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
[ 1, 26, 50, 40 ]
37
[ "1+26=27", "50-40=10", "27+10=37" ]
Current State: 37:[1, 26, 50, 40], Operations: [] Exploring Operation: 1+26=27, Resulting Numbers: [50, 40, 27] Generated Node #2: [50, 40, 27] from Operation: 1+26=27 Current State: 37:[50, 40, 27], Operations: ['1+26=27'] Exploring Operation: 50-40=10, Resulting Numbers: [27, 10] Generated Node #3: [27, 10] from Operation: 50-40=10 Current State: 37:[27, 10], Operations: ['1+26=27', '50-40=10'] Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[1, 26, 50, 40], Operations: [] Exploring Operation: 40-1=39, Resulting Numbers: [26, 50, 39] Generated Node #0,0: 37:[26, 50, 39] Operation: 40-1=39 Exploring Operation: 50-1=49, Resulting Numbers: [26, 40, 49] Generated Node #0,1: 37:[26, 40, 49] Operation: 50-1=49 Exploring Operation: 1+26=27, Resulting Numbers: [50, 40, 27] Generated Node #0,2: 37:[50, 40, 27] Operation: 1+26=27 Moving to Node #0,0 Current State: 37:[26, 50, 39], Operations: ['40-1=39'] Exploring Operation: 50-39=11, Resulting Numbers: [26, 11] Generated Node #0,0,0: 37:[26, 11] Operation: 50-39=11 Exploring Operation: 50-26=24, Resulting Numbers: [39, 24] Generated Node #0,0,1: 37:[39, 24] Operation: 50-26=24 Exploring Operation: 39-26=13, Resulting Numbers: [50, 13] Generated Node #0,0,2: 37:[50, 13] Operation: 39-26=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[39, 24], Operations: ['40-1=39', '50-26=24'] Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,37 unequal: No Solution Exploring Operation: 39*24=936, Resulting Numbers: [936] 936,37 unequal: No Solution Exploring Operation: 39+24=63, Resulting Numbers: [63] 63,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[26, 11], Operations: ['40-1=39', '50-39=11'] Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,37 unequal: No Solution Exploring Operation: 26*11=286, Resulting Numbers: [286] 286,37 unequal: No Solution Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[1, 26, 50, 40], Operations: [] Exploring Operation: 40-1=39, Resulting Numbers: [26, 50, 39] Generated Node #0,0: 37:[26, 50, 39] Operation: 40-1=39 Moving to Node #0,0 Current State: 37:[26, 50, 39], Operations: ['40-1=39'] Exploring Operation: 50-39=11, Resulting Numbers: [26, 11] Generated Node #0,0,0: 37:[26, 11] Operation: 50-39=11 Moving to Node #0,0,0 Current State: 37:[26, 11], Operations: ['40-1=39', '50-39=11'] Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 3, 4, 63, 24 ]
51
[ "3*4=12", "63-24=39", "12+39=51" ]
Current State: 51:[3, 4, 63, 24], Operations: [] Exploring Operation: 3*4=12, Resulting Numbers: [63, 24, 12] Generated Node #2: [63, 24, 12] from Operation: 3*4=12 Current State: 51:[63, 24, 12], Operations: ['3*4=12'] Exploring Operation: 63-24=39, Resulting Numbers: [12, 39] Generated Node #3: [12, 39] from Operation: 63-24=39 Current State: 51:[12, 39], Operations: ['3*4=12', '63-24=39'] Exploring Operation: 12+39=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[3, 4, 63, 24], Operations: [] Exploring Operation: 63/3=21, Resulting Numbers: [4, 24, 21] Generated Node #0,0: 51:[4, 24, 21] Operation: 63/3=21 Exploring Operation: 63-4=59, Resulting Numbers: [3, 24, 59] Generated Node #0,1: 51:[3, 24, 59] Operation: 63-4=59 Exploring Operation: 63-24=39, Resulting Numbers: [3, 4, 39] Generated Node #0,2: 51:[3, 4, 39] Operation: 63-24=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[4, 24, 21], Operations: ['63/3=21'] Exploring Operation: 24-21=3, Resulting Numbers: [4, 3] Generated Node #0,0,0: 51:[4, 3] Operation: 24-21=3 Exploring Operation: 24/4=6, Resulting Numbers: [21, 6] Generated Node #0,0,1: 51:[21, 6] Operation: 24/4=6 Exploring Operation: 24-4=20, Resulting Numbers: [21, 20] Generated Node #0,0,2: 51:[21, 20] Operation: 24-4=20 Moving to Node #0,0,0 Current State: 51:[4, 3], Operations: ['63/3=21', '24-21=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,51 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,51 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[21, 6], Operations: ['63/3=21', '24/4=6'] Exploring Operation: 21*6=126, Resulting Numbers: [126] 126,51 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 21+6=27, Resulting Numbers: [27] 27,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[21, 20], Operations: ['63/3=21', '24-4=20'] Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 21*20=420, Resulting Numbers: [420] 420,51 unequal: No Solution Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[3, 4, 39], Operations: ['63-24=39'] Exploring Operation: 39/3=13, Resulting Numbers: [4, 13] Generated Node #0,2,0: 51:[4, 13] Operation: 39/3=13 Exploring Operation: 3+39=42, Resulting Numbers: [4, 42] Generated Node #0,2,1: 51:[4, 42] Operation: 3+39=42 Exploring Operation: 4+39=43, Resulting Numbers: [3, 43] Generated Node #0,2,2: 51:[3, 43] Operation: 4+39=43 Moving to Node #0,2,0 Current State: 51:[4, 13], Operations: ['63-24=39', '39/3=13'] Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,51 unequal: No Solution Exploring Operation: 4*13=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 4+13=17, Resulting Numbers: [17] 17,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[3, 43], Operations: ['63-24=39', '4+39=43'] Exploring Operation: 3+43=46, Resulting Numbers: [46] 46,51 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,51 unequal: No Solution Exploring Operation: 3*43=129, Resulting Numbers: [129] 129,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[4, 42], Operations: ['63-24=39', '3+39=42'] Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,51 unequal: No Solution Exploring Operation: 4*42=168, Resulting Numbers: [168] 168,51 unequal: No Solution Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[3, 24, 59], Operations: ['63-4=59'] Exploring Operation: 24-3=21, Resulting Numbers: [59, 21] Generated Node #0,1,0: 51:[59, 21] Operation: 24-3=21 Exploring Operation: 59-3=56, Resulting Numbers: [24, 56] Generated Node #0,1,1: 51:[24, 56] Operation: 59-3=56 Exploring Operation: 24/3=8, Resulting Numbers: [59, 8] Generated Node #0,1,2: 51:[59, 8] Operation: 24/3=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 51:[59, 21], Operations: ['63-4=59', '24-3=21'] Exploring Operation: 59*21=1239, Resulting Numbers: [1239] 1239,51 unequal: No Solution Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,51 unequal: No Solution Exploring Operation: 59+21=80, Resulting Numbers: [80] 80,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[24, 56], Operations: ['63-4=59', '59-3=56'] Exploring Operation: 24+56=80, Resulting Numbers: [80] 80,51 unequal: No Solution Exploring Operation: 56-24=32, Resulting Numbers: [32] 32,51 unequal: No Solution Exploring Operation: 24*56=1344, Resulting Numbers: [1344] 1344,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 51:[59, 8], Operations: ['63-4=59', '24/3=8'] Exploring Operation: 59+8=67, Resulting Numbers: [67] 67,51 unequal: No Solution Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[3, 4, 63, 24], Operations: [] Exploring Operation: 63-4=59, Resulting Numbers: [3, 24, 59] Generated Node #0,1: 51:[3, 24, 59] Operation: 63-4=59 Moving to Node #0,1 Current State: 51:[3, 24, 59], Operations: ['63-4=59'] Exploring Operation: 24/3=8, Resulting Numbers: [59, 8] Generated Node #0,1,2: 51:[59, 8] Operation: 24/3=8 Moving to Node #0,1,2 Current State: 51:[59, 8], Operations: ['63-4=59', '24/3=8'] Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.963542
hs_3
sum_heuristic
[ 17, 95, 47, 5 ]
11
[ "47-17=30", "95/5=19", "30-19=11" ]
Current State: 11:[17, 95, 47, 5], Operations: [] Exploring Operation: 47-17=30, Resulting Numbers: [95, 5, 30] Generated Node #2: [95, 5, 30] from Operation: 47-17=30 Current State: 11:[95, 5, 30], Operations: ['47-17=30'] Exploring Operation: 95/5=19, Resulting Numbers: [30, 19] Generated Node #3: [30, 19] from Operation: 95/5=19 Current State: 11:[30, 19], Operations: ['47-17=30', '95/5=19'] Exploring Operation: 30-19=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[17, 95, 47, 5], Operations: [] Exploring Operation: 95-47=48, Resulting Numbers: [17, 5, 48] Generated Node #0,0: 11:[17, 5, 48] Operation: 95-47=48 Exploring Operation: 95/5=19, Resulting Numbers: [17, 47, 19] Generated Node #0,1: 11:[17, 47, 19] Operation: 95/5=19 Exploring Operation: 47-17=30, Resulting Numbers: [95, 5, 30] Generated Node #0,2: 11:[95, 5, 30] Operation: 47-17=30 Exploring Operation: 95-17=78, Resulting Numbers: [47, 5, 78] Generated Node #0,3: 11:[47, 5, 78] Operation: 95-17=78 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[17, 5, 48], Operations: ['95-47=48'] Exploring Operation: 48-5=43, Resulting Numbers: [17, 43] Generated Node #0,0,0: 11:[17, 43] Operation: 48-5=43 Exploring Operation: 17-5=12, Resulting Numbers: [48, 12] Generated Node #0,0,1: 11:[48, 12] Operation: 17-5=12 Exploring Operation: 17+5=22, Resulting Numbers: [48, 22] Generated Node #0,0,2: 11:[48, 22] Operation: 17+5=22 Exploring Operation: 48-17=31, Resulting Numbers: [5, 31] Generated Node #0,0,3: 11:[5, 31] Operation: 48-17=31 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 11:[5, 31], Operations: ['95-47=48', '48-17=31'] Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,11 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,11 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 #0,0,0 Current State: 11:[17, 43], Operations: ['95-47=48', '48-5=43'] Exploring Operation: 17+43=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 17*43=731, Resulting Numbers: [731] 731,11 unequal: No Solution Exploring Operation: 43-17=26, Resulting Numbers: [26] 26,11 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 #0,0,1 Current State: 11:[48, 12], Operations: ['95-47=48', '17-5=12'] Exploring Operation: 48-12=36, Resulting Numbers: [36] 36,11 unequal: No Solution Exploring Operation: 48+12=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 48*12=576, Resulting Numbers: [576] 576,11 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 #0,0,2 Current State: 11:[48, 22], Operations: ['95-47=48', '17+5=22'] Exploring Operation: 48*22=1056, Resulting Numbers: [1056] 1056,11 unequal: No Solution Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 48+22=70, Resulting Numbers: [70] 70,11 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: 11:[17, 47, 19], Operations: ['95/5=19'] Exploring Operation: 47-17=30, Resulting Numbers: [19, 30] Generated Node #0,1,0: 11:[19, 30] Operation: 47-17=30 Exploring Operation: 17+47=64, Resulting Numbers: [19, 64] Generated Node #0,1,1: 11:[19, 64] Operation: 17+47=64 Exploring Operation: 47-19=28, Resulting Numbers: [17, 28] Generated Node #0,1,2: 11:[17, 28] Operation: 47-19=28 Exploring Operation: 19-17=2, Resulting Numbers: [47, 2] Generated Node #0,1,3: 11:[47, 2] Operation: 19-17=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 11:[17, 28], Operations: ['95/5=19', '47-19=28'] Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[17, 95, 47, 5], Operations: [] Exploring Operation: 95/5=19, Resulting Numbers: [17, 47, 19] Generated Node #0,1: 11:[17, 47, 19] Operation: 95/5=19 Moving to Node #0,1 Current State: 11:[17, 47, 19], Operations: ['95/5=19'] Exploring Operation: 47-19=28, Resulting Numbers: [17, 28] Generated Node #0,1,2: 11:[17, 28] Operation: 47-19=28 Moving to Node #0,1,2 Current State: 11:[17, 28], Operations: ['95/5=19', '47-19=28'] Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 35, 8, 3, 48 ]
93
[ "8*48=384", "384/3=128", "128-35=93" ]
Current State: 93:[35, 8, 3, 48], Operations: [] Exploring Operation: 8*48=384, Resulting Numbers: [35, 3, 384] Generated Node #2: [35, 3, 384] from Operation: 8*48=384 Current State: 93:[35, 3, 384], Operations: ['8*48=384'] Exploring Operation: 384/3=128, Resulting Numbers: [35, 128] Generated Node #3: [35, 128] from Operation: 384/3=128 Current State: 93:[35, 128], Operations: ['8*48=384', '384/3=128'] Exploring Operation: 128-35=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[35, 8, 3, 48], Operations: [] Exploring Operation: 48-8=40, Resulting Numbers: [35, 3, 40] Generated Node #0,0: 93:[35, 3, 40] Operation: 48-8=40 Exploring Operation: 48/8=6, Resulting Numbers: [35, 3, 6] Generated Node #0,1: 93:[35, 3, 6] Operation: 48/8=6 Moving to Node #0,1 Current State: 93:[35, 3, 6], Operations: ['48/8=6'] Exploring Operation: 35-3=32, Resulting Numbers: [6, 32] Generated Node #0,1,0: 93:[6, 32] Operation: 35-3=32 Exploring Operation: 35-6=29, Resulting Numbers: [3, 29] Generated Node #0,1,1: 93:[3, 29] Operation: 35-6=29 Moving to Node #0,0 Current State: 93:[35, 3, 40], Operations: ['48-8=40'] Exploring Operation: 35-3=32, Resulting Numbers: [40, 32] Generated Node #0,0,0: 93:[40, 32] Operation: 35-3=32 Exploring Operation: 40-35=5, Resulting Numbers: [3, 5] Generated Node #0,0,1: 93:[3, 5] Operation: 40-35=5 Moving to Node #0,1,1 Current State: 93:[3, 29], Operations: ['48/8=6', '35-6=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,93 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[3, 5], Operations: ['48-8=40', '40-35=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,93 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,93 unequal: No Solution Moving to Node #0,1,0 Current State: 93:[6, 32], Operations: ['48/8=6', '35-3=32'] Exploring Operation: 6+32=38, Resulting Numbers: [38] 38,93 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[40, 32], Operations: ['48-8=40', '35-3=32'] Exploring Operation: 40+32=72, Resulting Numbers: [72] 72,93 unequal: No Solution Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,93 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 99, 16, 54, 71 ]
66
[ "99-16=83", "71-54=17", "83-17=66" ]
Current State: 66:[99, 16, 54, 71], Operations: [] Exploring Operation: 99-16=83, Resulting Numbers: [54, 71, 83] Generated Node #2: [54, 71, 83] from Operation: 99-16=83 Current State: 66:[54, 71, 83], Operations: ['99-16=83'] Exploring Operation: 71-54=17, Resulting Numbers: [83, 17] Generated Node #3: [83, 17] from Operation: 71-54=17 Current State: 66:[83, 17], Operations: ['99-16=83', '71-54=17'] Exploring Operation: 83-17=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[99, 16, 54, 71], Operations: [] Exploring Operation: 99-16=83, Resulting Numbers: [54, 71, 83] Generated Node #0,0: 66:[54, 71, 83] Operation: 99-16=83 Exploring Operation: 99-54=45, Resulting Numbers: [16, 71, 45] Generated Node #0,1: 66:[16, 71, 45] Operation: 99-54=45 Exploring Operation: 99-71=28, Resulting Numbers: [16, 54, 28] Generated Node #0,2: 66:[16, 54, 28] Operation: 99-71=28 Moving to Node #0,1 Current State: 66:[16, 71, 45], Operations: ['99-54=45'] Exploring Operation: 16+45=61, Resulting Numbers: [71, 61] Generated Node #0,1,0: 66:[71, 61] Operation: 16+45=61 Exploring Operation: 45-16=29, Resulting Numbers: [71, 29] Generated Node #0,1,1: 66:[71, 29] Operation: 45-16=29 Exploring Operation: 71-45=26, Resulting Numbers: [16, 26] Generated Node #0,1,2: 66:[16, 26] Operation: 71-45=26 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 66:[71, 29], Operations: ['99-54=45', '45-16=29'] Exploring Operation: 71*29=2059, Resulting Numbers: [2059] 2059,66 unequal: No Solution Exploring Operation: 71+29=100, Resulting Numbers: [100] 100,66 unequal: No Solution Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 66:[16, 26], Operations: ['99-54=45', '71-45=26'] Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,66 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 66:[71, 61], Operations: ['99-54=45', '16+45=61'] Exploring Operation: 71+61=132, Resulting Numbers: [132] 132,66 unequal: No Solution Exploring Operation: 71-61=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 71*61=4331, Resulting Numbers: [4331] 4331,66 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: 66:[16, 54, 28], Operations: ['99-71=28'] Exploring Operation: 54-16=38, Resulting Numbers: [28, 38] Generated Node #0,2,0: 66:[28, 38] Operation: 54-16=38 Exploring Operation: 16+54=70, Resulting Numbers: [28, 70] Generated Node #0,2,1: 66:[28, 70] Operation: 16+54=70 Exploring Operation: 54-28=26, Resulting Numbers: [16, 26] Generated Node #0,2,2: 66:[16, 26] Operation: 54-28=26 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 66:[28, 70], Operations: ['99-71=28', '16+54=70'] Exploring Operation: 28*70=1960, Resulting Numbers: [1960] 1960,66 unequal: No Solution Exploring Operation: 28+70=98, Resulting Numbers: [98] 98,66 unequal: No Solution Exploring Operation: 70-28=42, Resulting Numbers: [42] 42,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 66:[16, 26], Operations: ['99-71=28', '54-28=26'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,66 unequal: No Solution Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 66:[28, 38], Operations: ['99-71=28', '54-16=38'] Exploring Operation: 28+38=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[99, 16, 54, 71], Operations: [] Exploring Operation: 99-71=28, Resulting Numbers: [16, 54, 28] Generated Node #0,2: 66:[16, 54, 28] Operation: 99-71=28 Moving to Node #0,2 Current State: 66:[16, 54, 28], Operations: ['99-71=28'] Exploring Operation: 54-16=38, Resulting Numbers: [28, 38] Generated Node #0,2,0: 66:[28, 38] Operation: 54-16=38 Moving to Node #0,2,0 Current State: 66:[28, 38], Operations: ['99-71=28', '54-16=38'] Exploring Operation: 28+38=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
sum_heuristic
[ 51, 94, 7, 58 ]
80
[ "51+94=145", "7+58=65", "145-65=80" ]
Current State: 80:[51, 94, 7, 58], Operations: [] Exploring Operation: 51+94=145, Resulting Numbers: [7, 58, 145] Generated Node #2: [7, 58, 145] from Operation: 51+94=145 Current State: 80:[7, 58, 145], Operations: ['51+94=145'] Exploring Operation: 7+58=65, Resulting Numbers: [145, 65] Generated Node #3: [145, 65] from Operation: 7+58=65 Current State: 80:[145, 65], Operations: ['51+94=145', '7+58=65'] Exploring Operation: 145-65=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[51, 94, 7, 58], Operations: [] Exploring Operation: 94-58=36, Resulting Numbers: [51, 7, 36] Generated Node #0,0: 80:[51, 7, 36] Operation: 94-58=36 Exploring Operation: 94-51=43, Resulting Numbers: [7, 58, 43] Generated Node #0,1: 80:[7, 58, 43] Operation: 94-51=43 Exploring Operation: 58-51=7, Resulting Numbers: [94, 7, 7] Generated Node #0,2: 80:[94, 7, 7] Operation: 58-51=7 Moving to Node #0,0 Current State: 80:[51, 7, 36], Operations: ['94-58=36'] Exploring Operation: 51-7=44, Resulting Numbers: [36, 44] Generated Node #0,0,0: 80:[36, 44] Operation: 51-7=44 Exploring Operation: 51+36=87, Resulting Numbers: [7, 87] Generated Node #0,0,1: 80:[7, 87] Operation: 51+36=87 Exploring Operation: 51-36=15, Resulting Numbers: [7, 15] Generated Node #0,0,2: 80:[7, 15] Operation: 51-36=15 Moving to Node #0,2 Current State: 80:[94, 7, 7], Operations: ['58-51=7'] Exploring Operation: 94-7=87, Resulting Numbers: [7, 87] Generated Node #0,2,0: 80:[7, 87] Operation: 94-7=87 Exploring Operation: 7/7=1, Resulting Numbers: [94, 1] Generated Node #0,2,1: 80:[94, 1] Operation: 7/7=1 Exploring Operation: 94-7=87, Resulting Numbers: [7, 87] Generated Node #0,2,2: 80:[7, 87] Operation: 94-7=87 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[7, 87], Operations: ['58-51=7', '94-7=87'] Exploring Operation: 7*87=609, Resulting Numbers: [609] 609,80 unequal: No Solution Exploring Operation: 87-7=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[51, 94, 7, 58], Operations: [] Exploring Operation: 58-51=7, Resulting Numbers: [94, 7, 7] Generated Node #0,2: 80:[94, 7, 7] Operation: 58-51=7 Moving to Node #0,2 Current State: 80:[94, 7, 7], Operations: ['58-51=7'] Exploring Operation: 94-7=87, Resulting Numbers: [7, 87] Generated Node #0,2,0: 80:[7, 87] Operation: 94-7=87 Moving to Node #0,2,0 Current State: 80:[7, 87], Operations: ['58-51=7', '94-7=87'] Exploring Operation: 87-7=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 95, 19, 56, 6 ]
56
[ "95/19=5", "6-5=1", "56*1=56" ]
Current State: 56:[95, 19, 56, 6], Operations: [] Exploring Operation: 95/19=5, Resulting Numbers: [56, 6, 5] Generated Node #2: [56, 6, 5] from Operation: 95/19=5 Current State: 56:[56, 6, 5], Operations: ['95/19=5'] Exploring Operation: 6-5=1, Resulting Numbers: [56, 1] Generated Node #3: [56, 1] from Operation: 6-5=1 Current State: 56:[56, 1], Operations: ['95/19=5', '6-5=1'] Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[95, 19, 56, 6], Operations: [] Exploring Operation: 95-56=39, Resulting Numbers: [19, 6, 39] Generated Node #0,0: 56:[19, 6, 39] Operation: 95-56=39 Exploring Operation: 95/19=5, Resulting Numbers: [56, 6, 5] Generated Node #0,1: 56:[56, 6, 5] Operation: 95/19=5 Exploring Operation: 95-6=89, Resulting Numbers: [19, 56, 89] Generated Node #0,2: 56:[19, 56, 89] Operation: 95-6=89 Exploring Operation: 95-19=76, Resulting Numbers: [56, 6, 76] Generated Node #0,3: 56:[56, 6, 76] Operation: 95-19=76 Moving to Node #0,1 Current State: 56:[56, 6, 5], Operations: ['95/19=5'] Exploring Operation: 6+5=11, Resulting Numbers: [56, 11] Generated Node #0,1,0: 56:[56, 11] Operation: 6+5=11 Exploring Operation: 56+5=61, Resulting Numbers: [6, 61] Generated Node #0,1,1: 56:[6, 61] Operation: 56+5=61 Exploring Operation: 6*5=30, Resulting Numbers: [56, 30] Generated Node #0,1,2: 56:[56, 30] Operation: 6*5=30 Exploring Operation: 6-5=1, Resulting Numbers: [56, 1] Generated Node #0,1,3: 56:[56, 1] Operation: 6-5=1 Moving to Node #0,0 Current State: 56:[19, 6, 39], Operations: ['95-56=39'] Exploring Operation: 39-19=20, Resulting Numbers: [6, 20] Generated Node #0,0,0: 56:[6, 20] Operation: 39-19=20 Exploring Operation: 39-6=33, Resulting Numbers: [19, 33] Generated Node #0,0,1: 56:[19, 33] Operation: 39-6=33 Exploring Operation: 19-6=13, Resulting Numbers: [39, 13] Generated Node #0,0,2: 56:[39, 13] Operation: 19-6=13 Exploring Operation: 19+39=58, Resulting Numbers: [6, 58] Generated Node #0,0,3: 56:[6, 58] Operation: 19+39=58 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 56:[6, 58], Operations: ['95-56=39', '19+39=58'] Exploring Operation: 6+58=64, Resulting Numbers: [64] 64,56 unequal: No Solution Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 6*58=348, Resulting Numbers: [348] 348,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[6, 20], Operations: ['95-56=39', '39-19=20'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,56 unequal: No Solution Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,56 unequal: No Solution Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 56:[19, 33], Operations: ['95-56=39', '39-6=33'] Exploring Operation: 19*33=627, Resulting Numbers: [627] 627,56 unequal: No Solution Exploring Operation: 33-19=14, Resulting Numbers: [14] 14,56 unequal: No Solution Exploring Operation: 19+33=52, Resulting Numbers: [52] 52,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 56:[39, 13], Operations: ['95-56=39', '19-6=13'] Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,56 unequal: No Solution Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,56 unequal: No Solution Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 39*13=507, Resulting Numbers: [507] 507,56 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: 56:[56, 6, 76], Operations: ['95-19=76'] Exploring Operation: 56-6=50, Resulting Numbers: [76, 50] Generated Node #0,3,0: 56:[76, 50] Operation: 56-6=50 Exploring Operation: 76-6=70, Resulting Numbers: [56, 70] Generated Node #0,3,1: 56:[56, 70] Operation: 76-6=70 Exploring Operation: 56+6=62, Resulting Numbers: [76, 62] Generated Node #0,3,2: 56:[76, 62] Operation: 56+6=62 Exploring Operation: 76-56=20, Resulting Numbers: [6, 20] Generated Node #0,3,3: 56:[6, 20] Operation: 76-56=20 Moving to Node #0,2 Current State: 56:[19, 56, 89], Operations: ['95-6=89'] Exploring Operation: 89-56=33, Resulting Numbers: [19, 33] Generated Node #0,2,0: 56:[19, 33] Operation: 89-56=33 Exploring Operation: 56-19=37, Resulting Numbers: [89, 37] Generated Node #0,2,1: 56:[89, 37] Operation: 56-19=37 Exploring Operation: 19+56=75, Resulting Numbers: [89, 75] Generated Node #0,2,2: 56:[89, 75] Operation: 19+56=75 Exploring Operation: 89-19=70, Resulting Numbers: [56, 70] Generated Node #0,2,3: 56:[56, 70] Operation: 89-19=70 Moving to Node #0,1,3 Current State: 56:[56, 1], Operations: ['95/19=5', '6-5=1'] Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[95, 19, 56, 6], Operations: [] Exploring Operation: 95/19=5, Resulting Numbers: [56, 6, 5] Generated Node #0,1: 56:[56, 6, 5] Operation: 95/19=5 Moving to Node #0,1 Current State: 56:[56, 6, 5], Operations: ['95/19=5'] Exploring Operation: 6-5=1, Resulting Numbers: [56, 1] Generated Node #0,1,3: 56:[56, 1] Operation: 6-5=1 Moving to Node #0,1,3 Current State: 56:[56, 1], Operations: ['95/19=5', '6-5=1'] Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
0.967014
hs_4
mult_heuristic
[ 42, 20, 25, 44 ]
47
[ "42-20=22", "25+44=69", "69-22=47" ]
Current State: 47:[42, 20, 25, 44], Operations: [] Exploring Operation: 42-20=22, Resulting Numbers: [25, 44, 22] Generated Node #2: [25, 44, 22] from Operation: 42-20=22 Current State: 47:[25, 44, 22], Operations: ['42-20=22'] Exploring Operation: 25+44=69, Resulting Numbers: [22, 69] Generated Node #3: [22, 69] from Operation: 25+44=69 Current State: 47:[22, 69], Operations: ['42-20=22', '25+44=69'] Exploring Operation: 69-22=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[42, 20, 25, 44], Operations: [] Exploring Operation: 42+25=67, Resulting Numbers: [20, 44, 67] Generated Node #0,0: 47:[20, 44, 67] Operation: 42+25=67 Exploring Operation: 42+20=62, Resulting Numbers: [25, 44, 62] Generated Node #0,1: 47:[25, 44, 62] Operation: 42+20=62 Exploring Operation: 42-20=22, Resulting Numbers: [25, 44, 22] Generated Node #0,2: 47:[25, 44, 22] Operation: 42-20=22 Exploring Operation: 20+44=64, Resulting Numbers: [42, 25, 64] Generated Node #0,3: 47:[42, 25, 64] Operation: 20+44=64 Exploring Operation: 20+25=45, Resulting Numbers: [42, 44, 45] Generated Node #0,4: 47:[42, 44, 45] Operation: 20+25=45 Start Sub Search at level 1: Moving to Node #0,4 Current State: 47:[42, 44, 45], Operations: ['20+25=45'] Exploring Operation: 45-42=3, Resulting Numbers: [44, 3] Generated Node #0,4,0: 47:[44, 3] Operation: 45-42=3 Exploring Operation: 44+45=89, Resulting Numbers: [42, 89] Generated Node #0,4,1: 47:[42, 89] Operation: 44+45=89 Exploring Operation: 42+45=87, Resulting Numbers: [44, 87] Generated Node #0,4,2: 47:[44, 87] Operation: 42+45=87 Exploring Operation: 42+44=86, Resulting Numbers: [45, 86] Generated Node #0,4,3: 47:[45, 86] Operation: 42+44=86 Exploring Operation: 44-42=2, Resulting Numbers: [45, 2] Generated Node #0,4,4: 47:[45, 2] Operation: 44-42=2 Moving to Node #0,4,3 Current State: 47:[45, 86], Operations: ['20+25=45', '42+44=86'] Exploring Operation: 45+86=131, Resulting Numbers: [131] 131,47 unequal: No Solution Exploring Operation: 86-45=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 45*86=3870, Resulting Numbers: [3870] 3870,47 unequal: No Solution Moving to Node #0,4,2 Current State: 47:[44, 87], Operations: ['20+25=45', '42+45=87'] Exploring Operation: 87-44=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 44*87=3828, Resulting Numbers: [3828] 3828,47 unequal: No Solution Exploring Operation: 44+87=131, Resulting Numbers: [131] 131,47 unequal: No Solution Moving to Node #0,4,0 Current State: 47:[44, 3], Operations: ['20+25=45', '45-42=3'] Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[42, 20, 25, 44], Operations: [] Exploring Operation: 20+25=45, Resulting Numbers: [42, 44, 45] Generated Node #0,4: 47:[42, 44, 45] Operation: 20+25=45 Moving to Node #0,4 Current State: 47:[42, 44, 45], Operations: ['20+25=45'] Exploring Operation: 45-42=3, Resulting Numbers: [44, 3] Generated Node #0,4,0: 47:[44, 3] Operation: 45-42=3 Moving to Node #0,4,0 Current State: 47:[44, 3], Operations: ['20+25=45', '45-42=3'] Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 45, 92, 26, 16 ]
57
[ "92-45=47", "26-16=10", "47+10=57" ]
Current State: 57:[45, 92, 26, 16], Operations: [] Exploring Operation: 92-45=47, Resulting Numbers: [26, 16, 47] Generated Node #2: [26, 16, 47] from Operation: 92-45=47 Current State: 57:[26, 16, 47], Operations: ['92-45=47'] Exploring Operation: 26-16=10, Resulting Numbers: [47, 10] Generated Node #3: [47, 10] from Operation: 26-16=10 Current State: 57:[47, 10], Operations: ['92-45=47', '26-16=10'] Exploring Operation: 47+10=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[45, 92, 26, 16], Operations: [] Exploring Operation: 92-45=47, Resulting Numbers: [26, 16, 47] Generated Node #0,0: 57:[26, 16, 47] Operation: 92-45=47 Exploring Operation: 92-26=66, Resulting Numbers: [45, 16, 66] Generated Node #0,1: 57:[45, 16, 66] Operation: 92-26=66 Moving to Node #0,0 Current State: 57:[26, 16, 47], Operations: ['92-45=47'] Exploring Operation: 47-26=21, Resulting Numbers: [16, 21] Generated Node #0,0,0: 57:[16, 21] Operation: 47-26=21 Exploring Operation: 16+47=63, Resulting Numbers: [26, 63] Generated Node #0,0,1: 57:[26, 63] Operation: 16+47=63 Moving to Node #0,1 Current State: 57:[45, 16, 66], Operations: ['92-26=66'] Exploring Operation: 45+16=61, Resulting Numbers: [66, 61] Generated Node #0,1,0: 57:[66, 61] Operation: 45+16=61 Exploring Operation: 66-45=21, Resulting Numbers: [16, 21] Generated Node #0,1,1: 57:[16, 21] Operation: 66-45=21 Moving to Node #0,0,0 Current State: 57:[16, 21], Operations: ['92-45=47', '47-26=21'] Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,57 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[16, 21], Operations: ['92-26=66', '66-45=21'] Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,57 unequal: No Solution Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[26, 63], Operations: ['92-45=47', '16+47=63'] Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,57 unequal: No Solution Exploring Operation: 26+63=89, Resulting Numbers: [89] 89,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[66, 61], Operations: ['92-26=66', '45+16=61'] Exploring Operation: 66+61=127, Resulting Numbers: [127] 127,57 unequal: No Solution Exploring Operation: 66-61=5, Resulting Numbers: [5] 5,57 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 4, 54, 20, 24 ]
68
[ "24/4=6", "54+20=74", "74-6=68" ]
Current State: 68:[4, 54, 20, 24], Operations: [] Exploring Operation: 24/4=6, Resulting Numbers: [54, 20, 6] Generated Node #2: [54, 20, 6] from Operation: 24/4=6 Current State: 68:[54, 20, 6], Operations: ['24/4=6'] Exploring Operation: 54+20=74, Resulting Numbers: [6, 74] Generated Node #3: [6, 74] from Operation: 54+20=74 Current State: 68:[6, 74], Operations: ['24/4=6', '54+20=74'] Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[4, 54, 20, 24], Operations: [] Exploring Operation: 54+24=78, Resulting Numbers: [4, 20, 78] Generated Node #0,0: 68:[4, 20, 78] Operation: 54+24=78 Exploring Operation: 54-24=30, Resulting Numbers: [4, 20, 30] Generated Node #0,1: 68:[4, 20, 30] Operation: 54-24=30 Exploring Operation: 54-20=34, Resulting Numbers: [4, 24, 34] Generated Node #0,2: 68:[4, 24, 34] Operation: 54-20=34 Exploring Operation: 54+20=74, Resulting Numbers: [4, 24, 74] Generated Node #0,3: 68:[4, 24, 74] Operation: 54+20=74 Moving to Node #0,1 Current State: 68:[4, 20, 30], Operations: ['54-24=30'] Exploring Operation: 20/4=5, Resulting Numbers: [30, 5] Generated Node #0,1,0: 68:[30, 5] Operation: 20/4=5 Exploring Operation: 30-20=10, Resulting Numbers: [4, 10] Generated Node #0,1,1: 68:[4, 10] Operation: 30-20=10 Exploring Operation: 20-4=16, Resulting Numbers: [30, 16] Generated Node #0,1,2: 68:[30, 16] Operation: 20-4=16 Exploring Operation: 4+30=34, Resulting Numbers: [20, 34] Generated Node #0,1,3: 68:[20, 34] Operation: 4+30=34 Moving to Node #0,2 Current State: 68:[4, 24, 34], Operations: ['54-20=34'] Exploring Operation: 24-4=20, Resulting Numbers: [34, 20] Generated Node #0,2,0: 68:[34, 20] Operation: 24-4=20 Exploring Operation: 34-24=10, Resulting Numbers: [4, 10] Generated Node #0,2,1: 68:[4, 10] Operation: 34-24=10 Exploring Operation: 4+24=28, Resulting Numbers: [34, 28] Generated Node #0,2,2: 68:[34, 28] Operation: 4+24=28 Exploring Operation: 24/4=6, Resulting Numbers: [34, 6] Generated Node #0,2,3: 68:[34, 6] Operation: 24/4=6 Moving to Node #0,3 Current State: 68:[4, 24, 74], Operations: ['54+20=74'] Exploring Operation: 24-4=20, Resulting Numbers: [74, 20] Generated Node #0,3,0: 68:[74, 20] Operation: 24-4=20 Exploring Operation: 74-4=70, Resulting Numbers: [24, 70] Generated Node #0,3,1: 68:[24, 70] Operation: 74-4=70 Exploring Operation: 24/4=6, Resulting Numbers: [74, 6] Generated Node #0,3,2: 68:[74, 6] Operation: 24/4=6 Exploring Operation: 4+24=28, Resulting Numbers: [74, 28] Generated Node #0,3,3: 68:[74, 28] Operation: 4+24=28 Moving to Node #0,0 Current State: 68:[4, 20, 78], Operations: ['54+24=78'] Exploring Operation: 20/4=5, Resulting Numbers: [78, 5] Generated Node #0,0,0: 68:[78, 5] Operation: 20/4=5 Exploring Operation: 78-4=74, Resulting Numbers: [20, 74] Generated Node #0,0,1: 68:[20, 74] Operation: 78-4=74 Exploring Operation: 78-20=58, Resulting Numbers: [4, 58] Generated Node #0,0,2: 68:[4, 58] Operation: 78-20=58 Exploring Operation: 20-4=16, Resulting Numbers: [78, 16] Generated Node #0,0,3: 68:[78, 16] Operation: 20-4=16 Moving to Node #0,2,3 Current State: 68:[34, 6], Operations: ['54-20=34', '24/4=6'] Exploring Operation: 34+6=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,68 unequal: No Solution Exploring Operation: 34*6=204, Resulting Numbers: [204] 204,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[34, 20], Operations: ['54-20=34', '24-4=20'] Exploring Operation: 34*20=680, Resulting Numbers: [680] 680,68 unequal: No Solution Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,68 unequal: No Solution Exploring Operation: 34+20=54, Resulting Numbers: [54] 54,68 unequal: No Solution Moving to Node #0,1,3 Current State: 68:[20, 34], Operations: ['54-24=30', '4+30=34'] Exploring Operation: 20*34=680, Resulting Numbers: [680] 680,68 unequal: No Solution Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,68 unequal: No Solution Exploring Operation: 20+34=54, Resulting Numbers: [54] 54,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[30, 16], Operations: ['54-24=30', '20-4=16'] Exploring Operation: 30+16=46, Resulting Numbers: [46] 46,68 unequal: No Solution Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,68 unequal: No Solution Exploring Operation: 30*16=480, Resulting Numbers: [480] 480,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[30, 5], Operations: ['54-24=30', '20/4=5'] Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 30*5=150, Resulting Numbers: [150] 150,68 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,68 unequal: No Solution Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,68 unequal: No Solution Moving to Node #0,2,1 Current State: 68:[4, 10], Operations: ['54-20=34', '34-24=10'] Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,68 unequal: No Solution Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[4, 10], Operations: ['54-24=30', '30-20=10'] Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,68 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,68 unequal: No Solution Moving to Node #0,2,2 Current State: 68:[34, 28], Operations: ['54-20=34', '4+24=28'] Exploring Operation: 34+28=62, Resulting Numbers: [62] 62,68 unequal: No Solution Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 34*28=952, Resulting Numbers: [952] 952,68 unequal: No Solution Moving to Node #0,3,2 Current State: 68:[74, 6], Operations: ['54+20=74', '24/4=6'] Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[4, 54, 20, 24], Operations: [] Exploring Operation: 54+20=74, Resulting Numbers: [4, 24, 74] Generated Node #0,3: 68:[4, 24, 74] Operation: 54+20=74 Moving to Node #0,3 Current State: 68:[4, 24, 74], Operations: ['54+20=74'] Exploring Operation: 24/4=6, Resulting Numbers: [74, 6] Generated Node #0,3,2: 68:[74, 6] Operation: 24/4=6 Moving to Node #0,3,2 Current State: 68:[74, 6], Operations: ['54+20=74', '24/4=6'] Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
0.956597
hs_4
mult_heuristic
[ 65, 45, 31, 72 ]
21
[ "65-45=20", "72-31=41", "41-20=21" ]
Current State: 21:[65, 45, 31, 72], Operations: [] Exploring Operation: 65-45=20, Resulting Numbers: [31, 72, 20] Generated Node #2: [31, 72, 20] from Operation: 65-45=20 Current State: 21:[31, 72, 20], Operations: ['65-45=20'] Exploring Operation: 72-31=41, Resulting Numbers: [20, 41] Generated Node #3: [20, 41] from Operation: 72-31=41 Current State: 21:[20, 41], Operations: ['65-45=20', '72-31=41'] Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[65, 45, 31, 72], Operations: [] Exploring Operation: 65-31=34, Resulting Numbers: [45, 72, 34] Generated Node #0,0: 21:[45, 72, 34] Operation: 65-31=34 Exploring Operation: 72-45=27, Resulting Numbers: [65, 31, 27] Generated Node #0,1: 21:[65, 31, 27] Operation: 72-45=27 Exploring Operation: 72-65=7, Resulting Numbers: [45, 31, 7] Generated Node #0,2: 21:[45, 31, 7] Operation: 72-65=7 Exploring Operation: 72-31=41, Resulting Numbers: [65, 45, 41] Generated Node #0,3: 21:[65, 45, 41] Operation: 72-31=41 Exploring Operation: 65-45=20, Resulting Numbers: [31, 72, 20] Generated Node #0,4: 21:[31, 72, 20] Operation: 65-45=20 Moving to Node #0,2 Current State: 21:[45, 31, 7], Operations: ['72-65=7'] Exploring Operation: 45+7=52, Resulting Numbers: [31, 52] Generated Node #0,2,0: 21:[31, 52] Operation: 45+7=52 Exploring Operation: 45-7=38, Resulting Numbers: [31, 38] Generated Node #0,2,1: 21:[31, 38] Operation: 45-7=38 Exploring Operation: 31+7=38, Resulting Numbers: [45, 38] Generated Node #0,2,2: 21:[45, 38] Operation: 31+7=38 Exploring Operation: 45-31=14, Resulting Numbers: [7, 14] Generated Node #0,2,3: 21:[7, 14] Operation: 45-31=14 Exploring Operation: 31-7=24, Resulting Numbers: [45, 24] Generated Node #0,2,4: 21:[45, 24] Operation: 31-7=24 Moving to Node #0,1 Current State: 21:[65, 31, 27], Operations: ['72-45=27'] Exploring Operation: 65+31=96, Resulting Numbers: [27, 96] Generated Node #0,1,0: 21:[27, 96] Operation: 65+31=96 Exploring Operation: 65+27=92, Resulting Numbers: [31, 92] Generated Node #0,1,1: 21:[31, 92] Operation: 65+27=92 Exploring Operation: 65-27=38, Resulting Numbers: [31, 38] Generated Node #0,1,2: 21:[31, 38] Operation: 65-27=38 Exploring Operation: 65-31=34, Resulting Numbers: [27, 34] Generated Node #0,1,3: 21:[27, 34] Operation: 65-31=34 Exploring Operation: 31-27=4, Resulting Numbers: [65, 4] Generated Node #0,1,4: 21:[65, 4] Operation: 31-27=4 Moving to Node #0,4 Current State: 21:[31, 72, 20], Operations: ['65-45=20'] Exploring Operation: 31-20=11, Resulting Numbers: [72, 11] Generated Node #0,4,0: 21:[72, 11] Operation: 31-20=11 Exploring Operation: 72-31=41, Resulting Numbers: [20, 41] Generated Node #0,4,1: 21:[20, 41] Operation: 72-31=41 Exploring Operation: 72+20=92, Resulting Numbers: [31, 92] Generated Node #0,4,2: 21:[31, 92] Operation: 72+20=92 Exploring Operation: 31+20=51, Resulting Numbers: [72, 51] Generated Node #0,4,3: 21:[72, 51] Operation: 31+20=51 Exploring Operation: 72-20=52, Resulting Numbers: [31, 52] Generated Node #0,4,4: 21:[31, 52] Operation: 72-20=52 Moving to Node #0,0 Current State: 21:[45, 72, 34], Operations: ['65-31=34'] Exploring Operation: 72-34=38, Resulting Numbers: [45, 38] Generated Node #0,0,0: 21:[45, 38] Operation: 72-34=38 Exploring Operation: 45-34=11, Resulting Numbers: [72, 11] Generated Node #0,0,1: 21:[72, 11] Operation: 45-34=11 Exploring Operation: 72-45=27, Resulting Numbers: [34, 27] Generated Node #0,0,2: 21:[34, 27] Operation: 72-45=27 Exploring Operation: 45+34=79, Resulting Numbers: [72, 79] Generated Node #0,0,3: 21:[72, 79] Operation: 45+34=79 Exploring Operation: 45+72=117, Resulting Numbers: [34, 117] Generated Node #0,0,4: 21:[34, 117] Operation: 45+72=117 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 21:[34, 27], Operations: ['65-31=34', '72-45=27'] Exploring Operation: 34*27=918, Resulting Numbers: [918] 918,21 unequal: No Solution Exploring Operation: 34+27=61, Resulting Numbers: [61] 61,21 unequal: No Solution Exploring Operation: 34-27=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 #0,0,0 Current State: 21:[45, 38], Operations: ['65-31=34', '72-34=38'] Exploring Operation: 45+38=83, Resulting Numbers: [83] 83,21 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 45*38=1710, Resulting Numbers: [1710] 1710,21 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 #0,0,1 Current State: 21:[72, 11], Operations: ['65-31=34', '45-34=11'] Exploring Operation: 72*11=792, Resulting Numbers: [792] 792,21 unequal: No Solution Exploring Operation: 72+11=83, Resulting Numbers: [83] 83,21 unequal: No Solution Exploring Operation: 72-11=61, Resulting Numbers: [61] 61,21 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 #0,0,3 Current State: 21:[72, 79], Operations: ['65-31=34', '45+34=79'] Exploring Operation: 72+79=151, Resulting Numbers: [151] 151,21 unequal: No Solution Exploring Operation: 72*79=5688, Resulting Numbers: [5688] 5688,21 unequal: No Solution Exploring Operation: 79-72=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 #0,0,4 Current State: 21:[34, 117], Operations: ['65-31=34', '45+72=117'] Exploring Operation: 117-34=83, Resulting Numbers: [83] 83,21 unequal: No Solution Exploring Operation: 34*117=3978, Resulting Numbers: [3978] 3978,21 unequal: No Solution Exploring Operation: 34+117=151, Resulting Numbers: [151] 151,21 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:[65, 45, 41], Operations: ['72-31=41'] Exploring Operation: 65-45=20, Resulting Numbers: [41, 20] Generated Node #0,3,0: 21:[41, 20] Operation: 65-45=20 Exploring Operation: 65+41=106, Resulting Numbers: [45, 106] Generated Node #0,3,1: 21:[45, 106] Operation: 65+41=106 Exploring Operation: 65+45=110, Resulting Numbers: [41, 110] Generated Node #0,3,2: 21:[41, 110] Operation: 65+45=110 Exploring Operation: 65-41=24, Resulting Numbers: [45, 24] Generated Node #0,3,3: 21:[45, 24] Operation: 65-41=24 Exploring Operation: 45-41=4, Resulting Numbers: [65, 4] Generated Node #0,3,4: 21:[65, 4] Operation: 45-41=4 Moving to Node #0,2,3 Current State: 21:[7, 14], Operations: ['72-65=7', '45-31=14'] Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[65, 45, 31, 72], Operations: [] Exploring Operation: 72-65=7, Resulting Numbers: [45, 31, 7] Generated Node #0,2: 21:[45, 31, 7] Operation: 72-65=7 Moving to Node #0,2 Current State: 21:[45, 31, 7], Operations: ['72-65=7'] Exploring Operation: 45-31=14, Resulting Numbers: [7, 14] Generated Node #0,2,3: 21:[7, 14] Operation: 45-31=14 Moving to Node #0,2,3 Current State: 21:[7, 14], Operations: ['72-65=7', '45-31=14'] Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.956597
hs_5
mult_heuristic
[ 48, 29, 81, 52 ]
48
[ "48+29=77", "81-52=29", "77-29=48" ]
Current State: 48:[48, 29, 81, 52], Operations: [] Exploring Operation: 48+29=77, Resulting Numbers: [81, 52, 77] Generated Node #2: [81, 52, 77] from Operation: 48+29=77 Current State: 48:[81, 52, 77], Operations: ['48+29=77'] Exploring Operation: 81-52=29, Resulting Numbers: [77, 29] Generated Node #3: [77, 29] from Operation: 81-52=29 Current State: 48:[77, 29], Operations: ['48+29=77', '81-52=29'] Exploring Operation: 77-29=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[48, 29, 81, 52], Operations: [] Exploring Operation: 81-29=52, Resulting Numbers: [48, 52, 52] Generated Node #0,0: 48:[48, 52, 52] Operation: 81-29=52 Exploring Operation: 81-52=29, Resulting Numbers: [48, 29, 29] Generated Node #0,1: 48:[48, 29, 29] Operation: 81-52=29 Moving to Node #0,0 Current State: 48:[48, 52, 52], Operations: ['81-29=52'] Exploring Operation: 52-52=0, Resulting Numbers: [48, 0] Generated Node #0,0,0: 48:[48, 0] Operation: 52-52=0 Exploring Operation: 52/52=1, Resulting Numbers: [48, 1] Generated Node #0,0,1: 48:[48, 1] Operation: 52/52=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 48:[48, 1], Operations: ['81-29=52', '52/52=1'] Exploring Operation: 48*1=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[48, 29, 81, 52], Operations: [] Exploring Operation: 81-29=52, Resulting Numbers: [48, 52, 52] Generated Node #0,0: 48:[48, 52, 52] Operation: 81-29=52 Moving to Node #0,0 Current State: 48:[48, 52, 52], Operations: ['81-29=52'] Exploring Operation: 52/52=1, Resulting Numbers: [48, 1] Generated Node #0,0,1: 48:[48, 1] Operation: 52/52=1 Moving to Node #0,0,1 Current State: 48:[48, 1], Operations: ['81-29=52', '52/52=1'] Exploring Operation: 48*1=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 3, 20, 74, 80 ]
67
[ "74-3=71", "80/20=4", "71-4=67" ]
Current State: 67:[3, 20, 74, 80], Operations: [] Exploring Operation: 74-3=71, Resulting Numbers: [20, 80, 71] Generated Node #2: [20, 80, 71] from Operation: 74-3=71 Current State: 67:[20, 80, 71], Operations: ['74-3=71'] Exploring Operation: 80/20=4, Resulting Numbers: [71, 4] Generated Node #3: [71, 4] from Operation: 80/20=4 Current State: 67:[71, 4], Operations: ['74-3=71', '80/20=4'] Exploring Operation: 71-4=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[3, 20, 74, 80], Operations: [] Exploring Operation: 3*20=60, Resulting Numbers: [74, 80, 60] Generated Node #0,0: 67:[74, 80, 60] Operation: 3*20=60 Exploring Operation: 74-3=71, Resulting Numbers: [20, 80, 71] Generated Node #0,1: 67:[20, 80, 71] Operation: 74-3=71 Exploring Operation: 3+20=23, Resulting Numbers: [74, 80, 23] Generated Node #0,2: 67:[74, 80, 23] Operation: 3+20=23 Moving to Node #0,0 Current State: 67:[74, 80, 60], Operations: ['3*20=60'] Exploring Operation: 80-60=20, Resulting Numbers: [74, 20] Generated Node #0,0,0: 67:[74, 20] Operation: 80-60=20 Exploring Operation: 80-74=6, Resulting Numbers: [60, 6] Generated Node #0,0,1: 67:[60, 6] Operation: 80-74=6 Exploring Operation: 74-60=14, Resulting Numbers: [80, 14] Generated Node #0,0,2: 67:[80, 14] Operation: 74-60=14 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[74, 20], Operations: ['3*20=60', '80-60=20'] Exploring Operation: 74*20=1480, Resulting Numbers: [1480] 1480,67 unequal: No Solution Exploring Operation: 74+20=94, Resulting Numbers: [94] 94,67 unequal: No Solution Exploring Operation: 74-20=54, Resulting Numbers: [54] 54,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 67:[80, 14], Operations: ['3*20=60', '74-60=14'] Exploring Operation: 80+14=94, Resulting Numbers: [94] 94,67 unequal: No Solution Exploring Operation: 80*14=1120, Resulting Numbers: [1120] 1120,67 unequal: No Solution Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[60, 6], Operations: ['3*20=60', '80-74=6'] Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,67 unequal: No Solution Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 60+6=66, Resulting Numbers: [66] 66,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 67:[20, 80, 71], Operations: ['74-3=71'] Exploring Operation: 20+80=100, Resulting Numbers: [71, 100] Generated Node #0,1,0: 67:[71, 100] Operation: 20+80=100 Exploring Operation: 71-20=51, Resulting Numbers: [80, 51] Generated Node #0,1,1: 67:[80, 51] Operation: 71-20=51 Exploring Operation: 80-20=60, Resulting Numbers: [71, 60] Generated Node #0,1,2: 67:[71, 60] Operation: 80-20=60 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 67:[71, 60], Operations: ['74-3=71', '80-20=60'] Exploring Operation: 71+60=131, Resulting Numbers: [131] 131,67 unequal: No Solution Exploring Operation: 71-60=11, Resulting Numbers: [11] 11,67 unequal: No Solution Exploring Operation: 71*60=4260, Resulting Numbers: [4260] 4260,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 67:[80, 51], Operations: ['74-3=71', '71-20=51'] Exploring Operation: 80*51=4080, Resulting Numbers: [4080] 4080,67 unequal: No Solution Exploring Operation: 80-51=29, Resulting Numbers: [29] 29,67 unequal: No Solution Exploring Operation: 80+51=131, Resulting Numbers: [131] 131,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[71, 100], Operations: ['74-3=71', '20+80=100'] Exploring Operation: 71*100=7100, Resulting Numbers: [7100] 7100,67 unequal: No Solution Exploring Operation: 100-71=29, Resulting Numbers: [29] 29,67 unequal: No Solution Exploring Operation: 71+100=171, Resulting Numbers: [171] 171,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 67:[74, 80, 23], Operations: ['3+20=23'] Exploring Operation: 74-23=51, Resulting Numbers: [80, 51] Generated Node #0,2,0: 67:[80, 51] Operation: 74-23=51 Exploring Operation: 74+23=97, Resulting Numbers: [80, 97] Generated Node #0,2,1: 67:[80, 97] Operation: 74+23=97 Exploring Operation: 80-23=57, Resulting Numbers: [74, 57] Generated Node #0,2,2: 67:[74, 57] Operation: 80-23=57 Moving to Node #0,2,2 Current State: 67:[74, 57], Operations: ['3+20=23', '80-23=57'] Exploring Operation: 74*57=4218, Resulting Numbers: [4218] 4218,67 unequal: No Solution Exploring Operation: 74-57=17, Resulting Numbers: [17] 17,67 unequal: No Solution Exploring Operation: 74+57=131, Resulting Numbers: [131] 131,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[80, 51], Operations: ['3+20=23', '74-23=51'] Exploring Operation: 80*51=4080, Resulting Numbers: [4080] 4080,67 unequal: No Solution Exploring Operation: 80-51=29, Resulting Numbers: [29] 29,67 unequal: No Solution Exploring Operation: 80+51=131, Resulting Numbers: [131] 131,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[80, 97], Operations: ['3+20=23', '74+23=97'] Exploring Operation: 97-80=17, Resulting Numbers: [17] 17,67 unequal: No Solution Exploring Operation: 80*97=7760, Resulting Numbers: [7760] 7760,67 unequal: No Solution Exploring Operation: 80+97=177, Resulting Numbers: [177] 177,67 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 26, 32, 1, 93 ]
87
[ "32-26=6", "1*93=93", "93-6=87" ]
Current State: 87:[26, 32, 1, 93], Operations: [] Exploring Operation: 32-26=6, Resulting Numbers: [1, 93, 6] Generated Node #2: [1, 93, 6] from Operation: 32-26=6 Current State: 87:[1, 93, 6], Operations: ['32-26=6'] Exploring Operation: 1*93=93, Resulting Numbers: [6, 93] Generated Node #3: [6, 93] from Operation: 1*93=93 Current State: 87:[6, 93], Operations: ['32-26=6', '1*93=93'] Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[26, 32, 1, 93], Operations: [] Exploring Operation: 93-1=92, Resulting Numbers: [26, 32, 92] Generated Node #0,0: 87:[26, 32, 92] Operation: 93-1=92 Exploring Operation: 26+1=27, Resulting Numbers: [32, 93, 27] Generated Node #0,1: 87:[32, 93, 27] Operation: 26+1=27 Exploring Operation: 32-26=6, Resulting Numbers: [1, 93, 6] Generated Node #0,2: 87:[1, 93, 6] Operation: 32-26=6 Exploring Operation: 32-1=31, Resulting Numbers: [26, 93, 31] Generated Node #0,3: 87:[26, 93, 31] Operation: 32-1=31 Moving to Node #0,0 Current State: 87:[26, 32, 92], Operations: ['93-1=92'] Exploring Operation: 92-26=66, Resulting Numbers: [32, 66] Generated Node #0,0,0: 87:[32, 66] Operation: 92-26=66 Exploring Operation: 32-26=6, Resulting Numbers: [92, 6] Generated Node #0,0,1: 87:[92, 6] Operation: 32-26=6 Exploring Operation: 26+32=58, Resulting Numbers: [92, 58] Generated Node #0,0,2: 87:[92, 58] Operation: 26+32=58 Exploring Operation: 92-32=60, Resulting Numbers: [26, 60] Generated Node #0,0,3: 87:[26, 60] Operation: 92-32=60 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 87:[92, 6], Operations: ['93-1=92', '32-26=6'] Exploring Operation: 92*6=552, Resulting Numbers: [552] 552,87 unequal: No Solution Exploring Operation: 92-6=86, Resulting Numbers: [86] 86,87 unequal: No Solution Exploring Operation: 92+6=98, Resulting Numbers: [98] 98,87 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 #0,0,0 Current State: 87:[32, 66], Operations: ['93-1=92', '92-26=66'] Exploring Operation: 32+66=98, Resulting Numbers: [98] 98,87 unequal: No Solution Exploring Operation: 66-32=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 32*66=2112, Resulting Numbers: [2112] 2112,87 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 #0,0,3 Current State: 87:[26, 60], Operations: ['93-1=92', '92-32=60'] Exploring Operation: 26+60=86, Resulting Numbers: [86] 86,87 unequal: No Solution Exploring Operation: 26*60=1560, Resulting Numbers: [1560] 1560,87 unequal: No Solution Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,87 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 #0,0,2 Current State: 87:[92, 58], Operations: ['93-1=92', '26+32=58'] Exploring Operation: 92*58=5336, Resulting Numbers: [5336] 5336,87 unequal: No Solution Exploring Operation: 92+58=150, Resulting Numbers: [150] 150,87 unequal: No Solution Exploring Operation: 92-58=34, Resulting Numbers: [34] 34,87 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: 87:[1, 93, 6], Operations: ['32-26=6'] Exploring Operation: 1*93=93, Resulting Numbers: [6, 93] Generated Node #0,2,0: 87:[6, 93] Operation: 1*93=93 Exploring Operation: 93-6=87, Resulting Numbers: [1, 87] Generated Node #0,2,1: 87:[1, 87] Operation: 93-6=87 Exploring Operation: 6-1=5, Resulting Numbers: [93, 5] Generated Node #0,2,2: 87:[93, 5] Operation: 6-1=5 Exploring Operation: 93-1=92, Resulting Numbers: [6, 92] Generated Node #0,2,3: 87:[6, 92] Operation: 93-1=92 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 87:[1, 87], Operations: ['32-26=6', '93-6=87'] Exploring Operation: 1+87=88, Resulting Numbers: [88] 88,87 unequal: No Solution Exploring Operation: 1*87=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[26, 32, 1, 93], Operations: [] Exploring Operation: 32-26=6, Resulting Numbers: [1, 93, 6] Generated Node #0,2: 87:[1, 93, 6] Operation: 32-26=6 Moving to Node #0,2 Current State: 87:[1, 93, 6], Operations: ['32-26=6'] Exploring Operation: 93-6=87, Resulting Numbers: [1, 87] Generated Node #0,2,1: 87:[1, 87] Operation: 93-6=87 Moving to Node #0,2,1 Current State: 87:[1, 87], Operations: ['32-26=6', '93-6=87'] Exploring Operation: 1*87=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 62, 22, 32, 48 ]
100
[ "62+22=84", "48-32=16", "84+16=100" ]
Current State: 100:[62, 22, 32, 48], Operations: [] Exploring Operation: 62+22=84, Resulting Numbers: [32, 48, 84] Generated Node #2: [32, 48, 84] from Operation: 62+22=84 Current State: 100:[32, 48, 84], Operations: ['62+22=84'] Exploring Operation: 48-32=16, Resulting Numbers: [84, 16] Generated Node #3: [84, 16] from Operation: 48-32=16 Current State: 100:[84, 16], Operations: ['62+22=84', '48-32=16'] Exploring Operation: 84+16=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[62, 22, 32, 48], Operations: [] Exploring Operation: 62+32=94, Resulting Numbers: [22, 48, 94] Generated Node #0,0: 100:[22, 48, 94] Operation: 62+32=94 Exploring Operation: 62-32=30, Resulting Numbers: [22, 48, 30] Generated Node #0,1: 100:[22, 48, 30] Operation: 62-32=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[22, 48, 30], Operations: ['62-32=30'] Exploring Operation: 22+30=52, Resulting Numbers: [48, 52] Generated Node #0,1,0: 100:[48, 52] Operation: 22+30=52 Exploring Operation: 30-22=8, Resulting Numbers: [48, 8] Generated Node #0,1,1: 100:[48, 8] Operation: 30-22=8 Moving to Node #0,1,0 Current State: 100:[48, 52], Operations: ['62-32=30', '22+30=52'] Exploring Operation: 48+52=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[62, 22, 32, 48], Operations: [] Exploring Operation: 62-32=30, Resulting Numbers: [22, 48, 30] Generated Node #0,1: 100:[22, 48, 30] Operation: 62-32=30 Moving to Node #0,1 Current State: 100:[22, 48, 30], Operations: ['62-32=30'] Exploring Operation: 22+30=52, Resulting Numbers: [48, 52] Generated Node #0,1,0: 100:[48, 52] Operation: 22+30=52 Moving to Node #0,1,0 Current State: 100:[48, 52], Operations: ['62-32=30', '22+30=52'] Exploring Operation: 48+52=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 89, 16, 49, 85 ]
29
[ "89+16=105", "49+85=134", "134-105=29" ]
Current State: 29:[89, 16, 49, 85], Operations: [] Exploring Operation: 89+16=105, Resulting Numbers: [49, 85, 105] Generated Node #2: [49, 85, 105] from Operation: 89+16=105 Current State: 29:[49, 85, 105], Operations: ['89+16=105'] Exploring Operation: 49+85=134, Resulting Numbers: [105, 134] Generated Node #3: [105, 134] from Operation: 49+85=134 Current State: 29:[105, 134], Operations: ['89+16=105', '49+85=134'] Exploring Operation: 134-105=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[89, 16, 49, 85], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [16, 49, 4] Generated Node #0,0: 29:[16, 49, 4] Operation: 89-85=4 Moving to Node #0,0 Current State: 29:[16, 49, 4], Operations: ['89-85=4'] Exploring Operation: 49-16=33, Resulting Numbers: [4, 33] Generated Node #0,0,0: 29:[4, 33] Operation: 49-16=33 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[4, 33], Operations: ['89-85=4', '49-16=33'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[89, 16, 49, 85], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [16, 49, 4] Generated Node #0,0: 29:[16, 49, 4] Operation: 89-85=4 Moving to Node #0,0 Current State: 29:[16, 49, 4], Operations: ['89-85=4'] Exploring Operation: 49-16=33, Resulting Numbers: [4, 33] Generated Node #0,0,0: 29:[4, 33] Operation: 49-16=33 Moving to Node #0,0,0 Current State: 29:[4, 33], Operations: ['89-85=4', '49-16=33'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 89, 72, 16, 46 ]
99
[ "89+72=161", "16+46=62", "161-62=99" ]
Current State: 99:[89, 72, 16, 46], Operations: [] Exploring Operation: 89+72=161, Resulting Numbers: [16, 46, 161] Generated Node #2: [16, 46, 161] from Operation: 89+72=161 Current State: 99:[16, 46, 161], Operations: ['89+72=161'] Exploring Operation: 16+46=62, Resulting Numbers: [161, 62] Generated Node #3: [161, 62] from Operation: 16+46=62 Current State: 99:[161, 62], Operations: ['89+72=161', '16+46=62'] Exploring Operation: 161-62=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[89, 72, 16, 46], Operations: [] Exploring Operation: 72-46=26, Resulting Numbers: [89, 16, 26] Generated Node #0,0: 99:[89, 16, 26] Operation: 72-46=26 Exploring Operation: 89-72=17, Resulting Numbers: [16, 46, 17] Generated Node #0,1: 99:[16, 46, 17] Operation: 89-72=17 Exploring Operation: 72+16=88, Resulting Numbers: [89, 46, 88] Generated Node #0,2: 99:[89, 46, 88] Operation: 72+16=88 Moving to Node #0,0 Current State: 99:[89, 16, 26], Operations: ['72-46=26'] Exploring Operation: 26-16=10, Resulting Numbers: [89, 10] Generated Node #0,0,0: 99:[89, 10] Operation: 26-16=10 Exploring Operation: 89+16=105, Resulting Numbers: [26, 105] Generated Node #0,0,1: 99:[26, 105] Operation: 89+16=105 Exploring Operation: 16+26=42, Resulting Numbers: [89, 42] Generated Node #0,0,2: 99:[89, 42] Operation: 16+26=42 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[89, 10], Operations: ['72-46=26', '26-16=10'] Exploring Operation: 89-10=79, Resulting Numbers: [79] 79,99 unequal: No Solution Exploring Operation: 89+10=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[89, 72, 16, 46], Operations: [] Exploring Operation: 72-46=26, Resulting Numbers: [89, 16, 26] Generated Node #0,0: 99:[89, 16, 26] Operation: 72-46=26 Moving to Node #0,0 Current State: 99:[89, 16, 26], Operations: ['72-46=26'] Exploring Operation: 26-16=10, Resulting Numbers: [89, 10] Generated Node #0,0,0: 99:[89, 10] Operation: 26-16=10 Moving to Node #0,0,0 Current State: 99:[89, 10], Operations: ['72-46=26', '26-16=10'] Exploring Operation: 89+10=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 71, 40, 21, 49 ]
24
[ "71+49=120", "120/40=3", "21+3=24" ]
Current State: 24:[71, 40, 21, 49], Operations: [] Exploring Operation: 71+49=120, Resulting Numbers: [40, 21, 120] Generated Node #2: [40, 21, 120] from Operation: 71+49=120 Current State: 24:[40, 21, 120], Operations: ['71+49=120'] Exploring Operation: 120/40=3, Resulting Numbers: [21, 3] Generated Node #3: [21, 3] from Operation: 120/40=3 Current State: 24:[21, 3], Operations: ['71+49=120', '120/40=3'] Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[71, 40, 21, 49], Operations: [] Exploring Operation: 71-40=31, Resulting Numbers: [21, 49, 31] Generated Node #0,0: 24:[21, 49, 31] Operation: 71-40=31 Exploring Operation: 71-49=22, Resulting Numbers: [40, 21, 22] Generated Node #0,1: 24:[40, 21, 22] Operation: 71-49=22 Exploring Operation: 71-21=50, Resulting Numbers: [40, 49, 50] Generated Node #0,2: 24:[40, 49, 50] Operation: 71-21=50 Exploring Operation: 49-40=9, Resulting Numbers: [71, 21, 9] Generated Node #0,3: 24:[71, 21, 9] Operation: 49-40=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[40, 21, 22], Operations: ['71-49=22'] Exploring Operation: 40-21=19, Resulting Numbers: [22, 19] Generated Node #0,1,0: 24:[22, 19] Operation: 40-21=19 Exploring Operation: 22-21=1, Resulting Numbers: [40, 1] Generated Node #0,1,1: 24:[40, 1] Operation: 22-21=1 Exploring Operation: 21+22=43, Resulting Numbers: [40, 43] Generated Node #0,1,2: 24:[40, 43] Operation: 21+22=43 Exploring Operation: 40-22=18, Resulting Numbers: [21, 18] Generated Node #0,1,3: 24:[21, 18] Operation: 40-22=18 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 24:[22, 19], Operations: ['71-49=22', '40-21=19'] Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,24 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 24:[21, 18], Operations: ['71-49=22', '40-22=18'] Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,24 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 21+18=39, Resulting Numbers: [39] 39,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 24:[40, 1], Operations: ['71-49=22', '22-21=1'] Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,24 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,24 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,24 unequal: No Solution Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 24:[40, 43], Operations: ['71-49=22', '21+22=43'] Exploring Operation: 40*43=1720, Resulting Numbers: [1720] 1720,24 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 40+43=83, Resulting Numbers: [83] 83,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[21, 49, 31], Operations: ['71-40=31'] Exploring Operation: 31-21=10, Resulting Numbers: [49, 10] Generated Node #0,0,0: 24:[49, 10] Operation: 31-21=10 Exploring Operation: 21+49=70, Resulting Numbers: [31, 70] Generated Node #0,0,1: 24:[31, 70] Operation: 21+49=70 Exploring Operation: 49-31=18, Resulting Numbers: [21, 18] Generated Node #0,0,2: 24:[21, 18] Operation: 49-31=18 Exploring Operation: 49-21=28, Resulting Numbers: [31, 28] Generated Node #0,0,3: 24:[31, 28] Operation: 49-21=28 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 24:[21, 18], Operations: ['71-40=31', '49-31=18'] Exploring Operation: 21+18=39, Resulting Numbers: [39] 39,24 unequal: No Solution Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,24 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 24:[31, 28], Operations: ['71-40=31', '49-21=28'] Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,24 unequal: No Solution Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,24 unequal: No Solution Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[49, 10], Operations: ['71-40=31', '31-21=10'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,24 unequal: No Solution Exploring Operation: 49*10=490, Resulting Numbers: [490] 490,24 unequal: No Solution Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 24:[31, 70], Operations: ['71-40=31', '21+49=70'] Exploring Operation: 31+70=101, Resulting Numbers: [101] 101,24 unequal: No Solution Exploring Operation: 31*70=2170, Resulting Numbers: [2170] 2170,24 unequal: No Solution Exploring Operation: 70-31=39, Resulting Numbers: [39] 39,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 24:[71, 21, 9], Operations: ['49-40=9'] Exploring Operation: 71-9=62, Resulting Numbers: [21, 62] Generated Node #0,3,0: 24:[21, 62] Operation: 71-9=62 Exploring Operation: 21+9=30, Resulting Numbers: [71, 30] Generated Node #0,3,1: 24:[71, 30] Operation: 21+9=30 Exploring Operation: 21-9=12, Resulting Numbers: [71, 12] Generated Node #0,3,2: 24:[71, 12] Operation: 21-9=12 Exploring Operation: 71-21=50, Resulting Numbers: [9, 50] Generated Node #0,3,3: 24:[9, 50] Operation: 71-21=50 Moving to Node #0,3,3 Current State: 24:[9, 50], Operations: ['49-40=9', '71-21=50'] Exploring Operation: 9*50=450, Resulting Numbers: [450] 450,24 unequal: No Solution Exploring Operation: 50-9=41, Resulting Numbers: [41] 41,24 unequal: No Solution Exploring Operation: 9+50=59, Resulting Numbers: [59] 59,24 unequal: No Solution Moving to Node #0,3,0 Current State: 24:[21, 62], Operations: ['49-40=9', '71-9=62'] Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,24 unequal: No Solution Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,24 unequal: No Solution Exploring Operation: 21*62=1302, Resulting Numbers: [1302] 1302,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[71, 12], Operations: ['49-40=9', '21-9=12'] Exploring Operation: 71+12=83, Resulting Numbers: [83] 83,24 unequal: No Solution Exploring Operation: 71-12=59, Resulting Numbers: [59] 59,24 unequal: No Solution Exploring Operation: 71*12=852, Resulting Numbers: [852] 852,24 unequal: No Solution Moving to Node #0,3,1 Current State: 24:[71, 30], Operations: ['49-40=9', '21+9=30'] Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,24 unequal: No Solution Exploring Operation: 71*30=2130, Resulting Numbers: [2130] 2130,24 unequal: No Solution Exploring Operation: 71+30=101, Resulting Numbers: [101] 101,24 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 #0,2 Current State: 24:[40, 49, 50], Operations: ['71-21=50'] Exploring Operation: 50-40=10, Resulting Numbers: [49, 10] Generated Node #0,2,0: 24:[49, 10] Operation: 50-40=10 Exploring Operation: 50-49=1, Resulting Numbers: [40, 1] Generated Node #0,2,1: 24:[40, 1] Operation: 50-49=1 Exploring Operation: 40+49=89, Resulting Numbers: [50, 89] Generated Node #0,2,2: 24:[50, 89] Operation: 40+49=89 Exploring Operation: 49-40=9, Resulting Numbers: [50, 9] Generated Node #0,2,3: 24:[50, 9] Operation: 49-40=9 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 24:[40, 1], Operations: ['71-21=50', '50-49=1'] Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,24 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,24 unequal: No Solution Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,24 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 24:[49, 10], Operations: ['71-21=50', '50-40=10'] Exploring Operation: 49*10=490, Resulting Numbers: [490] 490,24 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,24 unequal: No Solution Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 24:[50, 9], Operations: ['71-21=50', '49-40=9'] Exploring Operation: 50*9=450, Resulting Numbers: [450] 450,24 unequal: No Solution Exploring Operation: 50-9=41, Resulting Numbers: [41] 41,24 unequal: No Solution Exploring Operation: 50+9=59, Resulting Numbers: [59] 59,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 24:[50, 89], Operations: ['71-21=50', '40+49=89'] Exploring Operation: 50*89=4450, Resulting Numbers: [4450] 4450,24 unequal: No Solution Exploring Operation: 50+89=139, Resulting Numbers: [139] 139,24 unequal: No Solution Exploring Operation: 89-50=39, Resulting Numbers: [39] 39,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 59, 7, 63, 10 ]
12
[ "63-59=4", "10-7=3", "4*3=12" ]
Current State: 12:[59, 7, 63, 10], Operations: [] Exploring Operation: 63-59=4, Resulting Numbers: [7, 10, 4] Generated Node #2: [7, 10, 4] from Operation: 63-59=4 Current State: 12:[7, 10, 4], Operations: ['63-59=4'] Exploring Operation: 10-7=3, Resulting Numbers: [4, 3] Generated Node #3: [4, 3] from Operation: 10-7=3 Current State: 12:[4, 3], Operations: ['63-59=4', '10-7=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[59, 7, 63, 10], Operations: [] Exploring Operation: 63-59=4, Resulting Numbers: [7, 10, 4] Generated Node #0,0: 12:[7, 10, 4] Operation: 63-59=4 Exploring Operation: 63/7=9, Resulting Numbers: [59, 10, 9] Generated Node #0,1: 12:[59, 10, 9] Operation: 63/7=9 Moving to Node #0,0 Current State: 12:[7, 10, 4], Operations: ['63-59=4'] Exploring Operation: 10-4=6, Resulting Numbers: [7, 6] Generated Node #0,0,0: 12:[7, 6] Operation: 10-4=6 Exploring Operation: 10-7=3, Resulting Numbers: [4, 3] Generated Node #0,0,1: 12:[4, 3] Operation: 10-7=3 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[4, 3], Operations: ['63-59=4', '10-7=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[59, 7, 63, 10], Operations: [] Exploring Operation: 63-59=4, Resulting Numbers: [7, 10, 4] Generated Node #0,0: 12:[7, 10, 4] Operation: 63-59=4 Moving to Node #0,0 Current State: 12:[7, 10, 4], Operations: ['63-59=4'] Exploring Operation: 10-7=3, Resulting Numbers: [4, 3] Generated Node #0,0,1: 12:[4, 3] Operation: 10-7=3 Moving to Node #0,0,1 Current State: 12:[4, 3], Operations: ['63-59=4', '10-7=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 13, 40, 19, 84 ]
52
[ "13*84=1092", "40-19=21", "1092/21=52" ]
Current State: 52:[13, 40, 19, 84], Operations: [] Exploring Operation: 13*84=1092, Resulting Numbers: [40, 19, 1092] Generated Node #2: [40, 19, 1092] from Operation: 13*84=1092 Current State: 52:[40, 19, 1092], Operations: ['13*84=1092'] Exploring Operation: 40-19=21, Resulting Numbers: [1092, 21] Generated Node #3: [1092, 21] from Operation: 40-19=21 Current State: 52:[1092, 21], Operations: ['13*84=1092', '40-19=21'] Exploring Operation: 1092/21=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[13, 40, 19, 84], Operations: [] Exploring Operation: 84-19=65, Resulting Numbers: [13, 40, 65] Generated Node #0,0: 52:[13, 40, 65] Operation: 84-19=65 Exploring Operation: 84-40=44, Resulting Numbers: [13, 19, 44] Generated Node #0,1: 52:[13, 19, 44] Operation: 84-40=44 Exploring Operation: 84-13=71, Resulting Numbers: [40, 19, 71] Generated Node #0,2: 52:[40, 19, 71] Operation: 84-13=71 Moving to Node #0,1 Current State: 52:[13, 19, 44], Operations: ['84-40=44'] Exploring Operation: 44-19=25, Resulting Numbers: [13, 25] Generated Node #0,1,0: 52:[13, 25] Operation: 44-19=25 Exploring Operation: 13+44=57, Resulting Numbers: [19, 57] Generated Node #0,1,1: 52:[19, 57] Operation: 13+44=57 Exploring Operation: 19-13=6, Resulting Numbers: [44, 6] Generated Node #0,1,2: 52:[44, 6] Operation: 19-13=6 Moving to Node #0,0 Current State: 52:[13, 40, 65], Operations: ['84-19=65'] Exploring Operation: 65-40=25, Resulting Numbers: [13, 25] Generated Node #0,0,0: 52:[13, 25] Operation: 65-40=25 Exploring Operation: 65/13=5, Resulting Numbers: [40, 5] Generated Node #0,0,1: 52:[40, 5] Operation: 65/13=5 Exploring Operation: 65-13=52, Resulting Numbers: [40, 52] Generated Node #0,0,2: 52:[40, 52] Operation: 65-13=52 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[13, 25], Operations: ['84-19=65', '65-40=25'] Exploring Operation: 13+25=38, Resulting Numbers: [38] 38,52 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 13*25=325, Resulting Numbers: [325] 325,52 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 #0,0,2 Current State: 52:[40, 52], Operations: ['84-19=65', '65-13=52'] Exploring Operation: 40+52=92, Resulting Numbers: [92] 92,52 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 40*52=2080, Resulting Numbers: [2080] 2080,52 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:[40, 5], Operations: ['84-19=65', '65/13=5'] Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,52 unequal: No Solution Exploring Operation: 40+5=45, Resulting Numbers: [45] 45,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 52:[40, 19, 71], Operations: ['84-13=71'] Exploring Operation: 71-40=31, Resulting Numbers: [19, 31] Generated Node #0,2,0: 52:[19, 31] Operation: 71-40=31 Exploring Operation: 40-19=21, Resulting Numbers: [71, 21] Generated Node #0,2,1: 52:[71, 21] Operation: 40-19=21 Exploring Operation: 71-19=52, Resulting Numbers: [40, 52] Generated Node #0,2,2: 52:[40, 52] Operation: 71-19=52 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 52:[19, 31], Operations: ['84-13=71', '71-40=31'] Exploring Operation: 19+31=50, Resulting Numbers: [50] 50,52 unequal: No Solution Exploring Operation: 19*31=589, Resulting Numbers: [589] 589,52 unequal: No Solution Exploring Operation: 31-19=12, Resulting Numbers: [12] 12,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 52:[40, 52], Operations: ['84-13=71', '71-19=52'] Exploring Operation: 40+52=92, Resulting Numbers: [92] 92,52 unequal: No Solution Exploring Operation: 40*52=2080, Resulting Numbers: [2080] 2080,52 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 52:[71, 21], Operations: ['84-13=71', '40-19=21'] Exploring Operation: 71+21=92, Resulting Numbers: [92] 92,52 unequal: No Solution Exploring Operation: 71-21=50, Resulting Numbers: [50] 50,52 unequal: No Solution Exploring Operation: 71*21=1491, Resulting Numbers: [1491] 1491,52 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: 52:[13, 25], Operations: ['84-40=44', '44-19=25'] Exploring Operation: 13+25=38, Resulting Numbers: [38] 38,52 unequal: No Solution Exploring Operation: 13*25=325, Resulting Numbers: [325] 325,52 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,52 unequal: No Solution Moving to Node #0,1,2 Current State: 52:[44, 6], Operations: ['84-40=44', '19-13=6'] Exploring Operation: 44*6=264, Resulting Numbers: [264] 264,52 unequal: No Solution Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,52 unequal: No Solution Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[19, 57], Operations: ['84-40=44', '13+44=57'] Exploring Operation: 57/19=3, Resulting Numbers: [3] 3,52 unequal: No Solution Exploring Operation: 57-19=38, Resulting Numbers: [38] 38,52 unequal: No Solution Exploring Operation: 19+57=76, Resulting Numbers: [76] 76,52 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 85, 57, 13, 3 ]
33
[ "85-13=72", "72/3=24", "57-24=33" ]
Current State: 33:[85, 57, 13, 3], Operations: [] Exploring Operation: 85-13=72, Resulting Numbers: [57, 3, 72] Generated Node #2: [57, 3, 72] from Operation: 85-13=72 Current State: 33:[57, 3, 72], Operations: ['85-13=72'] Exploring Operation: 72/3=24, Resulting Numbers: [57, 24] Generated Node #3: [57, 24] from Operation: 72/3=24 Current State: 33:[57, 24], Operations: ['85-13=72', '72/3=24'] Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[85, 57, 13, 3], Operations: [] Exploring Operation: 57/3=19, Resulting Numbers: [85, 13, 19] Generated Node #0,0: 33:[85, 13, 19] Operation: 57/3=19 Exploring Operation: 85-57=28, Resulting Numbers: [13, 3, 28] Generated Node #0,1: 33:[13, 3, 28] Operation: 85-57=28 Exploring Operation: 85-13=72, Resulting Numbers: [57, 3, 72] Generated Node #0,2: 33:[57, 3, 72] Operation: 85-13=72 Exploring Operation: 57-13=44, Resulting Numbers: [85, 3, 44] Generated Node #0,3: 33:[85, 3, 44] Operation: 57-13=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[13, 3, 28], Operations: ['85-57=28'] Exploring Operation: 13+28=41, Resulting Numbers: [3, 41] Generated Node #0,1,0: 33:[3, 41] Operation: 13+28=41 Exploring Operation: 28-13=15, Resulting Numbers: [3, 15] Generated Node #0,1,1: 33:[3, 15] Operation: 28-13=15 Exploring Operation: 3+28=31, Resulting Numbers: [13, 31] Generated Node #0,1,2: 33:[13, 31] Operation: 3+28=31 Exploring Operation: 13-3=10, Resulting Numbers: [28, 10] Generated Node #0,1,3: 33:[28, 10] Operation: 13-3=10 Moving to Node #0,1,1 Current State: 33:[3, 15], Operations: ['85-57=28', '28-13=15'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,33 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,33 unequal: No Solution Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,33 unequal: No Solution Moving to Node #0,1,2 Current State: 33:[13, 31], Operations: ['85-57=28', '3+28=31'] Exploring Operation: 13*31=403, Resulting Numbers: [403] 403,33 unequal: No Solution Exploring Operation: 13+31=44, Resulting Numbers: [44] 44,33 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,33 unequal: No Solution Moving to Node #0,1,3 Current State: 33:[28, 10], Operations: ['85-57=28', '13-3=10'] Exploring Operation: 28*10=280, Resulting Numbers: [280] 280,33 unequal: No Solution Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,33 unequal: No Solution Exploring Operation: 28+10=38, Resulting Numbers: [38] 38,33 unequal: No Solution Moving to Node #0,1,0 Current State: 33:[3, 41], Operations: ['85-57=28', '13+28=41'] Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,33 unequal: No Solution Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,33 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,33 unequal: No Solution No 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: 33:[85, 13, 19], Operations: ['57/3=19'] Exploring Operation: 85-19=66, Resulting Numbers: [13, 66] Generated Node #0,0,0: 33:[13, 66] Operation: 85-19=66 Exploring Operation: 85-13=72, Resulting Numbers: [19, 72] Generated Node #0,0,1: 33:[19, 72] Operation: 85-13=72 Exploring Operation: 19-13=6, Resulting Numbers: [85, 6] Generated Node #0,0,2: 33:[85, 6] Operation: 19-13=6 Exploring Operation: 13+19=32, Resulting Numbers: [85, 32] Generated Node #0,0,3: 33:[85, 32] Operation: 13+19=32 Moving to Node #0,0,0 Current State: 33:[13, 66], Operations: ['57/3=19', '85-19=66'] Exploring Operation: 13+66=79, Resulting Numbers: [79] 79,33 unequal: No Solution Exploring Operation: 66-13=53, Resulting Numbers: [53] 53,33 unequal: No Solution Exploring Operation: 13*66=858, Resulting Numbers: [858] 858,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[19, 72], Operations: ['57/3=19', '85-13=72'] Exploring Operation: 72-19=53, Resulting Numbers: [53] 53,33 unequal: No Solution Exploring Operation: 19*72=1368, Resulting Numbers: [1368] 1368,33 unequal: No Solution Exploring Operation: 19+72=91, Resulting Numbers: [91] 91,33 unequal: No Solution Moving to Node #0,0,3 Current State: 33:[85, 32], Operations: ['57/3=19', '13+19=32'] Exploring Operation: 85*32=2720, Resulting Numbers: [2720] 2720,33 unequal: No Solution Exploring Operation: 85+32=117, Resulting Numbers: [117] 117,33 unequal: No Solution Exploring Operation: 85-32=53, Resulting Numbers: [53] 53,33 unequal: No Solution Moving to Node #0,0,2 Current State: 33:[85, 6], Operations: ['57/3=19', '19-13=6'] Exploring Operation: 85-6=79, Resulting Numbers: [79] 79,33 unequal: No Solution Exploring Operation: 85+6=91, Resulting Numbers: [91] 91,33 unequal: No Solution Exploring Operation: 85*6=510, Resulting Numbers: [510] 510,33 unequal: No Solution No 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: 33:[57, 3, 72], Operations: ['85-13=72'] Exploring Operation: 72/3=24, Resulting Numbers: [57, 24] Generated Node #0,2,0: 33:[57, 24] Operation: 72/3=24 Exploring Operation: 72-57=15, Resulting Numbers: [3, 15] Generated Node #0,2,1: 33:[3, 15] Operation: 72-57=15 Exploring Operation: 57/3=19, Resulting Numbers: [72, 19] Generated Node #0,2,2: 33:[72, 19] Operation: 57/3=19 Exploring Operation: 57-3=54, Resulting Numbers: [72, 54] Generated Node #0,2,3: 33:[72, 54] Operation: 57-3=54 Moving to Node #0,2,1 Current State: 33:[3, 15], Operations: ['85-13=72', '72-57=15'] Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,33 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,33 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,33 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,33 unequal: No Solution Moving to Node #0,2,0 Current State: 33:[57, 24], Operations: ['85-13=72', '72/3=24'] Exploring Operation: 57+24=81, Resulting Numbers: [81] 81,33 unequal: No Solution Exploring Operation: 57*24=1368, Resulting Numbers: [1368] 1368,33 unequal: No Solution Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[85, 57, 13, 3], Operations: [] Exploring Operation: 85-13=72, Resulting Numbers: [57, 3, 72] Generated Node #0,2: 33:[57, 3, 72] Operation: 85-13=72 Moving to Node #0,2 Current State: 33:[57, 3, 72], Operations: ['85-13=72'] Exploring Operation: 72/3=24, Resulting Numbers: [57, 24] Generated Node #0,2,0: 33:[57, 24] Operation: 72/3=24 Moving to Node #0,2,0 Current State: 33:[57, 24], Operations: ['85-13=72', '72/3=24'] Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.954861
hs_4
sum_heuristic
[ 59, 72, 94, 35 ]
97
[ "59-35=24", "72/24=3", "94+3=97" ]
Current State: 97:[59, 72, 94, 35], Operations: [] Exploring Operation: 59-35=24, Resulting Numbers: [72, 94, 24] Generated Node #2: [72, 94, 24] from Operation: 59-35=24 Current State: 97:[72, 94, 24], Operations: ['59-35=24'] Exploring Operation: 72/24=3, Resulting Numbers: [94, 3] Generated Node #3: [94, 3] from Operation: 72/24=3 Current State: 97:[94, 3], Operations: ['59-35=24', '72/24=3'] Exploring Operation: 94+3=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[59, 72, 94, 35], Operations: [] Exploring Operation: 72+35=107, Resulting Numbers: [59, 94, 107] Generated Node #0,0: 97:[59, 94, 107] Operation: 72+35=107 Exploring Operation: 59+35=94, Resulting Numbers: [72, 94, 94] Generated Node #0,1: 97:[72, 94, 94] Operation: 59+35=94 Exploring Operation: 94+35=129, Resulting Numbers: [59, 72, 129] Generated Node #0,2: 97:[59, 72, 129] Operation: 94+35=129 Moving to Node #0,1 Current State: 97:[72, 94, 94], Operations: ['59+35=94'] Exploring Operation: 94-72=22, Resulting Numbers: [94, 22] Generated Node #0,1,0: 97:[94, 22] Operation: 94-72=22 Exploring Operation: 72+94=166, Resulting Numbers: [94, 166] Generated Node #0,1,1: 97:[94, 166] Operation: 72+94=166 Exploring Operation: 72+94=166, Resulting Numbers: [94, 166] Generated Node #0,1,2: 97:[94, 166] Operation: 72+94=166 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[94, 166], Operations: ['59+35=94', '72+94=166'] Exploring Operation: 94+166=260, Resulting Numbers: [260] 260,97 unequal: No Solution Exploring Operation: 166-94=72, Resulting Numbers: [72] 72,97 unequal: No Solution Exploring Operation: 94*166=15604, Resulting Numbers: [15604] 15604,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 97:[94, 166], Operations: ['59+35=94', '72+94=166'] Exploring Operation: 94*166=15604, Resulting Numbers: [15604] 15604,97 unequal: No Solution Exploring Operation: 94+166=260, Resulting Numbers: [260] 260,97 unequal: No Solution Exploring Operation: 166-94=72, Resulting Numbers: [72] 72,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[94, 22], Operations: ['59+35=94', '94-72=22'] Exploring Operation: 94*22=2068, Resulting Numbers: [2068] 2068,97 unequal: No Solution Exploring Operation: 94-22=72, Resulting Numbers: [72] 72,97 unequal: No Solution Exploring Operation: 94+22=116, Resulting Numbers: [116] 116,97 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: 97:[59, 94, 107], Operations: ['72+35=107'] Exploring Operation: 94-59=35, Resulting Numbers: [107, 35] Generated Node #0,0,0: 97:[107, 35] Operation: 94-59=35 Exploring Operation: 59+94=153, Resulting Numbers: [107, 153] Generated Node #0,0,1: 97:[107, 153] Operation: 59+94=153 Exploring Operation: 107-59=48, Resulting Numbers: [94, 48] Generated Node #0,0,2: 97:[94, 48] Operation: 107-59=48 Moving to Node #0,2 Current State: 97:[59, 72, 129], Operations: ['94+35=129'] Exploring Operation: 59+72=131, Resulting Numbers: [129, 131] Generated Node #0,2,0: 97:[129, 131] Operation: 59+72=131 Exploring Operation: 129-59=70, Resulting Numbers: [72, 70] Generated Node #0,2,1: 97:[72, 70] Operation: 129-59=70 Exploring Operation: 129-72=57, Resulting Numbers: [59, 57] Generated Node #0,2,2: 97:[59, 57] Operation: 129-72=57 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[72, 70], Operations: ['94+35=129', '129-59=70'] Exploring Operation: 72-70=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 72+70=142, Resulting Numbers: [142] 142,97 unequal: No Solution Exploring Operation: 72*70=5040, Resulting Numbers: [5040] 5040,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[129, 131], Operations: ['94+35=129', '59+72=131'] Exploring Operation: 129*131=16899, Resulting Numbers: [16899] 16899,97 unequal: No Solution Exploring Operation: 129+131=260, Resulting Numbers: [260] 260,97 unequal: No Solution Exploring Operation: 131-129=2, Resulting Numbers: [2] 2,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 97:[59, 57], Operations: ['94+35=129', '129-72=57'] Exploring Operation: 59-57=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 59*57=3363, Resulting Numbers: [3363] 3363,97 unequal: No Solution Exploring Operation: 59+57=116, Resulting Numbers: [116] 116,97 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: 97:[94, 48], Operations: ['72+35=107', '107-59=48'] Exploring Operation: 94-48=46, Resulting Numbers: [46] 46,97 unequal: No Solution Exploring Operation: 94*48=4512, Resulting Numbers: [4512] 4512,97 unequal: No Solution Exploring Operation: 94+48=142, Resulting Numbers: [142] 142,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[107, 153], Operations: ['72+35=107', '59+94=153'] Exploring Operation: 107+153=260, Resulting Numbers: [260] 260,97 unequal: No Solution Exploring Operation: 153-107=46, Resulting Numbers: [46] 46,97 unequal: No Solution Exploring Operation: 107*153=16371, Resulting Numbers: [16371] 16371,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[107, 35], Operations: ['72+35=107', '94-59=35'] Exploring Operation: 107*35=3745, Resulting Numbers: [3745] 3745,97 unequal: No Solution Exploring Operation: 107-35=72, Resulting Numbers: [72] 72,97 unequal: No Solution Exploring Operation: 107+35=142, Resulting Numbers: [142] 142,97 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 78, 30, 43, 40 ]
61
[ "78*40=3120", "3120/30=104", "104-43=61" ]
Current State: 61:[78, 30, 43, 40], Operations: [] Exploring Operation: 78*40=3120, Resulting Numbers: [30, 43, 3120] Generated Node #2: [30, 43, 3120] from Operation: 78*40=3120 Current State: 61:[30, 43, 3120], Operations: ['78*40=3120'] Exploring Operation: 3120/30=104, Resulting Numbers: [43, 104] Generated Node #3: [43, 104] from Operation: 3120/30=104 Current State: 61:[43, 104], Operations: ['78*40=3120', '3120/30=104'] Exploring Operation: 104-43=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[78, 30, 43, 40], Operations: [] Exploring Operation: 30+43=73, Resulting Numbers: [78, 40, 73] Generated Node #0,0: 61:[78, 40, 73] Operation: 30+43=73 Exploring Operation: 30+40=70, Resulting Numbers: [78, 43, 70] Generated Node #0,1: 61:[78, 43, 70] Operation: 30+40=70 Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[78, 43, 70], Operations: ['30+40=70'] Exploring Operation: 70-43=27, Resulting Numbers: [78, 27] Generated Node #0,1,0: 61:[78, 27] Operation: 70-43=27 Exploring Operation: 78-43=35, Resulting Numbers: [70, 35] Generated Node #0,1,1: 61:[70, 35] Operation: 78-43=35 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[70, 35], Operations: ['30+40=70', '78-43=35'] Exploring Operation: 70+35=105, Resulting Numbers: [105] 105,61 unequal: No Solution Exploring Operation: 70-35=35, Resulting Numbers: [35] 35,61 unequal: No Solution No 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: 61:[78, 27], Operations: ['30+40=70', '70-43=27'] Exploring Operation: 78+27=105, Resulting Numbers: [105] 105,61 unequal: No Solution Exploring Operation: 78-27=51, Resulting Numbers: [51] 51,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[78, 40, 73], Operations: ['30+43=73'] Exploring Operation: 78-40=38, Resulting Numbers: [73, 38] Generated Node #0,0,0: 61:[73, 38] Operation: 78-40=38 Exploring Operation: 73-40=33, Resulting Numbers: [78, 33] Generated Node #0,0,1: 61:[78, 33] Operation: 73-40=33 Moving to Node #0,0,0 Current State: 61:[73, 38], Operations: ['30+43=73', '78-40=38'] Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,61 unequal: No Solution Exploring Operation: 73+38=111, Resulting Numbers: [111] 111,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[78, 33], Operations: ['30+43=73', '73-40=33'] Exploring Operation: 78+33=111, Resulting Numbers: [111] 111,61 unequal: No Solution Exploring Operation: 78-33=45, Resulting Numbers: [45] 45,61 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
[ 58, 28, 2, 34 ]
32
[ "58-28=30", "34+30=64", "64/2=32" ]
Current State: 32:[58, 28, 2, 34], Operations: [] Exploring Operation: 58-28=30, Resulting Numbers: [2, 34, 30] Generated Node #2: [2, 34, 30] from Operation: 58-28=30 Current State: 32:[2, 34, 30], Operations: ['58-28=30'] Exploring Operation: 34+30=64, Resulting Numbers: [2, 64] Generated Node #3: [2, 64] from Operation: 34+30=64 Current State: 32:[2, 64], Operations: ['58-28=30', '34+30=64'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[58, 28, 2, 34], Operations: [] Exploring Operation: 34-28=6, Resulting Numbers: [58, 2, 6] Generated Node #0,0: 32:[58, 2, 6] Operation: 34-28=6 Exploring Operation: 58-28=30, Resulting Numbers: [2, 34, 30] Generated Node #0,1: 32:[2, 34, 30] Operation: 58-28=30 Exploring Operation: 58-2=56, Resulting Numbers: [28, 34, 56] Generated Node #0,2: 32:[28, 34, 56] Operation: 58-2=56 Exploring Operation: 58-34=24, Resulting Numbers: [28, 2, 24] Generated Node #0,3: 32:[28, 2, 24] Operation: 58-34=24 Exploring Operation: 58/2=29, Resulting Numbers: [28, 34, 29] Generated Node #0,4: 32:[28, 34, 29] Operation: 58/2=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[2, 34, 30], Operations: ['58-28=30'] Exploring Operation: 30/2=15, Resulting Numbers: [34, 15] Generated Node #0,1,0: 32:[34, 15] Operation: 30/2=15 Exploring Operation: 34/2=17, Resulting Numbers: [30, 17] Generated Node #0,1,1: 32:[30, 17] Operation: 34/2=17 Exploring Operation: 2+30=32, Resulting Numbers: [34, 32] Generated Node #0,1,2: 32:[34, 32] Operation: 2+30=32 Exploring Operation: 34-2=32, Resulting Numbers: [30, 32] Generated Node #0,1,3: 32:[30, 32] Operation: 34-2=32 Exploring Operation: 34-30=4, Resulting Numbers: [2, 4] Generated Node #0,1,4: 32:[2, 4] Operation: 34-30=4 Moving to Node #0,1,4 Current State: 32:[2, 4], Operations: ['58-28=30', '34-30=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,32 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,32 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,32 unequal: No Solution Moving to Node #0,1,3 Current State: 32:[30, 32], Operations: ['58-28=30', '34-2=32'] Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,32 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 30*32=960, Resulting Numbers: [960] 960,32 unequal: No Solution Moving to Node #0,1,2 Current State: 32:[34, 32], Operations: ['58-28=30', '2+30=32'] Exploring Operation: 34*32=1088, Resulting Numbers: [1088] 1088,32 unequal: No Solution Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 34+32=66, Resulting Numbers: [66] 66,32 unequal: No Solution Moving to Node #0,1,0 Current State: 32:[34, 15], Operations: ['58-28=30', '30/2=15'] Exploring Operation: 34+15=49, Resulting Numbers: [49] 49,32 unequal: No Solution Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 34*15=510, Resulting Numbers: [510] 510,32 unequal: No Solution Moving to Node #0,1,1 Current State: 32:[30, 17], Operations: ['58-28=30', '34/2=17'] Exploring Operation: 30+17=47, Resulting Numbers: [47] 47,32 unequal: No Solution Exploring Operation: 30*17=510, Resulting Numbers: [510] 510,32 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 32:[28, 34, 29], Operations: ['58/2=29'] Exploring Operation: 28+34=62, Resulting Numbers: [29, 62] Generated Node #0,4,0: 32:[29, 62] Operation: 28+34=62 Exploring Operation: 28+29=57, Resulting Numbers: [34, 57] Generated Node #0,4,1: 32:[34, 57] Operation: 28+29=57 Exploring Operation: 29-28=1, Resulting Numbers: [34, 1] Generated Node #0,4,2: 32:[34, 1] Operation: 29-28=1 Exploring Operation: 34-29=5, Resulting Numbers: [28, 5] Generated Node #0,4,3: 32:[28, 5] Operation: 34-29=5 Exploring Operation: 34-28=6, Resulting Numbers: [29, 6] Generated Node #0,4,4: 32:[29, 6] Operation: 34-28=6 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 32:[34, 1], Operations: ['58/2=29', '29-28=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,32 unequal: No Solution Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,32 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,32 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 32:[28, 5], Operations: ['58/2=29', '34-29=5'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,32 unequal: No Solution Exploring Operation: 28*5=140, Resulting Numbers: [140] 140,32 unequal: No Solution Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 32:[29, 6], Operations: ['58/2=29', '34-28=6'] Exploring Operation: 29*6=174, Resulting Numbers: [174] 174,32 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,32 unequal: No Solution Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 32:[34, 57], Operations: ['58/2=29', '28+29=57'] Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,32 unequal: No Solution Exploring Operation: 34*57=1938, Resulting Numbers: [1938] 1938,32 unequal: No Solution Exploring Operation: 34+57=91, Resulting Numbers: [91] 91,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 32:[29, 62], Operations: ['58/2=29', '28+34=62'] Exploring Operation: 29+62=91, Resulting Numbers: [91] 91,32 unequal: No Solution Exploring Operation: 62-29=33, Resulting Numbers: [33] 33,32 unequal: No Solution Exploring Operation: 29*62=1798, Resulting Numbers: [1798] 1798,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 32:[28, 2, 24], Operations: ['58-34=24'] Exploring Operation: 24/2=12, Resulting Numbers: [28, 12] Generated Node #0,3,0: 32:[28, 12] Operation: 24/2=12 Exploring Operation: 28/2=14, Resulting Numbers: [24, 14] Generated Node #0,3,1: 32:[24, 14] Operation: 28/2=14 Exploring Operation: 28+2=30, Resulting Numbers: [24, 30] Generated Node #0,3,2: 32:[24, 30] Operation: 28+2=30 Exploring Operation: 2+24=26, Resulting Numbers: [28, 26] Generated Node #0,3,3: 32:[28, 26] Operation: 2+24=26 Exploring Operation: 28-24=4, Resulting Numbers: [2, 4] Generated Node #0,3,4: 32:[2, 4] Operation: 28-24=4 Moving to Node #0,3,4 Current State: 32:[2, 4], Operations: ['58-34=24', '28-24=4'] Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,32 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,32 unequal: No Solution Moving to Node #0,3,0 Current State: 32:[28, 12], Operations: ['58-34=24', '24/2=12'] Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 28*12=336, Resulting Numbers: [336] 336,32 unequal: No Solution Moving to Node #0,3,1 Current State: 32:[24, 14], Operations: ['58-34=24', '28/2=14'] Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,32 unequal: No Solution Exploring Operation: 24*14=336, Resulting Numbers: [336] 336,32 unequal: No Solution Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,32 unequal: No Solution Moving to Node #0,3,2 Current State: 32:[24, 30], Operations: ['58-34=24', '28+2=30'] Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,32 unequal: No Solution Exploring Operation: 24*30=720, Resulting Numbers: [720] 720,32 unequal: No Solution Exploring Operation: 24+30=54, Resulting Numbers: [54] 54,32 unequal: No Solution Moving to Node #0,3,3 Current State: 32:[28, 26], Operations: ['58-34=24', '2+24=26'] Exploring Operation: 28+26=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 28*26=728, Resulting Numbers: [728] 728,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[58, 2, 6], Operations: ['34-28=6'] Exploring Operation: 58-6=52, Resulting Numbers: [2, 52] Generated Node #0,0,0: 32:[2, 52] Operation: 58-6=52 Exploring Operation: 58/2=29, Resulting Numbers: [6, 29] Generated Node #0,0,1: 32:[6, 29] Operation: 58/2=29 Exploring Operation: 6-2=4, Resulting Numbers: [58, 4] Generated Node #0,0,2: 32:[58, 4] Operation: 6-2=4 Exploring Operation: 2+6=8, Resulting Numbers: [58, 8] Generated Node #0,0,3: 32:[58, 8] Operation: 2+6=8 Exploring Operation: 58-2=56, Resulting Numbers: [6, 56] Generated Node #0,0,4: 32:[6, 56] Operation: 58-2=56 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 32:[6, 29], Operations: ['34-28=6', '58/2=29'] Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,32 unequal: No Solution Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,32 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[2, 52], Operations: ['34-28=6', '58-6=52'] Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 2*52=104, Resulting Numbers: [104] 104,32 unequal: No Solution Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,32 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 32:[58, 4], Operations: ['34-28=6', '6-2=4'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,32 unequal: No Solution Exploring Operation: 58*4=232, Resulting Numbers: [232] 232,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 32:[58, 8], Operations: ['34-28=6', '2+6=8'] Exploring Operation: 58*8=464, Resulting Numbers: [464] 464,32 unequal: No Solution Exploring Operation: 58+8=66, Resulting Numbers: [66] 66,32 unequal: No Solution Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 32:[6, 56], Operations: ['34-28=6', '58-2=56'] Exploring Operation: 6*56=336, Resulting Numbers: [336] 336,32 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,32 unequal: No Solution Exploring Operation: 6+56=62, Resulting Numbers: [62] 62,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[28, 34, 56], Operations: ['58-2=56'] Exploring Operation: 56-34=22, Resulting Numbers: [28, 22] Generated Node #0,2,0: 32:[28, 22] Operation: 56-34=22 Exploring Operation: 56-28=28, Resulting Numbers: [34, 28] Generated Node #0,2,1: 32:[34, 28] Operation: 56-28=28 Exploring Operation: 28+34=62, Resulting Numbers: [56, 62] Generated Node #0,2,2: 32:[56, 62] Operation: 28+34=62 Exploring Operation: 34-28=6, Resulting Numbers: [56, 6] Generated Node #0,2,3: 32:[56, 6] Operation: 34-28=6 Exploring Operation: 56/28=2, Resulting Numbers: [34, 2] Generated Node #0,2,4: 32:[34, 2] Operation: 56/28=2 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 32:[34, 2], Operations: ['58-2=56', '56/28=2'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[58, 28, 2, 34], Operations: [] Exploring Operation: 58-2=56, Resulting Numbers: [28, 34, 56] Generated Node #0,2: 32:[28, 34, 56] Operation: 58-2=56 Moving to Node #0,2 Current State: 32:[28, 34, 56], Operations: ['58-2=56'] Exploring Operation: 56/28=2, Resulting Numbers: [34, 2] Generated Node #0,2,4: 32:[34, 2] Operation: 56/28=2 Moving to Node #0,2,4 Current State: 32:[34, 2], Operations: ['58-2=56', '56/28=2'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.914063
hs_5
sum_heuristic
[ 28, 80, 43, 63 ]
24
[ "63-43=20", "80/20=4", "28-4=24" ]
Current State: 24:[28, 80, 43, 63], Operations: [] Exploring Operation: 63-43=20, Resulting Numbers: [28, 80, 20] Generated Node #2: [28, 80, 20] from Operation: 63-43=20 Current State: 24:[28, 80, 20], Operations: ['63-43=20'] Exploring Operation: 80/20=4, Resulting Numbers: [28, 4] Generated Node #3: [28, 4] from Operation: 80/20=4 Current State: 24:[28, 4], Operations: ['63-43=20', '80/20=4'] Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[28, 80, 43, 63], Operations: [] Exploring Operation: 80-63=17, Resulting Numbers: [28, 43, 17] Generated Node #0,0: 24:[28, 43, 17] Operation: 80-63=17 Moving to Node #0,0 Current State: 24:[28, 43, 17], Operations: ['80-63=17'] Exploring Operation: 43-17=26, Resulting Numbers: [28, 26] Generated Node #0,0,0: 24:[28, 26] Operation: 43-17=26 Moving to Node #0,0,0 Current State: 24:[28, 26], Operations: ['80-63=17', '43-17=26'] Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,24 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 18, 96, 31, 33 ]
30
[ "33-31=2", "96/2=48", "48-18=30" ]
Current State: 30:[18, 96, 31, 33], Operations: [] Exploring Operation: 33-31=2, Resulting Numbers: [18, 96, 2] Generated Node #2: [18, 96, 2] from Operation: 33-31=2 Current State: 30:[18, 96, 2], Operations: ['33-31=2'] Exploring Operation: 96/2=48, Resulting Numbers: [18, 48] Generated Node #3: [18, 48] from Operation: 96/2=48 Current State: 30:[18, 48], Operations: ['33-31=2', '96/2=48'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[18, 96, 31, 33], Operations: [] Exploring Operation: 96-33=63, Resulting Numbers: [18, 31, 63] Generated Node #0,0: 30:[18, 31, 63] Operation: 96-33=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[18, 31, 63], Operations: ['96-33=63'] Exploring Operation: 63-31=32, Resulting Numbers: [18, 32] Generated Node #0,0,0: 30:[18, 32] Operation: 63-31=32 Moving to Node #0,0,0 Current State: 30:[18, 32], Operations: ['96-33=63', '63-31=32'] Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,30 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
[ 63, 55, 2, 46 ]
31
[ "63-55=8", "46/2=23", "8+23=31" ]
Current State: 31:[63, 55, 2, 46], Operations: [] Exploring Operation: 63-55=8, Resulting Numbers: [2, 46, 8] Generated Node #2: [2, 46, 8] from Operation: 63-55=8 Current State: 31:[2, 46, 8], Operations: ['63-55=8'] Exploring Operation: 46/2=23, Resulting Numbers: [8, 23] Generated Node #3: [8, 23] from Operation: 46/2=23 Current State: 31:[8, 23], Operations: ['63-55=8', '46/2=23'] Exploring Operation: 8+23=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[63, 55, 2, 46], Operations: [] Exploring Operation: 46/2=23, Resulting Numbers: [63, 55, 23] Generated Node #0,0: 31:[63, 55, 23] Operation: 46/2=23 Exploring Operation: 55-2=53, Resulting Numbers: [63, 46, 53] Generated Node #0,1: 31:[63, 46, 53] Operation: 55-2=53 Exploring Operation: 63-46=17, Resulting Numbers: [55, 2, 17] Generated Node #0,2: 31:[55, 2, 17] Operation: 63-46=17 Exploring Operation: 63-55=8, Resulting Numbers: [2, 46, 8] Generated Node #0,3: 31:[2, 46, 8] Operation: 63-55=8 Exploring Operation: 63-2=61, Resulting Numbers: [55, 46, 61] Generated Node #0,4: 31:[55, 46, 61] Operation: 63-2=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[63, 55, 23], Operations: ['46/2=23'] Exploring Operation: 55-23=32, Resulting Numbers: [63, 32] Generated Node #0,0,0: 31:[63, 32] Operation: 55-23=32 Exploring Operation: 63-55=8, Resulting Numbers: [23, 8] Generated Node #0,0,1: 31:[23, 8] Operation: 63-55=8 Exploring Operation: 55+23=78, Resulting Numbers: [63, 78] Generated Node #0,0,2: 31:[63, 78] Operation: 55+23=78 Exploring Operation: 63-23=40, Resulting Numbers: [55, 40] Generated Node #0,0,3: 31:[55, 40] Operation: 63-23=40 Exploring Operation: 63+23=86, Resulting Numbers: [55, 86] Generated Node #0,0,4: 31:[55, 86] Operation: 63+23=86 Moving to Node #0,0,1 Current State: 31:[23, 8], Operations: ['46/2=23', '63-55=8'] Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,31 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[63, 55, 2, 46], Operations: [] Exploring Operation: 46/2=23, Resulting Numbers: [63, 55, 23] Generated Node #0,0: 31:[63, 55, 23] Operation: 46/2=23 Moving to Node #0,0 Current State: 31:[63, 55, 23], Operations: ['46/2=23'] Exploring Operation: 63-55=8, Resulting Numbers: [23, 8] Generated Node #0,0,1: 31:[23, 8] Operation: 63-55=8 Moving to Node #0,0,1 Current State: 31:[23, 8], Operations: ['46/2=23', '63-55=8'] Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 9, 43, 51, 28 ]
33
[ "51*28=1428", "1428-9=1419", "1419/43=33" ]
Current State: 33:[9, 43, 51, 28], Operations: [] Exploring Operation: 51*28=1428, Resulting Numbers: [9, 43, 1428] Generated Node #2: [9, 43, 1428] from Operation: 51*28=1428 Current State: 33:[9, 43, 1428], Operations: ['51*28=1428'] Exploring Operation: 1428-9=1419, Resulting Numbers: [43, 1419] Generated Node #3: [43, 1419] from Operation: 1428-9=1419 Current State: 33:[43, 1419], Operations: ['51*28=1428', '1428-9=1419'] Exploring Operation: 1419/43=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[9, 43, 51, 28], Operations: [] Exploring Operation: 51-43=8, Resulting Numbers: [9, 28, 8] Generated Node #0,0: 33:[9, 28, 8] Operation: 51-43=8 Exploring Operation: 51-28=23, Resulting Numbers: [9, 43, 23] Generated Node #0,1: 33:[9, 43, 23] Operation: 51-28=23 Exploring Operation: 51-9=42, Resulting Numbers: [43, 28, 42] Generated Node #0,2: 33:[43, 28, 42] Operation: 51-9=42 Exploring Operation: 43-9=34, Resulting Numbers: [51, 28, 34] Generated Node #0,3: 33:[51, 28, 34] Operation: 43-9=34 Moving to Node #0,0 Current State: 33:[9, 28, 8], Operations: ['51-43=8'] Exploring Operation: 28-9=19, Resulting Numbers: [8, 19] Generated Node #0,0,0: 33:[8, 19] Operation: 28-9=19 Exploring Operation: 9+28=37, Resulting Numbers: [8, 37] Generated Node #0,0,1: 33:[8, 37] Operation: 9+28=37 Exploring Operation: 28+8=36, Resulting Numbers: [9, 36] Generated Node #0,0,2: 33:[9, 36] Operation: 28+8=36 Exploring Operation: 9-8=1, Resulting Numbers: [28, 1] Generated Node #0,0,3: 33:[28, 1] Operation: 9-8=1 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 33:[9, 36], Operations: ['51-43=8', '28+8=36'] Exploring Operation: 9*36=324, Resulting Numbers: [324] 324,33 unequal: No Solution Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,33 unequal: No Solution Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,33 unequal: No Solution Exploring Operation: 9+36=45, Resulting Numbers: [45] 45,33 unequal: No Solution No 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: 33:[8, 37], Operations: ['51-43=8', '9+28=37'] Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 8+37=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 8*37=296, Resulting Numbers: [296] 296,33 unequal: No Solution No 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: 33:[28, 1], Operations: ['51-43=8', '9-8=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 28+1=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,33 unequal: No Solution Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,33 unequal: No Solution No 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: 33:[8, 19], Operations: ['51-43=8', '28-9=19'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,33 unequal: No Solution Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,33 unequal: No Solution Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,33 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: 33:[9, 43, 23], Operations: ['51-28=23'] Exploring Operation: 43-23=20, Resulting Numbers: [9, 20] Generated Node #0,1,0: 33:[9, 20] Operation: 43-23=20 Exploring Operation: 43-9=34, Resulting Numbers: [23, 34] Generated Node #0,1,1: 33:[23, 34] Operation: 43-9=34 Exploring Operation: 9+23=32, Resulting Numbers: [43, 32] Generated Node #0,1,2: 33:[43, 32] Operation: 9+23=32 Exploring Operation: 23-9=14, Resulting Numbers: [43, 14] Generated Node #0,1,3: 33:[43, 14] Operation: 23-9=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 33:[9, 20], Operations: ['51-28=23', '43-23=20'] Exploring Operation: 9*20=180, Resulting Numbers: [180] 180,33 unequal: No Solution Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,33 unequal: No Solution Exploring Operation: 9+20=29, Resulting Numbers: [29] 29,33 unequal: No Solution No 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: 33:[23, 34], Operations: ['51-28=23', '43-9=34'] Exploring Operation: 23*34=782, Resulting Numbers: [782] 782,33 unequal: No Solution Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,33 unequal: No Solution Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,33 unequal: No Solution No 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: 33:[43, 32], Operations: ['51-28=23', '9+23=32'] Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,33 unequal: No Solution Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,33 unequal: No Solution Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,33 unequal: No Solution No 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: 33:[43, 14], Operations: ['51-28=23', '23-9=14'] Exploring Operation: 43*14=602, Resulting Numbers: [602] 602,33 unequal: No Solution Exploring Operation: 43+14=57, Resulting Numbers: [57] 57,33 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,33 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: 33:[51, 28, 34], Operations: ['43-9=34'] Exploring Operation: 34-28=6, Resulting Numbers: [51, 6] Generated Node #0,3,0: 33:[51, 6] Operation: 34-28=6 Exploring Operation: 51+28=79, Resulting Numbers: [34, 79] Generated Node #0,3,1: 33:[34, 79] Operation: 51+28=79 Exploring Operation: 51-28=23, Resulting Numbers: [34, 23] Generated Node #0,3,2: 33:[34, 23] Operation: 51-28=23 Exploring Operation: 51-34=17, Resulting Numbers: [28, 17] Generated Node #0,3,3: 33:[28, 17] Operation: 51-34=17 Moving to Node #0,2 Current State: 33:[43, 28, 42], Operations: ['51-9=42'] Exploring Operation: 43-42=1, Resulting Numbers: [28, 1] Generated Node #0,2,0: 33:[28, 1] Operation: 43-42=1 Exploring Operation: 43-28=15, Resulting Numbers: [42, 15] Generated Node #0,2,1: 33:[42, 15] Operation: 43-28=15 Exploring Operation: 43+28=71, Resulting Numbers: [42, 71] Generated Node #0,2,2: 33:[42, 71] Operation: 43+28=71 Exploring Operation: 42-28=14, Resulting Numbers: [43, 14] Generated Node #0,2,3: 33:[43, 14] Operation: 42-28=14 Moving to Node #0,2,0 Current State: 33:[28, 1], Operations: ['51-9=42', '43-42=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 28+1=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,33 unequal: No Solution Moving to Node #0,3,2 Current State: 33:[34, 23], Operations: ['43-9=34', '51-28=23'] Exploring Operation: 34+23=57, Resulting Numbers: [57] 57,33 unequal: No Solution Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,33 unequal: No Solution Exploring Operation: 34*23=782, Resulting Numbers: [782] 782,33 unequal: No Solution Moving to Node #0,3,3 Current State: 33:[28, 17], Operations: ['43-9=34', '51-34=17'] Exploring Operation: 28*17=476, Resulting Numbers: [476] 476,33 unequal: No Solution Exploring Operation: 28+17=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,33 unequal: No Solution Moving to Node #0,2,1 Current State: 33:[42, 15], Operations: ['51-9=42', '43-28=15'] Exploring Operation: 42*15=630, Resulting Numbers: [630] 630,33 unequal: No Solution Exploring Operation: 42+15=57, Resulting Numbers: [57] 57,33 unequal: No Solution Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,33 unequal: No Solution Moving to Node #0,2,3 Current State: 33:[43, 14], Operations: ['51-9=42', '42-28=14'] Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 43*14=602, Resulting Numbers: [602] 602,33 unequal: No Solution Exploring Operation: 43+14=57, Resulting Numbers: [57] 57,33 unequal: No Solution Moving to Node #0,3,0 Current State: 33:[51, 6], Operations: ['43-9=34', '34-28=6'] Exploring Operation: 51*6=306, Resulting Numbers: [306] 306,33 unequal: No Solution Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 51+6=57, Resulting Numbers: [57] 57,33 unequal: No Solution Moving to Node #0,3,1 Current State: 33:[34, 79], Operations: ['43-9=34', '51+28=79'] Exploring Operation: 34+79=113, Resulting Numbers: [113] 113,33 unequal: No Solution Exploring Operation: 34*79=2686, Resulting Numbers: [2686] 2686,33 unequal: No Solution Exploring Operation: 79-34=45, Resulting Numbers: [45] 45,33 unequal: No Solution Moving to Node #0,2,2 Current State: 33:[42, 71], Operations: ['51-9=42', '43+28=71'] Exploring Operation: 42+71=113, Resulting Numbers: [113] 113,33 unequal: No Solution Exploring Operation: 42*71=2982, Resulting Numbers: [2982] 2982,33 unequal: No Solution Exploring Operation: 71-42=29, Resulting Numbers: [29] 29,33 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 2, 70, 44, 34 ]
74
[ "70+44=114", "34+114=148", "148/2=74" ]
Current State: 74:[2, 70, 44, 34], Operations: [] Exploring Operation: 70+44=114, Resulting Numbers: [2, 34, 114] Generated Node #2: [2, 34, 114] from Operation: 70+44=114 Current State: 74:[2, 34, 114], Operations: ['70+44=114'] Exploring Operation: 34+114=148, Resulting Numbers: [2, 148] Generated Node #3: [2, 148] from Operation: 34+114=148 Current State: 74:[2, 148], Operations: ['70+44=114', '34+114=148'] Exploring Operation: 148/2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[2, 70, 44, 34], Operations: [] Exploring Operation: 70-34=36, Resulting Numbers: [2, 44, 36] Generated Node #0,0: 74:[2, 44, 36] Operation: 70-34=36 Moving to Node #0,0 Current State: 74:[2, 44, 36], Operations: ['70-34=36'] Exploring Operation: 44-2=42, Resulting Numbers: [36, 42] Generated Node #0,0,0: 74:[36, 42] Operation: 44-2=42 Moving to Node #0,0,0 Current State: 74:[36, 42], Operations: ['70-34=36', '44-2=42'] Exploring Operation: 36+42=78, Resulting Numbers: [78] 78,74 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 61, 81, 76, 27 ]
83
[ "81-61=20", "76+27=103", "103-20=83" ]
Current State: 83:[61, 81, 76, 27], Operations: [] Exploring Operation: 81-61=20, Resulting Numbers: [76, 27, 20] Generated Node #2: [76, 27, 20] from Operation: 81-61=20 Current State: 83:[76, 27, 20], Operations: ['81-61=20'] Exploring Operation: 76+27=103, Resulting Numbers: [20, 103] Generated Node #3: [20, 103] from Operation: 76+27=103 Current State: 83:[20, 103], Operations: ['81-61=20', '76+27=103'] Exploring Operation: 103-20=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[61, 81, 76, 27], Operations: [] Exploring Operation: 81+27=108, Resulting Numbers: [61, 76, 108] Generated Node #0,0: 83:[61, 76, 108] Operation: 81+27=108 Exploring Operation: 76+27=103, Resulting Numbers: [61, 81, 103] Generated Node #0,1: 83:[61, 81, 103] Operation: 76+27=103 Exploring Operation: 61+27=88, Resulting Numbers: [81, 76, 88] Generated Node #0,2: 83:[81, 76, 88] Operation: 61+27=88 Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[81, 76, 88], Operations: ['61+27=88'] Exploring Operation: 88-76=12, Resulting Numbers: [81, 12] Generated Node #0,2,0: 83:[81, 12] Operation: 88-76=12 Exploring Operation: 81+76=157, Resulting Numbers: [88, 157] Generated Node #0,2,1: 83:[88, 157] Operation: 81+76=157 Exploring Operation: 81-76=5, Resulting Numbers: [88, 5] Generated Node #0,2,2: 83:[88, 5] Operation: 81-76=5 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[81, 12], Operations: ['61+27=88', '88-76=12'] Exploring Operation: 81-12=69, Resulting Numbers: [69] 69,83 unequal: No Solution Exploring Operation: 81+12=93, Resulting Numbers: [93] 93,83 unequal: No Solution Exploring Operation: 81*12=972, Resulting Numbers: [972] 972,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[88, 157], Operations: ['61+27=88', '81+76=157'] Exploring Operation: 88*157=13816, Resulting Numbers: [13816] 13816,83 unequal: No Solution Exploring Operation: 88+157=245, Resulting Numbers: [245] 245,83 unequal: No Solution Exploring Operation: 157-88=69, Resulting Numbers: [69] 69,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 83:[88, 5], Operations: ['61+27=88', '81-76=5'] Exploring Operation: 88-5=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[61, 81, 76, 27], Operations: [] Exploring Operation: 61+27=88, Resulting Numbers: [81, 76, 88] Generated Node #0,2: 83:[81, 76, 88] Operation: 61+27=88 Moving to Node #0,2 Current State: 83:[81, 76, 88], Operations: ['61+27=88'] Exploring Operation: 81-76=5, Resulting Numbers: [88, 5] Generated Node #0,2,2: 83:[88, 5] Operation: 81-76=5 Moving to Node #0,2,2 Current State: 83:[88, 5], Operations: ['61+27=88', '81-76=5'] Exploring Operation: 88-5=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 38, 74, 52, 12 ]
76
[ "74-38=36", "52-12=40", "36+40=76" ]
Current State: 76:[38, 74, 52, 12], Operations: [] Exploring Operation: 74-38=36, Resulting Numbers: [52, 12, 36] Generated Node #2: [52, 12, 36] from Operation: 74-38=36 Current State: 76:[52, 12, 36], Operations: ['74-38=36'] Exploring Operation: 52-12=40, Resulting Numbers: [36, 40] Generated Node #3: [36, 40] from Operation: 52-12=40 Current State: 76:[36, 40], Operations: ['74-38=36', '52-12=40'] Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[38, 74, 52, 12], Operations: [] Exploring Operation: 52-12=40, Resulting Numbers: [38, 74, 40] Generated Node #0,0: 76:[38, 74, 40] Operation: 52-12=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[38, 74, 40], Operations: ['52-12=40'] Exploring Operation: 40-38=2, Resulting Numbers: [74, 2] Generated Node #0,0,0: 76:[74, 2] Operation: 40-38=2 Moving to Node #0,0,0 Current State: 76:[74, 2], Operations: ['52-12=40', '40-38=2'] Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[38, 74, 52, 12], Operations: [] Exploring Operation: 52-12=40, Resulting Numbers: [38, 74, 40] Generated Node #0,0: 76:[38, 74, 40] Operation: 52-12=40 Moving to Node #0,0 Current State: 76:[38, 74, 40], Operations: ['52-12=40'] Exploring Operation: 40-38=2, Resulting Numbers: [74, 2] Generated Node #0,0,0: 76:[74, 2] Operation: 40-38=2 Moving to Node #0,0,0 Current State: 76:[74, 2], Operations: ['52-12=40', '40-38=2'] Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 15, 7, 13, 66 ]
38
[ "15-7=8", "13*8=104", "104-66=38" ]
Current State: 38:[15, 7, 13, 66], Operations: [] Exploring Operation: 15-7=8, Resulting Numbers: [13, 66, 8] Generated Node #2: [13, 66, 8] from Operation: 15-7=8 Current State: 38:[13, 66, 8], Operations: ['15-7=8'] Exploring Operation: 13*8=104, Resulting Numbers: [66, 104] Generated Node #3: [66, 104] from Operation: 13*8=104 Current State: 38:[66, 104], Operations: ['15-7=8', '13*8=104'] Exploring Operation: 104-66=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[15, 7, 13, 66], Operations: [] Exploring Operation: 66-15=51, Resulting Numbers: [7, 13, 51] Generated Node #0,0: 38:[7, 13, 51] Operation: 66-15=51 Exploring Operation: 66-7=59, Resulting Numbers: [15, 13, 59] Generated Node #0,1: 38:[15, 13, 59] Operation: 66-7=59 Exploring Operation: 66-13=53, Resulting Numbers: [15, 7, 53] Generated Node #0,2: 38:[15, 7, 53] Operation: 66-13=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[7, 13, 51], Operations: ['66-15=51'] Exploring Operation: 51-13=38, Resulting Numbers: [7, 38] Generated Node #0,0,0: 38:[7, 38] Operation: 51-13=38 Exploring Operation: 51-7=44, Resulting Numbers: [13, 44] Generated Node #0,0,1: 38:[13, 44] Operation: 51-7=44 Exploring Operation: 7+13=20, Resulting Numbers: [51, 20] Generated Node #0,0,2: 38:[51, 20] Operation: 7+13=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 38:[7, 38], Operations: ['66-15=51', '51-13=38'] Exploring Operation: 7*38=266, Resulting Numbers: [266] 266,38 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,38 unequal: No Solution Exploring Operation: 7+38=45, Resulting Numbers: [45] 45,38 unequal: No Solution No 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: 38:[13, 44], Operations: ['66-15=51', '51-7=44'] Exploring Operation: 13*44=572, Resulting Numbers: [572] 572,38 unequal: No Solution Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,38 unequal: No Solution Exploring Operation: 13+44=57, Resulting Numbers: [57] 57,38 unequal: No Solution No 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: 38:[51, 20], Operations: ['66-15=51', '7+13=20'] Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,38 unequal: No Solution Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,38 unequal: No Solution Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,38 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: 38:[15, 7, 53], Operations: ['66-13=53'] Exploring Operation: 15+7=22, Resulting Numbers: [53, 22] Generated Node #0,2,0: 38:[53, 22] Operation: 15+7=22 Exploring Operation: 53-15=38, Resulting Numbers: [7, 38] Generated Node #0,2,1: 38:[7, 38] Operation: 53-15=38 Exploring Operation: 53-7=46, Resulting Numbers: [15, 46] Generated Node #0,2,2: 38:[15, 46] Operation: 53-7=46 Moving to Node #0,2,1 Current State: 38:[7, 38], Operations: ['66-13=53', '53-15=38'] Exploring Operation: 7*38=266, Resulting Numbers: [266] 266,38 unequal: No Solution Exploring Operation: 7+38=45, Resulting Numbers: [45] 45,38 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[15, 46], Operations: ['66-13=53', '53-7=46'] Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,38 unequal: No Solution Exploring Operation: 15+46=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 15*46=690, Resulting Numbers: [690] 690,38 unequal: No Solution Moving to Node #0,2,0 Current State: 38:[53, 22], Operations: ['66-13=53', '15+7=22'] Exploring Operation: 53*22=1166, Resulting Numbers: [1166] 1166,38 unequal: No Solution Exploring Operation: 53-22=31, Resulting Numbers: [31] 31,38 unequal: No Solution Exploring Operation: 53+22=75, Resulting Numbers: [75] 75,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[15, 13, 59], Operations: ['66-7=59'] Exploring Operation: 59-15=44, Resulting Numbers: [13, 44] Generated Node #0,1,0: 38:[13, 44] Operation: 59-15=44 Exploring Operation: 59-13=46, Resulting Numbers: [15, 46] Generated Node #0,1,1: 38:[15, 46] Operation: 59-13=46 Exploring Operation: 15-13=2, Resulting Numbers: [59, 2] Generated Node #0,1,2: 38:[59, 2] Operation: 15-13=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 38:[13, 44], Operations: ['66-7=59', '59-15=44'] Exploring Operation: 13*44=572, Resulting Numbers: [572] 572,38 unequal: No Solution Exploring Operation: 13+44=57, Resulting Numbers: [57] 57,38 unequal: No Solution Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,38 unequal: No Solution No 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: 38:[15, 46], Operations: ['66-7=59', '59-13=46'] Exploring Operation: 15+46=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 15*46=690, Resulting Numbers: [690] 690,38 unequal: No Solution Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,38 unequal: No Solution No 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: 38:[59, 2], Operations: ['66-7=59', '15-13=2'] Exploring Operation: 59*2=118, Resulting Numbers: [118] 118,38 unequal: No Solution Exploring Operation: 59+2=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,38 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
[ 36, 49, 72, 47 ]
48
[ "72/36=2", "49+47=96", "96/2=48" ]
Current State: 48:[36, 49, 72, 47], Operations: [] Exploring Operation: 72/36=2, Resulting Numbers: [49, 47, 2] Generated Node #2: [49, 47, 2] from Operation: 72/36=2 Current State: 48:[49, 47, 2], Operations: ['72/36=2'] Exploring Operation: 49+47=96, Resulting Numbers: [2, 96] Generated Node #3: [2, 96] from Operation: 49+47=96 Current State: 48:[2, 96], Operations: ['72/36=2', '49+47=96'] Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[36, 49, 72, 47], Operations: [] Exploring Operation: 72/36=2, Resulting Numbers: [49, 47, 2] Generated Node #0,0: 48:[49, 47, 2] Operation: 72/36=2 Exploring Operation: 72-36=36, Resulting Numbers: [49, 47, 36] Generated Node #0,1: 48:[49, 47, 36] Operation: 72-36=36 Moving to Node #0,0 Current State: 48:[49, 47, 2], Operations: ['72/36=2'] Exploring Operation: 49-2=47, Resulting Numbers: [47, 47] Generated Node #0,0,0: 48:[47, 47] Operation: 49-2=47 Exploring Operation: 49-47=2, Resulting Numbers: [2, 2] Generated Node #0,0,1: 48:[2, 2] Operation: 49-47=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 48:[2, 2], Operations: ['72/36=2', '49-47=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,48 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[47, 47], Operations: ['72/36=2', '49-2=47'] Exploring Operation: 47-47=0, Resulting Numbers: [0] 0,48 unequal: No Solution Exploring Operation: 47/47=1, Resulting Numbers: [1] 1,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 48:[49, 47, 36], Operations: ['72-36=36'] Exploring Operation: 47-36=11, Resulting Numbers: [49, 11] Generated Node #0,1,0: 48:[49, 11] Operation: 47-36=11 Exploring Operation: 49-36=13, Resulting Numbers: [47, 13] Generated Node #0,1,1: 48:[47, 13] Operation: 49-36=13 Moving to Node #0,1,0 Current State: 48:[49, 11], Operations: ['72-36=36', '47-36=11'] Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[47, 13], Operations: ['72-36=36', '49-36=13'] Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,48 unequal: No Solution Exploring Operation: 47+13=60, Resulting Numbers: [60] 60,48 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 67, 14, 20, 7 ]
85
[ "67+20=87", "14/7=2", "87-2=85" ]
Current State: 85:[67, 14, 20, 7], Operations: [] Exploring Operation: 67+20=87, Resulting Numbers: [14, 7, 87] Generated Node #2: [14, 7, 87] from Operation: 67+20=87 Current State: 85:[14, 7, 87], Operations: ['67+20=87'] Exploring Operation: 14/7=2, Resulting Numbers: [87, 2] Generated Node #3: [87, 2] from Operation: 14/7=2 Current State: 85:[87, 2], Operations: ['67+20=87', '14/7=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[67, 14, 20, 7], Operations: [] Exploring Operation: 67+7=74, Resulting Numbers: [14, 20, 74] Generated Node #0,0: 85:[14, 20, 74] Operation: 67+7=74 Exploring Operation: 67+20=87, Resulting Numbers: [14, 7, 87] Generated Node #0,1: 85:[14, 7, 87] Operation: 67+20=87 Exploring Operation: 20-14=6, Resulting Numbers: [67, 7, 6] Generated Node #0,2: 85:[67, 7, 6] Operation: 20-14=6 Exploring Operation: 67+14=81, Resulting Numbers: [20, 7, 81] Generated Node #0,3: 85:[20, 7, 81] Operation: 67+14=81 Exploring Operation: 14-7=7, Resulting Numbers: [67, 20, 7] Generated Node #0,4: 85:[67, 20, 7] Operation: 14-7=7 Moving to Node #0,1 Current State: 85:[14, 7, 87], Operations: ['67+20=87'] Exploring Operation: 7+87=94, Resulting Numbers: [14, 94] Generated Node #0,1,0: 85:[14, 94] Operation: 7+87=94 Exploring Operation: 14+7=21, Resulting Numbers: [87, 21] Generated Node #0,1,1: 85:[87, 21] Operation: 14+7=21 Exploring Operation: 87-7=80, Resulting Numbers: [14, 80] Generated Node #0,1,2: 85:[14, 80] Operation: 87-7=80 Exploring Operation: 14/7=2, Resulting Numbers: [87, 2] Generated Node #0,1,3: 85:[87, 2] Operation: 14/7=2 Exploring Operation: 14-7=7, Resulting Numbers: [87, 7] Generated Node #0,1,4: 85:[87, 7] Operation: 14-7=7 Moving to Node #0,3 Current State: 85:[20, 7, 81], Operations: ['67+14=81'] Exploring Operation: 7+81=88, Resulting Numbers: [20, 88] Generated Node #0,3,0: 85:[20, 88] Operation: 7+81=88 Exploring Operation: 20-7=13, Resulting Numbers: [81, 13] Generated Node #0,3,1: 85:[81, 13] Operation: 20-7=13 Exploring Operation: 20+81=101, Resulting Numbers: [7, 101] Generated Node #0,3,2: 85:[7, 101] Operation: 20+81=101 Exploring Operation: 20+7=27, Resulting Numbers: [81, 27] Generated Node #0,3,3: 85:[81, 27] Operation: 20+7=27 Exploring Operation: 81-7=74, Resulting Numbers: [20, 74] Generated Node #0,3,4: 85:[20, 74] Operation: 81-7=74 Moving to Node #0,0 Current State: 85:[14, 20, 74], Operations: ['67+7=74'] Exploring Operation: 20-14=6, Resulting Numbers: [74, 6] Generated Node #0,0,0: 85:[74, 6] Operation: 20-14=6 Exploring Operation: 14+74=88, Resulting Numbers: [20, 88] Generated Node #0,0,1: 85:[20, 88] Operation: 14+74=88 Exploring Operation: 14+20=34, Resulting Numbers: [74, 34] Generated Node #0,0,2: 85:[74, 34] Operation: 14+20=34 Exploring Operation: 74-14=60, Resulting Numbers: [20, 60] Generated Node #0,0,3: 85:[20, 60] Operation: 74-14=60 Exploring Operation: 20+74=94, Resulting Numbers: [14, 94] Generated Node #0,0,4: 85:[14, 94] Operation: 20+74=94 Moving to Node #0,2 Current State: 85:[67, 7, 6], Operations: ['20-14=6'] Exploring Operation: 67-7=60, Resulting Numbers: [6, 60] Generated Node #0,2,0: 85:[6, 60] Operation: 67-7=60 Exploring Operation: 67+6=73, Resulting Numbers: [7, 73] Generated Node #0,2,1: 85:[7, 73] Operation: 67+6=73 Exploring Operation: 67+7=74, Resulting Numbers: [6, 74] Generated Node #0,2,2: 85:[6, 74] Operation: 67+7=74 Exploring Operation: 7+6=13, Resulting Numbers: [67, 13] Generated Node #0,2,3: 85:[67, 13] Operation: 7+6=13 Exploring Operation: 7-6=1, Resulting Numbers: [67, 1] Generated Node #0,2,4: 85:[67, 1] Operation: 7-6=1 Moving to Node #0,4 Current State: 85:[67, 20, 7], Operations: ['14-7=7'] Exploring Operation: 20+7=27, Resulting Numbers: [67, 27] Generated Node #0,4,0: 85:[67, 27] Operation: 20+7=27 Exploring Operation: 20-7=13, Resulting Numbers: [67, 13] Generated Node #0,4,1: 85:[67, 13] Operation: 20-7=13 Exploring Operation: 67-7=60, Resulting Numbers: [20, 60] Generated Node #0,4,2: 85:[20, 60] Operation: 67-7=60 Exploring Operation: 67+20=87, Resulting Numbers: [7, 87] Generated Node #0,4,3: 85:[7, 87] Operation: 67+20=87 Exploring Operation: 67+7=74, Resulting Numbers: [20, 74] Generated Node #0,4,4: 85:[20, 74] Operation: 67+7=74 Moving to Node #0,1,4 Current State: 85:[87, 7], Operations: ['67+20=87', '14-7=7'] Exploring Operation: 87+7=94, Resulting Numbers: [94] 94,85 unequal: No Solution Exploring Operation: 87*7=609, Resulting Numbers: [609] 609,85 unequal: No Solution Exploring Operation: 87-7=80, Resulting Numbers: [80] 80,85 unequal: No Solution Moving to Node #0,4,3 Current State: 85:[7, 87], Operations: ['14-7=7', '67+20=87'] Exploring Operation: 7*87=609, Resulting Numbers: [609] 609,85 unequal: No Solution Exploring Operation: 87-7=80, Resulting Numbers: [80] 80,85 unequal: No Solution Exploring Operation: 7+87=94, Resulting Numbers: [94] 94,85 unequal: No Solution Moving to Node #0,1,3 Current State: 85:[87, 2], Operations: ['67+20=87', '14/7=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,85 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[67, 14, 20, 7], Operations: [] Exploring Operation: 67+20=87, Resulting Numbers: [14, 7, 87] Generated Node #0,1: 85:[14, 7, 87] Operation: 67+20=87 Moving to Node #0,1 Current State: 85:[14, 7, 87], Operations: ['67+20=87'] Exploring Operation: 14/7=2, Resulting Numbers: [87, 2] Generated Node #0,1,3: 85:[87, 2] Operation: 14/7=2 Moving to Node #0,1,3 Current State: 85:[87, 2], Operations: ['67+20=87', '14/7=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
0.963542
hs_5
sum_heuristic
[ 28, 58, 15, 3 ]
71
[ "28+15=43", "3*43=129", "129-58=71" ]
Current State: 71:[28, 58, 15, 3], Operations: [] Exploring Operation: 28+15=43, Resulting Numbers: [58, 3, 43] Generated Node #2: [58, 3, 43] from Operation: 28+15=43 Current State: 71:[58, 3, 43], Operations: ['28+15=43'] Exploring Operation: 3*43=129, Resulting Numbers: [58, 129] Generated Node #3: [58, 129] from Operation: 3*43=129 Current State: 71:[58, 129], Operations: ['28+15=43', '3*43=129'] Exploring Operation: 129-58=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[28, 58, 15, 3], Operations: [] Exploring Operation: 28*3=84, Resulting Numbers: [58, 15, 84] Generated Node #0,0: 71:[58, 15, 84] Operation: 28*3=84 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[58, 15, 84], Operations: ['28*3=84'] Exploring Operation: 58+15=73, Resulting Numbers: [84, 73] Generated Node #0,0,0: 71:[84, 73] Operation: 58+15=73 Moving to Node #0,0,0 Current State: 71:[84, 73], Operations: ['28*3=84', '58+15=73'] Exploring Operation: 84-73=11, Resulting Numbers: [11] 11,71 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
[ 47, 24, 26, 69 ]
20
[ "47-24=23", "69-26=43", "43-23=20" ]
Current State: 20:[47, 24, 26, 69], Operations: [] Exploring Operation: 47-24=23, Resulting Numbers: [26, 69, 23] Generated Node #2: [26, 69, 23] from Operation: 47-24=23 Current State: 20:[26, 69, 23], Operations: ['47-24=23'] Exploring Operation: 69-26=43, Resulting Numbers: [23, 43] Generated Node #3: [23, 43] from Operation: 69-26=43 Current State: 20:[23, 43], Operations: ['47-24=23', '69-26=43'] Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[47, 24, 26, 69], Operations: [] Exploring Operation: 47-26=21, Resulting Numbers: [24, 69, 21] Generated Node #0,0: 20:[24, 69, 21] Operation: 47-26=21 Exploring Operation: 69-47=22, Resulting Numbers: [24, 26, 22] Generated Node #0,1: 20:[24, 26, 22] Operation: 69-47=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[24, 26, 22], Operations: ['69-47=22'] Exploring Operation: 26-24=2, Resulting Numbers: [22, 2] Generated Node #0,1,0: 20:[22, 2] Operation: 26-24=2 Exploring Operation: 26-22=4, Resulting Numbers: [24, 4] Generated Node #0,1,1: 20:[24, 4] Operation: 26-22=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 20:[22, 2], Operations: ['69-47=22', '26-24=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,20 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[47, 24, 26, 69], Operations: [] Exploring Operation: 69-47=22, Resulting Numbers: [24, 26, 22] Generated Node #0,1: 20:[24, 26, 22] Operation: 69-47=22 Moving to Node #0,1 Current State: 20:[24, 26, 22], Operations: ['69-47=22'] Exploring Operation: 26-24=2, Resulting Numbers: [22, 2] Generated Node #0,1,0: 20:[22, 2] Operation: 26-24=2 Moving to Node #0,1,0 Current State: 20:[22, 2], Operations: ['69-47=22', '26-24=2'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 83, 71, 9, 86 ]
98
[ "86-83=3", "9*3=27", "71+27=98" ]
Current State: 98:[83, 71, 9, 86], Operations: [] Exploring Operation: 86-83=3, Resulting Numbers: [71, 9, 3] Generated Node #2: [71, 9, 3] from Operation: 86-83=3 Current State: 98:[71, 9, 3], Operations: ['86-83=3'] Exploring Operation: 9*3=27, Resulting Numbers: [71, 27] Generated Node #3: [71, 27] from Operation: 9*3=27 Current State: 98:[71, 27], Operations: ['86-83=3', '9*3=27'] Exploring Operation: 71+27=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[83, 71, 9, 86], Operations: [] Exploring Operation: 83-71=12, Resulting Numbers: [9, 86, 12] Generated Node #0,0: 98:[9, 86, 12] Operation: 83-71=12 Exploring Operation: 86-71=15, Resulting Numbers: [83, 9, 15] Generated Node #0,1: 98:[83, 9, 15] Operation: 86-71=15 Exploring Operation: 83+9=92, Resulting Numbers: [71, 86, 92] Generated Node #0,2: 98:[71, 86, 92] Operation: 83+9=92 Exploring Operation: 86-83=3, Resulting Numbers: [71, 9, 3] Generated Node #0,3: 98:[71, 9, 3] Operation: 86-83=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[9, 86, 12], Operations: ['83-71=12'] Exploring Operation: 9+86=95, Resulting Numbers: [12, 95] Generated Node #0,0,0: 98:[12, 95] Operation: 9+86=95 Exploring Operation: 12-9=3, Resulting Numbers: [86, 3] Generated Node #0,0,1: 98:[86, 3] Operation: 12-9=3 Exploring Operation: 9+12=21, Resulting Numbers: [86, 21] Generated Node #0,0,2: 98:[86, 21] Operation: 9+12=21 Exploring Operation: 86+12=98, Resulting Numbers: [9, 98] Generated Node #0,0,3: 98:[9, 98] Operation: 86+12=98 Moving to Node #0,0,3 Current State: 98:[9, 98], Operations: ['83-71=12', '86+12=98'] Exploring Operation: 9+98=107, Resulting Numbers: [107] 107,98 unequal: No Solution Exploring Operation: 9*98=882, Resulting Numbers: [882] 882,98 unequal: No Solution Exploring Operation: 98-9=89, Resulting Numbers: [89] 89,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[12, 95], Operations: ['83-71=12', '9+86=95'] Exploring Operation: 12+95=107, Resulting Numbers: [107] 107,98 unequal: No Solution Exploring Operation: 12*95=1140, Resulting Numbers: [1140] 1140,98 unequal: No Solution Exploring Operation: 95-12=83, Resulting Numbers: [83] 83,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[86, 3], Operations: ['83-71=12', '12-9=3'] Exploring Operation: 86*3=258, Resulting Numbers: [258] 258,98 unequal: No Solution Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,98 unequal: No Solution Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[86, 21], Operations: ['83-71=12', '9+12=21'] Exploring Operation: 86+21=107, Resulting Numbers: [107] 107,98 unequal: No Solution Exploring Operation: 86*21=1806, Resulting Numbers: [1806] 1806,98 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[83, 9, 15], Operations: ['86-71=15'] Exploring Operation: 83+9=92, Resulting Numbers: [15, 92] Generated Node #0,1,0: 98:[15, 92] Operation: 83+9=92 Exploring Operation: 83-15=68, Resulting Numbers: [9, 68] Generated Node #0,1,1: 98:[9, 68] Operation: 83-15=68 Exploring Operation: 15-9=6, Resulting Numbers: [83, 6] Generated Node #0,1,2: 98:[83, 6] Operation: 15-9=6 Exploring Operation: 83+15=98, Resulting Numbers: [9, 98] Generated Node #0,1,3: 98:[9, 98] Operation: 83+15=98 Moving to Node #0,1,3 Current State: 98:[9, 98], Operations: ['86-71=15', '83+15=98'] Exploring Operation: 9+98=107, Resulting Numbers: [107] 107,98 unequal: No Solution Exploring Operation: 98-9=89, Resulting Numbers: [89] 89,98 unequal: No Solution Exploring Operation: 9*98=882, Resulting Numbers: [882] 882,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[15, 92], Operations: ['86-71=15', '83+9=92'] Exploring Operation: 15+92=107, Resulting Numbers: [107] 107,98 unequal: No Solution Exploring Operation: 15*92=1380, Resulting Numbers: [1380] 1380,98 unequal: No Solution Exploring Operation: 92-15=77, Resulting Numbers: [77] 77,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[83, 6], Operations: ['86-71=15', '15-9=6'] Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 83*6=498, Resulting Numbers: [498] 498,98 unequal: No Solution Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[9, 68], Operations: ['86-71=15', '83-15=68'] Exploring Operation: 9+68=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 9*68=612, Resulting Numbers: [612] 612,98 unequal: No Solution Exploring Operation: 68-9=59, Resulting Numbers: [59] 59,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 98:[71, 9, 3], Operations: ['86-83=3'] Exploring Operation: 71+9=80, Resulting Numbers: [3, 80] Generated Node #0,3,0: 98:[3, 80] Operation: 71+9=80 Exploring Operation: 9-3=6, Resulting Numbers: [71, 6] Generated Node #0,3,1: 98:[71, 6] Operation: 9-3=6 Exploring Operation: 71-3=68, Resulting Numbers: [9, 68] Generated Node #0,3,2: 98:[9, 68] Operation: 71-3=68 Exploring Operation: 71-9=62, Resulting Numbers: [3, 62] Generated Node #0,3,3: 98:[3, 62] Operation: 71-9=62 Moving to Node #0,3,3 Current State: 98:[3, 62], Operations: ['86-83=3', '71-9=62'] Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,98 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,98 unequal: No Solution Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,98 unequal: No Solution Moving to Node #0,3,0 Current State: 98:[3, 80], Operations: ['86-83=3', '71+9=80'] Exploring Operation: 3+80=83, Resulting Numbers: [83] 83,98 unequal: No Solution Exploring Operation: 3*80=240, Resulting Numbers: [240] 240,98 unequal: No Solution Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,98 unequal: No Solution Moving to Node #0,3,2 Current State: 98:[9, 68], Operations: ['86-83=3', '71-3=68'] Exploring Operation: 9+68=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 68-9=59, Resulting Numbers: [59] 59,98 unequal: No Solution Exploring Operation: 9*68=612, Resulting Numbers: [612] 612,98 unequal: No Solution Moving to Node #0,3,1 Current State: 98:[71, 6], Operations: ['86-83=3', '9-3=6'] Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,98 unequal: No Solution Exploring Operation: 71+6=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 71*6=426, Resulting Numbers: [426] 426,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[71, 86, 92], Operations: ['83+9=92'] Exploring Operation: 92-71=21, Resulting Numbers: [86, 21] Generated Node #0,2,0: 98:[86, 21] Operation: 92-71=21 Exploring Operation: 92-86=6, Resulting Numbers: [71, 6] Generated Node #0,2,1: 98:[71, 6] Operation: 92-86=6 Exploring Operation: 71+86=157, Resulting Numbers: [92, 157] Generated Node #0,2,2: 98:[92, 157] Operation: 71+86=157 Exploring Operation: 86-71=15, Resulting Numbers: [92, 15] Generated Node #0,2,3: 98:[92, 15] Operation: 86-71=15 Moving to Node #0,2,3 Current State: 98:[92, 15], Operations: ['83+9=92', '86-71=15'] Exploring Operation: 92-15=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 92*15=1380, Resulting Numbers: [1380] 1380,98 unequal: No Solution Exploring Operation: 92+15=107, Resulting Numbers: [107] 107,98 unequal: No Solution Moving to Node #0,2,0 Current State: 98:[86, 21], Operations: ['83+9=92', '92-71=21'] Exploring Operation: 86+21=107, Resulting Numbers: [107] 107,98 unequal: No Solution Exploring Operation: 86*21=1806, Resulting Numbers: [1806] 1806,98 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[71, 6], Operations: ['83+9=92', '92-86=6'] Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,98 unequal: No Solution Exploring Operation: 71+6=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 71*6=426, Resulting Numbers: [426] 426,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[92, 157], Operations: ['83+9=92', '71+86=157'] Exploring Operation: 157-92=65, Resulting Numbers: [65] 65,98 unequal: No Solution Exploring Operation: 92*157=14444, Resulting Numbers: [14444] 14444,98 unequal: No Solution Exploring Operation: 92+157=249, Resulting Numbers: [249] 249,98 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
[ 37, 15, 52, 89 ]
59
[ "37-15=22", "89-52=37", "22+37=59" ]
Current State: 59:[37, 15, 52, 89], Operations: [] Exploring Operation: 37-15=22, Resulting Numbers: [52, 89, 22] Generated Node #2: [52, 89, 22] from Operation: 37-15=22 Current State: 59:[52, 89, 22], Operations: ['37-15=22'] Exploring Operation: 89-52=37, Resulting Numbers: [22, 37] Generated Node #3: [22, 37] from Operation: 89-52=37 Current State: 59:[22, 37], Operations: ['37-15=22', '89-52=37'] Exploring Operation: 22+37=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[37, 15, 52, 89], Operations: [] Exploring Operation: 89-15=74, Resulting Numbers: [37, 52, 74] Generated Node #0,0: 59:[37, 52, 74] Operation: 89-15=74 Exploring Operation: 89-37=52, Resulting Numbers: [15, 52, 52] Generated Node #0,1: 59:[15, 52, 52] Operation: 89-37=52 Exploring Operation: 37+15=52, Resulting Numbers: [52, 89, 52] Generated Node #0,2: 59:[52, 89, 52] Operation: 37+15=52 Exploring Operation: 15+52=67, Resulting Numbers: [37, 89, 67] Generated Node #0,3: 59:[37, 89, 67] Operation: 15+52=67 Exploring Operation: 37-15=22, Resulting Numbers: [52, 89, 22] Generated Node #0,4: 59:[52, 89, 22] Operation: 37-15=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[37, 52, 74], Operations: ['89-15=74'] Exploring Operation: 74-52=22, Resulting Numbers: [37, 22] Generated Node #0,0,0: 59:[37, 22] Operation: 74-52=22 Exploring Operation: 37+74=111, Resulting Numbers: [52, 111] Generated Node #0,0,1: 59:[52, 111] Operation: 37+74=111 Exploring Operation: 74-37=37, Resulting Numbers: [52, 37] Generated Node #0,0,2: 59:[52, 37] Operation: 74-37=37 Exploring Operation: 52-37=15, Resulting Numbers: [74, 15] Generated Node #0,0,3: 59:[74, 15] Operation: 52-37=15 Exploring Operation: 37+52=89, Resulting Numbers: [74, 89] Generated Node #0,0,4: 59:[74, 89] Operation: 37+52=89 Moving to Node #0,0,2 Current State: 59:[52, 37], Operations: ['89-15=74', '74-37=37'] Exploring Operation: 52+37=89, Resulting Numbers: [89] 89,59 unequal: No Solution Exploring Operation: 52-37=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 52*37=1924, Resulting Numbers: [1924] 1924,59 unequal: No Solution Moving to Node #0,0,4 Current State: 59:[74, 89], Operations: ['89-15=74', '37+52=89'] Exploring Operation: 74+89=163, Resulting Numbers: [163] 163,59 unequal: No Solution Exploring Operation: 89-74=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 74*89=6586, Resulting Numbers: [6586] 6586,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[37, 22], Operations: ['89-15=74', '74-52=22'] Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 37+22=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[37, 15, 52, 89], Operations: [] Exploring Operation: 89-15=74, Resulting Numbers: [37, 52, 74] Generated Node #0,0: 59:[37, 52, 74] Operation: 89-15=74 Moving to Node #0,0 Current State: 59:[37, 52, 74], Operations: ['89-15=74'] Exploring Operation: 74-52=22, Resulting Numbers: [37, 22] Generated Node #0,0,0: 59:[37, 22] Operation: 74-52=22 Moving to Node #0,0,0 Current State: 59:[37, 22], Operations: ['89-15=74', '74-52=22'] Exploring Operation: 37+22=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 51, 41, 89, 22 ]
57
[ "51-41=10", "89-22=67", "67-10=57" ]
Current State: 57:[51, 41, 89, 22], Operations: [] Exploring Operation: 51-41=10, Resulting Numbers: [89, 22, 10] Generated Node #2: [89, 22, 10] from Operation: 51-41=10 Current State: 57:[89, 22, 10], Operations: ['51-41=10'] Exploring Operation: 89-22=67, Resulting Numbers: [10, 67] Generated Node #3: [10, 67] from Operation: 89-22=67 Current State: 57:[10, 67], Operations: ['51-41=10', '89-22=67'] Exploring Operation: 67-10=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[51, 41, 89, 22], Operations: [] Exploring Operation: 89-41=48, Resulting Numbers: [51, 22, 48] Generated Node #0,0: 57:[51, 22, 48] Operation: 89-41=48 Exploring Operation: 51-41=10, Resulting Numbers: [89, 22, 10] Generated Node #0,1: 57:[89, 22, 10] Operation: 51-41=10 Exploring Operation: 89-51=38, Resulting Numbers: [41, 22, 38] Generated Node #0,2: 57:[41, 22, 38] Operation: 89-51=38 Exploring Operation: 89-22=67, Resulting Numbers: [51, 41, 67] Generated Node #0,3: 57:[51, 41, 67] Operation: 89-22=67 Exploring Operation: 41-22=19, Resulting Numbers: [51, 89, 19] Generated Node #0,4: 57:[51, 89, 19] Operation: 41-22=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[51, 22, 48], Operations: ['89-41=48'] Exploring Operation: 22+48=70, Resulting Numbers: [51, 70] Generated Node #0,0,0: 57:[51, 70] Operation: 22+48=70 Exploring Operation: 48-22=26, Resulting Numbers: [51, 26] Generated Node #0,0,1: 57:[51, 26] Operation: 48-22=26 Exploring Operation: 51-22=29, Resulting Numbers: [48, 29] Generated Node #0,0,2: 57:[48, 29] Operation: 51-22=29 Exploring Operation: 51+22=73, Resulting Numbers: [48, 73] Generated Node #0,0,3: 57:[48, 73] Operation: 51+22=73 Exploring Operation: 51-48=3, Resulting Numbers: [22, 3] Generated Node #0,0,4: 57:[22, 3] Operation: 51-48=3 Moving to Node #0,0,4 Current State: 57:[22, 3], Operations: ['89-41=48', '51-48=3'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[51, 26], Operations: ['89-41=48', '48-22=26'] Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,57 unequal: No Solution Exploring Operation: 51+26=77, Resulting Numbers: [77] 77,57 unequal: No Solution Exploring Operation: 51*26=1326, Resulting Numbers: [1326] 1326,57 unequal: No Solution Moving to Node #0,0,0 Current State: 57:[51, 70], Operations: ['89-41=48', '22+48=70'] Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 51+70=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 51*70=3570, Resulting Numbers: [3570] 3570,57 unequal: No Solution Moving to Node #0,0,2 Current State: 57:[48, 29], Operations: ['89-41=48', '51-22=29'] Exploring Operation: 48-29=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 48*29=1392, Resulting Numbers: [1392] 1392,57 unequal: No Solution Exploring Operation: 48+29=77, Resulting Numbers: [77] 77,57 unequal: No Solution Moving to Node #0,0,3 Current State: 57:[48, 73], Operations: ['89-41=48', '51+22=73'] Exploring Operation: 48*73=3504, Resulting Numbers: [3504] 3504,57 unequal: No Solution Exploring Operation: 48+73=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 73-48=25, Resulting Numbers: [25] 25,57 unequal: No Solution No 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: 57:[51, 41, 67], Operations: ['89-22=67'] Exploring Operation: 41+67=108, Resulting Numbers: [51, 108] Generated Node #0,3,0: 57:[51, 108] Operation: 41+67=108 Exploring Operation: 51-41=10, Resulting Numbers: [67, 10] Generated Node #0,3,1: 57:[67, 10] Operation: 51-41=10 Exploring Operation: 67-51=16, Resulting Numbers: [41, 16] Generated Node #0,3,2: 57:[41, 16] Operation: 67-51=16 Exploring Operation: 51+41=92, Resulting Numbers: [67, 92] Generated Node #0,3,3: 57:[67, 92] Operation: 51+41=92 Exploring Operation: 67-41=26, Resulting Numbers: [51, 26] Generated Node #0,3,4: 57:[51, 26] Operation: 67-41=26 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 57:[51, 26], Operations: ['89-22=67', '67-41=26'] Exploring Operation: 51*26=1326, Resulting Numbers: [1326] 1326,57 unequal: No Solution Exploring Operation: 51+26=77, Resulting Numbers: [77] 77,57 unequal: No Solution Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 57:[67, 10], Operations: ['89-22=67', '51-41=10'] Exploring Operation: 67*10=670, Resulting Numbers: [670] 670,57 unequal: No Solution Exploring Operation: 67+10=77, Resulting Numbers: [77] 77,57 unequal: No Solution Exploring Operation: 67-10=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[51, 41, 89, 22], Operations: [] Exploring Operation: 89-22=67, Resulting Numbers: [51, 41, 67] Generated Node #0,3: 57:[51, 41, 67] Operation: 89-22=67 Moving to Node #0,3 Current State: 57:[51, 41, 67], Operations: ['89-22=67'] Exploring Operation: 51-41=10, Resulting Numbers: [67, 10] Generated Node #0,3,1: 57:[67, 10] Operation: 51-41=10 Moving to Node #0,3,1 Current State: 57:[67, 10], Operations: ['89-22=67', '51-41=10'] Exploring Operation: 67-10=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_5
mult_heuristic
[ 74, 42, 47, 45 ]
81
[ "74-47=27", "45-42=3", "27*3=81" ]
Current State: 81:[74, 42, 47, 45], Operations: [] Exploring Operation: 74-47=27, Resulting Numbers: [42, 45, 27] Generated Node #2: [42, 45, 27] from Operation: 74-47=27 Current State: 81:[42, 45, 27], Operations: ['74-47=27'] Exploring Operation: 45-42=3, Resulting Numbers: [27, 3] Generated Node #3: [27, 3] from Operation: 45-42=3 Current State: 81:[27, 3], Operations: ['74-47=27', '45-42=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[74, 42, 47, 45], Operations: [] Exploring Operation: 47-45=2, Resulting Numbers: [74, 42, 2] Generated Node #0,0: 81:[74, 42, 2] Operation: 47-45=2 Exploring Operation: 47-42=5, Resulting Numbers: [74, 45, 5] Generated Node #0,1: 81:[74, 45, 5] Operation: 47-42=5 Exploring Operation: 45-42=3, Resulting Numbers: [74, 47, 3] Generated Node #0,2: 81:[74, 47, 3] Operation: 45-42=3 Exploring Operation: 74-47=27, Resulting Numbers: [42, 45, 27] Generated Node #0,3: 81:[42, 45, 27] Operation: 74-47=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[74, 42, 2], Operations: ['47-45=2'] Exploring Operation: 42/2=21, Resulting Numbers: [74, 21] Generated Node #0,0,0: 81:[74, 21] Operation: 42/2=21 Exploring Operation: 74-42=32, Resulting Numbers: [2, 32] Generated Node #0,0,1: 81:[2, 32] Operation: 74-42=32 Exploring Operation: 42*2=84, Resulting Numbers: [74, 84] Generated Node #0,0,2: 81:[74, 84] Operation: 42*2=84 Exploring Operation: 74+2=76, Resulting Numbers: [42, 76] Generated Node #0,0,3: 81:[42, 76] Operation: 74+2=76 Moving to Node #0,0,1 Current State: 81:[2, 32], Operations: ['47-45=2', '74-42=32'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,81 unequal: No Solution Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,81 unequal: No Solution Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,81 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,81 unequal: No Solution Moving to Node #0,0,2 Current State: 81:[74, 84], Operations: ['47-45=2', '42*2=84'] Exploring Operation: 84-74=10, Resulting Numbers: [10] 10,81 unequal: No Solution Exploring Operation: 74+84=158, Resulting Numbers: [158] 158,81 unequal: No Solution Exploring Operation: 74*84=6216, Resulting Numbers: [6216] 6216,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[74, 21], Operations: ['47-45=2', '42/2=21'] Exploring Operation: 74+21=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 74*21=1554, Resulting Numbers: [1554] 1554,81 unequal: No Solution Exploring Operation: 74-21=53, Resulting Numbers: [53] 53,81 unequal: No Solution Moving to Node #0,0,3 Current State: 81:[42, 76], Operations: ['47-45=2', '74+2=76'] Exploring Operation: 76-42=34, Resulting Numbers: [34] 34,81 unequal: No Solution Exploring Operation: 42+76=118, Resulting Numbers: [118] 118,81 unequal: No Solution Exploring Operation: 42*76=3192, Resulting Numbers: [3192] 3192,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[74, 45, 5], Operations: ['47-42=5'] Exploring Operation: 74+5=79, Resulting Numbers: [45, 79] Generated Node #0,1,0: 81:[45, 79] Operation: 74+5=79 Exploring Operation: 74-45=29, Resulting Numbers: [5, 29] Generated Node #0,1,1: 81:[5, 29] Operation: 74-45=29 Exploring Operation: 45-5=40, Resulting Numbers: [74, 40] Generated Node #0,1,2: 81:[74, 40] Operation: 45-5=40 Exploring Operation: 45/5=9, Resulting Numbers: [74, 9] Generated Node #0,1,3: 81:[74, 9] Operation: 45/5=9 Moving to Node #0,1,1 Current State: 81:[5, 29], Operations: ['47-42=5', '74-45=29'] Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,81 unequal: No Solution Exploring Operation: 5*29=145, Resulting Numbers: [145] 145,81 unequal: No Solution Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,81 unequal: No Solution Moving to Node #0,1,3 Current State: 81:[74, 9], Operations: ['47-42=5', '45/5=9'] Exploring Operation: 74-9=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 74+9=83, Resulting Numbers: [83] 83,81 unequal: No Solution Exploring Operation: 74*9=666, Resulting Numbers: [666] 666,81 unequal: No Solution Moving to Node #0,1,2 Current State: 81:[74, 40], Operations: ['47-42=5', '45-5=40'] Exploring Operation: 74+40=114, Resulting Numbers: [114] 114,81 unequal: No Solution Exploring Operation: 74*40=2960, Resulting Numbers: [2960] 2960,81 unequal: No Solution Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[45, 79], Operations: ['47-42=5', '74+5=79'] Exploring Operation: 45*79=3555, Resulting Numbers: [3555] 3555,81 unequal: No Solution Exploring Operation: 45+79=124, Resulting Numbers: [124] 124,81 unequal: No Solution Exploring Operation: 79-45=34, Resulting Numbers: [34] 34,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[74, 47, 3], Operations: ['45-42=3'] Exploring Operation: 47-3=44, Resulting Numbers: [74, 44] Generated Node #0,2,0: 81:[74, 44] Operation: 47-3=44 Exploring Operation: 74-3=71, Resulting Numbers: [47, 71] Generated Node #0,2,1: 81:[47, 71] Operation: 74-3=71 Exploring Operation: 74+3=77, Resulting Numbers: [47, 77] Generated Node #0,2,2: 81:[47, 77] Operation: 74+3=77 Exploring Operation: 74-47=27, Resulting Numbers: [3, 27] Generated Node #0,2,3: 81:[3, 27] Operation: 74-47=27 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 81:[3, 27], Operations: ['45-42=3', '74-47=27'] Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[74, 42, 47, 45], Operations: [] Exploring Operation: 45-42=3, Resulting Numbers: [74, 47, 3] Generated Node #0,2: 81:[74, 47, 3] Operation: 45-42=3 Moving to Node #0,2 Current State: 81:[74, 47, 3], Operations: ['45-42=3'] Exploring Operation: 74-47=27, Resulting Numbers: [3, 27] Generated Node #0,2,3: 81:[3, 27] Operation: 74-47=27 Moving to Node #0,2,3 Current State: 81:[3, 27], Operations: ['45-42=3', '74-47=27'] Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.960069
hs_4
sum_heuristic
[ 66, 58, 76, 3 ]
81
[ "66-58=8", "76-3=73", "8+73=81" ]
Current State: 81:[66, 58, 76, 3], Operations: [] Exploring Operation: 66-58=8, Resulting Numbers: [76, 3, 8] Generated Node #2: [76, 3, 8] from Operation: 66-58=8 Current State: 81:[76, 3, 8], Operations: ['66-58=8'] Exploring Operation: 76-3=73, Resulting Numbers: [8, 73] Generated Node #3: [8, 73] from Operation: 76-3=73 Current State: 81:[8, 73], Operations: ['66-58=8', '76-3=73'] Exploring Operation: 8+73=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[66, 58, 76, 3], Operations: [] Exploring Operation: 76-58=18, Resulting Numbers: [66, 3, 18] Generated Node #0,0: 81:[66, 3, 18] Operation: 76-58=18 Exploring Operation: 66/3=22, Resulting Numbers: [58, 76, 22] Generated Node #0,1: 81:[58, 76, 22] Operation: 66/3=22 Exploring Operation: 76-66=10, Resulting Numbers: [58, 3, 10] Generated Node #0,2: 81:[58, 3, 10] Operation: 76-66=10 Exploring Operation: 66-58=8, Resulting Numbers: [76, 3, 8] Generated Node #0,3: 81:[76, 3, 8] Operation: 66-58=8 Moving to Node #0,3 Current State: 81:[76, 3, 8], Operations: ['66-58=8'] Exploring Operation: 3+8=11, Resulting Numbers: [76, 11] Generated Node #0,3,0: 81:[76, 11] Operation: 3+8=11 Exploring Operation: 76+3=79, Resulting Numbers: [8, 79] Generated Node #0,3,1: 81:[8, 79] Operation: 76+3=79 Exploring Operation: 76+8=84, Resulting Numbers: [3, 84] Generated Node #0,3,2: 81:[3, 84] Operation: 76+8=84 Exploring Operation: 8-3=5, Resulting Numbers: [76, 5] Generated Node #0,3,3: 81:[76, 5] Operation: 8-3=5 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 81:[8, 79], Operations: ['66-58=8', '76+3=79'] Exploring Operation: 79-8=71, Resulting Numbers: [71] 71,81 unequal: No Solution Exploring Operation: 8+79=87, Resulting Numbers: [87] 87,81 unequal: No Solution Exploring Operation: 8*79=632, Resulting Numbers: [632] 632,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 81:[3, 84], Operations: ['66-58=8', '76+8=84'] Exploring Operation: 3*84=252, Resulting Numbers: [252] 252,81 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,81 unequal: No Solution Exploring Operation: 3+84=87, Resulting Numbers: [87] 87,81 unequal: No Solution Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[66, 58, 76, 3], Operations: [] Exploring Operation: 66-58=8, Resulting Numbers: [76, 3, 8] Generated Node #0,3: 81:[76, 3, 8] Operation: 66-58=8 Moving to Node #0,3 Current State: 81:[76, 3, 8], Operations: ['66-58=8'] Exploring Operation: 76+8=84, Resulting Numbers: [3, 84] Generated Node #0,3,2: 81:[3, 84] Operation: 76+8=84 Moving to Node #0,3,2 Current State: 81:[3, 84], Operations: ['66-58=8', '76+8=84'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 63, 12, 60, 82 ]
91
[ "63-12=51", "60+82=142", "142-51=91" ]
Current State: 91:[63, 12, 60, 82], Operations: [] Exploring Operation: 63-12=51, Resulting Numbers: [60, 82, 51] Generated Node #2: [60, 82, 51] from Operation: 63-12=51 Current State: 91:[60, 82, 51], Operations: ['63-12=51'] Exploring Operation: 60+82=142, Resulting Numbers: [51, 142] Generated Node #3: [51, 142] from Operation: 60+82=142 Current State: 91:[51, 142], Operations: ['63-12=51', '60+82=142'] Exploring Operation: 142-51=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[63, 12, 60, 82], Operations: [] Exploring Operation: 63-60=3, Resulting Numbers: [12, 82, 3] Generated Node #0,0: 91:[12, 82, 3] Operation: 63-60=3 Exploring Operation: 82-63=19, Resulting Numbers: [12, 60, 19] Generated Node #0,1: 91:[12, 60, 19] Operation: 82-63=19 Moving to Node #0,0 Current State: 91:[12, 82, 3], Operations: ['63-60=3'] Exploring Operation: 12+82=94, Resulting Numbers: [3, 94] Generated Node #0,0,0: 91:[3, 94] Operation: 12+82=94 Exploring Operation: 82+3=85, Resulting Numbers: [12, 85] Generated Node #0,0,1: 91:[12, 85] Operation: 82+3=85 Moving to Node #0,1 Current State: 91:[12, 60, 19], Operations: ['82-63=19'] Exploring Operation: 60+19=79, Resulting Numbers: [12, 79] Generated Node #0,1,0: 91:[12, 79] Operation: 60+19=79 Exploring Operation: 60/12=5, Resulting Numbers: [19, 5] Generated Node #0,1,1: 91:[19, 5] Operation: 60/12=5 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 91:[19, 5], Operations: ['82-63=19', '60/12=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,91 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 91:[12, 79], Operations: ['82-63=19', '60+19=79'] Exploring Operation: 79-12=67, Resulting Numbers: [67] 67,91 unequal: No Solution Exploring Operation: 12+79=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[63, 12, 60, 82], Operations: [] Exploring Operation: 82-63=19, Resulting Numbers: [12, 60, 19] Generated Node #0,1: 91:[12, 60, 19] Operation: 82-63=19 Moving to Node #0,1 Current State: 91:[12, 60, 19], Operations: ['82-63=19'] Exploring Operation: 60+19=79, Resulting Numbers: [12, 79] Generated Node #0,1,0: 91:[12, 79] Operation: 60+19=79 Moving to Node #0,1,0 Current State: 91:[12, 79], Operations: ['82-63=19', '60+19=79'] Exploring Operation: 12+79=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_2
mult_heuristic
[ 20, 42, 62, 92 ]
28
[ "20*42=840", "92-62=30", "840/30=28" ]
Current State: 28:[20, 42, 62, 92], Operations: [] Exploring Operation: 20*42=840, Resulting Numbers: [62, 92, 840] Generated Node #2: [62, 92, 840] from Operation: 20*42=840 Current State: 28:[62, 92, 840], Operations: ['20*42=840'] Exploring Operation: 92-62=30, Resulting Numbers: [840, 30] Generated Node #3: [840, 30] from Operation: 92-62=30 Current State: 28:[840, 30], Operations: ['20*42=840', '92-62=30'] Exploring Operation: 840/30=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[20, 42, 62, 92], Operations: [] Exploring Operation: 92-62=30, Resulting Numbers: [20, 42, 30] Generated Node #0,0: 28:[20, 42, 30] Operation: 92-62=30 Moving to Node #0,0 Current State: 28:[20, 42, 30], Operations: ['92-62=30'] Exploring Operation: 42-20=22, Resulting Numbers: [30, 22] Generated Node #0,0,0: 28:[30, 22] Operation: 42-20=22 Moving to Node #0,0,0 Current State: 28:[30, 22], Operations: ['92-62=30', '42-20=22'] Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,28 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 72, 39, 33, 81 ]
64
[ "39+33=72", "72*72=5184", "5184/81=64" ]
Current State: 64:[72, 39, 33, 81], Operations: [] Exploring Operation: 39+33=72, Resulting Numbers: [72, 81, 72] Generated Node #2: [72, 81, 72] from Operation: 39+33=72 Current State: 64:[72, 81, 72], Operations: ['39+33=72'] Exploring Operation: 72*72=5184, Resulting Numbers: [81, 5184] Generated Node #3: [81, 5184] from Operation: 72*72=5184 Current State: 64:[81, 5184], Operations: ['39+33=72', '72*72=5184'] Exploring Operation: 5184/81=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[72, 39, 33, 81], Operations: [] Exploring Operation: 81-72=9, Resulting Numbers: [39, 33, 9] Generated Node #0,0: 64:[39, 33, 9] Operation: 81-72=9 Exploring Operation: 81-39=42, Resulting Numbers: [72, 33, 42] Generated Node #0,1: 64:[72, 33, 42] Operation: 81-39=42 Exploring Operation: 72-39=33, Resulting Numbers: [33, 81, 33] Generated Node #0,2: 64:[33, 81, 33] Operation: 72-39=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[39, 33, 9], Operations: ['81-72=9'] Exploring Operation: 39+33=72, Resulting Numbers: [9, 72] Generated Node #0,0,0: 64:[9, 72] Operation: 39+33=72 Exploring Operation: 39-9=30, Resulting Numbers: [33, 30] Generated Node #0,0,1: 64:[33, 30] Operation: 39-9=30 Exploring Operation: 39-33=6, Resulting Numbers: [9, 6] Generated Node #0,0,2: 64:[9, 6] Operation: 39-33=6 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 64:[33, 30], Operations: ['81-72=9', '39-9=30'] Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,64 unequal: No Solution Exploring Operation: 33*30=990, Resulting Numbers: [990] 990,64 unequal: No Solution Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 64:[9, 6], Operations: ['81-72=9', '39-33=6'] Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,64 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,64 unequal: No Solution Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 64:[9, 72], Operations: ['81-72=9', '39+33=72'] Exploring Operation: 9+72=81, Resulting Numbers: [81] 81,64 unequal: No Solution Exploring Operation: 72/9=8, Resulting Numbers: [8] 8,64 unequal: No Solution Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[72, 33, 42], Operations: ['81-39=42'] Exploring Operation: 42-33=9, Resulting Numbers: [72, 9] Generated Node #0,1,0: 64:[72, 9] Operation: 42-33=9 Exploring Operation: 72-42=30, Resulting Numbers: [33, 30] Generated Node #0,1,1: 64:[33, 30] Operation: 72-42=30 Exploring Operation: 72-33=39, Resulting Numbers: [42, 39] Generated Node #0,1,2: 64:[42, 39] Operation: 72-33=39 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 64:[33, 30], Operations: ['81-39=42', '72-42=30'] Exploring Operation: 33*30=990, Resulting Numbers: [990] 990,64 unequal: No Solution Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,64 unequal: No Solution Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 64:[72, 9], Operations: ['81-39=42', '42-33=9'] Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,64 unequal: No Solution Exploring Operation: 72+9=81, Resulting Numbers: [81] 81,64 unequal: No Solution Exploring Operation: 72/9=8, Resulting Numbers: [8] 8,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 64:[42, 39], Operations: ['81-39=42', '72-33=39'] Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,64 unequal: No Solution Exploring Operation: 42+39=81, Resulting Numbers: [81] 81,64 unequal: No Solution Exploring Operation: 42*39=1638, Resulting Numbers: [1638] 1638,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[33, 81, 33], Operations: ['72-39=33'] Exploring Operation: 81-33=48, Resulting Numbers: [33, 48] Generated Node #0,2,0: 64:[33, 48] Operation: 81-33=48 Exploring Operation: 33/33=1, Resulting Numbers: [81, 1] Generated Node #0,2,1: 64:[81, 1] Operation: 33/33=1 Exploring Operation: 81-33=48, Resulting Numbers: [33, 48] Generated Node #0,2,2: 64:[33, 48] Operation: 81-33=48 Moving to Node #0,2,0 Current State: 64:[33, 48], Operations: ['72-39=33', '81-33=48'] Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,64 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,64 unequal: No Solution Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,64 unequal: No Solution Moving to Node #0,2,2 Current State: 64:[33, 48], Operations: ['72-39=33', '81-33=48'] Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,64 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,64 unequal: No Solution Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,64 unequal: No Solution Moving to Node #0,2,1 Current State: 64:[81, 1], Operations: ['72-39=33', '33/33=1'] Exploring Operation: 81/1=81, Resulting Numbers: [81] 81,64 unequal: No Solution Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,64 unequal: No Solution Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,64 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
[ 79, 50, 40, 75 ]
60
[ "79-75=4", "40/4=10", "50+10=60" ]
Current State: 60:[79, 50, 40, 75], Operations: [] Exploring Operation: 79-75=4, Resulting Numbers: [50, 40, 4] Generated Node #2: [50, 40, 4] from Operation: 79-75=4 Current State: 60:[50, 40, 4], Operations: ['79-75=4'] Exploring Operation: 40/4=10, Resulting Numbers: [50, 10] Generated Node #3: [50, 10] from Operation: 40/4=10 Current State: 60:[50, 10], Operations: ['79-75=4', '40/4=10'] Exploring Operation: 50+10=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[79, 50, 40, 75], Operations: [] Exploring Operation: 79-75=4, Resulting Numbers: [50, 40, 4] Generated Node #0,0: 60:[50, 40, 4] Operation: 79-75=4 Exploring Operation: 79-50=29, Resulting Numbers: [40, 75, 29] Generated Node #0,1: 60:[40, 75, 29] Operation: 79-50=29 Exploring Operation: 50-40=10, Resulting Numbers: [79, 75, 10] Generated Node #0,2: 60:[79, 75, 10] Operation: 50-40=10 Exploring Operation: 79-40=39, Resulting Numbers: [50, 75, 39] Generated Node #0,3: 60:[50, 75, 39] Operation: 79-40=39 Exploring Operation: 75-50=25, Resulting Numbers: [79, 40, 25] Generated Node #0,4: 60:[79, 40, 25] Operation: 75-50=25 Moving to Node #0,0 Current State: 60:[50, 40, 4], Operations: ['79-75=4'] Exploring Operation: 50-4=46, Resulting Numbers: [40, 46] Generated Node #0,0,0: 60:[40, 46] Operation: 50-4=46 Exploring Operation: 40-4=36, Resulting Numbers: [50, 36] Generated Node #0,0,1: 60:[50, 36] Operation: 40-4=36 Exploring Operation: 40/4=10, Resulting Numbers: [50, 10] Generated Node #0,0,2: 60:[50, 10] Operation: 40/4=10 Exploring Operation: 50+4=54, Resulting Numbers: [40, 54] Generated Node #0,0,3: 60:[40, 54] Operation: 50+4=54 Exploring Operation: 50-40=10, Resulting Numbers: [4, 10] Generated Node #0,0,4: 60:[4, 10] Operation: 50-40=10 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 60:[4, 10], Operations: ['79-75=4', '50-40=10'] Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,60 unequal: No Solution Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,60 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[50, 10], Operations: ['79-75=4', '40/4=10'] Exploring Operation: 50+10=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[79, 50, 40, 75], Operations: [] Exploring Operation: 79-75=4, Resulting Numbers: [50, 40, 4] Generated Node #0,0: 60:[50, 40, 4] Operation: 79-75=4 Moving to Node #0,0 Current State: 60:[50, 40, 4], Operations: ['79-75=4'] Exploring Operation: 40/4=10, Resulting Numbers: [50, 10] Generated Node #0,0,2: 60:[50, 10] Operation: 40/4=10 Moving to Node #0,0,2 Current State: 60:[50, 10], Operations: ['79-75=4', '40/4=10'] Exploring Operation: 50+10=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 11, 72, 23, 24 ]
18
[ "23-11=12", "72/12=6", "24-6=18" ]
Current State: 18:[11, 72, 23, 24], Operations: [] Exploring Operation: 23-11=12, Resulting Numbers: [72, 24, 12] Generated Node #2: [72, 24, 12] from Operation: 23-11=12 Current State: 18:[72, 24, 12], Operations: ['23-11=12'] Exploring Operation: 72/12=6, Resulting Numbers: [24, 6] Generated Node #3: [24, 6] from Operation: 72/12=6 Current State: 18:[24, 6], Operations: ['23-11=12', '72/12=6'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[11, 72, 23, 24], Operations: [] Exploring Operation: 72-23=49, Resulting Numbers: [11, 24, 49] Generated Node #0,0: 18:[11, 24, 49] Operation: 72-23=49 Exploring Operation: 72-24=48, Resulting Numbers: [11, 23, 48] Generated Node #0,1: 18:[11, 23, 48] Operation: 72-24=48 Exploring Operation: 72-11=61, Resulting Numbers: [23, 24, 61] Generated Node #0,2: 18:[23, 24, 61] Operation: 72-11=61 Exploring Operation: 72/24=3, Resulting Numbers: [11, 23, 3] Generated Node #0,3: 18:[11, 23, 3] Operation: 72/24=3 Moving to Node #0,3 Current State: 18:[11, 23, 3], Operations: ['72/24=3'] Exploring Operation: 23-11=12, Resulting Numbers: [3, 12] Generated Node #0,3,0: 18:[3, 12] Operation: 23-11=12 Exploring Operation: 23-3=20, Resulting Numbers: [11, 20] Generated Node #0,3,1: 18:[11, 20] Operation: 23-3=20 Exploring Operation: 11-3=8, Resulting Numbers: [23, 8] Generated Node #0,3,2: 18:[23, 8] Operation: 11-3=8 Exploring Operation: 11+3=14, Resulting Numbers: [23, 14] Generated Node #0,3,3: 18:[23, 14] Operation: 11+3=14 Moving to Node #0,1 Current State: 18:[11, 23, 48], Operations: ['72-24=48'] Exploring Operation: 48-23=25, Resulting Numbers: [11, 25] Generated Node #0,1,0: 18:[11, 25] Operation: 48-23=25 Exploring Operation: 11+23=34, Resulting Numbers: [48, 34] Generated Node #0,1,1: 18:[48, 34] Operation: 11+23=34 Exploring Operation: 48-11=37, Resulting Numbers: [23, 37] Generated Node #0,1,2: 18:[23, 37] Operation: 48-11=37 Exploring Operation: 23-11=12, Resulting Numbers: [48, 12] Generated Node #0,1,3: 18:[48, 12] Operation: 23-11=12 Moving to Node #0,0 Current State: 18:[11, 24, 49], Operations: ['72-23=49'] Exploring Operation: 24-11=13, Resulting Numbers: [49, 13] Generated Node #0,0,0: 18:[49, 13] Operation: 24-11=13 Exploring Operation: 11+24=35, Resulting Numbers: [49, 35] Generated Node #0,0,1: 18:[49, 35] Operation: 11+24=35 Exploring Operation: 49-11=38, Resulting Numbers: [24, 38] Generated Node #0,0,2: 18:[24, 38] Operation: 49-11=38 Exploring Operation: 49-24=25, Resulting Numbers: [11, 25] Generated Node #0,0,3: 18:[11, 25] Operation: 49-24=25 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 18:[11, 25], Operations: ['72-23=49', '49-24=25'] Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 11*25=275, Resulting Numbers: [275] 275,18 unequal: No Solution Exploring Operation: 11+25=36, Resulting Numbers: [36] 36,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[24, 38], Operations: ['72-23=49', '49-11=38'] Exploring Operation: 24*38=912, Resulting Numbers: [912] 912,18 unequal: No Solution Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 24+38=62, Resulting Numbers: [62] 62,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[49, 13], Operations: ['72-23=49', '24-11=13'] Exploring Operation: 49+13=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 49*13=637, Resulting Numbers: [637] 637,18 unequal: No Solution Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[49, 35], Operations: ['72-23=49', '11+24=35'] Exploring Operation: 49*35=1715, Resulting Numbers: [1715] 1715,18 unequal: No Solution Exploring Operation: 49+35=84, Resulting Numbers: [84] 84,18 unequal: No Solution Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 18:[23, 24, 61], Operations: ['72-11=61'] Exploring Operation: 24-23=1, Resulting Numbers: [61, 1] Generated Node #0,2,0: 18:[61, 1] Operation: 24-23=1 Exploring Operation: 61-24=37, Resulting Numbers: [23, 37] Generated Node #0,2,1: 18:[23, 37] Operation: 61-24=37 Exploring Operation: 61-23=38, Resulting Numbers: [24, 38] Generated Node #0,2,2: 18:[24, 38] Operation: 61-23=38 Exploring Operation: 23+24=47, Resulting Numbers: [61, 47] Generated Node #0,2,3: 18:[61, 47] Operation: 23+24=47 Moving to Node #0,3,0 Current State: 18:[3, 12], Operations: ['72/24=3', '23-11=12'] Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,18 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,18 unequal: No Solution Moving to Node #0,3,1 Current State: 18:[11, 20], Operations: ['72/24=3', '23-3=20'] Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 11+20=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 11*20=220, Resulting Numbers: [220] 220,18 unequal: No Solution Moving to Node #0,3,2 Current State: 18:[23, 8], Operations: ['72/24=3', '11-3=8'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,18 unequal: No Solution Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,18 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[11, 25], Operations: ['72-24=48', '48-23=25'] Exploring Operation: 11+25=36, Resulting Numbers: [36] 36,18 unequal: No Solution Exploring Operation: 11*25=275, Resulting Numbers: [275] 275,18 unequal: No Solution Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,18 unequal: No Solution Moving to Node #0,3,3 Current State: 18:[23, 14], Operations: ['72/24=3', '11+3=14'] Exploring Operation: 23+14=37, Resulting Numbers: [37] 37,18 unequal: No Solution Exploring Operation: 23*14=322, Resulting Numbers: [322] 322,18 unequal: No Solution Exploring Operation: 23-14=9, Resulting Numbers: [9] 9,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[23, 37], Operations: ['72-24=48', '48-11=37'] Exploring Operation: 23+37=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 23*37=851, Resulting Numbers: [851] 851,18 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,18 unequal: No Solution Moving to Node #0,2,1 Current State: 18:[23, 37], Operations: ['72-11=61', '61-24=37'] Exploring Operation: 23*37=851, Resulting Numbers: [851] 851,18 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 23+37=60, Resulting Numbers: [60] 60,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[24, 38], Operations: ['72-11=61', '61-23=38'] Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 24+38=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 24*38=912, Resulting Numbers: [912] 912,18 unequal: No Solution Moving to Node #0,1,3 Current State: 18:[48, 12], Operations: ['72-24=48', '23-11=12'] Exploring Operation: 48*12=576, Resulting Numbers: [576] 576,18 unequal: No Solution Exploring Operation: 48-12=36, Resulting Numbers: [36] 36,18 unequal: No Solution Exploring Operation: 48+12=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[61, 1], Operations: ['72-11=61', '24-23=1'] Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 61*1=61, Resulting Numbers: [61] 61,18 unequal: No Solution Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,18 unequal: No Solution Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[48, 34], Operations: ['72-24=48', '11+23=34'] Exploring Operation: 48+34=82, Resulting Numbers: [82] 82,18 unequal: No Solution Exploring Operation: 48*34=1632, Resulting Numbers: [1632] 1632,18 unequal: No Solution Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,18 unequal: No Solution Moving to Node #0,2,3 Current State: 18:[61, 47], Operations: ['72-11=61', '23+24=47'] Exploring Operation: 61-47=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 61+47=108, Resulting Numbers: [108] 108,18 unequal: No Solution Exploring Operation: 61*47=2867, Resulting Numbers: [2867] 2867,18 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 93, 85, 37, 14 ]
15
[ "93-85=8", "37-14=23", "23-8=15" ]
Current State: 15:[93, 85, 37, 14], Operations: [] Exploring Operation: 93-85=8, Resulting Numbers: [37, 14, 8] Generated Node #2: [37, 14, 8] from Operation: 93-85=8 Current State: 15:[37, 14, 8], Operations: ['93-85=8'] Exploring Operation: 37-14=23, Resulting Numbers: [8, 23] Generated Node #3: [8, 23] from Operation: 37-14=23 Current State: 15:[8, 23], Operations: ['93-85=8', '37-14=23'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[93, 85, 37, 14], Operations: [] Exploring Operation: 93-37=56, Resulting Numbers: [85, 14, 56] Generated Node #0,0: 15:[85, 14, 56] Operation: 93-37=56 Exploring Operation: 85-37=48, Resulting Numbers: [93, 14, 48] Generated Node #0,1: 15:[93, 14, 48] Operation: 85-37=48 Exploring Operation: 93-85=8, Resulting Numbers: [37, 14, 8] Generated Node #0,2: 15:[37, 14, 8] Operation: 93-85=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 15:[37, 14, 8], Operations: ['93-85=8'] Exploring Operation: 37-8=29, Resulting Numbers: [14, 29] Generated Node #0,2,0: 15:[14, 29] Operation: 37-8=29 Exploring Operation: 14-8=6, Resulting Numbers: [37, 6] Generated Node #0,2,1: 15:[37, 6] Operation: 14-8=6 Exploring Operation: 37-14=23, Resulting Numbers: [8, 23] Generated Node #0,2,2: 15:[8, 23] Operation: 37-14=23 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 15:[8, 23], Operations: ['93-85=8', '37-14=23'] Exploring Operation: 8*23=184, Resulting Numbers: [184] 184,15 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[93, 85, 37, 14], Operations: [] Exploring Operation: 93-85=8, Resulting Numbers: [37, 14, 8] Generated Node #0,2: 15:[37, 14, 8] Operation: 93-85=8 Moving to Node #0,2 Current State: 15:[37, 14, 8], Operations: ['93-85=8'] Exploring Operation: 37-14=23, Resulting Numbers: [8, 23] Generated Node #0,2,2: 15:[8, 23] Operation: 37-14=23 Moving to Node #0,2,2 Current State: 15:[8, 23], Operations: ['93-85=8', '37-14=23'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 18, 88, 64, 89 ]
45
[ "88-18=70", "89-64=25", "70-25=45" ]
Current State: 45:[18, 88, 64, 89], Operations: [] Exploring Operation: 88-18=70, Resulting Numbers: [64, 89, 70] Generated Node #2: [64, 89, 70] from Operation: 88-18=70 Current State: 45:[64, 89, 70], Operations: ['88-18=70'] Exploring Operation: 89-64=25, Resulting Numbers: [70, 25] Generated Node #3: [70, 25] from Operation: 89-64=25 Current State: 45:[70, 25], Operations: ['88-18=70', '89-64=25'] Exploring Operation: 70-25=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[18, 88, 64, 89], Operations: [] Exploring Operation: 89-88=1, Resulting Numbers: [18, 64, 1] Generated Node #0,0: 45:[18, 64, 1] Operation: 89-88=1 Exploring Operation: 88-64=24, Resulting Numbers: [18, 89, 24] Generated Node #0,1: 45:[18, 89, 24] Operation: 88-64=24 Exploring Operation: 89-64=25, Resulting Numbers: [18, 88, 25] Generated Node #0,2: 45:[18, 88, 25] Operation: 89-64=25 Moving to Node #0,0 Current State: 45:[18, 64, 1], Operations: ['89-88=1'] Exploring Operation: 18-1=17, Resulting Numbers: [64, 17] Generated Node #0,0,0: 45:[64, 17] Operation: 18-1=17 Exploring Operation: 64-1=63, Resulting Numbers: [18, 63] Generated Node #0,0,1: 45:[18, 63] Operation: 64-1=63 Exploring Operation: 64-18=46, Resulting Numbers: [1, 46] Generated Node #0,0,2: 45:[1, 46] Operation: 64-18=46 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 45:[1, 46], Operations: ['89-88=1', '64-18=46'] Exploring Operation: 1*46=46, Resulting Numbers: [46] 46,45 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[18, 88, 64, 89], Operations: [] Exploring Operation: 89-88=1, Resulting Numbers: [18, 64, 1] Generated Node #0,0: 45:[18, 64, 1] Operation: 89-88=1 Moving to Node #0,0 Current State: 45:[18, 64, 1], Operations: ['89-88=1'] Exploring Operation: 64-18=46, Resulting Numbers: [1, 46] Generated Node #0,0,2: 45:[1, 46] Operation: 64-18=46 Moving to Node #0,0,2 Current State: 45:[1, 46], Operations: ['89-88=1', '64-18=46'] Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 60, 81, 65, 3 ]
83
[ "81-60=21", "65-3=62", "21+62=83" ]
Current State: 83:[60, 81, 65, 3], Operations: [] Exploring Operation: 81-60=21, Resulting Numbers: [65, 3, 21] Generated Node #2: [65, 3, 21] from Operation: 81-60=21 Current State: 83:[65, 3, 21], Operations: ['81-60=21'] Exploring Operation: 65-3=62, Resulting Numbers: [21, 62] Generated Node #3: [21, 62] from Operation: 65-3=62 Current State: 83:[21, 62], Operations: ['81-60=21', '65-3=62'] Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[60, 81, 65, 3], Operations: [] Exploring Operation: 60+3=63, Resulting Numbers: [81, 65, 63] Generated Node #0,0: 83:[81, 65, 63] Operation: 60+3=63 Moving to Node #0,0 Current State: 83:[81, 65, 63], Operations: ['60+3=63'] Exploring Operation: 65+63=128, Resulting Numbers: [81, 128] Generated Node #0,0,0: 83:[81, 128] Operation: 65+63=128 Moving to Node #0,0,0 Current State: 83:[81, 128], Operations: ['60+3=63', '65+63=128'] Exploring Operation: 128-81=47, Resulting Numbers: [47] 47,83 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 53, 83, 17, 60 ]
73
[ "83-53=30", "60-17=43", "30+43=73" ]
Current State: 73:[53, 83, 17, 60], Operations: [] Exploring Operation: 83-53=30, Resulting Numbers: [17, 60, 30] Generated Node #2: [17, 60, 30] from Operation: 83-53=30 Current State: 73:[17, 60, 30], Operations: ['83-53=30'] Exploring Operation: 60-17=43, Resulting Numbers: [30, 43] Generated Node #3: [30, 43] from Operation: 60-17=43 Current State: 73:[30, 43], Operations: ['83-53=30', '60-17=43'] Exploring Operation: 30+43=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[53, 83, 17, 60], Operations: [] Exploring Operation: 53+17=70, Resulting Numbers: [83, 60, 70] Generated Node #0,0: 73:[83, 60, 70] Operation: 53+17=70 Exploring Operation: 17+60=77, Resulting Numbers: [53, 83, 77] Generated Node #0,1: 73:[53, 83, 77] Operation: 17+60=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[83, 60, 70], Operations: ['53+17=70'] Exploring Operation: 60+70=130, Resulting Numbers: [83, 130] Generated Node #0,0,0: 73:[83, 130] Operation: 60+70=130 Exploring Operation: 83-60=23, Resulting Numbers: [70, 23] Generated Node #0,0,1: 73:[70, 23] Operation: 83-60=23 Moving to Node #0,0,1 Current State: 73:[70, 23], Operations: ['53+17=70', '83-60=23'] Exploring Operation: 70-23=47, Resulting Numbers: [47] 47,73 unequal: No Solution Exploring Operation: 70+23=93, Resulting Numbers: [93] 93,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[83, 130], Operations: ['53+17=70', '60+70=130'] Exploring Operation: 130-83=47, Resulting Numbers: [47] 47,73 unequal: No Solution Exploring Operation: 83+130=213, Resulting Numbers: [213] 213,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[53, 83, 77], Operations: ['17+60=77'] Exploring Operation: 77-53=24, Resulting Numbers: [83, 24] Generated Node #0,1,0: 73:[83, 24] Operation: 77-53=24 Exploring Operation: 83-53=30, Resulting Numbers: [77, 30] Generated Node #0,1,1: 73:[77, 30] Operation: 83-53=30 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[77, 30], Operations: ['17+60=77', '83-53=30'] Exploring Operation: 77-30=47, Resulting Numbers: [47] 47,73 unequal: No Solution Exploring Operation: 77+30=107, Resulting Numbers: [107] 107,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[83, 24], Operations: ['17+60=77', '77-53=24'] Exploring Operation: 83-24=59, Resulting Numbers: [59] 59,73 unequal: No Solution Exploring Operation: 83+24=107, Resulting Numbers: [107] 107,73 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, 6, 91, 8 ]
29
[ "2*91=182", "182-8=174", "174/6=29" ]
Current State: 29:[2, 6, 91, 8], Operations: [] Exploring Operation: 2*91=182, Resulting Numbers: [6, 8, 182] Generated Node #2: [6, 8, 182] from Operation: 2*91=182 Current State: 29:[6, 8, 182], Operations: ['2*91=182'] Exploring Operation: 182-8=174, Resulting Numbers: [6, 174] Generated Node #3: [6, 174] from Operation: 182-8=174 Current State: 29:[6, 174], Operations: ['2*91=182', '182-8=174'] Exploring Operation: 174/6=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[2, 6, 91, 8], Operations: [] Exploring Operation: 2+6=8, Resulting Numbers: [91, 8, 8] Generated Node #0,0: 29:[91, 8, 8] Operation: 2+6=8 Exploring Operation: 2*6=12, Resulting Numbers: [91, 8, 12] Generated Node #0,1: 29:[91, 8, 12] Operation: 2*6=12 Exploring Operation: 2*8=16, Resulting Numbers: [6, 91, 16] Generated Node #0,2: 29:[6, 91, 16] Operation: 2*8=16 Exploring Operation: 91-2=89, Resulting Numbers: [6, 8, 89] Generated Node #0,3: 29:[6, 8, 89] Operation: 91-2=89 Moving to Node #0,2 Current State: 29:[6, 91, 16], Operations: ['2*8=16'] Exploring Operation: 6+16=22, Resulting Numbers: [91, 22] Generated Node #0,2,0: 29:[91, 22] Operation: 6+16=22 Exploring Operation: 91-6=85, Resulting Numbers: [16, 85] Generated Node #0,2,1: 29:[16, 85] Operation: 91-6=85 Exploring Operation: 91-16=75, Resulting Numbers: [6, 75] Generated Node #0,2,2: 29:[6, 75] Operation: 91-16=75 Exploring Operation: 6+91=97, Resulting Numbers: [16, 97] Generated Node #0,2,3: 29:[16, 97] Operation: 6+91=97 Moving to Node #0,1 Current State: 29:[91, 8, 12], Operations: ['2*6=12'] Exploring Operation: 91+8=99, Resulting Numbers: [12, 99] Generated Node #0,1,0: 29:[12, 99] Operation: 91+8=99 Exploring Operation: 91-12=79, Resulting Numbers: [8, 79] Generated Node #0,1,1: 29:[8, 79] Operation: 91-12=79 Exploring Operation: 8+12=20, Resulting Numbers: [91, 20] Generated Node #0,1,2: 29:[91, 20] Operation: 8+12=20 Exploring Operation: 91-8=83, Resulting Numbers: [12, 83] Generated Node #0,1,3: 29:[12, 83] Operation: 91-8=83 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 29:[8, 79], Operations: ['2*6=12', '91-12=79'] Exploring Operation: 8+79=87, Resulting Numbers: [87] 87,29 unequal: No Solution Exploring Operation: 79-8=71, Resulting Numbers: [71] 71,29 unequal: No Solution Exploring Operation: 8*79=632, Resulting Numbers: [632] 632,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 29:[91, 20], Operations: ['2*6=12', '8+12=20'] Exploring Operation: 91+20=111, Resulting Numbers: [111] 111,29 unequal: No Solution Exploring Operation: 91-20=71, Resulting Numbers: [71] 71,29 unequal: No Solution Exploring Operation: 91*20=1820, Resulting Numbers: [1820] 1820,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 29:[12, 83], Operations: ['2*6=12', '91-8=83'] Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,29 unequal: No Solution Exploring Operation: 12+83=95, Resulting Numbers: [95] 95,29 unequal: No Solution Exploring Operation: 12*83=996, Resulting Numbers: [996] 996,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 29:[12, 99], Operations: ['2*6=12', '91+8=99'] Exploring Operation: 12*99=1188, Resulting Numbers: [1188] 1188,29 unequal: No Solution Exploring Operation: 12+99=111, Resulting Numbers: [111] 111,29 unequal: No Solution Exploring Operation: 99-12=87, Resulting Numbers: [87] 87,29 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: 29:[6, 8, 89], Operations: ['91-2=89'] Exploring Operation: 6+8=14, Resulting Numbers: [89, 14] Generated Node #0,3,0: 29:[89, 14] Operation: 6+8=14 Exploring Operation: 6*8=48, Resulting Numbers: [89, 48] Generated Node #0,3,1: 29:[89, 48] Operation: 6*8=48 Exploring Operation: 89-8=81, Resulting Numbers: [6, 81] Generated Node #0,3,2: 29:[6, 81] Operation: 89-8=81 Exploring Operation: 89-6=83, Resulting Numbers: [8, 83] Generated Node #0,3,3: 29:[8, 83] Operation: 89-6=83 Moving to Node #0,0 Current State: 29:[91, 8, 8], Operations: ['2+6=8'] Exploring Operation: 8/8=1, Resulting Numbers: [91, 1] Generated Node #0,0,0: 29:[91, 1] Operation: 8/8=1 Exploring Operation: 8+8=16, Resulting Numbers: [91, 16] Generated Node #0,0,1: 29:[91, 16] Operation: 8+8=16 Exploring Operation: 91-8=83, Resulting Numbers: [8, 83] Generated Node #0,0,2: 29:[8, 83] Operation: 91-8=83 Exploring Operation: 91-8=83, Resulting Numbers: [8, 83] Generated Node #0,0,3: 29:[8, 83] Operation: 91-8=83 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 29:[91, 16], Operations: ['2+6=8', '8+8=16'] Exploring Operation: 91-16=75, Resulting Numbers: [75] 75,29 unequal: No Solution Exploring Operation: 91*16=1456, Resulting Numbers: [1456] 1456,29 unequal: No Solution Exploring Operation: 91+16=107, Resulting Numbers: [107] 107,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 29:[8, 83], Operations: ['2+6=8', '91-8=83'] Exploring Operation: 8*83=664, Resulting Numbers: [664] 664,29 unequal: No Solution Exploring Operation: 8+83=91, Resulting Numbers: [91] 91,29 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 29:[8, 83], Operations: ['2+6=8', '91-8=83'] Exploring Operation: 8*83=664, Resulting Numbers: [664] 664,29 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,29 unequal: No Solution Exploring Operation: 8+83=91, Resulting Numbers: [91] 91,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[91, 1], Operations: ['2+6=8', '8/8=1'] Exploring Operation: 91+1=92, Resulting Numbers: [92] 92,29 unequal: No Solution Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,29 unequal: No Solution Exploring Operation: 91/1=91, Resulting Numbers: [91] 91,29 unequal: No Solution Exploring Operation: 91*1=91, Resulting Numbers: [91] 91,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 29:[91, 22], Operations: ['2*8=16', '6+16=22'] Exploring Operation: 91*22=2002, Resulting Numbers: [2002] 2002,29 unequal: No Solution Exploring Operation: 91-22=69, Resulting Numbers: [69] 69,29 unequal: No Solution Exploring Operation: 91+22=113, Resulting Numbers: [113] 113,29 unequal: No Solution Moving to Node #0,2,2 Current State: 29:[6, 75], Operations: ['2*8=16', '91-16=75'] Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,29 unequal: No Solution Exploring Operation: 6+75=81, Resulting Numbers: [81] 81,29 unequal: No Solution Exploring Operation: 6*75=450, Resulting Numbers: [450] 450,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[16, 85], Operations: ['2*8=16', '91-6=85'] Exploring Operation: 85-16=69, Resulting Numbers: [69] 69,29 unequal: No Solution Exploring Operation: 16*85=1360, Resulting Numbers: [1360] 1360,29 unequal: No Solution Exploring Operation: 16+85=101, Resulting Numbers: [101] 101,29 unequal: No Solution Moving to Node #0,3,3 Current State: 29:[8, 83], Operations: ['91-2=89', '89-6=83'] Exploring Operation: 8+83=91, Resulting Numbers: [91] 91,29 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,29 unequal: No Solution Exploring Operation: 8*83=664, Resulting Numbers: [664] 664,29 unequal: No Solution Moving to Node #0,3,2 Current State: 29:[6, 81], Operations: ['91-2=89', '89-8=81'] Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,29 unequal: No Solution Exploring Operation: 6*81=486, Resulting Numbers: [486] 486,29 unequal: No Solution Exploring Operation: 6+81=87, Resulting Numbers: [87] 87,29 unequal: No Solution Moving to Node #0,3,0 Current State: 29:[89, 14], Operations: ['91-2=89', '6+8=14'] Exploring Operation: 89*14=1246, Resulting Numbers: [1246] 1246,29 unequal: No Solution Exploring Operation: 89-14=75, Resulting Numbers: [75] 75,29 unequal: No Solution Exploring Operation: 89+14=103, Resulting Numbers: [103] 103,29 unequal: No Solution Moving to Node #0,3,1 Current State: 29:[89, 48], Operations: ['91-2=89', '6*8=48'] Exploring Operation: 89-48=41, Resulting Numbers: [41] 41,29 unequal: No Solution Exploring Operation: 89*48=4272, Resulting Numbers: [4272] 4272,29 unequal: No Solution Exploring Operation: 89+48=137, Resulting Numbers: [137] 137,29 unequal: No Solution Moving to Node #0,2,3 Current State: 29:[16, 97], Operations: ['2*8=16', '6+91=97'] Exploring Operation: 97-16=81, Resulting Numbers: [81] 81,29 unequal: No Solution Exploring Operation: 16+97=113, Resulting Numbers: [113] 113,29 unequal: No Solution Exploring Operation: 16*97=1552, Resulting Numbers: [1552] 1552,29 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 34, 81, 74, 80 ]
79
[ "74-34=40", "80/40=2", "81-2=79" ]
Current State: 79:[34, 81, 74, 80], Operations: [] Exploring Operation: 74-34=40, Resulting Numbers: [81, 80, 40] Generated Node #2: [81, 80, 40] from Operation: 74-34=40 Current State: 79:[81, 80, 40], Operations: ['74-34=40'] Exploring Operation: 80/40=2, Resulting Numbers: [81, 2] Generated Node #3: [81, 2] from Operation: 80/40=2 Current State: 79:[81, 2], Operations: ['74-34=40', '80/40=2'] Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[34, 81, 74, 80], Operations: [] Exploring Operation: 34+74=108, Resulting Numbers: [81, 80, 108] Generated Node #0,0: 79:[81, 80, 108] Operation: 34+74=108 Exploring Operation: 81-34=47, Resulting Numbers: [74, 80, 47] Generated Node #0,1: 79:[74, 80, 47] Operation: 81-34=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[81, 80, 108], Operations: ['34+74=108'] Exploring Operation: 108-80=28, Resulting Numbers: [81, 28] Generated Node #0,0,0: 79:[81, 28] Operation: 108-80=28 Exploring Operation: 108-81=27, Resulting Numbers: [80, 27] Generated Node #0,0,1: 79:[80, 27] Operation: 108-81=27 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[81, 28], Operations: ['34+74=108', '108-80=28'] Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,79 unequal: No Solution Exploring Operation: 81+28=109, Resulting Numbers: [109] 109,79 unequal: No Solution No 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: 79:[80, 27], Operations: ['34+74=108', '108-81=27'] Exploring Operation: 80-27=53, Resulting Numbers: [53] 53,79 unequal: No Solution Exploring Operation: 80+27=107, Resulting Numbers: [107] 107,79 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[74, 80, 47], Operations: ['81-34=47'] Exploring Operation: 80-47=33, Resulting Numbers: [74, 33] Generated Node #0,1,0: 79:[74, 33] Operation: 80-47=33 Exploring Operation: 74+47=121, Resulting Numbers: [80, 121] Generated Node #0,1,1: 79:[80, 121] Operation: 74+47=121 Moving to Node #0,1,1 Current State: 79:[80, 121], Operations: ['81-34=47', '74+47=121'] Exploring Operation: 80+121=201, Resulting Numbers: [201] 201,79 unequal: No Solution Exploring Operation: 121-80=41, Resulting Numbers: [41] 41,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[74, 33], Operations: ['81-34=47', '80-47=33'] Exploring Operation: 74+33=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 74-33=41, Resulting Numbers: [41] 41,79 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
[ 36, 79, 24, 27 ]
97
[ "24*27=648", "648/36=18", "79+18=97" ]
Current State: 97:[36, 79, 24, 27], Operations: [] Exploring Operation: 24*27=648, Resulting Numbers: [36, 79, 648] Generated Node #2: [36, 79, 648] from Operation: 24*27=648 Current State: 97:[36, 79, 648], Operations: ['24*27=648'] Exploring Operation: 648/36=18, Resulting Numbers: [79, 18] Generated Node #3: [79, 18] from Operation: 648/36=18 Current State: 97:[79, 18], Operations: ['24*27=648', '648/36=18'] Exploring Operation: 79+18=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[36, 79, 24, 27], Operations: [] Exploring Operation: 24+27=51, Resulting Numbers: [36, 79, 51] Generated Node #0,0: 97:[36, 79, 51] Operation: 24+27=51 Exploring Operation: 36+24=60, Resulting Numbers: [79, 27, 60] Generated Node #0,1: 97:[79, 27, 60] Operation: 36+24=60 Exploring Operation: 79+24=103, Resulting Numbers: [36, 27, 103] Generated Node #0,2: 97:[36, 27, 103] Operation: 79+24=103 Exploring Operation: 36+27=63, Resulting Numbers: [79, 24, 63] Generated Node #0,3: 97:[79, 24, 63] Operation: 36+27=63 Exploring Operation: 79+27=106, Resulting Numbers: [36, 24, 106] Generated Node #0,4: 97:[36, 24, 106] Operation: 79+27=106 Moving to Node #0,0 Current State: 97:[36, 79, 51], Operations: ['24+27=51'] Exploring Operation: 79+51=130, Resulting Numbers: [36, 130] Generated Node #0,0,0: 97:[36, 130] Operation: 79+51=130 Exploring Operation: 51-36=15, Resulting Numbers: [79, 15] Generated Node #0,0,1: 97:[79, 15] Operation: 51-36=15 Exploring Operation: 79-36=43, Resulting Numbers: [51, 43] Generated Node #0,0,2: 97:[51, 43] Operation: 79-36=43 Exploring Operation: 36+51=87, Resulting Numbers: [79, 87] Generated Node #0,0,3: 97:[79, 87] Operation: 36+51=87 Exploring Operation: 36+79=115, Resulting Numbers: [51, 115] Generated Node #0,0,4: 97:[51, 115] Operation: 36+79=115 Moving to Node #0,3 Current State: 97:[79, 24, 63], Operations: ['36+27=63'] Exploring Operation: 79-24=55, Resulting Numbers: [63, 55] Generated Node #0,3,0: 97:[63, 55] Operation: 79-24=55 Exploring Operation: 63-24=39, Resulting Numbers: [79, 39] Generated Node #0,3,1: 97:[79, 39] Operation: 63-24=39 Exploring Operation: 24+63=87, Resulting Numbers: [79, 87] Generated Node #0,3,2: 97:[79, 87] Operation: 24+63=87 Exploring Operation: 79+63=142, Resulting Numbers: [24, 142] Generated Node #0,3,3: 97:[24, 142] Operation: 79+63=142 Exploring Operation: 79+24=103, Resulting Numbers: [63, 103] Generated Node #0,3,4: 97:[63, 103] Operation: 79+24=103 Moving to Node #0,1 Current State: 97:[79, 27, 60], Operations: ['36+24=60'] Exploring Operation: 79+27=106, Resulting Numbers: [60, 106] Generated Node #0,1,0: 97:[60, 106] Operation: 79+27=106 Exploring Operation: 79-27=52, Resulting Numbers: [60, 52] Generated Node #0,1,1: 97:[60, 52] Operation: 79-27=52 Exploring Operation: 79+60=139, Resulting Numbers: [27, 139] Generated Node #0,1,2: 97:[27, 139] Operation: 79+60=139 Exploring Operation: 27+60=87, Resulting Numbers: [79, 87] Generated Node #0,1,3: 97:[79, 87] Operation: 27+60=87 Exploring Operation: 60-27=33, Resulting Numbers: [79, 33] Generated Node #0,1,4: 97:[79, 33] Operation: 60-27=33 Moving to Node #0,2 Current State: 97:[36, 27, 103], Operations: ['79+24=103'] Exploring Operation: 103-36=67, Resulting Numbers: [27, 67] Generated Node #0,2,0: 97:[27, 67] Operation: 103-36=67 Exploring Operation: 103-27=76, Resulting Numbers: [36, 76] Generated Node #0,2,1: 97:[36, 76] Operation: 103-27=76 Exploring Operation: 27+103=130, Resulting Numbers: [36, 130] Generated Node #0,2,2: 97:[36, 130] Operation: 27+103=130 Exploring Operation: 36-27=9, Resulting Numbers: [103, 9] Generated Node #0,2,3: 97:[103, 9] Operation: 36-27=9 Exploring Operation: 36+27=63, Resulting Numbers: [103, 63] Generated Node #0,2,4: 97:[103, 63] Operation: 36+27=63 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 97:[103, 63], Operations: ['79+24=103', '36+27=63'] Exploring Operation: 103*63=6489, Resulting Numbers: [6489] 6489,97 unequal: No Solution Exploring Operation: 103-63=40, Resulting Numbers: [40] 40,97 unequal: No Solution Exploring Operation: 103+63=166, Resulting Numbers: [166] 166,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[36, 76], Operations: ['79+24=103', '103-27=76'] Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,97 unequal: No Solution Exploring Operation: 36+76=112, Resulting Numbers: [112] 112,97 unequal: No Solution Exploring Operation: 36*76=2736, Resulting Numbers: [2736] 2736,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 97:[36, 130], Operations: ['79+24=103', '27+103=130'] Exploring Operation: 130-36=94, Resulting Numbers: [94] 94,97 unequal: No Solution Exploring Operation: 36+130=166, Resulting Numbers: [166] 166,97 unequal: No Solution Exploring Operation: 36*130=4680, Resulting Numbers: [4680] 4680,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 97:[103, 9], Operations: ['79+24=103', '36-27=9'] Exploring Operation: 103*9=927, Resulting Numbers: [927] 927,97 unequal: No Solution Exploring Operation: 103-9=94, Resulting Numbers: [94] 94,97 unequal: No Solution Exploring Operation: 103+9=112, Resulting Numbers: [112] 112,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[27, 67], Operations: ['79+24=103', '103-36=67'] Exploring Operation: 67-27=40, Resulting Numbers: [40] 40,97 unequal: No Solution Exploring Operation: 27*67=1809, Resulting Numbers: [1809] 1809,97 unequal: No Solution Exploring Operation: 27+67=94, Resulting Numbers: [94] 94,97 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: 97:[36, 24, 106], Operations: ['79+27=106'] Exploring Operation: 24+106=130, Resulting Numbers: [36, 130] Generated Node #0,4,0: 97:[36, 130] Operation: 24+106=130 Exploring Operation: 36-24=12, Resulting Numbers: [106, 12] Generated Node #0,4,1: 97:[106, 12] Operation: 36-24=12 Exploring Operation: 36+24=60, Resulting Numbers: [106, 60] Generated Node #0,4,2: 97:[106, 60] Operation: 36+24=60 Exploring Operation: 106-24=82, Resulting Numbers: [36, 82] Generated Node #0,4,3: 97:[36, 82] Operation: 106-24=82 Exploring Operation: 106-36=70, Resulting Numbers: [24, 70] Generated Node #0,4,4: 97:[24, 70] Operation: 106-36=70 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 97:[106, 60], Operations: ['79+27=106', '36+24=60'] Exploring Operation: 106*60=6360, Resulting Numbers: [6360] 6360,97 unequal: No Solution Exploring Operation: 106+60=166, Resulting Numbers: [166] 166,97 unequal: No Solution Exploring Operation: 106-60=46, Resulting Numbers: [46] 46,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 97:[36, 82], Operations: ['79+27=106', '106-24=82'] Exploring Operation: 36+82=118, Resulting Numbers: [118] 118,97 unequal: No Solution Exploring Operation: 82-36=46, Resulting Numbers: [46] 46,97 unequal: No Solution Exploring Operation: 36*82=2952, Resulting Numbers: [2952] 2952,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 97:[36, 130], Operations: ['79+27=106', '24+106=130'] Exploring Operation: 36*130=4680, Resulting Numbers: [4680] 4680,97 unequal: No Solution Exploring Operation: 36+130=166, Resulting Numbers: [166] 166,97 unequal: No Solution Exploring Operation: 130-36=94, Resulting Numbers: [94] 94,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 97:[106, 12], Operations: ['79+27=106', '36-24=12'] Exploring Operation: 106*12=1272, Resulting Numbers: [1272] 1272,97 unequal: No Solution Exploring Operation: 106+12=118, Resulting Numbers: [118] 118,97 unequal: No Solution Exploring Operation: 106-12=94, Resulting Numbers: [94] 94,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 97:[24, 70], Operations: ['79+27=106', '106-36=70'] Exploring Operation: 24*70=1680, Resulting Numbers: [1680] 1680,97 unequal: No Solution Exploring Operation: 70-24=46, Resulting Numbers: [46] 46,97 unequal: No Solution Exploring Operation: 24+70=94, Resulting Numbers: [94] 94,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 97:[79, 87], Operations: ['24+27=51', '36+51=87'] Exploring Operation: 79+87=166, Resulting Numbers: [166] 166,97 unequal: No Solution Exploring Operation: 87-79=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 79*87=6873, Resulting Numbers: [6873] 6873,97 unequal: No Solution Moving to Node #0,3,2 Current State: 97:[79, 87], Operations: ['36+27=63', '24+63=87'] Exploring Operation: 79+87=166, Resulting Numbers: [166] 166,97 unequal: No Solution Exploring Operation: 87-79=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 79*87=6873, Resulting Numbers: [6873] 6873,97 unequal: No Solution Moving to Node #0,1,3 Current State: 97:[79, 87], Operations: ['36+24=60', '27+60=87'] Exploring Operation: 79+87=166, Resulting Numbers: [166] 166,97 unequal: No Solution Exploring Operation: 87-79=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 79*87=6873, Resulting Numbers: [6873] 6873,97 unequal: No Solution Moving to Node #0,3,4 Current State: 97:[63, 103], Operations: ['36+27=63', '79+24=103'] Exploring Operation: 63*103=6489, Resulting Numbers: [6489] 6489,97 unequal: No Solution Exploring Operation: 103-63=40, Resulting Numbers: [40] 40,97 unequal: No Solution Exploring Operation: 63+103=166, Resulting Numbers: [166] 166,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[60, 106], Operations: ['36+24=60', '79+27=106'] Exploring Operation: 60*106=6360, Resulting Numbers: [6360] 6360,97 unequal: No Solution Exploring Operation: 106-60=46, Resulting Numbers: [46] 46,97 unequal: No Solution Exploring Operation: 60+106=166, Resulting Numbers: [166] 166,97 unequal: No Solution Moving to Node #0,0,4 Current State: 97:[51, 115], Operations: ['24+27=51', '36+79=115'] Exploring Operation: 51*115=5865, Resulting Numbers: [5865] 5865,97 unequal: No Solution Exploring Operation: 115-51=64, Resulting Numbers: [64] 64,97 unequal: No Solution Exploring Operation: 51+115=166, Resulting Numbers: [166] 166,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[63, 55], Operations: ['36+27=63', '79-24=55'] Exploring Operation: 63*55=3465, Resulting Numbers: [3465] 3465,97 unequal: No Solution Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 63+55=118, Resulting Numbers: [118] 118,97 unequal: No Solution Moving to Node #0,3,1 Current State: 97:[79, 39], Operations: ['36+27=63', '63-24=39'] Exploring Operation: 79+39=118, Resulting Numbers: [118] 118,97 unequal: No Solution Exploring Operation: 79-39=40, Resulting Numbers: [40] 40,97 unequal: No Solution Exploring Operation: 79*39=3081, Resulting Numbers: [3081] 3081,97 unequal: No Solution Moving to Node #0,1,4 Current State: 97:[79, 33], Operations: ['36+24=60', '60-27=33'] Exploring Operation: 79*33=2607, Resulting Numbers: [2607] 2607,97 unequal: No Solution Exploring Operation: 79+33=112, Resulting Numbers: [112] 112,97 unequal: No Solution Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[60, 52], Operations: ['36+24=60', '79-27=52'] Exploring Operation: 60-52=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 60*52=3120, Resulting Numbers: [3120] 3120,97 unequal: No Solution Exploring Operation: 60+52=112, Resulting Numbers: [112] 112,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[36, 130], Operations: ['24+27=51', '79+51=130'] Exploring Operation: 130-36=94, Resulting Numbers: [94] 94,97 unequal: No Solution Exploring Operation: 36*130=4680, Resulting Numbers: [4680] 4680,97 unequal: No Solution Exploring Operation: 36+130=166, Resulting Numbers: [166] 166,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[51, 43], Operations: ['24+27=51', '79-36=43'] Exploring Operation: 51*43=2193, Resulting Numbers: [2193] 2193,97 unequal: No Solution Exploring Operation: 51-43=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 51+43=94, Resulting Numbers: [94] 94,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[79, 15], Operations: ['24+27=51', '51-36=15'] Exploring Operation: 79-15=64, Resulting Numbers: [64] 64,97 unequal: No Solution Exploring Operation: 79+15=94, Resulting Numbers: [94] 94,97 unequal: No Solution Exploring Operation: 79*15=1185, Resulting Numbers: [1185] 1185,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[27, 139], Operations: ['36+24=60', '79+60=139'] Exploring Operation: 27*139=3753, Resulting Numbers: [3753] 3753,97 unequal: No Solution Exploring Operation: 27+139=166, Resulting Numbers: [166] 166,97 unequal: No Solution Exploring Operation: 139-27=112, Resulting Numbers: [112] 112,97 unequal: No Solution Moving to Node #0,3,3 Current State: 97:[24, 142], Operations: ['36+27=63', '79+63=142'] Exploring Operation: 142-24=118, Resulting Numbers: [118] 118,97 unequal: No Solution Exploring Operation: 24+142=166, Resulting Numbers: [166] 166,97 unequal: No Solution Exploring Operation: 24*142=3408, Resulting Numbers: [3408] 3408,97 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 19, 32, 52, 23 ]
42
[ "32-19=13", "52-23=29", "13+29=42" ]
Current State: 42:[19, 32, 52, 23], Operations: [] Exploring Operation: 32-19=13, Resulting Numbers: [52, 23, 13] Generated Node #2: [52, 23, 13] from Operation: 32-19=13 Current State: 42:[52, 23, 13], Operations: ['32-19=13'] Exploring Operation: 52-23=29, Resulting Numbers: [13, 29] Generated Node #3: [13, 29] from Operation: 52-23=29 Current State: 42:[13, 29], Operations: ['32-19=13', '52-23=29'] Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[19, 32, 52, 23], Operations: [] Exploring Operation: 52-23=29, Resulting Numbers: [19, 32, 29] Generated Node #0,0: 42:[19, 32, 29] Operation: 52-23=29 Exploring Operation: 52-32=20, Resulting Numbers: [19, 23, 20] Generated Node #0,1: 42:[19, 23, 20] Operation: 52-32=20 Exploring Operation: 32-23=9, Resulting Numbers: [19, 52, 9] Generated Node #0,2: 42:[19, 52, 9] Operation: 32-23=9 Exploring Operation: 32-19=13, Resulting Numbers: [52, 23, 13] Generated Node #0,3: 42:[52, 23, 13] Operation: 32-19=13 Exploring Operation: 19+23=42, Resulting Numbers: [32, 52, 42] Generated Node #0,4: 42:[32, 52, 42] Operation: 19+23=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[19, 23, 20], Operations: ['52-32=20'] Exploring Operation: 20-19=1, Resulting Numbers: [23, 1] Generated Node #0,1,0: 42:[23, 1] Operation: 20-19=1 Exploring Operation: 23-20=3, Resulting Numbers: [19, 3] Generated Node #0,1,1: 42:[19, 3] Operation: 23-20=3 Exploring Operation: 23+20=43, Resulting Numbers: [19, 43] Generated Node #0,1,2: 42:[19, 43] Operation: 23+20=43 Exploring Operation: 23-19=4, Resulting Numbers: [20, 4] Generated Node #0,1,3: 42:[20, 4] Operation: 23-19=4 Exploring Operation: 19+23=42, Resulting Numbers: [20, 42] Generated Node #0,1,4: 42:[20, 42] Operation: 19+23=42 Moving to Node #0,1,4 Current State: 42:[20, 42], Operations: ['52-32=20', '19+23=42'] Exploring Operation: 20*42=840, Resulting Numbers: [840] 840,42 unequal: No Solution Exploring Operation: 20+42=62, Resulting Numbers: [62] 62,42 unequal: No Solution Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,42 unequal: No Solution Moving to Node #0,1,3 Current State: 42:[20, 4], Operations: ['52-32=20', '23-19=4'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,42 unequal: No Solution Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[19, 3], Operations: ['52-32=20', '23-20=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,42 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[23, 1], Operations: ['52-32=20', '20-19=1'] Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[19, 43], Operations: ['52-32=20', '23+20=43'] Exploring Operation: 43-19=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 19*43=817, Resulting Numbers: [817] 817,42 unequal: No Solution Exploring Operation: 19+43=62, Resulting Numbers: [62] 62,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 42:[52, 23, 13], Operations: ['32-19=13'] Exploring Operation: 52/13=4, Resulting Numbers: [23, 4] Generated Node #0,3,0: 42:[23, 4] Operation: 52/13=4 Exploring Operation: 52-13=39, Resulting Numbers: [23, 39] Generated Node #0,3,1: 42:[23, 39] Operation: 52-13=39 Exploring Operation: 23-13=10, Resulting Numbers: [52, 10] Generated Node #0,3,2: 42:[52, 10] Operation: 23-13=10 Exploring Operation: 23+13=36, Resulting Numbers: [52, 36] Generated Node #0,3,3: 42:[52, 36] Operation: 23+13=36 Exploring Operation: 52-23=29, Resulting Numbers: [13, 29] Generated Node #0,3,4: 42:[13, 29] Operation: 52-23=29 Moving to Node #0,3,0 Current State: 42:[23, 4], Operations: ['32-19=13', '52/13=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,42 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,42 unequal: No Solution Moving to Node #0,3,1 Current State: 42:[23, 39], Operations: ['32-19=13', '52-13=39'] Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 23+39=62, Resulting Numbers: [62] 62,42 unequal: No Solution Exploring Operation: 23*39=897, Resulting Numbers: [897] 897,42 unequal: No Solution Moving to Node #0,3,4 Current State: 42:[13, 29], Operations: ['32-19=13', '52-23=29'] Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[19, 32, 52, 23], Operations: [] Exploring Operation: 32-19=13, Resulting Numbers: [52, 23, 13] Generated Node #0,3: 42:[52, 23, 13] Operation: 32-19=13 Moving to Node #0,3 Current State: 42:[52, 23, 13], Operations: ['32-19=13'] Exploring Operation: 52-23=29, Resulting Numbers: [13, 29] Generated Node #0,3,4: 42:[13, 29] Operation: 52-23=29 Moving to Node #0,3,4 Current State: 42:[13, 29], Operations: ['32-19=13', '52-23=29'] Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic
[ 11, 51, 66, 33 ]
15
[ "11*51=561", "561-66=495", "495/33=15" ]
Current State: 15:[11, 51, 66, 33], Operations: [] Exploring Operation: 11*51=561, Resulting Numbers: [66, 33, 561] Generated Node #2: [66, 33, 561] from Operation: 11*51=561 Current State: 15:[66, 33, 561], Operations: ['11*51=561'] Exploring Operation: 561-66=495, Resulting Numbers: [33, 495] Generated Node #3: [33, 495] from Operation: 561-66=495 Current State: 15:[33, 495], Operations: ['11*51=561', '561-66=495'] Exploring Operation: 495/33=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[11, 51, 66, 33], Operations: [] Exploring Operation: 66/33=2, Resulting Numbers: [11, 51, 2] Generated Node #0,0: 15:[11, 51, 2] Operation: 66/33=2 Exploring Operation: 66-51=15, Resulting Numbers: [11, 33, 15] Generated Node #0,1: 15:[11, 33, 15] Operation: 66-51=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[11, 33, 15], Operations: ['66-51=15'] Exploring Operation: 33-11=22, Resulting Numbers: [15, 22] Generated Node #0,1,0: 15:[15, 22] Operation: 33-11=22 Exploring Operation: 33/11=3, Resulting Numbers: [15, 3] Generated Node #0,1,1: 15:[15, 3] Operation: 33/11=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 15:[15, 3], Operations: ['66-51=15', '33/11=3'] Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,15 unequal: No Solution No 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: 15:[15, 22], Operations: ['66-51=15', '33-11=22'] Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,15 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: 15:[11, 51, 2], Operations: ['66/33=2'] Exploring Operation: 11+2=13, Resulting Numbers: [51, 13] Generated Node #0,0,0: 15:[51, 13] Operation: 11+2=13 Exploring Operation: 51-11=40, Resulting Numbers: [2, 40] Generated Node #0,0,1: 15:[2, 40] Operation: 51-11=40 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 15:[2, 40], Operations: ['66/33=2', '51-11=40'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,15 unequal: No Solution No 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: 15:[51, 13], Operations: ['66/33=2', '11+2=13'] Exploring Operation: 51+13=64, Resulting Numbers: [64] 64,15 unequal: No Solution Exploring Operation: 51-13=38, Resulting Numbers: [38] 38,15 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
[ 76, 31, 8, 84 ]
15
[ "76+31=107", "8+84=92", "107-92=15" ]
Current State: 15:[76, 31, 8, 84], Operations: [] Exploring Operation: 76+31=107, Resulting Numbers: [8, 84, 107] Generated Node #2: [8, 84, 107] from Operation: 76+31=107 Current State: 15:[8, 84, 107], Operations: ['76+31=107'] Exploring Operation: 8+84=92, Resulting Numbers: [107, 92] Generated Node #3: [107, 92] from Operation: 8+84=92 Current State: 15:[107, 92], Operations: ['76+31=107', '8+84=92'] Exploring Operation: 107-92=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[76, 31, 8, 84], Operations: [] Exploring Operation: 84-31=53, Resulting Numbers: [76, 8, 53] Generated Node #0,0: 15:[76, 8, 53] Operation: 84-31=53 Exploring Operation: 84-76=8, Resulting Numbers: [31, 8, 8] Generated Node #0,1: 15:[31, 8, 8] Operation: 84-76=8 Exploring Operation: 76-31=45, Resulting Numbers: [8, 84, 45] Generated Node #0,2: 15:[8, 84, 45] Operation: 76-31=45 Moving to Node #0,1 Current State: 15:[31, 8, 8], Operations: ['84-76=8'] Exploring Operation: 8+8=16, Resulting Numbers: [31, 16] Generated Node #0,1,0: 15:[31, 16] Operation: 8+8=16 Exploring Operation: 31-8=23, Resulting Numbers: [8, 23] Generated Node #0,1,1: 15:[8, 23] Operation: 31-8=23 Exploring Operation: 31-8=23, Resulting Numbers: [8, 23] Generated Node #0,1,2: 15:[8, 23] Operation: 31-8=23 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 15:[8, 23], Operations: ['84-76=8', '31-8=23'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[76, 31, 8, 84], Operations: [] Exploring Operation: 84-76=8, Resulting Numbers: [31, 8, 8] Generated Node #0,1: 15:[31, 8, 8] Operation: 84-76=8 Moving to Node #0,1 Current State: 15:[31, 8, 8], Operations: ['84-76=8'] Exploring Operation: 31-8=23, Resulting Numbers: [8, 23] Generated Node #0,1,1: 15:[8, 23] Operation: 31-8=23 Moving to Node #0,1,1 Current State: 15:[8, 23], Operations: ['84-76=8', '31-8=23'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 68, 7, 9, 12 ]
82
[ "68-7=61", "9+12=21", "61+21=82" ]
Current State: 82:[68, 7, 9, 12], Operations: [] Exploring Operation: 68-7=61, Resulting Numbers: [9, 12, 61] Generated Node #2: [9, 12, 61] from Operation: 68-7=61 Current State: 82:[9, 12, 61], Operations: ['68-7=61'] Exploring Operation: 9+12=21, Resulting Numbers: [61, 21] Generated Node #3: [61, 21] from Operation: 9+12=21 Current State: 82:[61, 21], Operations: ['68-7=61', '9+12=21'] Exploring Operation: 61+21=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[68, 7, 9, 12], Operations: [] Exploring Operation: 7*12=84, Resulting Numbers: [68, 9, 84] Generated Node #0,0: 82:[68, 9, 84] Operation: 7*12=84 Exploring Operation: 68+9=77, Resulting Numbers: [7, 12, 77] Generated Node #0,1: 82:[7, 12, 77] Operation: 68+9=77 Exploring Operation: 68+12=80, Resulting Numbers: [7, 9, 80] Generated Node #0,2: 82:[7, 9, 80] Operation: 68+12=80 Exploring Operation: 12-9=3, Resulting Numbers: [68, 7, 3] Generated Node #0,3: 82:[68, 7, 3] Operation: 12-9=3 Exploring Operation: 68+7=75, Resulting Numbers: [9, 12, 75] Generated Node #0,4: 82:[9, 12, 75] Operation: 68+7=75 Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[7, 9, 80], Operations: ['68+12=80'] Exploring Operation: 7+80=87, Resulting Numbers: [9, 87] Generated Node #0,2,0: 82:[9, 87] Operation: 7+80=87 Exploring Operation: 9+80=89, Resulting Numbers: [7, 89] Generated Node #0,2,1: 82:[7, 89] Operation: 9+80=89 Exploring Operation: 80-7=73, Resulting Numbers: [9, 73] Generated Node #0,2,2: 82:[9, 73] Operation: 80-7=73 Exploring Operation: 7+9=16, Resulting Numbers: [80, 16] Generated Node #0,2,3: 82:[80, 16] Operation: 7+9=16 Exploring Operation: 9-7=2, Resulting Numbers: [80, 2] Generated Node #0,2,4: 82:[80, 2] Operation: 9-7=2 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 82:[80, 2], Operations: ['68+12=80', '9-7=2'] Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,82 unequal: No Solution Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,82 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,82 unequal: No Solution Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[68, 7, 9, 12], Operations: [] Exploring Operation: 68+12=80, Resulting Numbers: [7, 9, 80] Generated Node #0,2: 82:[7, 9, 80] Operation: 68+12=80 Moving to Node #0,2 Current State: 82:[7, 9, 80], Operations: ['68+12=80'] Exploring Operation: 9-7=2, Resulting Numbers: [80, 2] Generated Node #0,2,4: 82:[80, 2] Operation: 9-7=2 Moving to Node #0,2,4 Current State: 82:[80, 2], Operations: ['68+12=80', '9-7=2'] Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 98, 98, 6, 4 ]
30
[ "98/98=1", "4+1=5", "6*5=30" ]
Current State: 30:[98, 98, 6, 4], Operations: [] Exploring Operation: 98/98=1, Resulting Numbers: [6, 4, 1] Generated Node #2: [6, 4, 1] from Operation: 98/98=1 Current State: 30:[6, 4, 1], Operations: ['98/98=1'] Exploring Operation: 4+1=5, Resulting Numbers: [6, 5] Generated Node #3: [6, 5] from Operation: 4+1=5 Current State: 30:[6, 5], Operations: ['98/98=1', '4+1=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[98, 98, 6, 4], Operations: [] Exploring Operation: 98-6=92, Resulting Numbers: [98, 4, 92] Generated Node #0,0: 30:[98, 4, 92] Operation: 98-6=92 Exploring Operation: 98-98=0, Resulting Numbers: [6, 4, 0] Generated Node #0,1: 30:[6, 4, 0] Operation: 98-98=0 Exploring Operation: 98/98=1, Resulting Numbers: [6, 4, 1] Generated Node #0,2: 30:[6, 4, 1] Operation: 98/98=1 Exploring Operation: 98-6=92, Resulting Numbers: [98, 4, 92] Generated Node #0,3: 30:[98, 4, 92] Operation: 98-6=92 Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[6, 4, 1], Operations: ['98/98=1'] Exploring Operation: 6-4=2, Resulting Numbers: [1, 2] Generated Node #0,2,0: 30:[1, 2] Operation: 6-4=2 Exploring Operation: 4-1=3, Resulting Numbers: [6, 3] Generated Node #0,2,1: 30:[6, 3] Operation: 4-1=3 Exploring Operation: 4+1=5, Resulting Numbers: [6, 5] Generated Node #0,2,2: 30:[6, 5] Operation: 4+1=5 Exploring Operation: 6+4=10, Resulting Numbers: [1, 10] Generated Node #0,2,3: 30:[1, 10] Operation: 6+4=10 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 30:[6, 3], Operations: ['98/98=1', '4-1=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,30 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,30 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 30:[6, 5], Operations: ['98/98=1', '4+1=5'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[98, 98, 6, 4], Operations: [] Exploring Operation: 98/98=1, Resulting Numbers: [6, 4, 1] Generated Node #0,2: 30:[6, 4, 1] Operation: 98/98=1 Moving to Node #0,2 Current State: 30:[6, 4, 1], Operations: ['98/98=1'] Exploring Operation: 4+1=5, Resulting Numbers: [6, 5] Generated Node #0,2,2: 30:[6, 5] Operation: 4+1=5 Moving to Node #0,2,2 Current State: 30:[6, 5], Operations: ['98/98=1', '4+1=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 38, 91, 70, 83 ]
45
[ "83-70=13", "91/13=7", "38+7=45" ]
Current State: 45:[38, 91, 70, 83], Operations: [] Exploring Operation: 83-70=13, Resulting Numbers: [38, 91, 13] Generated Node #2: [38, 91, 13] from Operation: 83-70=13 Current State: 45:[38, 91, 13], Operations: ['83-70=13'] Exploring Operation: 91/13=7, Resulting Numbers: [38, 7] Generated Node #3: [38, 7] from Operation: 91/13=7 Current State: 45:[38, 7], Operations: ['83-70=13', '91/13=7'] Exploring Operation: 38+7=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[38, 91, 70, 83], Operations: [] Exploring Operation: 83-70=13, Resulting Numbers: [38, 91, 13] Generated Node #0,0: 45:[38, 91, 13] Operation: 83-70=13 Exploring Operation: 91-83=8, Resulting Numbers: [38, 70, 8] Generated Node #0,1: 45:[38, 70, 8] Operation: 91-83=8 Exploring Operation: 91-70=21, Resulting Numbers: [38, 83, 21] Generated Node #0,2: 45:[38, 83, 21] Operation: 91-70=21 Moving to Node #0,1 Current State: 45:[38, 70, 8], Operations: ['91-83=8'] Exploring Operation: 70-8=62, Resulting Numbers: [38, 62] Generated Node #0,1,0: 45:[38, 62] Operation: 70-8=62 Exploring Operation: 70-38=32, Resulting Numbers: [8, 32] Generated Node #0,1,1: 45:[8, 32] Operation: 70-38=32 Exploring Operation: 38+8=46, Resulting Numbers: [70, 46] Generated Node #0,1,2: 45:[70, 46] Operation: 38+8=46 Moving to Node #0,2 Current State: 45:[38, 83, 21], Operations: ['91-70=21'] Exploring Operation: 83-38=45, Resulting Numbers: [21, 45] Generated Node #0,2,0: 45:[21, 45] Operation: 83-38=45 Exploring Operation: 38-21=17, Resulting Numbers: [83, 17] Generated Node #0,2,1: 45:[83, 17] Operation: 38-21=17 Exploring Operation: 83-21=62, Resulting Numbers: [38, 62] Generated Node #0,2,2: 45:[38, 62] Operation: 83-21=62 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 45:[21, 45], Operations: ['91-70=21', '83-38=45'] Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,45 unequal: No Solution Exploring Operation: 21*45=945, Resulting Numbers: [945] 945,45 unequal: No Solution Exploring Operation: 21+45=66, Resulting Numbers: [66] 66,45 unequal: No Solution No 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: 45:[38, 62], Operations: ['91-70=21', '83-21=62'] Exploring Operation: 38+62=100, Resulting Numbers: [100] 100,45 unequal: No Solution Exploring Operation: 62-38=24, Resulting Numbers: [24] 24,45 unequal: No Solution Exploring Operation: 38*62=2356, Resulting Numbers: [2356] 2356,45 unequal: No Solution No 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: 45:[83, 17], Operations: ['91-70=21', '38-21=17'] Exploring Operation: 83+17=100, Resulting Numbers: [100] 100,45 unequal: No Solution Exploring Operation: 83*17=1411, Resulting Numbers: [1411] 1411,45 unequal: No Solution Exploring Operation: 83-17=66, Resulting Numbers: [66] 66,45 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: 45:[38, 91, 13], Operations: ['83-70=13'] Exploring Operation: 91/13=7, Resulting Numbers: [38, 7] Generated Node #0,0,0: 45:[38, 7] Operation: 91/13=7 Exploring Operation: 91-13=78, Resulting Numbers: [38, 78] Generated Node #0,0,1: 45:[38, 78] Operation: 91-13=78 Exploring Operation: 91-38=53, Resulting Numbers: [13, 53] Generated Node #0,0,2: 45:[13, 53] Operation: 91-38=53 Moving to Node #0,0,0 Current State: 45:[38, 7], Operations: ['83-70=13', '91/13=7'] Exploring Operation: 38*7=266, Resulting Numbers: [266] 266,45 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,45 unequal: No Solution Exploring Operation: 38+7=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[38, 91, 70, 83], Operations: [] Exploring Operation: 83-70=13, Resulting Numbers: [38, 91, 13] Generated Node #0,0: 45:[38, 91, 13] Operation: 83-70=13 Moving to Node #0,0 Current State: 45:[38, 91, 13], Operations: ['83-70=13'] Exploring Operation: 91/13=7, Resulting Numbers: [38, 7] Generated Node #0,0,0: 45:[38, 7] Operation: 91/13=7 Moving to Node #0,0,0 Current State: 45:[38, 7], Operations: ['83-70=13', '91/13=7'] Exploring Operation: 38+7=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
0.975694
hs_3
mult_heuristic
[ 9, 96, 72, 98 ]
61
[ "96-9=87", "98-72=26", "87-26=61" ]
Current State: 61:[9, 96, 72, 98], Operations: [] Exploring Operation: 96-9=87, Resulting Numbers: [72, 98, 87] Generated Node #2: [72, 98, 87] from Operation: 96-9=87 Current State: 61:[72, 98, 87], Operations: ['96-9=87'] Exploring Operation: 98-72=26, Resulting Numbers: [87, 26] Generated Node #3: [87, 26] from Operation: 98-72=26 Current State: 61:[87, 26], Operations: ['96-9=87', '98-72=26'] Exploring Operation: 87-26=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[9, 96, 72, 98], Operations: [] Exploring Operation: 96-9=87, Resulting Numbers: [72, 98, 87] Generated Node #0,0: 61:[72, 98, 87] Operation: 96-9=87 Exploring Operation: 72-9=63, Resulting Numbers: [96, 98, 63] Generated Node #0,1: 61:[96, 98, 63] Operation: 72-9=63 Moving to Node #0,0 Current State: 61:[72, 98, 87], Operations: ['96-9=87'] Exploring Operation: 98-72=26, Resulting Numbers: [87, 26] Generated Node #0,0,0: 61:[87, 26] Operation: 98-72=26 Exploring Operation: 98-87=11, Resulting Numbers: [72, 11] Generated Node #0,0,1: 61:[72, 11] Operation: 98-87=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[87, 26], Operations: ['96-9=87', '98-72=26'] Exploring Operation: 87+26=113, Resulting Numbers: [113] 113,61 unequal: No Solution Exploring Operation: 87-26=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[9, 96, 72, 98], Operations: [] Exploring Operation: 96-9=87, Resulting Numbers: [72, 98, 87] Generated Node #0,0: 61:[72, 98, 87] Operation: 96-9=87 Moving to Node #0,0 Current State: 61:[72, 98, 87], Operations: ['96-9=87'] Exploring Operation: 98-72=26, Resulting Numbers: [87, 26] Generated Node #0,0,0: 61:[87, 26] Operation: 98-72=26 Moving to Node #0,0,0 Current State: 61:[87, 26], Operations: ['96-9=87', '98-72=26'] Exploring Operation: 87-26=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 24, 31, 36, 24 ]
67
[ "24+31=55", "36-24=12", "55+12=67" ]
Current State: 67:[24, 31, 36, 24], Operations: [] Exploring Operation: 24+31=55, Resulting Numbers: [36, 55] Generated Node #2: [36, 55] from Operation: 24+31=55 Current State: 67:[36, 55], Operations: ['24+31=55'] Exploring Operation: 36-24=12, Resulting Numbers: [55, 12] Generated Node #3: [55, 12] from Operation: 36-24=12 Current State: 67:[55, 12], Operations: ['24+31=55', '36-24=12'] Exploring Operation: 55+12=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[24, 31, 36, 24], Operations: [] Exploring Operation: 24+36=60, Resulting Numbers: [31, 24, 60] Generated Node #0,0: 67:[31, 24, 60] Operation: 24+36=60 Exploring Operation: 31+36=67, Resulting Numbers: [24, 24, 67] Generated Node #0,1: 67:[24, 24, 67] Operation: 31+36=67 Exploring Operation: 24+31=55, Resulting Numbers: [36, 24, 55] Generated Node #0,2: 67:[36, 24, 55] Operation: 24+31=55 Exploring Operation: 31+24=55, Resulting Numbers: [24, 36, 55] Generated Node #0,3: 67:[24, 36, 55] Operation: 31+24=55 Exploring Operation: 24+24=48, Resulting Numbers: [31, 36, 48] Generated Node #0,4: 67:[31, 36, 48] Operation: 24+24=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[31, 24, 60], Operations: ['24+36=60'] Exploring Operation: 31+60=91, Resulting Numbers: [24, 91] Generated Node #0,0,0: 67:[24, 91] Operation: 31+60=91 Exploring Operation: 24+60=84, Resulting Numbers: [31, 84] Generated Node #0,0,1: 67:[31, 84] Operation: 24+60=84 Exploring Operation: 31-24=7, Resulting Numbers: [60, 7] Generated Node #0,0,2: 67:[60, 7] Operation: 31-24=7 Exploring Operation: 31+24=55, Resulting Numbers: [60, 55] Generated Node #0,0,3: 67:[60, 55] Operation: 31+24=55 Exploring Operation: 60-24=36, Resulting Numbers: [31, 36] Generated Node #0,0,4: 67:[31, 36] Operation: 60-24=36 Moving to Node #0,0,3 Current State: 67:[60, 55], Operations: ['24+36=60', '31+24=55'] Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,67 unequal: No Solution Exploring Operation: 60+55=115, Resulting Numbers: [115] 115,67 unequal: No Solution Exploring Operation: 60*55=3300, Resulting Numbers: [3300] 3300,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[31, 84], Operations: ['24+36=60', '24+60=84'] Exploring Operation: 31+84=115, Resulting Numbers: [115] 115,67 unequal: No Solution Exploring Operation: 31*84=2604, Resulting Numbers: [2604] 2604,67 unequal: No Solution Exploring Operation: 84-31=53, Resulting Numbers: [53] 53,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[24, 91], Operations: ['24+36=60', '31+60=91'] Exploring Operation: 24+91=115, Resulting Numbers: [115] 115,67 unequal: No Solution Exploring Operation: 24*91=2184, Resulting Numbers: [2184] 2184,67 unequal: No Solution Exploring Operation: 91-24=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[24, 31, 36, 24], Operations: [] Exploring Operation: 24+36=60, Resulting Numbers: [31, 24, 60] Generated Node #0,0: 67:[31, 24, 60] Operation: 24+36=60 Moving to Node #0,0 Current State: 67:[31, 24, 60], Operations: ['24+36=60'] Exploring Operation: 31+60=91, Resulting Numbers: [24, 91] Generated Node #0,0,0: 67:[24, 91] Operation: 31+60=91 Moving to Node #0,0,0 Current State: 67:[24, 91], Operations: ['24+36=60', '31+60=91'] Exploring Operation: 91-24=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 13, 59, 75, 60 ]
88
[ "13+75=88", "60-59=1", "88*1=88" ]
Current State: 88:[13, 59, 75, 60], Operations: [] Exploring Operation: 13+75=88, Resulting Numbers: [59, 60, 88] Generated Node #2: [59, 60, 88] from Operation: 13+75=88 Current State: 88:[59, 60, 88], Operations: ['13+75=88'] Exploring Operation: 60-59=1, Resulting Numbers: [88, 1] Generated Node #3: [88, 1] from Operation: 60-59=1 Current State: 88:[88, 1], Operations: ['13+75=88', '60-59=1'] Exploring Operation: 88*1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[13, 59, 75, 60], Operations: [] Exploring Operation: 75-60=15, Resulting Numbers: [13, 59, 15] Generated Node #0,0: 88:[13, 59, 15] Operation: 75-60=15 Exploring Operation: 60-59=1, Resulting Numbers: [13, 75, 1] Generated Node #0,1: 88:[13, 75, 1] Operation: 60-59=1 Moving to Node #0,1 Current State: 88:[13, 75, 1], Operations: ['60-59=1'] Exploring Operation: 13+75=88, Resulting Numbers: [1, 88] Generated Node #0,1,0: 88:[1, 88] Operation: 13+75=88 Exploring Operation: 13-1=12, Resulting Numbers: [75, 12] Generated Node #0,1,1: 88:[75, 12] Operation: 13-1=12 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[1, 88], Operations: ['60-59=1', '13+75=88'] Exploring Operation: 88/1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[13, 59, 75, 60], Operations: [] Exploring Operation: 60-59=1, Resulting Numbers: [13, 75, 1] Generated Node #0,1: 88:[13, 75, 1] Operation: 60-59=1 Moving to Node #0,1 Current State: 88:[13, 75, 1], Operations: ['60-59=1'] Exploring Operation: 13+75=88, Resulting Numbers: [1, 88] Generated Node #0,1,0: 88:[1, 88] Operation: 13+75=88 Moving to Node #0,1,0 Current State: 88:[1, 88], Operations: ['60-59=1', '13+75=88'] Exploring Operation: 88/1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 57, 69, 54, 53 ]
43
[ "57*53=3021", "3021-54=2967", "2967/69=43" ]
Current State: 43:[57, 69, 54, 53], Operations: [] Exploring Operation: 57*53=3021, Resulting Numbers: [69, 54, 3021] Generated Node #2: [69, 54, 3021] from Operation: 57*53=3021 Current State: 43:[69, 54, 3021], Operations: ['57*53=3021'] Exploring Operation: 3021-54=2967, Resulting Numbers: [69, 2967] Generated Node #3: [69, 2967] from Operation: 3021-54=2967 Current State: 43:[69, 2967], Operations: ['57*53=3021', '3021-54=2967'] Exploring Operation: 2967/69=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[57, 69, 54, 53], Operations: [] Exploring Operation: 69-53=16, Resulting Numbers: [57, 54, 16] Generated Node #0,0: 43:[57, 54, 16] Operation: 69-53=16 Exploring Operation: 69-54=15, Resulting Numbers: [57, 53, 15] Generated Node #0,1: 43:[57, 53, 15] Operation: 69-54=15 Exploring Operation: 69-57=12, Resulting Numbers: [54, 53, 12] Generated Node #0,2: 43:[54, 53, 12] Operation: 69-57=12 Exploring Operation: 57-54=3, Resulting Numbers: [69, 53, 3] Generated Node #0,3: 43:[69, 53, 3] Operation: 57-54=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[57, 54, 16], Operations: ['69-53=16'] Exploring Operation: 54+16=70, Resulting Numbers: [57, 70] Generated Node #0,0,0: 43:[57, 70] Operation: 54+16=70 Exploring Operation: 54-16=38, Resulting Numbers: [57, 38] Generated Node #0,0,1: 43:[57, 38] Operation: 54-16=38 Exploring Operation: 57-16=41, Resulting Numbers: [54, 41] Generated Node #0,0,2: 43:[54, 41] Operation: 57-16=41 Exploring Operation: 57+16=73, Resulting Numbers: [54, 73] Generated Node #0,0,3: 43:[54, 73] Operation: 57+16=73 Moving to Node #0,0,2 Current State: 43:[54, 41], Operations: ['69-53=16', '57-16=41'] Exploring Operation: 54*41=2214, Resulting Numbers: [2214] 2214,43 unequal: No Solution Exploring Operation: 54+41=95, Resulting Numbers: [95] 95,43 unequal: No Solution Exploring Operation: 54-41=13, Resulting Numbers: [13] 13,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[57, 38], Operations: ['69-53=16', '54-16=38'] Exploring Operation: 57+38=95, Resulting Numbers: [95] 95,43 unequal: No Solution Exploring Operation: 57*38=2166, Resulting Numbers: [2166] 2166,43 unequal: No Solution Exploring Operation: 57-38=19, Resulting Numbers: [19] 19,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[54, 73], Operations: ['69-53=16', '57+16=73'] Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,43 unequal: No Solution Exploring Operation: 54+73=127, Resulting Numbers: [127] 127,43 unequal: No Solution Exploring Operation: 54*73=3942, Resulting Numbers: [3942] 3942,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[57, 70], Operations: ['69-53=16', '54+16=70'] Exploring Operation: 57+70=127, Resulting Numbers: [127] 127,43 unequal: No Solution Exploring Operation: 70-57=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 57*70=3990, Resulting Numbers: [3990] 3990,43 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 Current State: 43:[57, 53, 15], Operations: ['69-54=15'] Exploring Operation: 53-15=38, Resulting Numbers: [57, 38] Generated Node #0,1,0: 43:[57, 38] Operation: 53-15=38 Exploring Operation: 57+15=72, Resulting Numbers: [53, 72] Generated Node #0,1,1: 43:[53, 72] Operation: 57+15=72 Exploring Operation: 57-15=42, Resulting Numbers: [53, 42] Generated Node #0,1,2: 43:[53, 42] Operation: 57-15=42 Exploring Operation: 53+15=68, Resulting Numbers: [57, 68] Generated Node #0,1,3: 43:[57, 68] Operation: 53+15=68 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 43:[53, 42], Operations: ['69-54=15', '57-15=42'] Exploring Operation: 53*42=2226, Resulting Numbers: [2226] 2226,43 unequal: No Solution Exploring Operation: 53-42=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 53+42=95, Resulting Numbers: [95] 95,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 43:[57, 38], Operations: ['69-54=15', '53-15=38'] Exploring Operation: 57+38=95, Resulting Numbers: [95] 95,43 unequal: No Solution Exploring Operation: 57-38=19, Resulting Numbers: [19] 19,43 unequal: No Solution Exploring Operation: 57*38=2166, Resulting Numbers: [2166] 2166,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 43:[53, 72], Operations: ['69-54=15', '57+15=72'] Exploring Operation: 53+72=125, Resulting Numbers: [125] 125,43 unequal: No Solution Exploring Operation: 72-53=19, Resulting Numbers: [19] 19,43 unequal: No Solution Exploring Operation: 53*72=3816, Resulting Numbers: [3816] 3816,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 43:[57, 68], Operations: ['69-54=15', '53+15=68'] Exploring Operation: 57+68=125, Resulting Numbers: [125] 125,43 unequal: No Solution Exploring Operation: 57*68=3876, Resulting Numbers: [3876] 3876,43 unequal: No Solution Exploring Operation: 68-57=11, Resulting Numbers: [11] 11,43 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: 43:[54, 53, 12], Operations: ['69-57=12'] Exploring Operation: 54+12=66, Resulting Numbers: [53, 66] Generated Node #0,2,0: 43:[53, 66] Operation: 54+12=66 Exploring Operation: 53+12=65, Resulting Numbers: [54, 65] Generated Node #0,2,1: 43:[54, 65] Operation: 53+12=65 Exploring Operation: 54-12=42, Resulting Numbers: [53, 42] Generated Node #0,2,2: 43:[53, 42] Operation: 54-12=42 Exploring Operation: 53-12=41, Resulting Numbers: [54, 41] Generated Node #0,2,3: 43:[54, 41] Operation: 53-12=41 Moving to Node #0,2,2 Current State: 43:[53, 42], Operations: ['69-57=12', '54-12=42'] Exploring Operation: 53+42=95, Resulting Numbers: [95] 95,43 unequal: No Solution Exploring Operation: 53-42=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 53*42=2226, Resulting Numbers: [2226] 2226,43 unequal: No Solution Moving to Node #0,2,3 Current State: 43:[54, 41], Operations: ['69-57=12', '53-12=41'] Exploring Operation: 54+41=95, Resulting Numbers: [95] 95,43 unequal: No Solution Exploring Operation: 54*41=2214, Resulting Numbers: [2214] 2214,43 unequal: No Solution Exploring Operation: 54-41=13, Resulting Numbers: [13] 13,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[54, 65], Operations: ['69-57=12', '53+12=65'] Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 54*65=3510, Resulting Numbers: [3510] 3510,43 unequal: No Solution Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[53, 66], Operations: ['69-57=12', '54+12=66'] Exploring Operation: 53+66=119, Resulting Numbers: [119] 119,43 unequal: No Solution Exploring Operation: 53*66=3498, Resulting Numbers: [3498] 3498,43 unequal: No Solution Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,43 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 #0,3 Current State: 43:[69, 53, 3], Operations: ['57-54=3'] Exploring Operation: 69/3=23, Resulting Numbers: [53, 23] Generated Node #0,3,0: 43:[53, 23] Operation: 69/3=23 Exploring Operation: 69+3=72, Resulting Numbers: [53, 72] Generated Node #0,3,1: 43:[53, 72] Operation: 69+3=72 Exploring Operation: 53-3=50, Resulting Numbers: [69, 50] Generated Node #0,3,2: 43:[69, 50] Operation: 53-3=50 Exploring Operation: 69-3=66, Resulting Numbers: [53, 66] Generated Node #0,3,3: 43:[53, 66] Operation: 69-3=66 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 43:[53, 23], Operations: ['57-54=3', '69/3=23'] Exploring Operation: 53+23=76, Resulting Numbers: [76] 76,43 unequal: No Solution Exploring Operation: 53*23=1219, Resulting Numbers: [1219] 1219,43 unequal: No Solution Exploring Operation: 53-23=30, Resulting Numbers: [30] 30,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 43:[69, 50], Operations: ['57-54=3', '53-3=50'] Exploring Operation: 69+50=119, Resulting Numbers: [119] 119,43 unequal: No Solution Exploring Operation: 69*50=3450, Resulting Numbers: [3450] 3450,43 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 43:[53, 66], Operations: ['57-54=3', '69-3=66'] Exploring Operation: 53+66=119, Resulting Numbers: [119] 119,43 unequal: No Solution Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 53*66=3498, Resulting Numbers: [3498] 3498,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 43:[53, 72], Operations: ['57-54=3', '69+3=72'] Exploring Operation: 53+72=125, Resulting Numbers: [125] 125,43 unequal: No Solution Exploring Operation: 72-53=19, Resulting Numbers: [19] 19,43 unequal: No Solution Exploring Operation: 53*72=3816, Resulting Numbers: [3816] 3816,43 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
[ 29, 77, 78, 3 ]
31
[ "29+77=106", "78-3=75", "106-75=31" ]
Current State: 31:[29, 77, 78, 3], Operations: [] Exploring Operation: 29+77=106, Resulting Numbers: [78, 3, 106] Generated Node #2: [78, 3, 106] from Operation: 29+77=106 Current State: 31:[78, 3, 106], Operations: ['29+77=106'] Exploring Operation: 78-3=75, Resulting Numbers: [106, 75] Generated Node #3: [106, 75] from Operation: 78-3=75 Current State: 31:[106, 75], Operations: ['29+77=106', '78-3=75'] Exploring Operation: 106-75=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[29, 77, 78, 3], Operations: [] Exploring Operation: 78-77=1, Resulting Numbers: [29, 3, 1] Generated Node #0,0: 31:[29, 3, 1] Operation: 78-77=1 Exploring Operation: 78/3=26, Resulting Numbers: [29, 77, 26] Generated Node #0,1: 31:[29, 77, 26] Operation: 78/3=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[29, 77, 26], Operations: ['78/3=26'] Exploring Operation: 77-26=51, Resulting Numbers: [29, 51] Generated Node #0,1,0: 31:[29, 51] Operation: 77-26=51 Exploring Operation: 77-29=48, Resulting Numbers: [26, 48] Generated Node #0,1,1: 31:[26, 48] Operation: 77-29=48 Moving to Node #0,1,0 Current State: 31:[29, 51], Operations: ['78/3=26', '77-26=51'] Exploring Operation: 29+51=80, Resulting Numbers: [80] 80,31 unequal: No Solution Exploring Operation: 51-29=22, Resulting Numbers: [22] 22,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[26, 48], Operations: ['78/3=26', '77-29=48'] Exploring Operation: 26+48=74, Resulting Numbers: [74] 74,31 unequal: No Solution Exploring Operation: 48-26=22, Resulting Numbers: [22] 22,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[29, 3, 1], Operations: ['78-77=1'] Exploring Operation: 29+1=30, Resulting Numbers: [3, 30] Generated Node #0,0,0: 31:[3, 30] Operation: 29+1=30 Exploring Operation: 3+1=4, Resulting Numbers: [29, 4] Generated Node #0,0,1: 31:[29, 4] Operation: 3+1=4 Moving to Node #0,0,0 Current State: 31:[3, 30], Operations: ['78-77=1', '29+1=30'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[29, 4], Operations: ['78-77=1', '3+1=4'] Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,31 unequal: No Solution Exploring Operation: 29+4=33, Resulting Numbers: [33] 33,31 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
[ 54, 28, 90, 13 ]
25
[ "28-13=15", "90*15=1350", "1350/54=25" ]
Current State: 25:[54, 28, 90, 13], Operations: [] Exploring Operation: 28-13=15, Resulting Numbers: [54, 90, 15] Generated Node #2: [54, 90, 15] from Operation: 28-13=15 Current State: 25:[54, 90, 15], Operations: ['28-13=15'] Exploring Operation: 90*15=1350, Resulting Numbers: [54, 1350] Generated Node #3: [54, 1350] from Operation: 90*15=1350 Current State: 25:[54, 1350], Operations: ['28-13=15', '90*15=1350'] Exploring Operation: 1350/54=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[54, 28, 90, 13], Operations: [] Exploring Operation: 90-54=36, Resulting Numbers: [28, 13, 36] Generated Node #0,0: 25:[28, 13, 36] Operation: 90-54=36 Exploring Operation: 90-28=62, Resulting Numbers: [54, 13, 62] Generated Node #0,1: 25:[54, 13, 62] Operation: 90-28=62 Exploring Operation: 54-28=26, Resulting Numbers: [90, 13, 26] Generated Node #0,2: 25:[90, 13, 26] Operation: 54-28=26 Exploring Operation: 54-13=41, Resulting Numbers: [28, 90, 41] Generated Node #0,3: 25:[28, 90, 41] Operation: 54-13=41 Exploring Operation: 90-13=77, Resulting Numbers: [54, 28, 77] Generated Node #0,4: 25:[54, 28, 77] Operation: 90-13=77 Moving to Node #0,0 Current State: 25:[28, 13, 36], Operations: ['90-54=36'] Exploring Operation: 36-28=8, Resulting Numbers: [13, 8] Generated Node #0,0,0: 25:[13, 8] Operation: 36-28=8 Exploring Operation: 28+13=41, Resulting Numbers: [36, 41] Generated Node #0,0,1: 25:[36, 41] Operation: 28+13=41 Exploring Operation: 36-13=23, Resulting Numbers: [28, 23] Generated Node #0,0,2: 25:[28, 23] Operation: 36-13=23 Exploring Operation: 28-13=15, Resulting Numbers: [36, 15] Generated Node #0,0,3: 25:[36, 15] Operation: 28-13=15 Exploring Operation: 13+36=49, Resulting Numbers: [28, 49] Generated Node #0,0,4: 25:[28, 49] Operation: 13+36=49 Moving to Node #0,2 Current State: 25:[90, 13, 26], Operations: ['54-28=26'] Exploring Operation: 26-13=13, Resulting Numbers: [90, 13] Generated Node #0,2,0: 25:[90, 13] Operation: 26-13=13 Exploring Operation: 90+13=103, Resulting Numbers: [26, 103] Generated Node #0,2,1: 25:[26, 103] Operation: 90+13=103 Exploring Operation: 90-26=64, Resulting Numbers: [13, 64] Generated Node #0,2,2: 25:[13, 64] Operation: 90-26=64 Exploring Operation: 90-13=77, Resulting Numbers: [26, 77] Generated Node #0,2,3: 25:[26, 77] Operation: 90-13=77 Exploring Operation: 26/13=2, Resulting Numbers: [90, 2] Generated Node #0,2,4: 25:[90, 2] Operation: 26/13=2 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 25:[13, 64], Operations: ['54-28=26', '90-26=64'] Exploring Operation: 64-13=51, Resulting Numbers: [51] 51,25 unequal: No Solution Exploring Operation: 13+64=77, Resulting Numbers: [77] 77,25 unequal: No Solution Exploring Operation: 13*64=832, Resulting Numbers: [832] 832,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 25:[26, 77], Operations: ['54-28=26', '90-13=77'] Exploring Operation: 26+77=103, Resulting Numbers: [103] 103,25 unequal: No Solution Exploring Operation: 26*77=2002, Resulting Numbers: [2002] 2002,25 unequal: No Solution Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 25:[90, 2], Operations: ['54-28=26', '26/13=2'] Exploring Operation: 90+2=92, Resulting Numbers: [92] 92,25 unequal: No Solution Exploring Operation: 90*2=180, Resulting Numbers: [180] 180,25 unequal: No Solution Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,25 unequal: No Solution Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 25:[90, 13], Operations: ['54-28=26', '26-13=13'] Exploring Operation: 90+13=103, Resulting Numbers: [103] 103,25 unequal: No Solution Exploring Operation: 90-13=77, Resulting Numbers: [77] 77,25 unequal: No Solution Exploring Operation: 90*13=1170, Resulting Numbers: [1170] 1170,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 25:[26, 103], Operations: ['54-28=26', '90+13=103'] Exploring Operation: 26+103=129, Resulting Numbers: [129] 129,25 unequal: No Solution Exploring Operation: 103-26=77, Resulting Numbers: [77] 77,25 unequal: No Solution Exploring Operation: 26*103=2678, Resulting Numbers: [2678] 2678,25 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: 25:[54, 13, 62], Operations: ['90-28=62'] Exploring Operation: 13+62=75, Resulting Numbers: [54, 75] Generated Node #0,1,0: 25:[54, 75] Operation: 13+62=75 Exploring Operation: 62-13=49, Resulting Numbers: [54, 49] Generated Node #0,1,1: 25:[54, 49] Operation: 62-13=49 Exploring Operation: 62-54=8, Resulting Numbers: [13, 8] Generated Node #0,1,2: 25:[13, 8] Operation: 62-54=8 Exploring Operation: 54+13=67, Resulting Numbers: [62, 67] Generated Node #0,1,3: 25:[62, 67] Operation: 54+13=67 Exploring Operation: 54-13=41, Resulting Numbers: [62, 41] Generated Node #0,1,4: 25:[62, 41] Operation: 54-13=41 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 25:[13, 8], Operations: ['90-28=62', '62-54=8'] Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 13*8=104, Resulting Numbers: [104] 104,25 unequal: No Solution Exploring Operation: 13+8=21, Resulting Numbers: [21] 21,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 25:[54, 49], Operations: ['90-28=62', '62-13=49'] Exploring Operation: 54*49=2646, Resulting Numbers: [2646] 2646,25 unequal: No Solution Exploring Operation: 54+49=103, Resulting Numbers: [103] 103,25 unequal: No Solution Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 25:[62, 41], Operations: ['90-28=62', '54-13=41'] Exploring Operation: 62-41=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 62*41=2542, Resulting Numbers: [2542] 2542,25 unequal: No Solution Exploring Operation: 62+41=103, Resulting Numbers: [103] 103,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 25:[54, 75], Operations: ['90-28=62', '13+62=75'] Exploring Operation: 75-54=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 54*75=4050, Resulting Numbers: [4050] 4050,25 unequal: No Solution Exploring Operation: 54+75=129, Resulting Numbers: [129] 129,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 25:[62, 67], Operations: ['90-28=62', '54+13=67'] Exploring Operation: 67-62=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 62+67=129, Resulting Numbers: [129] 129,25 unequal: No Solution Exploring Operation: 62*67=4154, Resulting Numbers: [4154] 4154,25 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: 25:[28, 90, 41], Operations: ['54-13=41'] Exploring Operation: 28+41=69, Resulting Numbers: [90, 69] Generated Node #0,3,0: 25:[90, 69] Operation: 28+41=69 Exploring Operation: 41-28=13, Resulting Numbers: [90, 13] Generated Node #0,3,1: 25:[90, 13] Operation: 41-28=13 Exploring Operation: 90-41=49, Resulting Numbers: [28, 49] Generated Node #0,3,2: 25:[28, 49] Operation: 90-41=49 Exploring Operation: 90-28=62, Resulting Numbers: [41, 62] Generated Node #0,3,3: 25:[41, 62] Operation: 90-28=62 Exploring Operation: 28+90=118, Resulting Numbers: [41, 118] Generated Node #0,3,4: 25:[41, 118] Operation: 28+90=118 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 25:[28, 49], Operations: ['54-13=41', '90-41=49'] Exploring Operation: 49-28=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 28*49=1372, Resulting Numbers: [1372] 1372,25 unequal: No Solution Exploring Operation: 28+49=77, Resulting Numbers: [77] 77,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 25:[41, 62], Operations: ['54-13=41', '90-28=62'] Exploring Operation: 41+62=103, Resulting Numbers: [103] 103,25 unequal: No Solution Exploring Operation: 41*62=2542, Resulting Numbers: [2542] 2542,25 unequal: No Solution Exploring Operation: 62-41=21, Resulting Numbers: [21] 21,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 25:[90, 13], Operations: ['54-13=41', '41-28=13'] Exploring Operation: 90*13=1170, Resulting Numbers: [1170] 1170,25 unequal: No Solution Exploring Operation: 90+13=103, Resulting Numbers: [103] 103,25 unequal: No Solution Exploring Operation: 90-13=77, Resulting Numbers: [77] 77,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 25:[90, 69], Operations: ['54-13=41', '28+41=69'] Exploring Operation: 90*69=6210, Resulting Numbers: [6210] 6210,25 unequal: No Solution Exploring Operation: 90+69=159, Resulting Numbers: [159] 159,25 unequal: No Solution Exploring Operation: 90-69=21, Resulting Numbers: [21] 21,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 25:[41, 118], Operations: ['54-13=41', '28+90=118'] Exploring Operation: 118-41=77, Resulting Numbers: [77] 77,25 unequal: No Solution Exploring Operation: 41*118=4838, Resulting Numbers: [4838] 4838,25 unequal: No Solution Exploring Operation: 41+118=159, Resulting Numbers: [159] 159,25 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: 25:[54, 28, 77], Operations: ['90-13=77'] Exploring Operation: 77-54=23, Resulting Numbers: [28, 23] Generated Node #0,4,0: 25:[28, 23] Operation: 77-54=23 Exploring Operation: 54+77=131, Resulting Numbers: [28, 131] Generated Node #0,4,1: 25:[28, 131] Operation: 54+77=131 Exploring Operation: 54-28=26, Resulting Numbers: [77, 26] Generated Node #0,4,2: 25:[77, 26] Operation: 54-28=26 Exploring Operation: 77-28=49, Resulting Numbers: [54, 49] Generated Node #0,4,3: 25:[54, 49] Operation: 77-28=49 Exploring Operation: 54+28=82, Resulting Numbers: [77, 82] Generated Node #0,4,4: 25:[77, 82] Operation: 54+28=82 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 25:[28, 23], Operations: ['90-13=77', '77-54=23'] Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 28+23=51, Resulting Numbers: [51] 51,25 unequal: No Solution Exploring Operation: 28*23=644, Resulting Numbers: [644] 644,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 25:[77, 26], Operations: ['90-13=77', '54-28=26'] Exploring Operation: 77+26=103, Resulting Numbers: [103] 103,25 unequal: No Solution Exploring Operation: 77*26=2002, Resulting Numbers: [2002] 2002,25 unequal: No Solution Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 25:[54, 49], Operations: ['90-13=77', '77-28=49'] Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 54*49=2646, Resulting Numbers: [2646] 2646,25 unequal: No Solution Exploring Operation: 54+49=103, Resulting Numbers: [103] 103,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 25:[28, 131], Operations: ['90-13=77', '54+77=131'] Exploring Operation: 131-28=103, Resulting Numbers: [103] 103,25 unequal: No Solution Exploring Operation: 28*131=3668, Resulting Numbers: [3668] 3668,25 unequal: No Solution Exploring Operation: 28+131=159, Resulting Numbers: [159] 159,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 25:[77, 82], Operations: ['90-13=77', '54+28=82'] Exploring Operation: 82-77=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 77*82=6314, Resulting Numbers: [6314] 6314,25 unequal: No Solution Exploring Operation: 77+82=159, Resulting Numbers: [159] 159,25 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: 25:[28, 23], Operations: ['90-54=36', '36-13=23'] Exploring Operation: 28+23=51, Resulting Numbers: [51] 51,25 unequal: No Solution Exploring Operation: 28*23=644, Resulting Numbers: [644] 644,25 unequal: No Solution Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,25 unequal: No Solution Moving to Node #0,0,0 Current State: 25:[13, 8], Operations: ['90-54=36', '36-28=8'] Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 13+8=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 13*8=104, Resulting Numbers: [104] 104,25 unequal: No Solution Moving to Node #0,0,3 Current State: 25:[36, 15], Operations: ['90-54=36', '28-13=15'] Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 36+15=51, Resulting Numbers: [51] 51,25 unequal: No Solution Exploring Operation: 36*15=540, Resulting Numbers: [540] 540,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[36, 41], Operations: ['90-54=36', '28+13=41'] Exploring Operation: 36*41=1476, Resulting Numbers: [1476] 1476,25 unequal: No Solution Exploring Operation: 36+41=77, Resulting Numbers: [77] 77,25 unequal: No Solution Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,25 unequal: No Solution Moving to Node #0,0,4 Current State: 25:[28, 49], Operations: ['90-54=36', '13+36=49'] Exploring Operation: 49-28=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 28+49=77, Resulting Numbers: [77] 77,25 unequal: No Solution Exploring Operation: 28*49=1372, Resulting Numbers: [1372] 1372,25 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 38, 82, 63, 71 ]
14
[ "38+82=120", "63+71=134", "134-120=14" ]
Current State: 14:[38, 82, 63, 71], Operations: [] Exploring Operation: 38+82=120, Resulting Numbers: [63, 71, 120] Generated Node #2: [63, 71, 120] from Operation: 38+82=120 Current State: 14:[63, 71, 120], Operations: ['38+82=120'] Exploring Operation: 63+71=134, Resulting Numbers: [120, 134] Generated Node #3: [120, 134] from Operation: 63+71=134 Current State: 14:[120, 134], Operations: ['38+82=120', '63+71=134'] Exploring Operation: 134-120=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[38, 82, 63, 71], Operations: [] Exploring Operation: 82-71=11, Resulting Numbers: [38, 63, 11] Generated Node #0,0: 14:[38, 63, 11] Operation: 82-71=11 Exploring Operation: 82-38=44, Resulting Numbers: [63, 71, 44] Generated Node #0,1: 14:[63, 71, 44] Operation: 82-38=44 Exploring Operation: 71-63=8, Resulting Numbers: [38, 82, 8] Generated Node #0,2: 14:[38, 82, 8] Operation: 71-63=8 Exploring Operation: 82-63=19, Resulting Numbers: [38, 71, 19] Generated Node #0,3: 14:[38, 71, 19] Operation: 82-63=19 Exploring Operation: 63-38=25, Resulting Numbers: [82, 71, 25] Generated Node #0,4: 14:[82, 71, 25] Operation: 63-38=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[38, 63, 11], Operations: ['82-71=11'] Exploring Operation: 63+11=74, Resulting Numbers: [38, 74] Generated Node #0,0,0: 14:[38, 74] Operation: 63+11=74 Exploring Operation: 38-11=27, Resulting Numbers: [63, 27] Generated Node #0,0,1: 14:[63, 27] Operation: 38-11=27 Exploring Operation: 63-38=25, Resulting Numbers: [11, 25] Generated Node #0,0,2: 14:[11, 25] Operation: 63-38=25 Exploring Operation: 38+11=49, Resulting Numbers: [63, 49] Generated Node #0,0,3: 14:[63, 49] Operation: 38+11=49 Exploring Operation: 63-11=52, Resulting Numbers: [38, 52] Generated Node #0,0,4: 14:[38, 52] Operation: 63-11=52 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 14:[11, 25], Operations: ['82-71=11', '63-38=25'] Exploring Operation: 11+25=36, Resulting Numbers: [36] 36,14 unequal: No Solution Exploring Operation: 11*25=275, Resulting Numbers: [275] 275,14 unequal: No Solution Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[38, 82, 63, 71], Operations: [] Exploring Operation: 82-71=11, Resulting Numbers: [38, 63, 11] Generated Node #0,0: 14:[38, 63, 11] Operation: 82-71=11 Moving to Node #0,0 Current State: 14:[38, 63, 11], Operations: ['82-71=11'] Exploring Operation: 63-38=25, Resulting Numbers: [11, 25] Generated Node #0,0,2: 14:[11, 25] Operation: 63-38=25 Moving to Node #0,0,2 Current State: 14:[11, 25], Operations: ['82-71=11', '63-38=25'] Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 98, 6, 24, 2 ]
77
[ "98-24=74", "6/2=3", "74+3=77" ]
Current State: 77:[98, 6, 24, 2], Operations: [] Exploring Operation: 98-24=74, Resulting Numbers: [6, 2, 74] Generated Node #2: [6, 2, 74] from Operation: 98-24=74 Current State: 77:[6, 2, 74], Operations: ['98-24=74'] Exploring Operation: 6/2=3, Resulting Numbers: [74, 3] Generated Node #3: [74, 3] from Operation: 6/2=3 Current State: 77:[74, 3], Operations: ['98-24=74', '6/2=3'] Exploring Operation: 74+3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[98, 6, 24, 2], Operations: [] Exploring Operation: 98-24=74, Resulting Numbers: [6, 2, 74] Generated Node #0,0: 77:[6, 2, 74] Operation: 98-24=74 Moving to Node #0,0 Current State: 77:[6, 2, 74], Operations: ['98-24=74'] Exploring Operation: 2+74=76, Resulting Numbers: [6, 76] Generated Node #0,0,0: 77:[6, 76] Operation: 2+74=76 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[6, 76], Operations: ['98-24=74', '2+74=76'] Exploring Operation: 6+76=82, Resulting Numbers: [82] 82,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 65, 74, 86, 12 ]
79
[ "86-74=12", "12*12=144", "144-65=79" ]
Current State: 79:[65, 74, 86, 12], Operations: [] Exploring Operation: 86-74=12, Resulting Numbers: [65, 12, 12] Generated Node #2: [65, 12, 12] from Operation: 86-74=12 Current State: 79:[65, 12, 12], Operations: ['86-74=12'] Exploring Operation: 12*12=144, Resulting Numbers: [65, 144] Generated Node #3: [65, 144] from Operation: 12*12=144 Current State: 79:[65, 144], Operations: ['86-74=12', '12*12=144'] Exploring Operation: 144-65=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[65, 74, 86, 12], Operations: [] Exploring Operation: 65+12=77, Resulting Numbers: [74, 86, 77] Generated Node #0,0: 79:[74, 86, 77] Operation: 65+12=77 Exploring Operation: 86-12=74, Resulting Numbers: [65, 74, 74] Generated Node #0,1: 79:[65, 74, 74] Operation: 86-12=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[74, 86, 77], Operations: ['65+12=77'] Exploring Operation: 86-74=12, Resulting Numbers: [77, 12] Generated Node #0,0,0: 79:[77, 12] Operation: 86-74=12 Exploring Operation: 86-77=9, Resulting Numbers: [74, 9] Generated Node #0,0,1: 79:[74, 9] Operation: 86-77=9 Moving to Node #0,0,0 Current State: 79:[77, 12], Operations: ['65+12=77', '86-74=12'] Exploring Operation: 77+12=89, Resulting Numbers: [89] 89,79 unequal: No Solution Exploring Operation: 77-12=65, Resulting Numbers: [65] 65,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[74, 9], Operations: ['65+12=77', '86-77=9'] Exploring Operation: 74-9=65, Resulting Numbers: [65] 65,79 unequal: No Solution Exploring Operation: 74+9=83, Resulting Numbers: [83] 83,79 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 #0,1 Current State: 79:[65, 74, 74], Operations: ['86-12=74'] Exploring Operation: 65+74=139, Resulting Numbers: [74, 139] Generated Node #0,1,0: 79:[74, 139] Operation: 65+74=139 Exploring Operation: 65+74=139, Resulting Numbers: [74, 139] Generated Node #0,1,1: 79:[74, 139] Operation: 65+74=139 Moving to Node #0,1,0 Current State: 79:[74, 139], Operations: ['86-12=74', '65+74=139'] Exploring Operation: 74+139=213, Resulting Numbers: [213] 213,79 unequal: No Solution Exploring Operation: 139-74=65, Resulting Numbers: [65] 65,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[74, 139], Operations: ['86-12=74', '65+74=139'] Exploring Operation: 139-74=65, Resulting Numbers: [65] 65,79 unequal: No Solution Exploring Operation: 74+139=213, Resulting Numbers: [213] 213,79 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
[ 89, 61, 59, 79 ]
84
[ "89+79=168", "61-59=2", "168/2=84" ]
Current State: 84:[89, 61, 59, 79], Operations: [] Exploring Operation: 89+79=168, Resulting Numbers: [61, 59, 168] Generated Node #2: [61, 59, 168] from Operation: 89+79=168 Current State: 84:[61, 59, 168], Operations: ['89+79=168'] Exploring Operation: 61-59=2, Resulting Numbers: [168, 2] Generated Node #3: [168, 2] from Operation: 61-59=2 Current State: 84:[168, 2], Operations: ['89+79=168', '61-59=2'] Exploring Operation: 168/2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[89, 61, 59, 79], Operations: [] Exploring Operation: 89-61=28, Resulting Numbers: [59, 79, 28] Generated Node #0,0: 84:[59, 79, 28] Operation: 89-61=28 Exploring Operation: 61-59=2, Resulting Numbers: [89, 79, 2] Generated Node #0,1: 84:[89, 79, 2] Operation: 61-59=2 Moving to Node #0,1 Current State: 84:[89, 79, 2], Operations: ['61-59=2'] Exploring Operation: 89-2=87, Resulting Numbers: [79, 87] Generated Node #0,1,0: 84:[79, 87] Operation: 89-2=87 Exploring Operation: 89-79=10, Resulting Numbers: [2, 10] Generated Node #0,1,1: 84:[2, 10] Operation: 89-79=10 Moving to Node #0,0 Current State: 84:[59, 79, 28], Operations: ['89-61=28'] Exploring Operation: 59+28=87, Resulting Numbers: [79, 87] Generated Node #0,0,0: 84:[79, 87] Operation: 59+28=87 Exploring Operation: 79-59=20, Resulting Numbers: [28, 20] Generated Node #0,0,1: 84:[28, 20] Operation: 79-59=20 Moving to Node #0,0,1 Current State: 84:[28, 20], Operations: ['89-61=28', '79-59=20'] Exploring Operation: 28+20=48, Resulting Numbers: [48] 48,84 unequal: No Solution Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[2, 10], Operations: ['61-59=2', '89-79=10'] Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[79, 87], Operations: ['61-59=2', '89-2=87'] Exploring Operation: 79+87=166, Resulting Numbers: [166] 166,84 unequal: No Solution Exploring Operation: 87-79=8, Resulting Numbers: [8] 8,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[79, 87], Operations: ['89-61=28', '59+28=87'] Exploring Operation: 87-79=8, Resulting Numbers: [8] 8,84 unequal: No Solution Exploring Operation: 79+87=166, Resulting Numbers: [166] 166,84 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 8, 59, 41, 43 ]
17
[ "8+59=67", "41+43=84", "84-67=17" ]
Current State: 17:[8, 59, 41, 43], Operations: [] Exploring Operation: 8+59=67, Resulting Numbers: [41, 43, 67] Generated Node #2: [41, 43, 67] from Operation: 8+59=67 Current State: 17:[41, 43, 67], Operations: ['8+59=67'] Exploring Operation: 41+43=84, Resulting Numbers: [67, 84] Generated Node #3: [67, 84] from Operation: 41+43=84 Current State: 17:[67, 84], Operations: ['8+59=67', '41+43=84'] Exploring Operation: 84-67=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[8, 59, 41, 43], Operations: [] Exploring Operation: 59-41=18, Resulting Numbers: [8, 43, 18] Generated Node #0,0: 17:[8, 43, 18] Operation: 59-41=18 Exploring Operation: 59-43=16, Resulting Numbers: [8, 41, 16] Generated Node #0,1: 17:[8, 41, 16] Operation: 59-43=16 Exploring Operation: 43-41=2, Resulting Numbers: [8, 59, 2] Generated Node #0,2: 17:[8, 59, 2] Operation: 43-41=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[8, 41, 16], Operations: ['59-43=16'] Exploring Operation: 41-8=33, Resulting Numbers: [16, 33] Generated Node #0,1,0: 17:[16, 33] Operation: 41-8=33 Exploring Operation: 41-16=25, Resulting Numbers: [8, 25] Generated Node #0,1,1: 17:[8, 25] Operation: 41-16=25 Exploring Operation: 8+16=24, Resulting Numbers: [41, 24] Generated Node #0,1,2: 17:[41, 24] Operation: 8+16=24 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 17:[16, 33], Operations: ['59-43=16', '41-8=33'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[8, 59, 41, 43], Operations: [] Exploring Operation: 59-43=16, Resulting Numbers: [8, 41, 16] Generated Node #0,1: 17:[8, 41, 16] Operation: 59-43=16 Moving to Node #0,1 Current State: 17:[8, 41, 16], Operations: ['59-43=16'] Exploring Operation: 41-8=33, Resulting Numbers: [16, 33] Generated Node #0,1,0: 17:[16, 33] Operation: 41-8=33 Moving to Node #0,1,0 Current State: 17:[16, 33], Operations: ['59-43=16', '41-8=33'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 95, 16, 94, 78 ]
63
[ "95-16=79", "94-78=16", "79-16=63" ]
Current State: 63:[95, 16, 94, 78], Operations: [] Exploring Operation: 95-16=79, Resulting Numbers: [94, 78, 79] Generated Node #2: [94, 78, 79] from Operation: 95-16=79 Current State: 63:[94, 78, 79], Operations: ['95-16=79'] Exploring Operation: 94-78=16, Resulting Numbers: [79, 16] Generated Node #3: [79, 16] from Operation: 94-78=16 Current State: 63:[79, 16], Operations: ['95-16=79', '94-78=16'] Exploring Operation: 79-16=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[95, 16, 94, 78], Operations: [] Exploring Operation: 95-94=1, Resulting Numbers: [16, 78, 1] Generated Node #0,0: 63:[16, 78, 1] Operation: 95-94=1 Moving to Node #0,0 Current State: 63:[16, 78, 1], Operations: ['95-94=1'] Exploring Operation: 78-16=62, Resulting Numbers: [1, 62] Generated Node #0,0,0: 63:[1, 62] Operation: 78-16=62 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[1, 62], Operations: ['95-94=1', '78-16=62'] Exploring Operation: 1+62=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[95, 16, 94, 78], Operations: [] Exploring Operation: 95-94=1, Resulting Numbers: [16, 78, 1] Generated Node #0,0: 63:[16, 78, 1] Operation: 95-94=1 Moving to Node #0,0 Current State: 63:[16, 78, 1], Operations: ['95-94=1'] Exploring Operation: 78-16=62, Resulting Numbers: [1, 62] Generated Node #0,0,0: 63:[1, 62] Operation: 78-16=62 Moving to Node #0,0,0 Current State: 63:[1, 62], Operations: ['95-94=1', '78-16=62'] Exploring Operation: 1+62=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 21, 52, 13, 20 ]
95
[ "20-13=7", "21*7=147", "147-52=95" ]
Current State: 95:[21, 52, 13, 20], Operations: [] Exploring Operation: 20-13=7, Resulting Numbers: [21, 52, 7] Generated Node #2: [21, 52, 7] from Operation: 20-13=7 Current State: 95:[21, 52, 7], Operations: ['20-13=7'] Exploring Operation: 21*7=147, Resulting Numbers: [52, 147] Generated Node #3: [52, 147] from Operation: 21*7=147 Current State: 95:[52, 147], Operations: ['20-13=7', '21*7=147'] Exploring Operation: 147-52=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[21, 52, 13, 20], Operations: [] Exploring Operation: 52-20=32, Resulting Numbers: [21, 13, 32] Generated Node #0,0: 95:[21, 13, 32] Operation: 52-20=32 Exploring Operation: 52-21=31, Resulting Numbers: [13, 20, 31] Generated Node #0,1: 95:[13, 20, 31] Operation: 52-21=31 Exploring Operation: 52/13=4, Resulting Numbers: [21, 20, 4] Generated Node #0,2: 95:[21, 20, 4] Operation: 52/13=4 Moving to Node #0,2 Current State: 95:[21, 20, 4], Operations: ['52/13=4'] Exploring Operation: 21-20=1, Resulting Numbers: [4, 1] Generated Node #0,2,0: 95:[4, 1] Operation: 21-20=1 Exploring Operation: 20/4=5, Resulting Numbers: [21, 5] Generated Node #0,2,1: 95:[21, 5] Operation: 20/4=5 Exploring Operation: 21-4=17, Resulting Numbers: [20, 17] Generated Node #0,2,2: 95:[20, 17] Operation: 21-4=17 Moving to Node #0,1 Current State: 95:[13, 20, 31], Operations: ['52-21=31'] Exploring Operation: 20-13=7, Resulting Numbers: [31, 7] Generated Node #0,1,0: 95:[31, 7] Operation: 20-13=7 Exploring Operation: 31-13=18, Resulting Numbers: [20, 18] Generated Node #0,1,1: 95:[20, 18] Operation: 31-13=18 Exploring Operation: 31-20=11, Resulting Numbers: [13, 11] Generated Node #0,1,2: 95:[13, 11] Operation: 31-20=11 Moving to Node #0,0 Current State: 95:[21, 13, 32], Operations: ['52-20=32'] Exploring Operation: 32-21=11, Resulting Numbers: [13, 11] Generated Node #0,0,0: 95:[13, 11] Operation: 32-21=11 Exploring Operation: 21-13=8, Resulting Numbers: [32, 8] Generated Node #0,0,1: 95:[32, 8] Operation: 21-13=8 Exploring Operation: 32-13=19, Resulting Numbers: [21, 19] Generated Node #0,0,2: 95:[21, 19] Operation: 32-13=19 Moving to Node #0,2,1 Current State: 95:[21, 5], Operations: ['52/13=4', '20/4=5'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,95 unequal: No Solution Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,95 unequal: No Solution Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,95 unequal: No Solution Moving to Node #0,0,2 Current State: 95:[21, 19], Operations: ['52-20=32', '32-13=19'] Exploring Operation: 21+19=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 21*19=399, Resulting Numbers: [399] 399,95 unequal: No Solution Exploring Operation: 21-19=2, Resulting Numbers: [2] 2,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[20, 18], Operations: ['52-21=31', '31-13=18'] Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,95 unequal: No Solution Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,95 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,95 unequal: No Solution Moving to Node #0,2,2 Current State: 95:[20, 17], Operations: ['52/13=4', '21-4=17'] Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,95 unequal: No Solution Exploring Operation: 20*17=340, Resulting Numbers: [340] 340,95 unequal: No Solution Exploring Operation: 20+17=37, Resulting Numbers: [37] 37,95 unequal: No Solution Moving to Node #0,2,0 Current State: 95:[4, 1], Operations: ['52/13=4', '21-20=1'] Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,95 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,95 unequal: No Solution Moving to Node #0,1,2 Current State: 95:[13, 11], Operations: ['52-21=31', '31-20=11'] Exploring Operation: 13*11=143, Resulting Numbers: [143] 143,95 unequal: No Solution Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,95 unequal: No Solution Moving to Node #0,0,0 Current State: 95:[13, 11], Operations: ['52-20=32', '32-21=11'] Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,95 unequal: No Solution Exploring Operation: 13*11=143, Resulting Numbers: [143] 143,95 unequal: No Solution Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,95 unequal: No Solution Moving to Node #0,1,0 Current State: 95:[31, 7], Operations: ['52-21=31', '20-13=7'] Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 31+7=38, Resulting Numbers: [38] 38,95 unequal: No Solution Exploring Operation: 31*7=217, Resulting Numbers: [217] 217,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[32, 8], Operations: ['52-20=32', '21-13=8'] Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,95 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 32+8=40, Resulting Numbers: [40] 40,95 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 55, 68, 35, 37 ]
85
[ "68-55=13", "35+37=72", "13+72=85" ]
Current State: 85:[55, 68, 35, 37], Operations: [] Exploring Operation: 68-55=13, Resulting Numbers: [35, 37, 13] Generated Node #2: [35, 37, 13] from Operation: 68-55=13 Current State: 85:[35, 37, 13], Operations: ['68-55=13'] Exploring Operation: 35+37=72, Resulting Numbers: [13, 72] Generated Node #3: [13, 72] from Operation: 35+37=72 Current State: 85:[13, 72], Operations: ['68-55=13', '35+37=72'] Exploring Operation: 13+72=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[55, 68, 35, 37], Operations: [] Exploring Operation: 55-35=20, Resulting Numbers: [68, 37, 20] Generated Node #0,0: 85:[68, 37, 20] Operation: 55-35=20 Exploring Operation: 55-37=18, Resulting Numbers: [68, 35, 18] Generated Node #0,1: 85:[68, 35, 18] Operation: 55-37=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[68, 35, 18], Operations: ['55-37=18'] Exploring Operation: 68-35=33, Resulting Numbers: [18, 33] Generated Node #0,1,0: 85:[18, 33] Operation: 68-35=33 Exploring Operation: 35-18=17, Resulting Numbers: [68, 17] Generated Node #0,1,1: 85:[68, 17] Operation: 35-18=17 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 85:[18, 33], Operations: ['55-37=18', '68-35=33'] Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,85 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 85:[68, 17], Operations: ['55-37=18', '35-18=17'] Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 68+17=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[55, 68, 35, 37], Operations: [] Exploring Operation: 55-37=18, Resulting Numbers: [68, 35, 18] Generated Node #0,1: 85:[68, 35, 18] Operation: 55-37=18 Moving to Node #0,1 Current State: 85:[68, 35, 18], Operations: ['55-37=18'] Exploring Operation: 35-18=17, Resulting Numbers: [68, 17] Generated Node #0,1,1: 85:[68, 17] Operation: 35-18=17 Moving to Node #0,1,1 Current State: 85:[68, 17], Operations: ['55-37=18', '35-18=17'] Exploring Operation: 68+17=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 5, 90, 37, 76 ]
57
[ "90/5=18", "76-37=39", "18+39=57" ]
Current State: 57:[5, 90, 37, 76], Operations: [] Exploring Operation: 90/5=18, Resulting Numbers: [37, 76, 18] Generated Node #2: [37, 76, 18] from Operation: 90/5=18 Current State: 57:[37, 76, 18], Operations: ['90/5=18'] Exploring Operation: 76-37=39, Resulting Numbers: [18, 39] Generated Node #3: [18, 39] from Operation: 76-37=39 Current State: 57:[18, 39], Operations: ['90/5=18', '76-37=39'] Exploring Operation: 18+39=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[5, 90, 37, 76], Operations: [] Exploring Operation: 90-5=85, Resulting Numbers: [37, 76, 85] Generated Node #0,0: 57:[37, 76, 85] Operation: 90-5=85 Exploring Operation: 90-37=53, Resulting Numbers: [5, 76, 53] Generated Node #0,1: 57:[5, 76, 53] Operation: 90-37=53 Exploring Operation: 90-76=14, Resulting Numbers: [5, 37, 14] Generated Node #0,2: 57:[5, 37, 14] Operation: 90-76=14 Exploring Operation: 90/5=18, Resulting Numbers: [37, 76, 18] Generated Node #0,3: 57:[37, 76, 18] Operation: 90/5=18 Exploring Operation: 76-37=39, Resulting Numbers: [5, 90, 39] Generated Node #0,4: 57:[5, 90, 39] Operation: 76-37=39 Moving to Node #0,1 Current State: 57:[5, 76, 53], Operations: ['90-37=53'] Exploring Operation: 53-5=48, Resulting Numbers: [76, 48] Generated Node #0,1,0: 57:[76, 48] Operation: 53-5=48 Exploring Operation: 5+76=81, Resulting Numbers: [53, 81] Generated Node #0,1,1: 57:[53, 81] Operation: 5+76=81 Exploring Operation: 5+53=58, Resulting Numbers: [76, 58] Generated Node #0,1,2: 57:[76, 58] Operation: 5+53=58 Exploring Operation: 76-53=23, Resulting Numbers: [5, 23] Generated Node #0,1,3: 57:[5, 23] Operation: 76-53=23 Exploring Operation: 76-5=71, Resulting Numbers: [53, 71] Generated Node #0,1,4: 57:[53, 71] Operation: 76-5=71 Moving to Node #0,2 Current State: 57:[5, 37, 14], Operations: ['90-76=14'] Exploring Operation: 37-5=32, Resulting Numbers: [14, 32] Generated Node #0,2,0: 57:[14, 32] Operation: 37-5=32 Exploring Operation: 5+14=19, Resulting Numbers: [37, 19] Generated Node #0,2,1: 57:[37, 19] Operation: 5+14=19 Exploring Operation: 37+14=51, Resulting Numbers: [5, 51] Generated Node #0,2,2: 57:[5, 51] Operation: 37+14=51 Exploring Operation: 37-14=23, Resulting Numbers: [5, 23] Generated Node #0,2,3: 57:[5, 23] Operation: 37-14=23 Exploring Operation: 5+37=42, Resulting Numbers: [14, 42] Generated Node #0,2,4: 57:[14, 42] Operation: 5+37=42 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 57:[5, 23], Operations: ['90-76=14', '37-14=23'] Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,57 unequal: No Solution Exploring Operation: 5*23=115, Resulting Numbers: [115] 115,57 unequal: No Solution Exploring Operation: 5+23=28, Resulting Numbers: [28] 28,57 unequal: No Solution No 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: 57:[5, 51], Operations: ['90-76=14', '37+14=51'] Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 5*51=255, Resulting Numbers: [255] 255,57 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,57 unequal: No Solution No 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: 57:[14, 32], Operations: ['90-76=14', '37-5=32'] Exploring Operation: 14+32=46, Resulting Numbers: [46] 46,57 unequal: No Solution Exploring Operation: 14*32=448, Resulting Numbers: [448] 448,57 unequal: No Solution Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,57 unequal: No Solution No 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: 57:[37, 19], Operations: ['90-76=14', '5+14=19'] Exploring Operation: 37+19=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,57 unequal: No Solution Exploring Operation: 37*19=703, Resulting Numbers: [703] 703,57 unequal: No Solution No 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: 57:[14, 42], Operations: ['90-76=14', '5+37=42'] Exploring Operation: 42-14=28, Resulting Numbers: [28] 28,57 unequal: No Solution Exploring Operation: 14*42=588, Resulting Numbers: [588] 588,57 unequal: No Solution Exploring Operation: 42/14=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 14+42=56, Resulting Numbers: [56] 56,57 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: 57:[37, 76, 18], Operations: ['90/5=18'] Exploring Operation: 37+18=55, Resulting Numbers: [76, 55] Generated Node #0,3,0: 57:[76, 55] Operation: 37+18=55 Exploring Operation: 76+18=94, Resulting Numbers: [37, 94] Generated Node #0,3,1: 57:[37, 94] Operation: 76+18=94 Exploring Operation: 37-18=19, Resulting Numbers: [76, 19] Generated Node #0,3,2: 57:[76, 19] Operation: 37-18=19 Exploring Operation: 76-18=58, Resulting Numbers: [37, 58] Generated Node #0,3,3: 57:[37, 58] Operation: 76-18=58 Exploring Operation: 76-37=39, Resulting Numbers: [18, 39] Generated Node #0,3,4: 57:[18, 39] Operation: 76-37=39 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 57:[76, 19], Operations: ['90/5=18', '37-18=19'] Exploring Operation: 76+19=95, Resulting Numbers: [95] 95,57 unequal: No Solution Exploring Operation: 76*19=1444, Resulting Numbers: [1444] 1444,57 unequal: No Solution Exploring Operation: 76/19=4, Resulting Numbers: [4] 4,57 unequal: No Solution Exploring Operation: 76-19=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[5, 90, 37, 76], Operations: [] Exploring Operation: 90/5=18, Resulting Numbers: [37, 76, 18] Generated Node #0,3: 57:[37, 76, 18] Operation: 90/5=18 Moving to Node #0,3 Current State: 57:[37, 76, 18], Operations: ['90/5=18'] Exploring Operation: 37-18=19, Resulting Numbers: [76, 19] Generated Node #0,3,2: 57:[76, 19] Operation: 37-18=19 Moving to Node #0,3,2 Current State: 57:[76, 19], Operations: ['90/5=18', '37-18=19'] Exploring Operation: 76-19=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.961806
hs_5
sum_heuristic
[ 70, 56, 46, 47 ]
79
[ "70-56=14", "46+47=93", "93-14=79" ]
Current State: 79:[70, 56, 46, 47], Operations: [] Exploring Operation: 70-56=14, Resulting Numbers: [46, 47, 14] Generated Node #2: [46, 47, 14] from Operation: 70-56=14 Current State: 79:[46, 47, 14], Operations: ['70-56=14'] Exploring Operation: 46+47=93, Resulting Numbers: [14, 93] Generated Node #3: [14, 93] from Operation: 46+47=93 Current State: 79:[14, 93], Operations: ['70-56=14', '46+47=93'] Exploring Operation: 93-14=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[70, 56, 46, 47], Operations: [] Exploring Operation: 56+47=103, Resulting Numbers: [70, 46, 103] Generated Node #0,0: 79:[70, 46, 103] Operation: 56+47=103 Exploring Operation: 56+46=102, Resulting Numbers: [70, 47, 102] Generated Node #0,1: 79:[70, 47, 102] Operation: 56+46=102 Exploring Operation: 46+47=93, Resulting Numbers: [70, 56, 93] Generated Node #0,2: 79:[70, 56, 93] Operation: 46+47=93 Exploring Operation: 70+47=117, Resulting Numbers: [56, 46, 117] Generated Node #0,3: 79:[56, 46, 117] Operation: 70+47=117 Exploring Operation: 70+46=116, Resulting Numbers: [56, 47, 116] Generated Node #0,4: 79:[56, 47, 116] Operation: 70+46=116 Moving to Node #0,2 Current State: 79:[70, 56, 93], Operations: ['46+47=93'] Exploring Operation: 93-56=37, Resulting Numbers: [70, 37] Generated Node #0,2,0: 79:[70, 37] Operation: 93-56=37 Exploring Operation: 70+56=126, Resulting Numbers: [93, 126] Generated Node #0,2,1: 79:[93, 126] Operation: 70+56=126 Exploring Operation: 70-56=14, Resulting Numbers: [93, 14] Generated Node #0,2,2: 79:[93, 14] Operation: 70-56=14 Exploring Operation: 56+93=149, Resulting Numbers: [70, 149] Generated Node #0,2,3: 79:[70, 149] Operation: 56+93=149 Exploring Operation: 93-70=23, Resulting Numbers: [56, 23] Generated Node #0,2,4: 79:[56, 23] Operation: 93-70=23 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[70, 37], Operations: ['46+47=93', '93-56=37'] Exploring Operation: 70*37=2590, Resulting Numbers: [2590] 2590,79 unequal: No Solution Exploring Operation: 70-37=33, Resulting Numbers: [33] 33,79 unequal: No Solution Exploring Operation: 70+37=107, Resulting Numbers: [107] 107,79 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 #0,2,1 Current State: 79:[93, 126], Operations: ['46+47=93', '70+56=126'] Exploring Operation: 93+126=219, Resulting Numbers: [219] 219,79 unequal: No Solution Exploring Operation: 126-93=33, Resulting Numbers: [33] 33,79 unequal: No Solution Exploring Operation: 93*126=11718, Resulting Numbers: [11718] 11718,79 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 #0,2,2 Current State: 79:[93, 14], Operations: ['46+47=93', '70-56=14'] Exploring Operation: 93*14=1302, Resulting Numbers: [1302] 1302,79 unequal: No Solution Exploring Operation: 93+14=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 93-14=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[70, 56, 46, 47], Operations: [] Exploring Operation: 46+47=93, Resulting Numbers: [70, 56, 93] Generated Node #0,2: 79:[70, 56, 93] Operation: 46+47=93 Moving to Node #0,2 Current State: 79:[70, 56, 93], Operations: ['46+47=93'] Exploring Operation: 70-56=14, Resulting Numbers: [93, 14] Generated Node #0,2,2: 79:[93, 14] Operation: 70-56=14 Moving to Node #0,2,2 Current State: 79:[93, 14], Operations: ['46+47=93', '70-56=14'] Exploring Operation: 93-14=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 55, 38, 30, 42 ]
89
[ "55-38=17", "30+42=72", "17+72=89" ]
Current State: 89:[55, 38, 30, 42], Operations: [] Exploring Operation: 55-38=17, Resulting Numbers: [30, 42, 17] Generated Node #2: [30, 42, 17] from Operation: 55-38=17 Current State: 89:[30, 42, 17], Operations: ['55-38=17'] Exploring Operation: 30+42=72, Resulting Numbers: [17, 72] Generated Node #3: [17, 72] from Operation: 30+42=72 Current State: 89:[17, 72], Operations: ['55-38=17', '30+42=72'] Exploring Operation: 17+72=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[55, 38, 30, 42], Operations: [] Exploring Operation: 55+30=85, Resulting Numbers: [38, 42, 85] Generated Node #0,0: 89:[38, 42, 85] Operation: 55+30=85 Exploring Operation: 38+30=68, Resulting Numbers: [55, 42, 68] Generated Node #0,1: 89:[55, 42, 68] Operation: 38+30=68 Moving to Node #0,0 Current State: 89:[38, 42, 85], Operations: ['55+30=85'] Exploring Operation: 38+85=123, Resulting Numbers: [42, 123] Generated Node #0,0,0: 89:[42, 123] Operation: 38+85=123 Exploring Operation: 38+42=80, Resulting Numbers: [85, 80] Generated Node #0,0,1: 89:[85, 80] Operation: 38+42=80 Moving to Node #0,1 Current State: 89:[55, 42, 68], Operations: ['38+30=68'] Exploring Operation: 42+68=110, Resulting Numbers: [55, 110] Generated Node #0,1,0: 89:[55, 110] Operation: 42+68=110 Exploring Operation: 55+42=97, Resulting Numbers: [68, 97] Generated Node #0,1,1: 89:[68, 97] Operation: 55+42=97 Moving to Node #0,0,1 Current State: 89:[85, 80], Operations: ['55+30=85', '38+42=80'] Exploring Operation: 85-80=5, Resulting Numbers: [5] 5,89 unequal: No Solution Exploring Operation: 85+80=165, Resulting Numbers: [165] 165,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[68, 97], Operations: ['38+30=68', '55+42=97'] Exploring Operation: 68+97=165, Resulting Numbers: [165] 165,89 unequal: No Solution Exploring Operation: 97-68=29, Resulting Numbers: [29] 29,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[55, 110], Operations: ['38+30=68', '42+68=110'] Exploring Operation: 110-55=55, Resulting Numbers: [55] 55,89 unequal: No Solution Exploring Operation: 55+110=165, Resulting Numbers: [165] 165,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[42, 123], Operations: ['55+30=85', '38+85=123'] Exploring Operation: 42+123=165, Resulting Numbers: [165] 165,89 unequal: No Solution Exploring Operation: 123-42=81, Resulting Numbers: [81] 81,89 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 28, 37, 97, 24 ]
51
[ "28-24=4", "37*4=148", "148-97=51" ]
Current State: 51:[28, 37, 97, 24], Operations: [] Exploring Operation: 28-24=4, Resulting Numbers: [37, 97, 4] Generated Node #2: [37, 97, 4] from Operation: 28-24=4 Current State: 51:[37, 97, 4], Operations: ['28-24=4'] Exploring Operation: 37*4=148, Resulting Numbers: [97, 148] Generated Node #3: [97, 148] from Operation: 37*4=148 Current State: 51:[97, 148], Operations: ['28-24=4', '37*4=148'] Exploring Operation: 148-97=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[28, 37, 97, 24], Operations: [] Exploring Operation: 97-28=69, Resulting Numbers: [37, 24, 69] Generated Node #0,0: 51:[37, 24, 69] Operation: 97-28=69 Exploring Operation: 97-24=73, Resulting Numbers: [28, 37, 73] Generated Node #0,1: 51:[28, 37, 73] Operation: 97-24=73 Exploring Operation: 97-37=60, Resulting Numbers: [28, 24, 60] Generated Node #0,2: 51:[28, 24, 60] Operation: 97-37=60 Moving to Node #0,2 Current State: 51:[28, 24, 60], Operations: ['97-37=60'] Exploring Operation: 28+24=52, Resulting Numbers: [60, 52] Generated Node #0,2,0: 51:[60, 52] Operation: 28+24=52 Exploring Operation: 60-28=32, Resulting Numbers: [24, 32] Generated Node #0,2,1: 51:[24, 32] Operation: 60-28=32 Exploring Operation: 28-24=4, Resulting Numbers: [60, 4] Generated Node #0,2,2: 51:[60, 4] Operation: 28-24=4 Moving to Node #0,0 Current State: 51:[37, 24, 69], Operations: ['97-28=69'] Exploring Operation: 69-37=32, Resulting Numbers: [24, 32] Generated Node #0,0,0: 51:[24, 32] Operation: 69-37=32 Exploring Operation: 69-24=45, Resulting Numbers: [37, 45] Generated Node #0,0,1: 51:[37, 45] Operation: 69-24=45 Exploring Operation: 37-24=13, Resulting Numbers: [69, 13] Generated Node #0,0,2: 51:[69, 13] Operation: 37-24=13 Moving to Node #0,1 Current State: 51:[28, 37, 73], Operations: ['97-24=73'] Exploring Operation: 37-28=9, Resulting Numbers: [73, 9] Generated Node #0,1,0: 51:[73, 9] Operation: 37-28=9 Exploring Operation: 73-37=36, Resulting Numbers: [28, 36] Generated Node #0,1,1: 51:[28, 36] Operation: 73-37=36 Exploring Operation: 73-28=45, Resulting Numbers: [37, 45] Generated Node #0,1,2: 51:[37, 45] Operation: 73-28=45 Moving to Node #0,2,0 Current State: 51:[60, 52], Operations: ['97-37=60', '28+24=52'] Exploring Operation: 60*52=3120, Resulting Numbers: [3120] 3120,51 unequal: No Solution Exploring Operation: 60-52=8, Resulting Numbers: [8] 8,51 unequal: No Solution Exploring Operation: 60+52=112, Resulting Numbers: [112] 112,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[60, 4], Operations: ['97-37=60', '28-24=4'] Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 60+4=64, Resulting Numbers: [64] 64,51 unequal: No Solution Exploring Operation: 60-4=56, Resulting Numbers: [56] 56,51 unequal: No Solution Moving to Node #0,1,2 Current State: 51:[37, 45], Operations: ['97-24=73', '73-28=45'] Exploring Operation: 37*45=1665, Resulting Numbers: [1665] 1665,51 unequal: No Solution Exploring Operation: 45-37=8, Resulting Numbers: [8] 8,51 unequal: No Solution Exploring Operation: 37+45=82, Resulting Numbers: [82] 82,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[37, 45], Operations: ['97-28=69', '69-24=45'] Exploring Operation: 45-37=8, Resulting Numbers: [8] 8,51 unequal: No Solution Exploring Operation: 37+45=82, Resulting Numbers: [82] 82,51 unequal: No Solution Exploring Operation: 37*45=1665, Resulting Numbers: [1665] 1665,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[24, 32], Operations: ['97-37=60', '60-28=32'] Exploring Operation: 24+32=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 24*32=768, Resulting Numbers: [768] 768,51 unequal: No Solution Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[69, 13], Operations: ['97-28=69', '37-24=13'] Exploring Operation: 69+13=82, Resulting Numbers: [82] 82,51 unequal: No Solution Exploring Operation: 69-13=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 69*13=897, Resulting Numbers: [897] 897,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[24, 32], Operations: ['97-28=69', '69-37=32'] Exploring Operation: 24+32=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,51 unequal: No Solution Exploring Operation: 24*32=768, Resulting Numbers: [768] 768,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[28, 36], Operations: ['97-24=73', '73-37=36'] Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,51 unequal: No Solution Exploring Operation: 28+36=64, Resulting Numbers: [64] 64,51 unequal: No Solution Exploring Operation: 28*36=1008, Resulting Numbers: [1008] 1008,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[73, 9], Operations: ['97-24=73', '37-28=9'] Exploring Operation: 73-9=64, Resulting Numbers: [64] 64,51 unequal: No Solution Exploring Operation: 73*9=657, Resulting Numbers: [657] 657,51 unequal: No Solution Exploring Operation: 73+9=82, Resulting Numbers: [82] 82,51 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 59, 69, 32, 64 ]
42
[ "69-59=10", "64-32=32", "10+32=42" ]
Current State: 42:[59, 69, 32, 64], Operations: [] Exploring Operation: 69-59=10, Resulting Numbers: [32, 64, 10] Generated Node #2: [32, 64, 10] from Operation: 69-59=10 Current State: 42:[32, 64, 10], Operations: ['69-59=10'] Exploring Operation: 64-32=32, Resulting Numbers: [10, 32] Generated Node #3: [10, 32] from Operation: 64-32=32 Current State: 42:[10, 32], Operations: ['69-59=10', '64-32=32'] Exploring Operation: 10+32=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[59, 69, 32, 64], Operations: [] Exploring Operation: 69-64=5, Resulting Numbers: [59, 32, 5] Generated Node #0,0: 42:[59, 32, 5] Operation: 69-64=5 Moving to Node #0,0 Current State: 42:[59, 32, 5], Operations: ['69-64=5'] Exploring Operation: 59-32=27, Resulting Numbers: [5, 27] Generated Node #0,0,0: 42:[5, 27] Operation: 59-32=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[5, 27], Operations: ['69-64=5', '59-32=27'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 51, 29, 33, 60 ]
57
[ "51*33=1683", "29*60=1740", "1740-1683=57" ]
Current State: 57:[51, 29, 33, 60], Operations: [] Exploring Operation: 51*33=1683, Resulting Numbers: [29, 60, 1683] Generated Node #2: [29, 60, 1683] from Operation: 51*33=1683 Current State: 57:[29, 60, 1683], Operations: ['51*33=1683'] Exploring Operation: 29*60=1740, Resulting Numbers: [1683, 1740] Generated Node #3: [1683, 1740] from Operation: 29*60=1740 Current State: 57:[1683, 1740], Operations: ['51*33=1683', '29*60=1740'] Exploring Operation: 1740-1683=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[51, 29, 33, 60], Operations: [] Exploring Operation: 33-29=4, Resulting Numbers: [51, 60, 4] Generated Node #0,0: 57:[51, 60, 4] Operation: 33-29=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[51, 60, 4], Operations: ['33-29=4'] Exploring Operation: 51+4=55, Resulting Numbers: [60, 55] Generated Node #0,0,0: 57:[60, 55] Operation: 51+4=55 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[60, 55], Operations: ['33-29=4', '51+4=55'] Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 59, 84, 24, 6 ]
21
[ "84-59=25", "24/6=4", "25-4=21" ]
Current State: 21:[59, 84, 24, 6], Operations: [] Exploring Operation: 84-59=25, Resulting Numbers: [24, 6, 25] Generated Node #2: [24, 6, 25] from Operation: 84-59=25 Current State: 21:[24, 6, 25], Operations: ['84-59=25'] Exploring Operation: 24/6=4, Resulting Numbers: [25, 4] Generated Node #3: [25, 4] from Operation: 24/6=4 Current State: 21:[25, 4], Operations: ['84-59=25', '24/6=4'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[59, 84, 24, 6], Operations: [] Exploring Operation: 84/6=14, Resulting Numbers: [59, 24, 14] Generated Node #0,0: 21:[59, 24, 14] Operation: 84/6=14 Exploring Operation: 59-24=35, Resulting Numbers: [84, 6, 35] Generated Node #0,1: 21:[84, 6, 35] Operation: 59-24=35 Exploring Operation: 84-59=25, Resulting Numbers: [24, 6, 25] Generated Node #0,2: 21:[24, 6, 25] Operation: 84-59=25 Moving to Node #0,2 Current State: 21:[24, 6, 25], Operations: ['84-59=25'] Exploring Operation: 24/6=4, Resulting Numbers: [25, 4] Generated Node #0,2,0: 21:[25, 4] Operation: 24/6=4 Exploring Operation: 25-24=1, Resulting Numbers: [6, 1] Generated Node #0,2,1: 21:[6, 1] Operation: 25-24=1 Exploring Operation: 25-6=19, Resulting Numbers: [24, 19] Generated Node #0,2,2: 21:[24, 19] Operation: 25-6=19 Moving to Node #0,0 Current State: 21:[59, 24, 14], Operations: ['84/6=14'] Exploring Operation: 59-14=45, Resulting Numbers: [24, 45] Generated Node #0,0,0: 21:[24, 45] Operation: 59-14=45 Exploring Operation: 24-14=10, Resulting Numbers: [59, 10] Generated Node #0,0,1: 21:[59, 10] Operation: 24-14=10 Exploring Operation: 59-24=35, Resulting Numbers: [14, 35] Generated Node #0,0,2: 21:[14, 35] Operation: 59-24=35 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 21:[14, 35], Operations: ['84/6=14', '59-24=35'] Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[59, 84, 24, 6], Operations: [] Exploring Operation: 84/6=14, Resulting Numbers: [59, 24, 14] Generated Node #0,0: 21:[59, 24, 14] Operation: 84/6=14 Moving to Node #0,0 Current State: 21:[59, 24, 14], Operations: ['84/6=14'] Exploring Operation: 59-24=35, Resulting Numbers: [14, 35] Generated Node #0,0,2: 21:[14, 35] Operation: 59-24=35 Moving to Node #0,0,2 Current State: 21:[14, 35], Operations: ['84/6=14', '59-24=35'] Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 98, 22, 78, 25 ]
60
[ "98-78=20", "25-22=3", "20*3=60" ]
Current State: 60:[98, 22, 78, 25], Operations: [] Exploring Operation: 98-78=20, Resulting Numbers: [22, 25, 20] Generated Node #2: [22, 25, 20] from Operation: 98-78=20 Current State: 60:[22, 25, 20], Operations: ['98-78=20'] Exploring Operation: 25-22=3, Resulting Numbers: [20, 3] Generated Node #3: [20, 3] from Operation: 25-22=3 Current State: 60:[20, 3], Operations: ['98-78=20', '25-22=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[98, 22, 78, 25], Operations: [] Exploring Operation: 98-78=20, Resulting Numbers: [22, 25, 20] Generated Node #0,0: 60:[22, 25, 20] Operation: 98-78=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[22, 25, 20], Operations: ['98-78=20'] Exploring Operation: 25-22=3, Resulting Numbers: [20, 3] Generated Node #0,0,0: 60:[20, 3] Operation: 25-22=3 Moving to Node #0,0,0 Current State: 60:[20, 3], Operations: ['98-78=20', '25-22=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[98, 22, 78, 25], Operations: [] Exploring Operation: 98-78=20, Resulting Numbers: [22, 25, 20] Generated Node #0,0: 60:[22, 25, 20] Operation: 98-78=20 Moving to Node #0,0 Current State: 60:[22, 25, 20], Operations: ['98-78=20'] Exploring Operation: 25-22=3, Resulting Numbers: [20, 3] Generated Node #0,0,0: 60:[20, 3] Operation: 25-22=3 Moving to Node #0,0,0 Current State: 60:[20, 3], Operations: ['98-78=20', '25-22=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 23, 61, 5, 28 ]
62
[ "23+5=28", "28/28=1", "61+1=62" ]
Current State: 62:[23, 61, 5, 28], Operations: [] Exploring Operation: 23+5=28, Resulting Numbers: [61, 28, 28] Generated Node #2: [61, 28, 28] from Operation: 23+5=28 Current State: 62:[61, 28, 28], Operations: ['23+5=28'] Exploring Operation: 28/28=1, Resulting Numbers: [61, 1] Generated Node #3: [61, 1] from Operation: 28/28=1 Current State: 62:[61, 1], Operations: ['23+5=28', '28/28=1'] Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[23, 61, 5, 28], Operations: [] Exploring Operation: 23+5=28, Resulting Numbers: [61, 28, 28] Generated Node #0,0: 62:[61, 28, 28] Operation: 23+5=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[61, 28, 28], Operations: ['23+5=28'] Exploring Operation: 28/28=1, Resulting Numbers: [61, 1] Generated Node #0,0,0: 62:[61, 1] Operation: 28/28=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[61, 1], Operations: ['23+5=28', '28/28=1'] Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[23, 61, 5, 28], Operations: [] Exploring Operation: 23+5=28, Resulting Numbers: [61, 28, 28] Generated Node #0,0: 62:[61, 28, 28] Operation: 23+5=28 Moving to Node #0,0 Current State: 62:[61, 28, 28], Operations: ['23+5=28'] Exploring Operation: 28/28=1, Resulting Numbers: [61, 1] Generated Node #0,0,0: 62:[61, 1] Operation: 28/28=1 Moving to Node #0,0,0 Current State: 62:[61, 1], Operations: ['23+5=28', '28/28=1'] Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 7, 41, 36, 18 ]
20
[ "41-7=34", "36+18=54", "54-34=20" ]
Current State: 20:[7, 41, 36, 18], Operations: [] Exploring Operation: 41-7=34, Resulting Numbers: [36, 18, 34] Generated Node #2: [36, 18, 34] from Operation: 41-7=34 Current State: 20:[36, 18, 34], Operations: ['41-7=34'] Exploring Operation: 36+18=54, Resulting Numbers: [34, 54] Generated Node #3: [34, 54] from Operation: 36+18=54 Current State: 20:[34, 54], Operations: ['41-7=34', '36+18=54'] Exploring Operation: 54-34=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[7, 41, 36, 18], Operations: [] Exploring Operation: 36/18=2, Resulting Numbers: [7, 41, 2] Generated Node #0,0: 20:[7, 41, 2] Operation: 36/18=2 Exploring Operation: 41-36=5, Resulting Numbers: [7, 18, 5] Generated Node #0,1: 20:[7, 18, 5] Operation: 41-36=5 Exploring Operation: 41-18=23, Resulting Numbers: [7, 36, 23] Generated Node #0,2: 20:[7, 36, 23] Operation: 41-18=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[7, 18, 5], Operations: ['41-36=5'] Exploring Operation: 7-5=2, Resulting Numbers: [18, 2] Generated Node #0,1,0: 20:[18, 2] Operation: 7-5=2 Exploring Operation: 18-7=11, Resulting Numbers: [5, 11] Generated Node #0,1,1: 20:[5, 11] Operation: 18-7=11 Exploring Operation: 7+5=12, Resulting Numbers: [18, 12] Generated Node #0,1,2: 20:[18, 12] Operation: 7+5=12 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 20:[5, 11], Operations: ['41-36=5', '18-7=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,20 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,20 unequal: No Solution No 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: 20:[18, 2], Operations: ['41-36=5', '7-5=2'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[7, 41, 36, 18], Operations: [] Exploring Operation: 41-36=5, Resulting Numbers: [7, 18, 5] Generated Node #0,1: 20:[7, 18, 5] Operation: 41-36=5 Moving to Node #0,1 Current State: 20:[7, 18, 5], Operations: ['41-36=5'] Exploring Operation: 7-5=2, Resulting Numbers: [18, 2] Generated Node #0,1,0: 20:[18, 2] Operation: 7-5=2 Moving to Node #0,1,0 Current State: 20:[18, 2], Operations: ['41-36=5', '7-5=2'] Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 34, 27, 92, 6 ]
14
[ "34-27=7", "92+6=98", "98/7=14" ]
Current State: 14:[34, 27, 92, 6], Operations: [] Exploring Operation: 34-27=7, Resulting Numbers: [92, 6, 7] Generated Node #2: [92, 6, 7] from Operation: 34-27=7 Current State: 14:[92, 6, 7], Operations: ['34-27=7'] Exploring Operation: 92+6=98, Resulting Numbers: [7, 98] Generated Node #3: [7, 98] from Operation: 92+6=98 Current State: 14:[7, 98], Operations: ['34-27=7', '92+6=98'] Exploring Operation: 98/7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[34, 27, 92, 6], Operations: [] Exploring Operation: 92-34=58, Resulting Numbers: [27, 6, 58] Generated Node #0,0: 14:[27, 6, 58] Operation: 92-34=58 Exploring Operation: 92-27=65, Resulting Numbers: [34, 6, 65] Generated Node #0,1: 14:[34, 6, 65] Operation: 92-27=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[27, 6, 58], Operations: ['92-34=58'] Exploring Operation: 58-27=31, Resulting Numbers: [6, 31] Generated Node #0,0,0: 14:[6, 31] Operation: 58-27=31 Exploring Operation: 27-6=21, Resulting Numbers: [58, 21] Generated Node #0,0,1: 14:[58, 21] Operation: 27-6=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 14:[6, 31], Operations: ['92-34=58', '58-27=31'] Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 14:[58, 21], Operations: ['92-34=58', '27-6=21'] Exploring Operation: 58-21=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 58+21=79, Resulting Numbers: [79] 79,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[34, 6, 65], Operations: ['92-27=65'] Exploring Operation: 65-34=31, Resulting Numbers: [6, 31] Generated Node #0,1,0: 14:[6, 31] Operation: 65-34=31 Exploring Operation: 34-6=28, Resulting Numbers: [65, 28] Generated Node #0,1,1: 14:[65, 28] Operation: 34-6=28 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 14:[6, 31], Operations: ['92-27=65', '65-34=31'] Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 14:[65, 28], Operations: ['92-27=65', '34-6=28'] Exploring Operation: 65-28=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 65+28=93, Resulting Numbers: [93] 93,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 45, 57, 94, 24 ]
96
[ "57-45=12", "24/12=2", "94+2=96" ]
Current State: 96:[45, 57, 94, 24], Operations: [] Exploring Operation: 57-45=12, Resulting Numbers: [94, 24, 12] Generated Node #2: [94, 24, 12] from Operation: 57-45=12 Current State: 96:[94, 24, 12], Operations: ['57-45=12'] Exploring Operation: 24/12=2, Resulting Numbers: [94, 2] Generated Node #3: [94, 2] from Operation: 24/12=2 Current State: 96:[94, 2], Operations: ['57-45=12', '24/12=2'] Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[45, 57, 94, 24], Operations: [] Exploring Operation: 57-24=33, Resulting Numbers: [45, 94, 33] Generated Node #0,0: 96:[45, 94, 33] Operation: 57-24=33 Exploring Operation: 57-45=12, Resulting Numbers: [94, 24, 12] Generated Node #0,1: 96:[94, 24, 12] Operation: 57-45=12 Moving to Node #0,1 Current State: 96:[94, 24, 12], Operations: ['57-45=12'] Exploring Operation: 24/12=2, Resulting Numbers: [94, 2] Generated Node #0,1,0: 96:[94, 2] Operation: 24/12=2 Exploring Operation: 24-12=12, Resulting Numbers: [94, 12] Generated Node #0,1,1: 96:[94, 12] Operation: 24-12=12 Moving to Node #0,0 Current State: 96:[45, 94, 33], Operations: ['57-24=33'] Exploring Operation: 45-33=12, Resulting Numbers: [94, 12] Generated Node #0,0,0: 96:[94, 12] Operation: 45-33=12 Exploring Operation: 94-45=49, Resulting Numbers: [33, 49] Generated Node #0,0,1: 96:[33, 49] Operation: 94-45=49 Moving to Node #0,1,0 Current State: 96:[94, 2], Operations: ['57-45=12', '24/12=2'] Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[45, 57, 94, 24], Operations: [] Exploring Operation: 57-45=12, Resulting Numbers: [94, 24, 12] Generated Node #0,1: 96:[94, 24, 12] Operation: 57-45=12 Moving to Node #0,1 Current State: 96:[94, 24, 12], Operations: ['57-45=12'] Exploring Operation: 24/12=2, Resulting Numbers: [94, 2] Generated Node #0,1,0: 96:[94, 2] Operation: 24/12=2 Moving to Node #0,1,0 Current State: 96:[94, 2], Operations: ['57-45=12', '24/12=2'] Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 87, 10, 59, 97 ]
60
[ "87+10=97", "97/97=1", "59+1=60" ]
Current State: 60:[87, 10, 59, 97], Operations: [] Exploring Operation: 87+10=97, Resulting Numbers: [59, 97, 97] Generated Node #2: [59, 97, 97] from Operation: 87+10=97 Current State: 60:[59, 97, 97], Operations: ['87+10=97'] Exploring Operation: 97/97=1, Resulting Numbers: [59, 1] Generated Node #3: [59, 1] from Operation: 97/97=1 Current State: 60:[59, 1], Operations: ['87+10=97', '97/97=1'] Exploring Operation: 59+1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[87, 10, 59, 97], Operations: [] Exploring Operation: 97-59=38, Resulting Numbers: [87, 10, 38] Generated Node #0,0: 60:[87, 10, 38] Operation: 97-59=38 Exploring Operation: 87-10=77, Resulting Numbers: [59, 97, 77] Generated Node #0,1: 60:[59, 97, 77] Operation: 87-10=77 Exploring Operation: 97-87=10, Resulting Numbers: [10, 59, 10] Generated Node #0,2: 60:[10, 59, 10] Operation: 97-87=10 Exploring Operation: 87-59=28, Resulting Numbers: [10, 97, 28] Generated Node #0,3: 60:[10, 97, 28] Operation: 87-59=28 Exploring Operation: 97-10=87, Resulting Numbers: [87, 59, 87] Generated Node #0,4: 60:[87, 59, 87] Operation: 97-10=87 Start Sub Search at level 1: Moving to Node #0,2 Current State: 60:[10, 59, 10], Operations: ['97-87=10'] Exploring Operation: 10+59=69, Resulting Numbers: [10, 69] Generated Node #0,2,0: 60:[10, 69] Operation: 10+59=69 Exploring Operation: 10-10=0, Resulting Numbers: [59, 0] Generated Node #0,2,1: 60:[59, 0] Operation: 10-10=0 Exploring Operation: 59+10=69, Resulting Numbers: [10, 69] Generated Node #0,2,2: 60:[10, 69] Operation: 59+10=69 Exploring Operation: 10/10=1, Resulting Numbers: [59, 1] Generated Node #0,2,3: 60:[59, 1] Operation: 10/10=1 Exploring Operation: 10+10=20, Resulting Numbers: [59, 20] Generated Node #0,2,4: 60:[59, 20] Operation: 10+10=20 Moving to Node #0,2,4 Current State: 60:[59, 20], Operations: ['97-87=10', '10+10=20'] Exploring Operation: 59-20=39, Resulting Numbers: [39] 39,60 unequal: No Solution Exploring Operation: 59*20=1180, Resulting Numbers: [1180] 1180,60 unequal: No Solution Exploring Operation: 59+20=79, Resulting Numbers: [79] 79,60 unequal: No Solution Moving to Node #0,2,3 Current State: 60:[59, 1], Operations: ['97-87=10', '10/10=1'] Exploring Operation: 59-1=58, Resulting Numbers: [58] 58,60 unequal: No Solution Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 59+1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[87, 10, 59, 97], Operations: [] Exploring Operation: 97-87=10, Resulting Numbers: [10, 59, 10] Generated Node #0,2: 60:[10, 59, 10] Operation: 97-87=10 Moving to Node #0,2 Current State: 60:[10, 59, 10], Operations: ['97-87=10'] Exploring Operation: 10/10=1, Resulting Numbers: [59, 1] Generated Node #0,2,3: 60:[59, 1] Operation: 10/10=1 Moving to Node #0,2,3 Current State: 60:[59, 1], Operations: ['97-87=10', '10/10=1'] Exploring Operation: 59+1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 64, 8, 92, 57 ]
21
[ "64-8=56", "92-57=35", "56-35=21" ]
Current State: 21:[64, 8, 92, 57], Operations: [] Exploring Operation: 64-8=56, Resulting Numbers: [92, 57, 56] Generated Node #2: [92, 57, 56] from Operation: 64-8=56 Current State: 21:[92, 57, 56], Operations: ['64-8=56'] Exploring Operation: 92-57=35, Resulting Numbers: [56, 35] Generated Node #3: [56, 35] from Operation: 92-57=35 Current State: 21:[56, 35], Operations: ['64-8=56', '92-57=35'] Exploring Operation: 56-35=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[64, 8, 92, 57], Operations: [] Exploring Operation: 64-57=7, Resulting Numbers: [8, 92, 7] Generated Node #0,0: 21:[8, 92, 7] Operation: 64-57=7 Exploring Operation: 64/8=8, Resulting Numbers: [92, 57, 8] Generated Node #0,1: 21:[92, 57, 8] Operation: 64/8=8 Exploring Operation: 92-57=35, Resulting Numbers: [64, 8, 35] Generated Node #0,2: 21:[64, 8, 35] Operation: 92-57=35 Exploring Operation: 92-64=28, Resulting Numbers: [8, 57, 28] Generated Node #0,3: 21:[8, 57, 28] Operation: 92-64=28 Exploring Operation: 64-8=56, Resulting Numbers: [92, 57, 56] Generated Node #0,4: 21:[92, 57, 56] Operation: 64-8=56 Start Sub Search at level 1: Moving to Node #0,3 Current State: 21:[8, 57, 28], Operations: ['92-64=28'] Exploring Operation: 57-8=49, Resulting Numbers: [28, 49] Generated Node #0,3,0: 21:[28, 49] Operation: 57-8=49 Exploring Operation: 28-8=20, Resulting Numbers: [57, 20] Generated Node #0,3,1: 21:[57, 20] Operation: 28-8=20 Exploring Operation: 57-28=29, Resulting Numbers: [8, 29] Generated Node #0,3,2: 21:[8, 29] Operation: 57-28=29 Exploring Operation: 8+57=65, Resulting Numbers: [28, 65] Generated Node #0,3,3: 21:[28, 65] Operation: 8+57=65 Exploring Operation: 8+28=36, Resulting Numbers: [57, 36] Generated Node #0,3,4: 21:[57, 36] Operation: 8+28=36 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 21:[8, 29], Operations: ['92-64=28', '57-28=29'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[64, 8, 92, 57], Operations: [] Exploring Operation: 92-64=28, Resulting Numbers: [8, 57, 28] Generated Node #0,3: 21:[8, 57, 28] Operation: 92-64=28 Moving to Node #0,3 Current State: 21:[8, 57, 28], Operations: ['92-64=28'] Exploring Operation: 57-28=29, Resulting Numbers: [8, 29] Generated Node #0,3,2: 21:[8, 29] Operation: 57-28=29 Moving to Node #0,3,2 Current State: 21:[8, 29], Operations: ['92-64=28', '57-28=29'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 11, 6, 38, 18 ]
10
[ "11*6=66", "38+18=56", "66-56=10" ]
Current State: 10:[11, 6, 38, 18], Operations: [] Exploring Operation: 11*6=66, Resulting Numbers: [38, 18, 66] Generated Node #2: [38, 18, 66] from Operation: 11*6=66 Current State: 10:[38, 18, 66], Operations: ['11*6=66'] Exploring Operation: 38+18=56, Resulting Numbers: [66, 56] Generated Node #3: [66, 56] from Operation: 38+18=56 Current State: 10:[66, 56], Operations: ['11*6=66', '38+18=56'] Exploring Operation: 66-56=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[11, 6, 38, 18], Operations: [] Exploring Operation: 38-18=20, Resulting Numbers: [11, 6, 20] Generated Node #0,0: 10:[11, 6, 20] Operation: 38-18=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[11, 6, 20], Operations: ['38-18=20'] Exploring Operation: 20-11=9, Resulting Numbers: [6, 9] Generated Node #0,0,0: 10:[6, 9] Operation: 20-11=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[6, 9], Operations: ['38-18=20', '20-11=9'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 85, 28, 78, 89 ]
34
[ "89-85=4", "28*4=112", "112-78=34" ]
Current State: 34:[85, 28, 78, 89], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [28, 78, 4] Generated Node #2: [28, 78, 4] from Operation: 89-85=4 Current State: 34:[28, 78, 4], Operations: ['89-85=4'] Exploring Operation: 28*4=112, Resulting Numbers: [78, 112] Generated Node #3: [78, 112] from Operation: 28*4=112 Current State: 34:[78, 112], Operations: ['89-85=4', '28*4=112'] Exploring Operation: 112-78=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[85, 28, 78, 89], Operations: [] Exploring Operation: 89-78=11, Resulting Numbers: [85, 28, 11] Generated Node #0,0: 34:[85, 28, 11] Operation: 89-78=11 Exploring Operation: 85-78=7, Resulting Numbers: [28, 89, 7] Generated Node #0,1: 34:[28, 89, 7] Operation: 85-78=7 Exploring Operation: 89-85=4, Resulting Numbers: [28, 78, 4] Generated Node #0,2: 34:[28, 78, 4] Operation: 89-85=4 Moving to Node #0,2 Current State: 34:[28, 78, 4], Operations: ['89-85=4'] Exploring Operation: 78-4=74, Resulting Numbers: [28, 74] Generated Node #0,2,0: 34:[28, 74] Operation: 78-4=74 Exploring Operation: 78-28=50, Resulting Numbers: [4, 50] Generated Node #0,2,1: 34:[4, 50] Operation: 78-28=50 Exploring Operation: 28+4=32, Resulting Numbers: [78, 32] Generated Node #0,2,2: 34:[78, 32] Operation: 28+4=32 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 34:[4, 50], Operations: ['89-85=4', '78-28=50'] Exploring Operation: 4*50=200, Resulting Numbers: [200] 200,34 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,34 unequal: No Solution Exploring Operation: 4+50=54, Resulting Numbers: [54] 54,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 34:[28, 74], Operations: ['89-85=4', '78-4=74'] Exploring Operation: 28*74=2072, Resulting Numbers: [2072] 2072,34 unequal: No Solution Exploring Operation: 28+74=102, Resulting Numbers: [102] 102,34 unequal: No Solution Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 34:[78, 32], Operations: ['89-85=4', '28+4=32'] Exploring Operation: 78+32=110, Resulting Numbers: [110] 110,34 unequal: No Solution Exploring Operation: 78*32=2496, Resulting Numbers: [2496] 2496,34 unequal: No Solution Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,34 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: 34:[85, 28, 11], Operations: ['89-78=11'] Exploring Operation: 85-11=74, Resulting Numbers: [28, 74] Generated Node #0,0,0: 34:[28, 74] Operation: 85-11=74 Exploring Operation: 28-11=17, Resulting Numbers: [85, 17] Generated Node #0,0,1: 34:[85, 17] Operation: 28-11=17 Exploring Operation: 85-28=57, Resulting Numbers: [11, 57] Generated Node #0,0,2: 34:[11, 57] Operation: 85-28=57 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 34:[11, 57], Operations: ['89-78=11', '85-28=57'] Exploring Operation: 11+57=68, Resulting Numbers: [68] 68,34 unequal: No Solution Exploring Operation: 57-11=46, Resulting Numbers: [46] 46,34 unequal: No Solution Exploring Operation: 11*57=627, Resulting Numbers: [627] 627,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 34:[28, 74], Operations: ['89-78=11', '85-11=74'] Exploring Operation: 28+74=102, Resulting Numbers: [102] 102,34 unequal: No Solution Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,34 unequal: No Solution Exploring Operation: 28*74=2072, Resulting Numbers: [2072] 2072,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 34:[85, 17], Operations: ['89-78=11', '28-11=17'] Exploring Operation: 85/17=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 85-17=68, Resulting Numbers: [68] 68,34 unequal: No Solution Exploring Operation: 85+17=102, Resulting Numbers: [102] 102,34 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: 34:[28, 89, 7], Operations: ['85-78=7'] Exploring Operation: 28+7=35, Resulting Numbers: [89, 35] Generated Node #0,1,0: 34:[89, 35] Operation: 28+7=35 Exploring Operation: 89-28=61, Resulting Numbers: [7, 61] Generated Node #0,1,1: 34:[7, 61] Operation: 89-28=61 Exploring Operation: 89-7=82, Resulting Numbers: [28, 82] Generated Node #0,1,2: 34:[28, 82] Operation: 89-7=82 Moving to Node #0,1,1 Current State: 34:[7, 61], Operations: ['85-78=7', '89-28=61'] Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,34 unequal: No Solution Exploring Operation: 7+61=68, Resulting Numbers: [68] 68,34 unequal: No Solution Exploring Operation: 7*61=427, Resulting Numbers: [427] 427,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[28, 82], Operations: ['85-78=7', '89-7=82'] Exploring Operation: 28*82=2296, Resulting Numbers: [2296] 2296,34 unequal: No Solution Exploring Operation: 28+82=110, Resulting Numbers: [110] 110,34 unequal: No Solution Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,34 unequal: No Solution Moving to Node #0,1,0 Current State: 34:[89, 35], Operations: ['85-78=7', '28+7=35'] Exploring Operation: 89+35=124, Resulting Numbers: [124] 124,34 unequal: No Solution Exploring Operation: 89-35=54, Resulting Numbers: [54] 54,34 unequal: No Solution Exploring Operation: 89*35=3115, Resulting Numbers: [3115] 3115,34 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 63, 67, 73, 40 ]
18
[ "63*40=2520", "67+73=140", "2520/140=18" ]
Current State: 18:[63, 67, 73, 40], Operations: [] Exploring Operation: 63*40=2520, Resulting Numbers: [67, 73, 2520] Generated Node #2: [67, 73, 2520] from Operation: 63*40=2520 Current State: 18:[67, 73, 2520], Operations: ['63*40=2520'] Exploring Operation: 67+73=140, Resulting Numbers: [2520, 140] Generated Node #3: [2520, 140] from Operation: 67+73=140 Current State: 18:[2520, 140], Operations: ['63*40=2520', '67+73=140'] Exploring Operation: 2520/140=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[63, 67, 73, 40], Operations: [] Exploring Operation: 73-67=6, Resulting Numbers: [63, 40, 6] Generated Node #0,0: 18:[63, 40, 6] Operation: 73-67=6 Moving to Node #0,0 Current State: 18:[63, 40, 6], Operations: ['73-67=6'] Exploring Operation: 63-40=23, Resulting Numbers: [6, 23] Generated Node #0,0,0: 18:[6, 23] Operation: 63-40=23 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[6, 23], Operations: ['73-67=6', '63-40=23'] Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 8, 88, 12, 3 ]
66
[ "12-8=4", "88*3=264", "264/4=66" ]
Current State: 66:[8, 88, 12, 3], Operations: [] Exploring Operation: 12-8=4, Resulting Numbers: [88, 3, 4] Generated Node #2: [88, 3, 4] from Operation: 12-8=4 Current State: 66:[88, 3, 4], Operations: ['12-8=4'] Exploring Operation: 88*3=264, Resulting Numbers: [4, 264] Generated Node #3: [4, 264] from Operation: 88*3=264 Current State: 66:[4, 264], Operations: ['12-8=4', '88*3=264'] Exploring Operation: 264/4=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[8, 88, 12, 3], Operations: [] Exploring Operation: 88/8=11, Resulting Numbers: [12, 3, 11] Generated Node #0,0: 66:[12, 3, 11] Operation: 88/8=11 Exploring Operation: 88-12=76, Resulting Numbers: [8, 3, 76] Generated Node #0,1: 66:[8, 3, 76] Operation: 88-12=76 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[12, 3, 11], Operations: ['88/8=11'] Exploring Operation: 12+11=23, Resulting Numbers: [3, 23] Generated Node #0,0,0: 66:[3, 23] Operation: 12+11=23 Exploring Operation: 12/3=4, Resulting Numbers: [11, 4] Generated Node #0,0,1: 66:[11, 4] Operation: 12/3=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 66:[3, 23], Operations: ['88/8=11', '12+11=23'] Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,66 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 66:[11, 4], Operations: ['88/8=11', '12/3=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,66 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[8, 3, 76], Operations: ['88-12=76'] Exploring Operation: 76-8=68, Resulting Numbers: [3, 68] Generated Node #0,1,0: 66:[3, 68] Operation: 76-8=68 Exploring Operation: 76-3=73, Resulting Numbers: [8, 73] Generated Node #0,1,1: 66:[8, 73] Operation: 76-3=73 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 66:[3, 68], Operations: ['88-12=76', '76-8=68'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,66 unequal: No Solution Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 66:[8, 73], Operations: ['88-12=76', '76-3=73'] Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,66 unequal: No Solution Exploring Operation: 8+73=81, Resulting Numbers: [81] 81,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 16, 32, 86, 96 ]
84
[ "16+32=48", "96/48=2", "86-2=84" ]
Current State: 84:[16, 32, 86, 96], Operations: [] Exploring Operation: 16+32=48, Resulting Numbers: [86, 96, 48] Generated Node #2: [86, 96, 48] from Operation: 16+32=48 Current State: 84:[86, 96, 48], Operations: ['16+32=48'] Exploring Operation: 96/48=2, Resulting Numbers: [86, 2] Generated Node #3: [86, 2] from Operation: 96/48=2 Current State: 84:[86, 2], Operations: ['16+32=48', '96/48=2'] Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[16, 32, 86, 96], Operations: [] Exploring Operation: 96/32=3, Resulting Numbers: [16, 86, 3] Generated Node #0,0: 84:[16, 86, 3] Operation: 96/32=3 Exploring Operation: 96-86=10, Resulting Numbers: [16, 32, 10] Generated Node #0,1: 84:[16, 32, 10] Operation: 96-86=10 Exploring Operation: 96/16=6, Resulting Numbers: [32, 86, 6] Generated Node #0,2: 84:[32, 86, 6] Operation: 96/16=6 Moving to Node #0,0 Current State: 84:[16, 86, 3], Operations: ['96/32=3'] Exploring Operation: 86-3=83, Resulting Numbers: [16, 83] Generated Node #0,0,0: 84:[16, 83] Operation: 86-3=83 Exploring Operation: 16-3=13, Resulting Numbers: [86, 13] Generated Node #0,0,1: 84:[86, 13] Operation: 16-3=13 Exploring Operation: 16+3=19, Resulting Numbers: [86, 19] Generated Node #0,0,2: 84:[86, 19] Operation: 16+3=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[16, 83], Operations: ['96/32=3', '86-3=83'] Exploring Operation: 16+83=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 16*83=1328, Resulting Numbers: [1328] 1328,84 unequal: No Solution Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,84 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 #0,0,1 Current State: 84:[86, 13], Operations: ['96/32=3', '16-3=13'] Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,84 unequal: No Solution Exploring Operation: 86+13=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 86*13=1118, Resulting Numbers: [1118] 1118,84 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 #0,0,2 Current State: 84:[86, 19], Operations: ['96/32=3', '16+3=19'] Exploring Operation: 86+19=105, Resulting Numbers: [105] 105,84 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 86*19=1634, Resulting Numbers: [1634] 1634,84 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: 84:[32, 86, 6], Operations: ['96/16=6'] Exploring Operation: 86-6=80, Resulting Numbers: [32, 80] Generated Node #0,2,0: 84:[32, 80] Operation: 86-6=80 Exploring Operation: 32-6=26, Resulting Numbers: [86, 26] Generated Node #0,2,1: 84:[86, 26] Operation: 32-6=26 Exploring Operation: 32+6=38, Resulting Numbers: [86, 38] Generated Node #0,2,2: 84:[86, 38] Operation: 32+6=38 Moving to Node #0,1 Current State: 84:[16, 32, 10], Operations: ['96-86=10'] Exploring Operation: 32/16=2, Resulting Numbers: [10, 2] Generated Node #0,1,0: 84:[10, 2] Operation: 32/16=2 Exploring Operation: 32-10=22, Resulting Numbers: [16, 22] Generated Node #0,1,1: 84:[16, 22] Operation: 32-10=22 Exploring Operation: 32+10=42, Resulting Numbers: [16, 42] Generated Node #0,1,2: 84:[16, 42] Operation: 32+10=42 Moving to Node #0,1,0 Current State: 84:[10, 2], Operations: ['96-86=10', '32/16=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,84 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[16, 42], Operations: ['96-86=10', '32+10=42'] Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,84 unequal: No Solution Exploring Operation: 16*42=672, Resulting Numbers: [672] 672,84 unequal: No Solution Exploring Operation: 16+42=58, Resulting Numbers: [58] 58,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[16, 22], Operations: ['96-86=10', '32-10=22'] Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 16*22=352, Resulting Numbers: [352] 352,84 unequal: No Solution Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,84 unequal: No Solution Moving to Node #0,2,1 Current State: 84:[86, 26], Operations: ['96/16=6', '32-6=26'] Exploring Operation: 86-26=60, Resulting Numbers: [60] 60,84 unequal: No Solution Exploring Operation: 86*26=2236, Resulting Numbers: [2236] 2236,84 unequal: No Solution Exploring Operation: 86+26=112, Resulting Numbers: [112] 112,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[86, 38], Operations: ['96/16=6', '32+6=38'] Exploring Operation: 86-38=48, Resulting Numbers: [48] 48,84 unequal: No Solution Exploring Operation: 86*38=3268, Resulting Numbers: [3268] 3268,84 unequal: No Solution Exploring Operation: 86+38=124, Resulting Numbers: [124] 124,84 unequal: No Solution Moving to Node #0,2,0 Current State: 84:[32, 80], Operations: ['96/16=6', '86-6=80'] Exploring Operation: 32+80=112, Resulting Numbers: [112] 112,84 unequal: No Solution Exploring Operation: 32*80=2560, Resulting Numbers: [2560] 2560,84 unequal: No Solution Exploring Operation: 80-32=48, Resulting Numbers: [48] 48,84 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 7, 41, 64, 13 ]
43
[ "41-7=34", "64+13=77", "77-34=43" ]
Current State: 43:[7, 41, 64, 13], Operations: [] Exploring Operation: 41-7=34, Resulting Numbers: [64, 13, 34] Generated Node #2: [64, 13, 34] from Operation: 41-7=34 Current State: 43:[64, 13, 34], Operations: ['41-7=34'] Exploring Operation: 64+13=77, Resulting Numbers: [34, 77] Generated Node #3: [34, 77] from Operation: 64+13=77 Current State: 43:[34, 77], Operations: ['41-7=34', '64+13=77'] Exploring Operation: 77-34=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[7, 41, 64, 13], Operations: [] Exploring Operation: 64-7=57, Resulting Numbers: [41, 13, 57] Generated Node #0,0: 43:[41, 13, 57] Operation: 64-7=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[41, 13, 57], Operations: ['64-7=57'] Exploring Operation: 57-13=44, Resulting Numbers: [41, 44] Generated Node #0,0,0: 43:[41, 44] Operation: 57-13=44 Moving to Node #0,0,0 Current State: 43:[41, 44], Operations: ['64-7=57', '57-13=44'] Exploring Operation: 44-41=3, Resulting Numbers: [3] 3,43 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
[ 65, 4, 39, 42 ]
78
[ "65*42=2730", "39-4=35", "2730/35=78" ]
Current State: 78:[65, 4, 39, 42], Operations: [] Exploring Operation: 65*42=2730, Resulting Numbers: [4, 39, 2730] Generated Node #2: [4, 39, 2730] from Operation: 65*42=2730 Current State: 78:[4, 39, 2730], Operations: ['65*42=2730'] Exploring Operation: 39-4=35, Resulting Numbers: [2730, 35] Generated Node #3: [2730, 35] from Operation: 39-4=35 Current State: 78:[2730, 35], Operations: ['65*42=2730', '39-4=35'] Exploring Operation: 2730/35=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[65, 4, 39, 42], Operations: [] Exploring Operation: 65+4=69, Resulting Numbers: [39, 42, 69] Generated Node #0,0: 78:[39, 42, 69] Operation: 65+4=69 Exploring Operation: 65-42=23, Resulting Numbers: [4, 39, 23] Generated Node #0,1: 78:[4, 39, 23] Operation: 65-42=23 Exploring Operation: 65-39=26, Resulting Numbers: [4, 42, 26] Generated Node #0,2: 78:[4, 42, 26] Operation: 65-39=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[4, 39, 23], Operations: ['65-42=23'] Exploring Operation: 39-23=16, Resulting Numbers: [4, 16] Generated Node #0,1,0: 78:[4, 16] Operation: 39-23=16 Exploring Operation: 23-4=19, Resulting Numbers: [39, 19] Generated Node #0,1,1: 78:[39, 19] Operation: 23-4=19 Exploring Operation: 4+23=27, Resulting Numbers: [39, 27] Generated Node #0,1,2: 78:[39, 27] Operation: 4+23=27 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 78:[39, 27], Operations: ['65-42=23', '4+23=27'] Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,78 unequal: No Solution Exploring Operation: 39*27=1053, Resulting Numbers: [1053] 1053,78 unequal: No Solution Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 78:[4, 16], Operations: ['65-42=23', '39-23=16'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,78 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 78:[39, 19], Operations: ['65-42=23', '23-4=19'] Exploring Operation: 39*19=741, Resulting Numbers: [741] 741,78 unequal: No Solution Exploring Operation: 39+19=58, Resulting Numbers: [58] 58,78 unequal: No Solution Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 78:[4, 42, 26], Operations: ['65-39=26'] Exploring Operation: 42-26=16, Resulting Numbers: [4, 16] Generated Node #0,2,0: 78:[4, 16] Operation: 42-26=16 Exploring Operation: 4+42=46, Resulting Numbers: [26, 46] Generated Node #0,2,1: 78:[26, 46] Operation: 4+42=46 Exploring Operation: 42-4=38, Resulting Numbers: [26, 38] Generated Node #0,2,2: 78:[26, 38] Operation: 42-4=38 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 78:[26, 38], Operations: ['65-39=26', '42-4=38'] Exploring Operation: 26+38=64, Resulting Numbers: [64] 64,78 unequal: No Solution Exploring Operation: 26*38=988, Resulting Numbers: [988] 988,78 unequal: No Solution Exploring Operation: 38-26=12, Resulting Numbers: [12] 12,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 78:[4, 16], Operations: ['65-39=26', '42-26=16'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,78 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 78:[26, 46], Operations: ['65-39=26', '4+42=46'] Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,78 unequal: No Solution Exploring Operation: 26+46=72, Resulting Numbers: [72] 72,78 unequal: No Solution Exploring Operation: 26*46=1196, Resulting Numbers: [1196] 1196,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[39, 42, 69], Operations: ['65+4=69'] Exploring Operation: 42-39=3, Resulting Numbers: [69, 3] Generated Node #0,0,0: 78:[69, 3] Operation: 42-39=3 Exploring Operation: 69-42=27, Resulting Numbers: [39, 27] Generated Node #0,0,1: 78:[39, 27] Operation: 69-42=27 Exploring Operation: 69-39=30, Resulting Numbers: [42, 30] Generated Node #0,0,2: 78:[42, 30] Operation: 69-39=30 Moving to Node #0,0,1 Current State: 78:[39, 27], Operations: ['65+4=69', '69-42=27'] Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,78 unequal: No Solution Exploring Operation: 39*27=1053, Resulting Numbers: [1053] 1053,78 unequal: No Solution Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,78 unequal: No Solution Moving to Node #0,0,2 Current State: 78:[42, 30], Operations: ['65+4=69', '69-39=30'] Exploring Operation: 42*30=1260, Resulting Numbers: [1260] 1260,78 unequal: No Solution Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,78 unequal: No Solution Exploring Operation: 42+30=72, Resulting Numbers: [72] 72,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[69, 3], Operations: ['65+4=69', '42-39=3'] Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,78 unequal: No Solution Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 69+3=72, Resulting Numbers: [72] 72,78 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
[ 2, 66, 62, 88 ]
30
[ "2*62=124", "66+88=154", "154-124=30" ]
Current State: 30:[2, 66, 62, 88], Operations: [] Exploring Operation: 2*62=124, Resulting Numbers: [66, 88, 124] Generated Node #2: [66, 88, 124] from Operation: 2*62=124 Current State: 30:[66, 88, 124], Operations: ['2*62=124'] Exploring Operation: 66+88=154, Resulting Numbers: [124, 154] Generated Node #3: [124, 154] from Operation: 66+88=154 Current State: 30:[124, 154], Operations: ['2*62=124', '66+88=154'] Exploring Operation: 154-124=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[2, 66, 62, 88], Operations: [] Exploring Operation: 88-66=22, Resulting Numbers: [2, 62, 22] Generated Node #0,0: 30:[2, 62, 22] Operation: 88-66=22 Exploring Operation: 88-62=26, Resulting Numbers: [2, 66, 26] Generated Node #0,1: 30:[2, 66, 26] Operation: 88-62=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[2, 62, 22], Operations: ['88-66=22'] Exploring Operation: 62-22=40, Resulting Numbers: [2, 40] Generated Node #0,0,0: 30:[2, 40] Operation: 62-22=40 Exploring Operation: 62/2=31, Resulting Numbers: [22, 31] Generated Node #0,0,1: 30:[22, 31] Operation: 62/2=31 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[22, 31], Operations: ['88-66=22', '62/2=31'] Exploring Operation: 31-22=9, Resulting Numbers: [9] 9,30 unequal: No Solution Exploring Operation: 22+31=53, Resulting Numbers: [53] 53,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[2, 40], Operations: ['88-66=22', '62-22=40'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,30 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[2, 66, 26], Operations: ['88-62=26'] Exploring Operation: 66/2=33, Resulting Numbers: [26, 33] Generated Node #0,1,0: 30:[26, 33] Operation: 66/2=33 Exploring Operation: 66-26=40, Resulting Numbers: [2, 40] Generated Node #0,1,1: 30:[2, 40] Operation: 66-26=40 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[26, 33], Operations: ['88-62=26', '66/2=33'] Exploring Operation: 33-26=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 26+33=59, Resulting Numbers: [59] 59,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[2, 40], Operations: ['88-62=26', '66-26=40'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 2, 46, 31, 18 ]
51
[ "2*18=36", "46-31=15", "36+15=51" ]
Current State: 51:[2, 46, 31, 18], Operations: [] Exploring Operation: 2*18=36, Resulting Numbers: [46, 31, 36] Generated Node #2: [46, 31, 36] from Operation: 2*18=36 Current State: 51:[46, 31, 36], Operations: ['2*18=36'] Exploring Operation: 46-31=15, Resulting Numbers: [36, 15] Generated Node #3: [36, 15] from Operation: 46-31=15 Current State: 51:[36, 15], Operations: ['2*18=36', '46-31=15'] Exploring Operation: 36+15=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[2, 46, 31, 18], Operations: [] Exploring Operation: 46-31=15, Resulting Numbers: [2, 18, 15] Generated Node #0,0: 51:[2, 18, 15] Operation: 46-31=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[2, 18, 15], Operations: ['46-31=15'] Exploring Operation: 2+15=17, Resulting Numbers: [18, 17] Generated Node #0,0,0: 51:[18, 17] Operation: 2+15=17 Moving to Node #0,0,0 Current State: 51:[18, 17], Operations: ['46-31=15', '2+15=17'] Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,51 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
[ 22, 65, 72, 40 ]
69
[ "65-22=43", "72+40=112", "112-43=69" ]
Current State: 69:[22, 65, 72, 40], Operations: [] Exploring Operation: 65-22=43, Resulting Numbers: [72, 40, 43] Generated Node #2: [72, 40, 43] from Operation: 65-22=43 Current State: 69:[72, 40, 43], Operations: ['65-22=43'] Exploring Operation: 72+40=112, Resulting Numbers: [43, 112] Generated Node #3: [43, 112] from Operation: 72+40=112 Current State: 69:[43, 112], Operations: ['65-22=43', '72+40=112'] Exploring Operation: 112-43=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[22, 65, 72, 40], Operations: [] Exploring Operation: 65-40=25, Resulting Numbers: [22, 72, 25] Generated Node #0,0: 69:[22, 72, 25] Operation: 65-40=25 Exploring Operation: 40-22=18, Resulting Numbers: [65, 72, 18] Generated Node #0,1: 69:[65, 72, 18] Operation: 40-22=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[22, 72, 25], Operations: ['65-40=25'] Exploring Operation: 72-22=50, Resulting Numbers: [25, 50] Generated Node #0,0,0: 69:[25, 50] Operation: 72-22=50 Exploring Operation: 25-22=3, Resulting Numbers: [72, 3] Generated Node #0,0,1: 69:[72, 3] Operation: 25-22=3 Moving to Node #0,0,1 Current State: 69:[72, 3], Operations: ['65-40=25', '25-22=3'] Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,69 unequal: No Solution Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[22, 65, 72, 40], Operations: [] Exploring Operation: 65-40=25, Resulting Numbers: [22, 72, 25] Generated Node #0,0: 69:[22, 72, 25] Operation: 65-40=25 Moving to Node #0,0 Current State: 69:[22, 72, 25], Operations: ['65-40=25'] Exploring Operation: 25-22=3, Resulting Numbers: [72, 3] Generated Node #0,0,1: 69:[72, 3] Operation: 25-22=3 Moving to Node #0,0,1 Current State: 69:[72, 3], Operations: ['65-40=25', '25-22=3'] Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 32, 77, 92, 21 ]
38
[ "32+77=109", "92-21=71", "109-71=38" ]
Current State: 38:[32, 77, 92, 21], Operations: [] Exploring Operation: 32+77=109, Resulting Numbers: [92, 21, 109] Generated Node #2: [92, 21, 109] from Operation: 32+77=109 Current State: 38:[92, 21, 109], Operations: ['32+77=109'] Exploring Operation: 92-21=71, Resulting Numbers: [109, 71] Generated Node #3: [109, 71] from Operation: 92-21=71 Current State: 38:[109, 71], Operations: ['32+77=109', '92-21=71'] Exploring Operation: 109-71=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[32, 77, 92, 21], Operations: [] Exploring Operation: 77-32=45, Resulting Numbers: [92, 21, 45] Generated Node #0,0: 38:[92, 21, 45] Operation: 77-32=45 Exploring Operation: 92-32=60, Resulting Numbers: [77, 21, 60] Generated Node #0,1: 38:[77, 21, 60] Operation: 92-32=60 Exploring Operation: 92-77=15, Resulting Numbers: [32, 21, 15] Generated Node #0,2: 38:[32, 21, 15] Operation: 92-77=15 Exploring Operation: 77-21=56, Resulting Numbers: [32, 92, 56] Generated Node #0,3: 38:[32, 92, 56] Operation: 77-21=56 Exploring Operation: 92-21=71, Resulting Numbers: [32, 77, 71] Generated Node #0,4: 38:[32, 77, 71] Operation: 92-21=71 Moving to Node #0,2 Current State: 38:[32, 21, 15], Operations: ['92-77=15'] Exploring Operation: 21-15=6, Resulting Numbers: [32, 6] Generated Node #0,2,0: 38:[32, 6] Operation: 21-15=6 Exploring Operation: 32-15=17, Resulting Numbers: [21, 17] Generated Node #0,2,1: 38:[21, 17] Operation: 32-15=17 Exploring Operation: 32-21=11, Resulting Numbers: [15, 11] Generated Node #0,2,2: 38:[15, 11] Operation: 32-21=11 Exploring Operation: 32+15=47, Resulting Numbers: [21, 47] Generated Node #0,2,3: 38:[21, 47] Operation: 32+15=47 Exploring Operation: 21+15=36, Resulting Numbers: [32, 36] Generated Node #0,2,4: 38:[32, 36] Operation: 21+15=36 Moving to Node #0,1 Current State: 38:[77, 21, 60], Operations: ['92-32=60'] Exploring Operation: 77-60=17, Resulting Numbers: [21, 17] Generated Node #0,1,0: 38:[21, 17] Operation: 77-60=17 Exploring Operation: 60-21=39, Resulting Numbers: [77, 39] Generated Node #0,1,1: 38:[77, 39] Operation: 60-21=39 Exploring Operation: 77-21=56, Resulting Numbers: [60, 56] Generated Node #0,1,2: 38:[60, 56] Operation: 77-21=56 Exploring Operation: 77+21=98, Resulting Numbers: [60, 98] Generated Node #0,1,3: 38:[60, 98] Operation: 77+21=98 Exploring Operation: 21+60=81, Resulting Numbers: [77, 81] Generated Node #0,1,4: 38:[77, 81] Operation: 21+60=81 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 38:[21, 17], Operations: ['92-32=60', '77-60=17'] Exploring Operation: 21+17=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[32, 77, 92, 21], Operations: [] Exploring Operation: 92-32=60, Resulting Numbers: [77, 21, 60] Generated Node #0,1: 38:[77, 21, 60] Operation: 92-32=60 Moving to Node #0,1 Current State: 38:[77, 21, 60], Operations: ['92-32=60'] Exploring Operation: 77-60=17, Resulting Numbers: [21, 17] Generated Node #0,1,0: 38:[21, 17] Operation: 77-60=17 Moving to Node #0,1,0 Current State: 38:[21, 17], Operations: ['92-32=60', '77-60=17'] Exploring Operation: 21+17=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 24, 58, 26, 51 ]
57
[ "24+58=82", "51-26=25", "82-25=57" ]
Current State: 57:[24, 58, 26, 51], Operations: [] Exploring Operation: 24+58=82, Resulting Numbers: [26, 51, 82] Generated Node #2: [26, 51, 82] from Operation: 24+58=82 Current State: 57:[26, 51, 82], Operations: ['24+58=82'] Exploring Operation: 51-26=25, Resulting Numbers: [82, 25] Generated Node #3: [82, 25] from Operation: 51-26=25 Current State: 57:[82, 25], Operations: ['24+58=82', '51-26=25'] Exploring Operation: 82-25=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[24, 58, 26, 51], Operations: [] Exploring Operation: 24+26=50, Resulting Numbers: [58, 51, 50] Generated Node #0,0: 57:[58, 51, 50] Operation: 24+26=50 Exploring Operation: 26-24=2, Resulting Numbers: [58, 51, 2] Generated Node #0,1: 57:[58, 51, 2] Operation: 26-24=2 Exploring Operation: 51-26=25, Resulting Numbers: [24, 58, 25] Generated Node #0,2: 57:[24, 58, 25] Operation: 51-26=25 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[58, 51, 2], Operations: ['26-24=2'] Exploring Operation: 58-51=7, Resulting Numbers: [2, 7] Generated Node #0,1,0: 57:[2, 7] Operation: 58-51=7 Exploring Operation: 51+2=53, Resulting Numbers: [58, 53] Generated Node #0,1,1: 57:[58, 53] Operation: 51+2=53 Exploring Operation: 58-2=56, Resulting Numbers: [51, 56] Generated Node #0,1,2: 57:[51, 56] Operation: 58-2=56 Moving to Node #0,1,0 Current State: 57:[2, 7], Operations: ['26-24=2', '58-51=7'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,57 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[58, 53], Operations: ['26-24=2', '51+2=53'] Exploring Operation: 58*53=3074, Resulting Numbers: [3074] 3074,57 unequal: No Solution Exploring Operation: 58+53=111, Resulting Numbers: [111] 111,57 unequal: No Solution Exploring Operation: 58-53=5, Resulting Numbers: [5] 5,57 unequal: No Solution Moving to Node #0,1,2 Current State: 57:[51, 56], Operations: ['26-24=2', '58-2=56'] Exploring Operation: 51+56=107, Resulting Numbers: [107] 107,57 unequal: No Solution Exploring Operation: 51*56=2856, Resulting Numbers: [2856] 2856,57 unequal: No Solution Exploring Operation: 56-51=5, Resulting Numbers: [5] 5,57 unequal: No Solution No 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: 57:[24, 58, 25], Operations: ['51-26=25'] Exploring Operation: 58-25=33, Resulting Numbers: [24, 33] Generated Node #0,2,0: 57:[24, 33] Operation: 58-25=33 Exploring Operation: 24+25=49, Resulting Numbers: [58, 49] Generated Node #0,2,1: 57:[58, 49] Operation: 24+25=49 Exploring Operation: 25-24=1, Resulting Numbers: [58, 1] Generated Node #0,2,2: 57:[58, 1] Operation: 25-24=1 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 57:[58, 1], Operations: ['51-26=25', '25-24=1'] Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[24, 58, 26, 51], Operations: [] Exploring Operation: 51-26=25, Resulting Numbers: [24, 58, 25] Generated Node #0,2: 57:[24, 58, 25] Operation: 51-26=25 Moving to Node #0,2 Current State: 57:[24, 58, 25], Operations: ['51-26=25'] Exploring Operation: 25-24=1, Resulting Numbers: [58, 1] Generated Node #0,2,2: 57:[58, 1] Operation: 25-24=1 Moving to Node #0,2,2 Current State: 57:[58, 1], Operations: ['51-26=25', '25-24=1'] Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 55, 9, 14, 50 ]
100
[ "55+9=64", "50-14=36", "64+36=100" ]
Current State: 100:[55, 9, 14, 50], Operations: [] Exploring Operation: 55+9=64, Resulting Numbers: [14, 50, 64] Generated Node #2: [14, 50, 64] from Operation: 55+9=64 Current State: 100:[14, 50, 64], Operations: ['55+9=64'] Exploring Operation: 50-14=36, Resulting Numbers: [64, 36] Generated Node #3: [64, 36] from Operation: 50-14=36 Current State: 100:[64, 36], Operations: ['55+9=64', '50-14=36'] Exploring Operation: 64+36=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[55, 9, 14, 50], Operations: [] Exploring Operation: 55-50=5, Resulting Numbers: [9, 14, 5] Generated Node #0,0: 100:[9, 14, 5] Operation: 55-50=5 Exploring Operation: 9+14=23, Resulting Numbers: [55, 50, 23] Generated Node #0,1: 100:[55, 50, 23] Operation: 9+14=23 Exploring Operation: 55-9=46, Resulting Numbers: [14, 50, 46] Generated Node #0,2: 100:[14, 50, 46] Operation: 55-9=46 Exploring Operation: 14-9=5, Resulting Numbers: [55, 50, 5] Generated Node #0,3: 100:[55, 50, 5] Operation: 14-9=5 Exploring Operation: 55-14=41, Resulting Numbers: [9, 50, 41] Generated Node #0,4: 100:[9, 50, 41] Operation: 55-14=41 Moving to Node #0,0 Current State: 100:[9, 14, 5], Operations: ['55-50=5'] Exploring Operation: 14+5=19, Resulting Numbers: [9, 19] Generated Node #0,0,0: 100:[9, 19] Operation: 14+5=19 Exploring Operation: 9+14=23, Resulting Numbers: [5, 23] Generated Node #0,0,1: 100:[5, 23] Operation: 9+14=23 Exploring Operation: 14-9=5, Resulting Numbers: [5, 5] Generated Node #0,0,2: 100:[5, 5] Operation: 14-9=5 Exploring Operation: 14-5=9, Resulting Numbers: [9, 9] Generated Node #0,0,3: 100:[9, 9] Operation: 14-5=9 Exploring Operation: 9-5=4, Resulting Numbers: [14, 4] Generated Node #0,0,4: 100:[14, 4] Operation: 9-5=4 Moving to Node #0,3 Current State: 100:[55, 50, 5], Operations: ['14-9=5'] Exploring Operation: 55/5=11, Resulting Numbers: [50, 11] Generated Node #0,3,0: 100:[50, 11] Operation: 55/5=11 Exploring Operation: 55+50=105, Resulting Numbers: [5, 105] Generated Node #0,3,1: 100:[5, 105] Operation: 55+50=105 Exploring Operation: 55-5=50, Resulting Numbers: [50, 50] Generated Node #0,3,2: 100:[50, 50] Operation: 55-5=50 Exploring Operation: 50/5=10, Resulting Numbers: [55, 10] Generated Node #0,3,3: 100:[55, 10] Operation: 50/5=10 Exploring Operation: 55-50=5, Resulting Numbers: [5, 5] Generated Node #0,3,4: 100:[5, 5] Operation: 55-50=5 Moving to Node #0,1 Current State: 100:[55, 50, 23], Operations: ['9+14=23'] Exploring Operation: 55+23=78, Resulting Numbers: [50, 78] Generated Node #0,1,0: 100:[50, 78] Operation: 55+23=78 Exploring Operation: 55-23=32, Resulting Numbers: [50, 32] Generated Node #0,1,1: 100:[50, 32] Operation: 55-23=32 Exploring Operation: 55+50=105, Resulting Numbers: [23, 105] Generated Node #0,1,2: 100:[23, 105] Operation: 55+50=105 Exploring Operation: 55-50=5, Resulting Numbers: [23, 5] Generated Node #0,1,3: 100:[23, 5] Operation: 55-50=5 Exploring Operation: 50-23=27, Resulting Numbers: [55, 27] Generated Node #0,1,4: 100:[55, 27] Operation: 50-23=27 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 100:[23, 5], Operations: ['9+14=23', '55-50=5'] Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 23*5=115, Resulting Numbers: [115] 115,100 unequal: No Solution Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 100:[50, 32], Operations: ['9+14=23', '55-23=32'] Exploring Operation: 50*32=1600, Resulting Numbers: [1600] 1600,100 unequal: No Solution Exploring Operation: 50+32=82, Resulting Numbers: [82] 82,100 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 100:[23, 105], Operations: ['9+14=23', '55+50=105'] Exploring Operation: 105-23=82, Resulting Numbers: [82] 82,100 unequal: No Solution Exploring Operation: 23+105=128, Resulting Numbers: [128] 128,100 unequal: No Solution Exploring Operation: 23*105=2415, Resulting Numbers: [2415] 2415,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 100:[55, 27], Operations: ['9+14=23', '50-23=27'] Exploring Operation: 55*27=1485, Resulting Numbers: [1485] 1485,100 unequal: No Solution Exploring Operation: 55-27=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 55+27=82, Resulting Numbers: [82] 82,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 100:[50, 78], Operations: ['9+14=23', '55+23=78'] Exploring Operation: 50+78=128, Resulting Numbers: [128] 128,100 unequal: No Solution Exploring Operation: 78-50=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 50*78=3900, Resulting Numbers: [3900] 3900,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 100:[14, 50, 46], Operations: ['55-9=46'] Exploring Operation: 50-14=36, Resulting Numbers: [46, 36] Generated Node #0,2,0: 100:[46, 36] Operation: 50-14=36 Exploring Operation: 46-14=32, Resulting Numbers: [50, 32] Generated Node #0,2,1: 100:[50, 32] Operation: 46-14=32 Exploring Operation: 50-46=4, Resulting Numbers: [14, 4] Generated Node #0,2,2: 100:[14, 4] Operation: 50-46=4 Exploring Operation: 50+46=96, Resulting Numbers: [14, 96] Generated Node #0,2,3: 100:[14, 96] Operation: 50+46=96 Exploring Operation: 14+46=60, Resulting Numbers: [50, 60] Generated Node #0,2,4: 100:[50, 60] Operation: 14+46=60 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 100:[14, 4], Operations: ['55-9=46', '50-46=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 100:[50, 32], Operations: ['55-9=46', '46-14=32'] Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 50+32=82, Resulting Numbers: [82] 82,100 unequal: No Solution Exploring Operation: 50*32=1600, Resulting Numbers: [1600] 1600,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 100:[14, 96], Operations: ['55-9=46', '50+46=96'] Exploring Operation: 14*96=1344, Resulting Numbers: [1344] 1344,100 unequal: No Solution Exploring Operation: 96-14=82, Resulting Numbers: [82] 82,100 unequal: No Solution Exploring Operation: 14+96=110, Resulting Numbers: [110] 110,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 100:[50, 60], Operations: ['55-9=46', '14+46=60'] Exploring Operation: 60-50=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 50*60=3000, Resulting Numbers: [3000] 3000,100 unequal: No Solution Exploring Operation: 50+60=110, Resulting Numbers: [110] 110,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 100:[46, 36], Operations: ['55-9=46', '50-14=36'] Exploring Operation: 46*36=1656, Resulting Numbers: [1656] 1656,100 unequal: No Solution Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 46+36=82, Resulting Numbers: [82] 82,100 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: 100:[9, 50, 41], Operations: ['55-14=41'] Exploring Operation: 41-9=32, Resulting Numbers: [50, 32] Generated Node #0,4,0: 100:[50, 32] Operation: 41-9=32 Exploring Operation: 9+41=50, Resulting Numbers: [50, 50] Generated Node #0,4,1: 100:[50, 50] Operation: 9+41=50 Exploring Operation: 9+50=59, Resulting Numbers: [41, 59] Generated Node #0,4,2: 100:[41, 59] Operation: 9+50=59 Exploring Operation: 50-41=9, Resulting Numbers: [9, 9] Generated Node #0,4,3: 100:[9, 9] Operation: 50-41=9 Exploring Operation: 50+41=91, Resulting Numbers: [9, 91] Generated Node #0,4,4: 100:[9, 91] Operation: 50+41=91 Moving to Node #0,0,2 Current State: 100:[5, 5], Operations: ['55-50=5', '14-9=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,100 unequal: No Solution Moving to Node #0,3,2 Current State: 100:[50, 50], Operations: ['14-9=5', '55-5=50'] Exploring Operation: 50/50=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 50-50=0, Resulting Numbers: [0] 0,100 unequal: No Solution Exploring Operation: 50*50=2500, Resulting Numbers: [2500] 2500,100 unequal: No Solution Exploring Operation: 50+50=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[55, 9, 14, 50], Operations: [] Exploring Operation: 14-9=5, Resulting Numbers: [55, 50, 5] Generated Node #0,3: 100:[55, 50, 5] Operation: 14-9=5 Moving to Node #0,3 Current State: 100:[55, 50, 5], Operations: ['14-9=5'] Exploring Operation: 55-5=50, Resulting Numbers: [50, 50] Generated Node #0,3,2: 100:[50, 50] Operation: 55-5=50 Moving to Node #0,3,2 Current State: 100:[50, 50], Operations: ['14-9=5', '55-5=50'] Exploring Operation: 50+50=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.9375
hs_5
mult_heuristic