 44:[26, 52], Operations: ['50-27=23', '75-23=52'] Exploring Operation: 52/26=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 26+52=78, Resulting Numbers: [78] 78,44 unequal: No Solution Exploring Operation: 26*52=1352, Resulting Numbers: [1352] 1352,44 unequal: No Solution Exploring Operation: 52-26=26, Resulting Numbers: [26] 26,44 unequal: No Solution Moving to Node #0,3,0 Current State: 44:[25, 53], Operations: ['75-50=25', '26+27=53'] Exploring Operation: 25*53=1325, Resulting Numbers: [1325] 1325,44 unequal: No Solution Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,44 unequal: No Solution Exploring Operation: 25+53=78, Resulting Numbers: [78] 78,44 unequal: No Solution Moving to Node #0,2,3 Current State: 44:[75, 3], Operations: ['50-27=23', '26-23=3'] Exploring Operation: 75/3=25, Resulting Numbers: [25] 25,44 unequal: No Solution Exploring Operation: 75-3=72, Resulting Numbers: [72] 72,44 unequal: No Solution Exploring Operation: 75*3=225, Resulting Numbers: [225] 225,44 unequal: No Solution Exploring Operation: 75+3=78, Resulting Numbers: [78] 78,44 unequal: No Solution Moving to Node #0,1,3 Current State: 44:[48, 76], Operations: ['75-27=48', '26+50=76'] Exploring Operation: 48*76=3648, Resulting Numbers: [3648] 3648,44 unequal: No Solution Exploring Operation: 76-48=28, Resulting Numbers: [28] 28,44 unequal: No Solution Exploring Operation: 48+76=124, Resulting Numbers: [124] 124,44 unequal: No Solution Moving to Node #0,2,1 Current State: 44:[75, 49], Operations: ['50-27=23', '26+23=49'] Exploring Operation: 75+49=124, Resulting Numbers: [124] 124,44 unequal: No Solution Exploring Operation: 75-49=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 75*49=3675, Resulting Numbers: [3675] 3675,44 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 6, 92, 2, 31 ]
92
[ "6*31=186", "92+2=94", "186-94=92" ]
Current State: 92:[6, 92, 2, 31], Operations: [] Exploring Operation: 6*31=186, Resulting Numbers: [92, 2, 186] Generated Node #2: [92, 2, 186] from Operation: 6*31=186 Current State: 92:[92, 2, 186], Operations: ['6*31=186'] Exploring Operation: 92+2=94, Resulting Numbers: [186, 94] Generated Node #3: [186, 94] from Operation: 92+2=94 Current State: 92:[186, 94], Operations: ['6*31=186', '92+2=94'] Exploring Operation: 186-94=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[6, 92, 2, 31], Operations: [] Exploring Operation: 31-6=25, Resulting Numbers: [92, 2, 25] Generated Node #0,0: 92:[92, 2, 25] Operation: 31-6=25 Exploring Operation: 6+31=37, Resulting Numbers: [92, 2, 37] Generated Node #0,1: 92:[92, 2, 37] Operation: 6+31=37 Exploring Operation: 6/2=3, Resulting Numbers: [92, 31, 3] Generated Node #0,2: 92:[92, 31, 3] Operation: 6/2=3 Exploring Operation: 31-2=29, Resulting Numbers: [6, 92, 29] Generated Node #0,3: 92:[6, 92, 29] Operation: 31-2=29 Exploring Operation: 6-2=4, Resulting Numbers: [92, 31, 4] Generated Node #0,4: 92:[92, 31, 4] Operation: 6-2=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[92, 2, 25], Operations: ['31-6=25'] Exploring Operation: 25-2=23, Resulting Numbers: [92, 23] Generated Node #0,0,0: 92:[92, 23] Operation: 25-2=23 Exploring Operation: 2+25=27, Resulting Numbers: [92, 27] Generated Node #0,0,1: 92:[92, 27] Operation: 2+25=27 Exploring Operation: 92/2=46, Resulting Numbers: [25, 46] Generated Node #0,0,2: 92:[25, 46] Operation: 92/2=46 Exploring Operation: 92-2=90, Resulting Numbers: [25, 90] Generated Node #0,0,3: 92:[25, 90] Operation: 92-2=90 Exploring Operation: 92+2=94, Resulting Numbers: [25, 94] Generated Node #0,0,4: 92:[25, 94] Operation: 92+2=94 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[92, 23], Operations: ['31-6=25', '25-2=23'] Exploring Operation: 92/23=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 92+23=115, Resulting Numbers: [115] 115,92 unequal: No Solution Exploring Operation: 92-23=69, Resulting Numbers: [69] 69,92 unequal: No Solution Exploring Operation: 92*23=2116, Resulting Numbers: [2116] 2116,92 unequal: No Solution No 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: 92:[25, 46], Operations: ['31-6=25', '92/2=46'] Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,92 unequal: No Solution Exploring Operation: 25+46=71, Resulting Numbers: [71] 71,92 unequal: No Solution Exploring Operation: 25*46=1150, Resulting Numbers: [1150] 1150,92 unequal: No Solution No 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: 92:[92, 27], Operations: ['31-6=25', '2+25=27'] Exploring Operation: 92-27=65, Resulting Numbers: [65] 65,92 unequal: No Solution Exploring Operation: 92+27=119, Resulting Numbers: [119] 119,92 unequal: No Solution Exploring Operation: 92*27=2484, Resulting Numbers: [2484] 2484,92 unequal: No Solution No 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: 92:[25, 90], Operations: ['31-6=25', '92-2=90'] Exploring Operation: 25+90=115, Resulting Numbers: [115] 115,92 unequal: No Solution Exploring Operation: 25*90=2250, Resulting Numbers: [2250] 2250,92 unequal: No Solution Exploring Operation: 90-25=65, Resulting Numbers: [65] 65,92 unequal: No Solution No 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: 92:[25, 94], Operations: ['31-6=25', '92+2=94'] Exploring Operation: 25*94=2350, Resulting Numbers: [2350] 2350,92 unequal: No Solution Exploring Operation: 25+94=119, Resulting Numbers: [119] 119,92 unequal: No Solution Exploring Operation: 94-25=69, Resulting Numbers: [69] 69,92 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: 92:[6, 92, 29], Operations: ['31-2=29'] Exploring Operation: 92-29=63, Resulting Numbers: [6, 63] Generated Node #0,3,0: 92:[6, 63] Operation: 92-29=63 Exploring Operation: 6+92=98, Resulting Numbers: [29, 98] Generated Node #0,3,1: 92:[29, 98] Operation: 6+92=98 Exploring Operation: 29-6=23, Resulting Numbers: [92, 23] Generated Node #0,3,2: 92:[92, 23] Operation: 29-6=23 Exploring Operation: 92-6=86, Resulting Numbers: [29, 86] Generated Node #0,3,3: 92:[29, 86] Operation: 92-6=86 Exploring Operation: 6+29=35, Resulting Numbers: [92, 35] Generated Node #0,3,4: 92:[92, 35] Operation: 6+29=35 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 92:[92, 23], Operations: ['31-2=29', '29-6=23'] Exploring Operation: 92-23=69, Resulting Numbers: [69] 69,92 unequal: No Solution Exploring Operation: 92*23=2116, Resulting Numbers: [2116] 2116,92 unequal: No Solution Exploring Operation: 92/23=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 92+23=115, Resulting Numbers: [115] 115,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 92:[92, 35], Operations: ['31-2=29', '6+29=35'] Exploring Operation: 92+35=127, Resulting Numbers: [127] 127,92 unequal: No Solution Exploring Operation: 92*35=3220, Resulting Numbers: [3220] 3220,92 unequal: No Solution Exploring Operation: 92-35=57, Resulting Numbers: [57] 57,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 92:[29, 98], Operations: ['31-2=29', '6+92=98'] Exploring Operation: 29*98=2842, Resulting Numbers: [2842] 2842,92 unequal: No Solution Exploring Operation: 98-29=69, Resulting Numbers: [69] 69,92 unequal: No Solution Exploring Operation: 29+98=127, Resulting Numbers: [127] 127,92 unequal: No Solution No 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: 92:[29, 86], Operations: ['31-2=29', '92-6=86'] Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,92 unequal: No Solution Exploring Operation: 29*86=2494, Resulting Numbers: [2494] 2494,92 unequal: No Solution Exploring Operation: 29+86=115, Resulting Numbers: [115] 115,92 unequal: No Solution No 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: 92:[6, 63], Operations: ['31-2=29', '92-29=63'] Exploring Operation: 6*63=378, Resulting Numbers: [378] 378,92 unequal: No Solution Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,92 unequal: No Solution Exploring Operation: 6+63=69, Resulting Numbers: [69] 69,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 92:[92, 31, 4], Operations: ['6-2=4'] Exploring Operation: 31+4=35, Resulting Numbers: [92, 35] Generated Node #0,4,0: 92:[92, 35] Operation: 31+4=35 Exploring Operation: 31-4=27, Resulting Numbers: [92, 27] Generated Node #0,4,1: 92:[92, 27] Operation: 31-4=27 Exploring Operation: 92-4=88, Resulting Numbers: [31, 88] Generated Node #0,4,2: 92:[31, 88] Operation: 92-4=88 Exploring Operation: 92+4=96, Resulting Numbers: [31, 96] Generated Node #0,4,3: 92:[31, 96] Operation: 92+4=96 Exploring Operation: 92/4=23, Resulting Numbers: [31, 23] Generated Node #0,4,4: 92:[31, 23] Operation: 92/4=23 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 92:[92, 27], Operations: ['6-2=4', '31-4=27'] Exploring Operation: 92-27=65, Resulting Numbers: [65] 65,92 unequal: No Solution Exploring Operation: 92*27=2484, Resulting Numbers: [2484] 2484,92 unequal: No Solution Exploring Operation: 92+27=119, Resulting Numbers: [119] 119,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 92:[31, 23], Operations: ['6-2=4', '92/4=23'] Exploring Operation: 31*23=713, Resulting Numbers: [713] 713,92 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,92 unequal: No Solution Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 92:[92, 35], Operations: ['6-2=4', '31+4=35'] Exploring Operation: 92*35=3220, Resulting Numbers: [3220] 3220,92 unequal: No Solution Exploring Operation: 92-35=57, Resulting Numbers: [57] 57,92 unequal: No Solution Exploring Operation: 92+35=127, Resulting Numbers: [127] 127,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 92:[31, 88], Operations: ['6-2=4', '92-4=88'] Exploring Operation: 88-31=57, Resulting Numbers: [57] 57,92 unequal: No Solution Exploring Operation: 31*88=2728, Resulting Numbers: [2728] 2728,92 unequal: No Solution Exploring Operation: 31+88=119, Resulting Numbers: [119] 119,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 92:[31, 96], Operations: ['6-2=4', '92+4=96'] Exploring Operation: 31*96=2976, Resulting Numbers: [2976] 2976,92 unequal: No Solution Exploring Operation: 31+96=127, Resulting Numbers: [127] 127,92 unequal: No Solution Exploring Operation: 96-31=65, Resulting Numbers: [65] 65,92 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: 92:[92, 2, 37], Operations: ['6+31=37'] Exploring Operation: 92+2=94, Resulting Numbers: [37, 94] Generated Node #0,1,0: 92:[37, 94] Operation: 92+2=94 Exploring Operation: 2+37=39, Resulting Numbers: [92, 39] Generated Node #0,1,1: 92:[92, 39] Operation: 2+37=39 Exploring Operation: 92/2=46, Resulting Numbers: [37, 46] Generated Node #0,1,2: 92:[37, 46] Operation: 92/2=46 Exploring Operation: 92-37=55, Resulting Numbers: [2, 55] Generated Node #0,1,3: 92:[2, 55] Operation: 92-37=55 Exploring Operation: 92-2=90, Resulting Numbers: [37, 90] Generated Node #0,1,4: 92:[37, 90] Operation: 92-2=90 Moving to Node #0,1,1 Current State: 92:[92, 39], Operations: ['6+31=37', '2+37=39'] Exploring Operation: 92+39=131, Resulting Numbers: [131] 131,92 unequal: No Solution Exploring Operation: 92-39=53, Resulting Numbers: [53] 53,92 unequal: No Solution Exploring Operation: 92*39=3588, Resulting Numbers: [3588] 3588,92 unequal: No Solution Moving to Node #0,1,3 Current State: 92:[2, 55], Operations: ['6+31=37', '92-37=55'] Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,92 unequal: No Solution Exploring Operation: 2+55=57, Resulting Numbers: [57] 57,92 unequal: No Solution Exploring Operation: 2*55=110, Resulting Numbers: [110] 110,92 unequal: No Solution Moving to Node #0,1,2 Current State: 92:[37, 46], Operations: ['6+31=37', '92/2=46'] Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,92 unequal: No Solution Exploring Operation: 37*46=1702, Resulting Numbers: [1702] 1702,92 unequal: No Solution Exploring Operation: 37+46=83, Resulting Numbers: [83] 83,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[37, 94], Operations: ['6+31=37', '92+2=94'] Exploring Operation: 37*94=3478, Resulting Numbers: [3478] 3478,92 unequal: No Solution Exploring Operation: 37+94=131, Resulting Numbers: [131] 131,92 unequal: No Solution Exploring Operation: 94-37=57, Resulting Numbers: [57] 57,92 unequal: No Solution Moving to Node #0,1,4 Current State: 92:[37, 90], Operations: ['6+31=37', '92-2=90'] Exploring Operation: 90-37=53, Resulting Numbers: [53] 53,92 unequal: No Solution Exploring Operation: 37*90=3330, Resulting Numbers: [3330] 3330,92 unequal: No Solution Exploring Operation: 37+90=127, Resulting Numbers: [127] 127,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[92, 31, 3], Operations: ['6/2=3'] Exploring Operation: 31*3=93, Resulting Numbers: [92, 93] Generated Node #0,2,0: 92:[92, 93] Operation: 31*3=93 Exploring Operation: 92-3=89, Resulting Numbers: [31, 89] Generated Node #0,2,1: 92:[31, 89] Operation: 92-3=89 Exploring Operation: 31-3=28, Resulting Numbers: [92, 28] Generated Node #0,2,2: 92:[92, 28] Operation: 31-3=28 Exploring Operation: 31+3=34, Resulting Numbers: [92, 34] Generated Node #0,2,3: 92:[92, 34] Operation: 31+3=34 Exploring Operation: 92+3=95, Resulting Numbers: [31, 95] Generated Node #0,2,4: 92:[31, 95] Operation: 92+3=95 Moving to Node #0,2,0 Current State: 92:[92, 93], Operations: ['6/2=3', '31*3=93'] Exploring Operation: 93-92=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 92*93=8556, Resulting Numbers: [8556] 8556,92 unequal: No Solution Exploring Operation: 92+93=185, Resulting Numbers: [185] 185,92 unequal: No Solution Moving to Node #0,2,2 Current State: 92:[92, 28], Operations: ['6/2=3', '31-3=28'] Exploring Operation: 92*28=2576, Resulting Numbers: [2576] 2576,92 unequal: No Solution Exploring Operation: 92+28=120, Resulting Numbers: [120] 120,92 unequal: No Solution Exploring Operation: 92-28=64, Resulting Numbers: [64] 64,92 unequal: No Solution Moving to Node #0,2,1 Current State: 92:[31, 89], Operations: ['6/2=3', '92-3=89'] Exploring Operation: 31*89=2759, Resulting Numbers: [2759] 2759,92 unequal: No Solution Exploring Operation: 89-31=58, Resulting Numbers: [58] 58,92 unequal: No Solution Exploring Operation: 31+89=120, Resulting Numbers: [120] 120,92 unequal: No Solution Moving to Node #0,2,3 Current State: 92:[92, 34], Operations: ['6/2=3', '31+3=34'] Exploring Operation: 92-34=58, Resulting Numbers: [58] 58,92 unequal: No Solution Exploring Operation: 92*34=3128, Resulting Numbers: [3128] 3128,92 unequal: No Solution Exploring Operation: 92+34=126, Resulting Numbers: [126] 126,92 unequal: No Solution Moving to Node #0,2,4 Current State: 92:[31, 95], Operations: ['6/2=3', '92+3=95'] Exploring Operation: 95-31=64, Resulting Numbers: [64] 64,92 unequal: No Solution Exploring Operation: 31+95=126, Resulting Numbers: [126] 126,92 unequal: No Solution Exploring Operation: 31*95=2945, Resulting Numbers: [2945] 2945,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 8, 54, 60, 56 ]
70
[ "54-8=46", "60+56=116", "116-46=70" ]
Current State: 70:[8, 54, 60, 56], Operations: [] Exploring Operation: 54-8=46, Resulting Numbers: [60, 56, 46] Generated Node #2: [60, 56, 46] from Operation: 54-8=46 Current State: 70:[60, 56, 46], Operations: ['54-8=46'] Exploring Operation: 60+56=116, Resulting Numbers: [46, 116] Generated Node #3: [46, 116] from Operation: 60+56=116 Current State: 70:[46, 116], Operations: ['54-8=46', '60+56=116'] Exploring Operation: 116-46=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[8, 54, 60, 56], Operations: [] Exploring Operation: 60-54=6, Resulting Numbers: [8, 56, 6] Generated Node #0,0: 70:[8, 56, 6] Operation: 60-54=6 Exploring Operation: 56-54=2, Resulting Numbers: [8, 60, 2] Generated Node #0,1: 70:[8, 60, 2] Operation: 56-54=2 Moving to Node #0,1 Current State: 70:[8, 60, 2], Operations: ['56-54=2'] Exploring Operation: 60/2=30, Resulting Numbers: [8, 30] Generated Node #0,1,0: 70:[8, 30] Operation: 60/2=30 Exploring Operation: 8+60=68, Resulting Numbers: [2, 68] Generated Node #0,1,1: 70:[2, 68] Operation: 8+60=68 Moving to Node #0,0 Current State: 70:[8, 56, 6], Operations: ['60-54=6'] Exploring Operation: 8+56=64, Resulting Numbers: [6, 64] Generated Node #0,0,0: 70:[6, 64] Operation: 8+56=64 Exploring Operation: 56/8=7, Resulting Numbers: [6, 7] Generated Node #0,0,1: 70:[6, 7] Operation: 56/8=7 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 70:[6, 7], Operations: ['60-54=6', '56/8=7'] Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,70 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,70 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:[6, 64], Operations: ['60-54=6', '8+56=64'] Exploring Operation: 64-6=58, Resulting Numbers: [58] 58,70 unequal: No Solution Exploring Operation: 6+64=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[8, 54, 60, 56], Operations: [] Exploring Operation: 60-54=6, Resulting Numbers: [8, 56, 6] Generated Node #0,0: 70:[8, 56, 6] Operation: 60-54=6 Moving to Node #0,0 Current State: 70:[8, 56, 6], Operations: ['60-54=6'] Exploring Operation: 8+56=64, Resulting Numbers: [6, 64] Generated Node #0,0,0: 70:[6, 64] Operation: 8+56=64 Moving to Node #0,0,0 Current State: 70:[6, 64], Operations: ['60-54=6', '8+56=64'] Exploring Operation: 6+64=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_2
mult_heuristic
[ 32, 52, 69, 57 ]
42
[ "32+52=84", "69+57=126", "126-84=42" ]
Current State: 42:[32, 52, 69, 57], Operations: [] Exploring Operation: 32+52=84, Resulting Numbers: [69, 57, 84] Generated Node #2: [69, 57, 84] from Operation: 32+52=84 Current State: 42:[69, 57, 84], Operations: ['32+52=84'] Exploring Operation: 69+57=126, Resulting Numbers: [84, 126] Generated Node #3: [84, 126] from Operation: 69+57=126 Current State: 42:[84, 126], Operations: ['32+52=84', '69+57=126'] Exploring Operation: 126-84=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[32, 52, 69, 57], Operations: [] Exploring Operation: 69-52=17, Resulting Numbers: [32, 57, 17] Generated Node #0,0: 42:[32, 57, 17] Operation: 69-52=17 Exploring Operation: 69-32=37, Resulting Numbers: [52, 57, 37] Generated Node #0,1: 42:[52, 57, 37] Operation: 69-32=37 Exploring Operation: 69-57=12, Resulting Numbers: [32, 52, 12] Generated Node #0,2: 42:[32, 52, 12] Operation: 69-57=12 Start Sub Search at level 1: Moving to Node #0,2 Current State: 42:[32, 52, 12], Operations: ['69-57=12'] Exploring Operation: 32+12=44, Resulting Numbers: [52, 44] Generated Node #0,2,0: 42:[52, 44] Operation: 32+12=44 Exploring Operation: 52-32=20, Resulting Numbers: [12, 20] Generated Node #0,2,1: 42:[12, 20] Operation: 52-32=20 Exploring Operation: 32-12=20, Resulting Numbers: [52, 20] Generated Node #0,2,2: 42:[52, 20] Operation: 32-12=20 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 42:[12, 20], Operations: ['69-57=12', '52-32=20'] Exploring Operation: 12*20=240, Resulting Numbers: [240] 240,42 unequal: No Solution Exploring Operation: 12+20=32, Resulting Numbers: [32] 32,42 unequal: No Solution Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 42:[52, 20], Operations: ['69-57=12', '32-12=20'] Exploring Operation: 52+20=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 52-20=32, Resulting Numbers: [32] 32,42 unequal: No Solution Exploring Operation: 52*20=1040, Resulting Numbers: [1040] 1040,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 42:[52, 44], Operations: ['69-57=12', '32+12=44'] Exploring Operation: 52+44=96, Resulting Numbers: [96] 96,42 unequal: No Solution Exploring Operation: 52-44=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 52*44=2288, Resulting Numbers: [2288] 2288,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[32, 57, 17], Operations: ['69-52=17'] Exploring Operation: 32-17=15, Resulting Numbers: [57, 15] Generated Node #0,0,0: 42:[57, 15] Operation: 32-17=15 Exploring Operation: 57-17=40, Resulting Numbers: [32, 40] Generated Node #0,0,1: 42:[32, 40] Operation: 57-17=40 Exploring Operation: 57-32=25, Resulting Numbers: [17, 25] Generated Node #0,0,2: 42:[17, 25] Operation: 57-32=25 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 42:[17, 25], Operations: ['69-52=17', '57-32=25'] Exploring Operation: 17*25=425, Resulting Numbers: [425] 425,42 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[32, 52, 69, 57], Operations: [] Exploring Operation: 69-52=17, Resulting Numbers: [32, 57, 17] Generated Node #0,0: 42:[32, 57, 17] Operation: 69-52=17 Moving to Node #0,0 Current State: 42:[32, 57, 17], Operations: ['69-52=17'] Exploring Operation: 57-32=25, Resulting Numbers: [17, 25] Generated Node #0,0,2: 42:[17, 25] Operation: 57-32=25 Moving to Node #0,0,2 Current State: 42:[17, 25], Operations: ['69-52=17', '57-32=25'] Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 8, 19, 18, 10 ]
56
[ "10-8=2", "19*2=38", "18+38=56" ]
Current State: 56:[8, 19, 18, 10], Operations: [] Exploring Operation: 10-8=2, Resulting Numbers: [19, 18, 2] Generated Node #2: [19, 18, 2] from Operation: 10-8=2 Current State: 56:[19, 18, 2], Operations: ['10-8=2'] Exploring Operation: 19*2=38, Resulting Numbers: [18, 38] Generated Node #3: [18, 38] from Operation: 19*2=38 Current State: 56:[18, 38], Operations: ['10-8=2', '19*2=38'] Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[8, 19, 18, 10], Operations: [] Exploring Operation: 18+10=28, Resulting Numbers: [8, 19, 28] Generated Node #0,0: 56:[8, 19, 28] Operation: 18+10=28 Exploring Operation: 19+10=29, Resulting Numbers: [8, 18, 29] Generated Node #0,1: 56:[8, 18, 29] Operation: 19+10=29 Exploring Operation: 19-10=9, Resulting Numbers: [8, 18, 9] Generated Node #0,2: 56:[8, 18, 9] Operation: 19-10=9 Exploring Operation: 19-18=1, Resulting Numbers: [8, 10, 1] Generated Node #0,3: 56:[8, 10, 1] Operation: 19-18=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 56:[8, 10, 1], Operations: ['19-18=1'] Exploring Operation: 10-1=9, Resulting Numbers: [8, 9] Generated Node #0,3,0: 56:[8, 9] Operation: 10-1=9 Exploring Operation: 8*1=8, Resulting Numbers: [10, 8] Generated Node #0,3,1: 56:[10, 8] Operation: 8*1=8 Exploring Operation: 8-1=7, Resulting Numbers: [10, 7] Generated Node #0,3,2: 56:[10, 7] Operation: 8-1=7 Exploring Operation: 10-8=2, Resulting Numbers: [1, 2] Generated Node #0,3,3: 56:[1, 2] Operation: 10-8=2 Moving to Node #0,3,0 Current State: 56:[8, 9], Operations: ['19-18=1', '10-1=9'] Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,56 unequal: No Solution Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,56 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,56 unequal: No Solution Moving to Node #0,3,3 Current State: 56:[1, 2], Operations: ['19-18=1', '10-8=2'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,56 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,56 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,56 unequal: No Solution Moving to Node #0,3,2 Current State: 56:[10, 7], Operations: ['19-18=1', '8-1=7'] Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,56 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,56 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,56 unequal: No Solution Moving to Node #0,3,1 Current State: 56:[10, 8], Operations: ['19-18=1', '8*1=8'] Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,56 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[8, 19, 28], Operations: ['18+10=28'] Exploring Operation: 8+19=27, Resulting Numbers: [28, 27] Generated Node #0,0,0: 56:[28, 27] Operation: 8+19=27 Exploring Operation: 28-19=9, Resulting Numbers: [8, 9] Generated Node #0,0,1: 56:[8, 9] Operation: 28-19=9 Exploring Operation: 19+28=47, Resulting Numbers: [8, 47] Generated Node #0,0,2: 56:[8, 47] Operation: 19+28=47 Exploring Operation: 19-8=11, Resulting Numbers: [28, 11] Generated Node #0,0,3: 56:[28, 11] Operation: 19-8=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[28, 27], Operations: ['18+10=28', '8+19=27'] Exploring Operation: 28*27=756, Resulting Numbers: [756] 756,56 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 28+27=55, Resulting Numbers: [55] 55,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 56:[8, 9], Operations: ['18+10=28', '28-19=9'] Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,56 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 56:[28, 11], Operations: ['18+10=28', '19-8=11'] Exploring Operation: 28+11=39, Resulting Numbers: [39] 39,56 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,56 unequal: No Solution Exploring Operation: 28*11=308, Resulting Numbers: [308] 308,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 56:[8, 47], Operations: ['18+10=28', '19+28=47'] Exploring Operation: 8+47=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,56 unequal: No Solution Exploring Operation: 8*47=376, Resulting Numbers: [376] 376,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[8, 18, 29], Operations: ['19+10=29'] Exploring Operation: 18-8=10, Resulting Numbers: [29, 10] Generated Node #0,1,0: 56:[29, 10] Operation: 18-8=10 Exploring Operation: 8+18=26, Resulting Numbers: [29, 26] Generated Node #0,1,1: 56:[29, 26] Operation: 8+18=26 Exploring Operation: 29-18=11, Resulting Numbers: [8, 11] Generated Node #0,1,2: 56:[8, 11] Operation: 29-18=11 Exploring Operation: 18+29=47, Resulting Numbers: [8, 47] Generated Node #0,1,3: 56:[8, 47] Operation: 18+29=47 Moving to Node #0,1,0 Current State: 56:[29, 10], Operations: ['19+10=29', '18-8=10'] Exploring Operation: 29*10=290, Resulting Numbers: [290] 290,56 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,56 unequal: No Solution Moving to Node #0,1,2 Current State: 56:[8, 11], Operations: ['19+10=29', '29-18=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,56 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[29, 26], Operations: ['19+10=29', '8+18=26'] Exploring Operation: 29*26=754, Resulting Numbers: [754] 754,56 unequal: No Solution Exploring Operation: 29+26=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,56 unequal: No Solution Moving to Node #0,1,3 Current State: 56:[8, 47], Operations: ['19+10=29', '18+29=47'] Exploring Operation: 8*47=376, Resulting Numbers: [376] 376,56 unequal: No Solution Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,56 unequal: No Solution Exploring Operation: 8+47=55, Resulting Numbers: [55] 55,56 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 Current State: 56:[8, 18, 9], Operations: ['19-10=9'] Exploring Operation: 8+18=26, Resulting Numbers: [9, 26] Generated Node #0,2,0: 56:[9, 26] Operation: 8+18=26 Exploring Operation: 18/9=2, Resulting Numbers: [8, 2] Generated Node #0,2,1: 56:[8, 2] Operation: 18/9=2 Exploring Operation: 18-9=9, Resulting Numbers: [8, 9] Generated Node #0,2,2: 56:[8, 9] Operation: 18-9=9 Exploring Operation: 18+9=27, Resulting Numbers: [8, 27] Generated Node #0,2,3: 56:[8, 27] Operation: 18+9=27 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 56:[8, 2], Operations: ['19-10=9', '18/9=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,56 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,56 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 56:[8, 9], Operations: ['19-10=9', '18-9=9'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,56 unequal: No Solution Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 56:[8, 27], Operations: ['19-10=9', '18+9=27'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,56 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 56:[9, 26], Operations: ['19-10=9', '8+18=26'] Exploring Operation: 9*26=234, Resulting Numbers: [234] 234,56 unequal: No Solution Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 52, 10, 74, 53 ]
41
[ "52+10=62", "74-53=21", "62-21=41" ]
Current State: 41:[52, 10, 74, 53], Operations: [] Exploring Operation: 52+10=62, Resulting Numbers: [74, 53, 62] Generated Node #2: [74, 53, 62] from Operation: 52+10=62 Current State: 41:[74, 53, 62], Operations: ['52+10=62'] Exploring Operation: 74-53=21, Resulting Numbers: [62, 21] Generated Node #3: [62, 21] from Operation: 74-53=21 Current State: 41:[62, 21], Operations: ['52+10=62', '74-53=21'] Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[52, 10, 74, 53], Operations: [] Exploring Operation: 74-10=64, Resulting Numbers: [52, 53, 64] Generated Node #0,0: 41:[52, 53, 64] Operation: 74-10=64 Exploring Operation: 52-10=42, Resulting Numbers: [74, 53, 42] Generated Node #0,1: 41:[74, 53, 42] Operation: 52-10=42 Moving to Node #0,0 Current State: 41:[52, 53, 64], Operations: ['74-10=64'] Exploring Operation: 64-53=11, Resulting Numbers: [52, 11] Generated Node #0,0,0: 41:[52, 11] Operation: 64-53=11 Exploring Operation: 64-52=12, Resulting Numbers: [53, 12] Generated Node #0,0,1: 41:[53, 12] Operation: 64-52=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[52, 11], Operations: ['74-10=64', '64-53=11'] Exploring Operation: 52+11=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[52, 10, 74, 53], Operations: [] Exploring Operation: 74-10=64, Resulting Numbers: [52, 53, 64] Generated Node #0,0: 41:[52, 53, 64] Operation: 74-10=64 Moving to Node #0,0 Current State: 41:[52, 53, 64], Operations: ['74-10=64'] Exploring Operation: 64-53=11, Resulting Numbers: [52, 11] Generated Node #0,0,0: 41:[52, 11] Operation: 64-53=11 Moving to Node #0,0,0 Current State: 41:[52, 11], Operations: ['74-10=64', '64-53=11'] Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 92, 30, 2, 78 ]
68
[ "78-30=48", "48/2=24", "92-24=68" ]
Current State: 68:[92, 30, 2, 78], Operations: [] Exploring Operation: 78-30=48, Resulting Numbers: [92, 2, 48] Generated Node #2: [92, 2, 48] from Operation: 78-30=48 Current State: 68:[92, 2, 48], Operations: ['78-30=48'] Exploring Operation: 48/2=24, Resulting Numbers: [92, 24] Generated Node #3: [92, 24] from Operation: 48/2=24 Current State: 68:[92, 24], Operations: ['78-30=48', '48/2=24'] Exploring Operation: 92-24=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[92, 30, 2, 78], Operations: [] Exploring Operation: 92-30=62, Resulting Numbers: [2, 78, 62] Generated Node #0,0: 68:[2, 78, 62] Operation: 92-30=62 Exploring Operation: 92-78=14, Resulting Numbers: [30, 2, 14] Generated Node #0,1: 68:[30, 2, 14] Operation: 92-78=14 Moving to Node #0,1 Current State: 68:[30, 2, 14], Operations: ['92-78=14'] Exploring Operation: 30-14=16, Resulting Numbers: [2, 16] Generated Node #0,1,0: 68:[2, 16] Operation: 30-14=16 Exploring Operation: 30+2=32, Resulting Numbers: [14, 32] Generated Node #0,1,1: 68:[14, 32] Operation: 30+2=32 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 68:[2, 16], Operations: ['92-78=14', '30-14=16'] Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,68 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 68:[14, 32], Operations: ['92-78=14', '30+2=32'] Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,68 unequal: No Solution Exploring Operation: 14+32=46, Resulting Numbers: [46] 46,68 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: 68:[2, 78, 62], Operations: ['92-30=62'] Exploring Operation: 78/2=39, Resulting Numbers: [62, 39] Generated Node #0,0,0: 68:[62, 39] Operation: 78/2=39 Exploring Operation: 78-62=16, Resulting Numbers: [2, 16] Generated Node #0,0,1: 68:[2, 16] Operation: 78-62=16 Moving to Node #0,0,1 Current State: 68:[2, 16], Operations: ['92-30=62', '78-62=16'] Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,68 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[62, 39], Operations: ['92-30=62', '78/2=39'] Exploring Operation: 62-39=23, Resulting Numbers: [23] 23,68 unequal: No Solution Exploring Operation: 62+39=101, Resulting Numbers: [101] 101,68 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 25, 4, 97, 52 ]
49
[ "25*4=100", "97+52=149", "149-100=49" ]
Current State: 49:[25, 4, 97, 52], Operations: [] Exploring Operation: 25*4=100, Resulting Numbers: [97, 52, 100] Generated Node #2: [97, 52, 100] from Operation: 25*4=100 Current State: 49:[97, 52, 100], Operations: ['25*4=100'] Exploring Operation: 97+52=149, Resulting Numbers: [100, 149] Generated Node #3: [100, 149] from Operation: 97+52=149 Current State: 49:[100, 149], Operations: ['25*4=100', '97+52=149'] Exploring Operation: 149-100=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[25, 4, 97, 52], Operations: [] Exploring Operation: 97-52=45, Resulting Numbers: [25, 4, 45] Generated Node #0,0: 49:[25, 4, 45] Operation: 97-52=45 Exploring Operation: 25-4=21, Resulting Numbers: [97, 52, 21] Generated Node #0,1: 49:[97, 52, 21] Operation: 25-4=21 Exploring Operation: 97-25=72, Resulting Numbers: [4, 52, 72] Generated Node #0,2: 49:[4, 52, 72] Operation: 97-25=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[25, 4, 45], Operations: ['97-52=45'] Exploring Operation: 45-25=20, Resulting Numbers: [4, 20] Generated Node #0,0,0: 49:[4, 20] Operation: 45-25=20 Exploring Operation: 4+45=49, Resulting Numbers: [25, 49] Generated Node #0,0,1: 49:[25, 49] Operation: 4+45=49 Exploring Operation: 25-4=21, Resulting Numbers: [45, 21] Generated Node #0,0,2: 49:[45, 21] Operation: 25-4=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[4, 20], Operations: ['97-52=45', '45-25=20'] Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,49 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,49 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 #0,0,1 Current State: 49:[25, 49], Operations: ['97-52=45', '4+45=49'] Exploring Operation: 25+49=74, Resulting Numbers: [74] 74,49 unequal: No Solution Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,49 unequal: No Solution Exploring Operation: 25*49=1225, Resulting Numbers: [1225] 1225,49 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:[45, 21], Operations: ['97-52=45', '25-4=21'] Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,49 unequal: No Solution Exploring Operation: 45+21=66, Resulting Numbers: [66] 66,49 unequal: No Solution Exploring Operation: 45*21=945, Resulting Numbers: [945] 945,49 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: 49:[4, 52, 72], Operations: ['97-25=72'] Exploring Operation: 72/4=18, Resulting Numbers: [52, 18] Generated Node #0,2,0: 49:[52, 18] Operation: 72/4=18 Exploring Operation: 72-4=68, Resulting Numbers: [52, 68] Generated Node #0,2,1: 49:[52, 68] Operation: 72-4=68 Exploring Operation: 72-52=20, Resulting Numbers: [4, 20] Generated Node #0,2,2: 49:[4, 20] Operation: 72-52=20 Moving to Node #0,2,0 Current State: 49:[52, 18], Operations: ['97-25=72', '72/4=18'] Exploring Operation: 52*18=936, Resulting Numbers: [936] 936,49 unequal: No Solution Exploring Operation: 52-18=34, Resulting Numbers: [34] 34,49 unequal: No Solution Exploring Operation: 52+18=70, Resulting Numbers: [70] 70,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[4, 20], Operations: ['97-25=72', '72-52=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,49 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[52, 68], Operations: ['97-25=72', '72-4=68'] Exploring Operation: 68-52=16, Resulting Numbers: [16] 16,49 unequal: No Solution Exploring Operation: 52+68=120, Resulting Numbers: [120] 120,49 unequal: No Solution Exploring Operation: 52*68=3536, Resulting Numbers: [3536] 3536,49 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 #0,1 Current State: 49:[97, 52, 21], Operations: ['25-4=21'] Exploring Operation: 52-21=31, Resulting Numbers: [97, 31] Generated Node #0,1,0: 49:[97, 31] Operation: 52-21=31 Exploring Operation: 97-52=45, Resulting Numbers: [21, 45] Generated Node #0,1,1: 49:[21, 45] Operation: 97-52=45 Exploring Operation: 97-21=76, Resulting Numbers: [52, 76] Generated Node #0,1,2: 49:[52, 76] Operation: 97-21=76 Moving to Node #0,1,1 Current State: 49:[21, 45], Operations: ['25-4=21', '97-52=45'] Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,49 unequal: No Solution Exploring Operation: 21+45=66, Resulting Numbers: [66] 66,49 unequal: No Solution Exploring Operation: 21*45=945, Resulting Numbers: [945] 945,49 unequal: No Solution Moving to Node #0,1,2 Current State: 49:[52, 76], Operations: ['25-4=21', '97-21=76'] Exploring Operation: 52*76=3952, Resulting Numbers: [3952] 3952,49 unequal: No Solution Exploring Operation: 52+76=128, Resulting Numbers: [128] 128,49 unequal: No Solution Exploring Operation: 76-52=24, Resulting Numbers: [24] 24,49 unequal: No Solution Moving to Node #0,1,0 Current State: 49:[97, 31], Operations: ['25-4=21', '52-21=31'] Exploring Operation: 97*31=3007, Resulting Numbers: [3007] 3007,49 unequal: No Solution Exploring Operation: 97-31=66, Resulting Numbers: [66] 66,49 unequal: No Solution Exploring Operation: 97+31=128, Resulting Numbers: [128] 128,49 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
[ 84, 5, 54, 48 ]
23
[ "84-5=79", "54+48=102", "102-79=23" ]
Current State: 23:[84, 5, 54, 48], Operations: [] Exploring Operation: 84-5=79, Resulting Numbers: [54, 48, 79] Generated Node #2: [54, 48, 79] from Operation: 84-5=79 Current State: 23:[54, 48, 79], Operations: ['84-5=79'] Exploring Operation: 54+48=102, Resulting Numbers: [79, 102] Generated Node #3: [79, 102] from Operation: 54+48=102 Current State: 23:[79, 102], Operations: ['84-5=79', '54+48=102'] Exploring Operation: 102-79=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[84, 5, 54, 48], Operations: [] Exploring Operation: 84-54=30, Resulting Numbers: [5, 48, 30] Generated Node #0,0: 23:[5, 48, 30] Operation: 84-54=30 Moving to Node #0,0 Current State: 23:[5, 48, 30], Operations: ['84-54=30'] Exploring Operation: 48-30=18, Resulting Numbers: [5, 18] Generated Node #0,0,0: 23:[5, 18] Operation: 48-30=18 Moving to Node #0,0,0 Current State: 23:[5, 18], Operations: ['84-54=30', '48-30=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[84, 5, 54, 48], Operations: [] Exploring Operation: 84-54=30, Resulting Numbers: [5, 48, 30] Generated Node #0,0: 23:[5, 48, 30] Operation: 84-54=30 Moving to Node #0,0 Current State: 23:[5, 48, 30], Operations: ['84-54=30'] Exploring Operation: 48-30=18, Resulting Numbers: [5, 18] Generated Node #0,0,0: 23:[5, 18] Operation: 48-30=18 Moving to Node #0,0,0 Current State: 23:[5, 18], Operations: ['84-54=30', '48-30=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 63, 76, 55, 52 ]
81
[ "63-52=11", "55/11=5", "76+5=81" ]
Current State: 81:[63, 76, 55, 52], Operations: [] Exploring Operation: 63-52=11, Resulting Numbers: [76, 55, 11] Generated Node #2: [76, 55, 11] from Operation: 63-52=11 Current State: 81:[76, 55, 11], Operations: ['63-52=11'] Exploring Operation: 55/11=5, Resulting Numbers: [76, 5] Generated Node #3: [76, 5] from Operation: 55/11=5 Current State: 81:[76, 5], Operations: ['63-52=11', '55/11=5'] Exploring Operation: 76+5=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[63, 76, 55, 52], Operations: [] Exploring Operation: 55-52=3, Resulting Numbers: [63, 76, 3] Generated Node #0,0: 81:[63, 76, 3] Operation: 55-52=3 Moving to Node #0,0 Current State: 81:[63, 76, 3], Operations: ['55-52=3'] Exploring Operation: 76-63=13, Resulting Numbers: [3, 13] Generated Node #0,0,0: 81:[3, 13] Operation: 76-63=13 Moving to Node #0,0,0 Current State: 81:[3, 13], Operations: ['55-52=3', '76-63=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,81 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 3, 74, 93, 37 ]
94
[ "3+93=96", "74/37=2", "96-2=94" ]
Current State: 94:[3, 74, 93, 37], Operations: [] Exploring Operation: 3+93=96, Resulting Numbers: [74, 37, 96] Generated Node #2: [74, 37, 96] from Operation: 3+93=96 Current State: 94:[74, 37, 96], Operations: ['3+93=96'] Exploring Operation: 74/37=2, Resulting Numbers: [96, 2] Generated Node #3: [96, 2] from Operation: 74/37=2 Current State: 94:[96, 2], Operations: ['3+93=96', '74/37=2'] Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[3, 74, 93, 37], Operations: [] Exploring Operation: 74+37=111, Resulting Numbers: [3, 93, 111] Generated Node #0,0: 94:[3, 93, 111] Operation: 74+37=111 Exploring Operation: 74-37=37, Resulting Numbers: [3, 93, 37] Generated Node #0,1: 94:[3, 93, 37] Operation: 74-37=37 Exploring Operation: 74/37=2, Resulting Numbers: [3, 93, 2] Generated Node #0,2: 94:[3, 93, 2] Operation: 74/37=2 Exploring Operation: 3+74=77, Resulting Numbers: [93, 37, 77] Generated Node #0,3: 94:[93, 37, 77] Operation: 3+74=77 Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[3, 93, 2], Operations: ['74/37=2'] Exploring Operation: 3-2=1, Resulting Numbers: [93, 1] Generated Node #0,2,0: 94:[93, 1] Operation: 3-2=1 Exploring Operation: 3+93=96, Resulting Numbers: [2, 96] Generated Node #0,2,1: 94:[2, 96] Operation: 3+93=96 Exploring Operation: 93+2=95, Resulting Numbers: [3, 95] Generated Node #0,2,2: 94:[3, 95] Operation: 93+2=95 Exploring Operation: 93-3=90, Resulting Numbers: [2, 90] Generated Node #0,2,3: 94:[2, 90] Operation: 93-3=90 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 94:[93, 1], Operations: ['74/37=2', '3-2=1'] Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,94 unequal: No Solution Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[3, 74, 93, 37], Operations: [] Exploring Operation: 74/37=2, Resulting Numbers: [3, 93, 2] Generated Node #0,2: 94:[3, 93, 2] Operation: 74/37=2 Moving to Node #0,2 Current State: 94:[3, 93, 2], Operations: ['74/37=2'] Exploring Operation: 3-2=1, Resulting Numbers: [93, 1] Generated Node #0,2,0: 94:[93, 1] Operation: 3-2=1 Moving to Node #0,2,0 Current State: 94:[93, 1], Operations: ['74/37=2', '3-2=1'] Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 43, 4, 32, 37 ]
63
[ "37-32=5", "4*5=20", "43+20=63" ]
Current State: 63:[43, 4, 32, 37], Operations: [] Exploring Operation: 37-32=5, Resulting Numbers: [43, 4, 5] Generated Node #2: [43, 4, 5] from Operation: 37-32=5 Current State: 63:[43, 4, 5], Operations: ['37-32=5'] Exploring Operation: 4*5=20, Resulting Numbers: [43, 20] Generated Node #3: [43, 20] from Operation: 4*5=20 Current State: 63:[43, 20], Operations: ['37-32=5', '4*5=20'] Exploring Operation: 43+20=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[43, 4, 32, 37], Operations: [] Exploring Operation: 43-32=11, Resulting Numbers: [4, 37, 11] Generated Node #0,0: 63:[4, 37, 11] Operation: 43-32=11 Exploring Operation: 43-37=6, Resulting Numbers: [4, 32, 6] Generated Node #0,1: 63:[4, 32, 6] Operation: 43-37=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[4, 32, 6], Operations: ['43-37=6'] Exploring Operation: 32-6=26, Resulting Numbers: [4, 26] Generated Node #0,1,0: 63:[4, 26] Operation: 32-6=26 Exploring Operation: 32/4=8, Resulting Numbers: [6, 8] Generated Node #0,1,1: 63:[6, 8] Operation: 32/4=8 Moving to Node #0,1,1 Current State: 63:[6, 8], Operations: ['43-37=6', '32/4=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,63 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[4, 26], Operations: ['43-37=6', '32-6=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[4, 37, 11], Operations: ['43-32=11'] Exploring Operation: 37-11=26, Resulting Numbers: [4, 26] Generated Node #0,0,0: 63:[4, 26] Operation: 37-11=26 Exploring Operation: 37-4=33, Resulting Numbers: [11, 33] Generated Node #0,0,1: 63:[11, 33] Operation: 37-4=33 Moving to Node #0,0,0 Current State: 63:[4, 26], Operations: ['43-32=11', '37-11=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[11, 33], Operations: ['43-32=11', '37-4=33'] Exploring Operation: 33/11=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,63 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
[ 42, 61, 35, 93 ]
39
[ "61-42=19", "93-35=58", "58-19=39" ]
Current State: 39:[42, 61, 35, 93], Operations: [] Exploring Operation: 61-42=19, Resulting Numbers: [35, 93, 19] Generated Node #2: [35, 93, 19] from Operation: 61-42=19 Current State: 39:[35, 93, 19], Operations: ['61-42=19'] Exploring Operation: 93-35=58, Resulting Numbers: [19, 58] Generated Node #3: [19, 58] from Operation: 93-35=58 Current State: 39:[19, 58], Operations: ['61-42=19', '93-35=58'] Exploring Operation: 58-19=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[42, 61, 35, 93], Operations: [] Exploring Operation: 93-61=32, Resulting Numbers: [42, 35, 32] Generated Node #0,0: 39:[42, 35, 32] Operation: 93-61=32 Exploring Operation: 93-42=51, Resulting Numbers: [61, 35, 51] Generated Node #0,1: 39:[61, 35, 51] Operation: 93-42=51 Exploring Operation: 93-35=58, Resulting Numbers: [42, 61, 58] Generated Node #0,2: 39:[42, 61, 58] Operation: 93-35=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[42, 35, 32], Operations: ['93-61=32'] Exploring Operation: 35-32=3, Resulting Numbers: [42, 3] Generated Node #0,0,0: 39:[42, 3] Operation: 35-32=3 Exploring Operation: 42-32=10, Resulting Numbers: [35, 10] Generated Node #0,0,1: 39:[35, 10] Operation: 42-32=10 Exploring Operation: 42-35=7, Resulting Numbers: [32, 7] Generated Node #0,0,2: 39:[32, 7] Operation: 42-35=7 Moving to Node #0,0,0 Current State: 39:[42, 3], Operations: ['93-61=32', '35-32=3'] Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,39 unequal: No Solution Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,39 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[42, 61, 35, 93], Operations: [] Exploring Operation: 93-61=32, Resulting Numbers: [42, 35, 32] Generated Node #0,0: 39:[42, 35, 32] Operation: 93-61=32 Moving to Node #0,0 Current State: 39:[42, 35, 32], Operations: ['93-61=32'] Exploring Operation: 35-32=3, Resulting Numbers: [42, 3] Generated Node #0,0,0: 39:[42, 3] Operation: 35-32=3 Moving to Node #0,0,0 Current State: 39:[42, 3], Operations: ['93-61=32', '35-32=3'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 55, 27, 61, 74 ]
50
[ "61+74=135", "135/27=5", "55-5=50" ]
Current State: 50:[55, 27, 61, 74], Operations: [] Exploring Operation: 61+74=135, Resulting Numbers: [55, 27, 135] Generated Node #2: [55, 27, 135] from Operation: 61+74=135 Current State: 50:[55, 27, 135], Operations: ['61+74=135'] Exploring Operation: 135/27=5, Resulting Numbers: [55, 5] Generated Node #3: [55, 5] from Operation: 135/27=5 Current State: 50:[55, 5], Operations: ['61+74=135', '135/27=5'] Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[55, 27, 61, 74], Operations: [] Exploring Operation: 74-61=13, Resulting Numbers: [55, 27, 13] Generated Node #0,0: 50:[55, 27, 13] Operation: 74-61=13 Exploring Operation: 74-55=19, Resulting Numbers: [27, 61, 19] Generated Node #0,1: 50:[27, 61, 19] Operation: 74-55=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[55, 27, 13], Operations: ['74-61=13'] Exploring Operation: 27-13=14, Resulting Numbers: [55, 14] Generated Node #0,0,0: 50:[55, 14] Operation: 27-13=14 Exploring Operation: 55-27=28, Resulting Numbers: [13, 28] Generated Node #0,0,1: 50:[13, 28] Operation: 55-27=28 Moving to Node #0,0,1 Current State: 50:[13, 28], Operations: ['74-61=13', '55-27=28'] Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,50 unequal: No Solution Exploring Operation: 13+28=41, Resulting Numbers: [41] 41,50 unequal: No Solution Moving to Node #0,0,0 Current State: 50:[55, 14], Operations: ['74-61=13', '27-13=14'] Exploring Operation: 55+14=69, Resulting Numbers: [69] 69,50 unequal: No Solution Exploring Operation: 55-14=41, Resulting Numbers: [41] 41,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[27, 61, 19], Operations: ['74-55=19'] Exploring Operation: 61-19=42, Resulting Numbers: [27, 42] Generated Node #0,1,0: 50:[27, 42] Operation: 61-19=42 Exploring Operation: 27-19=8, Resulting Numbers: [61, 8] Generated Node #0,1,1: 50:[61, 8] Operation: 27-19=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 50:[27, 42], Operations: ['74-55=19', '61-19=42'] Exploring Operation: 27+42=69, Resulting Numbers: [69] 69,50 unequal: No Solution Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 50:[61, 8], Operations: ['74-55=19', '27-19=8'] Exploring Operation: 61-8=53, Resulting Numbers: [53] 53,50 unequal: No Solution Exploring Operation: 61+8=69, Resulting Numbers: [69] 69,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 58, 49, 42, 40 ]
18
[ "58-49=9", "42-40=2", "9*2=18" ]
Current State: 18:[58, 49, 42, 40], Operations: [] Exploring Operation: 58-49=9, Resulting Numbers: [42, 40, 9] Generated Node #2: [42, 40, 9] from Operation: 58-49=9 Current State: 18:[42, 40, 9], Operations: ['58-49=9'] Exploring Operation: 42-40=2, Resulting Numbers: [9, 2] Generated Node #3: [9, 2] from Operation: 42-40=2 Current State: 18:[9, 2], Operations: ['58-49=9', '42-40=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[58, 49, 42, 40], Operations: [] Exploring Operation: 58-49=9, Resulting Numbers: [42, 40, 9] Generated Node #0,0: 18:[42, 40, 9] Operation: 58-49=9 Exploring Operation: 58-42=16, Resulting Numbers: [49, 40, 16] Generated Node #0,1: 18:[49, 40, 16] Operation: 58-42=16 Exploring Operation: 49-42=7, Resulting Numbers: [58, 40, 7] Generated Node #0,2: 18:[58, 40, 7] Operation: 49-42=7 Exploring Operation: 58-40=18, Resulting Numbers: [49, 42, 18] Generated Node #0,3: 18:[49, 42, 18] Operation: 58-40=18 Moving to Node #0,0 Current State: 18:[42, 40, 9], Operations: ['58-49=9'] Exploring Operation: 40-9=31, Resulting Numbers: [42, 31] Generated Node #0,0,0: 18:[42, 31] Operation: 40-9=31 Exploring Operation: 42-40=2, Resulting Numbers: [9, 2] Generated Node #0,0,1: 18:[9, 2] Operation: 42-40=2 Exploring Operation: 42+9=51, Resulting Numbers: [40, 51] Generated Node #0,0,2: 18:[40, 51] Operation: 42+9=51 Exploring Operation: 42-9=33, Resulting Numbers: [40, 33] Generated Node #0,0,3: 18:[40, 33] Operation: 42-9=33 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[9, 2], Operations: ['58-49=9', '42-40=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[58, 49, 42, 40], Operations: [] Exploring Operation: 58-49=9, Resulting Numbers: [42, 40, 9] Generated Node #0,0: 18:[42, 40, 9] Operation: 58-49=9 Moving to Node #0,0 Current State: 18:[42, 40, 9], Operations: ['58-49=9'] Exploring Operation: 42-40=2, Resulting Numbers: [9, 2] Generated Node #0,0,1: 18:[9, 2] Operation: 42-40=2 Moving to Node #0,0,1 Current State: 18:[9, 2], Operations: ['58-49=9', '42-40=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 10, 45, 3, 23 ]
75
[ "10+45=55", "23-3=20", "55+20=75" ]
Current State: 75:[10, 45, 3, 23], Operations: [] Exploring Operation: 10+45=55, Resulting Numbers: [3, 23, 55] Generated Node #2: [3, 23, 55] from Operation: 10+45=55 Current State: 75:[3, 23, 55], Operations: ['10+45=55'] Exploring Operation: 23-3=20, Resulting Numbers: [55, 20] Generated Node #3: [55, 20] from Operation: 23-3=20 Current State: 75:[55, 20], Operations: ['10+45=55', '23-3=20'] Exploring Operation: 55+20=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[10, 45, 3, 23], Operations: [] Exploring Operation: 45-23=22, Resulting Numbers: [10, 3, 22] Generated Node #0,0: 75:[10, 3, 22] Operation: 45-23=22 Exploring Operation: 45+23=68, Resulting Numbers: [10, 3, 68] Generated Node #0,1: 75:[10, 3, 68] Operation: 45+23=68 Exploring Operation: 45/3=15, Resulting Numbers: [10, 23, 15] Generated Node #0,2: 75:[10, 23, 15] Operation: 45/3=15 Exploring Operation: 45-10=35, Resulting Numbers: [3, 23, 35] Generated Node #0,3: 75:[3, 23, 35] Operation: 45-10=35 Moving to Node #0,2 Current State: 75:[10, 23, 15], Operations: ['45/3=15'] Exploring Operation: 10+23=33, Resulting Numbers: [15, 33] Generated Node #0,2,0: 75:[15, 33] Operation: 10+23=33 Exploring Operation: 10+15=25, Resulting Numbers: [23, 25] Generated Node #0,2,1: 75:[23, 25] Operation: 10+15=25 Exploring Operation: 15-10=5, Resulting Numbers: [23, 5] Generated Node #0,2,2: 75:[23, 5] Operation: 15-10=5 Exploring Operation: 23-10=13, Resulting Numbers: [15, 13] Generated Node #0,2,3: 75:[15, 13] Operation: 23-10=13 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 75:[23, 25], Operations: ['45/3=15', '10+15=25'] Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 23*25=575, Resulting Numbers: [575] 575,75 unequal: No Solution Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 75:[23, 5], Operations: ['45/3=15', '15-10=5'] Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 23*5=115, Resulting Numbers: [115] 115,75 unequal: No Solution Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 75:[15, 13], Operations: ['45/3=15', '23-10=13'] Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 15*13=195, Resulting Numbers: [195] 195,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 75:[15, 33], Operations: ['45/3=15', '10+23=33'] Exploring Operation: 15+33=48, Resulting Numbers: [48] 48,75 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 15*33=495, Resulting Numbers: [495] 495,75 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: 75:[10, 3, 22], Operations: ['45-23=22'] Exploring Operation: 10+3=13, Resulting Numbers: [22, 13] Generated Node #0,0,0: 75:[22, 13] Operation: 10+3=13 Exploring Operation: 3+22=25, Resulting Numbers: [10, 25] Generated Node #0,0,1: 75:[10, 25] Operation: 3+22=25 Exploring Operation: 22-10=12, Resulting Numbers: [3, 12] Generated Node #0,0,2: 75:[3, 12] Operation: 22-10=12 Exploring Operation: 10-3=7, Resulting Numbers: [22, 7] Generated Node #0,0,3: 75:[22, 7] Operation: 10-3=7 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 75:[3, 12], Operations: ['45-23=22', '22-10=12'] Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,75 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[22, 13], Operations: ['45-23=22', '10+3=13'] Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 22+13=35, Resulting Numbers: [35] 35,75 unequal: No Solution Exploring Operation: 22*13=286, Resulting Numbers: [286] 286,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 75:[10, 25], Operations: ['45-23=22', '3+22=25'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,75 unequal: No Solution Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 75:[22, 7], Operations: ['45-23=22', '10-3=7'] Exploring Operation: 22+7=29, Resulting Numbers: [29] 29,75 unequal: No Solution Exploring Operation: 22*7=154, Resulting Numbers: [154] 154,75 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,75 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: 75:[3, 23, 35], Operations: ['45-10=35'] Exploring Operation: 23-3=20, Resulting Numbers: [35, 20] Generated Node #0,3,0: 75:[35, 20] Operation: 23-3=20 Exploring Operation: 3+23=26, Resulting Numbers: [35, 26] Generated Node #0,3,1: 75:[35, 26] Operation: 3+23=26 Exploring Operation: 35-23=12, Resulting Numbers: [3, 12] Generated Node #0,3,2: 75:[3, 12] Operation: 35-23=12 Exploring Operation: 35-3=32, Resulting Numbers: [23, 32] Generated Node #0,3,3: 75:[23, 32] Operation: 35-3=32 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 75:[3, 12], Operations: ['45-10=35', '35-23=12'] Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,75 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 75:[23, 32], Operations: ['45-10=35', '35-3=32'] Exploring Operation: 23+32=55, Resulting Numbers: [55] 55,75 unequal: No Solution Exploring Operation: 32-23=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 23*32=736, Resulting Numbers: [736] 736,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 75:[35, 26], Operations: ['45-10=35', '3+23=26'] Exploring Operation: 35-26=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 35*26=910, Resulting Numbers: [910] 910,75 unequal: No Solution Exploring Operation: 35+26=61, Resulting Numbers: [61] 61,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 75:[35, 20], Operations: ['45-10=35', '23-3=20'] Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 35+20=55, Resulting Numbers: [55] 55,75 unequal: No Solution Exploring Operation: 35*20=700, Resulting Numbers: [700] 700,75 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: 75:[10, 3, 68], Operations: ['45+23=68'] Exploring Operation: 10+3=13, Resulting Numbers: [68, 13] Generated Node #0,1,0: 75:[68, 13] Operation: 10+3=13 Exploring Operation: 3+68=71, Resulting Numbers: [10, 71] Generated Node #0,1,1: 75:[10, 71] Operation: 3+68=71 Exploring Operation: 10-3=7, Resulting Numbers: [68, 7] Generated Node #0,1,2: 75:[68, 7] Operation: 10-3=7 Exploring Operation: 10+68=78, Resulting Numbers: [3, 78] Generated Node #0,1,3: 75:[3, 78] Operation: 10+68=78 Moving to Node #0,1,3 Current State: 75:[3, 78], Operations: ['45+23=68', '10+68=78'] Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[10, 45, 3, 23], Operations: [] Exploring Operation: 45+23=68, Resulting Numbers: [10, 3, 68] Generated Node #0,1: 75:[10, 3, 68] Operation: 45+23=68 Moving to Node #0,1 Current State: 75:[10, 3, 68], Operations: ['45+23=68'] Exploring Operation: 10+68=78, Resulting Numbers: [3, 78] Generated Node #0,1,3: 75:[3, 78] Operation: 10+68=78 Moving to Node #0,1,3 Current State: 75:[3, 78], Operations: ['45+23=68', '10+68=78'] Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
0.945313
hs_4
mult_heuristic
[ 30, 60, 93, 87 ]
96
[ "30+60=90", "93-87=6", "90+6=96" ]
Current State: 96:[30, 60, 93, 87], Operations: [] Exploring Operation: 30+60=90, Resulting Numbers: [93, 87, 90] Generated Node #2: [93, 87, 90] from Operation: 30+60=90 Current State: 96:[93, 87, 90], Operations: ['30+60=90'] Exploring Operation: 93-87=6, Resulting Numbers: [90, 6] Generated Node #3: [90, 6] from Operation: 93-87=6 Current State: 96:[90, 6], Operations: ['30+60=90', '93-87=6'] Exploring Operation: 90+6=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[30, 60, 93, 87], Operations: [] Exploring Operation: 60/30=2, Resulting Numbers: [93, 87, 2] Generated Node #0,0: 96:[93, 87, 2] Operation: 60/30=2 Exploring Operation: 93-60=33, Resulting Numbers: [30, 87, 33] Generated Node #0,1: 96:[30, 87, 33] Operation: 93-60=33 Exploring Operation: 87-60=27, Resulting Numbers: [30, 93, 27] Generated Node #0,2: 96:[30, 93, 27] Operation: 87-60=27 Exploring Operation: 60-30=30, Resulting Numbers: [93, 87, 30] Generated Node #0,3: 96:[93, 87, 30] Operation: 60-30=30 Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[30, 93, 27], Operations: ['87-60=27'] Exploring Operation: 30-27=3, Resulting Numbers: [93, 3] Generated Node #0,2,0: 96:[93, 3] Operation: 30-27=3 Exploring Operation: 30+27=57, Resulting Numbers: [93, 57] Generated Node #0,2,1: 96:[93, 57] Operation: 30+27=57 Exploring Operation: 93-27=66, Resulting Numbers: [30, 66] Generated Node #0,2,2: 96:[30, 66] Operation: 93-27=66 Exploring Operation: 93-30=63, Resulting Numbers: [27, 63] Generated Node #0,2,3: 96:[27, 63] Operation: 93-30=63 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 96:[93, 3], Operations: ['87-60=27', '30-27=3'] Exploring Operation: 93*3=279, Resulting Numbers: [279] 279,96 unequal: No Solution Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,96 unequal: No Solution Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[30, 60, 93, 87], Operations: [] Exploring Operation: 87-60=27, Resulting Numbers: [30, 93, 27] Generated Node #0,2: 96:[30, 93, 27] Operation: 87-60=27 Moving to Node #0,2 Current State: 96:[30, 93, 27], Operations: ['87-60=27'] Exploring Operation: 30-27=3, Resulting Numbers: [93, 3] Generated Node #0,2,0: 96:[93, 3] Operation: 30-27=3 Moving to Node #0,2,0 Current State: 96:[93, 3], Operations: ['87-60=27', '30-27=3'] Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 12, 25, 26, 99 ]
88
[ "12+25=37", "26+99=125", "125-37=88" ]
Current State: 88:[12, 25, 26, 99], Operations: [] Exploring Operation: 12+25=37, Resulting Numbers: [26, 99, 37] Generated Node #2: [26, 99, 37] from Operation: 12+25=37 Current State: 88:[26, 99, 37], Operations: ['12+25=37'] Exploring Operation: 26+99=125, Resulting Numbers: [37, 125] Generated Node #3: [37, 125] from Operation: 26+99=125 Current State: 88:[37, 125], Operations: ['12+25=37', '26+99=125'] Exploring Operation: 125-37=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[12, 25, 26, 99], Operations: [] Exploring Operation: 99-12=87, Resulting Numbers: [25, 26, 87] Generated Node #0,0: 88:[25, 26, 87] Operation: 99-12=87 Exploring Operation: 26-25=1, Resulting Numbers: [12, 99, 1] Generated Node #0,1: 88:[12, 99, 1] Operation: 26-25=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[25, 26, 87], Operations: ['99-12=87'] Exploring Operation: 25+26=51, Resulting Numbers: [87, 51] Generated Node #0,0,0: 88:[87, 51] Operation: 25+26=51 Exploring Operation: 26-25=1, Resulting Numbers: [87, 1] Generated Node #0,0,1: 88:[87, 1] Operation: 26-25=1 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[87, 1], Operations: ['99-12=87', '26-25=1'] Exploring Operation: 87*1=87, Resulting Numbers: [87] 87,88 unequal: No Solution Exploring Operation: 87+1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[12, 25, 26, 99], Operations: [] Exploring Operation: 99-12=87, Resulting Numbers: [25, 26, 87] Generated Node #0,0: 88:[25, 26, 87] Operation: 99-12=87 Moving to Node #0,0 Current State: 88:[25, 26, 87], Operations: ['99-12=87'] Exploring Operation: 26-25=1, Resulting Numbers: [87, 1] Generated Node #0,0,1: 88:[87, 1] Operation: 26-25=1 Moving to Node #0,0,1 Current State: 88:[87, 1], Operations: ['99-12=87', '26-25=1'] Exploring Operation: 87+1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 83, 79, 11, 15 ]
77
[ "79+11=90", "90/15=6", "83-6=77" ]
Current State: 77:[83, 79, 11, 15], Operations: [] Exploring Operation: 79+11=90, Resulting Numbers: [83, 15, 90] Generated Node #2: [83, 15, 90] from Operation: 79+11=90 Current State: 77:[83, 15, 90], Operations: ['79+11=90'] Exploring Operation: 90/15=6, Resulting Numbers: [83, 6] Generated Node #3: [83, 6] from Operation: 90/15=6 Current State: 77:[83, 6], Operations: ['79+11=90', '90/15=6'] Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[83, 79, 11, 15], Operations: [] Exploring Operation: 83-79=4, Resulting Numbers: [11, 15, 4] Generated Node #0,0: 77:[11, 15, 4] Operation: 83-79=4 Moving to Node #0,0 Current State: 77:[11, 15, 4], Operations: ['83-79=4'] Exploring Operation: 15-4=11, Resulting Numbers: [11, 11] Generated Node #0,0,0: 77:[11, 11] Operation: 15-4=11 Moving to Node #0,0,0 Current State: 77:[11, 11], Operations: ['83-79=4', '15-4=11'] Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,77 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 2, 50, 58, 74 ]
20
[ "50+58=108", "108/2=54", "74-54=20" ]
Current State: 20:[2, 50, 58, 74], Operations: [] Exploring Operation: 50+58=108, Resulting Numbers: [2, 74, 108] Generated Node #2: [2, 74, 108] from Operation: 50+58=108 Current State: 20:[2, 74, 108], Operations: ['50+58=108'] Exploring Operation: 108/2=54, Resulting Numbers: [74, 54] Generated Node #3: [74, 54] from Operation: 108/2=54 Current State: 20:[74, 54], Operations: ['50+58=108', '108/2=54'] Exploring Operation: 74-54=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[2, 50, 58, 74], Operations: [] Exploring Operation: 74-50=24, Resulting Numbers: [2, 58, 24] Generated Node #0,0: 20:[2, 58, 24] Operation: 74-50=24 Exploring Operation: 58-50=8, Resulting Numbers: [2, 74, 8] Generated Node #0,1: 20:[2, 74, 8] Operation: 58-50=8 Exploring Operation: 74-58=16, Resulting Numbers: [2, 50, 16] Generated Node #0,2: 20:[2, 50, 16] Operation: 74-58=16 Moving to Node #0,2 Current State: 20:[2, 50, 16], Operations: ['74-58=16'] Exploring Operation: 50-2=48, Resulting Numbers: [16, 48] Generated Node #0,2,0: 20:[16, 48] Operation: 50-2=48 Exploring Operation: 50-16=34, Resulting Numbers: [2, 34] Generated Node #0,2,1: 20:[2, 34] Operation: 50-16=34 Exploring Operation: 50/2=25, Resulting Numbers: [16, 25] Generated Node #0,2,2: 20:[16, 25] Operation: 50/2=25 Moving to Node #0,0 Current State: 20:[2, 58, 24], Operations: ['74-50=24'] Exploring Operation: 58-2=56, Resulting Numbers: [24, 56] Generated Node #0,0,0: 20:[24, 56] Operation: 58-2=56 Exploring Operation: 58-24=34, Resulting Numbers: [2, 34] Generated Node #0,0,1: 20:[2, 34] Operation: 58-24=34 Exploring Operation: 58/2=29, Resulting Numbers: [24, 29] Generated Node #0,0,2: 20:[24, 29] Operation: 58/2=29 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 20:[24, 29], Operations: ['74-50=24', '58/2=29'] Exploring Operation: 29-24=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 24*29=696, Resulting Numbers: [696] 696,20 unequal: No Solution Exploring Operation: 24+29=53, Resulting Numbers: [53] 53,20 unequal: No Solution No 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: 20:[2, 34], Operations: ['74-50=24', '58-24=34'] Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,20 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,20 unequal: No Solution No 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: 20:[24, 56], Operations: ['74-50=24', '58-2=56'] Exploring Operation: 24*56=1344, Resulting Numbers: [1344] 1344,20 unequal: No Solution Exploring Operation: 56-24=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 24+56=80, Resulting Numbers: [80] 80,20 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: 20:[2, 74, 8], Operations: ['58-50=8'] Exploring Operation: 74/2=37, Resulting Numbers: [8, 37] Generated Node #0,1,0: 20:[8, 37] Operation: 74/2=37 Exploring Operation: 74-8=66, Resulting Numbers: [2, 66] Generated Node #0,1,1: 20:[2, 66] Operation: 74-8=66 Exploring Operation: 74-2=72, Resulting Numbers: [8, 72] Generated Node #0,1,2: 20:[8, 72] Operation: 74-2=72 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 20:[8, 37], Operations: ['58-50=8', '74/2=37'] Exploring Operation: 8+37=45, Resulting Numbers: [45] 45,20 unequal: No Solution Exploring Operation: 8*37=296, Resulting Numbers: [296] 296,20 unequal: No Solution Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,20 unequal: No Solution No 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: 20:[2, 66], Operations: ['58-50=8', '74-8=66'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,20 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,20 unequal: No Solution Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,20 unequal: No Solution No 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: 20:[8, 72], Operations: ['58-50=8', '74-2=72'] Exploring Operation: 8+72=80, Resulting Numbers: [80] 80,20 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,20 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: 20:[16, 25], Operations: ['74-58=16', '50/2=25'] Exploring Operation: 16+25=41, Resulting Numbers: [41] 41,20 unequal: No Solution Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 16*25=400, Resulting Numbers: [400] 400,20 unequal: No Solution Moving to Node #0,2,1 Current State: 20:[2, 34], Operations: ['74-58=16', '50-16=34'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,20 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,20 unequal: No Solution Moving to Node #0,2,0 Current State: 20:[16, 48], Operations: ['74-58=16', '50-2=48'] Exploring Operation: 16+48=64, Resulting Numbers: [64] 64,20 unequal: No Solution Exploring Operation: 48/16=3, Resulting Numbers: [3] 3,20 unequal: No Solution Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,20 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 41, 54, 71, 60 ]
36
[ "41+54=95", "71+60=131", "131-95=36" ]
Current State: 36:[41, 54, 71, 60], Operations: [] Exploring Operation: 41+54=95, Resulting Numbers: [71, 60, 95] Generated Node #2: [71, 60, 95] from Operation: 41+54=95 Current State: 36:[71, 60, 95], Operations: ['41+54=95'] Exploring Operation: 71+60=131, Resulting Numbers: [95, 131] Generated Node #3: [95, 131] from Operation: 71+60=131 Current State: 36:[95, 131], Operations: ['41+54=95', '71+60=131'] Exploring Operation: 131-95=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[41, 54, 71, 60], Operations: [] Exploring Operation: 71-60=11, Resulting Numbers: [41, 54, 11] Generated Node #0,0: 36:[41, 54, 11] Operation: 71-60=11 Moving to Node #0,0 Current State: 36:[41, 54, 11], Operations: ['71-60=11'] Exploring Operation: 54-41=13, Resulting Numbers: [11, 13] Generated Node #0,0,0: 36:[11, 13] Operation: 54-41=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[11, 13], Operations: ['71-60=11', '54-41=13'] Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,36 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
[ 47, 26, 27, 52 ]
58
[ "47-26=21", "27+52=79", "79-21=58" ]
Current State: 58:[47, 26, 27, 52], Operations: [] Exploring Operation: 47-26=21, Resulting Numbers: [27, 52, 21] Generated Node #2: [27, 52, 21] from Operation: 47-26=21 Current State: 58:[27, 52, 21], Operations: ['47-26=21'] Exploring Operation: 27+52=79, Resulting Numbers: [21, 79] Generated Node #3: [21, 79] from Operation: 27+52=79 Current State: 58:[21, 79], Operations: ['47-26=21', '27+52=79'] Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[47, 26, 27, 52], Operations: [] Exploring Operation: 52-47=5, Resulting Numbers: [26, 27, 5] Generated Node #0,0: 58:[26, 27, 5] Operation: 52-47=5 Moving to Node #0,0 Current State: 58:[26, 27, 5], Operations: ['52-47=5'] Exploring Operation: 27-26=1, Resulting Numbers: [5, 1] Generated Node #0,0,0: 58:[5, 1] Operation: 27-26=1 Moving to Node #0,0,0 Current State: 58:[5, 1], Operations: ['52-47=5', '27-26=1'] Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,58 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 82, 65, 2, 89 ]
36
[ "82-65=17", "89-17=72", "72/2=36" ]
Current State: 36:[82, 65, 2, 89], Operations: [] Exploring Operation: 82-65=17, Resulting Numbers: [2, 89, 17] Generated Node #2: [2, 89, 17] from Operation: 82-65=17 Current State: 36:[2, 89, 17], Operations: ['82-65=17'] Exploring Operation: 89-17=72, Resulting Numbers: [2, 72] Generated Node #3: [2, 72] from Operation: 89-17=72 Current State: 36:[2, 72], Operations: ['82-65=17', '89-17=72'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[82, 65, 2, 89], Operations: [] Exploring Operation: 82-2=80, Resulting Numbers: [65, 89, 80] Generated Node #0,0: 36:[65, 89, 80] Operation: 82-2=80 Exploring Operation: 82/2=41, Resulting Numbers: [65, 89, 41] Generated Node #0,1: 36:[65, 89, 41] Operation: 82/2=41 Exploring Operation: 82-65=17, Resulting Numbers: [2, 89, 17] Generated Node #0,2: 36:[2, 89, 17] Operation: 82-65=17 Exploring Operation: 89-65=24, Resulting Numbers: [82, 2, 24] Generated Node #0,3: 36:[82, 2, 24] Operation: 89-65=24 Exploring Operation: 89-82=7, Resulting Numbers: [65, 2, 7] Generated Node #0,4: 36:[65, 2, 7] Operation: 89-82=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 36:[65, 2, 7], Operations: ['89-82=7'] Exploring Operation: 2*7=14, Resulting Numbers: [65, 14] Generated Node #0,4,0: 36:[65, 14] Operation: 2*7=14 Exploring Operation: 65-2=63, Resulting Numbers: [7, 63] Generated Node #0,4,1: 36:[7, 63] Operation: 65-2=63 Exploring Operation: 65-7=58, Resulting Numbers: [2, 58] Generated Node #0,4,2: 36:[2, 58] Operation: 65-7=58 Exploring Operation: 2+7=9, Resulting Numbers: [65, 9] Generated Node #0,4,3: 36:[65, 9] Operation: 2+7=9 Exploring Operation: 7-2=5, Resulting Numbers: [65, 5] Generated Node #0,4,4: 36:[65, 5] Operation: 7-2=5 Moving to Node #0,4,2 Current State: 36:[2, 58], Operations: ['89-82=7', '65-7=58'] Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,36 unequal: No Solution Exploring Operation: 2*58=116, Resulting Numbers: [116] 116,36 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,36 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,36 unequal: No Solution Moving to Node #0,4,1 Current State: 36:[7, 63], Operations: ['89-82=7', '65-2=63'] Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 7+63=70, Resulting Numbers: [70] 70,36 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,36 unequal: No Solution Exploring Operation: 7*63=441, Resulting Numbers: [441] 441,36 unequal: No Solution Moving to Node #0,4,3 Current State: 36:[65, 9], Operations: ['89-82=7', '2+7=9'] Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,36 unequal: No Solution Exploring Operation: 65*9=585, Resulting Numbers: [585] 585,36 unequal: No Solution Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,36 unequal: No Solution Moving to Node #0,4,4 Current State: 36:[65, 5], Operations: ['89-82=7', '7-2=5'] Exploring Operation: 65-5=60, Resulting Numbers: [60] 60,36 unequal: No Solution Exploring Operation: 65+5=70, Resulting Numbers: [70] 70,36 unequal: No Solution Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 65*5=325, Resulting Numbers: [325] 325,36 unequal: No Solution Moving to Node #0,4,0 Current State: 36:[65, 14], Operations: ['89-82=7', '2*7=14'] Exploring Operation: 65+14=79, Resulting Numbers: [79] 79,36 unequal: No Solution Exploring Operation: 65*14=910, Resulting Numbers: [910] 910,36 unequal: No Solution Exploring Operation: 65-14=51, Resulting Numbers: [51] 51,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 36:[82, 2, 24], Operations: ['89-65=24'] Exploring Operation: 24/2=12, Resulting Numbers: [82, 12] Generated Node #0,3,0: 36:[82, 12] Operation: 24/2=12 Exploring Operation: 82/2=41, Resulting Numbers: [24, 41] Generated Node #0,3,1: 36:[24, 41] Operation: 82/2=41 Exploring Operation: 82-24=58, Resulting Numbers: [2, 58] Generated Node #0,3,2: 36:[2, 58] Operation: 82-24=58 Exploring Operation: 24-2=22, Resulting Numbers: [82, 22] Generated Node #0,3,3: 36:[82, 22] Operation: 24-2=22 Exploring Operation: 82-2=80, Resulting Numbers: [24, 80] Generated Node #0,3,4: 36:[24, 80] Operation: 82-2=80 Moving to Node #0,3,1 Current State: 36:[24, 41], Operations: ['89-65=24', '82/2=41'] Exploring Operation: 24*41=984, Resulting Numbers: [984] 984,36 unequal: No Solution Exploring Operation: 24+41=65, Resulting Numbers: [65] 65,36 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,36 unequal: No Solution Moving to Node #0,3,2 Current State: 36:[2, 58], Operations: ['89-65=24', '82-24=58'] Exploring Operation: 2*58=116, Resulting Numbers: [116] 116,36 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,36 unequal: No Solution Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,36 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,36 unequal: No Solution Moving to Node #0,3,0 Current State: 36:[82, 12], Operations: ['89-65=24', '24/2=12'] Exploring Operation: 82-12=70, Resulting Numbers: [70] 70,36 unequal: No Solution Exploring Operation: 82+12=94, Resulting Numbers: [94] 94,36 unequal: No Solution Exploring Operation: 82*12=984, Resulting Numbers: [984] 984,36 unequal: No Solution Moving to Node #0,3,3 Current State: 36:[82, 22], Operations: ['89-65=24', '24-2=22'] Exploring Operation: 82-22=60, Resulting Numbers: [60] 60,36 unequal: No Solution Exploring Operation: 82*22=1804, Resulting Numbers: [1804] 1804,36 unequal: No Solution Exploring Operation: 82+22=104, Resulting Numbers: [104] 104,36 unequal: No Solution Moving to Node #0,3,4 Current State: 36:[24, 80], Operations: ['89-65=24', '82-2=80'] Exploring Operation: 24*80=1920, Resulting Numbers: [1920] 1920,36 unequal: No Solution Exploring Operation: 24+80=104, Resulting Numbers: [104] 104,36 unequal: No Solution Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 36:[2, 89, 17], Operations: ['82-65=17'] Exploring Operation: 2*17=34, Resulting Numbers: [89, 34] Generated Node #0,2,0: 36:[89, 34] Operation: 2*17=34 Exploring Operation: 2+89=91, Resulting Numbers: [17, 91] Generated Node #0,2,1: 36:[17, 91] Operation: 2+89=91 Exploring Operation: 2+17=19, Resulting Numbers: [89, 19] Generated Node #0,2,2: 36:[89, 19] Operation: 2+17=19 Exploring Operation: 89-17=72, Resulting Numbers: [2, 72] Generated Node #0,2,3: 36:[2, 72] Operation: 89-17=72 Exploring Operation: 89-2=87, Resulting Numbers: [17, 87] Generated Node #0,2,4: 36:[17, 87] Operation: 89-2=87 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 36:[2, 72], Operations: ['82-65=17', '89-17=72'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[82, 65, 2, 89], Operations: [] Exploring Operation: 82-65=17, Resulting Numbers: [2, 89, 17] Generated Node #0,2: 36:[2, 89, 17] Operation: 82-65=17 Moving to Node #0,2 Current State: 36:[2, 89, 17], Operations: ['82-65=17'] Exploring Operation: 89-17=72, Resulting Numbers: [2, 72] Generated Node #0,2,3: 36:[2, 72] Operation: 89-17=72 Moving to Node #0,2,3 Current State: 36:[2, 72], Operations: ['82-65=17', '89-17=72'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.948785
hs_5
mult_heuristic
[ 56, 72, 31, 23 ]
70
[ "72-56=16", "31+23=54", "16+54=70" ]
Current State: 70:[56, 72, 31, 23], Operations: [] Exploring Operation: 72-56=16, Resulting Numbers: [31, 23, 16] Generated Node #2: [31, 23, 16] from Operation: 72-56=16 Current State: 70:[31, 23, 16], Operations: ['72-56=16'] Exploring Operation: 31+23=54, Resulting Numbers: [16, 54] Generated Node #3: [16, 54] from Operation: 31+23=54 Current State: 70:[16, 54], Operations: ['72-56=16', '31+23=54'] Exploring Operation: 16+54=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[56, 72, 31, 23], Operations: [] Exploring Operation: 56+23=79, Resulting Numbers: [72, 31, 79] Generated Node #0,0: 70:[72, 31, 79] Operation: 56+23=79 Exploring Operation: 56-31=25, Resulting Numbers: [72, 23, 25] Generated Node #0,1: 70:[72, 23, 25] Operation: 56-31=25 Exploring Operation: 72-56=16, Resulting Numbers: [31, 23, 16] Generated Node #0,2: 70:[31, 23, 16] Operation: 72-56=16 Exploring Operation: 56-23=33, Resulting Numbers: [72, 31, 33] Generated Node #0,3: 70:[72, 31, 33] Operation: 56-23=33 Exploring Operation: 31-23=8, Resulting Numbers: [56, 72, 8] Generated Node #0,4: 70:[56, 72, 8] Operation: 31-23=8 Moving to Node #0,3 Current State: 70:[72, 31, 33], Operations: ['56-23=33'] Exploring Operation: 72-33=39, Resulting Numbers: [31, 39] Generated Node #0,3,0: 70:[31, 39] Operation: 72-33=39 Exploring Operation: 31+33=64, Resulting Numbers: [72, 64] Generated Node #0,3,1: 70:[72, 64] Operation: 31+33=64 Exploring Operation: 72-31=41, Resulting Numbers: [33, 41] Generated Node #0,3,2: 70:[33, 41] Operation: 72-31=41 Exploring Operation: 33-31=2, Resulting Numbers: [72, 2] Generated Node #0,3,3: 70:[72, 2] Operation: 33-31=2 Exploring Operation: 72+31=103, Resulting Numbers: [33, 103] Generated Node #0,3,4: 70:[33, 103] Operation: 72+31=103 Moving to Node #0,2 Current State: 70:[31, 23, 16], Operations: ['72-56=16'] Exploring Operation: 23-16=7, Resulting Numbers: [31, 7] Generated Node #0,2,0: 70:[31, 7] Operation: 23-16=7 Exploring Operation: 31-16=15, Resulting Numbers: [23, 15] Generated Node #0,2,1: 70:[23, 15] Operation: 31-16=15 Exploring Operation: 23+16=39, Resulting Numbers: [31, 39] Generated Node #0,2,2: 70:[31, 39] Operation: 23+16=39 Exploring Operation: 31-23=8, Resulting Numbers: [16, 8] Generated Node #0,2,3: 70:[16, 8] Operation: 31-23=8 Exploring Operation: 31+23=54, Resulting Numbers: [16, 54] Generated Node #0,2,4: 70:[16, 54] Operation: 31+23=54 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 70:[16, 8], Operations: ['72-56=16', '31-23=8'] Exploring Operation: 16+8=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 16*8=128, Resulting Numbers: [128] 128,70 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,70 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:[31, 7], Operations: ['72-56=16', '23-16=7'] Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 31+7=38, Resulting Numbers: [38] 38,70 unequal: No Solution Exploring Operation: 31*7=217, Resulting Numbers: [217] 217,70 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:[31, 39], Operations: ['72-56=16', '23+16=39'] Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 31+39=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[56, 72, 31, 23], Operations: [] Exploring Operation: 72-56=16, Resulting Numbers: [31, 23, 16] Generated Node #0,2: 70:[31, 23, 16] Operation: 72-56=16 Moving to Node #0,2 Current State: 70:[31, 23, 16], Operations: ['72-56=16'] Exploring Operation: 23+16=39, Resulting Numbers: [31, 39] Generated Node #0,2,2: 70:[31, 39] Operation: 23+16=39 Moving to Node #0,2,2 Current State: 70:[31, 39], Operations: ['72-56=16', '23+16=39'] Exploring Operation: 31+39=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_5
mult_heuristic
[ 59, 95, 43, 91 ]
84
[ "95-59=36", "91-43=48", "36+48=84" ]
Current State: 84:[59, 95, 43, 91], Operations: [] Exploring Operation: 95-59=36, Resulting Numbers: [43, 91, 36] Generated Node #2: [43, 91, 36] from Operation: 95-59=36 Current State: 84:[43, 91, 36], Operations: ['95-59=36'] Exploring Operation: 91-43=48, Resulting Numbers: [36, 48] Generated Node #3: [36, 48] from Operation: 91-43=48 Current State: 84:[36, 48], Operations: ['95-59=36', '91-43=48'] Exploring Operation: 36+48=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[59, 95, 43, 91], Operations: [] Exploring Operation: 91-59=32, Resulting Numbers: [95, 43, 32] Generated Node #0,0: 84:[95, 43, 32] Operation: 91-59=32 Exploring Operation: 95-59=36, Resulting Numbers: [43, 91, 36] Generated Node #0,1: 84:[43, 91, 36] Operation: 95-59=36 Exploring Operation: 59-43=16, Resulting Numbers: [95, 91, 16] Generated Node #0,2: 84:[95, 91, 16] Operation: 59-43=16 Exploring Operation: 95-91=4, Resulting Numbers: [59, 43, 4] Generated Node #0,3: 84:[59, 43, 4] Operation: 95-91=4 Moving to Node #0,1 Current State: 84:[43, 91, 36], Operations: ['95-59=36'] Exploring Operation: 91-36=55, Resulting Numbers: [43, 55] Generated Node #0,1,0: 84:[43, 55] Operation: 91-36=55 Exploring Operation: 43+36=79, Resulting Numbers: [91, 79] Generated Node #0,1,1: 84:[91, 79] Operation: 43+36=79 Exploring Operation: 91-43=48, Resulting Numbers: [36, 48] Generated Node #0,1,2: 84:[36, 48] Operation: 91-43=48 Exploring Operation: 43-36=7, Resulting Numbers: [91, 7] Generated Node #0,1,3: 84:[91, 7] Operation: 43-36=7 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 84:[91, 7], Operations: ['95-59=36', '43-36=7'] Exploring Operation: 91*7=637, Resulting Numbers: [637] 637,84 unequal: No Solution Exploring Operation: 91+7=98, Resulting Numbers: [98] 98,84 unequal: No Solution Exploring Operation: 91/7=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 91-7=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[59, 95, 43, 91], Operations: [] Exploring Operation: 95-59=36, Resulting Numbers: [43, 91, 36] Generated Node #0,1: 84:[43, 91, 36] Operation: 95-59=36 Moving to Node #0,1 Current State: 84:[43, 91, 36], Operations: ['95-59=36'] Exploring Operation: 43-36=7, Resulting Numbers: [91, 7] Generated Node #0,1,3: 84:[91, 7] Operation: 43-36=7 Moving to Node #0,1,3 Current State: 84:[91, 7], Operations: ['95-59=36', '43-36=7'] Exploring Operation: 91-7=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 93, 3, 23, 40 ]
94
[ "93/3=31", "23+40=63", "31+63=94" ]
Current State: 94:[93, 3, 23, 40], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [23, 40, 31] Generated Node #2: [23, 40, 31] from Operation: 93/3=31 Current State: 94:[23, 40, 31], Operations: ['93/3=31'] Exploring Operation: 23+40=63, Resulting Numbers: [31, 63] Generated Node #3: [31, 63] from Operation: 23+40=63 Current State: 94:[31, 63], Operations: ['93/3=31', '23+40=63'] Exploring Operation: 31+63=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[93, 3, 23, 40], Operations: [] Exploring Operation: 23+40=63, Resulting Numbers: [93, 3, 63] Generated Node #0,0: 94:[93, 3, 63] Operation: 23+40=63 Exploring Operation: 40-23=17, Resulting Numbers: [93, 3, 17] Generated Node #0,1: 94:[93, 3, 17] Operation: 40-23=17 Exploring Operation: 23-3=20, Resulting Numbers: [93, 40, 20] Generated Node #0,2: 94:[93, 40, 20] Operation: 23-3=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[93, 3, 17], Operations: ['40-23=17'] Exploring Operation: 17-3=14, Resulting Numbers: [93, 14] Generated Node #0,1,0: 94:[93, 14] Operation: 17-3=14 Exploring Operation: 3*17=51, Resulting Numbers: [93, 51] Generated Node #0,1,1: 94:[93, 51] Operation: 3*17=51 Exploring Operation: 93+3=96, Resulting Numbers: [17, 96] Generated Node #0,1,2: 94:[17, 96] Operation: 93+3=96 Moving to Node #0,1,1 Current State: 94:[93, 51], Operations: ['40-23=17', '3*17=51'] Exploring Operation: 93+51=144, Resulting Numbers: [144] 144,94 unequal: No Solution Exploring Operation: 93*51=4743, Resulting Numbers: [4743] 4743,94 unequal: No Solution Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[93, 14], Operations: ['40-23=17', '17-3=14'] Exploring Operation: 93-14=79, Resulting Numbers: [79] 79,94 unequal: No Solution Exploring Operation: 93*14=1302, Resulting Numbers: [1302] 1302,94 unequal: No Solution Exploring Operation: 93+14=107, Resulting Numbers: [107] 107,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[17, 96], Operations: ['40-23=17', '93+3=96'] Exploring Operation: 96-17=79, Resulting Numbers: [79] 79,94 unequal: No Solution Exploring Operation: 17*96=1632, Resulting Numbers: [1632] 1632,94 unequal: No Solution Exploring Operation: 17+96=113, Resulting Numbers: [113] 113,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[93, 3, 63], Operations: ['23+40=63'] Exploring Operation: 93+3=96, Resulting Numbers: [63, 96] Generated Node #0,0,0: 94:[63, 96] Operation: 93+3=96 Exploring Operation: 93-63=30, Resulting Numbers: [3, 30] Generated Node #0,0,1: 94:[3, 30] Operation: 93-63=30 Exploring Operation: 63-3=60, Resulting Numbers: [93, 60] Generated Node #0,0,2: 94:[93, 60] Operation: 63-3=60 Moving to Node #0,0,2 Current State: 94:[93, 60], Operations: ['23+40=63', '63-3=60'] Exploring Operation: 93*60=5580, Resulting Numbers: [5580] 5580,94 unequal: No Solution Exploring Operation: 93+60=153, Resulting Numbers: [153] 153,94 unequal: No Solution Exploring Operation: 93-60=33, Resulting Numbers: [33] 33,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[63, 96], Operations: ['23+40=63', '93+3=96'] Exploring Operation: 63+96=159, Resulting Numbers: [159] 159,94 unequal: No Solution Exploring Operation: 96-63=33, Resulting Numbers: [33] 33,94 unequal: No Solution Exploring Operation: 63*96=6048, Resulting Numbers: [6048] 6048,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[3, 30], Operations: ['23+40=63', '93-63=30'] Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,94 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,94 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[93, 40, 20], Operations: ['23-3=20'] Exploring Operation: 40+20=60, Resulting Numbers: [93, 60] Generated Node #0,2,0: 94:[93, 60] Operation: 40+20=60 Exploring Operation: 40-20=20, Resulting Numbers: [93, 20] Generated Node #0,2,1: 94:[93, 20] Operation: 40-20=20 Exploring Operation: 40/20=2, Resulting Numbers: [93, 2] Generated Node #0,2,2: 94:[93, 2] Operation: 40/20=2 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 94:[93, 2], Operations: ['23-3=20', '40/20=2'] Exploring Operation: 93*2=186, Resulting Numbers: [186] 186,94 unequal: No Solution Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,94 unequal: No Solution Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,94 unequal: No Solution No 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: 94:[93, 60], Operations: ['23-3=20', '40+20=60'] Exploring Operation: 93-60=33, Resulting Numbers: [33] 33,94 unequal: No Solution Exploring Operation: 93+60=153, Resulting Numbers: [153] 153,94 unequal: No Solution Exploring Operation: 93*60=5580, Resulting Numbers: [5580] 5580,94 unequal: No Solution No 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: 94:[93, 20], Operations: ['23-3=20', '40-20=20'] Exploring Operation: 93+20=113, Resulting Numbers: [113] 113,94 unequal: No Solution Exploring Operation: 93-20=73, Resulting Numbers: [73] 73,94 unequal: No Solution Exploring Operation: 93*20=1860, Resulting Numbers: [1860] 1860,94 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
[ 17, 40, 53, 3 ]
79
[ "40-17=23", "53+3=56", "23+56=79" ]
Current State: 79:[17, 40, 53, 3], Operations: [] Exploring Operation: 40-17=23, Resulting Numbers: [53, 3, 23] Generated Node #2: [53, 3, 23] from Operation: 40-17=23 Current State: 79:[53, 3, 23], Operations: ['40-17=23'] Exploring Operation: 53+3=56, Resulting Numbers: [23, 56] Generated Node #3: [23, 56] from Operation: 53+3=56 Current State: 79:[23, 56], Operations: ['40-17=23', '53+3=56'] Exploring Operation: 23+56=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[17, 40, 53, 3], Operations: [] Exploring Operation: 17*3=51, Resulting Numbers: [40, 53, 51] Generated Node #0,0: 79:[40, 53, 51] Operation: 17*3=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[40, 53, 51], Operations: ['17*3=51'] Exploring Operation: 40+51=91, Resulting Numbers: [53, 91] Generated Node #0,0,0: 79:[53, 91] Operation: 40+51=91 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[53, 91], Operations: ['17*3=51', '40+51=91'] Exploring Operation: 91-53=38, Resulting Numbers: [38] 38,79 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
[ 58, 34, 36, 82 ]
17
[ "36-34=2", "82/2=41", "58-41=17" ]
Current State: 17:[58, 34, 36, 82], Operations: [] Exploring Operation: 36-34=2, Resulting Numbers: [58, 82, 2] Generated Node #2: [58, 82, 2] from Operation: 36-34=2 Current State: 17:[58, 82, 2], Operations: ['36-34=2'] Exploring Operation: 82/2=41, Resulting Numbers: [58, 41] Generated Node #3: [58, 41] from Operation: 82/2=41 Current State: 17:[58, 41], Operations: ['36-34=2', '82/2=41'] Exploring Operation: 58-41=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[58, 34, 36, 82], Operations: [] Exploring Operation: 58-36=22, Resulting Numbers: [34, 82, 22] Generated Node #0,0: 17:[34, 82, 22] Operation: 58-36=22 Exploring Operation: 82-58=24, Resulting Numbers: [34, 36, 24] Generated Node #0,1: 17:[34, 36, 24] Operation: 82-58=24 Moving to Node #0,1 Current State: 17:[34, 36, 24], Operations: ['82-58=24'] Exploring Operation: 36-24=12, Resulting Numbers: [34, 12] Generated Node #0,1,0: 17:[34, 12] Operation: 36-24=12 Exploring Operation: 36-34=2, Resulting Numbers: [24, 2] Generated Node #0,1,1: 17:[24, 2] Operation: 36-34=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 17:[34, 12], Operations: ['82-58=24', '36-24=12'] Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 34+12=46, Resulting Numbers: [46] 46,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 17:[24, 2], Operations: ['82-58=24', '36-34=2'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 17:[34, 82, 22], Operations: ['58-36=22'] Exploring Operation: 82-22=60, Resulting Numbers: [34, 60] Generated Node #0,0,0: 17:[34, 60] Operation: 82-22=60 Exploring Operation: 82-34=48, Resulting Numbers: [22, 48] Generated Node #0,0,1: 17:[22, 48] Operation: 82-34=48 Moving to Node #0,0,1 Current State: 17:[22, 48], Operations: ['58-36=22', '82-34=48'] Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,17 unequal: No Solution Exploring Operation: 22+48=70, Resulting Numbers: [70] 70,17 unequal: No Solution Moving to Node #0,0,0 Current State: 17:[34, 60], Operations: ['58-36=22', '82-22=60'] Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,17 unequal: No Solution Exploring Operation: 34+60=94, Resulting Numbers: [94] 94,17 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 83, 28, 15, 83 ]
28
[ "83-83=0", "15*0=0", "28+0=28" ]
Current State: 28:[83, 28, 15, 83], Operations: [] Exploring Operation: 83-83=0, Resulting Numbers: [28, 15, 0] Generated Node #2: [28, 15, 0] from Operation: 83-83=0 Current State: 28:[28, 15, 0], Operations: ['83-83=0'] Exploring Operation: 15*0=0, Resulting Numbers: [28, 0] Generated Node #3: [28, 0] from Operation: 15*0=0 Current State: 28:[28, 0], Operations: ['83-83=0', '15*0=0'] Exploring Operation: 28+0=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[83, 28, 15, 83], Operations: [] Exploring Operation: 83/83=1, Resulting Numbers: [28, 15, 1] Generated Node #0,0: 28:[28, 15, 1] Operation: 83/83=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[28, 15, 1], Operations: ['83/83=1'] Exploring Operation: 15-1=14, Resulting Numbers: [28, 14] Generated Node #0,0,0: 28:[28, 14] Operation: 15-1=14 Moving to Node #0,0,0 Current State: 28:[28, 14], Operations: ['83/83=1', '15-1=14'] Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,28 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
[ 6, 6, 95, 43 ]
43
[ "6-6=0", "95*0=0", "43+0=43" ]
Current State: 43:[6, 6, 95, 43], Operations: [] Exploring Operation: 6-6=0, Resulting Numbers: [95, 43, 0] Generated Node #2: [95, 43, 0] from Operation: 6-6=0 Current State: 43:[95, 43, 0], Operations: ['6-6=0'] Exploring Operation: 95*0=0, Resulting Numbers: [43, 0] Generated Node #3: [43, 0] from Operation: 95*0=0 Current State: 43:[43, 0], Operations: ['6-6=0', '95*0=0'] Exploring Operation: 43+0=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[6, 6, 95, 43], Operations: [] Exploring Operation: 6+6=12, Resulting Numbers: [95, 43, 12] Generated Node #0,0: 43:[95, 43, 12] Operation: 6+6=12 Exploring Operation: 95-6=89, Resulting Numbers: [6, 43, 89] Generated Node #0,1: 43:[6, 43, 89] Operation: 95-6=89 Exploring Operation: 6*6=36, Resulting Numbers: [95, 43, 36] Generated Node #0,2: 43:[95, 43, 36] Operation: 6*6=36 Moving to Node #0,2 Current State: 43:[95, 43, 36], Operations: ['6*6=36'] Exploring Operation: 95+36=131, Resulting Numbers: [43, 131] Generated Node #0,2,0: 43:[43, 131] Operation: 95+36=131 Exploring Operation: 95-43=52, Resulting Numbers: [36, 52] Generated Node #0,2,1: 43:[36, 52] Operation: 95-43=52 Exploring Operation: 95-36=59, Resulting Numbers: [43, 59] Generated Node #0,2,2: 43:[43, 59] Operation: 95-36=59 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 43:[36, 52], Operations: ['6*6=36', '95-43=52'] Exploring Operation: 36*52=1872, Resulting Numbers: [1872] 1872,43 unequal: No Solution Exploring Operation: 36+52=88, Resulting Numbers: [88] 88,43 unequal: No Solution Exploring Operation: 52-36=16, Resulting Numbers: [16] 16,43 unequal: No Solution No 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: 43:[43, 59], Operations: ['6*6=36', '95-36=59'] Exploring Operation: 43+59=102, Resulting Numbers: [102] 102,43 unequal: No Solution Exploring Operation: 43*59=2537, Resulting Numbers: [2537] 2537,43 unequal: No Solution Exploring Operation: 59-43=16, Resulting Numbers: [16] 16,43 unequal: No Solution No 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: 43:[43, 131], Operations: ['6*6=36', '95+36=131'] Exploring Operation: 43*131=5633, Resulting Numbers: [5633] 5633,43 unequal: No Solution Exploring Operation: 43+131=174, Resulting Numbers: [174] 174,43 unequal: No Solution Exploring Operation: 131-43=88, Resulting Numbers: [88] 88,43 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: 43:[95, 43, 12], Operations: ['6+6=12'] Exploring Operation: 95-43=52, Resulting Numbers: [12, 52] Generated Node #0,0,0: 43:[12, 52] Operation: 95-43=52 Exploring Operation: 95+12=107, Resulting Numbers: [43, 107] Generated Node #0,0,1: 43:[43, 107] Operation: 95+12=107 Exploring Operation: 95-12=83, Resulting Numbers: [43, 83] Generated Node #0,0,2: 43:[43, 83] Operation: 95-12=83 Moving to Node #0,1 Current State: 43:[6, 43, 89], Operations: ['95-6=89'] Exploring Operation: 6+43=49, Resulting Numbers: [89, 49] Generated Node #0,1,0: 43:[89, 49] Operation: 6+43=49 Exploring Operation: 89-6=83, Resulting Numbers: [43, 83] Generated Node #0,1,1: 43:[43, 83] Operation: 89-6=83 Exploring Operation: 89-43=46, Resulting Numbers: [6, 46] Generated Node #0,1,2: 43:[6, 46] Operation: 89-43=46 Moving to Node #0,0,0 Current State: 43:[12, 52], Operations: ['6+6=12', '95-43=52'] Exploring Operation: 12+52=64, Resulting Numbers: [64] 64,43 unequal: No Solution Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,43 unequal: No Solution Exploring Operation: 12*52=624, Resulting Numbers: [624] 624,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[43, 83], Operations: ['6+6=12', '95-12=83'] Exploring Operation: 83-43=40, Resulting Numbers: [40] 40,43 unequal: No Solution Exploring Operation: 43*83=3569, Resulting Numbers: [3569] 3569,43 unequal: No Solution Exploring Operation: 43+83=126, Resulting Numbers: [126] 126,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[6, 46], Operations: ['95-6=89', '89-43=46'] Exploring Operation: 6+46=52, Resulting Numbers: [52] 52,43 unequal: No Solution Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,43 unequal: No Solution Exploring Operation: 6*46=276, Resulting Numbers: [276] 276,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[43, 83], Operations: ['95-6=89', '89-6=83'] Exploring Operation: 43+83=126, Resulting Numbers: [126] 126,43 unequal: No Solution Exploring Operation: 43*83=3569, Resulting Numbers: [3569] 3569,43 unequal: No Solution Exploring Operation: 83-43=40, Resulting Numbers: [40] 40,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[89, 49], Operations: ['95-6=89', '6+43=49'] Exploring Operation: 89-49=40, Resulting Numbers: [40] 40,43 unequal: No Solution Exploring Operation: 89+49=138, Resulting Numbers: [138] 138,43 unequal: No Solution Exploring Operation: 89*49=4361, Resulting Numbers: [4361] 4361,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[43, 107], Operations: ['6+6=12', '95+12=107'] Exploring Operation: 107-43=64, Resulting Numbers: [64] 64,43 unequal: No Solution Exploring Operation: 43+107=150, Resulting Numbers: [150] 150,43 unequal: No Solution Exploring Operation: 43*107=4601, Resulting Numbers: [4601] 4601,43 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 44, 2, 60, 53 ]
61
[ "60-44=16", "16/2=8", "53+8=61" ]
Current State: 61:[44, 2, 60, 53], Operations: [] Exploring Operation: 60-44=16, Resulting Numbers: [2, 53, 16] Generated Node #2: [2, 53, 16] from Operation: 60-44=16 Current State: 61:[2, 53, 16], Operations: ['60-44=16'] Exploring Operation: 16/2=8, Resulting Numbers: [53, 8] Generated Node #3: [53, 8] from Operation: 16/2=8 Current State: 61:[53, 8], Operations: ['60-44=16', '16/2=8'] Exploring Operation: 53+8=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[44, 2, 60, 53], Operations: [] Exploring Operation: 44+2=46, Resulting Numbers: [60, 53, 46] Generated Node #0,0: 61:[60, 53, 46] Operation: 44+2=46 Exploring Operation: 2+53=55, Resulting Numbers: [44, 60, 55] Generated Node #0,1: 61:[44, 60, 55] Operation: 2+53=55 Exploring Operation: 2+60=62, Resulting Numbers: [44, 53, 62] Generated Node #0,2: 61:[44, 53, 62] Operation: 2+60=62 Moving to Node #0,0 Current State: 61:[60, 53, 46], Operations: ['44+2=46'] Exploring Operation: 60+46=106, Resulting Numbers: [53, 106] Generated Node #0,0,0: 61:[53, 106] Operation: 60+46=106 Exploring Operation: 53+46=99, Resulting Numbers: [60, 99] Generated Node #0,0,1: 61:[60, 99] Operation: 53+46=99 Exploring Operation: 60-46=14, Resulting Numbers: [53, 14] Generated Node #0,0,2: 61:[53, 14] Operation: 60-46=14 Moving to Node #0,1 Current State: 61:[44, 60, 55], Operations: ['2+53=55'] Exploring Operation: 44+60=104, Resulting Numbers: [55, 104] Generated Node #0,1,0: 61:[55, 104] Operation: 44+60=104 Exploring Operation: 60-44=16, Resulting Numbers: [55, 16] Generated Node #0,1,1: 61:[55, 16] Operation: 60-44=16 Exploring Operation: 44+55=99, Resulting Numbers: [60, 99] Generated Node #0,1,2: 61:[60, 99] Operation: 44+55=99 Moving to Node #0,2 Current State: 61:[44, 53, 62], Operations: ['2+60=62'] Exploring Operation: 62-44=18, Resulting Numbers: [53, 18] Generated Node #0,2,0: 61:[53, 18] Operation: 62-44=18 Exploring Operation: 44+53=97, Resulting Numbers: [62, 97] Generated Node #0,2,1: 61:[62, 97] Operation: 44+53=97 Exploring Operation: 53-44=9, Resulting Numbers: [62, 9] Generated Node #0,2,2: 61:[62, 9] Operation: 53-44=9 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 61:[62, 97], Operations: ['2+60=62', '44+53=97'] Exploring Operation: 97-62=35, Resulting Numbers: [35] 35,61 unequal: No Solution Exploring Operation: 62+97=159, Resulting Numbers: [159] 159,61 unequal: No Solution Exploring Operation: 62*97=6014, Resulting Numbers: [6014] 6014,61 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:[53, 18], Operations: ['2+60=62', '62-44=18'] Exploring Operation: 53-18=35, Resulting Numbers: [35] 35,61 unequal: No Solution Exploring Operation: 53*18=954, Resulting Numbers: [954] 954,61 unequal: No Solution Exploring Operation: 53+18=71, Resulting Numbers: [71] 71,61 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 #0,2,2 Current State: 61:[62, 9], Operations: ['2+60=62', '53-44=9'] Exploring Operation: 62*9=558, Resulting Numbers: [558] 558,61 unequal: No Solution Exploring Operation: 62+9=71, Resulting Numbers: [71] 71,61 unequal: No Solution Exploring Operation: 62-9=53, Resulting Numbers: [53] 53,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 61:[60, 99], Operations: ['44+2=46', '53+46=99'] Exploring Operation: 99-60=39, Resulting Numbers: [39] 39,61 unequal: No Solution Exploring Operation: 60+99=159, Resulting Numbers: [159] 159,61 unequal: No Solution Exploring Operation: 60*99=5940, Resulting Numbers: [5940] 5940,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[60, 99], Operations: ['2+53=55', '44+55=99'] Exploring Operation: 99-60=39, Resulting Numbers: [39] 39,61 unequal: No Solution Exploring Operation: 60+99=159, Resulting Numbers: [159] 159,61 unequal: No Solution Exploring Operation: 60*99=5940, Resulting Numbers: [5940] 5940,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[55, 104], Operations: ['2+53=55', '44+60=104'] Exploring Operation: 55*104=5720, Resulting Numbers: [5720] 5720,61 unequal: No Solution Exploring Operation: 104-55=49, Resulting Numbers: [49] 49,61 unequal: No Solution Exploring Operation: 55+104=159, Resulting Numbers: [159] 159,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[55, 16], Operations: ['2+53=55', '60-44=16'] Exploring Operation: 55-16=39, Resulting Numbers: [39] 39,61 unequal: No Solution Exploring Operation: 55+16=71, Resulting Numbers: [71] 71,61 unequal: No Solution Exploring Operation: 55*16=880, Resulting Numbers: [880] 880,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[53, 106], Operations: ['44+2=46', '60+46=106'] Exploring Operation: 106/53=2, Resulting Numbers: [2] 2,61 unequal: No Solution Exploring Operation: 106-53=53, Resulting Numbers: [53] 53,61 unequal: No Solution Exploring Operation: 53+106=159, Resulting Numbers: [159] 159,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[53, 14], Operations: ['44+2=46', '60-46=14'] Exploring Operation: 53*14=742, Resulting Numbers: [742] 742,61 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,61 unequal: No Solution Exploring Operation: 53+14=67, Resulting Numbers: [67] 67,61 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 29, 60, 75, 79 ]
65
[ "29+60=89", "75+79=154", "154-89=65" ]
Current State: 65:[29, 60, 75, 79], Operations: [] Exploring Operation: 29+60=89, Resulting Numbers: [75, 79, 89] Generated Node #2: [75, 79, 89] from Operation: 29+60=89 Current State: 65:[75, 79, 89], Operations: ['29+60=89'] Exploring Operation: 75+79=154, Resulting Numbers: [89, 154] Generated Node #3: [89, 154] from Operation: 75+79=154 Current State: 65:[89, 154], Operations: ['29+60=89', '75+79=154'] Exploring Operation: 154-89=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[29, 60, 75, 79], Operations: [] Exploring Operation: 79-29=50, Resulting Numbers: [60, 75, 50] Generated Node #0,0: 65:[60, 75, 50] Operation: 79-29=50 Exploring Operation: 79-75=4, Resulting Numbers: [29, 60, 4] Generated Node #0,1: 65:[29, 60, 4] Operation: 79-75=4 Moving to Node #0,1 Current State: 65:[29, 60, 4], Operations: ['79-75=4'] Exploring Operation: 29-4=25, Resulting Numbers: [60, 25] Generated Node #0,1,0: 65:[60, 25] Operation: 29-4=25 Exploring Operation: 60+4=64, Resulting Numbers: [29, 64] Generated Node #0,1,1: 65:[29, 64] Operation: 60+4=64 Moving to Node #0,0 Current State: 65:[60, 75, 50], Operations: ['79-29=50'] Exploring Operation: 60-50=10, Resulting Numbers: [75, 10] Generated Node #0,0,0: 65:[75, 10] Operation: 60-50=10 Exploring Operation: 75-60=15, Resulting Numbers: [50, 15] Generated Node #0,0,1: 65:[50, 15] Operation: 75-60=15 Moving to Node #0,0,0 Current State: 65:[75, 10], Operations: ['79-29=50', '60-50=10'] Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[29, 60, 75, 79], Operations: [] Exploring Operation: 79-29=50, Resulting Numbers: [60, 75, 50] Generated Node #0,0: 65:[60, 75, 50] Operation: 79-29=50 Moving to Node #0,0 Current State: 65:[60, 75, 50], Operations: ['79-29=50'] Exploring Operation: 60-50=10, Resulting Numbers: [75, 10] Generated Node #0,0,0: 65:[75, 10] Operation: 60-50=10 Moving to Node #0,0,0 Current State: 65:[75, 10], Operations: ['79-29=50', '60-50=10'] Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
0.990451
hs_2
sum_heuristic