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
[ 64, 3, 79, 2 ]
43
[ "64-3=61", "2*61=122", "122-79=43" ]
Current State: 43:[64, 3, 79, 2], Operations: [] Exploring Operation: 64-3=61, Resulting Numbers: [79, 2, 61] Generated Node #2: [79, 2, 61] from Operation: 64-3=61 Current State: 43:[79, 2, 61], Operations: ['64-3=61'] Exploring Operation: 2*61=122, Resulting Numbers: [79, 122] Generated Node #3: [79, 122] from Operation: 2*61=122 Current State: 43:[79, 122], Operations: ['64-3=61', '2*61=122'] Exploring Operation: 122-79=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[64, 3, 79, 2], Operations: [] Exploring Operation: 64-2=62, Resulting Numbers: [3, 79, 62] Generated Node #0,0: 43:[3, 79, 62] Operation: 64-2=62 Exploring Operation: 3*2=6, Resulting Numbers: [64, 79, 6] Generated Node #0,1: 43:[64, 79, 6] Operation: 3*2=6 Exploring Operation: 64-3=61, Resulting Numbers: [79, 2, 61] Generated Node #0,2: 43:[79, 2, 61] Operation: 64-3=61 Exploring Operation: 64/2=32, Resulting Numbers: [3, 79, 32] Generated Node #0,3: 43:[3, 79, 32] Operation: 64/2=32 Exploring Operation: 79-3=76, Resulting Numbers: [64, 2, 76] Generated Node #0,4: 43:[64, 2, 76] Operation: 79-3=76 Moving to Node #0,3 Current State: 43:[3, 79, 32], Operations: ['64/2=32'] Exploring Operation: 79-32=47, Resulting Numbers: [3, 47] Generated Node #0,3,0: 43:[3, 47] Operation: 79-32=47 Exploring Operation: 79-3=76, Resulting Numbers: [32, 76] Generated Node #0,3,1: 43:[32, 76] Operation: 79-3=76 Exploring Operation: 3+79=82, Resulting Numbers: [32, 82] Generated Node #0,3,2: 43:[32, 82] Operation: 3+79=82 Exploring Operation: 32-3=29, Resulting Numbers: [79, 29] Generated Node #0,3,3: 43:[79, 29] Operation: 32-3=29 Exploring Operation: 3+32=35, Resulting Numbers: [79, 35] Generated Node #0,3,4: 43:[79, 35] Operation: 3+32=35 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 43:[3, 47], Operations: ['64/2=32', '79-32=47'] Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,43 unequal: No Solution Exploring Operation: 3*47=141, Resulting Numbers: [141] 141,43 unequal: No Solution Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,43 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 #0,3,1 Current State: 43:[32, 76], Operations: ['64/2=32', '79-3=76'] Exploring Operation: 32+76=108, Resulting Numbers: [108] 108,43 unequal: No Solution Exploring Operation: 32*76=2432, Resulting Numbers: [2432] 2432,43 unequal: No Solution Exploring Operation: 76-32=44, Resulting Numbers: [44] 44,43 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 #0,3,4 Current State: 43:[79, 35], Operations: ['64/2=32', '3+32=35'] Exploring Operation: 79*35=2765, Resulting Numbers: [2765] 2765,43 unequal: No Solution Exploring Operation: 79+35=114, Resulting Numbers: [114] 114,43 unequal: No Solution Exploring Operation: 79-35=44, Resulting Numbers: [44] 44,43 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 #0,3,2 Current State: 43:[32, 82], Operations: ['64/2=32', '3+79=82'] Exploring Operation: 82-32=50, Resulting Numbers: [50] 50,43 unequal: No Solution Exploring Operation: 32*82=2624, Resulting Numbers: [2624] 2624,43 unequal: No Solution Exploring Operation: 32+82=114, Resulting Numbers: [114] 114,43 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 #0,3,3 Current State: 43:[79, 29], Operations: ['64/2=32', '32-3=29'] Exploring Operation: 79*29=2291, Resulting Numbers: [2291] 2291,43 unequal: No Solution Exploring Operation: 79+29=108, Resulting Numbers: [108] 108,43 unequal: No Solution Exploring Operation: 79-29=50, Resulting Numbers: [50] 50,43 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: 43:[64, 79, 6], Operations: ['3*2=6'] Exploring Operation: 79+6=85, Resulting Numbers: [64, 85] Generated Node #0,1,0: 43:[64, 85] Operation: 79+6=85 Exploring Operation: 64-6=58, Resulting Numbers: [79, 58] Generated Node #0,1,1: 43:[79, 58] Operation: 64-6=58 Exploring Operation: 64+6=70, Resulting Numbers: [79, 70] Generated Node #0,1,2: 43:[79, 70] Operation: 64+6=70 Exploring Operation: 79-64=15, Resulting Numbers: [6, 15] Generated Node #0,1,3: 43:[6, 15] Operation: 79-64=15 Exploring Operation: 79-6=73, Resulting Numbers: [64, 73] Generated Node #0,1,4: 43:[64, 73] Operation: 79-6=73 Moving to Node #0,0 Current State: 43:[3, 79, 62], Operations: ['64-2=62'] Exploring Operation: 3+79=82, Resulting Numbers: [62, 82] Generated Node #0,0,0: 43:[62, 82] Operation: 3+79=82 Exploring Operation: 3+62=65, Resulting Numbers: [79, 65] Generated Node #0,0,1: 43:[79, 65] Operation: 3+62=65 Exploring Operation: 79-3=76, Resulting Numbers: [62, 76] Generated Node #0,0,2: 43:[62, 76] Operation: 79-3=76 Exploring Operation: 62-3=59, Resulting Numbers: [79, 59] Generated Node #0,0,3: 43:[79, 59] Operation: 62-3=59 Exploring Operation: 79-62=17, Resulting Numbers: [3, 17] Generated Node #0,0,4: 43:[3, 17] Operation: 79-62=17 Moving to Node #0,2 Current State: 43:[79, 2, 61], Operations: ['64-3=61'] Exploring Operation: 79-61=18, Resulting Numbers: [2, 18] Generated Node #0,2,0: 43:[2, 18] Operation: 79-61=18 Exploring Operation: 79+2=81, Resulting Numbers: [61, 81] Generated Node #0,2,1: 43:[61, 81] Operation: 79+2=81 Exploring Operation: 2+61=63, Resulting Numbers: [79, 63] Generated Node #0,2,2: 43:[79, 63] Operation: 2+61=63 Exploring Operation: 61-2=59, Resulting Numbers: [79, 59] Generated Node #0,2,3: 43:[79, 59] Operation: 61-2=59 Exploring Operation: 79-2=77, Resulting Numbers: [61, 77] Generated Node #0,2,4: 43:[61, 77] Operation: 79-2=77 Moving to Node #0,4 Current State: 43:[64, 2, 76], Operations: ['79-3=76'] Exploring Operation: 64-2=62, Resulting Numbers: [76, 62] Generated Node #0,4,0: 43:[76, 62] Operation: 64-2=62 Exploring Operation: 76-2=74, Resulting Numbers: [64, 74] Generated Node #0,4,1: 43:[64, 74] Operation: 76-2=74 Exploring Operation: 76/2=38, Resulting Numbers: [64, 38] Generated Node #0,4,2: 43:[64, 38] Operation: 76/2=38 Exploring Operation: 64/2=32, Resulting Numbers: [76, 32] Generated Node #0,4,3: 43:[76, 32] Operation: 64/2=32 Exploring Operation: 64+2=66, Resulting Numbers: [76, 66] Generated Node #0,4,4: 43:[76, 66] Operation: 64+2=66 Moving to Node #0,4,2 Current State: 43:[64, 38], Operations: ['79-3=76', '76/2=38'] Exploring Operation: 64-38=26, Resulting Numbers: [26] 26,43 unequal: No Solution Exploring Operation: 64*38=2432, Resulting Numbers: [2432] 2432,43 unequal: No Solution Exploring Operation: 64+38=102, Resulting Numbers: [102] 102,43 unequal: No Solution Moving to Node #0,4,3 Current State: 43:[76, 32], Operations: ['79-3=76', '64/2=32'] Exploring Operation: 76*32=2432, Resulting Numbers: [2432] 2432,43 unequal: No Solution Exploring Operation: 76-32=44, Resulting Numbers: [44] 44,43 unequal: No Solution Exploring Operation: 76+32=108, Resulting Numbers: [108] 108,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[79, 58], Operations: ['3*2=6', '64-6=58'] Exploring Operation: 79+58=137, Resulting Numbers: [137] 137,43 unequal: No Solution Exploring Operation: 79*58=4582, Resulting Numbers: [4582] 4582,43 unequal: No Solution Exploring Operation: 79-58=21, Resulting Numbers: [21] 21,43 unequal: No Solution Moving to Node #0,1,4 Current State: 43:[64, 73], Operations: ['3*2=6', '79-6=73'] Exploring Operation: 73-64=9, Resulting Numbers: [9] 9,43 unequal: No Solution Exploring Operation: 64*73=4672, Resulting Numbers: [4672] 4672,43 unequal: No Solution Exploring Operation: 64+73=137, Resulting Numbers: [137] 137,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[62, 76], Operations: ['64-2=62', '79-3=76'] Exploring Operation: 62*76=4712, Resulting Numbers: [4712] 4712,43 unequal: No Solution Exploring Operation: 62+76=138, Resulting Numbers: [138] 138,43 unequal: No Solution Exploring Operation: 76-62=14, Resulting Numbers: [14] 14,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[79, 59], Operations: ['64-2=62', '62-3=59'] Exploring Operation: 79*59=4661, Resulting Numbers: [4661] 4661,43 unequal: No Solution Exploring Operation: 79+59=138, Resulting Numbers: [138] 138,43 unequal: No Solution Exploring Operation: 79-59=20, Resulting Numbers: [20] 20,43 unequal: No Solution Moving to Node #0,2,4 Current State: 43:[61, 77], Operations: ['64-3=61', '79-2=77'] Exploring Operation: 61+77=138, Resulting Numbers: [138] 138,43 unequal: No Solution Exploring Operation: 61*77=4697, Resulting Numbers: [4697] 4697,43 unequal: No Solution Exploring Operation: 77-61=16, Resulting Numbers: [16] 16,43 unequal: No Solution Moving to Node #0,2,3 Current State: 43:[79, 59], Operations: ['64-3=61', '61-2=59'] Exploring Operation: 79*59=4661, Resulting Numbers: [4661] 4661,43 unequal: No Solution Exploring Operation: 79-59=20, Resulting Numbers: [20] 20,43 unequal: No Solution Exploring Operation: 79+59=138, Resulting Numbers: [138] 138,43 unequal: No Solution Moving to Node #0,4,0 Current State: 43:[76, 62], Operations: ['79-3=76', '64-2=62'] Exploring Operation: 76-62=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 76*62=4712, Resulting Numbers: [4712] 4712,43 unequal: No Solution Exploring Operation: 76+62=138, Resulting Numbers: [138] 138,43 unequal: No Solution Moving to Node #0,4,1 Current State: 43:[64, 74], Operations: ['79-3=76', '76-2=74'] Exploring Operation: 64*74=4736, Resulting Numbers: [4736] 4736,43 unequal: No Solution Exploring Operation: 64+74=138, Resulting Numbers: [138] 138,43 unequal: No Solution Exploring Operation: 74-64=10, Resulting Numbers: [10] 10,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[79, 63], Operations: ['64-3=61', '2+61=63'] Exploring Operation: 79*63=4977, Resulting Numbers: [4977] 4977,43 unequal: No Solution Exploring Operation: 79+63=142, Resulting Numbers: [142] 142,43 unequal: No Solution Exploring Operation: 79-63=16, Resulting Numbers: [16] 16,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[61, 81], Operations: ['64-3=61', '79+2=81'] Exploring Operation: 61*81=4941, Resulting Numbers: [4941] 4941,43 unequal: No Solution Exploring Operation: 61+81=142, Resulting Numbers: [142] 142,43 unequal: No Solution Exploring Operation: 81-61=20, Resulting Numbers: [20] 20,43 unequal: No Solution Moving to Node #0,4,4 Current State: 43:[76, 66], Operations: ['79-3=76', '64+2=66'] Exploring Operation: 76-66=10, Resulting Numbers: [10] 10,43 unequal: No Solution Exploring Operation: 76+66=142, Resulting Numbers: [142] 142,43 unequal: No Solution Exploring Operation: 76*66=5016, Resulting Numbers: [5016] 5016,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[79, 65], Operations: ['64-2=62', '3+62=65'] Exploring Operation: 79+65=144, Resulting Numbers: [144] 144,43 unequal: No Solution Exploring Operation: 79*65=5135, Resulting Numbers: [5135] 5135,43 unequal: No Solution Exploring Operation: 79-65=14, Resulting Numbers: [14] 14,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[62, 82], Operations: ['64-2=62', '3+79=82'] Exploring Operation: 82-62=20, Resulting Numbers: [20] 20,43 unequal: No Solution Exploring Operation: 62*82=5084, Resulting Numbers: [5084] 5084,43 unequal: No Solution Exploring Operation: 62+82=144, Resulting Numbers: [144] 144,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[64, 85], Operations: ['3*2=6', '79+6=85'] Exploring Operation: 64*85=5440, Resulting Numbers: [5440] 5440,43 unequal: No Solution Exploring Operation: 85-64=21, Resulting Numbers: [21] 21,43 unequal: No Solution Exploring Operation: 64+85=149, Resulting Numbers: [149] 149,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[79, 70], Operations: ['3*2=6', '64+6=70'] Exploring Operation: 79+70=149, Resulting Numbers: [149] 149,43 unequal: No Solution Exploring Operation: 79*70=5530, Resulting Numbers: [5530] 5530,43 unequal: No Solution Exploring Operation: 79-70=9, Resulting Numbers: [9] 9,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[6, 15], Operations: ['3*2=6', '79-64=15'] Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,43 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,43 unequal: No Solution Moving to Node #0,0,4 Current State: 43:[3, 17], Operations: ['64-2=62', '79-62=17'] Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,43 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[2, 18], Operations: ['64-3=61', '79-61=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,43 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,43 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,43 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 22, 6, 41, 38 ]
19
[ "22-6=16", "41-38=3", "16+3=19" ]
Current State: 19:[22, 6, 41, 38], Operations: [] Exploring Operation: 22-6=16, Resulting Numbers: [41, 38, 16] Generated Node #2: [41, 38, 16] from Operation: 22-6=16 Current State: 19:[41, 38, 16], Operations: ['22-6=16'] Exploring Operation: 41-38=3, Resulting Numbers: [16, 3] Generated Node #3: [16, 3] from Operation: 41-38=3 Current State: 19:[16, 3], Operations: ['22-6=16', '41-38=3'] Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[22, 6, 41, 38], Operations: [] Exploring Operation: 41-22=19, Resulting Numbers: [6, 38, 19] Generated Node #0,0: 19:[6, 38, 19] Operation: 41-22=19 Exploring Operation: 41-38=3, Resulting Numbers: [22, 6, 3] Generated Node #0,1: 19:[22, 6, 3] Operation: 41-38=3 Exploring Operation: 38-22=16, Resulting Numbers: [6, 41, 16] Generated Node #0,2: 19:[6, 41, 16] Operation: 38-22=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[6, 38, 19], Operations: ['41-22=19'] Exploring Operation: 38-19=19, Resulting Numbers: [6, 19] Generated Node #0,0,0: 19:[6, 19] Operation: 38-19=19 Exploring Operation: 38-6=32, Resulting Numbers: [19, 32] Generated Node #0,0,1: 19:[19, 32] Operation: 38-6=32 Exploring Operation: 6+38=44, Resulting Numbers: [19, 44] Generated Node #0,0,2: 19:[19, 44] Operation: 6+38=44 Moving to Node #0,0,0 Current State: 19:[6, 19], Operations: ['41-22=19', '38-19=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,19 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,19 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,19 unequal: No Solution Moving to Node #0,0,1 Current State: 19:[19, 32], Operations: ['41-22=19', '38-6=32'] Exploring Operation: 19*32=608, Resulting Numbers: [608] 608,19 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,19 unequal: No Solution Exploring Operation: 19+32=51, Resulting Numbers: [51] 51,19 unequal: No Solution Moving to Node #0,0,2 Current State: 19:[19, 44], Operations: ['41-22=19', '6+38=44'] Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 19+44=63, Resulting Numbers: [63] 63,19 unequal: No Solution Exploring Operation: 19*44=836, Resulting Numbers: [836] 836,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[22, 6, 3], Operations: ['41-38=3'] Exploring Operation: 6*3=18, Resulting Numbers: [22, 18] Generated Node #0,1,0: 19:[22, 18] Operation: 6*3=18 Exploring Operation: 6+3=9, Resulting Numbers: [22, 9] Generated Node #0,1,1: 19:[22, 9] Operation: 6+3=9 Exploring Operation: 22-3=19, Resulting Numbers: [6, 19] Generated Node #0,1,2: 19:[6, 19] Operation: 22-3=19 Moving to Node #0,1,0 Current State: 19:[22, 18], Operations: ['41-38=3', '6*3=18'] Exploring Operation: 22+18=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 22*18=396, Resulting Numbers: [396] 396,19 unequal: No Solution Moving to Node #0,1,1 Current State: 19:[22, 9], Operations: ['41-38=3', '6+3=9'] Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,19 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,19 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,19 unequal: No Solution Moving to Node #0,1,2 Current State: 19:[6, 19], Operations: ['41-38=3', '22-3=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,19 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[6, 41, 16], Operations: ['38-22=16'] Exploring Operation: 41-16=25, Resulting Numbers: [6, 25] Generated Node #0,2,0: 19:[6, 25] Operation: 41-16=25 Exploring Operation: 6+16=22, Resulting Numbers: [41, 22] Generated Node #0,2,1: 19:[41, 22] Operation: 6+16=22 Exploring Operation: 41-6=35, Resulting Numbers: [16, 35] Generated Node #0,2,2: 19:[16, 35] Operation: 41-6=35 Moving to Node #0,2,0 Current State: 19:[6, 25], Operations: ['38-22=16', '41-16=25'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[22, 6, 41, 38], Operations: [] Exploring Operation: 38-22=16, Resulting Numbers: [6, 41, 16] Generated Node #0,2: 19:[6, 41, 16] Operation: 38-22=16 Moving to Node #0,2 Current State: 19:[6, 41, 16], Operations: ['38-22=16'] Exploring Operation: 41-16=25, Resulting Numbers: [6, 25] Generated Node #0,2,0: 19:[6, 25] Operation: 41-16=25 Moving to Node #0,2,0 Current State: 19:[6, 25], Operations: ['38-22=16', '41-16=25'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_3
sum_heuristic
[ 11, 29, 83, 47 ]
81
[ "11+47=58", "58/29=2", "83-2=81" ]
Current State: 81:[11, 29, 83, 47], Operations: [] Exploring Operation: 11+47=58, Resulting Numbers: [29, 83, 58] Generated Node #2: [29, 83, 58] from Operation: 11+47=58 Current State: 81:[29, 83, 58], Operations: ['11+47=58'] Exploring Operation: 58/29=2, Resulting Numbers: [83, 2] Generated Node #3: [83, 2] from Operation: 58/29=2 Current State: 81:[83, 2], Operations: ['11+47=58', '58/29=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[11, 29, 83, 47], Operations: [] Exploring Operation: 29+47=76, Resulting Numbers: [11, 83, 76] Generated Node #0,0: 81:[11, 83, 76] Operation: 29+47=76 Moving to Node #0,0 Current State: 81:[11, 83, 76], Operations: ['29+47=76'] Exploring Operation: 83-76=7, Resulting Numbers: [11, 7] Generated Node #0,0,0: 81:[11, 7] Operation: 83-76=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[11, 7], Operations: ['29+47=76', '83-76=7'] Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,81 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
[ 76, 45, 40, 10 ]
38
[ "45-40=5", "76*5=380", "380/10=38" ]
Current State: 38:[76, 45, 40, 10], Operations: [] Exploring Operation: 45-40=5, Resulting Numbers: [76, 10, 5] Generated Node #2: [76, 10, 5] from Operation: 45-40=5 Current State: 38:[76, 10, 5], Operations: ['45-40=5'] Exploring Operation: 76*5=380, Resulting Numbers: [10, 380] Generated Node #3: [10, 380] from Operation: 76*5=380 Current State: 38:[10, 380], Operations: ['45-40=5', '76*5=380'] Exploring Operation: 380/10=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[76, 45, 40, 10], Operations: [] Exploring Operation: 76-10=66, Resulting Numbers: [45, 40, 66] Generated Node #0,0: 38:[45, 40, 66] Operation: 76-10=66 Exploring Operation: 76-40=36, Resulting Numbers: [45, 10, 36] Generated Node #0,1: 38:[45, 10, 36] Operation: 76-40=36 Exploring Operation: 76-45=31, Resulting Numbers: [40, 10, 31] Generated Node #0,2: 38:[40, 10, 31] Operation: 76-45=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[45, 10, 36], Operations: ['76-40=36'] Exploring Operation: 45-36=9, Resulting Numbers: [10, 9] Generated Node #0,1,0: 38:[10, 9] Operation: 45-36=9 Exploring Operation: 45-10=35, Resulting Numbers: [36, 35] Generated Node #0,1,1: 38:[36, 35] Operation: 45-10=35 Exploring Operation: 36-10=26, Resulting Numbers: [45, 26] Generated Node #0,1,2: 38:[45, 26] Operation: 36-10=26 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 38:[36, 35], Operations: ['76-40=36', '45-10=35'] Exploring Operation: 36*35=1260, Resulting Numbers: [1260] 1260,38 unequal: No Solution Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 36+35=71, Resulting Numbers: [71] 71,38 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:[45, 26], Operations: ['76-40=36', '36-10=26'] Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 45*26=1170, Resulting Numbers: [1170] 1170,38 unequal: No Solution Exploring Operation: 45+26=71, Resulting Numbers: [71] 71,38 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 #0,1,0 Current State: 38:[10, 9], Operations: ['76-40=36', '45-36=9'] Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,38 unequal: No Solution Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,38 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:[40, 10, 31], Operations: ['76-45=31'] Exploring Operation: 40/10=4, Resulting Numbers: [31, 4] Generated Node #0,2,0: 38:[31, 4] Operation: 40/10=4 Exploring Operation: 10+31=41, Resulting Numbers: [40, 41] Generated Node #0,2,1: 38:[40, 41] Operation: 10+31=41 Exploring Operation: 31-10=21, Resulting Numbers: [40, 21] Generated Node #0,2,2: 38:[40, 21] Operation: 31-10=21 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 38:[40, 21], Operations: ['76-45=31', '31-10=21'] Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 40*21=840, Resulting Numbers: [840] 840,38 unequal: No Solution Exploring Operation: 40+21=61, Resulting Numbers: [61] 61,38 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 #0,2,1 Current State: 38:[40, 41], Operations: ['76-45=31', '10+31=41'] Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,38 unequal: No Solution Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,38 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,38 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 #0,2,0 Current State: 38:[31, 4], Operations: ['76-45=31', '40/10=4'] Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,38 unequal: No Solution Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,38 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,38 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 #0,0 Current State: 38:[45, 40, 66], Operations: ['76-10=66'] Exploring Operation: 66-40=26, Resulting Numbers: [45, 26] Generated Node #0,0,0: 38:[45, 26] Operation: 66-40=26 Exploring Operation: 45-40=5, Resulting Numbers: [66, 5] Generated Node #0,0,1: 38:[66, 5] Operation: 45-40=5 Exploring Operation: 66-45=21, Resulting Numbers: [40, 21] Generated Node #0,0,2: 38:[40, 21] Operation: 66-45=21 Moving to Node #0,0,2 Current State: 38:[40, 21], Operations: ['76-10=66', '66-45=21'] Exploring Operation: 40+21=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 40*21=840, Resulting Numbers: [840] 840,38 unequal: No Solution Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[45, 26], Operations: ['76-10=66', '66-40=26'] Exploring Operation: 45*26=1170, Resulting Numbers: [1170] 1170,38 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 45+26=71, Resulting Numbers: [71] 71,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[66, 5], Operations: ['76-10=66', '45-40=5'] Exploring Operation: 66*5=330, Resulting Numbers: [330] 330,38 unequal: No Solution Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,38 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
[ 37, 27, 36, 54 ]
100
[ "37-27=10", "36+54=90", "10+90=100" ]
Current State: 100:[37, 27, 36, 54], Operations: [] Exploring Operation: 37-27=10, Resulting Numbers: [36, 54, 10] Generated Node #2: [36, 54, 10] from Operation: 37-27=10 Current State: 100:[36, 54, 10], Operations: ['37-27=10'] Exploring Operation: 36+54=90, Resulting Numbers: [10, 90] Generated Node #3: [10, 90] from Operation: 36+54=90 Current State: 100:[10, 90], Operations: ['37-27=10', '36+54=90'] Exploring Operation: 10+90=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[37, 27, 36, 54], Operations: [] Exploring Operation: 37-27=10, Resulting Numbers: [36, 54, 10] Generated Node #0,0: 100:[36, 54, 10] Operation: 37-27=10 Exploring Operation: 36-27=9, Resulting Numbers: [37, 54, 9] Generated Node #0,1: 100:[37, 54, 9] Operation: 36-27=9 Exploring Operation: 54-36=18, Resulting Numbers: [37, 27, 18] Generated Node #0,2: 100:[37, 27, 18] Operation: 54-36=18 Exploring Operation: 37-36=1, Resulting Numbers: [27, 54, 1] Generated Node #0,3: 100:[27, 54, 1] Operation: 37-36=1 Exploring Operation: 54-37=17, Resulting Numbers: [27, 36, 17] Generated Node #0,4: 100:[27, 36, 17] Operation: 54-37=17 Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[27, 54, 1], Operations: ['37-36=1'] Exploring Operation: 54/27=2, Resulting Numbers: [1, 2] Generated Node #0,3,0: 100:[1, 2] Operation: 54/27=2 Exploring Operation: 27*1=27, Resulting Numbers: [54, 27] Generated Node #0,3,1: 100:[54, 27] Operation: 27*1=27 Exploring Operation: 54-27=27, Resulting Numbers: [1, 27] Generated Node #0,3,2: 100:[1, 27] Operation: 54-27=27 Exploring Operation: 54-1=53, Resulting Numbers: [27, 53] Generated Node #0,3,3: 100:[27, 53] Operation: 54-1=53 Exploring Operation: 27-1=26, Resulting Numbers: [54, 26] Generated Node #0,3,4: 100:[54, 26] Operation: 27-1=26 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 100:[1, 2], Operations: ['37-36=1', '54/27=2'] Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,100 unequal: No Solution No 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: 100:[1, 27], Operations: ['37-36=1', '54-27=27'] Exploring Operation: 1*27=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,100 unequal: No Solution Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 1+27=28, Resulting Numbers: [28] 28,100 unequal: No Solution No 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: 100:[27, 53], Operations: ['37-36=1', '54-1=53'] Exploring Operation: 27+53=80, Resulting Numbers: [80] 80,100 unequal: No Solution Exploring Operation: 27*53=1431, Resulting Numbers: [1431] 1431,100 unequal: No Solution Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 100:[54, 26], Operations: ['37-36=1', '27-1=26'] Exploring Operation: 54*26=1404, Resulting Numbers: [1404] 1404,100 unequal: No Solution Exploring Operation: 54+26=80, Resulting Numbers: [80] 80,100 unequal: No Solution Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,100 unequal: No Solution No 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: 100:[54, 27], Operations: ['37-36=1', '27*1=27'] Exploring Operation: 54*27=1458, Resulting Numbers: [1458] 1458,100 unequal: No Solution Exploring Operation: 54-27=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 54+27=81, Resulting Numbers: [81] 81,100 unequal: No Solution Exploring Operation: 54/27=2, Resulting Numbers: [2] 2,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[36, 54, 10], Operations: ['37-27=10'] Exploring Operation: 36+54=90, Resulting Numbers: [10, 90] Generated Node #0,0,0: 100:[10, 90] Operation: 36+54=90 Exploring Operation: 36-10=26, Resulting Numbers: [54, 26] Generated Node #0,0,1: 100:[54, 26] Operation: 36-10=26 Exploring Operation: 54-36=18, Resulting Numbers: [10, 18] Generated Node #0,0,2: 100:[10, 18] Operation: 54-36=18 Exploring Operation: 54-10=44, Resulting Numbers: [36, 44] Generated Node #0,0,3: 100:[36, 44] Operation: 54-10=44 Exploring Operation: 36+10=46, Resulting Numbers: [54, 46] Generated Node #0,0,4: 100:[54, 46] Operation: 36+10=46 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 100:[10, 18], Operations: ['37-27=10', '54-36=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,100 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,100 unequal: No Solution No 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: 100:[54, 26], Operations: ['37-27=10', '36-10=26'] Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 54*26=1404, Resulting Numbers: [1404] 1404,100 unequal: No Solution Exploring Operation: 54+26=80, Resulting Numbers: [80] 80,100 unequal: No Solution No 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: 100:[54, 46], Operations: ['37-27=10', '36+10=46'] Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,100 unequal: No Solution Exploring Operation: 54*46=2484, Resulting Numbers: [2484] 2484,100 unequal: No Solution Exploring Operation: 54+46=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[37, 27, 36, 54], Operations: [] Exploring Operation: 37-27=10, Resulting Numbers: [36, 54, 10] Generated Node #0,0: 100:[36, 54, 10] Operation: 37-27=10 Moving to Node #0,0 Current State: 100:[36, 54, 10], Operations: ['37-27=10'] Exploring Operation: 36+10=46, Resulting Numbers: [54, 46] Generated Node #0,0,4: 100:[54, 46] Operation: 36+10=46 Moving to Node #0,0,4 Current State: 100:[54, 46], Operations: ['37-27=10', '36+10=46'] Exploring Operation: 54+46=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.960069
hs_5
sum_heuristic
[ 33, 92, 53, 46 ]
26
[ "33+92=125", "53+46=99", "125-99=26" ]
Current State: 26:[33, 92, 53, 46], Operations: [] Exploring Operation: 33+92=125, Resulting Numbers: [53, 46, 125] Generated Node #2: [53, 46, 125] from Operation: 33+92=125 Current State: 26:[53, 46, 125], Operations: ['33+92=125'] Exploring Operation: 53+46=99, Resulting Numbers: [125, 99] Generated Node #3: [125, 99] from Operation: 53+46=99 Current State: 26:[125, 99], Operations: ['33+92=125', '53+46=99'] Exploring Operation: 125-99=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[33, 92, 53, 46], Operations: [] Exploring Operation: 92-46=46, Resulting Numbers: [33, 53, 46] Generated Node #0,0: 26:[33, 53, 46] Operation: 92-46=46 Exploring Operation: 53-46=7, Resulting Numbers: [33, 92, 7] Generated Node #0,1: 26:[33, 92, 7] Operation: 53-46=7 Exploring Operation: 92-53=39, Resulting Numbers: [33, 46, 39] Generated Node #0,2: 26:[33, 46, 39] Operation: 92-53=39 Exploring Operation: 92/46=2, Resulting Numbers: [33, 53, 2] Generated Node #0,3: 26:[33, 53, 2] Operation: 92/46=2 Moving to Node #0,3 Current State: 26:[33, 53, 2], Operations: ['92/46=2'] Exploring Operation: 33-2=31, Resulting Numbers: [53, 31] Generated Node #0,3,0: 26:[53, 31] Operation: 33-2=31 Exploring Operation: 33+2=35, Resulting Numbers: [53, 35] Generated Node #0,3,1: 26:[53, 35] Operation: 33+2=35 Exploring Operation: 53-33=20, Resulting Numbers: [2, 20] Generated Node #0,3,2: 26:[2, 20] Operation: 53-33=20 Exploring Operation: 53-2=51, Resulting Numbers: [33, 51] Generated Node #0,3,3: 26:[33, 51] Operation: 53-2=51 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 26:[2, 20], Operations: ['92/46=2', '53-33=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,26 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,26 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 26:[53, 31], Operations: ['92/46=2', '33-2=31'] Exploring Operation: 53+31=84, Resulting Numbers: [84] 84,26 unequal: No Solution Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,26 unequal: No Solution Exploring Operation: 53*31=1643, Resulting Numbers: [1643] 1643,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 26:[33, 51], Operations: ['92/46=2', '53-2=51'] Exploring Operation: 51-33=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 33*51=1683, Resulting Numbers: [1683] 1683,26 unequal: No Solution Exploring Operation: 33+51=84, Resulting Numbers: [84] 84,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 26:[53, 35], Operations: ['92/46=2', '33+2=35'] Exploring Operation: 53*35=1855, Resulting Numbers: [1855] 1855,26 unequal: No Solution Exploring Operation: 53+35=88, Resulting Numbers: [88] 88,26 unequal: No Solution Exploring Operation: 53-35=18, Resulting Numbers: [18] 18,26 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: 26:[33, 46, 39], Operations: ['92-53=39'] Exploring Operation: 46-39=7, Resulting Numbers: [33, 7] Generated Node #0,2,0: 26:[33, 7] Operation: 46-39=7 Exploring Operation: 39-33=6, Resulting Numbers: [46, 6] Generated Node #0,2,1: 26:[46, 6] Operation: 39-33=6 Exploring Operation: 33+46=79, Resulting Numbers: [39, 79] Generated Node #0,2,2: 26:[39, 79] Operation: 33+46=79 Exploring Operation: 46-33=13, Resulting Numbers: [39, 13] Generated Node #0,2,3: 26:[39, 13] Operation: 46-33=13 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 26:[33, 7], Operations: ['92-53=39', '46-39=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,26 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[33, 92, 53, 46], Operations: [] Exploring Operation: 92-53=39, Resulting Numbers: [33, 46, 39] Generated Node #0,2: 26:[33, 46, 39] Operation: 92-53=39 Moving to Node #0,2 Current State: 26:[33, 46, 39], Operations: ['92-53=39'] Exploring Operation: 46-39=7, Resulting Numbers: [33, 7] Generated Node #0,2,0: 26:[33, 7] Operation: 46-39=7 Moving to Node #0,2,0 Current State: 26:[33, 7], Operations: ['92-53=39', '46-39=7'] Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 95, 96, 2, 81 ]
78
[ "96-95=1", "81-2=79", "79-1=78" ]
Current State: 78:[95, 96, 2, 81], Operations: [] Exploring Operation: 96-95=1, Resulting Numbers: [2, 81, 1] Generated Node #2: [2, 81, 1] from Operation: 96-95=1 Current State: 78:[2, 81, 1], Operations: ['96-95=1'] Exploring Operation: 81-2=79, Resulting Numbers: [1, 79] Generated Node #3: [1, 79] from Operation: 81-2=79 Current State: 78:[1, 79], Operations: ['96-95=1', '81-2=79'] Exploring Operation: 79-1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[95, 96, 2, 81], Operations: [] Exploring Operation: 95-81=14, Resulting Numbers: [96, 2, 14] Generated Node #0,0: 78:[96, 2, 14] Operation: 95-81=14 Exploring Operation: 96-95=1, Resulting Numbers: [2, 81, 1] Generated Node #0,1: 78:[2, 81, 1] Operation: 96-95=1 Exploring Operation: 96-81=15, Resulting Numbers: [95, 2, 15] Generated Node #0,2: 78:[95, 2, 15] Operation: 96-81=15 Exploring Operation: 96/2=48, Resulting Numbers: [95, 81, 48] Generated Node #0,3: 78:[95, 81, 48] Operation: 96/2=48 Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[2, 81, 1], Operations: ['96-95=1'] Exploring Operation: 2+1=3, Resulting Numbers: [81, 3] Generated Node #0,1,0: 78:[81, 3] Operation: 2+1=3 Exploring Operation: 81-2=79, Resulting Numbers: [1, 79] Generated Node #0,1,1: 78:[1, 79] Operation: 81-2=79 Exploring Operation: 2*1=2, Resulting Numbers: [81, 2] Generated Node #0,1,2: 78:[81, 2] Operation: 2*1=2 Exploring Operation: 81-1=80, Resulting Numbers: [2, 80] Generated Node #0,1,3: 78:[2, 80] Operation: 81-1=80 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 78:[1, 79], Operations: ['96-95=1', '81-2=79'] Exploring Operation: 1*79=79, Resulting Numbers: [79] 79,78 unequal: No Solution Exploring Operation: 79-1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[95, 96, 2, 81], Operations: [] Exploring Operation: 96-95=1, Resulting Numbers: [2, 81, 1] Generated Node #0,1: 78:[2, 81, 1] Operation: 96-95=1 Moving to Node #0,1 Current State: 78:[2, 81, 1], Operations: ['96-95=1'] Exploring Operation: 81-2=79, Resulting Numbers: [1, 79] Generated Node #0,1,1: 78:[1, 79] Operation: 81-2=79 Moving to Node #0,1,1 Current State: 78:[1, 79], Operations: ['96-95=1', '81-2=79'] Exploring Operation: 79-1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 43, 72, 65, 68 ]
67
[ "68-65=3", "72/3=24", "43+24=67" ]
Current State: 67:[43, 72, 65, 68], Operations: [] Exploring Operation: 68-65=3, Resulting Numbers: [43, 72, 3] Generated Node #2: [43, 72, 3] from Operation: 68-65=3 Current State: 67:[43, 72, 3], Operations: ['68-65=3'] Exploring Operation: 72/3=24, Resulting Numbers: [43, 24] Generated Node #3: [43, 24] from Operation: 72/3=24 Current State: 67:[43, 24], Operations: ['68-65=3', '72/3=24'] Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[43, 72, 65, 68], Operations: [] Exploring Operation: 43+65=108, Resulting Numbers: [72, 68, 108] Generated Node #0,0: 67:[72, 68, 108] Operation: 43+65=108 Exploring Operation: 68-43=25, Resulting Numbers: [72, 65, 25] Generated Node #0,1: 67:[72, 65, 25] Operation: 68-43=25 Exploring Operation: 43+72=115, Resulting Numbers: [65, 68, 115] Generated Node #0,2: 67:[65, 68, 115] Operation: 43+72=115 Exploring Operation: 72-43=29, Resulting Numbers: [65, 68, 29] Generated Node #0,3: 67:[65, 68, 29] Operation: 72-43=29 Moving to Node #0,3 Current State: 67:[65, 68, 29], Operations: ['72-43=29'] Exploring Operation: 68-29=39, Resulting Numbers: [65, 39] Generated Node #0,3,0: 67:[65, 39] Operation: 68-29=39 Exploring Operation: 65+29=94, Resulting Numbers: [68, 94] Generated Node #0,3,1: 67:[68, 94] Operation: 65+29=94 Exploring Operation: 68+29=97, Resulting Numbers: [65, 97] Generated Node #0,3,2: 67:[65, 97] Operation: 68+29=97 Exploring Operation: 65-29=36, Resulting Numbers: [68, 36] Generated Node #0,3,3: 67:[68, 36] Operation: 65-29=36 Moving to Node #0,0 Current State: 67:[72, 68, 108], Operations: ['43+65=108'] Exploring Operation: 72+68=140, Resulting Numbers: [108, 140] Generated Node #0,0,0: 67:[108, 140] Operation: 72+68=140 Exploring Operation: 72-68=4, Resulting Numbers: [108, 4] Generated Node #0,0,1: 67:[108, 4] Operation: 72-68=4 Exploring Operation: 108-72=36, Resulting Numbers: [68, 36] Generated Node #0,0,2: 67:[68, 36] Operation: 108-72=36 Exploring Operation: 108-68=40, Resulting Numbers: [72, 40] Generated Node #0,0,3: 67:[72, 40] Operation: 108-68=40 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 67:[68, 36], Operations: ['43+65=108', '108-72=36'] Exploring Operation: 68-36=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 68+36=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 68*36=2448, Resulting Numbers: [2448] 2448,67 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 #0,0,3 Current State: 67:[72, 40], Operations: ['43+65=108', '108-68=40'] Exploring Operation: 72*40=2880, Resulting Numbers: [2880] 2880,67 unequal: No Solution Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 72+40=112, Resulting Numbers: [112] 112,67 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:[108, 4], Operations: ['43+65=108', '72-68=4'] Exploring Operation: 108*4=432, Resulting Numbers: [432] 432,67 unequal: No Solution Exploring Operation: 108+4=112, Resulting Numbers: [112] 112,67 unequal: No Solution Exploring Operation: 108/4=27, Resulting Numbers: [27] 27,67 unequal: No Solution Exploring Operation: 108-4=104, Resulting Numbers: [104] 104,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[108, 140], Operations: ['43+65=108', '72+68=140'] Exploring Operation: 108*140=15120, Resulting Numbers: [15120] 15120,67 unequal: No Solution Exploring Operation: 140-108=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 108+140=248, Resulting Numbers: [248] 248,67 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:[72, 65, 25], Operations: ['68-43=25'] Exploring Operation: 65+25=90, Resulting Numbers: [72, 90] Generated Node #0,1,0: 67:[72, 90] Operation: 65+25=90 Exploring Operation: 65-25=40, Resulting Numbers: [72, 40] Generated Node #0,1,1: 67:[72, 40] Operation: 65-25=40 Exploring Operation: 72+25=97, Resulting Numbers: [65, 97] Generated Node #0,1,2: 67:[65, 97] Operation: 72+25=97 Exploring Operation: 72-25=47, Resulting Numbers: [65, 47] Generated Node #0,1,3: 67:[65, 47] Operation: 72-25=47 Moving to Node #0,2 Current State: 67:[65, 68, 115], Operations: ['43+72=115'] Exploring Operation: 68-65=3, Resulting Numbers: [115, 3] Generated Node #0,2,0: 67:[115, 3] Operation: 68-65=3 Exploring Operation: 65+68=133, Resulting Numbers: [115, 133] Generated Node #0,2,1: 67:[115, 133] Operation: 65+68=133 Exploring Operation: 115-65=50, Resulting Numbers: [68, 50] Generated Node #0,2,2: 67:[68, 50] Operation: 115-65=50 Exploring Operation: 115-68=47, Resulting Numbers: [65, 47] Generated Node #0,2,3: 67:[65, 47] Operation: 115-68=47 Moving to Node #0,2,2 Current State: 67:[68, 50], Operations: ['43+72=115', '115-65=50'] Exploring Operation: 68*50=3400, Resulting Numbers: [3400] 3400,67 unequal: No Solution Exploring Operation: 68-50=18, Resulting Numbers: [18] 18,67 unequal: No Solution Exploring Operation: 68+50=118, Resulting Numbers: [118] 118,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[65, 47], Operations: ['68-43=25', '72-25=47'] Exploring Operation: 65-47=18, Resulting Numbers: [18] 18,67 unequal: No Solution Exploring Operation: 65*47=3055, Resulting Numbers: [3055] 3055,67 unequal: No Solution Exploring Operation: 65+47=112, Resulting Numbers: [112] 112,67 unequal: No Solution Moving to Node #0,2,3 Current State: 67:[65, 47], Operations: ['43+72=115', '115-68=47'] Exploring Operation: 65*47=3055, Resulting Numbers: [3055] 3055,67 unequal: No Solution Exploring Operation: 65+47=112, Resulting Numbers: [112] 112,67 unequal: No Solution Exploring Operation: 65-47=18, Resulting Numbers: [18] 18,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[72, 90], Operations: ['68-43=25', '65+25=90'] Exploring Operation: 72+90=162, Resulting Numbers: [162] 162,67 unequal: No Solution Exploring Operation: 72*90=6480, Resulting Numbers: [6480] 6480,67 unequal: No Solution Exploring Operation: 90-72=18, Resulting Numbers: [18] 18,67 unequal: No Solution Moving to Node #0,3,1 Current State: 67:[68, 94], Operations: ['72-43=29', '65+29=94'] Exploring Operation: 68+94=162, Resulting Numbers: [162] 162,67 unequal: No Solution Exploring Operation: 68*94=6392, Resulting Numbers: [6392] 6392,67 unequal: No Solution Exploring Operation: 94-68=26, Resulting Numbers: [26] 26,67 unequal: No Solution Moving to Node #0,3,0 Current State: 67:[65, 39], Operations: ['72-43=29', '68-29=39'] Exploring Operation: 65+39=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 65-39=26, Resulting Numbers: [26] 26,67 unequal: No Solution Exploring Operation: 65*39=2535, Resulting Numbers: [2535] 2535,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[72, 40], Operations: ['68-43=25', '65-25=40'] Exploring Operation: 72*40=2880, Resulting Numbers: [2880] 2880,67 unequal: No Solution Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 72+40=112, Resulting Numbers: [112] 112,67 unequal: No Solution Moving to Node #0,3,2 Current State: 67:[65, 97], Operations: ['72-43=29', '68+29=97'] Exploring Operation: 65*97=6305, Resulting Numbers: [6305] 6305,67 unequal: No Solution Exploring Operation: 97-65=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 65+97=162, Resulting Numbers: [162] 162,67 unequal: No Solution Moving to Node #0,3,3 Current State: 67:[68, 36], Operations: ['72-43=29', '65-29=36'] Exploring Operation: 68-36=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 68*36=2448, Resulting Numbers: [2448] 2448,67 unequal: No Solution Exploring Operation: 68+36=104, Resulting Numbers: [104] 104,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[65, 97], Operations: ['68-43=25', '72+25=97'] Exploring Operation: 65*97=6305, Resulting Numbers: [6305] 6305,67 unequal: No Solution Exploring Operation: 65+97=162, Resulting Numbers: [162] 162,67 unequal: No Solution Exploring Operation: 97-65=32, Resulting Numbers: [32] 32,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[115, 3], Operations: ['43+72=115', '68-65=3'] Exploring Operation: 115+3=118, Resulting Numbers: [118] 118,67 unequal: No Solution Exploring Operation: 115-3=112, Resulting Numbers: [112] 112,67 unequal: No Solution Exploring Operation: 115*3=345, Resulting Numbers: [345] 345,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[115, 133], Operations: ['43+72=115', '65+68=133'] Exploring Operation: 133-115=18, Resulting Numbers: [18] 18,67 unequal: No Solution Exploring Operation: 115*133=15295, Resulting Numbers: [15295] 15295,67 unequal: No Solution Exploring Operation: 115+133=248, Resulting Numbers: [248] 248,67 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 3, 45, 47, 96 ]
12
[ "45+47=92", "96-92=4", "3*4=12" ]
Current State: 12:[3, 45, 47, 96], Operations: [] Exploring Operation: 45+47=92, Resulting Numbers: [3, 96, 92] Generated Node #2: [3, 96, 92] from Operation: 45+47=92 Current State: 12:[3, 96, 92], Operations: ['45+47=92'] Exploring Operation: 96-92=4, Resulting Numbers: [3, 4] Generated Node #3: [3, 4] from Operation: 96-92=4 Current State: 12:[3, 4], Operations: ['45+47=92', '96-92=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[3, 45, 47, 96], Operations: [] Exploring Operation: 96-47=49, Resulting Numbers: [3, 45, 49] Generated Node #0,0: 12:[3, 45, 49] Operation: 96-47=49 Exploring Operation: 96-45=51, Resulting Numbers: [3, 47, 51] Generated Node #0,1: 12:[3, 47, 51] Operation: 96-45=51 Exploring Operation: 47-45=2, Resulting Numbers: [3, 96, 2] Generated Node #0,2: 12:[3, 96, 2] Operation: 47-45=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[3, 45, 49], Operations: ['96-47=49'] Exploring Operation: 45/3=15, Resulting Numbers: [49, 15] Generated Node #0,0,0: 12:[49, 15] Operation: 45/3=15 Exploring Operation: 49-45=4, Resulting Numbers: [3, 4] Generated Node #0,0,1: 12:[3, 4] Operation: 49-45=4 Exploring Operation: 45-3=42, Resulting Numbers: [49, 42] Generated Node #0,0,2: 12:[49, 42] Operation: 45-3=42 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 12:[3, 4], Operations: ['96-47=49', '49-45=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,12 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[3, 45, 47, 96], Operations: [] Exploring Operation: 96-47=49, Resulting Numbers: [3, 45, 49] Generated Node #0,0: 12:[3, 45, 49] Operation: 96-47=49 Moving to Node #0,0 Current State: 12:[3, 45, 49], Operations: ['96-47=49'] Exploring Operation: 49-45=4, Resulting Numbers: [3, 4] Generated Node #0,0,1: 12:[3, 4] Operation: 49-45=4 Moving to Node #0,0,1 Current State: 12:[3, 4], Operations: ['96-47=49', '49-45=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 27, 6, 4, 42 ]
45
[ "27+42=69", "6*4=24", "69-24=45" ]
Current State: 45:[27, 6, 4, 42], Operations: [] Exploring Operation: 27+42=69, Resulting Numbers: [6, 4, 69] Generated Node #2: [6, 4, 69] from Operation: 27+42=69 Current State: 45:[6, 4, 69], Operations: ['27+42=69'] Exploring Operation: 6*4=24, Resulting Numbers: [69, 24] Generated Node #3: [69, 24] from Operation: 6*4=24 Current State: 45:[69, 24], Operations: ['27+42=69', '6*4=24'] Exploring Operation: 69-24=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[27, 6, 4, 42], Operations: [] Exploring Operation: 42-27=15, Resulting Numbers: [6, 4, 15] Generated Node #0,0: 45:[6, 4, 15] Operation: 42-27=15 Exploring Operation: 27-4=23, Resulting Numbers: [6, 42, 23] Generated Node #0,1: 45:[6, 42, 23] Operation: 27-4=23 Exploring Operation: 27-6=21, Resulting Numbers: [4, 42, 21] Generated Node #0,2: 45:[4, 42, 21] Operation: 27-6=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[6, 4, 15], Operations: ['42-27=15'] Exploring Operation: 6-4=2, Resulting Numbers: [15, 2] Generated Node #0,0,0: 45:[15, 2] Operation: 6-4=2 Exploring Operation: 15-6=9, Resulting Numbers: [4, 9] Generated Node #0,0,1: 45:[4, 9] Operation: 15-6=9 Exploring Operation: 6+4=10, Resulting Numbers: [15, 10] Generated Node #0,0,2: 45:[15, 10] Operation: 6+4=10 Moving to Node #0,0,0 Current State: 45:[15, 2], Operations: ['42-27=15', '6-4=2'] Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,45 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,45 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[4, 9], Operations: ['42-27=15', '15-6=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,45 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,45 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[15, 10], Operations: ['42-27=15', '6+4=10'] Exploring Operation: 15*10=150, Resulting Numbers: [150] 150,45 unequal: No Solution Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 15+10=25, Resulting Numbers: [25] 25,45 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 Current State: 45:[4, 42, 21], Operations: ['27-6=21'] Exploring Operation: 4+42=46, Resulting Numbers: [21, 46] Generated Node #0,2,0: 45:[21, 46] Operation: 4+42=46 Exploring Operation: 42/21=2, Resulting Numbers: [4, 2] Generated Node #0,2,1: 45:[4, 2] Operation: 42/21=2 Exploring Operation: 21-4=17, Resulting Numbers: [42, 17] Generated Node #0,2,2: 45:[42, 17] Operation: 21-4=17 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 45:[4, 2], Operations: ['27-6=21', '42/21=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 45:[42, 17], Operations: ['27-6=21', '21-4=17'] Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,45 unequal: No Solution Exploring Operation: 42*17=714, Resulting Numbers: [714] 714,45 unequal: No Solution Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 45:[21, 46], Operations: ['27-6=21', '4+42=46'] Exploring Operation: 21*46=966, Resulting Numbers: [966] 966,45 unequal: No Solution Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,45 unequal: No Solution Exploring Operation: 21+46=67, Resulting Numbers: [67] 67,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[6, 42, 23], Operations: ['27-4=23'] Exploring Operation: 42/6=7, Resulting Numbers: [23, 7] Generated Node #0,1,0: 45:[23, 7] Operation: 42/6=7 Exploring Operation: 23-6=17, Resulting Numbers: [42, 17] Generated Node #0,1,1: 45:[42, 17] Operation: 23-6=17 Exploring Operation: 42-23=19, Resulting Numbers: [6, 19] Generated Node #0,1,2: 45:[6, 19] Operation: 42-23=19 Moving to Node #0,1,1 Current State: 45:[42, 17], Operations: ['27-4=23', '23-6=17'] Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,45 unequal: No Solution Exploring Operation: 42*17=714, Resulting Numbers: [714] 714,45 unequal: No Solution Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,45 unequal: No Solution Moving to Node #0,1,2 Current State: 45:[6, 19], Operations: ['27-4=23', '42-23=19'] Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,45 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,45 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[23, 7], Operations: ['27-4=23', '42/6=7'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 23*7=161, Resulting Numbers: [161] 161,45 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
[ 47, 81, 55, 3 ]
47
[ "81-47=34", "3*34=102", "102-55=47" ]
Current State: 47:[47, 81, 55, 3], Operations: [] Exploring Operation: 81-47=34, Resulting Numbers: [55, 3, 34] Generated Node #2: [55, 3, 34] from Operation: 81-47=34 Current State: 47:[55, 3, 34], Operations: ['81-47=34'] Exploring Operation: 3*34=102, Resulting Numbers: [55, 102] Generated Node #3: [55, 102] from Operation: 3*34=102 Current State: 47:[55, 102], Operations: ['81-47=34', '3*34=102'] Exploring Operation: 102-55=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[47, 81, 55, 3], Operations: [] Exploring Operation: 81/3=27, Resulting Numbers: [47, 55, 27] Generated Node #0,0: 47:[47, 55, 27] Operation: 81/3=27 Exploring Operation: 81-3=78, Resulting Numbers: [47, 55, 78] Generated Node #0,1: 47:[47, 55, 78] Operation: 81-3=78 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[47, 55, 27], Operations: ['81/3=27'] Exploring Operation: 47+27=74, Resulting Numbers: [55, 74] Generated Node #0,0,0: 47:[55, 74] Operation: 47+27=74 Exploring Operation: 55-27=28, Resulting Numbers: [47, 28] Generated Node #0,0,1: 47:[47, 28] Operation: 55-27=28 Moving to Node #0,0,1 Current State: 47:[47, 28], Operations: ['81/3=27', '55-27=28'] Exploring Operation: 47+28=75, Resulting Numbers: [75] 75,47 unequal: No Solution Exploring Operation: 47-28=19, Resulting Numbers: [19] 19,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[55, 74], Operations: ['81/3=27', '47+27=74'] Exploring Operation: 74-55=19, Resulting Numbers: [19] 19,47 unequal: No Solution Exploring Operation: 55+74=129, Resulting Numbers: [129] 129,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[47, 55, 78], Operations: ['81-3=78'] Exploring Operation: 78-55=23, Resulting Numbers: [47, 23] Generated Node #0,1,0: 47:[47, 23] Operation: 78-55=23 Exploring Operation: 78-47=31, Resulting Numbers: [55, 31] Generated Node #0,1,1: 47:[55, 31] Operation: 78-47=31 Moving to Node #0,1,0 Current State: 47:[47, 23], Operations: ['81-3=78', '78-55=23'] Exploring Operation: 47+23=70, Resulting Numbers: [70] 70,47 unequal: No Solution Exploring Operation: 47-23=24, Resulting Numbers: [24] 24,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[55, 31], Operations: ['81-3=78', '78-47=31'] Exploring Operation: 55+31=86, Resulting Numbers: [86] 86,47 unequal: No Solution Exploring Operation: 55-31=24, Resulting Numbers: [24] 24,47 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
[ 29, 56, 49, 23 ]
99
[ "56-29=27", "49+23=72", "27+72=99" ]
Current State: 99:[29, 56, 49, 23], Operations: [] Exploring Operation: 56-29=27, Resulting Numbers: [49, 23, 27] Generated Node #2: [49, 23, 27] from Operation: 56-29=27 Current State: 99:[49, 23, 27], Operations: ['56-29=27'] Exploring Operation: 49+23=72, Resulting Numbers: [27, 72] Generated Node #3: [27, 72] from Operation: 49+23=72 Current State: 99:[27, 72], Operations: ['56-29=27', '49+23=72'] Exploring Operation: 27+72=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[29, 56, 49, 23], Operations: [] Exploring Operation: 56+49=105, Resulting Numbers: [29, 23, 105] Generated Node #0,0: 99:[29, 23, 105] Operation: 56+49=105 Exploring Operation: 56-49=7, Resulting Numbers: [29, 23, 7] Generated Node #0,1: 99:[29, 23, 7] Operation: 56-49=7 Moving to Node #0,1 Current State: 99:[29, 23, 7], Operations: ['56-49=7'] Exploring Operation: 23+7=30, Resulting Numbers: [29, 30] Generated Node #0,1,0: 99:[29, 30] Operation: 23+7=30 Exploring Operation: 29-23=6, Resulting Numbers: [7, 6] Generated Node #0,1,1: 99:[7, 6] Operation: 29-23=6 Moving to Node #0,0 Current State: 99:[29, 23, 105], Operations: ['56+49=105'] Exploring Operation: 105-23=82, Resulting Numbers: [29, 82] Generated Node #0,0,0: 99:[29, 82] Operation: 105-23=82 Exploring Operation: 29-23=6, Resulting Numbers: [105, 6] Generated Node #0,0,1: 99:[105, 6] Operation: 29-23=6 Moving to Node #0,1,1 Current State: 99:[7, 6], Operations: ['56-49=7', '29-23=6'] Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,99 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[29, 30], Operations: ['56-49=7', '23+7=30'] Exploring Operation: 29+30=59, Resulting Numbers: [59] 59,99 unequal: No Solution Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[105, 6], Operations: ['56+49=105', '29-23=6'] Exploring Operation: 105+6=111, Resulting Numbers: [111] 111,99 unequal: No Solution Exploring Operation: 105-6=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[29, 56, 49, 23], Operations: [] Exploring Operation: 56+49=105, Resulting Numbers: [29, 23, 105] Generated Node #0,0: 99:[29, 23, 105] Operation: 56+49=105 Moving to Node #0,0 Current State: 99:[29, 23, 105], Operations: ['56+49=105'] Exploring Operation: 29-23=6, Resulting Numbers: [105, 6] Generated Node #0,0,1: 99:[105, 6] Operation: 29-23=6 Moving to Node #0,0,1 Current State: 99:[105, 6], Operations: ['56+49=105', '29-23=6'] Exploring Operation: 105-6=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 11, 29, 56, 4 ]
100
[ "11+29=40", "56+4=60", "40+60=100" ]
Current State: 100:[11, 29, 56, 4], Operations: [] Exploring Operation: 11+29=40, Resulting Numbers: [56, 4, 40] Generated Node #2: [56, 4, 40] from Operation: 11+29=40 Current State: 100:[56, 4, 40], Operations: ['11+29=40'] Exploring Operation: 56+4=60, Resulting Numbers: [40, 60] Generated Node #3: [40, 60] from Operation: 56+4=60 Current State: 100:[40, 60], Operations: ['11+29=40', '56+4=60'] Exploring Operation: 40+60=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[11, 29, 56, 4], Operations: [] Exploring Operation: 56-4=52, Resulting Numbers: [11, 29, 52] Generated Node #0,0: 100:[11, 29, 52] Operation: 56-4=52 Exploring Operation: 56-11=45, Resulting Numbers: [29, 4, 45] Generated Node #0,1: 100:[29, 4, 45] Operation: 56-11=45 Exploring Operation: 56-29=27, Resulting Numbers: [11, 4, 27] Generated Node #0,2: 100:[11, 4, 27] Operation: 56-29=27 Exploring Operation: 29-11=18, Resulting Numbers: [56, 4, 18] Generated Node #0,3: 100:[56, 4, 18] Operation: 29-11=18 Exploring Operation: 29-4=25, Resulting Numbers: [11, 56, 25] Generated Node #0,4: 100:[11, 56, 25] Operation: 29-4=25 Moving to Node #0,2 Current State: 100:[11, 4, 27], Operations: ['56-29=27'] Exploring Operation: 11+4=15, Resulting Numbers: [27, 15] Generated Node #0,2,0: 100:[27, 15] Operation: 11+4=15 Exploring Operation: 4+27=31, Resulting Numbers: [11, 31] Generated Node #0,2,1: 100:[11, 31] Operation: 4+27=31 Exploring Operation: 11-4=7, Resulting Numbers: [27, 7] Generated Node #0,2,2: 100:[27, 7] Operation: 11-4=7 Exploring Operation: 27-4=23, Resulting Numbers: [11, 23] Generated Node #0,2,3: 100:[11, 23] Operation: 27-4=23 Exploring Operation: 27-11=16, Resulting Numbers: [4, 16] Generated Node #0,2,4: 100:[4, 16] Operation: 27-11=16 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 100:[11, 23], Operations: ['56-29=27', '27-4=23'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 11+23=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 11*23=253, Resulting Numbers: [253] 253,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 100:[27, 7], Operations: ['56-29=27', '11-4=7'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,100 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:[4, 16], Operations: ['56-29=27', '27-11=16'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,100 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:[27, 15], Operations: ['56-29=27', '11+4=15'] Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,100 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,100 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:[11, 31], Operations: ['56-29=27', '4+27=31'] Exploring Operation: 11*31=341, Resulting Numbers: [341] 341,100 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,100 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:[11, 56, 25], Operations: ['29-4=25'] Exploring Operation: 56-11=45, Resulting Numbers: [25, 45] Generated Node #0,4,0: 100:[25, 45] Operation: 56-11=45 Exploring Operation: 11+25=36, Resulting Numbers: [56, 36] Generated Node #0,4,1: 100:[56, 36] Operation: 11+25=36 Exploring Operation: 56-25=31, Resulting Numbers: [11, 31] Generated Node #0,4,2: 100:[11, 31] Operation: 56-25=31 Exploring Operation: 11+56=67, Resulting Numbers: [25, 67] Generated Node #0,4,3: 100:[25, 67] Operation: 11+56=67 Exploring Operation: 25-11=14, Resulting Numbers: [56, 14] Generated Node #0,4,4: 100:[56, 14] Operation: 25-11=14 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 100:[25, 45], Operations: ['29-4=25', '56-11=45'] Exploring Operation: 25+45=70, Resulting Numbers: [70] 70,100 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 25*45=1125, Resulting Numbers: [1125] 1125,100 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 #0,4,2 Current State: 100:[11, 31], Operations: ['29-4=25', '56-25=31'] Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,100 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 11*31=341, Resulting Numbers: [341] 341,100 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 #0,4,4 Current State: 100:[56, 14], Operations: ['29-4=25', '25-11=14'] Exploring Operation: 56*14=784, Resulting Numbers: [784] 784,100 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 56+14=70, Resulting Numbers: [70] 70,100 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,100 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 #0,4,1 Current State: 100:[56, 36], Operations: ['29-4=25', '11+25=36'] Exploring Operation: 56+36=92, Resulting Numbers: [92] 92,100 unequal: No Solution Exploring Operation: 56*36=2016, Resulting Numbers: [2016] 2016,100 unequal: No Solution Exploring Operation: 56-36=20, Resulting Numbers: [20] 20,100 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 #0,4,3 Current State: 100:[25, 67], Operations: ['29-4=25', '11+56=67'] Exploring Operation: 25*67=1675, Resulting Numbers: [1675] 1675,100 unequal: No Solution Exploring Operation: 25+67=92, Resulting Numbers: [92] 92,100 unequal: No Solution Exploring Operation: 67-25=42, Resulting Numbers: [42] 42,100 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: 100:[11, 29, 52], Operations: ['56-4=52'] Exploring Operation: 11+29=40, Resulting Numbers: [52, 40] Generated Node #0,0,0: 100:[52, 40] Operation: 11+29=40 Exploring Operation: 52-11=41, Resulting Numbers: [29, 41] Generated Node #0,0,1: 100:[29, 41] Operation: 52-11=41 Exploring Operation: 11+52=63, Resulting Numbers: [29, 63] Generated Node #0,0,2: 100:[29, 63] Operation: 11+52=63 Exploring Operation: 52-29=23, Resulting Numbers: [11, 23] Generated Node #0,0,3: 100:[11, 23] Operation: 52-29=23 Exploring Operation: 29-11=18, Resulting Numbers: [52, 18] Generated Node #0,0,4: 100:[52, 18] Operation: 29-11=18 Moving to Node #0,3 Current State: 100:[56, 4, 18], Operations: ['29-11=18'] Exploring Operation: 56-4=52, Resulting Numbers: [18, 52] Generated Node #0,3,0: 100:[18, 52] Operation: 56-4=52 Exploring Operation: 56/4=14, Resulting Numbers: [18, 14] Generated Node #0,3,1: 100:[18, 14] Operation: 56/4=14 Exploring Operation: 4+18=22, Resulting Numbers: [56, 22] Generated Node #0,3,2: 100:[56, 22] Operation: 4+18=22 Exploring Operation: 18-4=14, Resulting Numbers: [56, 14] Generated Node #0,3,3: 100:[56, 14] Operation: 18-4=14 Exploring Operation: 56+4=60, Resulting Numbers: [18, 60] Generated Node #0,3,4: 100:[18, 60] Operation: 56+4=60 Moving to Node #0,1 Current State: 100:[29, 4, 45], Operations: ['56-11=45'] Exploring Operation: 4+45=49, Resulting Numbers: [29, 49] Generated Node #0,1,0: 100:[29, 49] Operation: 4+45=49 Exploring Operation: 45-4=41, Resulting Numbers: [29, 41] Generated Node #0,1,1: 100:[29, 41] Operation: 45-4=41 Exploring Operation: 29+4=33, Resulting Numbers: [45, 33] Generated Node #0,1,2: 100:[45, 33] Operation: 29+4=33 Exploring Operation: 29-4=25, Resulting Numbers: [45, 25] Generated Node #0,1,3: 100:[45, 25] Operation: 29-4=25 Exploring Operation: 45-29=16, Resulting Numbers: [4, 16] Generated Node #0,1,4: 100:[4, 16] Operation: 45-29=16 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 100:[4, 16], Operations: ['56-11=45', '45-29=16'] Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,100 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,100 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:[29, 49], Operations: ['56-11=45', '4+45=49'] Exploring Operation: 29*49=1421, Resulting Numbers: [1421] 1421,100 unequal: No Solution Exploring Operation: 29+49=78, Resulting Numbers: [78] 78,100 unequal: No Solution Exploring Operation: 49-29=20, Resulting Numbers: [20] 20,100 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 #0,1,3 Current State: 100:[45, 25], Operations: ['56-11=45', '29-4=25'] Exploring Operation: 45*25=1125, Resulting Numbers: [1125] 1125,100 unequal: No Solution Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,100 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,100 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:[29, 41], Operations: ['56-11=45', '45-4=41'] Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,100 unequal: No Solution Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,100 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 100:[45, 33], Operations: ['56-11=45', '29+4=33'] Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 45*33=1485, Resulting Numbers: [1485] 1485,100 unequal: No Solution Exploring Operation: 45+33=78, Resulting Numbers: [78] 78,100 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: 100:[11, 23], Operations: ['56-4=52', '52-29=23'] Exploring Operation: 11+23=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 11*23=253, Resulting Numbers: [253] 253,100 unequal: No Solution Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,100 unequal: No Solution Moving to Node #0,3,0 Current State: 100:[18, 52], Operations: ['29-11=18', '56-4=52'] Exploring Operation: 18*52=936, Resulting Numbers: [936] 936,100 unequal: No Solution Exploring Operation: 52-18=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 18+52=70, Resulting Numbers: [70] 70,100 unequal: No Solution Moving to Node #0,0,4 Current State: 100:[52, 18], Operations: ['56-4=52', '29-11=18'] Exploring Operation: 52*18=936, Resulting Numbers: [936] 936,100 unequal: No Solution Exploring Operation: 52-18=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 52+18=70, Resulting Numbers: [70] 70,100 unequal: No Solution Moving to Node #0,3,1 Current State: 100:[18, 14], Operations: ['29-11=18', '56/4=14'] Exploring Operation: 18+14=32, Resulting Numbers: [32] 32,100 unequal: No Solution Exploring Operation: 18*14=252, Resulting Numbers: [252] 252,100 unequal: No Solution Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,100 unequal: No Solution Moving to Node #0,3,2 Current State: 100:[56, 22], Operations: ['29-11=18', '4+18=22'] Exploring Operation: 56+22=78, Resulting Numbers: [78] 78,100 unequal: No Solution Exploring Operation: 56*22=1232, Resulting Numbers: [1232] 1232,100 unequal: No Solution Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,100 unequal: No Solution Moving to Node #0,3,3 Current State: 100:[56, 14], Operations: ['29-11=18', '18-4=14'] Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 56+14=70, Resulting Numbers: [70] 70,100 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,100 unequal: No Solution Exploring Operation: 56*14=784, Resulting Numbers: [784] 784,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[52, 40], Operations: ['56-4=52', '11+29=40'] Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 52+40=92, Resulting Numbers: [92] 92,100 unequal: No Solution Exploring Operation: 52*40=2080, Resulting Numbers: [2080] 2080,100 unequal: No Solution Moving to Node #0,3,4 Current State: 100:[18, 60], Operations: ['29-11=18', '56+4=60'] Exploring Operation: 60-18=42, Resulting Numbers: [42] 42,100 unequal: No Solution Exploring Operation: 18+60=78, Resulting Numbers: [78] 78,100 unequal: No Solution Exploring Operation: 18*60=1080, Resulting Numbers: [1080] 1080,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[29, 41], Operations: ['56-4=52', '52-11=41'] Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,100 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,100 unequal: No Solution Moving to Node #0,0,2 Current State: 100:[29, 63], Operations: ['56-4=52', '11+52=63'] Exploring Operation: 29*63=1827, Resulting Numbers: [1827] 1827,100 unequal: No Solution Exploring Operation: 29+63=92, Resulting Numbers: [92] 92,100 unequal: No Solution Exploring Operation: 63-29=34, Resulting Numbers: [34] 34,100 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 56, 75, 51, 74 ]
59
[ "56-51=5", "75/5=15", "74-15=59" ]
Current State: 59:[56, 75, 51, 74], Operations: [] Exploring Operation: 56-51=5, Resulting Numbers: [75, 74, 5] Generated Node #2: [75, 74, 5] from Operation: 56-51=5 Current State: 59:[75, 74, 5], Operations: ['56-51=5'] Exploring Operation: 75/5=15, Resulting Numbers: [74, 15] Generated Node #3: [74, 15] from Operation: 75/5=15 Current State: 59:[74, 15], Operations: ['56-51=5', '75/5=15'] Exploring Operation: 74-15=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[56, 75, 51, 74], Operations: [] Exploring Operation: 75-56=19, Resulting Numbers: [51, 74, 19] Generated Node #0,0: 59:[51, 74, 19] Operation: 75-56=19 Exploring Operation: 74-51=23, Resulting Numbers: [56, 75, 23] Generated Node #0,1: 59:[56, 75, 23] Operation: 74-51=23 Exploring Operation: 74-56=18, Resulting Numbers: [75, 51, 18] Generated Node #0,2: 59:[75, 51, 18] Operation: 74-56=18 Exploring Operation: 75-51=24, Resulting Numbers: [56, 74, 24] Generated Node #0,3: 59:[56, 74, 24] Operation: 75-51=24 Moving to Node #0,3 Current State: 59:[56, 74, 24], Operations: ['75-51=24'] Exploring Operation: 56+24=80, Resulting Numbers: [74, 80] Generated Node #0,3,0: 59:[74, 80] Operation: 56+24=80 Exploring Operation: 74-24=50, Resulting Numbers: [56, 50] Generated Node #0,3,1: 59:[56, 50] Operation: 74-24=50 Exploring Operation: 74+24=98, Resulting Numbers: [56, 98] Generated Node #0,3,2: 59:[56, 98] Operation: 74+24=98 Exploring Operation: 56-24=32, Resulting Numbers: [74, 32] Generated Node #0,3,3: 59:[74, 32] Operation: 56-24=32 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 59:[56, 50], Operations: ['75-51=24', '74-24=50'] Exploring Operation: 56+50=106, Resulting Numbers: [106] 106,59 unequal: No Solution Exploring Operation: 56*50=2800, Resulting Numbers: [2800] 2800,59 unequal: No Solution Exploring Operation: 56-50=6, Resulting Numbers: [6] 6,59 unequal: No Solution No 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: 59:[74, 80], Operations: ['75-51=24', '56+24=80'] Exploring Operation: 74+80=154, Resulting Numbers: [154] 154,59 unequal: No Solution Exploring Operation: 80-74=6, Resulting Numbers: [6] 6,59 unequal: No Solution Exploring Operation: 74*80=5920, Resulting Numbers: [5920] 5920,59 unequal: No Solution No 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: 59:[56, 98], Operations: ['75-51=24', '74+24=98'] Exploring Operation: 56+98=154, Resulting Numbers: [154] 154,59 unequal: No Solution Exploring Operation: 56*98=5488, Resulting Numbers: [5488] 5488,59 unequal: No Solution Exploring Operation: 98-56=42, Resulting Numbers: [42] 42,59 unequal: No Solution No 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: 59:[74, 32], Operations: ['75-51=24', '56-24=32'] Exploring Operation: 74-32=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 74+32=106, Resulting Numbers: [106] 106,59 unequal: No Solution Exploring Operation: 74*32=2368, Resulting Numbers: [2368] 2368,59 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: 59:[56, 75, 23], Operations: ['74-51=23'] Exploring Operation: 75+23=98, Resulting Numbers: [56, 98] Generated Node #0,1,0: 59:[56, 98] Operation: 75+23=98 Exploring Operation: 75-23=52, Resulting Numbers: [56, 52] Generated Node #0,1,1: 59:[56, 52] Operation: 75-23=52 Exploring Operation: 56+23=79, Resulting Numbers: [75, 79] Generated Node #0,1,2: 59:[75, 79] Operation: 56+23=79 Exploring Operation: 56-23=33, Resulting Numbers: [75, 33] Generated Node #0,1,3: 59:[75, 33] Operation: 56-23=33 Moving to Node #0,0 Current State: 59:[51, 74, 19], Operations: ['75-56=19'] Exploring Operation: 74+19=93, Resulting Numbers: [51, 93] Generated Node #0,0,0: 59:[51, 93] Operation: 74+19=93 Exploring Operation: 51+19=70, Resulting Numbers: [74, 70] Generated Node #0,0,1: 59:[74, 70] Operation: 51+19=70 Exploring Operation: 74-19=55, Resulting Numbers: [51, 55] Generated Node #0,0,2: 59:[51, 55] Operation: 74-19=55 Exploring Operation: 51-19=32, Resulting Numbers: [74, 32] Generated Node #0,0,3: 59:[74, 32] Operation: 51-19=32 Moving to Node #0,2 Current State: 59:[75, 51, 18], Operations: ['74-56=18'] Exploring Operation: 75+18=93, Resulting Numbers: [51, 93] Generated Node #0,2,0: 59:[51, 93] Operation: 75+18=93 Exploring Operation: 51-18=33, Resulting Numbers: [75, 33] Generated Node #0,2,1: 59:[75, 33] Operation: 51-18=33 Exploring Operation: 75-18=57, Resulting Numbers: [51, 57] Generated Node #0,2,2: 59:[51, 57] Operation: 75-18=57 Exploring Operation: 51+18=69, Resulting Numbers: [75, 69] Generated Node #0,2,3: 59:[75, 69] Operation: 51+18=69 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[51, 57], Operations: ['74-56=18', '75-18=57'] Exploring Operation: 51*57=2907, Resulting Numbers: [2907] 2907,59 unequal: No Solution Exploring Operation: 57-51=6, Resulting Numbers: [6] 6,59 unequal: No Solution Exploring Operation: 51+57=108, Resulting Numbers: [108] 108,59 unequal: No Solution No 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: 59:[75, 69], Operations: ['74-56=18', '51+18=69'] Exploring Operation: 75+69=144, Resulting Numbers: [144] 144,59 unequal: No Solution Exploring Operation: 75*69=5175, Resulting Numbers: [5175] 5175,59 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,59 unequal: No Solution No 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: 59:[51, 93], Operations: ['74-56=18', '75+18=93'] Exploring Operation: 51*93=4743, Resulting Numbers: [4743] 4743,59 unequal: No Solution Exploring Operation: 51+93=144, Resulting Numbers: [144] 144,59 unequal: No Solution Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,59 unequal: No Solution No 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: 59:[75, 33], Operations: ['74-56=18', '51-18=33'] Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 75+33=108, Resulting Numbers: [108] 108,59 unequal: No Solution Exploring Operation: 75*33=2475, Resulting Numbers: [2475] 2475,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 59:[56, 52], Operations: ['74-51=23', '75-23=52'] Exploring Operation: 56*52=2912, Resulting Numbers: [2912] 2912,59 unequal: No Solution Exploring Operation: 56+52=108, Resulting Numbers: [108] 108,59 unequal: No Solution Exploring Operation: 56-52=4, Resulting Numbers: [4] 4,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[51, 55], Operations: ['75-56=19', '74-19=55'] Exploring Operation: 51+55=106, Resulting Numbers: [106] 106,59 unequal: No Solution Exploring Operation: 55-51=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 51*55=2805, Resulting Numbers: [2805] 2805,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[74, 70], Operations: ['75-56=19', '51+19=70'] Exploring Operation: 74*70=5180, Resulting Numbers: [5180] 5180,59 unequal: No Solution Exploring Operation: 74-70=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 74+70=144, Resulting Numbers: [144] 144,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[75, 79], Operations: ['74-51=23', '56+23=79'] Exploring Operation: 75*79=5925, Resulting Numbers: [5925] 5925,59 unequal: No Solution Exploring Operation: 75+79=154, Resulting Numbers: [154] 154,59 unequal: No Solution Exploring Operation: 79-75=4, Resulting Numbers: [4] 4,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[56, 98], Operations: ['74-51=23', '75+23=98'] Exploring Operation: 56+98=154, Resulting Numbers: [154] 154,59 unequal: No Solution Exploring Operation: 98-56=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 56*98=5488, Resulting Numbers: [5488] 5488,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[51, 93], Operations: ['75-56=19', '74+19=93'] Exploring Operation: 51*93=4743, Resulting Numbers: [4743] 4743,59 unequal: No Solution Exploring Operation: 51+93=144, Resulting Numbers: [144] 144,59 unequal: No Solution Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[74, 32], Operations: ['75-56=19', '51-19=32'] Exploring Operation: 74-32=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 74*32=2368, Resulting Numbers: [2368] 2368,59 unequal: No Solution Exploring Operation: 74+32=106, Resulting Numbers: [106] 106,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[75, 33], Operations: ['74-51=23', '56-23=33'] Exploring Operation: 75*33=2475, Resulting Numbers: [2475] 2475,59 unequal: No Solution Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 75+33=108, Resulting Numbers: [108] 108,59 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 79, 44, 46, 81 ]
70
[ "79-44=35", "81-46=35", "35+35=70" ]
Current State: 70:[79, 44, 46, 81], Operations: [] Exploring Operation: 79-44=35, Resulting Numbers: [46, 81, 35] Generated Node #2: [46, 81, 35] from Operation: 79-44=35 Current State: 70:[46, 81, 35], Operations: ['79-44=35'] Exploring Operation: 81-46=35, Resulting Numbers: [35, 35] Generated Node #3: [35, 35] from Operation: 81-46=35 Current State: 70:[35, 35], Operations: ['79-44=35', '81-46=35'] Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[79, 44, 46, 81], Operations: [] Exploring Operation: 81-46=35, Resulting Numbers: [79, 44, 35] Generated Node #0,0: 70:[79, 44, 35] Operation: 81-46=35 Exploring Operation: 79-44=35, Resulting Numbers: [46, 81, 35] Generated Node #0,1: 70:[46, 81, 35] Operation: 79-44=35 Exploring Operation: 81-79=2, Resulting Numbers: [44, 46, 2] Generated Node #0,2: 70:[44, 46, 2] Operation: 81-79=2 Exploring Operation: 46-44=2, Resulting Numbers: [79, 81, 2] Generated Node #0,3: 70:[79, 81, 2] Operation: 46-44=2 Moving to Node #0,0 Current State: 70:[79, 44, 35], Operations: ['81-46=35'] Exploring Operation: 44+35=79, Resulting Numbers: [79, 79] Generated Node #0,0,0: 70:[79, 79] Operation: 44+35=79 Exploring Operation: 79-44=35, Resulting Numbers: [35, 35] Generated Node #0,0,1: 70:[35, 35] Operation: 79-44=35 Exploring Operation: 79-35=44, Resulting Numbers: [44, 44] Generated Node #0,0,2: 70:[44, 44] Operation: 79-35=44 Exploring Operation: 44-35=9, Resulting Numbers: [79, 9] Generated Node #0,0,3: 70:[79, 9] Operation: 44-35=9 Moving to Node #0,3 Current State: 70:[79, 81, 2], Operations: ['46-44=2'] Exploring Operation: 81-2=79, Resulting Numbers: [79, 79] Generated Node #0,3,0: 70:[79, 79] Operation: 81-2=79 Exploring Operation: 79+2=81, Resulting Numbers: [81, 81] Generated Node #0,3,1: 70:[81, 81] Operation: 79+2=81 Exploring Operation: 79-2=77, Resulting Numbers: [81, 77] Generated Node #0,3,2: 70:[81, 77] Operation: 79-2=77 Exploring Operation: 81-79=2, Resulting Numbers: [2, 2] Generated Node #0,3,3: 70:[2, 2] Operation: 81-79=2 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 70:[2, 2], Operations: ['46-44=2', '81-79=2'] Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,70 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,70 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 70:[79, 79], Operations: ['46-44=2', '81-2=79'] Exploring Operation: 79-79=0, Resulting Numbers: [0] 0,70 unequal: No Solution Exploring Operation: 79/79=1, Resulting Numbers: [1] 1,70 unequal: No Solution Exploring Operation: 79*79=6241, Resulting Numbers: [6241] 6241,70 unequal: No Solution Exploring Operation: 79+79=158, Resulting Numbers: [158] 158,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 70:[81, 77], Operations: ['46-44=2', '79-2=77'] Exploring Operation: 81-77=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 81*77=6237, Resulting Numbers: [6237] 6237,70 unequal: No Solution Exploring Operation: 81+77=158, Resulting Numbers: [158] 158,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 70:[81, 81], Operations: ['46-44=2', '79+2=81'] Exploring Operation: 81/81=1, Resulting Numbers: [1] 1,70 unequal: No Solution Exploring Operation: 81+81=162, Resulting Numbers: [162] 162,70 unequal: No Solution Exploring Operation: 81*81=6561, Resulting Numbers: [6561] 6561,70 unequal: No Solution Exploring Operation: 81-81=0, Resulting Numbers: [0] 0,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 70:[44, 46, 2], Operations: ['81-79=2'] Exploring Operation: 46-2=44, Resulting Numbers: [44, 44] Generated Node #0,2,0: 70:[44, 44] Operation: 46-2=44 Exploring Operation: 44-2=42, Resulting Numbers: [46, 42] Generated Node #0,2,1: 70:[46, 42] Operation: 44-2=42 Exploring Operation: 46-44=2, Resulting Numbers: [2, 2] Generated Node #0,2,2: 70:[2, 2] Operation: 46-44=2 Exploring Operation: 46/2=23, Resulting Numbers: [44, 23] Generated Node #0,2,3: 70:[44, 23] Operation: 46/2=23 Moving to Node #0,1 Current State: 70:[46, 81, 35], Operations: ['79-44=35'] Exploring Operation: 46+35=81, Resulting Numbers: [81, 81] Generated Node #0,1,0: 70:[81, 81] Operation: 46+35=81 Exploring Operation: 81-46=35, Resulting Numbers: [35, 35] Generated Node #0,1,1: 70:[35, 35] Operation: 81-46=35 Exploring Operation: 81-35=46, Resulting Numbers: [46, 46] Generated Node #0,1,2: 70:[46, 46] Operation: 81-35=46 Exploring Operation: 46-35=11, Resulting Numbers: [81, 11] Generated Node #0,1,3: 70:[81, 11] Operation: 46-35=11 Moving to Node #0,0,1 Current State: 70:[35, 35], Operations: ['81-46=35', '79-44=35'] Exploring Operation: 35*35=1225, Resulting Numbers: [1225] 1225,70 unequal: No Solution Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[79, 44, 46, 81], Operations: [] Exploring Operation: 81-46=35, Resulting Numbers: [79, 44, 35] Generated Node #0,0: 70:[79, 44, 35] Operation: 81-46=35 Moving to Node #0,0 Current State: 70:[79, 44, 35], Operations: ['81-46=35'] Exploring Operation: 79-44=35, Resulting Numbers: [35, 35] Generated Node #0,0,1: 70:[35, 35] Operation: 79-44=35 Moving to Node #0,0,1 Current State: 70:[35, 35], Operations: ['81-46=35', '79-44=35'] Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
0.96441
hs_4
sum_heuristic
[ 36, 41, 66, 28 ]
89
[ "41-36=5", "66+28=94", "94-5=89" ]
Current State: 89:[36, 41, 66, 28], Operations: [] Exploring Operation: 41-36=5, Resulting Numbers: [66, 28, 5] Generated Node #2: [66, 28, 5] from Operation: 41-36=5 Current State: 89:[66, 28, 5], Operations: ['41-36=5'] Exploring Operation: 66+28=94, Resulting Numbers: [5, 94] Generated Node #3: [5, 94] from Operation: 66+28=94 Current State: 89:[5, 94], Operations: ['41-36=5', '66+28=94'] Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[36, 41, 66, 28], Operations: [] Exploring Operation: 66+28=94, Resulting Numbers: [36, 41, 94] Generated Node #0,0: 89:[36, 41, 94] Operation: 66+28=94 Exploring Operation: 36+41=77, Resulting Numbers: [66, 28, 77] Generated Node #0,1: 89:[66, 28, 77] Operation: 36+41=77 Exploring Operation: 41+28=69, Resulting Numbers: [36, 66, 69] Generated Node #0,2: 89:[36, 66, 69] Operation: 41+28=69 Exploring Operation: 36+66=102, Resulting Numbers: [41, 28, 102] Generated Node #0,3: 89:[41, 28, 102] Operation: 36+66=102 Exploring Operation: 36+28=64, Resulting Numbers: [41, 66, 64] Generated Node #0,4: 89:[41, 66, 64] Operation: 36+28=64 Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[66, 28, 77], Operations: ['36+41=77'] Exploring Operation: 66+28=94, Resulting Numbers: [77, 94] Generated Node #0,1,0: 89:[77, 94] Operation: 66+28=94 Exploring Operation: 66-28=38, Resulting Numbers: [77, 38] Generated Node #0,1,1: 89:[77, 38] Operation: 66-28=38 Exploring Operation: 77-28=49, Resulting Numbers: [66, 49] Generated Node #0,1,2: 89:[66, 49] Operation: 77-28=49 Exploring Operation: 28+77=105, Resulting Numbers: [66, 105] Generated Node #0,1,3: 89:[66, 105] Operation: 28+77=105 Exploring Operation: 66+77=143, Resulting Numbers: [28, 143] Generated Node #0,1,4: 89:[28, 143] Operation: 66+77=143 Moving to Node #0,1,0 Current State: 89:[77, 94], Operations: ['36+41=77', '66+28=94'] Exploring Operation: 77+94=171, Resulting Numbers: [171] 171,89 unequal: No Solution Exploring Operation: 77*94=7238, Resulting Numbers: [7238] 7238,89 unequal: No Solution Exploring Operation: 94-77=17, Resulting Numbers: [17] 17,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[66, 105], Operations: ['36+41=77', '28+77=105'] Exploring Operation: 66+105=171, Resulting Numbers: [171] 171,89 unequal: No Solution Exploring Operation: 105-66=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 66*105=6930, Resulting Numbers: [6930] 6930,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[77, 38], Operations: ['36+41=77', '66-28=38'] Exploring Operation: 77+38=115, Resulting Numbers: [115] 115,89 unequal: No Solution Exploring Operation: 77*38=2926, Resulting Numbers: [2926] 2926,89 unequal: No Solution Exploring Operation: 77-38=39, Resulting Numbers: [39] 39,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[66, 49], Operations: ['36+41=77', '77-28=49'] Exploring Operation: 66*49=3234, Resulting Numbers: [3234] 3234,89 unequal: No Solution Exploring Operation: 66+49=115, Resulting Numbers: [115] 115,89 unequal: No Solution Exploring Operation: 66-49=17, Resulting Numbers: [17] 17,89 unequal: No Solution Moving to Node #0,1,4 Current State: 89:[28, 143], Operations: ['36+41=77', '66+77=143'] Exploring Operation: 28*143=4004, Resulting Numbers: [4004] 4004,89 unequal: No Solution Exploring Operation: 28+143=171, Resulting Numbers: [171] 171,89 unequal: No Solution Exploring Operation: 143-28=115, Resulting Numbers: [115] 115,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[36, 66, 69], Operations: ['41+28=69'] Exploring Operation: 66+69=135, Resulting Numbers: [36, 135] Generated Node #0,2,0: 89:[36, 135] Operation: 66+69=135 Exploring Operation: 36+69=105, Resulting Numbers: [66, 105] Generated Node #0,2,1: 89:[66, 105] Operation: 36+69=105 Exploring Operation: 69-36=33, Resulting Numbers: [66, 33] Generated Node #0,2,2: 89:[66, 33] Operation: 69-36=33 Exploring Operation: 66-36=30, Resulting Numbers: [69, 30] Generated Node #0,2,3: 89:[69, 30] Operation: 66-36=30 Exploring Operation: 36+66=102, Resulting Numbers: [69, 102] Generated Node #0,2,4: 89:[69, 102] Operation: 36+66=102 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 89:[69, 102], Operations: ['41+28=69', '36+66=102'] Exploring Operation: 69*102=7038, Resulting Numbers: [7038] 7038,89 unequal: No Solution Exploring Operation: 102-69=33, Resulting Numbers: [33] 33,89 unequal: No Solution Exploring Operation: 69+102=171, Resulting Numbers: [171] 171,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 89:[66, 105], Operations: ['41+28=69', '36+69=105'] Exploring Operation: 66*105=6930, Resulting Numbers: [6930] 6930,89 unequal: No Solution Exploring Operation: 66+105=171, Resulting Numbers: [171] 171,89 unequal: No Solution Exploring Operation: 105-66=39, Resulting Numbers: [39] 39,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 89:[66, 33], Operations: ['41+28=69', '69-36=33'] Exploring Operation: 66-33=33, Resulting Numbers: [33] 33,89 unequal: No Solution Exploring Operation: 66+33=99, Resulting Numbers: [99] 99,89 unequal: No Solution Exploring Operation: 66/33=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 66*33=2178, Resulting Numbers: [2178] 2178,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 89:[69, 30], Operations: ['41+28=69', '66-36=30'] Exploring Operation: 69*30=2070, Resulting Numbers: [2070] 2070,89 unequal: No Solution Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 69+30=99, Resulting Numbers: [99] 99,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 89:[36, 135], Operations: ['41+28=69', '66+69=135'] Exploring Operation: 36+135=171, Resulting Numbers: [171] 171,89 unequal: No Solution Exploring Operation: 36*135=4860, Resulting Numbers: [4860] 4860,89 unequal: No Solution Exploring Operation: 135-36=99, Resulting Numbers: [99] 99,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 89:[41, 66, 64], Operations: ['36+28=64'] Exploring Operation: 41+66=107, Resulting Numbers: [64, 107] Generated Node #0,4,0: 89:[64, 107] Operation: 41+66=107 Exploring Operation: 64-41=23, Resulting Numbers: [66, 23] Generated Node #0,4,1: 89:[66, 23] Operation: 64-41=23 Exploring Operation: 66+64=130, Resulting Numbers: [41, 130] Generated Node #0,4,2: 89:[41, 130] Operation: 66+64=130 Exploring Operation: 41+64=105, Resulting Numbers: [66, 105] Generated Node #0,4,3: 89:[66, 105] Operation: 41+64=105 Exploring Operation: 66-41=25, Resulting Numbers: [64, 25] Generated Node #0,4,4: 89:[64, 25] Operation: 66-41=25 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 89:[66, 105], Operations: ['36+28=64', '41+64=105'] Exploring Operation: 105-66=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 66*105=6930, Resulting Numbers: [6930] 6930,89 unequal: No Solution Exploring Operation: 66+105=171, Resulting Numbers: [171] 171,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 89:[64, 107], Operations: ['36+28=64', '41+66=107'] Exploring Operation: 64*107=6848, Resulting Numbers: [6848] 6848,89 unequal: No Solution Exploring Operation: 64+107=171, Resulting Numbers: [171] 171,89 unequal: No Solution Exploring Operation: 107-64=43, Resulting Numbers: [43] 43,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 89:[66, 23], Operations: ['36+28=64', '64-41=23'] Exploring Operation: 66+23=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[36, 41, 66, 28], Operations: [] Exploring Operation: 36+28=64, Resulting Numbers: [41, 66, 64] Generated Node #0,4: 89:[41, 66, 64] Operation: 36+28=64 Moving to Node #0,4 Current State: 89:[41, 66, 64], Operations: ['36+28=64'] Exploring Operation: 64-41=23, Resulting Numbers: [66, 23] Generated Node #0,4,1: 89:[66, 23] Operation: 64-41=23 Moving to Node #0,4,1 Current State: 89:[66, 23], Operations: ['36+28=64', '64-41=23'] Exploring Operation: 66+23=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.946181
hs_5
mult_heuristic
[ 4, 51, 2, 11 ]
64
[ "4+51=55", "11-2=9", "55+9=64" ]
Current State: 64:[4, 51, 2, 11], Operations: [] Exploring Operation: 4+51=55, Resulting Numbers: [2, 11, 55] Generated Node #2: [2, 11, 55] from Operation: 4+51=55 Current State: 64:[2, 11, 55], Operations: ['4+51=55'] Exploring Operation: 11-2=9, Resulting Numbers: [55, 9] Generated Node #3: [55, 9] from Operation: 11-2=9 Current State: 64:[55, 9], Operations: ['4+51=55', '11-2=9'] Exploring Operation: 55+9=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[4, 51, 2, 11], Operations: [] Exploring Operation: 51-11=40, Resulting Numbers: [4, 2, 40] Generated Node #0,0: 64:[4, 2, 40] Operation: 51-11=40 Exploring Operation: 51+11=62, Resulting Numbers: [4, 2, 62] Generated Node #0,1: 64:[4, 2, 62] Operation: 51+11=62 Moving to Node #0,1 Current State: 64:[4, 2, 62], Operations: ['51+11=62'] Exploring Operation: 62/2=31, Resulting Numbers: [4, 31] Generated Node #0,1,0: 64:[4, 31] Operation: 62/2=31 Exploring Operation: 2+62=64, Resulting Numbers: [4, 64] Generated Node #0,1,1: 64:[4, 64] Operation: 2+62=64 Moving to Node #0,0 Current State: 64:[4, 2, 40], Operations: ['51-11=40'] Exploring Operation: 40/4=10, Resulting Numbers: [2, 10] Generated Node #0,0,0: 64:[2, 10] Operation: 40/4=10 Exploring Operation: 40-4=36, Resulting Numbers: [2, 36] Generated Node #0,0,1: 64:[2, 36] Operation: 40-4=36 Moving to Node #0,1,1 Current State: 64:[4, 64], Operations: ['51+11=62', '2+62=64'] Exploring Operation: 4+64=68, Resulting Numbers: [68] 68,64 unequal: No Solution Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,64 unequal: No Solution Moving to Node #0,1,0 Current State: 64:[4, 31], Operations: ['51+11=62', '62/2=31'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,64 unequal: No Solution Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,64 unequal: No Solution Moving to Node #0,0,0 Current State: 64:[2, 10], Operations: ['51-11=40', '40/4=10'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,64 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[2, 36], Operations: ['51-11=40', '40-4=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,64 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,64 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 77, 88, 42, 23 ]
79
[ "88-42=46", "46/23=2", "77+2=79" ]
Current State: 79:[77, 88, 42, 23], Operations: [] Exploring Operation: 88-42=46, Resulting Numbers: [77, 23, 46] Generated Node #2: [77, 23, 46] from Operation: 88-42=46 Current State: 79:[77, 23, 46], Operations: ['88-42=46'] Exploring Operation: 46/23=2, Resulting Numbers: [77, 2] Generated Node #3: [77, 2] from Operation: 46/23=2 Current State: 79:[77, 2], Operations: ['88-42=46', '46/23=2'] Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[77, 88, 42, 23], Operations: [] Exploring Operation: 42+23=65, Resulting Numbers: [77, 88, 65] Generated Node #0,0: 79:[77, 88, 65] Operation: 42+23=65 Exploring Operation: 77+23=100, Resulting Numbers: [88, 42, 100] Generated Node #0,1: 79:[88, 42, 100] Operation: 77+23=100 Exploring Operation: 88-23=65, Resulting Numbers: [77, 42, 65] Generated Node #0,2: 79:[77, 42, 65] Operation: 88-23=65 Exploring Operation: 77-23=54, Resulting Numbers: [88, 42, 54] Generated Node #0,3: 79:[88, 42, 54] Operation: 77-23=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[77, 88, 65], Operations: ['42+23=65'] Exploring Operation: 88-65=23, Resulting Numbers: [77, 23] Generated Node #0,0,0: 79:[77, 23] Operation: 88-65=23 Exploring Operation: 77+65=142, Resulting Numbers: [88, 142] Generated Node #0,0,1: 79:[88, 142] Operation: 77+65=142 Exploring Operation: 77-65=12, Resulting Numbers: [88, 12] Generated Node #0,0,2: 79:[88, 12] Operation: 77-65=12 Exploring Operation: 88+65=153, Resulting Numbers: [77, 153] Generated Node #0,0,3: 79:[77, 153] Operation: 88+65=153 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[77, 23], Operations: ['42+23=65', '88-65=23'] Exploring Operation: 77-23=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 77+23=100, Resulting Numbers: [100] 100,79 unequal: No Solution Exploring Operation: 77*23=1771, Resulting Numbers: [1771] 1771,79 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:[88, 142], Operations: ['42+23=65', '77+65=142'] Exploring Operation: 142-88=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 88+142=230, Resulting Numbers: [230] 230,79 unequal: No Solution Exploring Operation: 88*142=12496, Resulting Numbers: [12496] 12496,79 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 #0,0,2 Current State: 79:[88, 12], Operations: ['42+23=65', '77-65=12'] Exploring Operation: 88+12=100, Resulting Numbers: [100] 100,79 unequal: No Solution Exploring Operation: 88-12=76, Resulting Numbers: [76] 76,79 unequal: No Solution Exploring Operation: 88*12=1056, Resulting Numbers: [1056] 1056,79 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 #0,0,3 Current State: 79:[77, 153], Operations: ['42+23=65', '88+65=153'] Exploring Operation: 77*153=11781, Resulting Numbers: [11781] 11781,79 unequal: No Solution Exploring Operation: 77+153=230, Resulting Numbers: [230] 230,79 unequal: No Solution Exploring Operation: 153-77=76, Resulting Numbers: [76] 76,79 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 #0,2 Current State: 79:[77, 42, 65], Operations: ['88-23=65'] Exploring Operation: 77+42=119, Resulting Numbers: [65, 119] Generated Node #0,2,0: 79:[65, 119] Operation: 77+42=119 Exploring Operation: 42+65=107, Resulting Numbers: [77, 107] Generated Node #0,2,1: 79:[77, 107] Operation: 42+65=107 Exploring Operation: 65-42=23, Resulting Numbers: [77, 23] Generated Node #0,2,2: 79:[77, 23] Operation: 65-42=23 Exploring Operation: 77-42=35, Resulting Numbers: [65, 35] Generated Node #0,2,3: 79:[65, 35] Operation: 77-42=35 Moving to Node #0,2,1 Current State: 79:[77, 107], Operations: ['88-23=65', '42+65=107'] Exploring Operation: 107-77=30, Resulting Numbers: [30] 30,79 unequal: No Solution Exploring Operation: 77*107=8239, Resulting Numbers: [8239] 8239,79 unequal: No Solution Exploring Operation: 77+107=184, Resulting Numbers: [184] 184,79 unequal: No Solution Moving to Node #0,2,0 Current State: 79:[65, 119], Operations: ['88-23=65', '77+42=119'] Exploring Operation: 119-65=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 65*119=7735, Resulting Numbers: [7735] 7735,79 unequal: No Solution Exploring Operation: 65+119=184, Resulting Numbers: [184] 184,79 unequal: No Solution Moving to Node #0,2,3 Current State: 79:[65, 35], Operations: ['88-23=65', '77-42=35'] Exploring Operation: 65+35=100, Resulting Numbers: [100] 100,79 unequal: No Solution Exploring Operation: 65*35=2275, Resulting Numbers: [2275] 2275,79 unequal: No Solution Exploring Operation: 65-35=30, Resulting Numbers: [30] 30,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[77, 23], Operations: ['88-23=65', '65-42=23'] Exploring Operation: 77+23=100, Resulting Numbers: [100] 100,79 unequal: No Solution Exploring Operation: 77*23=1771, Resulting Numbers: [1771] 1771,79 unequal: No Solution Exploring Operation: 77-23=54, Resulting Numbers: [54] 54,79 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:[88, 42, 100], Operations: ['77+23=100'] Exploring Operation: 100-42=58, Resulting Numbers: [88, 58] Generated Node #0,1,0: 79:[88, 58] Operation: 100-42=58 Exploring Operation: 88-42=46, Resulting Numbers: [100, 46] Generated Node #0,1,1: 79:[100, 46] Operation: 88-42=46 Exploring Operation: 42+100=142, Resulting Numbers: [88, 142] Generated Node #0,1,2: 79:[88, 142] Operation: 42+100=142 Exploring Operation: 88+42=130, Resulting Numbers: [100, 130] Generated Node #0,1,3: 79:[100, 130] Operation: 88+42=130 Moving to Node #0,1,0 Current State: 79:[88, 58], Operations: ['77+23=100', '100-42=58'] Exploring Operation: 88+58=146, Resulting Numbers: [146] 146,79 unequal: No Solution Exploring Operation: 88-58=30, Resulting Numbers: [30] 30,79 unequal: No Solution Exploring Operation: 88*58=5104, Resulting Numbers: [5104] 5104,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[100, 46], Operations: ['77+23=100', '88-42=46'] Exploring Operation: 100-46=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 100*46=4600, Resulting Numbers: [4600] 4600,79 unequal: No Solution Exploring Operation: 100+46=146, Resulting Numbers: [146] 146,79 unequal: No Solution Moving to Node #0,1,3 Current State: 79:[100, 130], Operations: ['77+23=100', '88+42=130'] Exploring Operation: 100+130=230, Resulting Numbers: [230] 230,79 unequal: No Solution Exploring Operation: 130-100=30, Resulting Numbers: [30] 30,79 unequal: No Solution Exploring Operation: 100*130=13000, Resulting Numbers: [13000] 13000,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[88, 142], Operations: ['77+23=100', '42+100=142'] Exploring Operation: 88+142=230, Resulting Numbers: [230] 230,79 unequal: No Solution Exploring Operation: 142-88=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 88*142=12496, Resulting Numbers: [12496] 12496,79 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 #0,3 Current State: 79:[88, 42, 54], Operations: ['77-23=54'] Exploring Operation: 88+42=130, Resulting Numbers: [54, 130] Generated Node #0,3,0: 79:[54, 130] Operation: 88+42=130 Exploring Operation: 88-42=46, Resulting Numbers: [54, 46] Generated Node #0,3,1: 79:[54, 46] Operation: 88-42=46 Exploring Operation: 54-42=12, Resulting Numbers: [88, 12] Generated Node #0,3,2: 79:[88, 12] Operation: 54-42=12 Exploring Operation: 42+54=96, Resulting Numbers: [88, 96] Generated Node #0,3,3: 79:[88, 96] Operation: 42+54=96 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 79:[88, 96], Operations: ['77-23=54', '42+54=96'] Exploring Operation: 88+96=184, Resulting Numbers: [184] 184,79 unequal: No Solution Exploring Operation: 96-88=8, Resulting Numbers: [8] 8,79 unequal: No Solution Exploring Operation: 88*96=8448, Resulting Numbers: [8448] 8448,79 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 #0,3,1 Current State: 79:[54, 46], Operations: ['77-23=54', '88-42=46'] Exploring Operation: 54+46=100, Resulting Numbers: [100] 100,79 unequal: No Solution Exploring Operation: 54*46=2484, Resulting Numbers: [2484] 2484,79 unequal: No Solution Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,79 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 #0,3,0 Current State: 79:[54, 130], Operations: ['77-23=54', '88+42=130'] Exploring Operation: 54+130=184, Resulting Numbers: [184] 184,79 unequal: No Solution Exploring Operation: 130-54=76, Resulting Numbers: [76] 76,79 unequal: No Solution Exploring Operation: 54*130=7020, Resulting Numbers: [7020] 7020,79 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 #0,3,2 Current State: 79:[88, 12], Operations: ['77-23=54', '54-42=12'] Exploring Operation: 88-12=76, Resulting Numbers: [76] 76,79 unequal: No Solution Exploring Operation: 88+12=100, Resulting Numbers: [100] 100,79 unequal: No Solution Exploring Operation: 88*12=1056, Resulting Numbers: [1056] 1056,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 37, 64, 27, 74 ]
75
[ "64-37=27", "27/27=1", "74+1=75" ]
Current State: 75:[37, 64, 27, 74], Operations: [] Exploring Operation: 64-37=27, Resulting Numbers: [27, 74, 27] Generated Node #2: [27, 74, 27] from Operation: 64-37=27 Current State: 75:[27, 74, 27], Operations: ['64-37=27'] Exploring Operation: 27/27=1, Resulting Numbers: [74, 1] Generated Node #3: [74, 1] from Operation: 27/27=1 Current State: 75:[74, 1], Operations: ['64-37=27', '27/27=1'] Exploring Operation: 74+1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[37, 64, 27, 74], Operations: [] Exploring Operation: 37-27=10, Resulting Numbers: [64, 74, 10] Generated Node #0,0: 75:[64, 74, 10] Operation: 37-27=10 Exploring Operation: 64-37=27, Resulting Numbers: [27, 74, 27] Generated Node #0,1: 75:[27, 74, 27] Operation: 64-37=27 Exploring Operation: 74/37=2, Resulting Numbers: [64, 27, 2] Generated Node #0,2: 75:[64, 27, 2] Operation: 74/37=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[27, 74, 27], Operations: ['64-37=27'] Exploring Operation: 27-27=0, Resulting Numbers: [74, 0] Generated Node #0,1,0: 75:[74, 0] Operation: 27-27=0 Exploring Operation: 27+27=54, Resulting Numbers: [74, 54] Generated Node #0,1,1: 75:[74, 54] Operation: 27+27=54 Exploring Operation: 27/27=1, Resulting Numbers: [74, 1] Generated Node #0,1,2: 75:[74, 1] Operation: 27/27=1 Moving to Node #0,1,2 Current State: 75:[74, 1], Operations: ['64-37=27', '27/27=1'] Exploring Operation: 74*1=74, Resulting Numbers: [74] 74,75 unequal: No Solution Exploring Operation: 74/1=74, Resulting Numbers: [74] 74,75 unequal: No Solution Exploring Operation: 74+1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[37, 64, 27, 74], Operations: [] Exploring Operation: 64-37=27, Resulting Numbers: [27, 74, 27] Generated Node #0,1: 75:[27, 74, 27] Operation: 64-37=27 Moving to Node #0,1 Current State: 75:[27, 74, 27], Operations: ['64-37=27'] Exploring Operation: 27/27=1, Resulting Numbers: [74, 1] Generated Node #0,1,2: 75:[74, 1] Operation: 27/27=1 Moving to Node #0,1,2 Current State: 75:[74, 1], Operations: ['64-37=27', '27/27=1'] Exploring Operation: 74+1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 69, 48, 6, 98 ]
21
[ "98-69=29", "48/6=8", "29-8=21" ]
Current State: 21:[69, 48, 6, 98], Operations: [] Exploring Operation: 98-69=29, Resulting Numbers: [48, 6, 29] Generated Node #2: [48, 6, 29] from Operation: 98-69=29 Current State: 21:[48, 6, 29], Operations: ['98-69=29'] Exploring Operation: 48/6=8, Resulting Numbers: [29, 8] Generated Node #3: [29, 8] from Operation: 48/6=8 Current State: 21:[29, 8], Operations: ['98-69=29', '48/6=8'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[69, 48, 6, 98], Operations: [] Exploring Operation: 69-48=21, Resulting Numbers: [6, 98, 21] Generated Node #0,0: 21:[6, 98, 21] Operation: 69-48=21 Exploring Operation: 48/6=8, Resulting Numbers: [69, 98, 8] Generated Node #0,1: 21:[69, 98, 8] Operation: 48/6=8 Exploring Operation: 98-69=29, Resulting Numbers: [48, 6, 29] Generated Node #0,2: 21:[48, 6, 29] Operation: 98-69=29 Exploring Operation: 69-6=63, Resulting Numbers: [48, 98, 63] Generated Node #0,3: 21:[48, 98, 63] Operation: 69-6=63 Exploring Operation: 98-48=50, Resulting Numbers: [69, 6, 50] Generated Node #0,4: 21:[69, 6, 50] Operation: 98-48=50 Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[48, 6, 29], Operations: ['98-69=29'] Exploring Operation: 48+6=54, Resulting Numbers: [29, 54] Generated Node #0,2,0: 21:[29, 54] Operation: 48+6=54 Exploring Operation: 48-29=19, Resulting Numbers: [6, 19] Generated Node #0,2,1: 21:[6, 19] Operation: 48-29=19 Exploring Operation: 29-6=23, Resulting Numbers: [48, 23] Generated Node #0,2,2: 21:[48, 23] Operation: 29-6=23 Exploring Operation: 48-6=42, Resulting Numbers: [29, 42] Generated Node #0,2,3: 21:[29, 42] Operation: 48-6=42 Exploring Operation: 48/6=8, Resulting Numbers: [29, 8] Generated Node #0,2,4: 21:[29, 8] Operation: 48/6=8 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 21:[6, 19], Operations: ['98-69=29', '48-29=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,21 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,21 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 21:[29, 8], Operations: ['98-69=29', '48/6=8'] Exploring Operation: 29*8=232, Resulting Numbers: [232] 232,21 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[69, 48, 6, 98], Operations: [] Exploring Operation: 98-69=29, Resulting Numbers: [48, 6, 29] Generated Node #0,2: 21:[48, 6, 29] Operation: 98-69=29 Moving to Node #0,2 Current State: 21:[48, 6, 29], Operations: ['98-69=29'] Exploring Operation: 48/6=8, Resulting Numbers: [29, 8] Generated Node #0,2,4: 21:[29, 8] Operation: 48/6=8 Moving to Node #0,2,4 Current State: 21:[29, 8], Operations: ['98-69=29', '48/6=8'] 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
0.983507
hs_5
sum_heuristic
[ 62, 44, 62, 43 ]
86
[ "62/62=1", "44+43=87", "87-1=86" ]
Current State: 86:[62, 44, 62, 43], Operations: [] Exploring Operation: 62/62=1, Resulting Numbers: [44, 43, 1] Generated Node #2: [44, 43, 1] from Operation: 62/62=1 Current State: 86:[44, 43, 1], Operations: ['62/62=1'] Exploring Operation: 44+43=87, Resulting Numbers: [1, 87] Generated Node #3: [1, 87] from Operation: 44+43=87 Current State: 86:[1, 87], Operations: ['62/62=1', '44+43=87'] Exploring Operation: 87-1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[62, 44, 62, 43], Operations: [] Exploring Operation: 62/62=1, Resulting Numbers: [44, 43, 1] Generated Node #0,0: 86:[44, 43, 1] Operation: 62/62=1 Exploring Operation: 62-43=19, Resulting Numbers: [44, 62, 19] Generated Node #0,1: 86:[44, 62, 19] Operation: 62-43=19 Exploring Operation: 62-44=18, Resulting Numbers: [62, 43, 18] Generated Node #0,2: 86:[62, 43, 18] Operation: 62-44=18 Exploring Operation: 62-62=0, Resulting Numbers: [44, 43, 0] Generated Node #0,3: 86:[44, 43, 0] Operation: 62-62=0 Exploring Operation: 62-44=18, Resulting Numbers: [62, 43, 18] Generated Node #0,4: 86:[62, 43, 18] Operation: 62-44=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[44, 43, 1], Operations: ['62/62=1'] Exploring Operation: 43*1=43, Resulting Numbers: [44, 43] Generated Node #0,0,0: 86:[44, 43] Operation: 43*1=43 Exploring Operation: 43/1=43, Resulting Numbers: [44, 43] Generated Node #0,0,1: 86:[44, 43] Operation: 43/1=43 Exploring Operation: 44*1=44, Resulting Numbers: [43, 44] Generated Node #0,0,2: 86:[43, 44] Operation: 44*1=44 Exploring Operation: 44-1=43, Resulting Numbers: [43, 43] Generated Node #0,0,3: 86:[43, 43] Operation: 44-1=43 Exploring Operation: 44/1=44, Resulting Numbers: [43, 44] Generated Node #0,0,4: 86:[43, 44] Operation: 44/1=44 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 86:[43, 43], Operations: ['62/62=1', '44-1=43'] Exploring Operation: 43-43=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 43*43=1849, Resulting Numbers: [1849] 1849,86 unequal: No Solution Exploring Operation: 43/43=1, Resulting Numbers: [1] 1,86 unequal: No Solution Exploring Operation: 43+43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[62, 44, 62, 43], Operations: [] Exploring Operation: 62/62=1, Resulting Numbers: [44, 43, 1] Generated Node #0,0: 86:[44, 43, 1] Operation: 62/62=1 Moving to Node #0,0 Current State: 86:[44, 43, 1], Operations: ['62/62=1'] Exploring Operation: 44-1=43, Resulting Numbers: [43, 43] Generated Node #0,0,3: 86:[43, 43] Operation: 44-1=43 Moving to Node #0,0,3 Current State: 86:[43, 43], Operations: ['62/62=1', '44-1=43'] Exploring Operation: 43+43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 56, 65, 57, 97 ]
31
[ "65-56=9", "97-57=40", "40-9=31" ]
Current State: 31:[56, 65, 57, 97], Operations: [] Exploring Operation: 65-56=9, Resulting Numbers: [57, 97, 9] Generated Node #2: [57, 97, 9] from Operation: 65-56=9 Current State: 31:[57, 97, 9], Operations: ['65-56=9'] Exploring Operation: 97-57=40, Resulting Numbers: [9, 40] Generated Node #3: [9, 40] from Operation: 97-57=40 Current State: 31:[9, 40], Operations: ['65-56=9', '97-57=40'] Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[56, 65, 57, 97], Operations: [] Exploring Operation: 97-65=32, Resulting Numbers: [56, 57, 32] Generated Node #0,0: 31:[56, 57, 32] Operation: 97-65=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[56, 57, 32], Operations: ['97-65=32'] Exploring Operation: 57-56=1, Resulting Numbers: [32, 1] Generated Node #0,0,0: 31:[32, 1] Operation: 57-56=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[32, 1], Operations: ['97-65=32', '57-56=1'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[56, 65, 57, 97], Operations: [] Exploring Operation: 97-65=32, Resulting Numbers: [56, 57, 32] Generated Node #0,0: 31:[56, 57, 32] Operation: 97-65=32 Moving to Node #0,0 Current State: 31:[56, 57, 32], Operations: ['97-65=32'] Exploring Operation: 57-56=1, Resulting Numbers: [32, 1] Generated Node #0,0,0: 31:[32, 1] Operation: 57-56=1 Moving to Node #0,0,0 Current State: 31:[32, 1], Operations: ['97-65=32', '57-56=1'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 88, 90, 55, 78 ]
64
[ "88-78=10", "90/10=9", "55+9=64" ]
Current State: 64:[88, 90, 55, 78], Operations: [] Exploring Operation: 88-78=10, Resulting Numbers: [90, 55, 10] Generated Node #2: [90, 55, 10] from Operation: 88-78=10 Current State: 64:[90, 55, 10], Operations: ['88-78=10'] Exploring Operation: 90/10=9, Resulting Numbers: [55, 9] Generated Node #3: [55, 9] from Operation: 90/10=9 Current State: 64:[55, 9], Operations: ['88-78=10', '90/10=9'] Exploring Operation: 55+9=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[88, 90, 55, 78], Operations: [] Exploring Operation: 88-78=10, Resulting Numbers: [90, 55, 10] Generated Node #0,0: 64:[90, 55, 10] Operation: 88-78=10 Exploring Operation: 90-78=12, Resulting Numbers: [88, 55, 12] Generated Node #0,1: 64:[88, 55, 12] Operation: 90-78=12 Exploring Operation: 90-88=2, Resulting Numbers: [55, 78, 2] Generated Node #0,2: 64:[55, 78, 2] Operation: 90-88=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[55, 78, 2], Operations: ['90-88=2'] Exploring Operation: 78/2=39, Resulting Numbers: [55, 39] Generated Node #0,2,0: 64:[55, 39] Operation: 78/2=39 Exploring Operation: 78-55=23, Resulting Numbers: [2, 23] Generated Node #0,2,1: 64:[2, 23] Operation: 78-55=23 Exploring Operation: 55+2=57, Resulting Numbers: [78, 57] Generated Node #0,2,2: 64:[78, 57] Operation: 55+2=57 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 64:[2, 23], Operations: ['90-88=2', '78-55=23'] Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,64 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,64 unequal: No Solution Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,64 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 #0,2,0 Current State: 64:[55, 39], Operations: ['90-88=2', '78/2=39'] Exploring Operation: 55-39=16, Resulting Numbers: [16] 16,64 unequal: No Solution Exploring Operation: 55+39=94, Resulting Numbers: [94] 94,64 unequal: No Solution Exploring Operation: 55*39=2145, Resulting Numbers: [2145] 2145,64 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 #0,2,2 Current State: 64:[78, 57], Operations: ['90-88=2', '55+2=57'] Exploring Operation: 78*57=4446, Resulting Numbers: [4446] 4446,64 unequal: No Solution Exploring Operation: 78-57=21, Resulting Numbers: [21] 21,64 unequal: No Solution Exploring Operation: 78+57=135, Resulting Numbers: [135] 135,64 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 #0,0 Current State: 64:[90, 55, 10], Operations: ['88-78=10'] Exploring Operation: 90/10=9, Resulting Numbers: [55, 9] Generated Node #0,0,0: 64:[55, 9] Operation: 90/10=9 Exploring Operation: 90-10=80, Resulting Numbers: [55, 80] Generated Node #0,0,1: 64:[55, 80] Operation: 90-10=80 Exploring Operation: 90-55=35, Resulting Numbers: [10, 35] Generated Node #0,0,2: 64:[10, 35] Operation: 90-55=35 Moving to Node #0,0,2 Current State: 64:[10, 35], Operations: ['88-78=10', '90-55=35'] Exploring Operation: 35-10=25, Resulting Numbers: [25] 25,64 unequal: No Solution Exploring Operation: 10*35=350, Resulting Numbers: [350] 350,64 unequal: No Solution Exploring Operation: 10+35=45, Resulting Numbers: [45] 45,64 unequal: No Solution Moving to Node #0,0,0 Current State: 64:[55, 9], Operations: ['88-78=10', '90/10=9'] Exploring Operation: 55+9=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[88, 90, 55, 78], Operations: [] Exploring Operation: 88-78=10, Resulting Numbers: [90, 55, 10] Generated Node #0,0: 64:[90, 55, 10] Operation: 88-78=10 Moving to Node #0,0 Current State: 64:[90, 55, 10], Operations: ['88-78=10'] Exploring Operation: 90/10=9, Resulting Numbers: [55, 9] Generated Node #0,0,0: 64:[55, 9] Operation: 90/10=9 Moving to Node #0,0,0 Current State: 64:[55, 9], Operations: ['88-78=10', '90/10=9'] Exploring Operation: 55+9=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_3
mult_heuristic
[ 22, 45, 82, 84 ]
65
[ "22+45=67", "84-82=2", "67-2=65" ]
Current State: 65:[22, 45, 82, 84], Operations: [] Exploring Operation: 22+45=67, Resulting Numbers: [82, 84, 67] Generated Node #2: [82, 84, 67] from Operation: 22+45=67 Current State: 65:[82, 84, 67], Operations: ['22+45=67'] Exploring Operation: 84-82=2, Resulting Numbers: [67, 2] Generated Node #3: [67, 2] from Operation: 84-82=2 Current State: 65:[67, 2], Operations: ['22+45=67', '84-82=2'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[22, 45, 82, 84], Operations: [] Exploring Operation: 84-82=2, Resulting Numbers: [22, 45, 2] Generated Node #0,0: 65:[22, 45, 2] Operation: 84-82=2 Moving to Node #0,0 Current State: 65:[22, 45, 2], Operations: ['84-82=2'] Exploring Operation: 22+45=67, Resulting Numbers: [2, 67] Generated Node #0,0,0: 65:[2, 67] Operation: 22+45=67 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[2, 67], Operations: ['84-82=2', '22+45=67'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[22, 45, 82, 84], Operations: [] Exploring Operation: 84-82=2, Resulting Numbers: [22, 45, 2] Generated Node #0,0: 65:[22, 45, 2] Operation: 84-82=2 Moving to Node #0,0 Current State: 65:[22, 45, 2], Operations: ['84-82=2'] Exploring Operation: 22+45=67, Resulting Numbers: [2, 67] Generated Node #0,0,0: 65:[2, 67] Operation: 22+45=67 Moving to Node #0,0,0 Current State: 65:[2, 67], Operations: ['84-82=2', '22+45=67'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 7, 80, 70, 58 ]
16
[ "70-7=63", "63-58=5", "80/5=16" ]
Current State: 16:[7, 80, 70, 58], Operations: [] Exploring Operation: 70-7=63, Resulting Numbers: [80, 58, 63] Generated Node #2: [80, 58, 63] from Operation: 70-7=63 Current State: 16:[80, 58, 63], Operations: ['70-7=63'] Exploring Operation: 63-58=5, Resulting Numbers: [80, 5] Generated Node #3: [80, 5] from Operation: 63-58=5 Current State: 16:[80, 5], Operations: ['70-7=63', '63-58=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[7, 80, 70, 58], Operations: [] Exploring Operation: 70/7=10, Resulting Numbers: [80, 58, 10] Generated Node #0,0: 16:[80, 58, 10] Operation: 70/7=10 Exploring Operation: 70-58=12, Resulting Numbers: [7, 80, 12] Generated Node #0,1: 16:[7, 80, 12] Operation: 70-58=12 Exploring Operation: 80-70=10, Resulting Numbers: [7, 58, 10] Generated Node #0,2: 16:[7, 58, 10] Operation: 80-70=10 Exploring Operation: 80-58=22, Resulting Numbers: [7, 70, 22] Generated Node #0,3: 16:[7, 70, 22] Operation: 80-58=22 Moving to Node #0,2 Current State: 16:[7, 58, 10], Operations: ['80-70=10'] Exploring Operation: 58-7=51, Resulting Numbers: [10, 51] Generated Node #0,2,0: 16:[10, 51] Operation: 58-7=51 Exploring Operation: 10-7=3, Resulting Numbers: [58, 3] Generated Node #0,2,1: 16:[58, 3] Operation: 10-7=3 Exploring Operation: 58-10=48, Resulting Numbers: [7, 48] Generated Node #0,2,2: 16:[7, 48] Operation: 58-10=48 Exploring Operation: 7+10=17, Resulting Numbers: [58, 17] Generated Node #0,2,3: 16:[58, 17] Operation: 7+10=17 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 16:[7, 48], Operations: ['80-70=10', '58-10=48'] Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,16 unequal: No Solution Exploring Operation: 7*48=336, Resulting Numbers: [336] 336,16 unequal: No Solution Exploring Operation: 7+48=55, Resulting Numbers: [55] 55,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 16:[10, 51], Operations: ['80-70=10', '58-7=51'] Exploring Operation: 51-10=41, Resulting Numbers: [41] 41,16 unequal: No Solution Exploring Operation: 10+51=61, Resulting Numbers: [61] 61,16 unequal: No Solution Exploring Operation: 10*51=510, Resulting Numbers: [510] 510,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 16:[58, 3], Operations: ['80-70=10', '10-7=3'] Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,16 unequal: No Solution Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 16:[58, 17], Operations: ['80-70=10', '7+10=17'] Exploring Operation: 58+17=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 58-17=41, Resulting Numbers: [41] 41,16 unequal: No Solution Exploring Operation: 58*17=986, Resulting Numbers: [986] 986,16 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: 16:[7, 70, 22], Operations: ['80-58=22'] Exploring Operation: 22-7=15, Resulting Numbers: [70, 15] Generated Node #0,3,0: 16:[70, 15] Operation: 22-7=15 Exploring Operation: 70-22=48, Resulting Numbers: [7, 48] Generated Node #0,3,1: 16:[7, 48] Operation: 70-22=48 Exploring Operation: 70-7=63, Resulting Numbers: [22, 63] Generated Node #0,3,2: 16:[22, 63] Operation: 70-7=63 Exploring Operation: 70/7=10, Resulting Numbers: [22, 10] Generated Node #0,3,3: 16:[22, 10] Operation: 70/7=10 Moving to Node #0,1 Current State: 16:[7, 80, 12], Operations: ['70-58=12'] Exploring Operation: 12-7=5, Resulting Numbers: [80, 5] Generated Node #0,1,0: 16:[80, 5] Operation: 12-7=5 Exploring Operation: 80-12=68, Resulting Numbers: [7, 68] Generated Node #0,1,1: 16:[7, 68] Operation: 80-12=68 Exploring Operation: 80-7=73, Resulting Numbers: [12, 73] Generated Node #0,1,2: 16:[12, 73] Operation: 80-7=73 Exploring Operation: 7+12=19, Resulting Numbers: [80, 19] Generated Node #0,1,3: 16:[80, 19] Operation: 7+12=19 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 16:[7, 68], Operations: ['70-58=12', '80-12=68'] Exploring Operation: 7+68=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 7*68=476, Resulting Numbers: [476] 476,16 unequal: No Solution Exploring Operation: 68-7=61, Resulting Numbers: [61] 61,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 16:[12, 73], Operations: ['70-58=12', '80-7=73'] Exploring Operation: 12*73=876, Resulting Numbers: [876] 876,16 unequal: No Solution Exploring Operation: 73-12=61, Resulting Numbers: [61] 61,16 unequal: No Solution Exploring Operation: 12+73=85, Resulting Numbers: [85] 85,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[80, 5], Operations: ['70-58=12', '12-7=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[7, 80, 70, 58], Operations: [] Exploring Operation: 70-58=12, Resulting Numbers: [7, 80, 12] Generated Node #0,1: 16:[7, 80, 12] Operation: 70-58=12 Moving to Node #0,1 Current State: 16:[7, 80, 12], Operations: ['70-58=12'] Exploring Operation: 12-7=5, Resulting Numbers: [80, 5] Generated Node #0,1,0: 16:[80, 5] Operation: 12-7=5 Moving to Node #0,1,0 Current State: 16:[80, 5], Operations: ['70-58=12', '12-7=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_4
sum_heuristic
[ 77, 52, 45, 63 ]
52
[ "52-45=7", "77/7=11", "63-11=52" ]
Current State: 52:[77, 52, 45, 63], Operations: [] Exploring Operation: 52-45=7, Resulting Numbers: [77, 63, 7] Generated Node #2: [77, 63, 7] from Operation: 52-45=7 Current State: 52:[77, 63, 7], Operations: ['52-45=7'] Exploring Operation: 77/7=11, Resulting Numbers: [63, 11] Generated Node #3: [63, 11] from Operation: 77/7=11 Current State: 52:[63, 11], Operations: ['52-45=7', '77/7=11'] Exploring Operation: 63-11=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[77, 52, 45, 63], Operations: [] Exploring Operation: 77-45=32, Resulting Numbers: [52, 63, 32] Generated Node #0,0: 52:[52, 63, 32] Operation: 77-45=32 Exploring Operation: 63-52=11, Resulting Numbers: [77, 45, 11] Generated Node #0,1: 52:[77, 45, 11] Operation: 63-52=11 Exploring Operation: 77-52=25, Resulting Numbers: [45, 63, 25] Generated Node #0,2: 52:[45, 63, 25] Operation: 77-52=25 Exploring Operation: 63-45=18, Resulting Numbers: [77, 52, 18] Generated Node #0,3: 52:[77, 52, 18] Operation: 63-45=18 Exploring Operation: 77-63=14, Resulting Numbers: [52, 45, 14] Generated Node #0,4: 52:[52, 45, 14] Operation: 77-63=14 Start Sub Search at level 1: Moving to Node #0,4 Current State: 52:[52, 45, 14], Operations: ['77-63=14'] Exploring Operation: 45+14=59, Resulting Numbers: [52, 59] Generated Node #0,4,0: 52:[52, 59] Operation: 45+14=59 Exploring Operation: 52-45=7, Resulting Numbers: [14, 7] Generated Node #0,4,1: 52:[14, 7] Operation: 52-45=7 Exploring Operation: 45-14=31, Resulting Numbers: [52, 31] Generated Node #0,4,2: 52:[52, 31] Operation: 45-14=31 Exploring Operation: 52+14=66, Resulting Numbers: [45, 66] Generated Node #0,4,3: 52:[45, 66] Operation: 52+14=66 Exploring Operation: 52-14=38, Resulting Numbers: [45, 38] Generated Node #0,4,4: 52:[45, 38] Operation: 52-14=38 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 52:[14, 7], Operations: ['77-63=14', '52-45=7'] Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,52 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 52:[52, 31], Operations: ['77-63=14', '45-14=31'] Exploring Operation: 52+31=83, Resulting Numbers: [83] 83,52 unequal: No Solution Exploring Operation: 52*31=1612, Resulting Numbers: [1612] 1612,52 unequal: No Solution Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 52:[52, 59], Operations: ['77-63=14', '45+14=59'] Exploring Operation: 52+59=111, Resulting Numbers: [111] 111,52 unequal: No Solution Exploring Operation: 52*59=3068, Resulting Numbers: [3068] 3068,52 unequal: No Solution Exploring Operation: 59-52=7, Resulting Numbers: [7] 7,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 52:[45, 38], Operations: ['77-63=14', '52-14=38'] Exploring Operation: 45*38=1710, Resulting Numbers: [1710] 1710,52 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 45+38=83, Resulting Numbers: [83] 83,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 52:[45, 66], Operations: ['77-63=14', '52+14=66'] Exploring Operation: 45+66=111, Resulting Numbers: [111] 111,52 unequal: No Solution Exploring Operation: 45*66=2970, Resulting Numbers: [2970] 2970,52 unequal: No Solution Exploring Operation: 66-45=21, Resulting Numbers: [21] 21,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[52, 63, 32], Operations: ['77-45=32'] Exploring Operation: 63+32=95, Resulting Numbers: [52, 95] Generated Node #0,0,0: 52:[52, 95] Operation: 63+32=95 Exploring Operation: 63-52=11, Resulting Numbers: [32, 11] Generated Node #0,0,1: 52:[32, 11] Operation: 63-52=11 Exploring Operation: 63-32=31, Resulting Numbers: [52, 31] Generated Node #0,0,2: 52:[52, 31] Operation: 63-32=31 Exploring Operation: 52+32=84, Resulting Numbers: [63, 84] Generated Node #0,0,3: 52:[63, 84] Operation: 52+32=84 Exploring Operation: 52-32=20, Resulting Numbers: [63, 20] Generated Node #0,0,4: 52:[63, 20] Operation: 52-32=20 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 52:[52, 31], Operations: ['77-45=32', '63-32=31'] Exploring Operation: 52+31=83, Resulting Numbers: [83] 83,52 unequal: No Solution Exploring Operation: 52*31=1612, Resulting Numbers: [1612] 1612,52 unequal: No Solution Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[32, 11], Operations: ['77-45=32', '63-52=11'] Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 32*11=352, Resulting Numbers: [352] 352,52 unequal: No Solution Exploring Operation: 32+11=43, Resulting Numbers: [43] 43,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 52:[63, 20], Operations: ['77-45=32', '52-32=20'] Exploring Operation: 63*20=1260, Resulting Numbers: [1260] 1260,52 unequal: No Solution Exploring Operation: 63+20=83, Resulting Numbers: [83] 83,52 unequal: No Solution Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[52, 95], Operations: ['77-45=32', '63+32=95'] Exploring Operation: 95-52=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 52*95=4940, Resulting Numbers: [4940] 4940,52 unequal: No Solution Exploring Operation: 52+95=147, Resulting Numbers: [147] 147,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 52:[63, 84], Operations: ['77-45=32', '52+32=84'] Exploring Operation: 63*84=5292, Resulting Numbers: [5292] 5292,52 unequal: No Solution Exploring Operation: 63+84=147, Resulting Numbers: [147] 147,52 unequal: No Solution Exploring Operation: 84-63=21, Resulting Numbers: [21] 21,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[45, 63, 25], Operations: ['77-52=25'] Exploring Operation: 45+25=70, Resulting Numbers: [63, 70] Generated Node #0,2,0: 52:[63, 70] Operation: 45+25=70 Exploring Operation: 63-45=18, Resulting Numbers: [25, 18] Generated Node #0,2,1: 52:[25, 18] Operation: 63-45=18 Exploring Operation: 63-25=38, Resulting Numbers: [45, 38] Generated Node #0,2,2: 52:[45, 38] Operation: 63-25=38 Exploring Operation: 45-25=20, Resulting Numbers: [63, 20] Generated Node #0,2,3: 52:[63, 20] Operation: 45-25=20 Exploring Operation: 63+25=88, Resulting Numbers: [45, 88] Generated Node #0,2,4: 52:[45, 88] Operation: 63+25=88 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 52:[25, 18], Operations: ['77-52=25', '63-45=18'] Exploring Operation: 25+18=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 25*18=450, Resulting Numbers: [450] 450,52 unequal: No Solution Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 52:[63, 20], Operations: ['77-52=25', '45-25=20'] Exploring Operation: 63*20=1260, Resulting Numbers: [1260] 1260,52 unequal: No Solution Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 63+20=83, Resulting Numbers: [83] 83,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 52:[45, 38], Operations: ['77-52=25', '63-25=38'] Exploring Operation: 45*38=1710, Resulting Numbers: [1710] 1710,52 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 45+38=83, Resulting Numbers: [83] 83,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 52:[63, 70], Operations: ['77-52=25', '45+25=70'] Exploring Operation: 63*70=4410, Resulting Numbers: [4410] 4410,52 unequal: No Solution Exploring Operation: 70-63=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 63+70=133, Resulting Numbers: [133] 133,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 52:[45, 88], Operations: ['77-52=25', '63+25=88'] Exploring Operation: 45*88=3960, Resulting Numbers: [3960] 3960,52 unequal: No Solution Exploring Operation: 88-45=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 45+88=133, Resulting Numbers: [133] 133,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[77, 52, 18], Operations: ['63-45=18'] Exploring Operation: 77-18=59, Resulting Numbers: [52, 59] Generated Node #0,3,0: 52:[52, 59] Operation: 77-18=59 Exploring Operation: 77-52=25, Resulting Numbers: [18, 25] Generated Node #0,3,1: 52:[18, 25] Operation: 77-52=25 Exploring Operation: 52-18=34, Resulting Numbers: [77, 34] Generated Node #0,3,2: 52:[77, 34] Operation: 52-18=34 Exploring Operation: 52+18=70, Resulting Numbers: [77, 70] Generated Node #0,3,3: 52:[77, 70] Operation: 52+18=70 Exploring Operation: 77+18=95, Resulting Numbers: [52, 95] Generated Node #0,3,4: 52:[52, 95] Operation: 77+18=95 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 52:[18, 25], Operations: ['63-45=18', '77-52=25'] Exploring Operation: 18*25=450, Resulting Numbers: [450] 450,52 unequal: No Solution Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 18+25=43, Resulting Numbers: [43] 43,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 52:[52, 59], Operations: ['63-45=18', '77-18=59'] Exploring Operation: 52*59=3068, Resulting Numbers: [3068] 3068,52 unequal: No Solution Exploring Operation: 59-52=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 52+59=111, Resulting Numbers: [111] 111,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 52:[77, 34], Operations: ['63-45=18', '52-18=34'] Exploring Operation: 77+34=111, Resulting Numbers: [111] 111,52 unequal: No Solution Exploring Operation: 77*34=2618, Resulting Numbers: [2618] 2618,52 unequal: No Solution Exploring Operation: 77-34=43, Resulting Numbers: [43] 43,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 52:[77, 70], Operations: ['63-45=18', '52+18=70'] Exploring Operation: 77+70=147, Resulting Numbers: [147] 147,52 unequal: No Solution Exploring Operation: 77-70=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 77*70=5390, Resulting Numbers: [5390] 5390,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 52:[52, 95], Operations: ['63-45=18', '77+18=95'] Exploring Operation: 95-52=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 52+95=147, Resulting Numbers: [147] 147,52 unequal: No Solution Exploring Operation: 52*95=4940, Resulting Numbers: [4940] 4940,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[77, 45, 11], Operations: ['63-52=11'] Exploring Operation: 45+11=56, Resulting Numbers: [77, 56] Generated Node #0,1,0: 52:[77, 56] Operation: 45+11=56 Exploring Operation: 77-11=66, Resulting Numbers: [45, 66] Generated Node #0,1,1: 52:[45, 66] Operation: 77-11=66 Exploring Operation: 77/11=7, Resulting Numbers: [45, 7] Generated Node #0,1,2: 52:[45, 7] Operation: 77/11=7 Exploring Operation: 45-11=34, Resulting Numbers: [77, 34] Generated Node #0,1,3: 52:[77, 34] Operation: 45-11=34 Exploring Operation: 77-45=32, Resulting Numbers: [11, 32] Generated Node #0,1,4: 52:[11, 32] Operation: 77-45=32 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 52:[11, 32], Operations: ['63-52=11', '77-45=32'] Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 11*32=352, Resulting Numbers: [352] 352,52 unequal: No Solution Exploring Operation: 11+32=43, Resulting Numbers: [43] 43,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[45, 7], Operations: ['63-52=11', '77/11=7'] Exploring Operation: 45*7=315, Resulting Numbers: [315] 315,52 unequal: No Solution Exploring Operation: 45+7=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[77, 52, 45, 63], Operations: [] Exploring Operation: 63-52=11, Resulting Numbers: [77, 45, 11] Generated Node #0,1: 52:[77, 45, 11] Operation: 63-52=11 Moving to Node #0,1 Current State: 52:[77, 45, 11], Operations: ['63-52=11'] Exploring Operation: 77/11=7, Resulting Numbers: [45, 7] Generated Node #0,1,2: 52:[45, 7] Operation: 77/11=7 Moving to Node #0,1,2 Current State: 52:[45, 7], Operations: ['63-52=11', '77/11=7'] Exploring Operation: 45+7=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.913194
hs_5
sum_heuristic
[ 21, 86, 92, 40 ]
13
[ "86-21=65", "92-40=52", "65-52=13" ]
Current State: 13:[21, 86, 92, 40], Operations: [] Exploring Operation: 86-21=65, Resulting Numbers: [92, 40, 65] Generated Node #2: [92, 40, 65] from Operation: 86-21=65 Current State: 13:[92, 40, 65], Operations: ['86-21=65'] Exploring Operation: 92-40=52, Resulting Numbers: [65, 52] Generated Node #3: [65, 52] from Operation: 92-40=52 Current State: 13:[65, 52], Operations: ['86-21=65', '92-40=52'] Exploring Operation: 65-52=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[21, 86, 92, 40], Operations: [] Exploring Operation: 92-86=6, Resulting Numbers: [21, 40, 6] Generated Node #0,0: 13:[21, 40, 6] Operation: 92-86=6 Moving to Node #0,0 Current State: 13:[21, 40, 6], Operations: ['92-86=6'] Exploring Operation: 40-21=19, Resulting Numbers: [6, 19] Generated Node #0,0,0: 13:[6, 19] Operation: 40-21=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 13:[6, 19], Operations: ['92-86=6', '40-21=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[21, 86, 92, 40], Operations: [] Exploring Operation: 92-86=6, Resulting Numbers: [21, 40, 6] Generated Node #0,0: 13:[21, 40, 6] Operation: 92-86=6 Moving to Node #0,0 Current State: 13:[21, 40, 6], Operations: ['92-86=6'] Exploring Operation: 40-21=19, Resulting Numbers: [6, 19] Generated Node #0,0,0: 13:[6, 19] Operation: 40-21=19 Moving to Node #0,0,0 Current State: 13:[6, 19], Operations: ['92-86=6', '40-21=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 24, 74, 12, 95 ]
57
[ "74-24=50", "12+95=107", "107-50=57" ]
Current State: 57:[24, 74, 12, 95], Operations: [] Exploring Operation: 74-24=50, Resulting Numbers: [12, 95, 50] Generated Node #2: [12, 95, 50] from Operation: 74-24=50 Current State: 57:[12, 95, 50], Operations: ['74-24=50'] Exploring Operation: 12+95=107, Resulting Numbers: [50, 107] Generated Node #3: [50, 107] from Operation: 12+95=107 Current State: 57:[50, 107], Operations: ['74-24=50', '12+95=107'] Exploring Operation: 107-50=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[24, 74, 12, 95], Operations: [] Exploring Operation: 74-24=50, Resulting Numbers: [12, 95, 50] Generated Node #0,0: 57:[12, 95, 50] Operation: 74-24=50 Exploring Operation: 95-74=21, Resulting Numbers: [24, 12, 21] Generated Node #0,1: 57:[24, 12, 21] Operation: 95-74=21 Exploring Operation: 95-12=83, Resulting Numbers: [24, 74, 83] Generated Node #0,2: 57:[24, 74, 83] Operation: 95-12=83 Exploring Operation: 95-24=71, Resulting Numbers: [74, 12, 71] Generated Node #0,3: 57:[74, 12, 71] Operation: 95-24=71 Exploring Operation: 74-12=62, Resulting Numbers: [24, 95, 62] Generated Node #0,4: 57:[24, 95, 62] Operation: 74-12=62 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[24, 12, 21], Operations: ['95-74=21'] Exploring Operation: 24-21=3, Resulting Numbers: [12, 3] Generated Node #0,1,0: 57:[12, 3] Operation: 24-21=3 Exploring Operation: 24+12=36, Resulting Numbers: [21, 36] Generated Node #0,1,1: 57:[21, 36] Operation: 24+12=36 Exploring Operation: 24-12=12, Resulting Numbers: [21, 12] Generated Node #0,1,2: 57:[21, 12] Operation: 24-12=12 Exploring Operation: 21-12=9, Resulting Numbers: [24, 9] Generated Node #0,1,3: 57:[24, 9] Operation: 21-12=9 Exploring Operation: 24/12=2, Resulting Numbers: [21, 2] Generated Node #0,1,4: 57:[21, 2] Operation: 24/12=2 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 57:[21, 2], Operations: ['95-74=21', '24/12=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,57 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,57 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,57 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 #0,1,0 Current State: 57:[12, 3], Operations: ['95-74=21', '24-21=3'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,57 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,57 unequal: No Solution Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,57 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 #0,1,2 Current State: 57:[21, 12], Operations: ['95-74=21', '24-12=12'] Exploring Operation: 21*12=252, Resulting Numbers: [252] 252,57 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,57 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 #0,1,3 Current State: 57:[24, 9], Operations: ['95-74=21', '21-12=9'] Exploring Operation: 24+9=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,57 unequal: No Solution Exploring Operation: 24*9=216, Resulting Numbers: [216] 216,57 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 #0,1,1 Current State: 57:[21, 36], Operations: ['95-74=21', '24+12=36'] Exploring Operation: 21+36=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[24, 74, 12, 95], Operations: [] Exploring Operation: 95-74=21, Resulting Numbers: [24, 12, 21] Generated Node #0,1: 57:[24, 12, 21] Operation: 95-74=21 Moving to Node #0,1 Current State: 57:[24, 12, 21], Operations: ['95-74=21'] Exploring Operation: 24+12=36, Resulting Numbers: [21, 36] Generated Node #0,1,1: 57:[21, 36] Operation: 24+12=36 Moving to Node #0,1,1 Current State: 57:[21, 36], Operations: ['95-74=21', '24+12=36'] Exploring Operation: 21+36=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.975694
hs_5
mult_heuristic
[ 84, 45, 19, 61 ]
41
[ "84-45=39", "19+61=80", "80-39=41" ]
Current State: 41:[84, 45, 19, 61], Operations: [] Exploring Operation: 84-45=39, Resulting Numbers: [19, 61, 39] Generated Node #2: [19, 61, 39] from Operation: 84-45=39 Current State: 41:[19, 61, 39], Operations: ['84-45=39'] Exploring Operation: 19+61=80, Resulting Numbers: [39, 80] Generated Node #3: [39, 80] from Operation: 19+61=80 Current State: 41:[39, 80], Operations: ['84-45=39', '19+61=80'] Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[84, 45, 19, 61], Operations: [] Exploring Operation: 84-61=23, Resulting Numbers: [45, 19, 23] Generated Node #0,0: 41:[45, 19, 23] Operation: 84-61=23 Exploring Operation: 84-19=65, Resulting Numbers: [45, 61, 65] Generated Node #0,1: 41:[45, 61, 65] Operation: 84-19=65 Exploring Operation: 84-45=39, Resulting Numbers: [19, 61, 39] Generated Node #0,2: 41:[19, 61, 39] Operation: 84-45=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[45, 19, 23], Operations: ['84-61=23'] Exploring Operation: 19+23=42, Resulting Numbers: [45, 42] Generated Node #0,0,0: 41:[45, 42] Operation: 19+23=42 Exploring Operation: 45+19=64, Resulting Numbers: [23, 64] Generated Node #0,0,1: 41:[23, 64] Operation: 45+19=64 Exploring Operation: 45-19=26, Resulting Numbers: [23, 26] Generated Node #0,0,2: 41:[23, 26] Operation: 45-19=26 Moving to Node #0,0,0 Current State: 41:[45, 42], Operations: ['84-61=23', '19+23=42'] Exploring Operation: 45+42=87, Resulting Numbers: [87] 87,41 unequal: No Solution Exploring Operation: 45*42=1890, Resulting Numbers: [1890] 1890,41 unequal: No Solution Exploring Operation: 45-42=3, Resulting Numbers: [3] 3,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[23, 26], Operations: ['84-61=23', '45-19=26'] Exploring Operation: 23*26=598, Resulting Numbers: [598] 598,41 unequal: No Solution Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,41 unequal: No Solution Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[23, 64], Operations: ['84-61=23', '45+19=64'] Exploring Operation: 23+64=87, Resulting Numbers: [87] 87,41 unequal: No Solution Exploring Operation: 23*64=1472, Resulting Numbers: [1472] 1472,41 unequal: No Solution Exploring Operation: 64-23=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[84, 45, 19, 61], Operations: [] Exploring Operation: 84-61=23, Resulting Numbers: [45, 19, 23] Generated Node #0,0: 41:[45, 19, 23] Operation: 84-61=23 Moving to Node #0,0 Current State: 41:[45, 19, 23], Operations: ['84-61=23'] Exploring Operation: 45+19=64, Resulting Numbers: [23, 64] Generated Node #0,0,1: 41:[23, 64] Operation: 45+19=64 Moving to Node #0,0,1 Current State: 41:[23, 64], Operations: ['84-61=23', '45+19=64'] Exploring Operation: 64-23=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 47, 96, 64, 36 ]
71
[ "64*36=2304", "2304/96=24", "47+24=71" ]
Current State: 71:[47, 96, 64, 36], Operations: [] Exploring Operation: 64*36=2304, Resulting Numbers: [47, 96, 2304] Generated Node #2: [47, 96, 2304] from Operation: 64*36=2304 Current State: 71:[47, 96, 2304], Operations: ['64*36=2304'] Exploring Operation: 2304/96=24, Resulting Numbers: [47, 24] Generated Node #3: [47, 24] from Operation: 2304/96=24 Current State: 71:[47, 24], Operations: ['64*36=2304', '2304/96=24'] Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[47, 96, 64, 36], Operations: [] Exploring Operation: 47+36=83, Resulting Numbers: [96, 64, 83] Generated Node #0,0: 71:[96, 64, 83] Operation: 47+36=83 Exploring Operation: 96-36=60, Resulting Numbers: [47, 64, 60] Generated Node #0,1: 71:[47, 64, 60] Operation: 96-36=60 Moving to Node #0,1 Current State: 71:[47, 64, 60], Operations: ['96-36=60'] Exploring Operation: 47+60=107, Resulting Numbers: [64, 107] Generated Node #0,1,0: 71:[64, 107] Operation: 47+60=107 Exploring Operation: 47+64=111, Resulting Numbers: [60, 111] Generated Node #0,1,1: 71:[60, 111] Operation: 47+64=111 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 71:[64, 107], Operations: ['96-36=60', '47+60=107'] Exploring Operation: 64+107=171, Resulting Numbers: [171] 171,71 unequal: No Solution Exploring Operation: 107-64=43, Resulting Numbers: [43] 43,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 71:[60, 111], Operations: ['96-36=60', '47+64=111'] Exploring Operation: 111-60=51, Resulting Numbers: [51] 51,71 unequal: No Solution Exploring Operation: 60+111=171, Resulting Numbers: [171] 171,71 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: 71:[96, 64, 83], Operations: ['47+36=83'] Exploring Operation: 96-83=13, Resulting Numbers: [64, 13] Generated Node #0,0,0: 71:[64, 13] Operation: 96-83=13 Exploring Operation: 96-64=32, Resulting Numbers: [83, 32] Generated Node #0,0,1: 71:[83, 32] Operation: 96-64=32 Moving to Node #0,0,1 Current State: 71:[83, 32], Operations: ['47+36=83', '96-64=32'] Exploring Operation: 83+32=115, Resulting Numbers: [115] 115,71 unequal: No Solution Exploring Operation: 83-32=51, Resulting Numbers: [51] 51,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[64, 13], Operations: ['47+36=83', '96-83=13'] Exploring Operation: 64-13=51, Resulting Numbers: [51] 51,71 unequal: No Solution Exploring Operation: 64+13=77, Resulting Numbers: [77] 77,71 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 30, 71, 72, 18 ]
49
[ "71-30=41", "72+18=90", "90-41=49" ]
Current State: 49:[30, 71, 72, 18], Operations: [] Exploring Operation: 71-30=41, Resulting Numbers: [72, 18, 41] Generated Node #2: [72, 18, 41] from Operation: 71-30=41 Current State: 49:[72, 18, 41], Operations: ['71-30=41'] Exploring Operation: 72+18=90, Resulting Numbers: [41, 90] Generated Node #3: [41, 90] from Operation: 72+18=90 Current State: 49:[41, 90], Operations: ['71-30=41', '72+18=90'] Exploring Operation: 90-41=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[30, 71, 72, 18], Operations: [] Exploring Operation: 72-30=42, Resulting Numbers: [71, 18, 42] Generated Node #0,0: 49:[71, 18, 42] Operation: 72-30=42 Exploring Operation: 72-71=1, Resulting Numbers: [30, 18, 1] Generated Node #0,1: 49:[30, 18, 1] Operation: 72-71=1 Moving to Node #0,1 Current State: 49:[30, 18, 1], Operations: ['72-71=1'] Exploring Operation: 30-18=12, Resulting Numbers: [1, 12] Generated Node #0,1,0: 49:[1, 12] Operation: 30-18=12 Exploring Operation: 30+18=48, Resulting Numbers: [1, 48] Generated Node #0,1,1: 49:[1, 48] Operation: 30+18=48 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 49:[1, 48], Operations: ['72-71=1', '30+18=48'] Exploring Operation: 1*48=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 1+48=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[30, 71, 72, 18], Operations: [] Exploring Operation: 72-71=1, Resulting Numbers: [30, 18, 1] Generated Node #0,1: 49:[30, 18, 1] Operation: 72-71=1 Moving to Node #0,1 Current State: 49:[30, 18, 1], Operations: ['72-71=1'] Exploring Operation: 30+18=48, Resulting Numbers: [1, 48] Generated Node #0,1,1: 49:[1, 48] Operation: 30+18=48 Moving to Node #0,1,1 Current State: 49:[1, 48], Operations: ['72-71=1', '30+18=48'] Exploring Operation: 1+48=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 25, 36, 33, 72 ]
29
[ "25+33=58", "72/36=2", "58/2=29" ]
Current State: 29:[25, 36, 33, 72], Operations: [] Exploring Operation: 25+33=58, Resulting Numbers: [36, 72, 58] Generated Node #2: [36, 72, 58] from Operation: 25+33=58 Current State: 29:[36, 72, 58], Operations: ['25+33=58'] Exploring Operation: 72/36=2, Resulting Numbers: [58, 2] Generated Node #3: [58, 2] from Operation: 72/36=2 Current State: 29:[58, 2], Operations: ['25+33=58', '72/36=2'] Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[25, 36, 33, 72], Operations: [] Exploring Operation: 72-25=47, Resulting Numbers: [36, 33, 47] Generated Node #0,0: 29:[36, 33, 47] Operation: 72-25=47 Exploring Operation: 72-33=39, Resulting Numbers: [25, 36, 39] Generated Node #0,1: 29:[25, 36, 39] Operation: 72-33=39 Exploring Operation: 36-25=11, Resulting Numbers: [33, 72, 11] Generated Node #0,2: 29:[33, 72, 11] Operation: 36-25=11 Exploring Operation: 72-36=36, Resulting Numbers: [25, 33, 36] Generated Node #0,3: 29:[25, 33, 36] Operation: 72-36=36 Exploring Operation: 72/36=2, Resulting Numbers: [25, 33, 2] Generated Node #0,4: 29:[25, 33, 2] Operation: 72/36=2 Moving to Node #0,3 Current State: 29:[25, 33, 36], Operations: ['72-36=36'] Exploring Operation: 36-25=11, Resulting Numbers: [33, 11] Generated Node #0,3,0: 29:[33, 11] Operation: 36-25=11 Exploring Operation: 25+33=58, Resulting Numbers: [36, 58] Generated Node #0,3,1: 29:[36, 58] Operation: 25+33=58 Exploring Operation: 36-33=3, Resulting Numbers: [25, 3] Generated Node #0,3,2: 29:[25, 3] Operation: 36-33=3 Exploring Operation: 25+36=61, Resulting Numbers: [33, 61] Generated Node #0,3,3: 29:[33, 61] Operation: 25+36=61 Exploring Operation: 33-25=8, Resulting Numbers: [36, 8] Generated Node #0,3,4: 29:[36, 8] Operation: 33-25=8 Moving to Node #0,1 Current State: 29:[25, 36, 39], Operations: ['72-33=39'] Exploring Operation: 39-36=3, Resulting Numbers: [25, 3] Generated Node #0,1,0: 29:[25, 3] Operation: 39-36=3 Exploring Operation: 39-25=14, Resulting Numbers: [36, 14] Generated Node #0,1,1: 29:[36, 14] Operation: 39-25=14 Exploring Operation: 25+39=64, Resulting Numbers: [36, 64] Generated Node #0,1,2: 29:[36, 64] Operation: 25+39=64 Exploring Operation: 36-25=11, Resulting Numbers: [39, 11] Generated Node #0,1,3: 29:[39, 11] Operation: 36-25=11 Exploring Operation: 25+36=61, Resulting Numbers: [39, 61] Generated Node #0,1,4: 29:[39, 61] Operation: 25+36=61 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 29:[36, 14], Operations: ['72-33=39', '39-25=14'] Exploring Operation: 36+14=50, Resulting Numbers: [50] 50,29 unequal: No Solution Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 36*14=504, Resulting Numbers: [504] 504,29 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:[39, 11], Operations: ['72-33=39', '36-25=11'] Exploring Operation: 39+11=50, Resulting Numbers: [50] 50,29 unequal: No Solution Exploring Operation: 39*11=429, Resulting Numbers: [429] 429,29 unequal: No Solution Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,29 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:[25, 3], Operations: ['72-33=39', '39-36=3'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,29 unequal: No Solution Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,29 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:[36, 64], Operations: ['72-33=39', '25+39=64'] Exploring Operation: 64-36=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 36*64=2304, Resulting Numbers: [2304] 2304,29 unequal: No Solution Exploring Operation: 36+64=100, Resulting Numbers: [100] 100,29 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 #0,1,4 Current State: 29:[39, 61], Operations: ['72-33=39', '25+36=61'] Exploring Operation: 39*61=2379, Resulting Numbers: [2379] 2379,29 unequal: No Solution Exploring Operation: 39+61=100, Resulting Numbers: [100] 100,29 unequal: No Solution Exploring Operation: 61-39=22, Resulting Numbers: [22] 22,29 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: 29:[36, 33, 47], Operations: ['72-25=47'] Exploring Operation: 36+47=83, Resulting Numbers: [33, 83] Generated Node #0,0,0: 29:[33, 83] Operation: 36+47=83 Exploring Operation: 36+33=69, Resulting Numbers: [47, 69] Generated Node #0,0,1: 29:[47, 69] Operation: 36+33=69 Exploring Operation: 47-33=14, Resulting Numbers: [36, 14] Generated Node #0,0,2: 29:[36, 14] Operation: 47-33=14 Exploring Operation: 47-36=11, Resulting Numbers: [33, 11] Generated Node #0,0,3: 29:[33, 11] Operation: 47-36=11 Exploring Operation: 36-33=3, Resulting Numbers: [47, 3] Generated Node #0,0,4: 29:[47, 3] Operation: 36-33=3 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 29:[36, 14], Operations: ['72-25=47', '47-33=14'] Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 36*14=504, Resulting Numbers: [504] 504,29 unequal: No Solution Exploring Operation: 36+14=50, Resulting Numbers: [50] 50,29 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:[33, 11], Operations: ['72-25=47', '47-36=11'] Exploring Operation: 33/11=3, Resulting Numbers: [3] 3,29 unequal: No Solution Exploring Operation: 33*11=363, Resulting Numbers: [363] 363,29 unequal: No Solution Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 33+11=44, Resulting Numbers: [44] 44,29 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 #0,0,4 Current State: 29:[47, 3], Operations: ['72-25=47', '36-33=3'] Exploring Operation: 47+3=50, Resulting Numbers: [50] 50,29 unequal: No Solution Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,29 unequal: No Solution Exploring Operation: 47*3=141, Resulting Numbers: [141] 141,29 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:[33, 83], Operations: ['72-25=47', '36+47=83'] Exploring Operation: 33*83=2739, Resulting Numbers: [2739] 2739,29 unequal: No Solution Exploring Operation: 83-33=50, Resulting Numbers: [50] 50,29 unequal: No Solution Exploring Operation: 33+83=116, Resulting Numbers: [116] 116,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 29:[47, 69], Operations: ['72-25=47', '36+33=69'] Exploring Operation: 47+69=116, Resulting Numbers: [116] 116,29 unequal: No Solution Exploring Operation: 47*69=3243, Resulting Numbers: [3243] 3243,29 unequal: No Solution Exploring Operation: 69-47=22, Resulting Numbers: [22] 22,29 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: 29:[25, 33, 2], Operations: ['72/36=2'] Exploring Operation: 33-2=31, Resulting Numbers: [25, 31] Generated Node #0,4,0: 29:[25, 31] Operation: 33-2=31 Exploring Operation: 33+2=35, Resulting Numbers: [25, 35] Generated Node #0,4,1: 29:[25, 35] Operation: 33+2=35 Exploring Operation: 25-2=23, Resulting Numbers: [33, 23] Generated Node #0,4,2: 29:[33, 23] Operation: 25-2=23 Exploring Operation: 25*2=50, Resulting Numbers: [33, 50] Generated Node #0,4,3: 29:[33, 50] Operation: 25*2=50 Exploring Operation: 25+2=27, Resulting Numbers: [33, 27] Generated Node #0,4,4: 29:[33, 27] Operation: 25+2=27 Moving to Node #0,2 Current State: 29:[33, 72, 11], Operations: ['36-25=11'] Exploring Operation: 33-11=22, Resulting Numbers: [72, 22] Generated Node #0,2,0: 29:[72, 22] Operation: 33-11=22 Exploring Operation: 72-33=39, Resulting Numbers: [11, 39] Generated Node #0,2,1: 29:[11, 39] Operation: 72-33=39 Exploring Operation: 72+11=83, Resulting Numbers: [33, 83] Generated Node #0,2,2: 29:[33, 83] Operation: 72+11=83 Exploring Operation: 33+11=44, Resulting Numbers: [72, 44] Generated Node #0,2,3: 29:[72, 44] Operation: 33+11=44 Exploring Operation: 72-11=61, Resulting Numbers: [33, 61] Generated Node #0,2,4: 29:[33, 61] Operation: 72-11=61 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 29:[11, 39], Operations: ['36-25=11', '72-33=39'] Exploring Operation: 11*39=429, Resulting Numbers: [429] 429,29 unequal: No Solution Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 11+39=50, Resulting Numbers: [50] 50,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 29:[33, 61], Operations: ['36-25=11', '72-11=61'] Exploring Operation: 33+61=94, Resulting Numbers: [94] 94,29 unequal: No Solution Exploring Operation: 61-33=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 33*61=2013, Resulting Numbers: [2013] 2013,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[72, 22], Operations: ['36-25=11', '33-11=22'] Exploring Operation: 72+22=94, Resulting Numbers: [94] 94,29 unequal: No Solution Exploring Operation: 72*22=1584, Resulting Numbers: [1584] 1584,29 unequal: No Solution Exploring Operation: 72-22=50, Resulting Numbers: [50] 50,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 29:[33, 83], Operations: ['36-25=11', '72+11=83'] Exploring Operation: 33+83=116, Resulting Numbers: [116] 116,29 unequal: No Solution Exploring Operation: 83-33=50, Resulting Numbers: [50] 50,29 unequal: No Solution Exploring Operation: 33*83=2739, Resulting Numbers: [2739] 2739,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 29:[72, 44], Operations: ['36-25=11', '33+11=44'] Exploring Operation: 72*44=3168, Resulting Numbers: [3168] 3168,29 unequal: No Solution Exploring Operation: 72+44=116, Resulting Numbers: [116] 116,29 unequal: No Solution Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,0 Current State: 29:[25, 31], Operations: ['72/36=2', '33-2=31'] Exploring Operation: 25*31=775, Resulting Numbers: [775] 775,29 unequal: No Solution Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 25+31=56, Resulting Numbers: [56] 56,29 unequal: No Solution Moving to Node #0,4,4 Current State: 29:[33, 27], Operations: ['72/36=2', '25+2=27'] Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,29 unequal: No Solution Moving to Node #0,4,1 Current State: 29:[25, 35], Operations: ['72/36=2', '33+2=35'] Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 25*35=875, Resulting Numbers: [875] 875,29 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,29 unequal: No Solution Moving to Node #0,4,2 Current State: 29:[33, 23], Operations: ['72/36=2', '25-2=23'] Exploring Operation: 33*23=759, Resulting Numbers: [759] 759,29 unequal: No Solution Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 33+23=56, Resulting Numbers: [56] 56,29 unequal: No Solution Moving to Node #0,3,0 Current State: 29:[33, 11], Operations: ['72-36=36', '36-25=11'] Exploring Operation: 33/11=3, Resulting Numbers: [3] 3,29 unequal: No Solution Exploring Operation: 33*11=363, Resulting Numbers: [363] 363,29 unequal: No Solution Exploring Operation: 33+11=44, Resulting Numbers: [44] 44,29 unequal: No Solution Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,29 unequal: No Solution Moving to Node #0,4,3 Current State: 29:[33, 50], Operations: ['72/36=2', '25*2=50'] Exploring Operation: 50-33=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 33+50=83, Resulting Numbers: [83] 83,29 unequal: No Solution Exploring Operation: 33*50=1650, Resulting Numbers: [1650] 1650,29 unequal: No Solution Moving to Node #0,3,4 Current State: 29:[36, 8], Operations: ['72-36=36', '33-25=8'] Exploring Operation: 36+8=44, Resulting Numbers: [44] 44,29 unequal: No Solution Exploring Operation: 36*8=288, Resulting Numbers: [288] 288,29 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,29 unequal: No Solution Moving to Node #0,3,2 Current State: 29:[25, 3], Operations: ['72-36=36', '36-33=3'] Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,29 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,29 unequal: No Solution Moving to Node #0,3,3 Current State: 29:[33, 61], Operations: ['72-36=36', '25+36=61'] Exploring Operation: 33*61=2013, Resulting Numbers: [2013] 2013,29 unequal: No Solution Exploring Operation: 33+61=94, Resulting Numbers: [94] 94,29 unequal: No Solution Exploring Operation: 61-33=28, Resulting Numbers: [28] 28,29 unequal: No Solution Moving to Node #0,3,1 Current State: 29:[36, 58], Operations: ['72-36=36', '25+33=58'] Exploring Operation: 36*58=2088, Resulting Numbers: [2088] 2088,29 unequal: No Solution Exploring Operation: 36+58=94, Resulting Numbers: [94] 94,29 unequal: No Solution Exploring Operation: 58-36=22, Resulting Numbers: [22] 22,29 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 30, 50, 74, 6 ]
100
[ "50-30=20", "74+6=80", "20+80=100" ]
Current State: 100:[30, 50, 74, 6], Operations: [] Exploring Operation: 50-30=20, Resulting Numbers: [74, 6, 20] Generated Node #2: [74, 6, 20] from Operation: 50-30=20 Current State: 100:[74, 6, 20], Operations: ['50-30=20'] Exploring Operation: 74+6=80, Resulting Numbers: [20, 80] Generated Node #3: [20, 80] from Operation: 74+6=80 Current State: 100:[20, 80], Operations: ['50-30=20', '74+6=80'] Exploring Operation: 20+80=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[30, 50, 74, 6], Operations: [] Exploring Operation: 74-50=24, Resulting Numbers: [30, 6, 24] Generated Node #0,0: 100:[30, 6, 24] Operation: 74-50=24 Exploring Operation: 30/6=5, Resulting Numbers: [50, 74, 5] Generated Node #0,1: 100:[50, 74, 5] Operation: 30/6=5 Exploring Operation: 74-30=44, Resulting Numbers: [50, 6, 44] Generated Node #0,2: 100:[50, 6, 44] Operation: 74-30=44 Exploring Operation: 30+74=104, Resulting Numbers: [50, 6, 104] Generated Node #0,3: 100:[50, 6, 104] Operation: 30+74=104 Exploring Operation: 74-6=68, Resulting Numbers: [30, 50, 68] Generated Node #0,4: 100:[30, 50, 68] Operation: 74-6=68 Moving to Node #0,3 Current State: 100:[50, 6, 104], Operations: ['30+74=104'] Exploring Operation: 104-6=98, Resulting Numbers: [50, 98] Generated Node #0,3,0: 100:[50, 98] Operation: 104-6=98 Exploring Operation: 104-50=54, Resulting Numbers: [6, 54] Generated Node #0,3,1: 100:[6, 54] Operation: 104-50=54 Exploring Operation: 50-6=44, Resulting Numbers: [104, 44] Generated Node #0,3,2: 100:[104, 44] Operation: 50-6=44 Exploring Operation: 6+104=110, Resulting Numbers: [50, 110] Generated Node #0,3,3: 100:[50, 110] Operation: 6+104=110 Exploring Operation: 50+6=56, Resulting Numbers: [104, 56] Generated Node #0,3,4: 100:[104, 56] Operation: 50+6=56 Moving to Node #0,2 Current State: 100:[50, 6, 44], Operations: ['74-30=44'] Exploring Operation: 6+44=50, Resulting Numbers: [50, 50] Generated Node #0,2,0: 100:[50, 50] Operation: 6+44=50 Exploring Operation: 50-6=44, Resulting Numbers: [44, 44] Generated Node #0,2,1: 100:[44, 44] Operation: 50-6=44 Exploring Operation: 50+44=94, Resulting Numbers: [6, 94] Generated Node #0,2,2: 100:[6, 94] Operation: 50+44=94 Exploring Operation: 50+6=56, Resulting Numbers: [44, 56] Generated Node #0,2,3: 100:[44, 56] Operation: 50+6=56 Exploring Operation: 50-44=6, Resulting Numbers: [6, 6] Generated Node #0,2,4: 100:[6, 6] Operation: 50-44=6 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 100:[50, 50], Operations: ['74-30=44', '6+44=50'] Exploring Operation: 50*50=2500, Resulting Numbers: [2500] 2500,100 unequal: No Solution Exploring Operation: 50/50=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 50+50=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[30, 50, 74, 6], Operations: [] Exploring Operation: 74-30=44, Resulting Numbers: [50, 6, 44] Generated Node #0,2: 100:[50, 6, 44] Operation: 74-30=44 Moving to Node #0,2 Current State: 100:[50, 6, 44], Operations: ['74-30=44'] Exploring Operation: 6+44=50, Resulting Numbers: [50, 50] Generated Node #0,2,0: 100:[50, 50] Operation: 6+44=50 Moving to Node #0,2,0 Current State: 100:[50, 50], Operations: ['74-30=44', '6+44=50'] Exploring Operation: 50+50=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 46, 9, 97, 11 ]
54
[ "97-9=88", "88/11=8", "46+8=54" ]
Current State: 54:[46, 9, 97, 11], Operations: [] Exploring Operation: 97-9=88, Resulting Numbers: [46, 11, 88] Generated Node #2: [46, 11, 88] from Operation: 97-9=88 Current State: 54:[46, 11, 88], Operations: ['97-9=88'] Exploring Operation: 88/11=8, Resulting Numbers: [46, 8] Generated Node #3: [46, 8] from Operation: 88/11=8 Current State: 54:[46, 8], Operations: ['97-9=88', '88/11=8'] Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[46, 9, 97, 11], Operations: [] Exploring Operation: 97-11=86, Resulting Numbers: [46, 9, 86] Generated Node #0,0: 54:[46, 9, 86] Operation: 97-11=86 Exploring Operation: 97-9=88, Resulting Numbers: [46, 11, 88] Generated Node #0,1: 54:[46, 11, 88] Operation: 97-9=88 Exploring Operation: 97-46=51, Resulting Numbers: [9, 11, 51] Generated Node #0,2: 54:[9, 11, 51] Operation: 97-46=51 Exploring Operation: 46+9=55, Resulting Numbers: [97, 11, 55] Generated Node #0,3: 54:[97, 11, 55] Operation: 46+9=55 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[9, 11, 51], Operations: ['97-46=51'] Exploring Operation: 9+11=20, Resulting Numbers: [51, 20] Generated Node #0,2,0: 54:[51, 20] Operation: 9+11=20 Exploring Operation: 11+51=62, Resulting Numbers: [9, 62] Generated Node #0,2,1: 54:[9, 62] Operation: 11+51=62 Exploring Operation: 11-9=2, Resulting Numbers: [51, 2] Generated Node #0,2,2: 54:[51, 2] Operation: 11-9=2 Exploring Operation: 9+51=60, Resulting Numbers: [11, 60] Generated Node #0,2,3: 54:[11, 60] Operation: 9+51=60 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 54:[51, 2], Operations: ['97-46=51', '11-9=2'] Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,54 unequal: No Solution Exploring Operation: 51*2=102, Resulting Numbers: [102] 102,54 unequal: No Solution Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 54:[51, 20], Operations: ['97-46=51', '9+11=20'] Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,54 unequal: No Solution Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,54 unequal: No Solution Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 54:[9, 62], Operations: ['97-46=51', '11+51=62'] Exploring Operation: 62-9=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 9*62=558, Resulting Numbers: [558] 558,54 unequal: No Solution Exploring Operation: 9+62=71, Resulting Numbers: [71] 71,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 54:[11, 60], Operations: ['97-46=51', '9+51=60'] Exploring Operation: 60-11=49, Resulting Numbers: [49] 49,54 unequal: No Solution Exploring Operation: 11*60=660, Resulting Numbers: [660] 660,54 unequal: No Solution Exploring Operation: 11+60=71, Resulting Numbers: [71] 71,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[46, 9, 86], Operations: ['97-11=86'] Exploring Operation: 46+9=55, Resulting Numbers: [86, 55] Generated Node #0,0,0: 54:[86, 55] Operation: 46+9=55 Exploring Operation: 86-46=40, Resulting Numbers: [9, 40] Generated Node #0,0,1: 54:[9, 40] Operation: 86-46=40 Exploring Operation: 46-9=37, Resulting Numbers: [86, 37] Generated Node #0,0,2: 54:[86, 37] Operation: 46-9=37 Exploring Operation: 86-9=77, Resulting Numbers: [46, 77] Generated Node #0,0,3: 54:[46, 77] Operation: 86-9=77 Moving to Node #0,0,1 Current State: 54:[9, 40], Operations: ['97-11=86', '86-46=40'] Exploring Operation: 9+40=49, Resulting Numbers: [49] 49,54 unequal: No Solution Exploring Operation: 9*40=360, Resulting Numbers: [360] 360,54 unequal: No Solution Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,54 unequal: No Solution Moving to Node #0,0,3 Current State: 54:[46, 77], Operations: ['97-11=86', '86-9=77'] Exploring Operation: 46+77=123, Resulting Numbers: [123] 123,54 unequal: No Solution Exploring Operation: 77-46=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 46*77=3542, Resulting Numbers: [3542] 3542,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[86, 55], Operations: ['97-11=86', '46+9=55'] Exploring Operation: 86-55=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 86+55=141, Resulting Numbers: [141] 141,54 unequal: No Solution Exploring Operation: 86*55=4730, Resulting Numbers: [4730] 4730,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[86, 37], Operations: ['97-11=86', '46-9=37'] Exploring Operation: 86+37=123, Resulting Numbers: [123] 123,54 unequal: No Solution Exploring Operation: 86*37=3182, Resulting Numbers: [3182] 3182,54 unequal: No Solution Exploring Operation: 86-37=49, Resulting Numbers: [49] 49,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[46, 11, 88], Operations: ['97-9=88'] Exploring Operation: 46+11=57, Resulting Numbers: [88, 57] Generated Node #0,1,0: 54:[88, 57] Operation: 46+11=57 Exploring Operation: 88/11=8, Resulting Numbers: [46, 8] Generated Node #0,1,1: 54:[46, 8] Operation: 88/11=8 Exploring Operation: 88-46=42, Resulting Numbers: [11, 42] Generated Node #0,1,2: 54:[11, 42] Operation: 88-46=42 Exploring Operation: 88-11=77, Resulting Numbers: [46, 77] Generated Node #0,1,3: 54:[46, 77] Operation: 88-11=77 Moving to Node #0,1,1 Current State: 54:[46, 8], Operations: ['97-9=88', '88/11=8'] Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[46, 9, 97, 11], Operations: [] Exploring Operation: 97-9=88, Resulting Numbers: [46, 11, 88] Generated Node #0,1: 54:[46, 11, 88] Operation: 97-9=88 Moving to Node #0,1 Current State: 54:[46, 11, 88], Operations: ['97-9=88'] Exploring Operation: 88/11=8, Resulting Numbers: [46, 8] Generated Node #0,1,1: 54:[46, 8] Operation: 88/11=8 Moving to Node #0,1,1 Current State: 54:[46, 8], Operations: ['97-9=88', '88/11=8'] Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.960938
hs_4
mult_heuristic
[ 25, 36, 80, 41 ]
20
[ "25*36=900", "900-80=820", "820/41=20" ]
Current State: 20:[25, 36, 80, 41], Operations: [] Exploring Operation: 25*36=900, Resulting Numbers: [80, 41, 900] Generated Node #2: [80, 41, 900] from Operation: 25*36=900 Current State: 20:[80, 41, 900], Operations: ['25*36=900'] Exploring Operation: 900-80=820, Resulting Numbers: [41, 820] Generated Node #3: [41, 820] from Operation: 900-80=820 Current State: 20:[41, 820], Operations: ['25*36=900', '900-80=820'] Exploring Operation: 820/41=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[25, 36, 80, 41], Operations: [] Exploring Operation: 80-41=39, Resulting Numbers: [25, 36, 39] Generated Node #0,0: 20:[25, 36, 39] Operation: 80-41=39 Moving to Node #0,0 Current State: 20:[25, 36, 39], Operations: ['80-41=39'] Exploring Operation: 39-36=3, Resulting Numbers: [25, 3] Generated Node #0,0,0: 20:[25, 3] Operation: 39-36=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[25, 3], Operations: ['80-41=39', '39-36=3'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,20 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
[ 37, 63, 52, 2 ]
33
[ "52-37=15", "2*15=30", "63-30=33" ]
Current State: 33:[37, 63, 52, 2], Operations: [] Exploring Operation: 52-37=15, Resulting Numbers: [63, 2, 15] Generated Node #2: [63, 2, 15] from Operation: 52-37=15 Current State: 33:[63, 2, 15], Operations: ['52-37=15'] Exploring Operation: 2*15=30, Resulting Numbers: [63, 30] Generated Node #3: [63, 30] from Operation: 2*15=30 Current State: 33:[63, 30], Operations: ['52-37=15', '2*15=30'] Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[37, 63, 52, 2], Operations: [] Exploring Operation: 52/2=26, Resulting Numbers: [37, 63, 26] Generated Node #0,0: 33:[37, 63, 26] Operation: 52/2=26 Exploring Operation: 52-37=15, Resulting Numbers: [63, 2, 15] Generated Node #0,1: 33:[63, 2, 15] Operation: 52-37=15 Exploring Operation: 63-52=11, Resulting Numbers: [37, 2, 11] Generated Node #0,2: 33:[37, 2, 11] Operation: 63-52=11 Exploring Operation: 63-37=26, Resulting Numbers: [52, 2, 26] Generated Node #0,3: 33:[52, 2, 26] Operation: 63-37=26 Moving to Node #0,2 Current State: 33:[37, 2, 11], Operations: ['63-52=11'] Exploring Operation: 2+11=13, Resulting Numbers: [37, 13] Generated Node #0,2,0: 33:[37, 13] Operation: 2+11=13 Exploring Operation: 11-2=9, Resulting Numbers: [37, 9] Generated Node #0,2,1: 33:[37, 9] Operation: 11-2=9 Exploring Operation: 37+2=39, Resulting Numbers: [11, 39] Generated Node #0,2,2: 33:[11, 39] Operation: 37+2=39 Exploring Operation: 37-2=35, Resulting Numbers: [11, 35] Generated Node #0,2,3: 33:[11, 35] Operation: 37-2=35 Moving to Node #0,3 Current State: 33:[52, 2, 26], Operations: ['63-37=26'] Exploring Operation: 52/26=2, Resulting Numbers: [2, 2] Generated Node #0,3,0: 33:[2, 2] Operation: 52/26=2 Exploring Operation: 52/2=26, Resulting Numbers: [26, 26] Generated Node #0,3,1: 33:[26, 26] Operation: 52/2=26 Exploring Operation: 52-26=26, Resulting Numbers: [2, 26] Generated Node #0,3,2: 33:[2, 26] Operation: 52-26=26 Exploring Operation: 26/2=13, Resulting Numbers: [52, 13] Generated Node #0,3,3: 33:[52, 13] Operation: 26/2=13 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 33:[2, 2], Operations: ['63-37=26', '52/26=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,33 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,33 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,33 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,33 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 #0,3,2 Current State: 33:[2, 26], Operations: ['63-37=26', '52-26=26'] Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,33 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 #0,3,1 Current State: 33:[26, 26], Operations: ['63-37=26', '52/2=26'] Exploring Operation: 26*26=676, Resulting Numbers: [676] 676,33 unequal: No Solution Exploring Operation: 26-26=0, Resulting Numbers: [0] 0,33 unequal: No Solution Exploring Operation: 26+26=52, Resulting Numbers: [52] 52,33 unequal: No Solution Exploring Operation: 26/26=1, Resulting Numbers: [1] 1,33 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 #0,3,3 Current State: 33:[52, 13], Operations: ['63-37=26', '26/2=13'] Exploring Operation: 52+13=65, Resulting Numbers: [65] 65,33 unequal: No Solution Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,33 unequal: No Solution Exploring Operation: 52*13=676, Resulting Numbers: [676] 676,33 unequal: No Solution Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,33 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:[63, 2, 15], Operations: ['52-37=15'] Exploring Operation: 63-2=61, Resulting Numbers: [15, 61] Generated Node #0,1,0: 33:[15, 61] Operation: 63-2=61 Exploring Operation: 15-2=13, Resulting Numbers: [63, 13] Generated Node #0,1,1: 33:[63, 13] Operation: 15-2=13 Exploring Operation: 2*15=30, Resulting Numbers: [63, 30] Generated Node #0,1,2: 33:[63, 30] Operation: 2*15=30 Exploring Operation: 63-15=48, Resulting Numbers: [2, 48] Generated Node #0,1,3: 33:[2, 48] Operation: 63-15=48 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 33:[2, 48], Operations: ['52-37=15', '63-15=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,33 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,33 unequal: No Solution Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,33 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 #0,1,0 Current State: 33:[15, 61], Operations: ['52-37=15', '63-2=61'] Exploring Operation: 15*61=915, Resulting Numbers: [915] 915,33 unequal: No Solution Exploring Operation: 15+61=76, Resulting Numbers: [76] 76,33 unequal: No Solution Exploring Operation: 61-15=46, Resulting Numbers: [46] 46,33 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:[63, 13], Operations: ['52-37=15', '15-2=13'] Exploring Operation: 63*13=819, Resulting Numbers: [819] 819,33 unequal: No Solution Exploring Operation: 63+13=76, Resulting Numbers: [76] 76,33 unequal: No Solution Exploring Operation: 63-13=50, Resulting Numbers: [50] 50,33 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:[63, 30], Operations: ['52-37=15', '2*15=30'] Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[37, 63, 52, 2], Operations: [] Exploring Operation: 52-37=15, Resulting Numbers: [63, 2, 15] Generated Node #0,1: 33:[63, 2, 15] Operation: 52-37=15 Moving to Node #0,1 Current State: 33:[63, 2, 15], Operations: ['52-37=15'] Exploring Operation: 2*15=30, Resulting Numbers: [63, 30] Generated Node #0,1,2: 33:[63, 30] Operation: 2*15=30 Moving to Node #0,1,2 Current State: 33:[63, 30], Operations: ['52-37=15', '2*15=30'] Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_4
mult_heuristic
[ 69, 55, 83, 56 ]
41
[ "69-55=14", "83-56=27", "14+27=41" ]
Current State: 41:[69, 55, 83, 56], Operations: [] Exploring Operation: 69-55=14, Resulting Numbers: [83, 56, 14] Generated Node #2: [83, 56, 14] from Operation: 69-55=14 Current State: 41:[83, 56, 14], Operations: ['69-55=14'] Exploring Operation: 83-56=27, Resulting Numbers: [14, 27] Generated Node #3: [14, 27] from Operation: 83-56=27 Current State: 41:[14, 27], Operations: ['69-55=14', '83-56=27'] Exploring Operation: 14+27=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[69, 55, 83, 56], Operations: [] Exploring Operation: 83-55=28, Resulting Numbers: [69, 56, 28] Generated Node #0,0: 41:[69, 56, 28] Operation: 83-55=28 Exploring Operation: 69-55=14, Resulting Numbers: [83, 56, 14] Generated Node #0,1: 41:[83, 56, 14] Operation: 69-55=14 Exploring Operation: 83-69=14, Resulting Numbers: [55, 56, 14] Generated Node #0,2: 41:[55, 56, 14] Operation: 83-69=14 Exploring Operation: 83-56=27, Resulting Numbers: [69, 55, 27] Generated Node #0,3: 41:[69, 55, 27] Operation: 83-56=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[69, 56, 28], Operations: ['83-55=28'] Exploring Operation: 69-28=41, Resulting Numbers: [56, 41] Generated Node #0,0,0: 41:[56, 41] Operation: 69-28=41 Exploring Operation: 69-56=13, Resulting Numbers: [28, 13] Generated Node #0,0,1: 41:[28, 13] Operation: 69-56=13 Exploring Operation: 56-28=28, Resulting Numbers: [69, 28] Generated Node #0,0,2: 41:[69, 28] Operation: 56-28=28 Exploring Operation: 56/28=2, Resulting Numbers: [69, 2] Generated Node #0,0,3: 41:[69, 2] Operation: 56/28=2 Moving to Node #0,0,0 Current State: 41:[56, 41], Operations: ['83-55=28', '69-28=41'] Exploring Operation: 56*41=2296, Resulting Numbers: [2296] 2296,41 unequal: No Solution Exploring Operation: 56+41=97, Resulting Numbers: [97] 97,41 unequal: No Solution Exploring Operation: 56-41=15, Resulting Numbers: [15] 15,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[69, 28], Operations: ['83-55=28', '56-28=28'] Exploring Operation: 69+28=97, Resulting Numbers: [97] 97,41 unequal: No Solution Exploring Operation: 69*28=1932, Resulting Numbers: [1932] 1932,41 unequal: No Solution Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[69, 55, 83, 56], Operations: [] Exploring Operation: 83-55=28, Resulting Numbers: [69, 56, 28] Generated Node #0,0: 41:[69, 56, 28] Operation: 83-55=28 Moving to Node #0,0 Current State: 41:[69, 56, 28], Operations: ['83-55=28'] Exploring Operation: 56-28=28, Resulting Numbers: [69, 28] Generated Node #0,0,2: 41:[69, 28] Operation: 56-28=28 Moving to Node #0,0,2 Current State: 41:[69, 28], Operations: ['83-55=28', '56-28=28'] Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 51, 29, 92, 4 ]
83
[ "51*4=204", "29+92=121", "204-121=83" ]
Current State: 83:[51, 29, 92, 4], Operations: [] Exploring Operation: 51*4=204, Resulting Numbers: [29, 92, 204] Generated Node #2: [29, 92, 204] from Operation: 51*4=204 Current State: 83:[29, 92, 204], Operations: ['51*4=204'] Exploring Operation: 29+92=121, Resulting Numbers: [204, 121] Generated Node #3: [204, 121] from Operation: 29+92=121 Current State: 83:[204, 121], Operations: ['51*4=204', '29+92=121'] Exploring Operation: 204-121=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[51, 29, 92, 4], Operations: [] Exploring Operation: 51+4=55, Resulting Numbers: [29, 92, 55] Generated Node #0,0: 83:[29, 92, 55] Operation: 51+4=55 Exploring Operation: 51+29=80, Resulting Numbers: [92, 4, 80] Generated Node #0,1: 83:[92, 4, 80] Operation: 51+29=80 Exploring Operation: 29+4=33, Resulting Numbers: [51, 92, 33] Generated Node #0,2: 83:[51, 92, 33] Operation: 29+4=33 Exploring Operation: 29*4=116, Resulting Numbers: [51, 92, 116] Generated Node #0,3: 83:[51, 92, 116] Operation: 29*4=116 Moving to Node #0,3 Current State: 83:[51, 92, 116], Operations: ['29*4=116'] Exploring Operation: 92-51=41, Resulting Numbers: [116, 41] Generated Node #0,3,0: 83:[116, 41] Operation: 92-51=41 Exploring Operation: 116-51=65, Resulting Numbers: [92, 65] Generated Node #0,3,1: 83:[92, 65] Operation: 116-51=65 Exploring Operation: 51+92=143, Resulting Numbers: [116, 143] Generated Node #0,3,2: 83:[116, 143] Operation: 51+92=143 Exploring Operation: 116-92=24, Resulting Numbers: [51, 24] Generated Node #0,3,3: 83:[51, 24] Operation: 116-92=24 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 83:[92, 65], Operations: ['29*4=116', '116-51=65'] Exploring Operation: 92*65=5980, Resulting Numbers: [5980] 5980,83 unequal: No Solution Exploring Operation: 92+65=157, Resulting Numbers: [157] 157,83 unequal: No Solution Exploring Operation: 92-65=27, Resulting Numbers: [27] 27,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 83:[116, 41], Operations: ['29*4=116', '92-51=41'] Exploring Operation: 116*41=4756, Resulting Numbers: [4756] 4756,83 unequal: No Solution Exploring Operation: 116+41=157, Resulting Numbers: [157] 157,83 unequal: No Solution Exploring Operation: 116-41=75, Resulting Numbers: [75] 75,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 83:[51, 24], Operations: ['29*4=116', '116-92=24'] Exploring Operation: 51*24=1224, Resulting Numbers: [1224] 1224,83 unequal: No Solution Exploring Operation: 51+24=75, Resulting Numbers: [75] 75,83 unequal: No Solution Exploring Operation: 51-24=27, Resulting Numbers: [27] 27,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 83:[116, 143], Operations: ['29*4=116', '51+92=143'] Exploring Operation: 116*143=16588, Resulting Numbers: [16588] 16588,83 unequal: No Solution Exploring Operation: 116+143=259, Resulting Numbers: [259] 259,83 unequal: No Solution Exploring Operation: 143-116=27, Resulting Numbers: [27] 27,83 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: 83:[92, 4, 80], Operations: ['51+29=80'] Exploring Operation: 4+80=84, Resulting Numbers: [92, 84] Generated Node #0,1,0: 83:[92, 84] Operation: 4+80=84 Exploring Operation: 92+4=96, Resulting Numbers: [80, 96] Generated Node #0,1,1: 83:[80, 96] Operation: 92+4=96 Exploring Operation: 80-4=76, Resulting Numbers: [92, 76] Generated Node #0,1,2: 83:[92, 76] Operation: 80-4=76 Exploring Operation: 92-4=88, Resulting Numbers: [80, 88] Generated Node #0,1,3: 83:[80, 88] Operation: 92-4=88 Moving to Node #0,0 Current State: 83:[29, 92, 55], Operations: ['51+4=55'] Exploring Operation: 92-29=63, Resulting Numbers: [55, 63] Generated Node #0,0,0: 83:[55, 63] Operation: 92-29=63 Exploring Operation: 29+92=121, Resulting Numbers: [55, 121] Generated Node #0,0,1: 83:[55, 121] Operation: 29+92=121 Exploring Operation: 29+55=84, Resulting Numbers: [92, 84] Generated Node #0,0,2: 83:[92, 84] Operation: 29+55=84 Exploring Operation: 55-29=26, Resulting Numbers: [92, 26] Generated Node #0,0,3: 83:[92, 26] Operation: 55-29=26 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[92, 84], Operations: ['51+4=55', '29+55=84'] Exploring Operation: 92*84=7728, Resulting Numbers: [7728] 7728,83 unequal: No Solution Exploring Operation: 92+84=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 92-84=8, Resulting Numbers: [8] 8,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[55, 63], Operations: ['51+4=55', '92-29=63'] Exploring Operation: 55*63=3465, Resulting Numbers: [3465] 3465,83 unequal: No Solution Exploring Operation: 55+63=118, Resulting Numbers: [118] 118,83 unequal: No Solution Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[55, 121], Operations: ['51+4=55', '29+92=121'] Exploring Operation: 55+121=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 55*121=6655, Resulting Numbers: [6655] 6655,83 unequal: No Solution Exploring Operation: 121-55=66, Resulting Numbers: [66] 66,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 83:[92, 26], Operations: ['51+4=55', '55-29=26'] Exploring Operation: 92+26=118, Resulting Numbers: [118] 118,83 unequal: No Solution Exploring Operation: 92*26=2392, Resulting Numbers: [2392] 2392,83 unequal: No Solution Exploring Operation: 92-26=66, Resulting Numbers: [66] 66,83 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: 83:[51, 92, 33], Operations: ['29+4=33'] Exploring Operation: 92-33=59, Resulting Numbers: [51, 59] Generated Node #0,2,0: 83:[51, 59] Operation: 92-33=59 Exploring Operation: 51+33=84, Resulting Numbers: [92, 84] Generated Node #0,2,1: 83:[92, 84] Operation: 51+33=84 Exploring Operation: 92+33=125, Resulting Numbers: [51, 125] Generated Node #0,2,2: 83:[51, 125] Operation: 92+33=125 Exploring Operation: 51-33=18, Resulting Numbers: [92, 18] Generated Node #0,2,3: 83:[92, 18] Operation: 51-33=18 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 83:[92, 84], Operations: ['29+4=33', '51+33=84'] Exploring Operation: 92-84=8, Resulting Numbers: [8] 8,83 unequal: No Solution Exploring Operation: 92+84=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 92*84=7728, Resulting Numbers: [7728] 7728,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 83:[51, 59], Operations: ['29+4=33', '92-33=59'] Exploring Operation: 51*59=3009, Resulting Numbers: [3009] 3009,83 unequal: No Solution Exploring Operation: 51+59=110, Resulting Numbers: [110] 110,83 unequal: No Solution Exploring Operation: 59-51=8, Resulting Numbers: [8] 8,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 83:[51, 125], Operations: ['29+4=33', '92+33=125'] Exploring Operation: 51+125=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 125-51=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 51*125=6375, Resulting Numbers: [6375] 6375,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 83:[92, 18], Operations: ['29+4=33', '51-33=18'] Exploring Operation: 92-18=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 92*18=1656, Resulting Numbers: [1656] 1656,83 unequal: No Solution Exploring Operation: 92+18=110, Resulting Numbers: [110] 110,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 83:[80, 88], Operations: ['51+29=80', '92-4=88'] Exploring Operation: 80+88=168, Resulting Numbers: [168] 168,83 unequal: No Solution Exploring Operation: 80*88=7040, Resulting Numbers: [7040] 7040,83 unequal: No Solution Exploring Operation: 88-80=8, Resulting Numbers: [8] 8,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[92, 84], Operations: ['51+29=80', '4+80=84'] Exploring Operation: 92-84=8, Resulting Numbers: [8] 8,83 unequal: No Solution Exploring Operation: 92+84=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 92*84=7728, Resulting Numbers: [7728] 7728,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[92, 76], Operations: ['51+29=80', '80-4=76'] Exploring Operation: 92*76=6992, Resulting Numbers: [6992] 6992,83 unequal: No Solution Exploring Operation: 92-76=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 92+76=168, Resulting Numbers: [168] 168,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[80, 96], Operations: ['51+29=80', '92+4=96'] Exploring Operation: 96-80=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 80*96=7680, Resulting Numbers: [7680] 7680,83 unequal: No Solution Exploring Operation: 80+96=176, Resulting Numbers: [176] 176,83 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 91, 31, 89, 42 ]
71
[ "91-31=60", "89+42=131", "131-60=71" ]
Current State: 71:[91, 31, 89, 42], Operations: [] Exploring Operation: 91-31=60, Resulting Numbers: [89, 42, 60] Generated Node #2: [89, 42, 60] from Operation: 91-31=60 Current State: 71:[89, 42, 60], Operations: ['91-31=60'] Exploring Operation: 89+42=131, Resulting Numbers: [60, 131] Generated Node #3: [60, 131] from Operation: 89+42=131 Current State: 71:[60, 131], Operations: ['91-31=60', '89+42=131'] Exploring Operation: 131-60=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[91, 31, 89, 42], Operations: [] Exploring Operation: 31+42=73, Resulting Numbers: [91, 89, 73] Generated Node #0,0: 71:[91, 89, 73] Operation: 31+42=73 Exploring Operation: 91-31=60, Resulting Numbers: [89, 42, 60] Generated Node #0,1: 71:[89, 42, 60] Operation: 91-31=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[91, 89, 73], Operations: ['31+42=73'] Exploring Operation: 91-73=18, Resulting Numbers: [89, 18] Generated Node #0,0,0: 71:[89, 18] Operation: 91-73=18 Exploring Operation: 91-89=2, Resulting Numbers: [73, 2] Generated Node #0,0,1: 71:[73, 2] Operation: 91-89=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[89, 18], Operations: ['31+42=73', '91-73=18'] Exploring Operation: 89-18=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[91, 31, 89, 42], Operations: [] Exploring Operation: 31+42=73, Resulting Numbers: [91, 89, 73] Generated Node #0,0: 71:[91, 89, 73] Operation: 31+42=73 Moving to Node #0,0 Current State: 71:[91, 89, 73], Operations: ['31+42=73'] Exploring Operation: 91-73=18, Resulting Numbers: [89, 18] Generated Node #0,0,0: 71:[89, 18] Operation: 91-73=18 Moving to Node #0,0,0 Current State: 71:[89, 18], Operations: ['31+42=73', '91-73=18'] Exploring Operation: 89-18=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 73, 35, 67, 4 ]
85
[ "73-35=38", "4*38=152", "152-67=85" ]
Current State: 85:[73, 35, 67, 4], Operations: [] Exploring Operation: 73-35=38, Resulting Numbers: [67, 4, 38] Generated Node #2: [67, 4, 38] from Operation: 73-35=38 Current State: 85:[67, 4, 38], Operations: ['73-35=38'] Exploring Operation: 4*38=152, Resulting Numbers: [67, 152] Generated Node #3: [67, 152] from Operation: 4*38=152 Current State: 85:[67, 152], Operations: ['73-35=38', '4*38=152'] Exploring Operation: 152-67=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[73, 35, 67, 4], Operations: [] Exploring Operation: 35+67=102, Resulting Numbers: [73, 4, 102] Generated Node #0,0: 85:[73, 4, 102] Operation: 35+67=102 Exploring Operation: 73+35=108, Resulting Numbers: [67, 4, 108] Generated Node #0,1: 85:[67, 4, 108] Operation: 73+35=108 Exploring Operation: 73-67=6, Resulting Numbers: [35, 4, 6] Generated Node #0,2: 85:[35, 4, 6] Operation: 73-67=6 Exploring Operation: 67-35=32, Resulting Numbers: [73, 4, 32] Generated Node #0,3: 85:[73, 4, 32] Operation: 67-35=32 Exploring Operation: 73-35=38, Resulting Numbers: [67, 4, 38] Generated Node #0,4: 85:[67, 4, 38] Operation: 73-35=38 Start Sub Search at level 1: Moving to Node #0,2 Current State: 85:[35, 4, 6], Operations: ['73-67=6'] Exploring Operation: 35-6=29, Resulting Numbers: [4, 29] Generated Node #0,2,0: 85:[4, 29] Operation: 35-6=29 Exploring Operation: 6-4=2, Resulting Numbers: [35, 2] Generated Node #0,2,1: 85:[35, 2] Operation: 6-4=2 Exploring Operation: 35+4=39, Resulting Numbers: [6, 39] Generated Node #0,2,2: 85:[6, 39] Operation: 35+4=39 Exploring Operation: 35-4=31, Resulting Numbers: [6, 31] Generated Node #0,2,3: 85:[6, 31] Operation: 35-4=31 Exploring Operation: 4+6=10, Resulting Numbers: [35, 10] Generated Node #0,2,4: 85:[35, 10] Operation: 4+6=10 Moving to Node #0,2,0 Current State: 85:[4, 29], Operations: ['73-67=6', '35-6=29'] Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,85 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,85 unequal: No Solution Moving to Node #0,2,3 Current State: 85:[6, 31], Operations: ['73-67=6', '35-4=31'] Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,85 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[35, 2], Operations: ['73-67=6', '6-4=2'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,85 unequal: No Solution Moving to Node #0,2,2 Current State: 85:[6, 39], Operations: ['73-67=6', '35+4=39'] Exploring Operation: 6*39=234, Resulting Numbers: [234] 234,85 unequal: No Solution Exploring Operation: 6+39=45, Resulting Numbers: [45] 45,85 unequal: No Solution Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,85 unequal: No Solution Moving to Node #0,2,4 Current State: 85:[35, 10], Operations: ['73-67=6', '4+6=10'] Exploring Operation: 35-10=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 35+10=45, Resulting Numbers: [45] 45,85 unequal: No Solution Exploring Operation: 35*10=350, Resulting Numbers: [350] 350,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 85:[73, 4, 32], Operations: ['67-35=32'] Exploring Operation: 73-32=41, Resulting Numbers: [4, 41] Generated Node #0,3,0: 85:[4, 41] Operation: 73-32=41 Exploring Operation: 73+32=105, Resulting Numbers: [4, 105] Generated Node #0,3,1: 85:[4, 105] Operation: 73+32=105 Exploring Operation: 73+4=77, Resulting Numbers: [32, 77] Generated Node #0,3,2: 85:[32, 77] Operation: 73+4=77 Exploring Operation: 32-4=28, Resulting Numbers: [73, 28] Generated Node #0,3,3: 85:[73, 28] Operation: 32-4=28 Exploring Operation: 32/4=8, Resulting Numbers: [73, 8] Generated Node #0,3,4: 85:[73, 8] Operation: 32/4=8 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 85:[73, 8], Operations: ['67-35=32', '32/4=8'] Exploring Operation: 73+8=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,85 unequal: No Solution Exploring Operation: 73*8=584, Resulting Numbers: [584] 584,85 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 #0,3,1 Current State: 85:[4, 105], Operations: ['67-35=32', '73+32=105'] Exploring Operation: 4*105=420, Resulting Numbers: [420] 420,85 unequal: No Solution Exploring Operation: 4+105=109, Resulting Numbers: [109] 109,85 unequal: No Solution Exploring Operation: 105-4=101, Resulting Numbers: [101] 101,85 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 #0,3,2 Current State: 85:[32, 77], Operations: ['67-35=32', '73+4=77'] Exploring Operation: 32*77=2464, Resulting Numbers: [2464] 2464,85 unequal: No Solution Exploring Operation: 32+77=109, Resulting Numbers: [109] 109,85 unequal: No Solution Exploring Operation: 77-32=45, Resulting Numbers: [45] 45,85 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 #0,3,3 Current State: 85:[73, 28], Operations: ['67-35=32', '32-4=28'] Exploring Operation: 73*28=2044, Resulting Numbers: [2044] 2044,85 unequal: No Solution Exploring Operation: 73+28=101, Resulting Numbers: [101] 101,85 unequal: No Solution Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,85 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 #0,3,0 Current State: 85:[4, 41], Operations: ['67-35=32', '73-32=41'] Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,85 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[73, 4, 102], Operations: ['35+67=102'] Exploring Operation: 102-73=29, Resulting Numbers: [4, 29] Generated Node #0,0,0: 85:[4, 29] Operation: 102-73=29 Exploring Operation: 73-4=69, Resulting Numbers: [102, 69] Generated Node #0,0,1: 85:[102, 69] Operation: 73-4=69 Exploring Operation: 4+102=106, Resulting Numbers: [73, 106] Generated Node #0,0,2: 85:[73, 106] Operation: 4+102=106 Exploring Operation: 102-4=98, Resulting Numbers: [73, 98] Generated Node #0,0,3: 85:[73, 98] Operation: 102-4=98 Exploring Operation: 73+4=77, Resulting Numbers: [102, 77] Generated Node #0,0,4: 85:[102, 77] Operation: 73+4=77 Moving to Node #0,0,0 Current State: 85:[4, 29], Operations: ['35+67=102', '102-73=29'] Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,85 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,85 unequal: No Solution Moving to Node #0,0,4 Current State: 85:[102, 77], Operations: ['35+67=102', '73+4=77'] Exploring Operation: 102-77=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 102+77=179, Resulting Numbers: [179] 179,85 unequal: No Solution Exploring Operation: 102*77=7854, Resulting Numbers: [7854] 7854,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[73, 98], Operations: ['35+67=102', '102-4=98'] Exploring Operation: 73*98=7154, Resulting Numbers: [7154] 7154,85 unequal: No Solution Exploring Operation: 98-73=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 73+98=171, Resulting Numbers: [171] 171,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[102, 69], Operations: ['35+67=102', '73-4=69'] Exploring Operation: 102-69=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 102*69=7038, Resulting Numbers: [7038] 7038,85 unequal: No Solution Exploring Operation: 102+69=171, Resulting Numbers: [171] 171,85 unequal: No Solution Moving to Node #0,0,2 Current State: 85:[73, 106], Operations: ['35+67=102', '4+102=106'] Exploring Operation: 73+106=179, Resulting Numbers: [179] 179,85 unequal: No Solution Exploring Operation: 73*106=7738, Resulting Numbers: [7738] 7738,85 unequal: No Solution Exploring Operation: 106-73=33, Resulting Numbers: [33] 33,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 85:[67, 4, 38], Operations: ['73-35=38'] Exploring Operation: 67-38=29, Resulting Numbers: [4, 29] Generated Node #0,4,0: 85:[4, 29] Operation: 67-38=29 Exploring Operation: 67+38=105, Resulting Numbers: [4, 105] Generated Node #0,4,1: 85:[4, 105] Operation: 67+38=105 Exploring Operation: 67-4=63, Resulting Numbers: [38, 63] Generated Node #0,4,2: 85:[38, 63] Operation: 67-4=63 Exploring Operation: 38-4=34, Resulting Numbers: [67, 34] Generated Node #0,4,3: 85:[67, 34] Operation: 38-4=34 Exploring Operation: 67+4=71, Resulting Numbers: [38, 71] Generated Node #0,4,4: 85:[38, 71] Operation: 67+4=71 Moving to Node #0,4,0 Current State: 85:[4, 29], Operations: ['73-35=38', '67-38=29'] Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,85 unequal: No Solution Moving to Node #0,4,1 Current State: 85:[4, 105], Operations: ['73-35=38', '67+38=105'] Exploring Operation: 105-4=101, Resulting Numbers: [101] 101,85 unequal: No Solution Exploring Operation: 4*105=420, Resulting Numbers: [420] 420,85 unequal: No Solution Exploring Operation: 4+105=109, Resulting Numbers: [109] 109,85 unequal: No Solution Moving to Node #0,4,3 Current State: 85:[67, 34], Operations: ['73-35=38', '38-4=34'] Exploring Operation: 67-34=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 67*34=2278, Resulting Numbers: [2278] 2278,85 unequal: No Solution Exploring Operation: 67+34=101, Resulting Numbers: [101] 101,85 unequal: No Solution Moving to Node #0,4,4 Current State: 85:[38, 71], Operations: ['73-35=38', '67+4=71'] Exploring Operation: 71-38=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 38+71=109, Resulting Numbers: [109] 109,85 unequal: No Solution Exploring Operation: 38*71=2698, Resulting Numbers: [2698] 2698,85 unequal: No Solution Moving to Node #0,4,2 Current State: 85:[38, 63], Operations: ['73-35=38', '67-4=63'] Exploring Operation: 38*63=2394, Resulting Numbers: [2394] 2394,85 unequal: No Solution Exploring Operation: 63-38=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 38+63=101, Resulting Numbers: [101] 101,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[67, 4, 108], Operations: ['73+35=108'] Exploring Operation: 108-4=104, Resulting Numbers: [67, 104] Generated Node #0,1,0: 85:[67, 104] Operation: 108-4=104 Exploring Operation: 67+4=71, Resulting Numbers: [108, 71] Generated Node #0,1,1: 85:[108, 71] Operation: 67+4=71 Exploring Operation: 108/4=27, Resulting Numbers: [67, 27] Generated Node #0,1,2: 85:[67, 27] Operation: 108/4=27 Exploring Operation: 108-67=41, Resulting Numbers: [4, 41] Generated Node #0,1,3: 85:[4, 41] Operation: 108-67=41 Exploring Operation: 67-4=63, Resulting Numbers: [108, 63] Generated Node #0,1,4: 85:[108, 63] Operation: 67-4=63 Moving to Node #0,1,3 Current State: 85:[4, 41], Operations: ['73+35=108', '108-67=41'] Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,85 unequal: No Solution Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[67, 27], Operations: ['73+35=108', '108/4=27'] Exploring Operation: 67+27=94, Resulting Numbers: [94] 94,85 unequal: No Solution Exploring Operation: 67-27=40, Resulting Numbers: [40] 40,85 unequal: No Solution Exploring Operation: 67*27=1809, Resulting Numbers: [1809] 1809,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[67, 104], Operations: ['73+35=108', '108-4=104'] Exploring Operation: 67+104=171, Resulting Numbers: [171] 171,85 unequal: No Solution Exploring Operation: 67*104=6968, Resulting Numbers: [6968] 6968,85 unequal: No Solution Exploring Operation: 104-67=37, Resulting Numbers: [37] 37,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[108, 71], Operations: ['73+35=108', '67+4=71'] Exploring Operation: 108-71=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 108*71=7668, Resulting Numbers: [7668] 7668,85 unequal: No Solution Exploring Operation: 108+71=179, Resulting Numbers: [179] 179,85 unequal: No Solution Moving to Node #0,1,4 Current State: 85:[108, 63], Operations: ['73+35=108', '67-4=63'] Exploring Operation: 108+63=171, Resulting Numbers: [171] 171,85 unequal: No Solution Exploring Operation: 108*63=6804, Resulting Numbers: [6804] 6804,85 unequal: No Solution Exploring Operation: 108-63=45, Resulting Numbers: [45] 45,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 42, 58, 47, 15 ]
35
[ "58+47=105", "105/15=7", "42-7=35" ]
Current State: 35:[42, 58, 47, 15], Operations: [] Exploring Operation: 58+47=105, Resulting Numbers: [42, 15, 105] Generated Node #2: [42, 15, 105] from Operation: 58+47=105 Current State: 35:[42, 15, 105], Operations: ['58+47=105'] Exploring Operation: 105/15=7, Resulting Numbers: [42, 7] Generated Node #3: [42, 7] from Operation: 105/15=7 Current State: 35:[42, 7], Operations: ['58+47=105', '105/15=7'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[42, 58, 47, 15], Operations: [] Exploring Operation: 58-15=43, Resulting Numbers: [42, 47, 43] Generated Node #0,0: 35:[42, 47, 43] Operation: 58-15=43 Exploring Operation: 47-15=32, Resulting Numbers: [42, 58, 32] Generated Node #0,1: 35:[42, 58, 32] Operation: 47-15=32 Exploring Operation: 58-42=16, Resulting Numbers: [47, 15, 16] Generated Node #0,2: 35:[47, 15, 16] Operation: 58-42=16 Exploring Operation: 47-42=5, Resulting Numbers: [58, 15, 5] Generated Node #0,3: 35:[58, 15, 5] Operation: 47-42=5 Exploring Operation: 58-47=11, Resulting Numbers: [42, 15, 11] Generated Node #0,4: 35:[42, 15, 11] Operation: 58-47=11 Start Sub Search at level 1: Moving to Node #0,4 Current State: 35:[42, 15, 11], Operations: ['58-47=11'] Exploring Operation: 15+11=26, Resulting Numbers: [42, 26] Generated Node #0,4,0: 35:[42, 26] Operation: 15+11=26 Exploring Operation: 15-11=4, Resulting Numbers: [42, 4] Generated Node #0,4,1: 35:[42, 4] Operation: 15-11=4 Exploring Operation: 42-11=31, Resulting Numbers: [15, 31] Generated Node #0,4,2: 35:[15, 31] Operation: 42-11=31 Exploring Operation: 42-15=27, Resulting Numbers: [11, 27] Generated Node #0,4,3: 35:[11, 27] Operation: 42-15=27 Exploring Operation: 42+15=57, Resulting Numbers: [11, 57] Generated Node #0,4,4: 35:[11, 57] Operation: 42+15=57 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 35:[42, 4], Operations: ['58-47=11', '15-11=4'] Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,35 unequal: No Solution Exploring Operation: 42*4=168, Resulting Numbers: [168] 168,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 35:[15, 31], Operations: ['58-47=11', '42-11=31'] Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 15*31=465, Resulting Numbers: [465] 465,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 35:[11, 27], Operations: ['58-47=11', '42-15=27'] Exploring Operation: 11*27=297, Resulting Numbers: [297] 297,35 unequal: No Solution Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,35 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 35:[42, 26], Operations: ['58-47=11', '15+11=26'] Exploring Operation: 42*26=1092, Resulting Numbers: [1092] 1092,35 unequal: No Solution Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 42+26=68, Resulting Numbers: [68] 68,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 35:[11, 57], Operations: ['58-47=11', '42+15=57'] Exploring Operation: 11+57=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 11*57=627, Resulting Numbers: [627] 627,35 unequal: No Solution Exploring Operation: 57-11=46, Resulting Numbers: [46] 46,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[42, 47, 43], Operations: ['58-15=43'] Exploring Operation: 42+43=85, Resulting Numbers: [47, 85] Generated Node #0,0,0: 35:[47, 85] Operation: 42+43=85 Exploring Operation: 42+47=89, Resulting Numbers: [43, 89] Generated Node #0,0,1: 35:[43, 89] Operation: 42+47=89 Exploring Operation: 47-42=5, Resulting Numbers: [43, 5] Generated Node #0,0,2: 35:[43, 5] Operation: 47-42=5 Exploring Operation: 43-42=1, Resulting Numbers: [47, 1] Generated Node #0,0,3: 35:[47, 1] Operation: 43-42=1 Exploring Operation: 47-43=4, Resulting Numbers: [42, 4] Generated Node #0,0,4: 35:[42, 4] Operation: 47-43=4 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 35:[43, 5], Operations: ['58-15=43', '47-42=5'] Exploring Operation: 43+5=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 43*5=215, Resulting Numbers: [215] 215,35 unequal: No Solution Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 35:[42, 4], Operations: ['58-15=43', '47-43=4'] Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,35 unequal: No Solution Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 42*4=168, Resulting Numbers: [168] 168,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 35:[47, 1], Operations: ['58-15=43', '43-42=1'] Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[47, 85], Operations: ['58-15=43', '42+43=85'] Exploring Operation: 47*85=3995, Resulting Numbers: [3995] 3995,35 unequal: No Solution Exploring Operation: 47+85=132, Resulting Numbers: [132] 132,35 unequal: No Solution Exploring Operation: 85-47=38, Resulting Numbers: [38] 38,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 35:[43, 89], Operations: ['58-15=43', '42+47=89'] Exploring Operation: 43*89=3827, Resulting Numbers: [3827] 3827,35 unequal: No Solution Exploring Operation: 89-43=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 43+89=132, Resulting Numbers: [132] 132,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[47, 15, 16], Operations: ['58-42=16'] Exploring Operation: 16-15=1, Resulting Numbers: [47, 1] Generated Node #0,2,0: 35:[47, 1] Operation: 16-15=1 Exploring Operation: 15+16=31, Resulting Numbers: [47, 31] Generated Node #0,2,1: 35:[47, 31] Operation: 15+16=31 Exploring Operation: 47+15=62, Resulting Numbers: [16, 62] Generated Node #0,2,2: 35:[16, 62] Operation: 47+15=62 Exploring Operation: 47-16=31, Resulting Numbers: [15, 31] Generated Node #0,2,3: 35:[15, 31] Operation: 47-16=31 Exploring Operation: 47-15=32, Resulting Numbers: [16, 32] Generated Node #0,2,4: 35:[16, 32] Operation: 47-15=32 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 35:[15, 31], Operations: ['58-42=16', '47-16=31'] Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 15*31=465, Resulting Numbers: [465] 465,35 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 35:[16, 32], Operations: ['58-42=16', '47-15=32'] Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 16*32=512, Resulting Numbers: [512] 512,35 unequal: No Solution Exploring Operation: 16+32=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 35:[47, 1], Operations: ['58-42=16', '16-15=1'] Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 35:[47, 31], Operations: ['58-42=16', '15+16=31'] Exploring Operation: 47*31=1457, Resulting Numbers: [1457] 1457,35 unequal: No Solution Exploring Operation: 47-31=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 47+31=78, Resulting Numbers: [78] 78,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 35:[16, 62], Operations: ['58-42=16', '47+15=62'] Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 16*62=992, Resulting Numbers: [992] 992,35 unequal: No Solution Exploring Operation: 16+62=78, Resulting Numbers: [78] 78,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 35:[58, 15, 5], Operations: ['47-42=5'] Exploring Operation: 58-5=53, Resulting Numbers: [15, 53] Generated Node #0,3,0: 35:[15, 53] Operation: 58-5=53 Exploring Operation: 58-15=43, Resulting Numbers: [5, 43] Generated Node #0,3,1: 35:[5, 43] Operation: 58-15=43 Exploring Operation: 58+5=63, Resulting Numbers: [15, 63] Generated Node #0,3,2: 35:[15, 63] Operation: 58+5=63 Exploring Operation: 15-5=10, Resulting Numbers: [58, 10] Generated Node #0,3,3: 35:[58, 10] Operation: 15-5=10 Exploring Operation: 15/5=3, Resulting Numbers: [58, 3] Generated Node #0,3,4: 35:[58, 3] Operation: 15/5=3 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 35:[5, 43], Operations: ['47-42=5', '58-15=43'] Exploring Operation: 5*43=215, Resulting Numbers: [215] 215,35 unequal: No Solution Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,35 unequal: No Solution Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 35:[58, 3], Operations: ['47-42=5', '15/5=3'] Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,35 unequal: No Solution Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,35 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 35:[15, 53], Operations: ['47-42=5', '58-5=53'] Exploring Operation: 53-15=38, Resulting Numbers: [38] 38,35 unequal: No Solution Exploring Operation: 15+53=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 15*53=795, Resulting Numbers: [795] 795,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 35:[58, 10], Operations: ['47-42=5', '15-5=10'] Exploring Operation: 58*10=580, Resulting Numbers: [580] 580,35 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 35:[15, 63], Operations: ['47-42=5', '58+5=63'] Exploring Operation: 15+63=78, Resulting Numbers: [78] 78,35 unequal: No Solution Exploring Operation: 15*63=945, Resulting Numbers: [945] 945,35 unequal: No Solution Exploring Operation: 63-15=48, Resulting Numbers: [48] 48,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[42, 58, 32], Operations: ['47-15=32'] Exploring Operation: 42+32=74, Resulting Numbers: [58, 74] Generated Node #0,1,0: 35:[58, 74] Operation: 42+32=74 Exploring Operation: 58+32=90, Resulting Numbers: [42, 90] Generated Node #0,1,1: 35:[42, 90] Operation: 58+32=90 Exploring Operation: 58-42=16, Resulting Numbers: [32, 16] Generated Node #0,1,2: 35:[32, 16] Operation: 58-42=16 Exploring Operation: 42-32=10, Resulting Numbers: [58, 10] Generated Node #0,1,3: 35:[58, 10] Operation: 42-32=10 Exploring Operation: 58-32=26, Resulting Numbers: [42, 26] Generated Node #0,1,4: 35:[42, 26] Operation: 58-32=26 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 35:[32, 16], Operations: ['47-15=32', '58-42=16'] Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 32*16=512, Resulting Numbers: [512] 512,35 unequal: No Solution Exploring Operation: 32+16=48, Resulting Numbers: [48] 48,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 35:[42, 26], Operations: ['47-15=32', '58-32=26'] Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 42+26=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 42*26=1092, Resulting Numbers: [1092] 1092,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 35:[58, 10], Operations: ['47-15=32', '42-32=10'] Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 58*10=580, Resulting Numbers: [580] 580,35 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 35:[58, 74], Operations: ['47-15=32', '42+32=74'] Exploring Operation: 74-58=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 58*74=4292, Resulting Numbers: [4292] 4292,35 unequal: No Solution Exploring Operation: 58+74=132, Resulting Numbers: [132] 132,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 35:[42, 90], Operations: ['47-15=32', '58+32=90'] Exploring Operation: 42*90=3780, Resulting Numbers: [3780] 3780,35 unequal: No Solution Exploring Operation: 90-42=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 42+90=132, Resulting Numbers: [132] 132,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 90, 92, 66, 90 ]
25
[ "90/90=1", "92-66=26", "26-1=25" ]
Current State: 25:[90, 92, 66, 90], Operations: [] Exploring Operation: 90/90=1, Resulting Numbers: [92, 66, 1] Generated Node #2: [92, 66, 1] from Operation: 90/90=1 Current State: 25:[92, 66, 1], Operations: ['90/90=1'] Exploring Operation: 92-66=26, Resulting Numbers: [1, 26] Generated Node #3: [1, 26] from Operation: 92-66=26 Current State: 25:[1, 26], Operations: ['90/90=1', '92-66=26'] Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[90, 92, 66, 90], Operations: [] Exploring Operation: 90/90=1, Resulting Numbers: [92, 66, 1] Generated Node #0,0: 25:[92, 66, 1] Operation: 90/90=1 Exploring Operation: 92-90=2, Resulting Numbers: [66, 90, 2] Generated Node #0,1: 25:[66, 90, 2] Operation: 92-90=2 Exploring Operation: 92-90=2, Resulting Numbers: [90, 66, 2] Generated Node #0,2: 25:[90, 66, 2] Operation: 92-90=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[66, 90, 2], Operations: ['92-90=2'] Exploring Operation: 66/2=33, Resulting Numbers: [90, 33] Generated Node #0,1,0: 25:[90, 33] Operation: 66/2=33 Exploring Operation: 90/2=45, Resulting Numbers: [66, 45] Generated Node #0,1,1: 25:[66, 45] Operation: 90/2=45 Exploring Operation: 90-66=24, Resulting Numbers: [2, 24] Generated Node #0,1,2: 25:[2, 24] Operation: 90-66=24 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 25:[2, 24], Operations: ['92-90=2', '90-66=24'] Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,25 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 25:[66, 45], Operations: ['92-90=2', '90/2=45'] Exploring Operation: 66-45=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 66*45=2970, Resulting Numbers: [2970] 2970,25 unequal: No Solution Exploring Operation: 66+45=111, Resulting Numbers: [111] 111,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[90, 33], Operations: ['92-90=2', '66/2=33'] Exploring Operation: 90-33=57, Resulting Numbers: [57] 57,25 unequal: No Solution Exploring Operation: 90*33=2970, Resulting Numbers: [2970] 2970,25 unequal: No Solution Exploring Operation: 90+33=123, Resulting Numbers: [123] 123,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[90, 66, 2], Operations: ['92-90=2'] Exploring Operation: 90-66=24, Resulting Numbers: [2, 24] Generated Node #0,2,0: 25:[2, 24] Operation: 90-66=24 Exploring Operation: 90/2=45, Resulting Numbers: [66, 45] Generated Node #0,2,1: 25:[66, 45] Operation: 90/2=45 Exploring Operation: 66/2=33, Resulting Numbers: [90, 33] Generated Node #0,2,2: 25:[90, 33] Operation: 66/2=33 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 25:[2, 24], Operations: ['92-90=2', '90-66=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,25 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,25 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 25:[66, 45], Operations: ['92-90=2', '90/2=45'] Exploring Operation: 66-45=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 66+45=111, Resulting Numbers: [111] 111,25 unequal: No Solution Exploring Operation: 66*45=2970, Resulting Numbers: [2970] 2970,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 25:[90, 33], Operations: ['92-90=2', '66/2=33'] Exploring Operation: 90+33=123, Resulting Numbers: [123] 123,25 unequal: No Solution Exploring Operation: 90-33=57, Resulting Numbers: [57] 57,25 unequal: No Solution Exploring Operation: 90*33=2970, Resulting Numbers: [2970] 2970,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[92, 66, 1], Operations: ['90/90=1'] Exploring Operation: 92-66=26, Resulting Numbers: [1, 26] Generated Node #0,0,0: 25:[1, 26] Operation: 92-66=26 Exploring Operation: 66-1=65, Resulting Numbers: [92, 65] Generated Node #0,0,1: 25:[92, 65] Operation: 66-1=65 Exploring Operation: 92-1=91, Resulting Numbers: [66, 91] Generated Node #0,0,2: 25:[66, 91] Operation: 92-1=91 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[1, 26], Operations: ['90/90=1', '92-66=26'] Exploring Operation: 1*26=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[90, 92, 66, 90], Operations: [] Exploring Operation: 90/90=1, Resulting Numbers: [92, 66, 1] Generated Node #0,0: 25:[92, 66, 1] Operation: 90/90=1 Moving to Node #0,0 Current State: 25:[92, 66, 1], Operations: ['90/90=1'] Exploring Operation: 92-66=26, Resulting Numbers: [1, 26] Generated Node #0,0,0: 25:[1, 26] Operation: 92-66=26 Moving to Node #0,0,0 Current State: 25:[1, 26], Operations: ['90/90=1', '92-66=26'] Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_3
sum_heuristic
[ 28, 80, 40, 62 ]
36
[ "62-28=34", "80/40=2", "34+2=36" ]
Current State: 36:[28, 80, 40, 62], Operations: [] Exploring Operation: 62-28=34, Resulting Numbers: [80, 40, 34] Generated Node #2: [80, 40, 34] from Operation: 62-28=34 Current State: 36:[80, 40, 34], Operations: ['62-28=34'] Exploring Operation: 80/40=2, Resulting Numbers: [34, 2] Generated Node #3: [34, 2] from Operation: 80/40=2 Current State: 36:[34, 2], Operations: ['62-28=34', '80/40=2'] Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[28, 80, 40, 62], Operations: [] Exploring Operation: 80-40=40, Resulting Numbers: [28, 62, 40] Generated Node #0,0: 36:[28, 62, 40] Operation: 80-40=40 Exploring Operation: 62-28=34, Resulting Numbers: [80, 40, 34] Generated Node #0,1: 36:[80, 40, 34] Operation: 62-28=34 Exploring Operation: 80/40=2, Resulting Numbers: [28, 62, 2] Generated Node #0,2: 36:[28, 62, 2] Operation: 80/40=2 Exploring Operation: 80-28=52, Resulting Numbers: [40, 62, 52] Generated Node #0,3: 36:[40, 62, 52] Operation: 80-28=52 Exploring Operation: 80-62=18, Resulting Numbers: [28, 40, 18] Generated Node #0,4: 36:[28, 40, 18] Operation: 80-62=18 Moving to Node #0,4 Current State: 36:[28, 40, 18], Operations: ['80-62=18'] Exploring Operation: 28-18=10, Resulting Numbers: [40, 10] Generated Node #0,4,0: 36:[40, 10] Operation: 28-18=10 Exploring Operation: 40-18=22, Resulting Numbers: [28, 22] Generated Node #0,4,1: 36:[28, 22] Operation: 40-18=22 Exploring Operation: 40-28=12, Resulting Numbers: [18, 12] Generated Node #0,4,2: 36:[18, 12] Operation: 40-28=12 Exploring Operation: 40+18=58, Resulting Numbers: [28, 58] Generated Node #0,4,3: 36:[28, 58] Operation: 40+18=58 Exploring Operation: 28+18=46, Resulting Numbers: [40, 46] Generated Node #0,4,4: 36:[40, 46] Operation: 28+18=46 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 36:[18, 12], Operations: ['80-62=18', '40-28=12'] Exploring Operation: 18*12=216, Resulting Numbers: [216] 216,36 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,36 unequal: No Solution Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 36:[40, 10], Operations: ['80-62=18', '28-18=10'] Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,36 unequal: No Solution Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,36 unequal: No Solution Exploring Operation: 40*10=400, Resulting Numbers: [400] 400,36 unequal: No Solution Exploring Operation: 40+10=50, Resulting Numbers: [50] 50,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 36:[28, 22], Operations: ['80-62=18', '40-18=22'] Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,36 unequal: No Solution Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,36 unequal: No Solution Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 36:[40, 46], Operations: ['80-62=18', '28+18=46'] Exploring Operation: 40*46=1840, Resulting Numbers: [1840] 1840,36 unequal: No Solution Exploring Operation: 46-40=6, Resulting Numbers: [6] 6,36 unequal: No Solution Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 36:[28, 58], Operations: ['80-62=18', '40+18=58'] Exploring Operation: 58-28=30, Resulting Numbers: [30] 30,36 unequal: No Solution Exploring Operation: 28*58=1624, Resulting Numbers: [1624] 1624,36 unequal: No Solution Exploring Operation: 28+58=86, Resulting Numbers: [86] 86,36 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: 36:[28, 62, 2], Operations: ['80/40=2'] Exploring Operation: 62-28=34, Resulting Numbers: [2, 34] Generated Node #0,2,0: 36:[2, 34] Operation: 62-28=34 Exploring Operation: 62/2=31, Resulting Numbers: [28, 31] Generated Node #0,2,1: 36:[28, 31] Operation: 62/2=31 Exploring Operation: 28+2=30, Resulting Numbers: [62, 30] Generated Node #0,2,2: 36:[62, 30] Operation: 28+2=30 Exploring Operation: 62-2=60, Resulting Numbers: [28, 60] Generated Node #0,2,3: 36:[28, 60] Operation: 62-2=60 Exploring Operation: 28/2=14, Resulting Numbers: [62, 14] Generated Node #0,2,4: 36:[62, 14] Operation: 28/2=14 Moving to Node #0,0 Current State: 36:[28, 62, 40], Operations: ['80-40=40'] Exploring Operation: 62-40=22, Resulting Numbers: [28, 22] Generated Node #0,0,0: 36:[28, 22] Operation: 62-40=22 Exploring Operation: 62-28=34, Resulting Numbers: [40, 34] Generated Node #0,0,1: 36:[40, 34] Operation: 62-28=34 Exploring Operation: 28+40=68, Resulting Numbers: [62, 68] Generated Node #0,0,2: 36:[62, 68] Operation: 28+40=68 Exploring Operation: 40-28=12, Resulting Numbers: [62, 12] Generated Node #0,0,3: 36:[62, 12] Operation: 40-28=12 Exploring Operation: 28+62=90, Resulting Numbers: [40, 90] Generated Node #0,0,4: 36:[40, 90] Operation: 28+62=90 Moving to Node #0,3 Current State: 36:[40, 62, 52], Operations: ['80-28=52'] Exploring Operation: 62-40=22, Resulting Numbers: [52, 22] Generated Node #0,3,0: 36:[52, 22] Operation: 62-40=22 Exploring Operation: 52-40=12, Resulting Numbers: [62, 12] Generated Node #0,3,1: 36:[62, 12] Operation: 52-40=12 Exploring Operation: 62-52=10, Resulting Numbers: [40, 10] Generated Node #0,3,2: 36:[40, 10] Operation: 62-52=10 Exploring Operation: 40+62=102, Resulting Numbers: [52, 102] Generated Node #0,3,3: 36:[52, 102] Operation: 40+62=102 Exploring Operation: 40+52=92, Resulting Numbers: [62, 92] Generated Node #0,3,4: 36:[62, 92] Operation: 40+52=92 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 36:[40, 10], Operations: ['80-28=52', '62-52=10'] Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,36 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,36 unequal: No Solution Exploring Operation: 40+10=50, Resulting Numbers: [50] 50,36 unequal: No Solution Exploring Operation: 40*10=400, Resulting Numbers: [400] 400,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 36:[52, 22], Operations: ['80-28=52', '62-40=22'] Exploring Operation: 52-22=30, Resulting Numbers: [30] 30,36 unequal: No Solution Exploring Operation: 52*22=1144, Resulting Numbers: [1144] 1144,36 unequal: No Solution Exploring Operation: 52+22=74, Resulting Numbers: [74] 74,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 36:[62, 12], Operations: ['80-28=52', '52-40=12'] Exploring Operation: 62*12=744, Resulting Numbers: [744] 744,36 unequal: No Solution Exploring Operation: 62-12=50, Resulting Numbers: [50] 50,36 unequal: No Solution Exploring Operation: 62+12=74, Resulting Numbers: [74] 74,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 36:[52, 102], Operations: ['80-28=52', '40+62=102'] Exploring Operation: 52*102=5304, Resulting Numbers: [5304] 5304,36 unequal: No Solution Exploring Operation: 102-52=50, Resulting Numbers: [50] 50,36 unequal: No Solution Exploring Operation: 52+102=154, Resulting Numbers: [154] 154,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 36:[62, 92], Operations: ['80-28=52', '40+52=92'] Exploring Operation: 62+92=154, Resulting Numbers: [154] 154,36 unequal: No Solution Exploring Operation: 92-62=30, Resulting Numbers: [30] 30,36 unequal: No Solution Exploring Operation: 62*92=5704, Resulting Numbers: [5704] 5704,36 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: 36:[80, 40, 34], Operations: ['62-28=34'] Exploring Operation: 80-34=46, Resulting Numbers: [40, 46] Generated Node #0,1,0: 36:[40, 46] Operation: 80-34=46 Exploring Operation: 80-40=40, Resulting Numbers: [34, 40] Generated Node #0,1,1: 36:[34, 40] Operation: 80-40=40 Exploring Operation: 40-34=6, Resulting Numbers: [80, 6] Generated Node #0,1,2: 36:[80, 6] Operation: 40-34=6 Exploring Operation: 80+34=114, Resulting Numbers: [40, 114] Generated Node #0,1,3: 36:[40, 114] Operation: 80+34=114 Exploring Operation: 80/40=2, Resulting Numbers: [34, 2] Generated Node #0,1,4: 36:[34, 2] Operation: 80/40=2 Moving to Node #0,2,0 Current State: 36:[2, 34], Operations: ['80/40=2', '62-28=34'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,36 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[28, 80, 40, 62], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [28, 62, 2] Generated Node #0,2: 36:[28, 62, 2] Operation: 80/40=2 Moving to Node #0,2 Current State: 36:[28, 62, 2], Operations: ['80/40=2'] Exploring Operation: 62-28=34, Resulting Numbers: [2, 34] Generated Node #0,2,0: 36:[2, 34] Operation: 62-28=34 Moving to Node #0,2,0 Current State: 36:[2, 34], Operations: ['80/40=2', '62-28=34'] Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
0.940972
hs_5
sum_heuristic
[ 29, 37, 4, 11 ]
76
[ "37-29=8", "11+8=19", "4*19=76" ]
Current State: 76:[29, 37, 4, 11], Operations: [] Exploring Operation: 37-29=8, Resulting Numbers: [4, 11, 8] Generated Node #2: [4, 11, 8] from Operation: 37-29=8 Current State: 76:[4, 11, 8], Operations: ['37-29=8'] Exploring Operation: 11+8=19, Resulting Numbers: [4, 19] Generated Node #3: [4, 19] from Operation: 11+8=19 Current State: 76:[4, 19], Operations: ['37-29=8', '11+8=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[29, 37, 4, 11], Operations: [] Exploring Operation: 37-29=8, Resulting Numbers: [4, 11, 8] Generated Node #0,0: 76:[4, 11, 8] Operation: 37-29=8 Exploring Operation: 29-11=18, Resulting Numbers: [37, 4, 18] Generated Node #0,1: 76:[37, 4, 18] Operation: 29-11=18 Exploring Operation: 29+11=40, Resulting Numbers: [37, 4, 40] Generated Node #0,2: 76:[37, 4, 40] Operation: 29+11=40 Exploring Operation: 29+4=33, Resulting Numbers: [37, 11, 33] Generated Node #0,3: 76:[37, 11, 33] Operation: 29+4=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[37, 4, 18], Operations: ['29-11=18'] Exploring Operation: 37-18=19, Resulting Numbers: [4, 19] Generated Node #0,1,0: 76:[4, 19] Operation: 37-18=19 Exploring Operation: 37+4=41, Resulting Numbers: [18, 41] Generated Node #0,1,1: 76:[18, 41] Operation: 37+4=41 Exploring Operation: 4+18=22, Resulting Numbers: [37, 22] Generated Node #0,1,2: 76:[37, 22] Operation: 4+18=22 Exploring Operation: 4*18=72, Resulting Numbers: [37, 72] Generated Node #0,1,3: 76:[37, 72] Operation: 4*18=72 Moving to Node #0,1,0 Current State: 76:[4, 19], Operations: ['29-11=18', '37-18=19'] Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,76 unequal: No Solution Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[29, 37, 4, 11], Operations: [] Exploring Operation: 29-11=18, Resulting Numbers: [37, 4, 18] Generated Node #0,1: 76:[37, 4, 18] Operation: 29-11=18 Moving to Node #0,1 Current State: 76:[37, 4, 18], Operations: ['29-11=18'] Exploring Operation: 37-18=19, Resulting Numbers: [4, 19] Generated Node #0,1,0: 76:[4, 19] Operation: 37-18=19 Moving to Node #0,1,0 Current State: 76:[4, 19], Operations: ['29-11=18', '37-18=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 1, 89, 5, 8 ]
48
[ "89-1=88", "5*8=40", "88-40=48" ]
Current State: 48:[1, 89, 5, 8], Operations: [] Exploring Operation: 89-1=88, Resulting Numbers: [5, 8, 88] Generated Node #2: [5, 8, 88] from Operation: 89-1=88 Current State: 48:[5, 8, 88], Operations: ['89-1=88'] Exploring Operation: 5*8=40, Resulting Numbers: [88, 40] Generated Node #3: [88, 40] from Operation: 5*8=40 Current State: 48:[88, 40], Operations: ['89-1=88', '5*8=40'] Exploring Operation: 88-40=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[1, 89, 5, 8], Operations: [] Exploring Operation: 5-1=4, Resulting Numbers: [89, 8, 4] Generated Node #0,0: 48:[89, 8, 4] Operation: 5-1=4 Exploring Operation: 89-1=88, Resulting Numbers: [5, 8, 88] Generated Node #0,1: 48:[5, 8, 88] Operation: 89-1=88 Exploring Operation: 1+5=6, Resulting Numbers: [89, 8, 6] Generated Node #0,2: 48:[89, 8, 6] Operation: 1+5=6 Exploring Operation: 89-5=84, Resulting Numbers: [1, 8, 84] Generated Node #0,3: 48:[1, 8, 84] Operation: 89-5=84 Exploring Operation: 89-8=81, Resulting Numbers: [1, 5, 81] Generated Node #0,4: 48:[1, 5, 81] Operation: 89-8=81 Moving to Node #0,4 Current State: 48:[1, 5, 81], Operations: ['89-8=81'] Exploring Operation: 1*5=5, Resulting Numbers: [81, 5] Generated Node #0,4,0: 48:[81, 5] Operation: 1*5=5 Exploring Operation: 5-1=4, Resulting Numbers: [81, 4] Generated Node #0,4,1: 48:[81, 4] Operation: 5-1=4 Exploring Operation: 1+5=6, Resulting Numbers: [81, 6] Generated Node #0,4,2: 48:[81, 6] Operation: 1+5=6 Exploring Operation: 81-1=80, Resulting Numbers: [5, 80] Generated Node #0,4,3: 48:[5, 80] Operation: 81-1=80 Exploring Operation: 81-5=76, Resulting Numbers: [1, 76] Generated Node #0,4,4: 48:[1, 76] Operation: 81-5=76 Moving to Node #0,3 Current State: 48:[1, 8, 84], Operations: ['89-5=84'] Exploring Operation: 84-8=76, Resulting Numbers: [1, 76] Generated Node #0,3,0: 48:[1, 76] Operation: 84-8=76 Exploring Operation: 8/1=8, Resulting Numbers: [84, 8] Generated Node #0,3,1: 48:[84, 8] Operation: 8/1=8 Exploring Operation: 84-1=83, Resulting Numbers: [8, 83] Generated Node #0,3,2: 48:[8, 83] Operation: 84-1=83 Exploring Operation: 1*84=84, Resulting Numbers: [8, 84] Generated Node #0,3,3: 48:[8, 84] Operation: 1*84=84 Exploring Operation: 1*8=8, Resulting Numbers: [84, 8] Generated Node #0,3,4: 48:[84, 8] Operation: 1*8=8 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 48:[1, 76], Operations: ['89-5=84', '84-8=76'] Exploring Operation: 1*76=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 1+76=77, Resulting Numbers: [77] 77,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 48:[8, 83], Operations: ['89-5=84', '84-1=83'] Exploring Operation: 8*83=664, Resulting Numbers: [664] 664,48 unequal: No Solution Exploring Operation: 8+83=91, Resulting Numbers: [91] 91,48 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 48:[84, 8], Operations: ['89-5=84', '8/1=8'] Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 84+8=92, Resulting Numbers: [92] 92,48 unequal: No Solution Exploring Operation: 84*8=672, Resulting Numbers: [672] 672,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 48:[8, 84], Operations: ['89-5=84', '1*84=84'] Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 8+84=92, Resulting Numbers: [92] 92,48 unequal: No Solution Exploring Operation: 8*84=672, Resulting Numbers: [672] 672,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 48:[84, 8], Operations: ['89-5=84', '1*8=8'] Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 84+8=92, Resulting Numbers: [92] 92,48 unequal: No Solution Exploring Operation: 84*8=672, Resulting Numbers: [672] 672,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 48:[89, 8, 4], Operations: ['5-1=4'] Exploring Operation: 89-8=81, Resulting Numbers: [4, 81] Generated Node #0,0,0: 48:[4, 81] Operation: 89-8=81 Exploring Operation: 8+4=12, Resulting Numbers: [89, 12] Generated Node #0,0,1: 48:[89, 12] Operation: 8+4=12 Exploring Operation: 8/4=2, Resulting Numbers: [89, 2] Generated Node #0,0,2: 48:[89, 2] Operation: 8/4=2 Exploring Operation: 89-4=85, Resulting Numbers: [8, 85] Generated Node #0,0,3: 48:[8, 85] Operation: 89-4=85 Exploring Operation: 8-4=4, Resulting Numbers: [89, 4] Generated Node #0,0,4: 48:[89, 4] Operation: 8-4=4 Moving to Node #0,1 Current State: 48:[5, 8, 88], Operations: ['89-1=88'] Exploring Operation: 5+8=13, Resulting Numbers: [88, 13] Generated Node #0,1,0: 48:[88, 13] Operation: 5+8=13 Exploring Operation: 88/8=11, Resulting Numbers: [5, 11] Generated Node #0,1,1: 48:[5, 11] Operation: 88/8=11 Exploring Operation: 88-5=83, Resulting Numbers: [8, 83] Generated Node #0,1,2: 48:[8, 83] Operation: 88-5=83 Exploring Operation: 88-8=80, Resulting Numbers: [5, 80] Generated Node #0,1,3: 48:[5, 80] Operation: 88-8=80 Exploring Operation: 8-5=3, Resulting Numbers: [88, 3] Generated Node #0,1,4: 48:[88, 3] Operation: 8-5=3 Moving to Node #0,2 Current State: 48:[89, 8, 6], Operations: ['1+5=6'] Exploring Operation: 8+6=14, Resulting Numbers: [89, 14] Generated Node #0,2,0: 48:[89, 14] Operation: 8+6=14 Exploring Operation: 89-8=81, Resulting Numbers: [6, 81] Generated Node #0,2,1: 48:[6, 81] Operation: 89-8=81 Exploring Operation: 8*6=48, Resulting Numbers: [89, 48] Generated Node #0,2,2: 48:[89, 48] Operation: 8*6=48 Exploring Operation: 89-6=83, Resulting Numbers: [8, 83] Generated Node #0,2,3: 48:[8, 83] Operation: 89-6=83 Exploring Operation: 8-6=2, Resulting Numbers: [89, 2] Generated Node #0,2,4: 48:[89, 2] Operation: 8-6=2 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 48:[6, 81], Operations: ['1+5=6', '89-8=81'] Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 6+81=87, Resulting Numbers: [87] 87,48 unequal: No Solution Exploring Operation: 6*81=486, Resulting Numbers: [486] 486,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 48:[8, 83], Operations: ['1+5=6', '89-6=83'] Exploring Operation: 8+83=91, Resulting Numbers: [91] 91,48 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 8*83=664, Resulting Numbers: [664] 664,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 48:[89, 48], Operations: ['1+5=6', '8*6=48'] Exploring Operation: 89+48=137, Resulting Numbers: [137] 137,48 unequal: No Solution Exploring Operation: 89*48=4272, Resulting Numbers: [4272] 4272,48 unequal: No Solution Exploring Operation: 89-48=41, Resulting Numbers: [41] 41,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 48:[89, 2], Operations: ['1+5=6', '8-6=2'] Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,48 unequal: No Solution Exploring Operation: 89*2=178, Resulting Numbers: [178] 178,48 unequal: No Solution Exploring Operation: 89+2=91, Resulting Numbers: [91] 91,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 48:[89, 14], Operations: ['1+5=6', '8+6=14'] Exploring Operation: 89+14=103, Resulting Numbers: [103] 103,48 unequal: No Solution Exploring Operation: 89*14=1246, Resulting Numbers: [1246] 1246,48 unequal: No Solution Exploring Operation: 89-14=75, Resulting Numbers: [75] 75,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 48:[5, 11], Operations: ['89-1=88', '88/8=11'] Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,48 unequal: No Solution Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,48 unequal: No Solution Moving to Node #0,4,4 Current State: 48:[1, 76], Operations: ['89-8=81', '81-5=76'] Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 1*76=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 1+76=77, Resulting Numbers: [77] 77,48 unequal: No Solution Moving to Node #0,4,2 Current State: 48:[81, 6], Operations: ['89-8=81', '1+5=6'] Exploring Operation: 81*6=486, Resulting Numbers: [486] 486,48 unequal: No Solution Exploring Operation: 81+6=87, Resulting Numbers: [87] 87,48 unequal: No Solution Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,48 unequal: No Solution Moving to Node #0,0,0 Current State: 48:[4, 81], Operations: ['5-1=4', '89-8=81'] Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,48 unequal: No Solution Exploring Operation: 4+81=85, Resulting Numbers: [85] 85,48 unequal: No Solution Exploring Operation: 4*81=324, Resulting Numbers: [324] 324,48 unequal: No Solution Moving to Node #0,1,3 Current State: 48:[5, 80], Operations: ['89-1=88', '88-8=80'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 5*80=400, Resulting Numbers: [400] 400,48 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,48 unequal: No Solution Moving to Node #0,4,1 Current State: 48:[81, 4], Operations: ['89-8=81', '5-1=4'] Exploring Operation: 81*4=324, Resulting Numbers: [324] 324,48 unequal: No Solution Exploring Operation: 81+4=85, Resulting Numbers: [85] 85,48 unequal: No Solution Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,48 unequal: No Solution Moving to Node #0,4,3 Current State: 48:[5, 80], Operations: ['89-8=81', '81-1=80'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,48 unequal: No Solution Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 5*80=400, Resulting Numbers: [400] 400,48 unequal: No Solution Moving to Node #0,4,0 Current State: 48:[81, 5], Operations: ['89-8=81', '1*5=5'] Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 81+5=86, Resulting Numbers: [86] 86,48 unequal: No Solution Exploring Operation: 81*5=405, Resulting Numbers: [405] 405,48 unequal: No Solution Moving to Node #0,1,2 Current State: 48:[8, 83], Operations: ['89-1=88', '88-5=83'] Exploring Operation: 8+83=91, Resulting Numbers: [91] 91,48 unequal: No Solution Exploring Operation: 8*83=664, Resulting Numbers: [664] 664,48 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,48 unequal: No Solution Moving to Node #0,0,3 Current State: 48:[8, 85], Operations: ['5-1=4', '89-4=85'] Exploring Operation: 85-8=77, Resulting Numbers: [77] 77,48 unequal: No Solution Exploring Operation: 8+85=93, Resulting Numbers: [93] 93,48 unequal: No Solution Exploring Operation: 8*85=680, Resulting Numbers: [680] 680,48 unequal: No Solution Moving to Node #0,1,4 Current State: 48:[88, 3], Operations: ['89-1=88', '8-5=3'] Exploring Operation: 88*3=264, Resulting Numbers: [264] 264,48 unequal: No Solution Exploring Operation: 88+3=91, Resulting Numbers: [91] 91,48 unequal: No Solution Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[89, 12], Operations: ['5-1=4', '8+4=12'] Exploring Operation: 89-12=77, Resulting Numbers: [77] 77,48 unequal: No Solution Exploring Operation: 89+12=101, Resulting Numbers: [101] 101,48 unequal: No Solution Exploring Operation: 89*12=1068, Resulting Numbers: [1068] 1068,48 unequal: No Solution Moving to Node #0,1,0 Current State: 48:[88, 13], Operations: ['89-1=88', '5+8=13'] Exploring Operation: 88+13=101, Resulting Numbers: [101] 101,48 unequal: No Solution Exploring Operation: 88-13=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 88*13=1144, Resulting Numbers: [1144] 1144,48 unequal: No Solution Moving to Node #0,0,4 Current State: 48:[89, 4], Operations: ['5-1=4', '8-4=4'] Exploring Operation: 89*4=356, Resulting Numbers: [356] 356,48 unequal: No Solution Exploring Operation: 89-4=85, Resulting Numbers: [85] 85,48 unequal: No Solution Exploring Operation: 89+4=93, Resulting Numbers: [93] 93,48 unequal: No Solution Moving to Node #0,0,2 Current State: 48:[89, 2], Operations: ['5-1=4', '8/4=2'] Exploring Operation: 89*2=178, Resulting Numbers: [178] 178,48 unequal: No Solution Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,48 unequal: No Solution Exploring Operation: 89+2=91, Resulting Numbers: [91] 91,48 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 96, 16, 9, 54 ]
39
[ "96/16=6", "54-9=45", "45-6=39" ]
Current State: 39:[96, 16, 9, 54], Operations: [] Exploring Operation: 96/16=6, Resulting Numbers: [9, 54, 6] Generated Node #2: [9, 54, 6] from Operation: 96/16=6 Current State: 39:[9, 54, 6], Operations: ['96/16=6'] Exploring Operation: 54-9=45, Resulting Numbers: [6, 45] Generated Node #3: [6, 45] from Operation: 54-9=45 Current State: 39:[6, 45], Operations: ['96/16=6', '54-9=45'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[96, 16, 9, 54], Operations: [] Exploring Operation: 96-16=80, Resulting Numbers: [9, 54, 80] Generated Node #0,0: 39:[9, 54, 80] Operation: 96-16=80 Exploring Operation: 96/16=6, Resulting Numbers: [9, 54, 6] Generated Node #0,1: 39:[9, 54, 6] Operation: 96/16=6 Exploring Operation: 96-54=42, Resulting Numbers: [16, 9, 42] Generated Node #0,2: 39:[16, 9, 42] Operation: 96-54=42 Moving to Node #0,2 Current State: 39:[16, 9, 42], Operations: ['96-54=42'] Exploring Operation: 16+9=25, Resulting Numbers: [42, 25] Generated Node #0,2,0: 39:[42, 25] Operation: 16+9=25 Exploring Operation: 42-9=33, Resulting Numbers: [16, 33] Generated Node #0,2,1: 39:[16, 33] Operation: 42-9=33 Exploring Operation: 16-9=7, Resulting Numbers: [42, 7] Generated Node #0,2,2: 39:[42, 7] Operation: 16-9=7 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 39:[42, 7], Operations: ['96-54=42', '16-9=7'] Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 42+7=49, Resulting Numbers: [49] 49,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 39:[16, 33], Operations: ['96-54=42', '42-9=33'] Exploring Operation: 16*33=528, Resulting Numbers: [528] 528,39 unequal: No Solution Exploring Operation: 16+33=49, Resulting Numbers: [49] 49,39 unequal: No Solution Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[42, 25], Operations: ['96-54=42', '16+9=25'] Exploring Operation: 42+25=67, Resulting Numbers: [67] 67,39 unequal: No Solution Exploring Operation: 42-25=17, Resulting Numbers: [17] 17,39 unequal: No Solution Exploring Operation: 42*25=1050, Resulting Numbers: [1050] 1050,39 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: 39:[9, 54, 6], Operations: ['96/16=6'] Exploring Operation: 54/9=6, Resulting Numbers: [6, 6] Generated Node #0,1,0: 39:[6, 6] Operation: 54/9=6 Exploring Operation: 54/6=9, Resulting Numbers: [9, 9] Generated Node #0,1,1: 39:[9, 9] Operation: 54/6=9 Exploring Operation: 54-9=45, Resulting Numbers: [6, 45] Generated Node #0,1,2: 39:[6, 45] Operation: 54-9=45 Moving to Node #0,0 Current State: 39:[9, 54, 80], Operations: ['96-16=80'] Exploring Operation: 54-9=45, Resulting Numbers: [80, 45] Generated Node #0,0,0: 39:[80, 45] Operation: 54-9=45 Exploring Operation: 54/9=6, Resulting Numbers: [80, 6] Generated Node #0,0,1: 39:[80, 6] Operation: 54/9=6 Exploring Operation: 80-54=26, Resulting Numbers: [9, 26] Generated Node #0,0,2: 39:[9, 26] Operation: 80-54=26 Moving to Node #0,1,0 Current State: 39:[6, 6], Operations: ['96/16=6', '54/9=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[9, 9], Operations: ['96/16=6', '54/6=9'] Exploring Operation: 9-9=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 9/9=1, Resulting Numbers: [1] 1,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[6, 45], Operations: ['96/16=6', '54-9=45'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[96, 16, 9, 54], Operations: [] Exploring Operation: 96/16=6, Resulting Numbers: [9, 54, 6] Generated Node #0,1: 39:[9, 54, 6] Operation: 96/16=6 Moving to Node #0,1 Current State: 39:[9, 54, 6], Operations: ['96/16=6'] Exploring Operation: 54-9=45, Resulting Numbers: [6, 45] Generated Node #0,1,2: 39:[6, 45] Operation: 54-9=45 Moving to Node #0,1,2 Current State: 39:[6, 45], Operations: ['96/16=6', '54-9=45'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
0.972222
hs_3
mult_heuristic
[ 35, 80, 25, 5 ]
32
[ "80-5=75", "75/25=3", "35-3=32" ]
Current State: 32:[35, 80, 25, 5], Operations: [] Exploring Operation: 80-5=75, Resulting Numbers: [35, 25, 75] Generated Node #2: [35, 25, 75] from Operation: 80-5=75 Current State: 32:[35, 25, 75], Operations: ['80-5=75'] Exploring Operation: 75/25=3, Resulting Numbers: [35, 3] Generated Node #3: [35, 3] from Operation: 75/25=3 Current State: 32:[35, 3], Operations: ['80-5=75', '75/25=3'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[35, 80, 25, 5], Operations: [] Exploring Operation: 80-35=45, Resulting Numbers: [25, 5, 45] Generated Node #0,0: 32:[25, 5, 45] Operation: 80-35=45 Exploring Operation: 80/5=16, Resulting Numbers: [35, 25, 16] Generated Node #0,1: 32:[35, 25, 16] Operation: 80/5=16 Moving to Node #0,1 Current State: 32:[35, 25, 16], Operations: ['80/5=16'] Exploring Operation: 25-16=9, Resulting Numbers: [35, 9] Generated Node #0,1,0: 32:[35, 9] Operation: 25-16=9 Exploring Operation: 35-25=10, Resulting Numbers: [16, 10] Generated Node #0,1,1: 32:[16, 10] Operation: 35-25=10 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[16, 10], Operations: ['80/5=16', '35-25=10'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,32 unequal: No Solution Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,32 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 #0,1,0 Current State: 32:[35, 9], Operations: ['80/5=16', '25-16=9'] Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,32 unequal: No Solution Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,32 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: 32:[25, 5, 45], Operations: ['80-35=45'] Exploring Operation: 45/5=9, Resulting Numbers: [25, 9] Generated Node #0,0,0: 32:[25, 9] Operation: 45/5=9 Exploring Operation: 45-25=20, Resulting Numbers: [5, 20] Generated Node #0,0,1: 32:[5, 20] Operation: 45-25=20 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[5, 20], Operations: ['80-35=45', '45-25=20'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,32 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 #0,0,0 Current State: 32:[25, 9], Operations: ['80-35=45', '45/5=9'] Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,32 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,32 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
[ 2, 69, 39, 90 ]
99
[ "2*39=78", "90-69=21", "78+21=99" ]
Current State: 99:[2, 69, 39, 90], Operations: [] Exploring Operation: 2*39=78, Resulting Numbers: [69, 90, 78] Generated Node #2: [69, 90, 78] from Operation: 2*39=78 Current State: 99:[69, 90, 78], Operations: ['2*39=78'] Exploring Operation: 90-69=21, Resulting Numbers: [78, 21] Generated Node #3: [78, 21] from Operation: 90-69=21 Current State: 99:[78, 21], Operations: ['2*39=78', '90-69=21'] Exploring Operation: 78+21=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[2, 69, 39, 90], Operations: [] Exploring Operation: 69-39=30, Resulting Numbers: [2, 90, 30] Generated Node #0,0: 99:[2, 90, 30] Operation: 69-39=30 Exploring Operation: 90-69=21, Resulting Numbers: [2, 39, 21] Generated Node #0,1: 99:[2, 39, 21] Operation: 90-69=21 Moving to Node #0,0 Current State: 99:[2, 90, 30], Operations: ['69-39=30'] Exploring Operation: 2+90=92, Resulting Numbers: [30, 92] Generated Node #0,0,0: 99:[30, 92] Operation: 2+90=92 Exploring Operation: 90/30=3, Resulting Numbers: [2, 3] Generated Node #0,0,1: 99:[2, 3] Operation: 90/30=3 Moving to Node #0,1 Current State: 99:[2, 39, 21], Operations: ['90-69=21'] Exploring Operation: 39-21=18, Resulting Numbers: [2, 18] Generated Node #0,1,0: 99:[2, 18] Operation: 39-21=18 Exploring Operation: 39-2=37, Resulting Numbers: [21, 37] Generated Node #0,1,1: 99:[21, 37] Operation: 39-2=37 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[2, 18], Operations: ['90-69=21', '39-21=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,99 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[21, 37], Operations: ['90-69=21', '39-2=37'] Exploring Operation: 21+37=58, Resulting Numbers: [58] 58,99 unequal: No Solution Exploring Operation: 37-21=16, Resulting Numbers: [16] 16,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 99:[2, 3], Operations: ['69-39=30', '90/30=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[30, 92], Operations: ['69-39=30', '2+90=92'] Exploring Operation: 92-30=62, Resulting Numbers: [62] 62,99 unequal: No Solution Exploring Operation: 30+92=122, Resulting Numbers: [122] 122,99 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 80, 8, 97, 1 ]
25
[ "80-8=72", "97*1=97", "97-72=25" ]
Current State: 25:[80, 8, 97, 1], Operations: [] Exploring Operation: 80-8=72, Resulting Numbers: [97, 1, 72] Generated Node #2: [97, 1, 72] from Operation: 80-8=72 Current State: 25:[97, 1, 72], Operations: ['80-8=72'] Exploring Operation: 97*1=97, Resulting Numbers: [72, 97] Generated Node #3: [72, 97] from Operation: 97*1=97 Current State: 25:[72, 97], Operations: ['80-8=72', '97*1=97'] Exploring Operation: 97-72=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[80, 8, 97, 1], Operations: [] Exploring Operation: 97-80=17, Resulting Numbers: [8, 1, 17] Generated Node #0,0: 25:[8, 1, 17] Operation: 97-80=17 Moving to Node #0,0 Current State: 25:[8, 1, 17], Operations: ['97-80=17'] Exploring Operation: 8+17=25, Resulting Numbers: [1, 25] Generated Node #0,0,0: 25:[1, 25] Operation: 8+17=25 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[1, 25], Operations: ['97-80=17', '8+17=25'] Exploring Operation: 1*25=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[80, 8, 97, 1], Operations: [] Exploring Operation: 97-80=17, Resulting Numbers: [8, 1, 17] Generated Node #0,0: 25:[8, 1, 17] Operation: 97-80=17 Moving to Node #0,0 Current State: 25:[8, 1, 17], Operations: ['97-80=17'] Exploring Operation: 8+17=25, Resulting Numbers: [1, 25] Generated Node #0,0,0: 25:[1, 25] Operation: 8+17=25 Moving to Node #0,0,0 Current State: 25:[1, 25], Operations: ['97-80=17', '8+17=25'] Exploring Operation: 1*25=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 13, 23, 48, 19 ]
65
[ "13+23=36", "48-19=29", "36+29=65" ]
Current State: 65:[13, 23, 48, 19], Operations: [] Exploring Operation: 13+23=36, Resulting Numbers: [48, 19, 36] Generated Node #2: [48, 19, 36] from Operation: 13+23=36 Current State: 65:[48, 19, 36], Operations: ['13+23=36'] Exploring Operation: 48-19=29, Resulting Numbers: [36, 29] Generated Node #3: [36, 29] from Operation: 48-19=29 Current State: 65:[36, 29], Operations: ['13+23=36', '48-19=29'] Exploring Operation: 36+29=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[13, 23, 48, 19], Operations: [] Exploring Operation: 13+48=61, Resulting Numbers: [23, 19, 61] Generated Node #0,0: 65:[23, 19, 61] Operation: 13+48=61 Exploring Operation: 48-23=25, Resulting Numbers: [13, 19, 25] Generated Node #0,1: 65:[13, 19, 25] Operation: 48-23=25 Exploring Operation: 23+48=71, Resulting Numbers: [13, 19, 71] Generated Node #0,2: 65:[13, 19, 71] Operation: 23+48=71 Exploring Operation: 48+19=67, Resulting Numbers: [13, 23, 67] Generated Node #0,3: 65:[13, 23, 67] Operation: 48+19=67 Exploring Operation: 23-19=4, Resulting Numbers: [13, 48, 4] Generated Node #0,4: 65:[13, 48, 4] Operation: 23-19=4 Moving to Node #0,2 Current State: 65:[13, 19, 71], Operations: ['23+48=71'] Exploring Operation: 13+71=84, Resulting Numbers: [19, 84] Generated Node #0,2,0: 65:[19, 84] Operation: 13+71=84 Exploring Operation: 19-13=6, Resulting Numbers: [71, 6] Generated Node #0,2,1: 65:[71, 6] Operation: 19-13=6 Exploring Operation: 71-19=52, Resulting Numbers: [13, 52] Generated Node #0,2,2: 65:[13, 52] Operation: 71-19=52 Exploring Operation: 13+19=32, Resulting Numbers: [71, 32] Generated Node #0,2,3: 65:[71, 32] Operation: 13+19=32 Exploring Operation: 71-13=58, Resulting Numbers: [19, 58] Generated Node #0,2,4: 65:[19, 58] Operation: 71-13=58 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 65:[71, 6], Operations: ['23+48=71', '19-13=6'] Exploring Operation: 71*6=426, Resulting Numbers: [426] 426,65 unequal: No Solution Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[13, 23, 48, 19], Operations: [] Exploring Operation: 23+48=71, Resulting Numbers: [13, 19, 71] Generated Node #0,2: 65:[13, 19, 71] Operation: 23+48=71 Moving to Node #0,2 Current State: 65:[13, 19, 71], Operations: ['23+48=71'] Exploring Operation: 19-13=6, Resulting Numbers: [71, 6] Generated Node #0,2,1: 65:[71, 6] Operation: 19-13=6 Moving to Node #0,2,1 Current State: 65:[71, 6], Operations: ['23+48=71', '19-13=6'] Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 67, 74, 36, 77 ]
78
[ "67+77=144", "144/36=4", "74+4=78" ]
Current State: 78:[67, 74, 36, 77], Operations: [] Exploring Operation: 67+77=144, Resulting Numbers: [74, 36, 144] Generated Node #2: [74, 36, 144] from Operation: 67+77=144 Current State: 78:[74, 36, 144], Operations: ['67+77=144'] Exploring Operation: 144/36=4, Resulting Numbers: [74, 4] Generated Node #3: [74, 4] from Operation: 144/36=4 Current State: 78:[74, 4], Operations: ['67+77=144', '144/36=4'] Exploring Operation: 74+4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[67, 74, 36, 77], Operations: [] Exploring Operation: 74-67=7, Resulting Numbers: [36, 77, 7] Generated Node #0,0: 78:[36, 77, 7] Operation: 74-67=7 Exploring Operation: 67-36=31, Resulting Numbers: [74, 77, 31] Generated Node #0,1: 78:[74, 77, 31] Operation: 67-36=31 Exploring Operation: 77-67=10, Resulting Numbers: [74, 36, 10] Generated Node #0,2: 78:[74, 36, 10] Operation: 77-67=10 Exploring Operation: 74-36=38, Resulting Numbers: [67, 77, 38] Generated Node #0,3: 78:[67, 77, 38] Operation: 74-36=38 Moving to Node #0,0 Current State: 78:[36, 77, 7], Operations: ['74-67=7'] Exploring Operation: 77/7=11, Resulting Numbers: [36, 11] Generated Node #0,0,0: 78:[36, 11] Operation: 77/7=11 Exploring Operation: 77-36=41, Resulting Numbers: [7, 41] Generated Node #0,0,1: 78:[7, 41] Operation: 77-36=41 Exploring Operation: 36+7=43, Resulting Numbers: [77, 43] Generated Node #0,0,2: 78:[77, 43] Operation: 36+7=43 Exploring Operation: 36-7=29, Resulting Numbers: [77, 29] Generated Node #0,0,3: 78:[77, 29] Operation: 36-7=29 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[7, 41], Operations: ['74-67=7', '77-36=41'] Exploring Operation: 7*41=287, Resulting Numbers: [287] 287,78 unequal: No Solution Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 7+41=48, Resulting Numbers: [48] 48,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 78:[77, 29], Operations: ['74-67=7', '36-7=29'] Exploring Operation: 77+29=106, Resulting Numbers: [106] 106,78 unequal: No Solution Exploring Operation: 77*29=2233, Resulting Numbers: [2233] 2233,78 unequal: No Solution Exploring Operation: 77-29=48, Resulting Numbers: [48] 48,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[36, 11], Operations: ['74-67=7', '77/7=11'] Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,78 unequal: No Solution Exploring Operation: 36*11=396, Resulting Numbers: [396] 396,78 unequal: No Solution Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 78:[77, 43], Operations: ['74-67=7', '36+7=43'] Exploring Operation: 77-43=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 77*43=3311, Resulting Numbers: [3311] 3311,78 unequal: No Solution Exploring Operation: 77+43=120, Resulting Numbers: [120] 120,78 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: 78:[74, 36, 10], Operations: ['77-67=10'] Exploring Operation: 36+10=46, Resulting Numbers: [74, 46] Generated Node #0,2,0: 78:[74, 46] Operation: 36+10=46 Exploring Operation: 74-36=38, Resulting Numbers: [10, 38] Generated Node #0,2,1: 78:[10, 38] Operation: 74-36=38 Exploring Operation: 36-10=26, Resulting Numbers: [74, 26] Generated Node #0,2,2: 78:[74, 26] Operation: 36-10=26 Exploring Operation: 74+10=84, Resulting Numbers: [36, 84] Generated Node #0,2,3: 78:[36, 84] Operation: 74+10=84 Moving to Node #0,1 Current State: 78:[74, 77, 31], Operations: ['67-36=31'] Exploring Operation: 77-31=46, Resulting Numbers: [74, 46] Generated Node #0,1,0: 78:[74, 46] Operation: 77-31=46 Exploring Operation: 74-31=43, Resulting Numbers: [77, 43] Generated Node #0,1,1: 78:[77, 43] Operation: 74-31=43 Exploring Operation: 74+31=105, Resulting Numbers: [77, 105] Generated Node #0,1,2: 78:[77, 105] Operation: 74+31=105 Exploring Operation: 77-74=3, Resulting Numbers: [31, 3] Generated Node #0,1,3: 78:[31, 3] Operation: 77-74=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[77, 43], Operations: ['67-36=31', '74-31=43'] Exploring Operation: 77*43=3311, Resulting Numbers: [3311] 3311,78 unequal: No Solution Exploring Operation: 77-43=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 77+43=120, Resulting Numbers: [120] 120,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 78:[31, 3], Operations: ['67-36=31', '77-74=3'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[74, 46], Operations: ['67-36=31', '77-31=46'] Exploring Operation: 74*46=3404, Resulting Numbers: [3404] 3404,78 unequal: No Solution Exploring Operation: 74+46=120, Resulting Numbers: [120] 120,78 unequal: No Solution Exploring Operation: 74-46=28, Resulting Numbers: [28] 28,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 78:[77, 105], Operations: ['67-36=31', '74+31=105'] Exploring Operation: 77*105=8085, Resulting Numbers: [8085] 8085,78 unequal: No Solution Exploring Operation: 105-77=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 77+105=182, Resulting Numbers: [182] 182,78 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: 78:[67, 77, 38], Operations: ['74-36=38'] Exploring Operation: 77-67=10, Resulting Numbers: [38, 10] Generated Node #0,3,0: 78:[38, 10] Operation: 77-67=10 Exploring Operation: 67-38=29, Resulting Numbers: [77, 29] Generated Node #0,3,1: 78:[77, 29] Operation: 67-38=29 Exploring Operation: 67+38=105, Resulting Numbers: [77, 105] Generated Node #0,3,2: 78:[77, 105] Operation: 67+38=105 Exploring Operation: 77-38=39, Resulting Numbers: [67, 39] Generated Node #0,3,3: 78:[67, 39] Operation: 77-38=39 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 78:[38, 10], Operations: ['74-36=38', '77-67=10'] Exploring Operation: 38*10=380, Resulting Numbers: [380] 380,78 unequal: No Solution Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 38+10=48, Resulting Numbers: [48] 48,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 78:[77, 29], Operations: ['74-36=38', '67-38=29'] Exploring Operation: 77+29=106, Resulting Numbers: [106] 106,78 unequal: No Solution Exploring Operation: 77-29=48, Resulting Numbers: [48] 48,78 unequal: No Solution Exploring Operation: 77*29=2233, Resulting Numbers: [2233] 2233,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 78:[67, 39], Operations: ['74-36=38', '77-38=39'] Exploring Operation: 67*39=2613, Resulting Numbers: [2613] 2613,78 unequal: No Solution Exploring Operation: 67-39=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 67+39=106, Resulting Numbers: [106] 106,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 78:[77, 105], Operations: ['74-36=38', '67+38=105'] Exploring Operation: 77+105=182, Resulting Numbers: [182] 182,78 unequal: No Solution Exploring Operation: 105-77=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 77*105=8085, Resulting Numbers: [8085] 8085,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 78:[10, 38], Operations: ['77-67=10', '74-36=38'] Exploring Operation: 10*38=380, Resulting Numbers: [380] 380,78 unequal: No Solution Exploring Operation: 10+38=48, Resulting Numbers: [48] 48,78 unequal: No Solution Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,78 unequal: No Solution Moving to Node #0,2,2 Current State: 78:[74, 26], Operations: ['77-67=10', '36-10=26'] Exploring Operation: 74+26=100, Resulting Numbers: [100] 100,78 unequal: No Solution Exploring Operation: 74*26=1924, Resulting Numbers: [1924] 1924,78 unequal: No Solution Exploring Operation: 74-26=48, Resulting Numbers: [48] 48,78 unequal: No Solution Moving to Node #0,2,3 Current State: 78:[36, 84], Operations: ['77-67=10', '74+10=84'] Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,78 unequal: No Solution Exploring Operation: 36*84=3024, Resulting Numbers: [3024] 3024,78 unequal: No Solution Exploring Operation: 36+84=120, Resulting Numbers: [120] 120,78 unequal: No Solution Moving to Node #0,2,0 Current State: 78:[74, 46], Operations: ['77-67=10', '36+10=46'] Exploring Operation: 74*46=3404, Resulting Numbers: [3404] 3404,78 unequal: No Solution Exploring Operation: 74-46=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 74+46=120, Resulting Numbers: [120] 120,78 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 32, 8, 36, 5 ]
14
[ "32/8=4", "36/4=9", "5+9=14" ]
Current State: 14:[32, 8, 36, 5], Operations: [] Exploring Operation: 32/8=4, Resulting Numbers: [36, 5, 4] Generated Node #2: [36, 5, 4] from Operation: 32/8=4 Current State: 14:[36, 5, 4], Operations: ['32/8=4'] Exploring Operation: 36/4=9, Resulting Numbers: [5, 9] Generated Node #3: [5, 9] from Operation: 36/4=9 Current State: 14:[5, 9], Operations: ['32/8=4', '36/4=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[32, 8, 36, 5], Operations: [] Exploring Operation: 32/8=4, Resulting Numbers: [36, 5, 4] Generated Node #0,0: 14:[36, 5, 4] Operation: 32/8=4 Exploring Operation: 36-32=4, Resulting Numbers: [8, 5, 4] Generated Node #0,1: 14:[8, 5, 4] Operation: 36-32=4 Moving to Node #0,1 Current State: 14:[8, 5, 4], Operations: ['36-32=4'] Exploring Operation: 8/4=2, Resulting Numbers: [5, 2] Generated Node #0,1,0: 14:[5, 2] Operation: 8/4=2 Exploring Operation: 5-4=1, Resulting Numbers: [8, 1] Generated Node #0,1,1: 14:[8, 1] Operation: 5-4=1 Moving to Node #0,0 Current State: 14:[36, 5, 4], Operations: ['32/8=4'] Exploring Operation: 36/4=9, Resulting Numbers: [5, 9] Generated Node #0,0,0: 14:[5, 9] Operation: 36/4=9 Exploring Operation: 36-5=31, Resulting Numbers: [4, 31] Generated Node #0,0,1: 14:[4, 31] Operation: 36-5=31 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[5, 9], Operations: ['32/8=4', '36/4=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[32, 8, 36, 5], Operations: [] Exploring Operation: 32/8=4, Resulting Numbers: [36, 5, 4] Generated Node #0,0: 14:[36, 5, 4] Operation: 32/8=4 Moving to Node #0,0 Current State: 14:[36, 5, 4], Operations: ['32/8=4'] Exploring Operation: 36/4=9, Resulting Numbers: [5, 9] Generated Node #0,0,0: 14:[5, 9] Operation: 36/4=9 Moving to Node #0,0,0 Current State: 14:[5, 9], Operations: ['32/8=4', '36/4=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 94, 29, 38, 22 ]
49
[ "94-29=65", "38-22=16", "65-16=49" ]
Current State: 49:[94, 29, 38, 22], Operations: [] Exploring Operation: 94-29=65, Resulting Numbers: [38, 22, 65] Generated Node #2: [38, 22, 65] from Operation: 94-29=65 Current State: 49:[38, 22, 65], Operations: ['94-29=65'] Exploring Operation: 38-22=16, Resulting Numbers: [65, 16] Generated Node #3: [65, 16] from Operation: 38-22=16 Current State: 49:[65, 16], Operations: ['94-29=65', '38-22=16'] Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[94, 29, 38, 22], Operations: [] Exploring Operation: 94-29=65, Resulting Numbers: [38, 22, 65] Generated Node #0,0: 49:[38, 22, 65] Operation: 94-29=65 Exploring Operation: 94-22=72, Resulting Numbers: [29, 38, 72] Generated Node #0,1: 49:[29, 38, 72] Operation: 94-22=72 Exploring Operation: 94-38=56, Resulting Numbers: [29, 22, 56] Generated Node #0,2: 49:[29, 22, 56] Operation: 94-38=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[38, 22, 65], Operations: ['94-29=65'] Exploring Operation: 65-22=43, Resulting Numbers: [38, 43] Generated Node #0,0,0: 49:[38, 43] Operation: 65-22=43 Exploring Operation: 38+22=60, Resulting Numbers: [65, 60] Generated Node #0,0,1: 49:[65, 60] Operation: 38+22=60 Exploring Operation: 38-22=16, Resulting Numbers: [65, 16] Generated Node #0,0,2: 49:[65, 16] Operation: 38-22=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[38, 43], Operations: ['94-29=65', '65-22=43'] Exploring Operation: 43-38=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 38*43=1634, Resulting Numbers: [1634] 1634,49 unequal: No Solution Exploring Operation: 38+43=81, Resulting Numbers: [81] 81,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 49:[65, 16], Operations: ['94-29=65', '38-22=16'] Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[94, 29, 38, 22], Operations: [] Exploring Operation: 94-29=65, Resulting Numbers: [38, 22, 65] Generated Node #0,0: 49:[38, 22, 65] Operation: 94-29=65 Moving to Node #0,0 Current State: 49:[38, 22, 65], Operations: ['94-29=65'] Exploring Operation: 38-22=16, Resulting Numbers: [65, 16] Generated Node #0,0,2: 49:[65, 16] Operation: 38-22=16 Moving to Node #0,0,2 Current State: 49:[65, 16], Operations: ['94-29=65', '38-22=16'] Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 53, 44, 3, 19 ]
98
[ "53-19=34", "44*3=132", "132-34=98" ]
Current State: 98:[53, 44, 3, 19], Operations: [] Exploring Operation: 53-19=34, Resulting Numbers: [44, 3, 34] Generated Node #2: [44, 3, 34] from Operation: 53-19=34 Current State: 98:[44, 3, 34], Operations: ['53-19=34'] Exploring Operation: 44*3=132, Resulting Numbers: [34, 132] Generated Node #3: [34, 132] from Operation: 44*3=132 Current State: 98:[34, 132], Operations: ['53-19=34', '44*3=132'] Exploring Operation: 132-34=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[53, 44, 3, 19], Operations: [] Exploring Operation: 53-3=50, Resulting Numbers: [44, 19, 50] Generated Node #0,0: 98:[44, 19, 50] Operation: 53-3=50 Exploring Operation: 53-44=9, Resulting Numbers: [3, 19, 9] Generated Node #0,1: 98:[3, 19, 9] Operation: 53-44=9 Exploring Operation: 53+44=97, Resulting Numbers: [3, 19, 97] Generated Node #0,2: 98:[3, 19, 97] Operation: 53+44=97 Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[3, 19, 97], Operations: ['53+44=97'] Exploring Operation: 19-3=16, Resulting Numbers: [97, 16] Generated Node #0,2,0: 98:[97, 16] Operation: 19-3=16 Exploring Operation: 3+97=100, Resulting Numbers: [19, 100] Generated Node #0,2,1: 98:[19, 100] Operation: 3+97=100 Exploring Operation: 3+19=22, Resulting Numbers: [97, 22] Generated Node #0,2,2: 98:[97, 22] Operation: 3+19=22 Moving to Node #0,2,0 Current State: 98:[97, 16], Operations: ['53+44=97', '19-3=16'] Exploring Operation: 97+16=113, Resulting Numbers: [113] 113,98 unequal: No Solution Exploring Operation: 97-16=81, Resulting Numbers: [81] 81,98 unequal: No Solution Exploring Operation: 97*16=1552, Resulting Numbers: [1552] 1552,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[19, 100], Operations: ['53+44=97', '3+97=100'] Exploring Operation: 100-19=81, Resulting Numbers: [81] 81,98 unequal: No Solution Exploring Operation: 19+100=119, Resulting Numbers: [119] 119,98 unequal: No Solution Exploring Operation: 19*100=1900, Resulting Numbers: [1900] 1900,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[97, 22], Operations: ['53+44=97', '3+19=22'] Exploring Operation: 97*22=2134, Resulting Numbers: [2134] 2134,98 unequal: No Solution Exploring Operation: 97+22=119, Resulting Numbers: [119] 119,98 unequal: No Solution Exploring Operation: 97-22=75, Resulting Numbers: [75] 75,98 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:[3, 19, 9], Operations: ['53-44=9'] Exploring Operation: 19-3=16, Resulting Numbers: [9, 16] Generated Node #0,1,0: 98:[9, 16] Operation: 19-3=16 Exploring Operation: 9-3=6, Resulting Numbers: [19, 6] Generated Node #0,1,1: 98:[19, 6] Operation: 9-3=6 Exploring Operation: 19-9=10, Resulting Numbers: [3, 10] Generated Node #0,1,2: 98:[3, 10] Operation: 19-9=10 Moving to Node #0,1,0 Current State: 98:[9, 16], Operations: ['53-44=9', '19-3=16'] Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,98 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,98 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[3, 10], Operations: ['53-44=9', '19-9=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,98 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,98 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[19, 6], Operations: ['53-44=9', '9-3=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,98 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,98 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,98 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 #0,0 Current State: 98:[44, 19, 50], Operations: ['53-3=50'] Exploring Operation: 44-19=25, Resulting Numbers: [50, 25] Generated Node #0,0,0: 98:[50, 25] Operation: 44-19=25 Exploring Operation: 50-44=6, Resulting Numbers: [19, 6] Generated Node #0,0,1: 98:[19, 6] Operation: 50-44=6 Exploring Operation: 44+50=94, Resulting Numbers: [19, 94] Generated Node #0,0,2: 98:[19, 94] Operation: 44+50=94 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 98:[19, 6], Operations: ['53-3=50', '50-44=6'] Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,98 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,98 unequal: No Solution Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,98 unequal: No Solution No 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: 98:[19, 94], Operations: ['53-3=50', '44+50=94'] Exploring Operation: 94-19=75, Resulting Numbers: [75] 75,98 unequal: No Solution Exploring Operation: 19*94=1786, Resulting Numbers: [1786] 1786,98 unequal: No Solution Exploring Operation: 19+94=113, Resulting Numbers: [113] 113,98 unequal: No Solution No 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: 98:[50, 25], Operations: ['53-3=50', '44-19=25'] Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,98 unequal: No Solution Exploring Operation: 50+25=75, Resulting Numbers: [75] 75,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 1, 45, 4, 62 ]
71
[ "1+4=5", "45/5=9", "62+9=71" ]
Current State: 71:[1, 45, 4, 62], Operations: [] Exploring Operation: 1+4=5, Resulting Numbers: [45, 62, 5] Generated Node #2: [45, 62, 5] from Operation: 1+4=5 Current State: 71:[45, 62, 5], Operations: ['1+4=5'] Exploring Operation: 45/5=9, Resulting Numbers: [62, 9] Generated Node #3: [62, 9] from Operation: 45/5=9 Current State: 71:[62, 9], Operations: ['1+4=5', '45/5=9'] Exploring Operation: 62+9=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[1, 45, 4, 62], Operations: [] Exploring Operation: 1+4=5, Resulting Numbers: [45, 62, 5] Generated Node #0,0: 71:[45, 62, 5] Operation: 1+4=5 Exploring Operation: 1+45=46, Resulting Numbers: [4, 62, 46] Generated Node #0,1: 71:[4, 62, 46] Operation: 1+45=46 Exploring Operation: 1+62=63, Resulting Numbers: [45, 4, 63] Generated Node #0,2: 71:[45, 4, 63] Operation: 1+62=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[45, 62, 5], Operations: ['1+4=5'] Exploring Operation: 62+5=67, Resulting Numbers: [45, 67] Generated Node #0,0,0: 71:[45, 67] Operation: 62+5=67 Exploring Operation: 45+5=50, Resulting Numbers: [62, 50] Generated Node #0,0,1: 71:[62, 50] Operation: 45+5=50 Exploring Operation: 45-5=40, Resulting Numbers: [62, 40] Generated Node #0,0,2: 71:[62, 40] Operation: 45-5=40 Moving to Node #0,0,0 Current State: 71:[45, 67], Operations: ['1+4=5', '62+5=67'] Exploring Operation: 67-45=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 45+67=112, Resulting Numbers: [112] 112,71 unequal: No Solution Exploring Operation: 45*67=3015, Resulting Numbers: [3015] 3015,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[62, 50], Operations: ['1+4=5', '45+5=50'] Exploring Operation: 62+50=112, Resulting Numbers: [112] 112,71 unequal: No Solution Exploring Operation: 62*50=3100, Resulting Numbers: [3100] 3100,71 unequal: No Solution Exploring Operation: 62-50=12, Resulting Numbers: [12] 12,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[62, 40], Operations: ['1+4=5', '45-5=40'] Exploring Operation: 62*40=2480, Resulting Numbers: [2480] 2480,71 unequal: No Solution Exploring Operation: 62-40=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 62+40=102, Resulting Numbers: [102] 102,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[4, 62, 46], Operations: ['1+45=46'] Exploring Operation: 62-4=58, Resulting Numbers: [46, 58] Generated Node #0,1,0: 71:[46, 58] Operation: 62-4=58 Exploring Operation: 4+62=66, Resulting Numbers: [46, 66] Generated Node #0,1,1: 71:[46, 66] Operation: 4+62=66 Exploring Operation: 4+46=50, Resulting Numbers: [62, 50] Generated Node #0,1,2: 71:[62, 50] Operation: 4+46=50 Moving to Node #0,1,1 Current State: 71:[46, 66], Operations: ['1+45=46', '4+62=66'] Exploring Operation: 66-46=20, Resulting Numbers: [20] 20,71 unequal: No Solution Exploring Operation: 46*66=3036, Resulting Numbers: [3036] 3036,71 unequal: No Solution Exploring Operation: 46+66=112, Resulting Numbers: [112] 112,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[62, 50], Operations: ['1+45=46', '4+46=50'] Exploring Operation: 62-50=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 62+50=112, Resulting Numbers: [112] 112,71 unequal: No Solution Exploring Operation: 62*50=3100, Resulting Numbers: [3100] 3100,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[46, 58], Operations: ['1+45=46', '62-4=58'] Exploring Operation: 46+58=104, Resulting Numbers: [104] 104,71 unequal: No Solution Exploring Operation: 58-46=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 46*58=2668, Resulting Numbers: [2668] 2668,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[45, 4, 63], Operations: ['1+62=63'] Exploring Operation: 4+63=67, Resulting Numbers: [45, 67] Generated Node #0,2,0: 71:[45, 67] Operation: 4+63=67 Exploring Operation: 45+4=49, Resulting Numbers: [63, 49] Generated Node #0,2,1: 71:[63, 49] Operation: 45+4=49 Exploring Operation: 45-4=41, Resulting Numbers: [63, 41] Generated Node #0,2,2: 71:[63, 41] Operation: 45-4=41 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 71:[45, 67], Operations: ['1+62=63', '4+63=67'] Exploring Operation: 45*67=3015, Resulting Numbers: [3015] 3015,71 unequal: No Solution Exploring Operation: 67-45=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 45+67=112, Resulting Numbers: [112] 112,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 71:[63, 49], Operations: ['1+62=63', '45+4=49'] Exploring Operation: 63*49=3087, Resulting Numbers: [3087] 3087,71 unequal: No Solution Exploring Operation: 63-49=14, Resulting Numbers: [14] 14,71 unequal: No Solution Exploring Operation: 63+49=112, Resulting Numbers: [112] 112,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 71:[63, 41], Operations: ['1+62=63', '45-4=41'] Exploring Operation: 63+41=104, Resulting Numbers: [104] 104,71 unequal: No Solution Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 63*41=2583, Resulting Numbers: [2583] 2583,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 40, 42, 37, 47 ]
15
[ "40-37=3", "47-42=5", "3*5=15" ]
Current State: 15:[40, 42, 37, 47], Operations: [] Exploring Operation: 40-37=3, Resulting Numbers: [42, 47, 3] Generated Node #2: [42, 47, 3] from Operation: 40-37=3 Current State: 15:[42, 47, 3], Operations: ['40-37=3'] Exploring Operation: 47-42=5, Resulting Numbers: [3, 5] Generated Node #3: [3, 5] from Operation: 47-42=5 Current State: 15:[3, 5], Operations: ['40-37=3', '47-42=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[40, 42, 37, 47], Operations: [] Exploring Operation: 47-40=7, Resulting Numbers: [42, 37, 7] Generated Node #0,0: 15:[42, 37, 7] Operation: 47-40=7 Exploring Operation: 47-42=5, Resulting Numbers: [40, 37, 5] Generated Node #0,1: 15:[40, 37, 5] Operation: 47-42=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[40, 37, 5], Operations: ['47-42=5'] Exploring Operation: 40-37=3, Resulting Numbers: [5, 3] Generated Node #0,1,0: 15:[5, 3] Operation: 40-37=3 Exploring Operation: 40/5=8, Resulting Numbers: [37, 8] Generated Node #0,1,1: 15:[37, 8] Operation: 40/5=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 15:[5, 3], Operations: ['47-42=5', '40-37=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[40, 42, 37, 47], Operations: [] Exploring Operation: 47-42=5, Resulting Numbers: [40, 37, 5] Generated Node #0,1: 15:[40, 37, 5] Operation: 47-42=5 Moving to Node #0,1 Current State: 15:[40, 37, 5], Operations: ['47-42=5'] Exploring Operation: 40-37=3, Resulting Numbers: [5, 3] Generated Node #0,1,0: 15:[5, 3] Operation: 40-37=3 Moving to Node #0,1,0 Current State: 15:[5, 3], Operations: ['47-42=5', '40-37=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 17, 1, 8, 60 ]
77
[ "17*8=136", "60-1=59", "136-59=77" ]
Current State: 77:[17, 1, 8, 60], Operations: [] Exploring Operation: 17*8=136, Resulting Numbers: [1, 60, 136] Generated Node #2: [1, 60, 136] from Operation: 17*8=136 Current State: 77:[1, 60, 136], Operations: ['17*8=136'] Exploring Operation: 60-1=59, Resulting Numbers: [136, 59] Generated Node #3: [136, 59] from Operation: 60-1=59 Current State: 77:[136, 59], Operations: ['17*8=136', '60-1=59'] Exploring Operation: 136-59=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[17, 1, 8, 60], Operations: [] Exploring Operation: 17+60=77, Resulting Numbers: [1, 8, 77] Generated Node #0,0: 77:[1, 8, 77] Operation: 17+60=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[1, 8, 77], Operations: ['17+60=77'] Exploring Operation: 8-1=7, Resulting Numbers: [77, 7] Generated Node #0,0,0: 77:[77, 7] Operation: 8-1=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[77, 7], Operations: ['17+60=77', '8-1=7'] Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 56, 15, 12, 19 ]
64
[ "56+15=71", "19-12=7", "71-7=64" ]
Current State: 64:[56, 15, 12, 19], Operations: [] Exploring Operation: 56+15=71, Resulting Numbers: [12, 19, 71] Generated Node #2: [12, 19, 71] from Operation: 56+15=71 Current State: 64:[12, 19, 71], Operations: ['56+15=71'] Exploring Operation: 19-12=7, Resulting Numbers: [71, 7] Generated Node #3: [71, 7] from Operation: 19-12=7 Current State: 64:[71, 7], Operations: ['56+15=71', '19-12=7'] Exploring Operation: 71-7=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[56, 15, 12, 19], Operations: [] Exploring Operation: 56+12=68, Resulting Numbers: [15, 19, 68] Generated Node #0,0: 64:[15, 19, 68] Operation: 56+12=68 Moving to Node #0,0 Current State: 64:[15, 19, 68], Operations: ['56+12=68'] Exploring Operation: 19-15=4, Resulting Numbers: [68, 4] Generated Node #0,0,0: 64:[68, 4] Operation: 19-15=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[68, 4], Operations: ['56+12=68', '19-15=4'] Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[56, 15, 12, 19], Operations: [] Exploring Operation: 56+12=68, Resulting Numbers: [15, 19, 68] Generated Node #0,0: 64:[15, 19, 68] Operation: 56+12=68 Moving to Node #0,0 Current State: 64:[15, 19, 68], Operations: ['56+12=68'] Exploring Operation: 19-15=4, Resulting Numbers: [68, 4] Generated Node #0,0,0: 64:[68, 4] Operation: 19-15=4 Moving to Node #0,0,0 Current State: 64:[68, 4], Operations: ['56+12=68', '19-15=4'] Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 53, 53, 67, 34 ]
100
[ "53/53=1", "67+34=101", "101-1=100" ]
Current State: 100:[53, 53, 67, 34], Operations: [] Exploring Operation: 53/53=1, Resulting Numbers: [67, 34, 1] Generated Node #2: [67, 34, 1] from Operation: 53/53=1 Current State: 100:[67, 34, 1], Operations: ['53/53=1'] Exploring Operation: 67+34=101, Resulting Numbers: [1, 101] Generated Node #3: [1, 101] from Operation: 67+34=101 Current State: 100:[1, 101], Operations: ['53/53=1', '67+34=101'] Exploring Operation: 101-1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[53, 53, 67, 34], Operations: [] Exploring Operation: 67+34=101, Resulting Numbers: [53, 53, 101] Generated Node #0,0: 100:[53, 53, 101] Operation: 67+34=101 Exploring Operation: 67-53=14, Resulting Numbers: [53, 34, 14] Generated Node #0,1: 100:[53, 34, 14] Operation: 67-53=14 Exploring Operation: 67-53=14, Resulting Numbers: [53, 34, 14] Generated Node #0,2: 100:[53, 34, 14] Operation: 67-53=14 Exploring Operation: 53-34=19, Resulting Numbers: [53, 67, 19] Generated Node #0,3: 100:[53, 67, 19] Operation: 53-34=19 Exploring Operation: 67-34=33, Resulting Numbers: [53, 53, 33] Generated Node #0,4: 100:[53, 53, 33] Operation: 67-34=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[53, 53, 101], Operations: ['67+34=101'] Exploring Operation: 101-53=48, Resulting Numbers: [53, 48] Generated Node #0,0,0: 100:[53, 48] Operation: 101-53=48 Exploring Operation: 53-53=0, Resulting Numbers: [101, 0] Generated Node #0,0,1: 100:[101, 0] Operation: 53-53=0 Exploring Operation: 101-53=48, Resulting Numbers: [53, 48] Generated Node #0,0,2: 100:[53, 48] Operation: 101-53=48 Exploring Operation: 53/53=1, Resulting Numbers: [101, 1] Generated Node #0,0,3: 100:[101, 1] Operation: 53/53=1 Exploring Operation: 53+53=106, Resulting Numbers: [101, 106] Generated Node #0,0,4: 100:[101, 106] Operation: 53+53=106 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 100:[101, 1], Operations: ['67+34=101', '53/53=1'] Exploring Operation: 101+1=102, Resulting Numbers: [102] 102,100 unequal: No Solution Exploring Operation: 101*1=101, Resulting Numbers: [101] 101,100 unequal: No Solution Exploring Operation: 101/1=101, Resulting Numbers: [101] 101,100 unequal: No Solution Exploring Operation: 101-1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[53, 53, 67, 34], Operations: [] Exploring Operation: 67+34=101, Resulting Numbers: [53, 53, 101] Generated Node #0,0: 100:[53, 53, 101] Operation: 67+34=101 Moving to Node #0,0 Current State: 100:[53, 53, 101], Operations: ['67+34=101'] Exploring Operation: 53/53=1, Resulting Numbers: [101, 1] Generated Node #0,0,3: 100:[101, 1] Operation: 53/53=1 Moving to Node #0,0,3 Current State: 100:[101, 1], Operations: ['67+34=101', '53/53=1'] Exploring Operation: 101-1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 63, 46, 45, 89 ]
25
[ "63+46=109", "45+89=134", "134-109=25" ]
Current State: 25:[63, 46, 45, 89], Operations: [] Exploring Operation: 63+46=109, Resulting Numbers: [45, 89, 109] Generated Node #2: [45, 89, 109] from Operation: 63+46=109 Current State: 25:[45, 89, 109], Operations: ['63+46=109'] Exploring Operation: 45+89=134, Resulting Numbers: [109, 134] Generated Node #3: [109, 134] from Operation: 45+89=134 Current State: 25:[109, 134], Operations: ['63+46=109', '45+89=134'] Exploring Operation: 134-109=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[63, 46, 45, 89], Operations: [] Exploring Operation: 63-46=17, Resulting Numbers: [45, 89, 17] Generated Node #0,0: 25:[45, 89, 17] Operation: 63-46=17 Exploring Operation: 63-45=18, Resulting Numbers: [46, 89, 18] Generated Node #0,1: 25:[46, 89, 18] Operation: 63-45=18 Exploring Operation: 89-45=44, Resulting Numbers: [63, 46, 44] Generated Node #0,2: 25:[63, 46, 44] Operation: 89-45=44 Exploring Operation: 89-46=43, Resulting Numbers: [63, 45, 43] Generated Node #0,3: 25:[63, 45, 43] Operation: 89-46=43 Exploring Operation: 89-63=26, Resulting Numbers: [46, 45, 26] Generated Node #0,4: 25:[46, 45, 26] Operation: 89-63=26 Moving to Node #0,4 Current State: 25:[46, 45, 26], Operations: ['89-63=26'] Exploring Operation: 46-26=20, Resulting Numbers: [45, 20] Generated Node #0,4,0: 25:[45, 20] Operation: 46-26=20 Exploring Operation: 45-26=19, Resulting Numbers: [46, 19] Generated Node #0,4,1: 25:[46, 19] Operation: 45-26=19 Exploring Operation: 46-45=1, Resulting Numbers: [26, 1] Generated Node #0,4,2: 25:[26, 1] Operation: 46-45=1 Exploring Operation: 46+45=91, Resulting Numbers: [26, 91] Generated Node #0,4,3: 25:[26, 91] Operation: 46+45=91 Exploring Operation: 46+26=72, Resulting Numbers: [45, 72] Generated Node #0,4,4: 25:[45, 72] Operation: 46+26=72 Moving to Node #0,3 Current State: 25:[63, 45, 43], Operations: ['89-46=43'] Exploring Operation: 63-43=20, Resulting Numbers: [45, 20] Generated Node #0,3,0: 25:[45, 20] Operation: 63-43=20 Exploring Operation: 63+43=106, Resulting Numbers: [45, 106] Generated Node #0,3,1: 25:[45, 106] Operation: 63+43=106 Exploring Operation: 45-43=2, Resulting Numbers: [63, 2] Generated Node #0,3,2: 25:[63, 2] Operation: 45-43=2 Exploring Operation: 63-45=18, Resulting Numbers: [43, 18] Generated Node #0,3,3: 25:[43, 18] Operation: 63-45=18 Exploring Operation: 63+45=108, Resulting Numbers: [43, 108] Generated Node #0,3,4: 25:[43, 108] Operation: 63+45=108 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 25:[45, 20], Operations: ['89-46=43', '63-43=20'] Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[63, 46, 45, 89], Operations: [] Exploring Operation: 89-46=43, Resulting Numbers: [63, 45, 43] Generated Node #0,3: 25:[63, 45, 43] Operation: 89-46=43 Moving to Node #0,3 Current State: 25:[63, 45, 43], Operations: ['89-46=43'] Exploring Operation: 63-43=20, Resulting Numbers: [45, 20] Generated Node #0,3,0: 25:[45, 20] Operation: 63-43=20 Moving to Node #0,3,0 Current State: 25:[45, 20], Operations: ['89-46=43', '63-43=20'] Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 15, 48, 39, 57 ]
78
[ "48-39=9", "15*9=135", "135-57=78" ]
Current State: 78:[15, 48, 39, 57], Operations: [] Exploring Operation: 48-39=9, Resulting Numbers: [15, 57, 9] Generated Node #2: [15, 57, 9] from Operation: 48-39=9 Current State: 78:[15, 57, 9], Operations: ['48-39=9'] Exploring Operation: 15*9=135, Resulting Numbers: [57, 135] Generated Node #3: [57, 135] from Operation: 15*9=135 Current State: 78:[57, 135], Operations: ['48-39=9', '15*9=135'] Exploring Operation: 135-57=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[15, 48, 39, 57], Operations: [] Exploring Operation: 57-15=42, Resulting Numbers: [48, 39, 42] Generated Node #0,0: 78:[48, 39, 42] Operation: 57-15=42 Exploring Operation: 57-48=9, Resulting Numbers: [15, 39, 9] Generated Node #0,1: 78:[15, 39, 9] Operation: 57-48=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[15, 39, 9], Operations: ['57-48=9'] Exploring Operation: 15-9=6, Resulting Numbers: [39, 6] Generated Node #0,1,0: 78:[39, 6] Operation: 15-9=6 Exploring Operation: 15+9=24, Resulting Numbers: [39, 24] Generated Node #0,1,1: 78:[39, 24] Operation: 15+9=24 Moving to Node #0,1,0 Current State: 78:[39, 6], Operations: ['57-48=9', '15-9=6'] Exploring Operation: 39+6=45, Resulting Numbers: [45] 45,78 unequal: No Solution Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[39, 24], Operations: ['57-48=9', '15+9=24'] Exploring Operation: 39+24=63, Resulting Numbers: [63] 63,78 unequal: No Solution Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[48, 39, 42], Operations: ['57-15=42'] Exploring Operation: 48-42=6, Resulting Numbers: [39, 6] Generated Node #0,0,0: 78:[39, 6] Operation: 48-42=6 Exploring Operation: 48-39=9, Resulting Numbers: [42, 9] Generated Node #0,0,1: 78:[42, 9] Operation: 48-39=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 78:[39, 6], Operations: ['57-15=42', '48-42=6'] Exploring Operation: 39+6=45, Resulting Numbers: [45] 45,78 unequal: No Solution Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 78:[42, 9], Operations: ['57-15=42', '48-39=9'] Exploring Operation: 42+9=51, Resulting Numbers: [51] 51,78 unequal: No Solution Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,78 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 No solution found.
0
hs_2
mult_heuristic
[ 80, 36, 51, 20 ]
83
[ "80/20=4", "36+51=87", "87-4=83" ]
Current State: 83:[80, 36, 51, 20], Operations: [] Exploring Operation: 80/20=4, Resulting Numbers: [36, 51, 4] Generated Node #2: [36, 51, 4] from Operation: 80/20=4 Current State: 83:[36, 51, 4], Operations: ['80/20=4'] Exploring Operation: 36+51=87, Resulting Numbers: [4, 87] Generated Node #3: [4, 87] from Operation: 36+51=87 Current State: 83:[4, 87], Operations: ['80/20=4', '36+51=87'] Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[80, 36, 51, 20], Operations: [] Exploring Operation: 51+20=71, Resulting Numbers: [80, 36, 71] Generated Node #0,0: 83:[80, 36, 71] Operation: 51+20=71 Exploring Operation: 36+20=56, Resulting Numbers: [80, 51, 56] Generated Node #0,1: 83:[80, 51, 56] Operation: 36+20=56 Exploring Operation: 36+51=87, Resulting Numbers: [80, 20, 87] Generated Node #0,2: 83:[80, 20, 87] Operation: 36+51=87 Moving to Node #0,0 Current State: 83:[80, 36, 71], Operations: ['51+20=71'] Exploring Operation: 80-36=44, Resulting Numbers: [71, 44] Generated Node #0,0,0: 83:[71, 44] Operation: 80-36=44 Exploring Operation: 36+71=107, Resulting Numbers: [80, 107] Generated Node #0,0,1: 83:[80, 107] Operation: 36+71=107 Exploring Operation: 80+36=116, Resulting Numbers: [71, 116] Generated Node #0,0,2: 83:[71, 116] Operation: 80+36=116 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[80, 107], Operations: ['51+20=71', '36+71=107'] Exploring Operation: 80+107=187, Resulting Numbers: [187] 187,83 unequal: No Solution Exploring Operation: 107-80=27, Resulting Numbers: [27] 27,83 unequal: No Solution Exploring Operation: 80*107=8560, Resulting Numbers: [8560] 8560,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[71, 116], Operations: ['51+20=71', '80+36=116'] Exploring Operation: 116-71=45, Resulting Numbers: [45] 45,83 unequal: No Solution Exploring Operation: 71+116=187, Resulting Numbers: [187] 187,83 unequal: No Solution Exploring Operation: 71*116=8236, Resulting Numbers: [8236] 8236,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[71, 44], Operations: ['51+20=71', '80-36=44'] Exploring Operation: 71+44=115, Resulting Numbers: [115] 115,83 unequal: No Solution Exploring Operation: 71-44=27, Resulting Numbers: [27] 27,83 unequal: No Solution Exploring Operation: 71*44=3124, Resulting Numbers: [3124] 3124,83 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: 83:[80, 51, 56], Operations: ['36+20=56'] Exploring Operation: 80-51=29, Resulting Numbers: [56, 29] Generated Node #0,1,0: 83:[56, 29] Operation: 80-51=29 Exploring Operation: 51+56=107, Resulting Numbers: [80, 107] Generated Node #0,1,1: 83:[80, 107] Operation: 51+56=107 Exploring Operation: 80+51=131, Resulting Numbers: [56, 131] Generated Node #0,1,2: 83:[56, 131] Operation: 80+51=131 Moving to Node #0,2 Current State: 83:[80, 20, 87], Operations: ['36+51=87'] Exploring Operation: 80-20=60, Resulting Numbers: [87, 60] Generated Node #0,2,0: 83:[87, 60] Operation: 80-20=60 Exploring Operation: 87-20=67, Resulting Numbers: [80, 67] Generated Node #0,2,1: 83:[80, 67] Operation: 87-20=67 Exploring Operation: 80+20=100, Resulting Numbers: [87, 100] Generated Node #0,2,2: 83:[87, 100] Operation: 80+20=100 Moving to Node #0,2,1 Current State: 83:[80, 67], Operations: ['36+51=87', '87-20=67'] Exploring Operation: 80-67=13, Resulting Numbers: [13] 13,83 unequal: No Solution Exploring Operation: 80+67=147, Resulting Numbers: [147] 147,83 unequal: No Solution Exploring Operation: 80*67=5360, Resulting Numbers: [5360] 5360,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[87, 100], Operations: ['36+51=87', '80+20=100'] Exploring Operation: 87+100=187, Resulting Numbers: [187] 187,83 unequal: No Solution Exploring Operation: 100-87=13, Resulting Numbers: [13] 13,83 unequal: No Solution Exploring Operation: 87*100=8700, Resulting Numbers: [8700] 8700,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[87, 60], Operations: ['36+51=87', '80-20=60'] Exploring Operation: 87+60=147, Resulting Numbers: [147] 147,83 unequal: No Solution Exploring Operation: 87-60=27, Resulting Numbers: [27] 27,83 unequal: No Solution Exploring Operation: 87*60=5220, Resulting Numbers: [5220] 5220,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[80, 107], Operations: ['36+20=56', '51+56=107'] Exploring Operation: 80*107=8560, Resulting Numbers: [8560] 8560,83 unequal: No Solution Exploring Operation: 80+107=187, Resulting Numbers: [187] 187,83 unequal: No Solution Exploring Operation: 107-80=27, Resulting Numbers: [27] 27,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[56, 131], Operations: ['36+20=56', '80+51=131'] Exploring Operation: 56+131=187, Resulting Numbers: [187] 187,83 unequal: No Solution Exploring Operation: 131-56=75, Resulting Numbers: [75] 75,83 unequal: No Solution Exploring Operation: 56*131=7336, Resulting Numbers: [7336] 7336,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[56, 29], Operations: ['36+20=56', '80-51=29'] Exploring Operation: 56+29=85, Resulting Numbers: [85] 85,83 unequal: No Solution Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,83 unequal: No Solution Exploring Operation: 56*29=1624, Resulting Numbers: [1624] 1624,83 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 40, 60, 21, 50 ]
91
[ "60-40=20", "21+50=71", "20+71=91" ]
Current State: 91:[40, 60, 21, 50], Operations: [] Exploring Operation: 60-40=20, Resulting Numbers: [21, 50, 20] Generated Node #2: [21, 50, 20] from Operation: 60-40=20 Current State: 91:[21, 50, 20], Operations: ['60-40=20'] Exploring Operation: 21+50=71, Resulting Numbers: [20, 71] Generated Node #3: [20, 71] from Operation: 21+50=71 Current State: 91:[20, 71], Operations: ['60-40=20', '21+50=71'] Exploring Operation: 20+71=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[40, 60, 21, 50], Operations: [] Exploring Operation: 50-40=10, Resulting Numbers: [60, 21, 10] Generated Node #0,0: 91:[60, 21, 10] Operation: 50-40=10 Exploring Operation: 40+50=90, Resulting Numbers: [60, 21, 90] Generated Node #0,1: 91:[60, 21, 90] Operation: 40+50=90 Exploring Operation: 60-50=10, Resulting Numbers: [40, 21, 10] Generated Node #0,2: 91:[40, 21, 10] Operation: 60-50=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[40, 21, 10], Operations: ['60-50=10'] Exploring Operation: 40-21=19, Resulting Numbers: [10, 19] Generated Node #0,2,0: 91:[10, 19] Operation: 40-21=19 Exploring Operation: 40/10=4, Resulting Numbers: [21, 4] Generated Node #0,2,1: 91:[21, 4] Operation: 40/10=4 Exploring Operation: 40-10=30, Resulting Numbers: [21, 30] Generated Node #0,2,2: 91:[21, 30] Operation: 40-10=30 Moving to Node #0,2,0 Current State: 91:[10, 19], Operations: ['60-50=10', '40-21=19'] Exploring Operation: 10+19=29, Resulting Numbers: [29] 29,91 unequal: No Solution Exploring Operation: 10*19=190, Resulting Numbers: [190] 190,91 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[21, 4], Operations: ['60-50=10', '40/10=4'] Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,91 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,91 unequal: No Solution Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[21, 30], Operations: ['60-50=10', '40-10=30'] Exploring Operation: 21*30=630, Resulting Numbers: [630] 630,91 unequal: No Solution Exploring Operation: 30-21=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 21+30=51, Resulting Numbers: [51] 51,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[60, 21, 90], Operations: ['40+50=90'] Exploring Operation: 60+21=81, Resulting Numbers: [90, 81] Generated Node #0,1,0: 91:[90, 81] Operation: 60+21=81 Exploring Operation: 90-60=30, Resulting Numbers: [21, 30] Generated Node #0,1,1: 91:[21, 30] Operation: 90-60=30 Exploring Operation: 60-21=39, Resulting Numbers: [90, 39] Generated Node #0,1,2: 91:[90, 39] Operation: 60-21=39 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[90, 81], Operations: ['40+50=90', '60+21=81'] Exploring Operation: 90*81=7290, Resulting Numbers: [7290] 7290,91 unequal: No Solution Exploring Operation: 90-81=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 90+81=171, Resulting Numbers: [171] 171,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[21, 30], Operations: ['40+50=90', '90-60=30'] Exploring Operation: 21+30=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 30-21=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 21*30=630, Resulting Numbers: [630] 630,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 91:[90, 39], Operations: ['40+50=90', '60-21=39'] Exploring Operation: 90*39=3510, Resulting Numbers: [3510] 3510,91 unequal: No Solution Exploring Operation: 90-39=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 90+39=129, Resulting Numbers: [129] 129,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[60, 21, 10], Operations: ['50-40=10'] Exploring Operation: 60-21=39, Resulting Numbers: [10, 39] Generated Node #0,0,0: 91:[10, 39] Operation: 60-21=39 Exploring Operation: 60+21=81, Resulting Numbers: [10, 81] Generated Node #0,0,1: 91:[10, 81] Operation: 60+21=81 Exploring Operation: 60/10=6, Resulting Numbers: [21, 6] Generated Node #0,0,2: 91:[21, 6] Operation: 60/10=6 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 91:[21, 6], Operations: ['50-40=10', '60/10=6'] Exploring Operation: 21*6=126, Resulting Numbers: [126] 126,91 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,91 unequal: No Solution Exploring Operation: 21+6=27, Resulting Numbers: [27] 27,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[10, 81], Operations: ['50-40=10', '60+21=81'] Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,91 unequal: No Solution Exploring Operation: 10*81=810, Resulting Numbers: [810] 810,91 unequal: No Solution Exploring Operation: 10+81=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[40, 60, 21, 50], Operations: [] Exploring Operation: 50-40=10, Resulting Numbers: [60, 21, 10] Generated Node #0,0: 91:[60, 21, 10] Operation: 50-40=10 Moving to Node #0,0 Current State: 91:[60, 21, 10], Operations: ['50-40=10'] Exploring Operation: 60+21=81, Resulting Numbers: [10, 81] Generated Node #0,0,1: 91:[10, 81] Operation: 60+21=81 Moving to Node #0,0,1 Current State: 91:[10, 81], Operations: ['50-40=10', '60+21=81'] Exploring Operation: 10+81=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_3
mult_heuristic
[ 20, 11, 60, 20 ]
13
[ "60-20=40", "40/20=2", "11+2=13" ]
Current State: 13:[20, 11, 60, 20], Operations: [] Exploring Operation: 60-20=40, Resulting Numbers: [11, 40] Generated Node #2: [11, 40] from Operation: 60-20=40 Current State: 13:[11, 40], Operations: ['60-20=40'] Exploring Operation: 40/20=2, Resulting Numbers: [11, 2] Generated Node #3: [11, 2] from Operation: 40/20=2 Current State: 13:[11, 2], Operations: ['60-20=40', '40/20=2'] Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[20, 11, 60, 20], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [20, 11, 3] Generated Node #0,0: 13:[20, 11, 3] Operation: 60/20=3 Exploring Operation: 60/20=3, Resulting Numbers: [11, 20, 3] Generated Node #0,1: 13:[11, 20, 3] Operation: 60/20=3 Exploring Operation: 60-11=49, Resulting Numbers: [20, 20, 49] Generated Node #0,2: 13:[20, 20, 49] Operation: 60-11=49 Exploring Operation: 60-20=40, Resulting Numbers: [20, 11, 40] Generated Node #0,3: 13:[20, 11, 40] Operation: 60-20=40 Exploring Operation: 60-20=40, Resulting Numbers: [11, 20, 40] Generated Node #0,4: 13:[11, 20, 40] Operation: 60-20=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[20, 11, 3], Operations: ['60/20=3'] Exploring Operation: 20-3=17, Resulting Numbers: [11, 17] Generated Node #0,0,0: 13:[11, 17] Operation: 20-3=17 Exploring Operation: 20-11=9, Resulting Numbers: [3, 9] Generated Node #0,0,1: 13:[3, 9] Operation: 20-11=9 Exploring Operation: 11+3=14, Resulting Numbers: [20, 14] Generated Node #0,0,2: 13:[20, 14] Operation: 11+3=14 Exploring Operation: 11-3=8, Resulting Numbers: [20, 8] Generated Node #0,0,3: 13:[20, 8] Operation: 11-3=8 Exploring Operation: 20+3=23, Resulting Numbers: [11, 23] Generated Node #0,0,4: 13:[11, 23] Operation: 20+3=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[11, 17], Operations: ['60/20=3', '20-3=17'] Exploring Operation: 11+17=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 11*17=187, Resulting Numbers: [187] 187,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 13:[20, 14], Operations: ['60/20=3', '11+3=14'] Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,13 unequal: No Solution Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,13 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 13:[20, 8], Operations: ['60/20=3', '11-3=8'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,13 unequal: No Solution Exploring Operation: 20*8=160, Resulting Numbers: [160] 160,13 unequal: No Solution Exploring Operation: 20+8=28, Resulting Numbers: [28] 28,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 13:[11, 23], Operations: ['60/20=3', '20+3=23'] Exploring Operation: 11*23=253, Resulting Numbers: [253] 253,13 unequal: No Solution Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,13 unequal: No Solution Exploring Operation: 11+23=34, Resulting Numbers: [34] 34,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 13:[3, 9], Operations: ['60/20=3', '20-11=9'] Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,13 unequal: No Solution Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[11, 20, 3], Operations: ['60/20=3'] Exploring Operation: 20-11=9, Resulting Numbers: [3, 9] Generated Node #0,1,0: 13:[3, 9] Operation: 20-11=9 Exploring Operation: 20+3=23, Resulting Numbers: [11, 23] Generated Node #0,1,1: 13:[11, 23] Operation: 20+3=23 Exploring Operation: 20-3=17, Resulting Numbers: [11, 17] Generated Node #0,1,2: 13:[11, 17] Operation: 20-3=17 Exploring Operation: 11-3=8, Resulting Numbers: [20, 8] Generated Node #0,1,3: 13:[20, 8] Operation: 11-3=8 Exploring Operation: 11+3=14, Resulting Numbers: [20, 14] Generated Node #0,1,4: 13:[20, 14] Operation: 11+3=14 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 13:[11, 17], Operations: ['60/20=3', '20-3=17'] Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 11+17=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 11*17=187, Resulting Numbers: [187] 187,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 13:[20, 14], Operations: ['60/20=3', '11+3=14'] Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,13 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,13 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[11, 23], Operations: ['60/20=3', '20+3=23'] Exploring Operation: 11*23=253, Resulting Numbers: [253] 253,13 unequal: No Solution Exploring Operation: 11+23=34, Resulting Numbers: [34] 34,13 unequal: No Solution Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 13:[20, 8], Operations: ['60/20=3', '11-3=8'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,13 unequal: No Solution Exploring Operation: 20+8=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 20*8=160, Resulting Numbers: [160] 160,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 13:[3, 9], Operations: ['60/20=3', '20-11=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,13 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 13:[20, 11, 40], Operations: ['60-20=40'] Exploring Operation: 20+11=31, Resulting Numbers: [40, 31] Generated Node #0,3,0: 13:[40, 31] Operation: 20+11=31 Exploring Operation: 40-11=29, Resulting Numbers: [20, 29] Generated Node #0,3,1: 13:[20, 29] Operation: 40-11=29 Exploring Operation: 20-11=9, Resulting Numbers: [40, 9] Generated Node #0,3,2: 13:[40, 9] Operation: 20-11=9 Exploring Operation: 40-20=20, Resulting Numbers: [11, 20] Generated Node #0,3,3: 13:[11, 20] Operation: 40-20=20 Exploring Operation: 40/20=2, Resulting Numbers: [11, 2] Generated Node #0,3,4: 13:[11, 2] Operation: 40/20=2 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 13:[11, 20], Operations: ['60-20=40', '40-20=20'] Exploring Operation: 11*20=220, Resulting Numbers: [220] 220,13 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 11+20=31, Resulting Numbers: [31] 31,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 13:[11, 2], Operations: ['60-20=40', '40/20=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,13 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[20, 11, 60, 20], Operations: [] Exploring Operation: 60-20=40, Resulting Numbers: [20, 11, 40] Generated Node #0,3: 13:[20, 11, 40] Operation: 60-20=40 Moving to Node #0,3 Current State: 13:[20, 11, 40], Operations: ['60-20=40'] Exploring Operation: 40/20=2, Resulting Numbers: [11, 2] Generated Node #0,3,4: 13:[11, 2] Operation: 40/20=2 Moving to Node #0,3,4 Current State: 13:[11, 2], Operations: ['60-20=40', '40/20=2'] Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.946181
hs_5
sum_heuristic
[ 39, 98, 78, 32 ]
34
[ "78/39=2", "32*2=64", "98-64=34" ]
Current State: 34:[39, 98, 78, 32], Operations: [] Exploring Operation: 78/39=2, Resulting Numbers: [98, 32, 2] Generated Node #2: [98, 32, 2] from Operation: 78/39=2 Current State: 34:[98, 32, 2], Operations: ['78/39=2'] Exploring Operation: 32*2=64, Resulting Numbers: [98, 64] Generated Node #3: [98, 64] from Operation: 32*2=64 Current State: 34:[98, 64], Operations: ['78/39=2', '32*2=64'] Exploring Operation: 98-64=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[39, 98, 78, 32], Operations: [] Exploring Operation: 78/39=2, Resulting Numbers: [98, 32, 2] Generated Node #0,0: 34:[98, 32, 2] Operation: 78/39=2 Exploring Operation: 98-39=59, Resulting Numbers: [78, 32, 59] Generated Node #0,1: 34:[78, 32, 59] Operation: 98-39=59 Exploring Operation: 98-78=20, Resulting Numbers: [39, 32, 20] Generated Node #0,2: 34:[39, 32, 20] Operation: 98-78=20 Moving to Node #0,2 Current State: 34:[39, 32, 20], Operations: ['98-78=20'] Exploring Operation: 39-20=19, Resulting Numbers: [32, 19] Generated Node #0,2,0: 34:[32, 19] Operation: 39-20=19 Exploring Operation: 39-32=7, Resulting Numbers: [20, 7] Generated Node #0,2,1: 34:[20, 7] Operation: 39-32=7 Exploring Operation: 32-20=12, Resulting Numbers: [39, 12] Generated Node #0,2,2: 34:[39, 12] Operation: 32-20=12 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 34:[32, 19], Operations: ['98-78=20', '39-20=19'] Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,34 unequal: No Solution Exploring Operation: 32*19=608, Resulting Numbers: [608] 608,34 unequal: No Solution Exploring Operation: 32+19=51, Resulting Numbers: [51] 51,34 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 #0,2,1 Current State: 34:[20, 7], Operations: ['98-78=20', '39-32=7'] Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 20*7=140, Resulting Numbers: [140] 140,34 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,34 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:[39, 12], Operations: ['98-78=20', '32-20=12'] Exploring Operation: 39-12=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 39+12=51, Resulting Numbers: [51] 51,34 unequal: No Solution Exploring Operation: 39*12=468, Resulting Numbers: [468] 468,34 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:[98, 32, 2], Operations: ['78/39=2'] Exploring Operation: 98/2=49, Resulting Numbers: [32, 49] Generated Node #0,0,0: 34:[32, 49] Operation: 98/2=49 Exploring Operation: 98-32=66, Resulting Numbers: [2, 66] Generated Node #0,0,1: 34:[2, 66] Operation: 98-32=66 Exploring Operation: 98-2=96, Resulting Numbers: [32, 96] Generated Node #0,0,2: 34:[32, 96] Operation: 98-2=96 Moving to Node #0,1 Current State: 34:[78, 32, 59], Operations: ['98-39=59'] Exploring Operation: 78-59=19, Resulting Numbers: [32, 19] Generated Node #0,1,0: 34:[32, 19] Operation: 78-59=19 Exploring Operation: 78-32=46, Resulting Numbers: [59, 46] Generated Node #0,1,1: 34:[59, 46] Operation: 78-32=46 Exploring Operation: 59-32=27, Resulting Numbers: [78, 27] Generated Node #0,1,2: 34:[78, 27] Operation: 59-32=27 Moving to Node #0,1,0 Current State: 34:[32, 19], Operations: ['98-39=59', '78-59=19'] Exploring Operation: 32*19=608, Resulting Numbers: [608] 608,34 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,34 unequal: No Solution Exploring Operation: 32+19=51, Resulting Numbers: [51] 51,34 unequal: No Solution Moving to Node #0,0,0 Current State: 34:[32, 49], Operations: ['78/39=2', '98/2=49'] Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,34 unequal: No Solution Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,34 unequal: No Solution Moving to Node #0,0,1 Current State: 34:[2, 66], Operations: ['78/39=2', '98-32=66'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,34 unequal: No Solution Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[59, 46], Operations: ['98-39=59', '78-32=46'] Exploring Operation: 59+46=105, Resulting Numbers: [105] 105,34 unequal: No Solution Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,34 unequal: No Solution Exploring Operation: 59*46=2714, Resulting Numbers: [2714] 2714,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[78, 27], Operations: ['98-39=59', '59-32=27'] Exploring Operation: 78+27=105, Resulting Numbers: [105] 105,34 unequal: No Solution Exploring Operation: 78*27=2106, Resulting Numbers: [2106] 2106,34 unequal: No Solution Exploring Operation: 78-27=51, Resulting Numbers: [51] 51,34 unequal: No Solution Moving to Node #0,0,2 Current State: 34:[32, 96], Operations: ['78/39=2', '98-2=96'] Exploring Operation: 96/32=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 96-32=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 32+96=128, Resulting Numbers: [128] 128,34 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 56, 80, 1, 27 ]
52
[ "80-56=24", "1+27=28", "24+28=52" ]
Current State: 52:[56, 80, 1, 27], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [1, 27, 24] Generated Node #2: [1, 27, 24] from Operation: 80-56=24 Current State: 52:[1, 27, 24], Operations: ['80-56=24'] Exploring Operation: 1+27=28, Resulting Numbers: [24, 28] Generated Node #3: [24, 28] from Operation: 1+27=28 Current State: 52:[24, 28], Operations: ['80-56=24', '1+27=28'] Exploring Operation: 24+28=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[56, 80, 1, 27], Operations: [] Exploring Operation: 56-27=29, Resulting Numbers: [80, 1, 29] Generated Node #0,0: 52:[80, 1, 29] Operation: 56-27=29 Exploring Operation: 56-1=55, Resulting Numbers: [80, 27, 55] Generated Node #0,1: 52:[80, 27, 55] Operation: 56-1=55 Exploring Operation: 80-56=24, Resulting Numbers: [1, 27, 24] Generated Node #0,2: 52:[1, 27, 24] Operation: 80-56=24 Exploring Operation: 80-27=53, Resulting Numbers: [56, 1, 53] Generated Node #0,3: 52:[56, 1, 53] Operation: 80-27=53 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[1, 27, 24], Operations: ['80-56=24'] Exploring Operation: 1+24=25, Resulting Numbers: [27, 25] Generated Node #0,2,0: 52:[27, 25] Operation: 1+24=25 Exploring Operation: 27+24=51, Resulting Numbers: [1, 51] Generated Node #0,2,1: 52:[1, 51] Operation: 27+24=51 Exploring Operation: 27-1=26, Resulting Numbers: [24, 26] Generated Node #0,2,2: 52:[24, 26] Operation: 27-1=26 Exploring Operation: 27-24=3, Resulting Numbers: [1, 3] Generated Node #0,2,3: 52:[1, 3] Operation: 27-24=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 52:[27, 25], Operations: ['80-56=24', '1+24=25'] Exploring Operation: 27*25=675, Resulting Numbers: [675] 675,52 unequal: No Solution Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 27+25=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[56, 80, 1, 27], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [1, 27, 24] Generated Node #0,2: 52:[1, 27, 24] Operation: 80-56=24 Moving to Node #0,2 Current State: 52:[1, 27, 24], Operations: ['80-56=24'] Exploring Operation: 1+24=25, Resulting Numbers: [27, 25] Generated Node #0,2,0: 52:[27, 25] Operation: 1+24=25 Moving to Node #0,2,0 Current State: 52:[27, 25], Operations: ['80-56=24', '1+24=25'] Exploring Operation: 27+25=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 30, 90, 70, 32 ]
35
[ "90/30=3", "70-32=38", "38-3=35" ]
Current State: 35:[30, 90, 70, 32], Operations: [] Exploring Operation: 90/30=3, Resulting Numbers: [70, 32, 3] Generated Node #2: [70, 32, 3] from Operation: 90/30=3 Current State: 35:[70, 32, 3], Operations: ['90/30=3'] Exploring Operation: 70-32=38, Resulting Numbers: [3, 38] Generated Node #3: [3, 38] from Operation: 70-32=38 Current State: 35:[3, 38], Operations: ['90/30=3', '70-32=38'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[30, 90, 70, 32], Operations: [] Exploring Operation: 90-70=20, Resulting Numbers: [30, 32, 20] Generated Node #0,0: 35:[30, 32, 20] Operation: 90-70=20 Exploring Operation: 90/30=3, Resulting Numbers: [70, 32, 3] Generated Node #0,1: 35:[70, 32, 3] Operation: 90/30=3 Moving to Node #0,0 Current State: 35:[30, 32, 20], Operations: ['90-70=20'] Exploring Operation: 30-20=10, Resulting Numbers: [32, 10] Generated Node #0,0,0: 35:[32, 10] Operation: 30-20=10 Exploring Operation: 32-20=12, Resulting Numbers: [30, 12] Generated Node #0,0,1: 35:[30, 12] Operation: 32-20=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[32, 10], Operations: ['90-70=20', '30-20=10'] Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,35 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 35:[30, 12], Operations: ['90-70=20', '32-20=12'] Exploring Operation: 30+12=42, Resulting Numbers: [42] 42,35 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 35:[70, 32, 3], Operations: ['90/30=3'] Exploring Operation: 70-32=38, Resulting Numbers: [3, 38] Generated Node #0,1,0: 35:[3, 38] Operation: 70-32=38 Exploring Operation: 70-3=67, Resulting Numbers: [32, 67] Generated Node #0,1,1: 35:[32, 67] Operation: 70-3=67 Moving to Node #0,1,0 Current State: 35:[3, 38], Operations: ['90/30=3', '70-32=38'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[30, 90, 70, 32], Operations: [] Exploring Operation: 90/30=3, Resulting Numbers: [70, 32, 3] Generated Node #0,1: 35:[70, 32, 3] Operation: 90/30=3 Moving to Node #0,1 Current State: 35:[70, 32, 3], Operations: ['90/30=3'] Exploring Operation: 70-32=38, Resulting Numbers: [3, 38] Generated Node #0,1,0: 35:[3, 38] Operation: 70-32=38 Moving to Node #0,1,0 Current State: 35:[3, 38], Operations: ['90/30=3', '70-32=38'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 33, 43, 68, 21 ]
29
[ "33+43=76", "68-21=47", "76-47=29" ]
Current State: 29:[33, 43, 68, 21], Operations: [] Exploring Operation: 33+43=76, Resulting Numbers: [68, 21, 76] Generated Node #2: [68, 21, 76] from Operation: 33+43=76 Current State: 29:[68, 21, 76], Operations: ['33+43=76'] Exploring Operation: 68-21=47, Resulting Numbers: [76, 47] Generated Node #3: [76, 47] from Operation: 68-21=47 Current State: 29:[76, 47], Operations: ['33+43=76', '68-21=47'] Exploring Operation: 76-47=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[33, 43, 68, 21], Operations: [] Exploring Operation: 68-33=35, Resulting Numbers: [43, 21, 35] Generated Node #0,0: 29:[43, 21, 35] Operation: 68-33=35 Exploring Operation: 68-43=25, Resulting Numbers: [33, 21, 25] Generated Node #0,1: 29:[33, 21, 25] Operation: 68-43=25 Moving to Node #0,1 Current State: 29:[33, 21, 25], Operations: ['68-43=25'] Exploring Operation: 21+25=46, Resulting Numbers: [33, 46] Generated Node #0,1,0: 29:[33, 46] Operation: 21+25=46 Exploring Operation: 33-21=12, Resulting Numbers: [25, 12] Generated Node #0,1,1: 29:[25, 12] Operation: 33-21=12 Moving to Node #0,0 Current State: 29:[43, 21, 35], Operations: ['68-33=35'] Exploring Operation: 43-21=22, Resulting Numbers: [35, 22] Generated Node #0,0,0: 29:[35, 22] Operation: 43-21=22 Exploring Operation: 43-35=8, Resulting Numbers: [21, 8] Generated Node #0,0,1: 29:[21, 8] Operation: 43-35=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[35, 22], Operations: ['68-33=35', '43-21=22'] Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 29:[21, 8], Operations: ['68-33=35', '43-35=8'] Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[33, 43, 68, 21], Operations: [] Exploring Operation: 68-33=35, Resulting Numbers: [43, 21, 35] Generated Node #0,0: 29:[43, 21, 35] Operation: 68-33=35 Moving to Node #0,0 Current State: 29:[43, 21, 35], Operations: ['68-33=35'] Exploring Operation: 43-35=8, Resulting Numbers: [21, 8] Generated Node #0,0,1: 29:[21, 8] Operation: 43-35=8 Moving to Node #0,0,1 Current State: 29:[21, 8], Operations: ['68-33=35', '43-35=8'] Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_2
mult_heuristic
[ 11, 77, 40, 9 ]
17
[ "77-11=66", "40+9=49", "66-49=17" ]
Current State: 17:[11, 77, 40, 9], Operations: [] Exploring Operation: 77-11=66, Resulting Numbers: [40, 9, 66] Generated Node #2: [40, 9, 66] from Operation: 77-11=66 Current State: 17:[40, 9, 66], Operations: ['77-11=66'] Exploring Operation: 40+9=49, Resulting Numbers: [66, 49] Generated Node #3: [66, 49] from Operation: 40+9=49 Current State: 17:[66, 49], Operations: ['77-11=66', '40+9=49'] Exploring Operation: 66-49=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[11, 77, 40, 9], Operations: [] Exploring Operation: 77-11=66, Resulting Numbers: [40, 9, 66] Generated Node #0,0: 17:[40, 9, 66] Operation: 77-11=66 Exploring Operation: 77/11=7, Resulting Numbers: [40, 9, 7] Generated Node #0,1: 17:[40, 9, 7] Operation: 77/11=7 Exploring Operation: 40-11=29, Resulting Numbers: [77, 9, 29] Generated Node #0,2: 17:[77, 9, 29] Operation: 40-11=29 Exploring Operation: 77-40=37, Resulting Numbers: [11, 9, 37] Generated Node #0,3: 17:[11, 9, 37] Operation: 77-40=37 Start Sub Search at level 1: Moving to Node #0,3 Current State: 17:[11, 9, 37], Operations: ['77-40=37'] Exploring Operation: 11-9=2, Resulting Numbers: [37, 2] Generated Node #0,3,0: 17:[37, 2] Operation: 11-9=2 Exploring Operation: 37-9=28, Resulting Numbers: [11, 28] Generated Node #0,3,1: 17:[11, 28] Operation: 37-9=28 Exploring Operation: 37-11=26, Resulting Numbers: [9, 26] Generated Node #0,3,2: 17:[9, 26] Operation: 37-11=26 Exploring Operation: 11+9=20, Resulting Numbers: [37, 20] Generated Node #0,3,3: 17:[37, 20] Operation: 11+9=20 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 17:[11, 28], Operations: ['77-40=37', '37-9=28'] Exploring Operation: 11+28=39, Resulting Numbers: [39] 39,17 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[11, 77, 40, 9], Operations: [] Exploring Operation: 77-40=37, Resulting Numbers: [11, 9, 37] Generated Node #0,3: 17:[11, 9, 37] Operation: 77-40=37 Moving to Node #0,3 Current State: 17:[11, 9, 37], Operations: ['77-40=37'] Exploring Operation: 37-9=28, Resulting Numbers: [11, 28] Generated Node #0,3,1: 17:[11, 28] Operation: 37-9=28 Moving to Node #0,3,1 Current State: 17:[11, 28], Operations: ['77-40=37', '37-9=28'] Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 41, 70, 57, 82 ]
83
[ "82/41=2", "70*2=140", "140-57=83" ]
Current State: 83:[41, 70, 57, 82], Operations: [] Exploring Operation: 82/41=2, Resulting Numbers: [70, 57, 2] Generated Node #2: [70, 57, 2] from Operation: 82/41=2 Current State: 83:[70, 57, 2], Operations: ['82/41=2'] Exploring Operation: 70*2=140, Resulting Numbers: [57, 140] Generated Node #3: [57, 140] from Operation: 70*2=140 Current State: 83:[57, 140], Operations: ['82/41=2', '70*2=140'] Exploring Operation: 140-57=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[41, 70, 57, 82], Operations: [] Exploring Operation: 41+70=111, Resulting Numbers: [57, 82, 111] Generated Node #0,0: 83:[57, 82, 111] Operation: 41+70=111 Exploring Operation: 41+82=123, Resulting Numbers: [70, 57, 123] Generated Node #0,1: 83:[70, 57, 123] Operation: 41+82=123 Exploring Operation: 41+57=98, Resulting Numbers: [70, 82, 98] Generated Node #0,2: 83:[70, 82, 98] Operation: 41+57=98 Moving to Node #0,2 Current State: 83:[70, 82, 98], Operations: ['41+57=98'] Exploring Operation: 98-70=28, Resulting Numbers: [82, 28] Generated Node #0,2,0: 83:[82, 28] Operation: 98-70=28 Exploring Operation: 98-82=16, Resulting Numbers: [70, 16] Generated Node #0,2,1: 83:[70, 16] Operation: 98-82=16 Exploring Operation: 70+82=152, Resulting Numbers: [98, 152] Generated Node #0,2,2: 83:[98, 152] Operation: 70+82=152 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 83:[82, 28], Operations: ['41+57=98', '98-70=28'] Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,83 unequal: No Solution Exploring Operation: 82*28=2296, Resulting Numbers: [2296] 2296,83 unequal: No Solution Exploring Operation: 82+28=110, Resulting Numbers: [110] 110,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 83:[70, 16], Operations: ['41+57=98', '98-82=16'] Exploring Operation: 70*16=1120, Resulting Numbers: [1120] 1120,83 unequal: No Solution Exploring Operation: 70-16=54, Resulting Numbers: [54] 54,83 unequal: No Solution Exploring Operation: 70+16=86, Resulting Numbers: [86] 86,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 83:[98, 152], Operations: ['41+57=98', '70+82=152'] Exploring Operation: 98+152=250, Resulting Numbers: [250] 250,83 unequal: No Solution Exploring Operation: 152-98=54, Resulting Numbers: [54] 54,83 unequal: No Solution Exploring Operation: 98*152=14896, Resulting Numbers: [14896] 14896,83 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: 83:[57, 82, 111], Operations: ['41+70=111'] Exploring Operation: 111-82=29, Resulting Numbers: [57, 29] Generated Node #0,0,0: 83:[57, 29] Operation: 111-82=29 Exploring Operation: 111-57=54, Resulting Numbers: [82, 54] Generated Node #0,0,1: 83:[82, 54] Operation: 111-57=54 Exploring Operation: 57+82=139, Resulting Numbers: [111, 139] Generated Node #0,0,2: 83:[111, 139] Operation: 57+82=139 Moving to Node #0,1 Current State: 83:[70, 57, 123], Operations: ['41+82=123'] Exploring Operation: 70+57=127, Resulting Numbers: [123, 127] Generated Node #0,1,0: 83:[123, 127] Operation: 70+57=127 Exploring Operation: 123-57=66, Resulting Numbers: [70, 66] Generated Node #0,1,1: 83:[70, 66] Operation: 123-57=66 Exploring Operation: 123-70=53, Resulting Numbers: [57, 53] Generated Node #0,1,2: 83:[57, 53] Operation: 123-70=53 Moving to Node #0,0,1 Current State: 83:[82, 54], Operations: ['41+70=111', '111-57=54'] Exploring Operation: 82-54=28, Resulting Numbers: [28] 28,83 unequal: No Solution Exploring Operation: 82+54=136, Resulting Numbers: [136] 136,83 unequal: No Solution Exploring Operation: 82*54=4428, Resulting Numbers: [4428] 4428,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[70, 66], Operations: ['41+82=123', '123-57=66'] Exploring Operation: 70+66=136, Resulting Numbers: [136] 136,83 unequal: No Solution Exploring Operation: 70-66=4, Resulting Numbers: [4] 4,83 unequal: No Solution Exploring Operation: 70*66=4620, Resulting Numbers: [4620] 4620,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[57, 53], Operations: ['41+82=123', '123-70=53'] Exploring Operation: 57*53=3021, Resulting Numbers: [3021] 3021,83 unequal: No Solution Exploring Operation: 57+53=110, Resulting Numbers: [110] 110,83 unequal: No Solution Exploring Operation: 57-53=4, Resulting Numbers: [4] 4,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[57, 29], Operations: ['41+70=111', '111-82=29'] Exploring Operation: 57*29=1653, Resulting Numbers: [1653] 1653,83 unequal: No Solution Exploring Operation: 57-29=28, Resulting Numbers: [28] 28,83 unequal: No Solution Exploring Operation: 57+29=86, Resulting Numbers: [86] 86,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[123, 127], Operations: ['41+82=123', '70+57=127'] Exploring Operation: 123+127=250, Resulting Numbers: [250] 250,83 unequal: No Solution Exploring Operation: 123*127=15621, Resulting Numbers: [15621] 15621,83 unequal: No Solution Exploring Operation: 127-123=4, Resulting Numbers: [4] 4,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[111, 139], Operations: ['41+70=111', '57+82=139'] Exploring Operation: 139-111=28, Resulting Numbers: [28] 28,83 unequal: No Solution Exploring Operation: 111*139=15429, Resulting Numbers: [15429] 15429,83 unequal: No Solution Exploring Operation: 111+139=250, Resulting Numbers: [250] 250,83 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 92, 7, 12, 4 ]
56
[ "92+4=96", "7*96=672", "672/12=56" ]
Current State: 56:[92, 7, 12, 4], Operations: [] Exploring Operation: 92+4=96, Resulting Numbers: [7, 12, 96] Generated Node #2: [7, 12, 96] from Operation: 92+4=96 Current State: 56:[7, 12, 96], Operations: ['92+4=96'] Exploring Operation: 7*96=672, Resulting Numbers: [12, 672] Generated Node #3: [12, 672] from Operation: 7*96=672 Current State: 56:[12, 672], Operations: ['92+4=96', '7*96=672'] Exploring Operation: 672/12=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[92, 7, 12, 4], Operations: [] Exploring Operation: 92-12=80, Resulting Numbers: [7, 4, 80] Generated Node #0,0: 56:[7, 4, 80] Operation: 92-12=80 Exploring Operation: 92-4=88, Resulting Numbers: [7, 12, 88] Generated Node #0,1: 56:[7, 12, 88] Operation: 92-4=88 Exploring Operation: 92-7=85, Resulting Numbers: [12, 4, 85] Generated Node #0,2: 56:[12, 4, 85] Operation: 92-7=85 Exploring Operation: 92/4=23, Resulting Numbers: [7, 12, 23] Generated Node #0,3: 56:[7, 12, 23] Operation: 92/4=23 Moving to Node #0,3 Current State: 56:[7, 12, 23], Operations: ['92/4=23'] Exploring Operation: 23-12=11, Resulting Numbers: [7, 11] Generated Node #0,3,0: 56:[7, 11] Operation: 23-12=11 Exploring Operation: 23-7=16, Resulting Numbers: [12, 16] Generated Node #0,3,1: 56:[12, 16] Operation: 23-7=16 Exploring Operation: 12-7=5, Resulting Numbers: [23, 5] Generated Node #0,3,2: 56:[23, 5] Operation: 12-7=5 Exploring Operation: 7+23=30, Resulting Numbers: [12, 30] Generated Node #0,3,3: 56:[12, 30] Operation: 7+23=30 Moving to Node #0,0 Current State: 56:[7, 4, 80], Operations: ['92-12=80'] Exploring Operation: 80/4=20, Resulting Numbers: [7, 20] Generated Node #0,0,0: 56:[7, 20] Operation: 80/4=20 Exploring Operation: 80-4=76, Resulting Numbers: [7, 76] Generated Node #0,0,1: 56:[7, 76] Operation: 80-4=76 Exploring Operation: 7*4=28, Resulting Numbers: [80, 28] Generated Node #0,0,2: 56:[80, 28] Operation: 7*4=28 Exploring Operation: 80-7=73, Resulting Numbers: [4, 73] Generated Node #0,0,3: 56:[4, 73] Operation: 80-7=73 Moving to Node #0,2 Current State: 56:[12, 4, 85], Operations: ['92-7=85'] Exploring Operation: 12-4=8, Resulting Numbers: [85, 8] Generated Node #0,2,0: 56:[85, 8] Operation: 12-4=8 Exploring Operation: 85-4=81, Resulting Numbers: [12, 81] Generated Node #0,2,1: 56:[12, 81] Operation: 85-4=81 Exploring Operation: 12/4=3, Resulting Numbers: [85, 3] Generated Node #0,2,2: 56:[85, 3] Operation: 12/4=3 Exploring Operation: 85-12=73, Resulting Numbers: [4, 73] Generated Node #0,2,3: 56:[4, 73] Operation: 85-12=73 Moving to Node #0,1 Current State: 56:[7, 12, 88], Operations: ['92-4=88'] Exploring Operation: 88-7=81, Resulting Numbers: [12, 81] Generated Node #0,1,0: 56:[12, 81] Operation: 88-7=81 Exploring Operation: 88-12=76, Resulting Numbers: [7, 76] Generated Node #0,1,1: 56:[7, 76] Operation: 88-12=76 Exploring Operation: 7+12=19, Resulting Numbers: [88, 19] Generated Node #0,1,2: 56:[88, 19] Operation: 7+12=19 Exploring Operation: 12-7=5, Resulting Numbers: [88, 5] Generated Node #0,1,3: 56:[88, 5] Operation: 12-7=5 Moving to Node #0,3,0 Current State: 56:[7, 11], Operations: ['92/4=23', '23-12=11'] Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,56 unequal: No Solution Moving to Node #0,3,3 Current State: 56:[12, 30], Operations: ['92/4=23', '7+23=30'] Exploring Operation: 12+30=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 12*30=360, Resulting Numbers: [360] 360,56 unequal: No Solution Moving to Node #0,3,1 Current State: 56:[12, 16], Operations: ['92/4=23', '23-7=16'] Exploring Operation: 12*16=192, Resulting Numbers: [192] 192,56 unequal: No Solution Exploring Operation: 12+16=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[7, 20], Operations: ['92-12=80', '80/4=20'] Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,56 unequal: No Solution Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,56 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,56 unequal: No Solution Moving to Node #0,3,2 Current State: 56:[23, 5], Operations: ['92/4=23', '12-7=5'] Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 23*5=115, Resulting Numbers: [115] 115,56 unequal: No Solution Moving to Node #0,0,3 Current State: 56:[4, 73], Operations: ['92-12=80', '80-7=73'] Exploring Operation: 4+73=77, Resulting Numbers: [77] 77,56 unequal: No Solution Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 4*73=292, Resulting Numbers: [292] 292,56 unequal: No Solution Moving to Node #0,2,3 Current State: 56:[4, 73], Operations: ['92-7=85', '85-12=73'] Exploring Operation: 4*73=292, Resulting Numbers: [292] 292,56 unequal: No Solution Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 4+73=77, Resulting Numbers: [77] 77,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[7, 76], Operations: ['92-12=80', '80-4=76'] Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 7*76=532, Resulting Numbers: [532] 532,56 unequal: No Solution Exploring Operation: 7+76=83, Resulting Numbers: [83] 83,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[7, 76], Operations: ['92-4=88', '88-12=76'] Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 7*76=532, Resulting Numbers: [532] 532,56 unequal: No Solution Exploring Operation: 7+76=83, Resulting Numbers: [83] 83,56 unequal: No Solution Moving to Node #0,0,2 Current State: 56:[80, 28], Operations: ['92-12=80', '7*4=28'] Exploring Operation: 80*28=2240, Resulting Numbers: [2240] 2240,56 unequal: No Solution Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 80+28=108, Resulting Numbers: [108] 108,56 unequal: No Solution Moving to Node #0,2,1 Current State: 56:[12, 81], Operations: ['92-7=85', '85-4=81'] Exploring Operation: 81-12=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 12+81=93, Resulting Numbers: [93] 93,56 unequal: No Solution Exploring Operation: 12*81=972, Resulting Numbers: [972] 972,56 unequal: No Solution Moving to Node #0,1,0 Current State: 56:[12, 81], Operations: ['92-4=88', '88-7=81'] Exploring Operation: 81-12=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 12*81=972, Resulting Numbers: [972] 972,56 unequal: No Solution Exploring Operation: 12+81=93, Resulting Numbers: [93] 93,56 unequal: No Solution Moving to Node #0,2,0 Current State: 56:[85, 8], Operations: ['92-7=85', '12-4=8'] Exploring Operation: 85-8=77, Resulting Numbers: [77] 77,56 unequal: No Solution Exploring Operation: 85+8=93, Resulting Numbers: [93] 93,56 unequal: No Solution Exploring Operation: 85*8=680, Resulting Numbers: [680] 680,56 unequal: No Solution Moving to Node #0,2,2 Current State: 56:[85, 3], Operations: ['92-7=85', '12/4=3'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,56 unequal: No Solution Exploring Operation: 85*3=255, Resulting Numbers: [255] 255,56 unequal: No Solution Exploring Operation: 85+3=88, Resulting Numbers: [88] 88,56 unequal: No Solution Moving to Node #0,1,3 Current State: 56:[88, 5], Operations: ['92-4=88', '12-7=5'] Exploring Operation: 88*5=440, Resulting Numbers: [440] 440,56 unequal: No Solution Exploring Operation: 88+5=93, Resulting Numbers: [93] 93,56 unequal: No Solution Exploring Operation: 88-5=83, Resulting Numbers: [83] 83,56 unequal: No Solution Moving to Node #0,1,2 Current State: 56:[88, 19], Operations: ['92-4=88', '7+12=19'] Exploring Operation: 88-19=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 88+19=107, Resulting Numbers: [107] 107,56 unequal: No Solution Exploring Operation: 88*19=1672, Resulting Numbers: [1672] 1672,56 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 84, 4, 78, 3 ]
27
[ "84-78=6", "4*6=24", "3+24=27" ]
Current State: 27:[84, 4, 78, 3], Operations: [] Exploring Operation: 84-78=6, Resulting Numbers: [4, 3, 6] Generated Node #2: [4, 3, 6] from Operation: 84-78=6 Current State: 27:[4, 3, 6], Operations: ['84-78=6'] Exploring Operation: 4*6=24, Resulting Numbers: [3, 24] Generated Node #3: [3, 24] from Operation: 4*6=24 Current State: 27:[3, 24], Operations: ['84-78=6', '4*6=24'] Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[84, 4, 78, 3], Operations: [] Exploring Operation: 84/3=28, Resulting Numbers: [4, 78, 28] Generated Node #0,0: 27:[4, 78, 28] Operation: 84/3=28 Exploring Operation: 84-78=6, Resulting Numbers: [4, 3, 6] Generated Node #0,1: 27:[4, 3, 6] Operation: 84-78=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[4, 3, 6], Operations: ['84-78=6'] Exploring Operation: 4+6=10, Resulting Numbers: [3, 10] Generated Node #0,1,0: 27:[3, 10] Operation: 4+6=10 Exploring Operation: 6-4=2, Resulting Numbers: [3, 2] Generated Node #0,1,1: 27:[3, 2] Operation: 6-4=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 27:[3, 10], Operations: ['84-78=6', '4+6=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,27 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,27 unequal: No Solution No 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: 27:[3, 2], Operations: ['84-78=6', '6-4=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[4, 78, 28], Operations: ['84/3=28'] Exploring Operation: 78-28=50, Resulting Numbers: [4, 50] Generated Node #0,0,0: 27:[4, 50] Operation: 78-28=50 Exploring Operation: 78-4=74, Resulting Numbers: [28, 74] Generated Node #0,0,1: 27:[28, 74] Operation: 78-4=74 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[4, 50], Operations: ['84/3=28', '78-28=50'] Exploring Operation: 4+50=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,27 unequal: No Solution No 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: 27:[28, 74], Operations: ['84/3=28', '78-4=74'] Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,27 unequal: No Solution Exploring Operation: 28+74=102, Resulting Numbers: [102] 102,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 22, 56, 79, 79 ]
56
[ "79-79=0", "22*0=0", "56+0=56" ]
Current State: 56:[22, 56, 79, 79], Operations: [] Exploring Operation: 79-79=0, Resulting Numbers: [22, 56, 0] Generated Node #2: [22, 56, 0] from Operation: 79-79=0 Current State: 56:[22, 56, 0], Operations: ['79-79=0'] Exploring Operation: 22*0=0, Resulting Numbers: [56, 0] Generated Node #3: [56, 0] from Operation: 22*0=0 Current State: 56:[56, 0], Operations: ['79-79=0', '22*0=0'] Exploring Operation: 56+0=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[22, 56, 79, 79], Operations: [] Exploring Operation: 79/79=1, Resulting Numbers: [22, 56, 1] Generated Node #0,0: 56:[22, 56, 1] Operation: 79/79=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[22, 56, 1], Operations: ['79/79=1'] Exploring Operation: 22+1=23, Resulting Numbers: [56, 23] Generated Node #0,0,0: 56:[56, 23] Operation: 22+1=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[56, 23], Operations: ['79/79=1', '22+1=23'] Exploring Operation: 56-23=33, Resulting Numbers: [33] 33,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 42, 9, 55, 10 ]
14
[ "42+9=51", "55+10=65", "65-51=14" ]
Current State: 14:[42, 9, 55, 10], Operations: [] Exploring Operation: 42+9=51, Resulting Numbers: [55, 10, 51] Generated Node #2: [55, 10, 51] from Operation: 42+9=51 Current State: 14:[55, 10, 51], Operations: ['42+9=51'] Exploring Operation: 55+10=65, Resulting Numbers: [51, 65] Generated Node #3: [51, 65] from Operation: 55+10=65 Current State: 14:[51, 65], Operations: ['42+9=51', '55+10=65'] Exploring Operation: 65-51=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[42, 9, 55, 10], Operations: [] Exploring Operation: 55-42=13, Resulting Numbers: [9, 10, 13] Generated Node #0,0: 14:[9, 10, 13] Operation: 55-42=13 Exploring Operation: 42-10=32, Resulting Numbers: [9, 55, 32] Generated Node #0,1: 14:[9, 55, 32] Operation: 42-10=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[9, 10, 13], Operations: ['55-42=13'] Exploring Operation: 13-10=3, Resulting Numbers: [9, 3] Generated Node #0,0,0: 14:[9, 3] Operation: 13-10=3 Exploring Operation: 10-9=1, Resulting Numbers: [13, 1] Generated Node #0,0,1: 14:[13, 1] Operation: 10-9=1 Moving to Node #0,0,1 Current State: 14:[13, 1], Operations: ['55-42=13', '10-9=1'] Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[42, 9, 55, 10], Operations: [] Exploring Operation: 55-42=13, Resulting Numbers: [9, 10, 13] Generated Node #0,0: 14:[9, 10, 13] Operation: 55-42=13 Moving to Node #0,0 Current State: 14:[9, 10, 13], Operations: ['55-42=13'] Exploring Operation: 10-9=1, Resulting Numbers: [13, 1] Generated Node #0,0,1: 14:[13, 1] Operation: 10-9=1 Moving to Node #0,0,1 Current State: 14:[13, 1], Operations: ['55-42=13', '10-9=1'] Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 74, 48, 70, 20 ]
24
[ "74-48=26", "70-20=50", "50-26=24" ]
Current State: 24:[74, 48, 70, 20], Operations: [] Exploring Operation: 74-48=26, Resulting Numbers: [70, 20, 26] Generated Node #2: [70, 20, 26] from Operation: 74-48=26 Current State: 24:[70, 20, 26], Operations: ['74-48=26'] Exploring Operation: 70-20=50, Resulting Numbers: [26, 50] Generated Node #3: [26, 50] from Operation: 70-20=50 Current State: 24:[26, 50], Operations: ['74-48=26', '70-20=50'] Exploring Operation: 50-26=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[74, 48, 70, 20], Operations: [] Exploring Operation: 74-70=4, Resulting Numbers: [48, 20, 4] Generated Node #0,0: 24:[48, 20, 4] Operation: 74-70=4 Exploring Operation: 70-48=22, Resulting Numbers: [74, 20, 22] Generated Node #0,1: 24:[74, 20, 22] Operation: 70-48=22 Exploring Operation: 74-20=54, Resulting Numbers: [48, 70, 54] Generated Node #0,2: 24:[48, 70, 54] Operation: 74-20=54 Exploring Operation: 48-20=28, Resulting Numbers: [74, 70, 28] Generated Node #0,3: 24:[74, 70, 28] Operation: 48-20=28 Exploring Operation: 74-48=26, Resulting Numbers: [70, 20, 26] Generated Node #0,4: 24:[70, 20, 26] Operation: 74-48=26 Moving to Node #0,0 Current State: 24:[48, 20, 4], Operations: ['74-70=4'] Exploring Operation: 20+4=24, Resulting Numbers: [48, 24] Generated Node #0,0,0: 24:[48, 24] Operation: 20+4=24 Exploring Operation: 48/4=12, Resulting Numbers: [20, 12] Generated Node #0,0,1: 24:[20, 12] Operation: 48/4=12 Exploring Operation: 20/4=5, Resulting Numbers: [48, 5] Generated Node #0,0,2: 24:[48, 5] Operation: 20/4=5 Exploring Operation: 48-20=28, Resulting Numbers: [4, 28] Generated Node #0,0,3: 24:[4, 28] Operation: 48-20=28 Exploring Operation: 48-4=44, Resulting Numbers: [20, 44] Generated Node #0,0,4: 24:[20, 44] Operation: 48-4=44 Moving to Node #0,4 Current State: 24:[70, 20, 26], Operations: ['74-48=26'] Exploring Operation: 70+20=90, Resulting Numbers: [26, 90] Generated Node #0,4,0: 24:[26, 90] Operation: 70+20=90 Exploring Operation: 20+26=46, Resulting Numbers: [70, 46] Generated Node #0,4,1: 24:[70, 46] Operation: 20+26=46 Exploring Operation: 70-26=44, Resulting Numbers: [20, 44] Generated Node #0,4,2: 24:[20, 44] Operation: 70-26=44 Exploring Operation: 26-20=6, Resulting Numbers: [70, 6] Generated Node #0,4,3: 24:[70, 6] Operation: 26-20=6 Exploring Operation: 70-20=50, Resulting Numbers: [26, 50] Generated Node #0,4,4: 24:[26, 50] Operation: 70-20=50 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 24:[20, 44], Operations: ['74-48=26', '70-26=44'] Exploring Operation: 20+44=64, Resulting Numbers: [64] 64,24 unequal: No Solution Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[74, 48, 70, 20], Operations: [] Exploring Operation: 74-48=26, Resulting Numbers: [70, 20, 26] Generated Node #0,4: 24:[70, 20, 26] Operation: 74-48=26 Moving to Node #0,4 Current State: 24:[70, 20, 26], Operations: ['74-48=26'] Exploring Operation: 70-26=44, Resulting Numbers: [20, 44] Generated Node #0,4,2: 24:[20, 44] Operation: 70-26=44 Moving to Node #0,4,2 Current State: 24:[20, 44], Operations: ['74-48=26', '70-26=44'] Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 55, 36, 48, 4 ]
52
[ "48-36=12", "12/4=3", "55-3=52" ]
Current State: 52:[55, 36, 48, 4], Operations: [] Exploring Operation: 48-36=12, Resulting Numbers: [55, 4, 12] Generated Node #2: [55, 4, 12] from Operation: 48-36=12 Current State: 52:[55, 4, 12], Operations: ['48-36=12'] Exploring Operation: 12/4=3, Resulting Numbers: [55, 3] Generated Node #3: [55, 3] from Operation: 12/4=3 Current State: 52:[55, 3], Operations: ['48-36=12', '12/4=3'] Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[55, 36, 48, 4], Operations: [] Exploring Operation: 55-36=19, Resulting Numbers: [48, 4, 19] Generated Node #0,0: 52:[48, 4, 19] Operation: 55-36=19 Exploring Operation: 48-36=12, Resulting Numbers: [55, 4, 12] Generated Node #0,1: 52:[55, 4, 12] Operation: 48-36=12 Moving to Node #0,1 Current State: 52:[55, 4, 12], Operations: ['48-36=12'] Exploring Operation: 55-4=51, Resulting Numbers: [12, 51] Generated Node #0,1,0: 52:[12, 51] Operation: 55-4=51 Exploring Operation: 12/4=3, Resulting Numbers: [55, 3] Generated Node #0,1,1: 52:[55, 3] Operation: 12/4=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 52:[12, 51], Operations: ['48-36=12', '55-4=51'] Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 12+51=63, Resulting Numbers: [63] 63,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 52:[55, 3], Operations: ['48-36=12', '12/4=3'] Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[55, 36, 48, 4], Operations: [] Exploring Operation: 48-36=12, Resulting Numbers: [55, 4, 12] Generated Node #0,1: 52:[55, 4, 12] Operation: 48-36=12 Moving to Node #0,1 Current State: 52:[55, 4, 12], Operations: ['48-36=12'] Exploring Operation: 12/4=3, Resulting Numbers: [55, 3] Generated Node #0,1,1: 52:[55, 3] Operation: 12/4=3 Moving to Node #0,1,1 Current State: 52:[55, 3], Operations: ['48-36=12', '12/4=3'] Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 36, 81, 2, 50 ]
26
[ "81-50=31", "2*31=62", "62-36=26" ]
Current State: 26:[36, 81, 2, 50], Operations: [] Exploring Operation: 81-50=31, Resulting Numbers: [36, 2, 31] Generated Node #2: [36, 2, 31] from Operation: 81-50=31 Current State: 26:[36, 2, 31], Operations: ['81-50=31'] Exploring Operation: 2*31=62, Resulting Numbers: [36, 62] Generated Node #3: [36, 62] from Operation: 2*31=62 Current State: 26:[36, 62], Operations: ['81-50=31', '2*31=62'] Exploring Operation: 62-36=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[36, 81, 2, 50], Operations: [] Exploring Operation: 81-50=31, Resulting Numbers: [36, 2, 31] Generated Node #0,0: 26:[36, 2, 31] Operation: 81-50=31 Exploring Operation: 50-36=14, Resulting Numbers: [81, 2, 14] Generated Node #0,1: 26:[81, 2, 14] Operation: 50-36=14 Exploring Operation: 81-36=45, Resulting Numbers: [2, 50, 45] Generated Node #0,2: 26:[2, 50, 45] Operation: 81-36=45 Exploring Operation: 36/2=18, Resulting Numbers: [81, 50, 18] Generated Node #0,3: 26:[81, 50, 18] Operation: 36/2=18 Exploring Operation: 50/2=25, Resulting Numbers: [36, 81, 25] Generated Node #0,4: 26:[36, 81, 25] Operation: 50/2=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[36, 2, 31], Operations: ['81-50=31'] Exploring Operation: 36/2=18, Resulting Numbers: [31, 18] Generated Node #0,0,0: 26:[31, 18] Operation: 36/2=18 Exploring Operation: 36+2=38, Resulting Numbers: [31, 38] Generated Node #0,0,1: 26:[31, 38] Operation: 36+2=38 Exploring Operation: 36-31=5, Resulting Numbers: [2, 5] Generated Node #0,0,2: 26:[2, 5] Operation: 36-31=5 Exploring Operation: 36-2=34, Resulting Numbers: [31, 34] Generated Node #0,0,3: 26:[31, 34] Operation: 36-2=34 Exploring Operation: 31-2=29, Resulting Numbers: [36, 29] Generated Node #0,0,4: 26:[36, 29] Operation: 31-2=29 Moving to Node #0,0,2 Current State: 26:[2, 5], Operations: ['81-50=31', '36-31=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,26 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,26 unequal: No Solution Moving to Node #0,0,0 Current State: 26:[31, 18], Operations: ['81-50=31', '36/2=18'] Exploring Operation: 31*18=558, Resulting Numbers: [558] 558,26 unequal: No Solution Exploring Operation: 31+18=49, Resulting Numbers: [49] 49,26 unequal: No Solution Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,26 unequal: No Solution Moving to Node #0,0,3 Current State: 26:[31, 34], Operations: ['81-50=31', '36-2=34'] Exploring Operation: 34-31=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 31+34=65, Resulting Numbers: [65] 65,26 unequal: No Solution Exploring Operation: 31*34=1054, Resulting Numbers: [1054] 1054,26 unequal: No Solution Moving to Node #0,0,4 Current State: 26:[36, 29], Operations: ['81-50=31', '31-2=29'] Exploring Operation: 36*29=1044, Resulting Numbers: [1044] 1044,26 unequal: No Solution Exploring Operation: 36-29=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 36+29=65, Resulting Numbers: [65] 65,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[31, 38], Operations: ['81-50=31', '36+2=38'] Exploring Operation: 31+38=69, Resulting Numbers: [69] 69,26 unequal: No Solution Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 31*38=1178, Resulting Numbers: [1178] 1178,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 26:[2, 50, 45], Operations: ['81-36=45'] Exploring Operation: 50-2=48, Resulting Numbers: [45, 48] Generated Node #0,2,0: 26:[45, 48] Operation: 50-2=48 Exploring Operation: 2+50=52, Resulting Numbers: [45, 52] Generated Node #0,2,1: 26:[45, 52] Operation: 2+50=52 Exploring Operation: 45-2=43, Resulting Numbers: [50, 43] Generated Node #0,2,2: 26:[50, 43] Operation: 45-2=43 Exploring Operation: 50/2=25, Resulting Numbers: [45, 25] Generated Node #0,2,3: 26:[45, 25] Operation: 50/2=25 Exploring Operation: 50-45=5, Resulting Numbers: [2, 5] Generated Node #0,2,4: 26:[2, 5] Operation: 50-45=5 Moving to Node #0,2,4 Current State: 26:[2, 5], Operations: ['81-36=45', '50-45=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,26 unequal: No Solution Moving to Node #0,2,3 Current State: 26:[45, 25], Operations: ['81-36=45', '50/2=25'] Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,26 unequal: No Solution Exploring Operation: 45*25=1125, Resulting Numbers: [1125] 1125,26 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[45, 48], Operations: ['81-36=45', '50-2=48'] Exploring Operation: 45*48=2160, Resulting Numbers: [2160] 2160,26 unequal: No Solution Exploring Operation: 45+48=93, Resulting Numbers: [93] 93,26 unequal: No Solution Exploring Operation: 48-45=3, Resulting Numbers: [3] 3,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[50, 43], Operations: ['81-36=45', '45-2=43'] Exploring Operation: 50*43=2150, Resulting Numbers: [2150] 2150,26 unequal: No Solution Exploring Operation: 50-43=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 50+43=93, Resulting Numbers: [93] 93,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[45, 52], Operations: ['81-36=45', '2+50=52'] Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 45*52=2340, Resulting Numbers: [2340] 2340,26 unequal: No Solution Exploring Operation: 45+52=97, Resulting Numbers: [97] 97,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[81, 2, 14], Operations: ['50-36=14'] Exploring Operation: 81-2=79, Resulting Numbers: [14, 79] Generated Node #0,1,0: 26:[14, 79] Operation: 81-2=79 Exploring Operation: 2*14=28, Resulting Numbers: [81, 28] Generated Node #0,1,1: 26:[81, 28] Operation: 2*14=28 Exploring Operation: 14-2=12, Resulting Numbers: [81, 12] Generated Node #0,1,2: 26:[81, 12] Operation: 14-2=12 Exploring Operation: 81-14=67, Resulting Numbers: [2, 67] Generated Node #0,1,3: 26:[2, 67] Operation: 81-14=67 Exploring Operation: 81+2=83, Resulting Numbers: [14, 83] Generated Node #0,1,4: 26:[14, 83] Operation: 81+2=83 Moving to Node #0,1,3 Current State: 26:[2, 67], Operations: ['50-36=14', '81-14=67'] Exploring Operation: 2+67=69, Resulting Numbers: [69] 69,26 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,26 unequal: No Solution Exploring Operation: 2*67=134, Resulting Numbers: [134] 134,26 unequal: No Solution Moving to Node #0,1,0 Current State: 26:[14, 79], Operations: ['50-36=14', '81-2=79'] Exploring Operation: 14*79=1106, Resulting Numbers: [1106] 1106,26 unequal: No Solution Exploring Operation: 79-14=65, Resulting Numbers: [65] 65,26 unequal: No Solution Exploring Operation: 14+79=93, Resulting Numbers: [93] 93,26 unequal: No Solution Moving to Node #0,1,2 Current State: 26:[81, 12], Operations: ['50-36=14', '14-2=12'] Exploring Operation: 81*12=972, Resulting Numbers: [972] 972,26 unequal: No Solution Exploring Operation: 81-12=69, Resulting Numbers: [69] 69,26 unequal: No Solution Exploring Operation: 81+12=93, Resulting Numbers: [93] 93,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[81, 28], Operations: ['50-36=14', '2*14=28'] Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,26 unequal: No Solution Exploring Operation: 81*28=2268, Resulting Numbers: [2268] 2268,26 unequal: No Solution Exploring Operation: 81+28=109, Resulting Numbers: [109] 109,26 unequal: No Solution Moving to Node #0,1,4 Current State: 26:[14, 83], Operations: ['50-36=14', '81+2=83'] Exploring Operation: 14+83=97, Resulting Numbers: [97] 97,26 unequal: No Solution Exploring Operation: 14*83=1162, Resulting Numbers: [1162] 1162,26 unequal: No Solution Exploring Operation: 83-14=69, Resulting Numbers: [69] 69,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 26:[36, 81, 25], Operations: ['50/2=25'] Exploring Operation: 81+25=106, Resulting Numbers: [36, 106] Generated Node #0,4,0: 26:[36, 106] Operation: 81+25=106 Exploring Operation: 36+25=61, Resulting Numbers: [81, 61] Generated Node #0,4,1: 26:[81, 61] Operation: 36+25=61 Exploring Operation: 36-25=11, Resulting Numbers: [81, 11] Generated Node #0,4,2: 26:[81, 11] Operation: 36-25=11 Exploring Operation: 81-25=56, Resulting Numbers: [36, 56] Generated Node #0,4,3: 26:[36, 56] Operation: 81-25=56 Exploring Operation: 81-36=45, Resulting Numbers: [25, 45] Generated Node #0,4,4: 26:[25, 45] Operation: 81-36=45 Moving to Node #0,4,4 Current State: 26:[25, 45], Operations: ['50/2=25', '81-36=45'] Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,26 unequal: No Solution Exploring Operation: 25*45=1125, Resulting Numbers: [1125] 1125,26 unequal: No Solution Exploring Operation: 25+45=70, Resulting Numbers: [70] 70,26 unequal: No Solution Moving to Node #0,4,3 Current State: 26:[36, 56], Operations: ['50/2=25', '81-25=56'] Exploring Operation: 56-36=20, Resulting Numbers: [20] 20,26 unequal: No Solution Exploring Operation: 36*56=2016, Resulting Numbers: [2016] 2016,26 unequal: No Solution Exploring Operation: 36+56=92, Resulting Numbers: [92] 92,26 unequal: No Solution Moving to Node #0,4,2 Current State: 26:[81, 11], Operations: ['50/2=25', '36-25=11'] Exploring Operation: 81+11=92, Resulting Numbers: [92] 92,26 unequal: No Solution Exploring Operation: 81*11=891, Resulting Numbers: [891] 891,26 unequal: No Solution Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,26 unequal: No Solution Moving to Node #0,4,0 Current State: 26:[36, 106], Operations: ['50/2=25', '81+25=106'] Exploring Operation: 36+106=142, Resulting Numbers: [142] 142,26 unequal: No Solution Exploring Operation: 36*106=3816, Resulting Numbers: [3816] 3816,26 unequal: No Solution Exploring Operation: 106-36=70, Resulting Numbers: [70] 70,26 unequal: No Solution Moving to Node #0,4,1 Current State: 26:[81, 61], Operations: ['50/2=25', '36+25=61'] Exploring Operation: 81-61=20, Resulting Numbers: [20] 20,26 unequal: No Solution Exploring Operation: 81+61=142, Resulting Numbers: [142] 142,26 unequal: No Solution Exploring Operation: 81*61=4941, Resulting Numbers: [4941] 4941,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 26:[81, 50, 18], Operations: ['36/2=18'] Exploring Operation: 50-18=32, Resulting Numbers: [81, 32] Generated Node #0,3,0: 26:[81, 32] Operation: 50-18=32 Exploring Operation: 81-18=63, Resulting Numbers: [50, 63] Generated Node #0,3,1: 26:[50, 63] Operation: 81-18=63 Exploring Operation: 50+18=68, Resulting Numbers: [81, 68] Generated Node #0,3,2: 26:[81, 68] Operation: 50+18=68 Exploring Operation: 81-50=31, Resulting Numbers: [18, 31] Generated Node #0,3,3: 26:[18, 31] Operation: 81-50=31 Exploring Operation: 81+18=99, Resulting Numbers: [50, 99] Generated Node #0,3,4: 26:[50, 99] Operation: 81+18=99 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 26:[18, 31], Operations: ['36/2=18', '81-50=31'] Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,26 unequal: No Solution Exploring Operation: 18+31=49, Resulting Numbers: [49] 49,26 unequal: No Solution Exploring Operation: 18*31=558, Resulting Numbers: [558] 558,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 26:[81, 32], Operations: ['36/2=18', '50-18=32'] Exploring Operation: 81+32=113, Resulting Numbers: [113] 113,26 unequal: No Solution Exploring Operation: 81*32=2592, Resulting Numbers: [2592] 2592,26 unequal: No Solution Exploring Operation: 81-32=49, Resulting Numbers: [49] 49,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 26:[50, 63], Operations: ['36/2=18', '81-18=63'] Exploring Operation: 50+63=113, Resulting Numbers: [113] 113,26 unequal: No Solution Exploring Operation: 63-50=13, Resulting Numbers: [13] 13,26 unequal: No Solution Exploring Operation: 50*63=3150, Resulting Numbers: [3150] 3150,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 26:[81, 68], Operations: ['36/2=18', '50+18=68'] Exploring Operation: 81+68=149, Resulting Numbers: [149] 149,26 unequal: No Solution Exploring Operation: 81*68=5508, Resulting Numbers: [5508] 5508,26 unequal: No Solution Exploring Operation: 81-68=13, Resulting Numbers: [13] 13,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 26:[50, 99], Operations: ['36/2=18', '81+18=99'] Exploring Operation: 99-50=49, Resulting Numbers: [49] 49,26 unequal: No Solution Exploring Operation: 50+99=149, Resulting Numbers: [149] 149,26 unequal: No Solution Exploring Operation: 50*99=4950, Resulting Numbers: [4950] 4950,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 9, 47, 55, 34 ]
46
[ "47+34=81", "81/9=9", "55-9=46" ]
Current State: 46:[9, 47, 55, 34], Operations: [] Exploring Operation: 47+34=81, Resulting Numbers: [9, 55, 81] Generated Node #2: [9, 55, 81] from Operation: 47+34=81 Current State: 46:[9, 55, 81], Operations: ['47+34=81'] Exploring Operation: 81/9=9, Resulting Numbers: [55, 9] Generated Node #3: [55, 9] from Operation: 81/9=9 Current State: 46:[55, 9], Operations: ['47+34=81', '81/9=9'] Exploring Operation: 55-9=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[9, 47, 55, 34], Operations: [] Exploring Operation: 55-34=21, Resulting Numbers: [9, 47, 21] Generated Node #0,0: 46:[9, 47, 21] Operation: 55-34=21 Moving to Node #0,0 Current State: 46:[9, 47, 21], Operations: ['55-34=21'] Exploring Operation: 9+21=30, Resulting Numbers: [47, 30] Generated Node #0,0,0: 46:[47, 30] Operation: 9+21=30 Moving to Node #0,0,0 Current State: 46:[47, 30], Operations: ['55-34=21', '9+21=30'] Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,46 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 10, 51, 7, 23 ]
40
[ "10-7=3", "51/3=17", "23+17=40" ]
Current State: 40:[10, 51, 7, 23], Operations: [] Exploring Operation: 10-7=3, Resulting Numbers: [51, 23, 3] Generated Node #2: [51, 23, 3] from Operation: 10-7=3 Current State: 40:[51, 23, 3], Operations: ['10-7=3'] Exploring Operation: 51/3=17, Resulting Numbers: [23, 17] Generated Node #3: [23, 17] from Operation: 51/3=17 Current State: 40:[23, 17], Operations: ['10-7=3', '51/3=17'] Exploring Operation: 23+17=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[10, 51, 7, 23], Operations: [] Exploring Operation: 51-7=44, Resulting Numbers: [10, 23, 44] Generated Node #0,0: 40:[10, 23, 44] Operation: 51-7=44 Exploring Operation: 10-7=3, Resulting Numbers: [51, 23, 3] Generated Node #0,1: 40:[51, 23, 3] Operation: 10-7=3 Exploring Operation: 51-10=41, Resulting Numbers: [7, 23, 41] Generated Node #0,2: 40:[7, 23, 41] Operation: 51-10=41 Exploring Operation: 51-23=28, Resulting Numbers: [10, 7, 28] Generated Node #0,3: 40:[10, 7, 28] Operation: 51-23=28 Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[7, 23, 41], Operations: ['51-10=41'] Exploring Operation: 41-23=18, Resulting Numbers: [7, 18] Generated Node #0,2,0: 40:[7, 18] Operation: 41-23=18 Exploring Operation: 23-7=16, Resulting Numbers: [41, 16] Generated Node #0,2,1: 40:[41, 16] Operation: 23-7=16 Exploring Operation: 7+23=30, Resulting Numbers: [41, 30] Generated Node #0,2,2: 40:[41, 30] Operation: 7+23=30 Exploring Operation: 41-7=34, Resulting Numbers: [23, 34] Generated Node #0,2,3: 40:[23, 34] Operation: 41-7=34 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 40:[7, 18], Operations: ['51-10=41', '41-23=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,40 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,40 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,40 unequal: No Solution No 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: 40:[41, 16], Operations: ['51-10=41', '23-7=16'] Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,40 unequal: No Solution Exploring Operation: 41+16=57, Resulting Numbers: [57] 57,40 unequal: No Solution Exploring Operation: 41*16=656, Resulting Numbers: [656] 656,40 unequal: No Solution No 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: 40:[23, 34], Operations: ['51-10=41', '41-7=34'] Exploring Operation: 23*34=782, Resulting Numbers: [782] 782,40 unequal: No Solution Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,40 unequal: No Solution Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,40 unequal: No Solution No 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: 40:[41, 30], Operations: ['51-10=41', '7+23=30'] Exploring Operation: 41*30=1230, Resulting Numbers: [1230] 1230,40 unequal: No Solution Exploring Operation: 41-30=11, Resulting Numbers: [11] 11,40 unequal: No Solution Exploring Operation: 41+30=71, Resulting Numbers: [71] 71,40 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: 40:[10, 23, 44], Operations: ['51-7=44'] Exploring Operation: 10+23=33, Resulting Numbers: [44, 33] Generated Node #0,0,0: 40:[44, 33] Operation: 10+23=33 Exploring Operation: 23-10=13, Resulting Numbers: [44, 13] Generated Node #0,0,1: 40:[44, 13] Operation: 23-10=13 Exploring Operation: 44-23=21, Resulting Numbers: [10, 21] Generated Node #0,0,2: 40:[10, 21] Operation: 44-23=21 Exploring Operation: 44-10=34, Resulting Numbers: [23, 34] Generated Node #0,0,3: 40:[23, 34] Operation: 44-10=34 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 40:[10, 21], Operations: ['51-7=44', '44-23=21'] Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,40 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,40 unequal: No Solution Exploring Operation: 10*21=210, Resulting Numbers: [210] 210,40 unequal: No Solution No 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: 40:[44, 13], Operations: ['51-7=44', '23-10=13'] Exploring Operation: 44*13=572, Resulting Numbers: [572] 572,40 unequal: No Solution Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,40 unequal: No Solution Exploring Operation: 44+13=57, Resulting Numbers: [57] 57,40 unequal: No Solution No 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: 40:[23, 34], Operations: ['51-7=44', '44-10=34'] Exploring Operation: 23*34=782, Resulting Numbers: [782] 782,40 unequal: No Solution Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,40 unequal: No Solution Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,40 unequal: No Solution No 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: 40:[44, 33], Operations: ['51-7=44', '10+23=33'] Exploring Operation: 44+33=77, Resulting Numbers: [77] 77,40 unequal: No Solution Exploring Operation: 44*33=1452, Resulting Numbers: [1452] 1452,40 unequal: No Solution Exploring Operation: 44-33=11, Resulting Numbers: [11] 11,40 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: 40:[10, 7, 28], Operations: ['51-23=28'] Exploring Operation: 28-10=18, Resulting Numbers: [7, 18] Generated Node #0,3,0: 40:[7, 18] Operation: 28-10=18 Exploring Operation: 28-7=21, Resulting Numbers: [10, 21] Generated Node #0,3,1: 40:[10, 21] Operation: 28-7=21 Exploring Operation: 10+28=38, Resulting Numbers: [7, 38] Generated Node #0,3,2: 40:[7, 38] Operation: 10+28=38 Exploring Operation: 28/7=4, Resulting Numbers: [10, 4] Generated Node #0,3,3: 40:[10, 4] Operation: 28/7=4 Moving to Node #0,3,3 Current State: 40:[10, 4], Operations: ['51-23=28', '28/7=4'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[10, 51, 7, 23], Operations: [] Exploring Operation: 51-23=28, Resulting Numbers: [10, 7, 28] Generated Node #0,3: 40:[10, 7, 28] Operation: 51-23=28 Moving to Node #0,3 Current State: 40:[10, 7, 28], Operations: ['51-23=28'] Exploring Operation: 28/7=4, Resulting Numbers: [10, 4] Generated Node #0,3,3: 40:[10, 4] Operation: 28/7=4 Moving to Node #0,3,3 Current State: 40:[10, 4], Operations: ['51-23=28', '28/7=4'] Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.960069
hs_4
sum_heuristic
[ 83, 14, 34, 98 ]
12
[ "83-34=49", "98/49=2", "14-2=12" ]
Current State: 12:[83, 14, 34, 98], Operations: [] Exploring Operation: 83-34=49, Resulting Numbers: [14, 98, 49] Generated Node #2: [14, 98, 49] from Operation: 83-34=49 Current State: 12:[14, 98, 49], Operations: ['83-34=49'] Exploring Operation: 98/49=2, Resulting Numbers: [14, 2] Generated Node #3: [14, 2] from Operation: 98/49=2 Current State: 12:[14, 2], Operations: ['83-34=49', '98/49=2'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[83, 14, 34, 98], Operations: [] Exploring Operation: 98-83=15, Resulting Numbers: [14, 34, 15] Generated Node #0,0: 12:[14, 34, 15] Operation: 98-83=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[14, 34, 15], Operations: ['98-83=15'] Exploring Operation: 34-15=19, Resulting Numbers: [14, 19] Generated Node #0,0,0: 12:[14, 19] Operation: 34-15=19 Moving to Node #0,0,0 Current State: 12:[14, 19], Operations: ['98-83=15', '34-15=19'] Exploring Operation: 19-14=5, Resulting Numbers: [5] 5,12 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
[ 14, 45, 32, 38 ]
66
[ "45-38=7", "14*7=98", "98-32=66" ]
Current State: 66:[14, 45, 32, 38], Operations: [] Exploring Operation: 45-38=7, Resulting Numbers: [14, 32, 7] Generated Node #2: [14, 32, 7] from Operation: 45-38=7 Current State: 66:[14, 32, 7], Operations: ['45-38=7'] Exploring Operation: 14*7=98, Resulting Numbers: [32, 98] Generated Node #3: [32, 98] from Operation: 14*7=98 Current State: 66:[32, 98], Operations: ['45-38=7', '14*7=98'] Exploring Operation: 98-32=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[14, 45, 32, 38], Operations: [] Exploring Operation: 45-32=13, Resulting Numbers: [14, 38, 13] Generated Node #0,0: 66:[14, 38, 13] Operation: 45-32=13 Exploring Operation: 45-14=31, Resulting Numbers: [32, 38, 31] Generated Node #0,1: 66:[32, 38, 31] Operation: 45-14=31 Exploring Operation: 14+45=59, Resulting Numbers: [32, 38, 59] Generated Node #0,2: 66:[32, 38, 59] Operation: 14+45=59 Exploring Operation: 45-38=7, Resulting Numbers: [14, 32, 7] Generated Node #0,3: 66:[14, 32, 7] Operation: 45-38=7 Start Sub Search at level 1: Moving to Node #0,3 Current State: 66:[14, 32, 7], Operations: ['45-38=7'] Exploring Operation: 32-14=18, Resulting Numbers: [7, 18] Generated Node #0,3,0: 66:[7, 18] Operation: 32-14=18 Exploring Operation: 14+7=21, Resulting Numbers: [32, 21] Generated Node #0,3,1: 66:[32, 21] Operation: 14+7=21 Exploring Operation: 14-7=7, Resulting Numbers: [32, 7] Generated Node #0,3,2: 66:[32, 7] Operation: 14-7=7 Exploring Operation: 14/7=2, Resulting Numbers: [32, 2] Generated Node #0,3,3: 66:[32, 2] Operation: 14/7=2 Moving to Node #0,3,3 Current State: 66:[32, 2], Operations: ['45-38=7', '14/7=2'] Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,66 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,66 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,66 unequal: No Solution Moving to Node #0,3,2 Current State: 66:[32, 7], Operations: ['45-38=7', '14-7=7'] Exploring Operation: 32+7=39, Resulting Numbers: [39] 39,66 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,66 unequal: No Solution Exploring Operation: 32*7=224, Resulting Numbers: [224] 224,66 unequal: No Solution Moving to Node #0,3,1 Current State: 66:[32, 21], Operations: ['45-38=7', '14+7=21'] Exploring Operation: 32+21=53, Resulting Numbers: [53] 53,66 unequal: No Solution Exploring Operation: 32*21=672, Resulting Numbers: [672] 672,66 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,66 unequal: No Solution Moving to Node #0,3,0 Current State: 66:[7, 18], Operations: ['45-38=7', '32-14=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,66 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,66 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,66 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 Current State: 66:[32, 38, 31], Operations: ['45-14=31'] Exploring Operation: 38-32=6, Resulting Numbers: [31, 6] Generated Node #0,1,0: 66:[31, 6] Operation: 38-32=6 Exploring Operation: 38+31=69, Resulting Numbers: [32, 69] Generated Node #0,1,1: 66:[32, 69] Operation: 38+31=69 Exploring Operation: 32+38=70, Resulting Numbers: [31, 70] Generated Node #0,1,2: 66:[31, 70] Operation: 32+38=70 Exploring Operation: 38-31=7, Resulting Numbers: [32, 7] Generated Node #0,1,3: 66:[32, 7] Operation: 38-31=7 Moving to Node #0,1,0 Current State: 66:[31, 6], Operations: ['45-14=31', '38-32=6'] Exploring Operation: 31+6=37, Resulting Numbers: [37] 37,66 unequal: No Solution Exploring Operation: 31*6=186, Resulting Numbers: [186] 186,66 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,66 unequal: No Solution Moving to Node #0,1,3 Current State: 66:[32, 7], Operations: ['45-14=31', '38-31=7'] Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,66 unequal: No Solution Exploring Operation: 32*7=224, Resulting Numbers: [224] 224,66 unequal: No Solution Exploring Operation: 32+7=39, Resulting Numbers: [39] 39,66 unequal: No Solution Moving to Node #0,1,1 Current State: 66:[32, 69], Operations: ['45-14=31', '38+31=69'] Exploring Operation: 32+69=101, Resulting Numbers: [101] 101,66 unequal: No Solution Exploring Operation: 32*69=2208, Resulting Numbers: [2208] 2208,66 unequal: No Solution Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,66 unequal: No Solution Moving to Node #0,1,2 Current State: 66:[31, 70], Operations: ['45-14=31', '32+38=70'] Exploring Operation: 70-31=39, Resulting Numbers: [39] 39,66 unequal: No Solution Exploring Operation: 31*70=2170, Resulting Numbers: [2170] 2170,66 unequal: No Solution Exploring Operation: 31+70=101, Resulting Numbers: [101] 101,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[14, 38, 13], Operations: ['45-32=13'] Exploring Operation: 14-13=1, Resulting Numbers: [38, 1] Generated Node #0,0,0: 66:[38, 1] Operation: 14-13=1 Exploring Operation: 38-14=24, Resulting Numbers: [13, 24] Generated Node #0,0,1: 66:[13, 24] Operation: 38-14=24 Exploring Operation: 38-13=25, Resulting Numbers: [14, 25] Generated Node #0,0,2: 66:[14, 25] Operation: 38-13=25 Exploring Operation: 14+13=27, Resulting Numbers: [38, 27] Generated Node #0,0,3: 66:[38, 27] Operation: 14+13=27 Moving to Node #0,0,1 Current State: 66:[13, 24], Operations: ['45-32=13', '38-14=24'] Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,66 unequal: No Solution Exploring Operation: 13*24=312, Resulting Numbers: [312] 312,66 unequal: No Solution Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,66 unequal: No Solution Moving to Node #0,0,2 Current State: 66:[14, 25], Operations: ['45-32=13', '38-13=25'] Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,66 unequal: No Solution Exploring Operation: 14+25=39, Resulting Numbers: [39] 39,66 unequal: No Solution Exploring Operation: 14*25=350, Resulting Numbers: [350] 350,66 unequal: No Solution Moving to Node #0,0,0 Current State: 66:[38, 1], Operations: ['45-32=13', '14-13=1'] Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,66 unequal: No Solution Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,66 unequal: No Solution Exploring Operation: 38+1=39, Resulting Numbers: [39] 39,66 unequal: No Solution Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,66 unequal: No Solution Moving to Node #0,0,3 Current State: 66:[38, 27], Operations: ['45-32=13', '14+13=27'] Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,66 unequal: No Solution Exploring Operation: 38*27=1026, Resulting Numbers: [1026] 1026,66 unequal: No Solution Exploring Operation: 38+27=65, Resulting Numbers: [65] 65,66 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 Current State: 66:[32, 38, 59], Operations: ['14+45=59'] Exploring Operation: 59-32=27, Resulting Numbers: [38, 27] Generated Node #0,2,0: 66:[38, 27] Operation: 59-32=27 Exploring Operation: 32+38=70, Resulting Numbers: [59, 70] Generated Node #0,2,1: 66:[59, 70] Operation: 32+38=70 Exploring Operation: 38-32=6, Resulting Numbers: [59, 6] Generated Node #0,2,2: 66:[59, 6] Operation: 38-32=6 Exploring Operation: 59-38=21, Resulting Numbers: [32, 21] Generated Node #0,2,3: 66:[32, 21] Operation: 59-38=21 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 66:[32, 21], Operations: ['14+45=59', '59-38=21'] Exploring Operation: 32+21=53, Resulting Numbers: [53] 53,66 unequal: No Solution Exploring Operation: 32*21=672, Resulting Numbers: [672] 672,66 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 66:[59, 6], Operations: ['14+45=59', '38-32=6'] Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,66 unequal: No Solution Exploring Operation: 59+6=65, Resulting Numbers: [65] 65,66 unequal: No Solution Exploring Operation: 59*6=354, Resulting Numbers: [354] 354,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 66:[38, 27], Operations: ['14+45=59', '59-32=27'] Exploring Operation: 38*27=1026, Resulting Numbers: [1026] 1026,66 unequal: No Solution Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,66 unequal: No Solution Exploring Operation: 38+27=65, Resulting Numbers: [65] 65,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 66:[59, 70], Operations: ['14+45=59', '32+38=70'] Exploring Operation: 59*70=4130, Resulting Numbers: [4130] 4130,66 unequal: No Solution Exploring Operation: 70-59=11, Resulting Numbers: [11] 11,66 unequal: No Solution Exploring Operation: 59+70=129, Resulting Numbers: [129] 129,66 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_4
sum_heuristic
[ 87, 29, 96, 92 ]
12
[ "87/29=3", "96-92=4", "3*4=12" ]
Current State: 12:[87, 29, 96, 92], Operations: [] Exploring Operation: 87/29=3, Resulting Numbers: [96, 92, 3] Generated Node #2: [96, 92, 3] from Operation: 87/29=3 Current State: 12:[96, 92, 3], Operations: ['87/29=3'] Exploring Operation: 96-92=4, Resulting Numbers: [3, 4] Generated Node #3: [3, 4] from Operation: 96-92=4 Current State: 12:[3, 4], Operations: ['87/29=3', '96-92=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[87, 29, 96, 92], Operations: [] Exploring Operation: 96-92=4, Resulting Numbers: [87, 29, 4] Generated Node #0,0: 12:[87, 29, 4] Operation: 96-92=4 Moving to Node #0,0 Current State: 12:[87, 29, 4], Operations: ['96-92=4'] Exploring Operation: 87/29=3, Resulting Numbers: [4, 3] Generated Node #0,0,0: 12:[4, 3] Operation: 87/29=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[4, 3], Operations: ['96-92=4', '87/29=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[87, 29, 96, 92], Operations: [] Exploring Operation: 96-92=4, Resulting Numbers: [87, 29, 4] Generated Node #0,0: 12:[87, 29, 4] Operation: 96-92=4 Moving to Node #0,0 Current State: 12:[87, 29, 4], Operations: ['96-92=4'] Exploring Operation: 87/29=3, Resulting Numbers: [4, 3] Generated Node #0,0,0: 12:[4, 3] Operation: 87/29=3 Moving to Node #0,0,0 Current State: 12:[4, 3], Operations: ['96-92=4', '87/29=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 32, 74, 98, 90 ]
70
[ "98-90=8", "32/8=4", "74-4=70" ]
Current State: 70:[32, 74, 98, 90], Operations: [] Exploring Operation: 98-90=8, Resulting Numbers: [32, 74, 8] Generated Node #2: [32, 74, 8] from Operation: 98-90=8 Current State: 70:[32, 74, 8], Operations: ['98-90=8'] Exploring Operation: 32/8=4, Resulting Numbers: [74, 4] Generated Node #3: [74, 4] from Operation: 32/8=4 Current State: 70:[74, 4], Operations: ['98-90=8', '32/8=4'] Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[32, 74, 98, 90], Operations: [] Exploring Operation: 98-90=8, Resulting Numbers: [32, 74, 8] Generated Node #0,0: 70:[32, 74, 8] Operation: 98-90=8 Exploring Operation: 98-32=66, Resulting Numbers: [74, 90, 66] Generated Node #0,1: 70:[74, 90, 66] Operation: 98-32=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[32, 74, 8], Operations: ['98-90=8'] Exploring Operation: 74-8=66, Resulting Numbers: [32, 66] Generated Node #0,0,0: 70:[32, 66] Operation: 74-8=66 Exploring Operation: 32/8=4, Resulting Numbers: [74, 4] Generated Node #0,0,1: 70:[74, 4] Operation: 32/8=4 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 70:[74, 4], Operations: ['98-90=8', '32/8=4'] Exploring Operation: 74+4=78, Resulting Numbers: [78] 78,70 unequal: No Solution Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[32, 74, 98, 90], Operations: [] Exploring Operation: 98-90=8, Resulting Numbers: [32, 74, 8] Generated Node #0,0: 70:[32, 74, 8] Operation: 98-90=8 Moving to Node #0,0 Current State: 70:[32, 74, 8], Operations: ['98-90=8'] Exploring Operation: 32/8=4, Resulting Numbers: [74, 4] Generated Node #0,0,1: 70:[74, 4] Operation: 32/8=4 Moving to Node #0,0,1 Current State: 70:[74, 4], Operations: ['98-90=8', '32/8=4'] Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 37, 75, 99, 61 ]
48
[ "37+75=112", "99+61=160", "160-112=48" ]
Current State: 48:[37, 75, 99, 61], Operations: [] Exploring Operation: 37+75=112, Resulting Numbers: [99, 61, 112] Generated Node #2: [99, 61, 112] from Operation: 37+75=112 Current State: 48:[99, 61, 112], Operations: ['37+75=112'] Exploring Operation: 99+61=160, Resulting Numbers: [112, 160] Generated Node #3: [112, 160] from Operation: 99+61=160 Current State: 48:[112, 160], Operations: ['37+75=112', '99+61=160'] Exploring Operation: 160-112=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[37, 75, 99, 61], Operations: [] Exploring Operation: 99-61=38, Resulting Numbers: [37, 75, 38] Generated Node #0,0: 48:[37, 75, 38] Operation: 99-61=38 Exploring Operation: 99-75=24, Resulting Numbers: [37, 61, 24] Generated Node #0,1: 48:[37, 61, 24] Operation: 99-75=24 Moving to Node #0,1 Current State: 48:[37, 61, 24], Operations: ['99-75=24'] Exploring Operation: 61-37=24, Resulting Numbers: [24, 24] Generated Node #0,1,0: 48:[24, 24] Operation: 61-37=24 Exploring Operation: 37-24=13, Resulting Numbers: [61, 13] Generated Node #0,1,1: 48:[61, 13] Operation: 37-24=13 Moving to Node #0,0 Current State: 48:[37, 75, 38], Operations: ['99-61=38'] Exploring Operation: 75-38=37, Resulting Numbers: [37, 37] Generated Node #0,0,0: 48:[37, 37] Operation: 75-38=37 Exploring Operation: 75-37=38, Resulting Numbers: [38, 38] Generated Node #0,0,1: 48:[38, 38] Operation: 75-37=38 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 48:[38, 38], Operations: ['99-61=38', '75-37=38'] Exploring Operation: 38-38=0, Resulting Numbers: [0] 0,48 unequal: No Solution Exploring Operation: 38/38=1, Resulting Numbers: [1] 1,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[37, 37], Operations: ['99-61=38', '75-38=37'] Exploring Operation: 37/37=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 37-37=0, Resulting Numbers: [0] 0,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 48:[24, 24], Operations: ['99-75=24', '61-37=24'] Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[37, 75, 99, 61], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [37, 61, 24] Generated Node #0,1: 48:[37, 61, 24] Operation: 99-75=24 Moving to Node #0,1 Current State: 48:[37, 61, 24], Operations: ['99-75=24'] Exploring Operation: 61-37=24, Resulting Numbers: [24, 24] Generated Node #0,1,0: 48:[24, 24] Operation: 61-37=24 Moving to Node #0,1,0 Current State: 48:[24, 24], Operations: ['99-75=24', '61-37=24'] Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 33, 37, 76, 39 ]
71
[ "39-37=2", "76/2=38", "33+38=71" ]
Current State: 71:[33, 37, 76, 39], Operations: [] Exploring Operation: 39-37=2, Resulting Numbers: [33, 76, 2] Generated Node #2: [33, 76, 2] from Operation: 39-37=2 Current State: 71:[33, 76, 2], Operations: ['39-37=2'] Exploring Operation: 76/2=38, Resulting Numbers: [33, 38] Generated Node #3: [33, 38] from Operation: 76/2=38 Current State: 71:[33, 38], Operations: ['39-37=2', '76/2=38'] Exploring Operation: 33+38=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[33, 37, 76, 39], Operations: [] Exploring Operation: 33+37=70, Resulting Numbers: [76, 39, 70] Generated Node #0,0: 71:[76, 39, 70] Operation: 33+37=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[76, 39, 70], Operations: ['33+37=70'] Exploring Operation: 76-39=37, Resulting Numbers: [70, 37] Generated Node #0,0,0: 71:[70, 37] Operation: 76-39=37 Moving to Node #0,0,0 Current State: 71:[70, 37], Operations: ['33+37=70', '76-39=37'] Exploring Operation: 70+37=107, Resulting Numbers: [107] 107,71 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
[ 75, 81, 31, 45 ]
82
[ "81-75=6", "31+45=76", "6+76=82" ]
Current State: 82:[75, 81, 31, 45], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [31, 45, 6] Generated Node #2: [31, 45, 6] from Operation: 81-75=6 Current State: 82:[31, 45, 6], Operations: ['81-75=6'] Exploring Operation: 31+45=76, Resulting Numbers: [6, 76] Generated Node #3: [6, 76] from Operation: 31+45=76 Current State: 82:[6, 76], Operations: ['81-75=6', '31+45=76'] Exploring Operation: 6+76=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[75, 81, 31, 45], Operations: [] Exploring Operation: 31+45=76, Resulting Numbers: [75, 81, 76] Generated Node #0,0: 82:[75, 81, 76] Operation: 31+45=76 Exploring Operation: 75-31=44, Resulting Numbers: [81, 45, 44] Generated Node #0,1: 82:[81, 45, 44] Operation: 75-31=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[81, 45, 44], Operations: ['75-31=44'] Exploring Operation: 45-44=1, Resulting Numbers: [81, 1] Generated Node #0,1,0: 82:[81, 1] Operation: 45-44=1 Exploring Operation: 81-45=36, Resulting Numbers: [44, 36] Generated Node #0,1,1: 82:[44, 36] Operation: 81-45=36 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[81, 1], Operations: ['75-31=44', '45-44=1'] Exploring Operation: 81+1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[75, 81, 31, 45], Operations: [] Exploring Operation: 75-31=44, Resulting Numbers: [81, 45, 44] Generated Node #0,1: 82:[81, 45, 44] Operation: 75-31=44 Moving to Node #0,1 Current State: 82:[81, 45, 44], Operations: ['75-31=44'] Exploring Operation: 45-44=1, Resulting Numbers: [81, 1] Generated Node #0,1,0: 82:[81, 1] Operation: 45-44=1 Moving to Node #0,1,0 Current State: 82:[81, 1], Operations: ['75-31=44', '45-44=1'] Exploring Operation: 81+1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 65, 2, 52, 55 ]
22
[ "65*2=130", "52*55=2860", "2860/130=22" ]
Current State: 22:[65, 2, 52, 55], Operations: [] Exploring Operation: 65*2=130, Resulting Numbers: [52, 55, 130] Generated Node #2: [52, 55, 130] from Operation: 65*2=130 Current State: 22:[52, 55, 130], Operations: ['65*2=130'] Exploring Operation: 52*55=2860, Resulting Numbers: [130, 2860] Generated Node #3: [130, 2860] from Operation: 52*55=2860 Current State: 22:[130, 2860], Operations: ['65*2=130', '52*55=2860'] Exploring Operation: 2860/130=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[65, 2, 52, 55], Operations: [] Exploring Operation: 52/2=26, Resulting Numbers: [65, 55, 26] Generated Node #0,0: 22:[65, 55, 26] Operation: 52/2=26 Exploring Operation: 65-52=13, Resulting Numbers: [2, 55, 13] Generated Node #0,1: 22:[2, 55, 13] Operation: 65-52=13 Exploring Operation: 65-55=10, Resulting Numbers: [2, 52, 10] Generated Node #0,2: 22:[2, 52, 10] Operation: 65-55=10 Exploring Operation: 55-52=3, Resulting Numbers: [65, 2, 3] Generated Node #0,3: 22:[65, 2, 3] Operation: 55-52=3 Moving to Node #0,2 Current State: 22:[2, 52, 10], Operations: ['65-55=10'] Exploring Operation: 52-2=50, Resulting Numbers: [10, 50] Generated Node #0,2,0: 22:[10, 50] Operation: 52-2=50 Exploring Operation: 2+10=12, Resulting Numbers: [52, 12] Generated Node #0,2,1: 22:[52, 12] Operation: 2+10=12 Exploring Operation: 52/2=26, Resulting Numbers: [10, 26] Generated Node #0,2,2: 22:[10, 26] Operation: 52/2=26 Exploring Operation: 52-10=42, Resulting Numbers: [2, 42] Generated Node #0,2,3: 22:[2, 42] Operation: 52-10=42 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 22:[10, 26], Operations: ['65-55=10', '52/2=26'] Exploring Operation: 10+26=36, Resulting Numbers: [36] 36,22 unequal: No Solution Exploring Operation: 10*26=260, Resulting Numbers: [260] 260,22 unequal: No Solution Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 22:[2, 42], Operations: ['65-55=10', '52-10=42'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,22 unequal: No Solution Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,22 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,22 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 22:[10, 50], Operations: ['65-55=10', '52-2=50'] Exploring Operation: 10*50=500, Resulting Numbers: [500] 500,22 unequal: No Solution Exploring Operation: 10+50=60, Resulting Numbers: [60] 60,22 unequal: No Solution Exploring Operation: 50/10=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 22:[52, 12], Operations: ['65-55=10', '2+10=12'] Exploring Operation: 52*12=624, Resulting Numbers: [624] 624,22 unequal: No Solution Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,22 unequal: No Solution Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,22 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: 22:[2, 55, 13], Operations: ['65-52=13'] Exploring Operation: 13-2=11, Resulting Numbers: [55, 11] Generated Node #0,1,0: 22:[55, 11] Operation: 13-2=11 Exploring Operation: 2+55=57, Resulting Numbers: [13, 57] Generated Node #0,1,1: 22:[13, 57] Operation: 2+55=57 Exploring Operation: 55-13=42, Resulting Numbers: [2, 42] Generated Node #0,1,2: 22:[2, 42] Operation: 55-13=42 Exploring Operation: 55-2=53, Resulting Numbers: [13, 53] Generated Node #0,1,3: 22:[13, 53] Operation: 55-2=53 Moving to Node #0,3 Current State: 22:[65, 2, 3], Operations: ['55-52=3'] Exploring Operation: 3-2=1, Resulting Numbers: [65, 1] Generated Node #0,3,0: 22:[65, 1] Operation: 3-2=1 Exploring Operation: 65+2=67, Resulting Numbers: [3, 67] Generated Node #0,3,1: 22:[3, 67] Operation: 65+2=67 Exploring Operation: 65-2=63, Resulting Numbers: [3, 63] Generated Node #0,3,2: 22:[3, 63] Operation: 65-2=63 Exploring Operation: 65-3=62, Resulting Numbers: [2, 62] Generated Node #0,3,3: 22:[2, 62] Operation: 65-3=62 Moving to Node #0,0 Current State: 22:[65, 55, 26], Operations: ['52/2=26'] Exploring Operation: 65-55=10, Resulting Numbers: [26, 10] Generated Node #0,0,0: 22:[26, 10] Operation: 65-55=10 Exploring Operation: 55-26=29, Resulting Numbers: [65, 29] Generated Node #0,0,1: 22:[65, 29] Operation: 55-26=29 Exploring Operation: 65-26=39, Resulting Numbers: [55, 39] Generated Node #0,0,2: 22:[55, 39] Operation: 65-26=39 Exploring Operation: 65+55=120, Resulting Numbers: [26, 120] Generated Node #0,0,3: 22:[26, 120] Operation: 65+55=120 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[26, 10], Operations: ['52/2=26', '65-55=10'] Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,22 unequal: No Solution Exploring Operation: 26+10=36, Resulting Numbers: [36] 36,22 unequal: No Solution Exploring Operation: 26*10=260, Resulting Numbers: [260] 260,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 22:[65, 29], Operations: ['52/2=26', '55-26=29'] Exploring Operation: 65+29=94, Resulting Numbers: [94] 94,22 unequal: No Solution Exploring Operation: 65-29=36, Resulting Numbers: [36] 36,22 unequal: No Solution Exploring Operation: 65*29=1885, Resulting Numbers: [1885] 1885,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 22:[55, 39], Operations: ['52/2=26', '65-26=39'] Exploring Operation: 55+39=94, Resulting Numbers: [94] 94,22 unequal: No Solution Exploring Operation: 55*39=2145, Resulting Numbers: [2145] 2145,22 unequal: No Solution Exploring Operation: 55-39=16, Resulting Numbers: [16] 16,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 22:[26, 120], Operations: ['52/2=26', '65+55=120'] Exploring Operation: 26+120=146, Resulting Numbers: [146] 146,22 unequal: No Solution Exploring Operation: 26*120=3120, Resulting Numbers: [3120] 3120,22 unequal: No Solution Exploring Operation: 120-26=94, Resulting Numbers: [94] 94,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 22:[2, 42], Operations: ['65-52=13', '55-13=42'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,22 unequal: No Solution Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,22 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,22 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,22 unequal: No Solution Moving to Node #0,1,3 Current State: 22:[13, 53], Operations: ['65-52=13', '55-2=53'] Exploring Operation: 13+53=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,22 unequal: No Solution Exploring Operation: 13*53=689, Resulting Numbers: [689] 689,22 unequal: No Solution Moving to Node #0,1,0 Current State: 22:[55, 11], Operations: ['65-52=13', '13-2=11'] Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 55+11=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 55*11=605, Resulting Numbers: [605] 605,22 unequal: No Solution Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[13, 57], Operations: ['65-52=13', '2+55=57'] Exploring Operation: 13*57=741, Resulting Numbers: [741] 741,22 unequal: No Solution Exploring Operation: 13+57=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 57-13=44, Resulting Numbers: [44] 44,22 unequal: No Solution Moving to Node #0,3,3 Current State: 22:[2, 62], Operations: ['55-52=3', '65-3=62'] Exploring Operation: 2*62=124, Resulting Numbers: [124] 124,22 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,22 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,22 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,22 unequal: No Solution Moving to Node #0,3,2 Current State: 22:[3, 63], Operations: ['55-52=3', '65-2=63'] Exploring Operation: 3*63=189, Resulting Numbers: [189] 189,22 unequal: No Solution Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,22 unequal: No Solution Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,22 unequal: No Solution Exploring Operation: 3+63=66, Resulting Numbers: [66] 66,22 unequal: No Solution Moving to Node #0,3,0 Current State: 22:[65, 1], Operations: ['55-52=3', '3-2=1'] Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 65*1=65, Resulting Numbers: [65] 65,22 unequal: No Solution Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,22 unequal: No Solution Moving to Node #0,3,1 Current State: 22:[3, 67], Operations: ['55-52=3', '65+2=67'] Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,22 unequal: No Solution Exploring Operation: 3+67=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 3*67=201, Resulting Numbers: [201] 201,22 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 90, 80, 10, 95 ]
94
[ "90-80=10", "10/10=1", "95-1=94" ]
Current State: 94:[90, 80, 10, 95], Operations: [] Exploring Operation: 90-80=10, Resulting Numbers: [10, 95, 10] Generated Node #2: [10, 95, 10] from Operation: 90-80=10 Current State: 94:[10, 95, 10], Operations: ['90-80=10'] Exploring Operation: 10/10=1, Resulting Numbers: [95, 1] Generated Node #3: [95, 1] from Operation: 10/10=1 Current State: 94:[95, 1], Operations: ['90-80=10', '10/10=1'] Exploring Operation: 95-1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[90, 80, 10, 95], Operations: [] Exploring Operation: 80+10=90, Resulting Numbers: [90, 95, 90] Generated Node #0,0: 94:[90, 95, 90] Operation: 80+10=90 Exploring Operation: 90-80=10, Resulting Numbers: [10, 95, 10] Generated Node #0,1: 94:[10, 95, 10] Operation: 90-80=10 Exploring Operation: 90+10=100, Resulting Numbers: [80, 95, 100] Generated Node #0,2: 94:[80, 95, 100] Operation: 90+10=100 Exploring Operation: 80/10=8, Resulting Numbers: [90, 95, 8] Generated Node #0,3: 94:[90, 95, 8] Operation: 80/10=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[90, 95, 90], Operations: ['80+10=90'] Exploring Operation: 95-90=5, Resulting Numbers: [90, 5] Generated Node #0,0,0: 94:[90, 5] Operation: 95-90=5 Exploring Operation: 95-90=5, Resulting Numbers: [90, 5] Generated Node #0,0,1: 94:[90, 5] Operation: 95-90=5 Exploring Operation: 90/90=1, Resulting Numbers: [95, 1] Generated Node #0,0,2: 94:[95, 1] Operation: 90/90=1 Exploring Operation: 90-90=0, Resulting Numbers: [95, 0] Generated Node #0,0,3: 94:[95, 0] Operation: 90-90=0 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 94:[95, 1], Operations: ['80+10=90', '90/90=1'] Exploring Operation: 95*1=95, Resulting Numbers: [95] 95,94 unequal: No Solution Exploring Operation: 95/1=95, Resulting Numbers: [95] 95,94 unequal: No Solution Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,94 unequal: No Solution Exploring Operation: 95-1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[90, 80, 10, 95], Operations: [] Exploring Operation: 80+10=90, Resulting Numbers: [90, 95, 90] Generated Node #0,0: 94:[90, 95, 90] Operation: 80+10=90 Moving to Node #0,0 Current State: 94:[90, 95, 90], Operations: ['80+10=90'] Exploring Operation: 90/90=1, Resulting Numbers: [95, 1] Generated Node #0,0,2: 94:[95, 1] Operation: 90/90=1 Moving to Node #0,0,2 Current State: 94:[95, 1], Operations: ['80+10=90', '90/90=1'] Exploring Operation: 95-1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 36, 69, 42, 7 ]
63
[ "69-36=33", "42-33=9", "7*9=63" ]
Current State: 63:[36, 69, 42, 7], Operations: [] Exploring Operation: 69-36=33, Resulting Numbers: [42, 7, 33] Generated Node #2: [42, 7, 33] from Operation: 69-36=33 Current State: 63:[42, 7, 33], Operations: ['69-36=33'] Exploring Operation: 42-33=9, Resulting Numbers: [7, 9] Generated Node #3: [7, 9] from Operation: 42-33=9 Current State: 63:[7, 9], Operations: ['69-36=33', '42-33=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[36, 69, 42, 7], Operations: [] Exploring Operation: 36+42=78, Resulting Numbers: [69, 7, 78] Generated Node #0,0: 63:[69, 7, 78] Operation: 36+42=78 Exploring Operation: 42-36=6, Resulting Numbers: [69, 7, 6] Generated Node #0,1: 63:[69, 7, 6] Operation: 42-36=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[69, 7, 6], Operations: ['42-36=6'] Exploring Operation: 69-6=63, Resulting Numbers: [7, 63] Generated Node #0,1,0: 63:[7, 63] Operation: 69-6=63 Exploring Operation: 69-7=62, Resulting Numbers: [6, 62] Generated Node #0,1,1: 63:[6, 62] Operation: 69-7=62 Moving to Node #0,1,0 Current State: 63:[7, 63], Operations: ['42-36=6', '69-6=63'] Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 7+63=70, Resulting Numbers: [70] 70,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[6, 62], Operations: ['42-36=6', '69-7=62'] Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,63 unequal: No Solution Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[69, 7, 78], Operations: ['36+42=78'] Exploring Operation: 78-7=71, Resulting Numbers: [69, 71] Generated Node #0,0,0: 63:[69, 71] Operation: 78-7=71 Exploring Operation: 78-69=9, Resulting Numbers: [7, 9] Generated Node #0,0,1: 63:[7, 9] Operation: 78-69=9 Moving to Node #0,0,1 Current State: 63:[7, 9], Operations: ['36+42=78', '78-69=9'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[36, 69, 42, 7], Operations: [] Exploring Operation: 36+42=78, Resulting Numbers: [69, 7, 78] Generated Node #0,0: 63:[69, 7, 78] Operation: 36+42=78 Moving to Node #0,0 Current State: 63:[69, 7, 78], Operations: ['36+42=78'] Exploring Operation: 78-69=9, Resulting Numbers: [7, 9] Generated Node #0,0,1: 63:[7, 9] Operation: 78-69=9 Moving to Node #0,0,1 Current State: 63:[7, 9], Operations: ['36+42=78', '78-69=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 63, 71, 35, 42 ]
15
[ "71-63=8", "42-35=7", "8+7=15" ]
Current State: 15:[63, 71, 35, 42], Operations: [] Exploring Operation: 71-63=8, Resulting Numbers: [35, 42, 8] Generated Node #2: [35, 42, 8] from Operation: 71-63=8 Current State: 15:[35, 42, 8], Operations: ['71-63=8'] Exploring Operation: 42-35=7, Resulting Numbers: [8, 7] Generated Node #3: [8, 7] from Operation: 42-35=7 Current State: 15:[8, 7], Operations: ['71-63=8', '42-35=7'] Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[63, 71, 35, 42], Operations: [] Exploring Operation: 63-42=21, Resulting Numbers: [71, 35, 21] Generated Node #0,0: 15:[71, 35, 21] Operation: 63-42=21 Exploring Operation: 71-63=8, Resulting Numbers: [35, 42, 8] Generated Node #0,1: 15:[35, 42, 8] Operation: 71-63=8 Exploring Operation: 71-42=29, Resulting Numbers: [63, 35, 29] Generated Node #0,2: 15:[63, 35, 29] Operation: 71-42=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[35, 42, 8], Operations: ['71-63=8'] Exploring Operation: 42-8=34, Resulting Numbers: [35, 34] Generated Node #0,1,0: 15:[35, 34] Operation: 42-8=34 Exploring Operation: 42-35=7, Resulting Numbers: [8, 7] Generated Node #0,1,1: 15:[8, 7] Operation: 42-35=7 Exploring Operation: 35-8=27, Resulting Numbers: [42, 27] Generated Node #0,1,2: 15:[42, 27] Operation: 35-8=27 Moving to Node #0,1,1 Current State: 15:[8, 7], Operations: ['71-63=8', '42-35=7'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,15 unequal: No Solution Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[63, 71, 35, 42], Operations: [] Exploring Operation: 71-63=8, Resulting Numbers: [35, 42, 8] Generated Node #0,1: 15:[35, 42, 8] Operation: 71-63=8 Moving to Node #0,1 Current State: 15:[35, 42, 8], Operations: ['71-63=8'] Exploring Operation: 42-35=7, Resulting Numbers: [8, 7] Generated Node #0,1,1: 15:[8, 7] Operation: 42-35=7 Moving to Node #0,1,1 Current State: 15:[8, 7], Operations: ['71-63=8', '42-35=7'] Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 58, 63, 55, 34 ]
16
[ "63-58=5", "55-34=21", "21-5=16" ]
Current State: 16:[58, 63, 55, 34], Operations: [] Exploring Operation: 63-58=5, Resulting Numbers: [55, 34, 5] Generated Node #2: [55, 34, 5] from Operation: 63-58=5 Current State: 16:[55, 34, 5], Operations: ['63-58=5'] Exploring Operation: 55-34=21, Resulting Numbers: [5, 21] Generated Node #3: [5, 21] from Operation: 55-34=21 Current State: 16:[5, 21], Operations: ['63-58=5', '55-34=21'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[58, 63, 55, 34], Operations: [] Exploring Operation: 63-55=8, Resulting Numbers: [58, 34, 8] Generated Node #0,0: 16:[58, 34, 8] Operation: 63-55=8 Exploring Operation: 63-58=5, Resulting Numbers: [55, 34, 5] Generated Node #0,1: 16:[55, 34, 5] Operation: 63-58=5 Exploring Operation: 58-55=3, Resulting Numbers: [63, 34, 3] Generated Node #0,2: 16:[63, 34, 3] Operation: 58-55=3 Exploring Operation: 58-34=24, Resulting Numbers: [63, 55, 24] Generated Node #0,3: 16:[63, 55, 24] Operation: 58-34=24 Moving to Node #0,1 Current State: 16:[55, 34, 5], Operations: ['63-58=5'] Exploring Operation: 34-5=29, Resulting Numbers: [55, 29] Generated Node #0,1,0: 16:[55, 29] Operation: 34-5=29 Exploring Operation: 55-5=50, Resulting Numbers: [34, 50] Generated Node #0,1,1: 16:[34, 50] Operation: 55-5=50 Exploring Operation: 55/5=11, Resulting Numbers: [34, 11] Generated Node #0,1,2: 16:[34, 11] Operation: 55/5=11 Exploring Operation: 55-34=21, Resulting Numbers: [5, 21] Generated Node #0,1,3: 16:[5, 21] Operation: 55-34=21 Moving to Node #0,0 Current State: 16:[58, 34, 8], Operations: ['63-55=8'] Exploring Operation: 58-34=24, Resulting Numbers: [8, 24] Generated Node #0,0,0: 16:[8, 24] Operation: 58-34=24 Exploring Operation: 58+8=66, Resulting Numbers: [34, 66] Generated Node #0,0,1: 16:[34, 66] Operation: 58+8=66 Exploring Operation: 58-8=50, Resulting Numbers: [34, 50] Generated Node #0,0,2: 16:[34, 50] Operation: 58-8=50 Exploring Operation: 34-8=26, Resulting Numbers: [58, 26] Generated Node #0,0,3: 16:[58, 26] Operation: 34-8=26 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[8, 24], Operations: ['63-55=8', '58-34=24'] Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[58, 63, 55, 34], Operations: [] Exploring Operation: 63-55=8, Resulting Numbers: [58, 34, 8] Generated Node #0,0: 16:[58, 34, 8] Operation: 63-55=8 Moving to Node #0,0 Current State: 16:[58, 34, 8], Operations: ['63-55=8'] Exploring Operation: 58-34=24, Resulting Numbers: [8, 24] Generated Node #0,0,0: 16:[8, 24] Operation: 58-34=24 Moving to Node #0,0,0 Current State: 16:[8, 24], Operations: ['63-55=8', '58-34=24'] Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 8, 94, 81, 24 ]
29
[ "94-8=86", "81-24=57", "86-57=29" ]
Current State: 29:[8, 94, 81, 24], Operations: [] Exploring Operation: 94-8=86, Resulting Numbers: [81, 24, 86] Generated Node #2: [81, 24, 86] from Operation: 94-8=86 Current State: 29:[81, 24, 86], Operations: ['94-8=86'] Exploring Operation: 81-24=57, Resulting Numbers: [86, 57] Generated Node #3: [86, 57] from Operation: 81-24=57 Current State: 29:[86, 57], Operations: ['94-8=86', '81-24=57'] Exploring Operation: 86-57=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[8, 94, 81, 24], Operations: [] Exploring Operation: 94-81=13, Resulting Numbers: [8, 24, 13] Generated Node #0,0: 29:[8, 24, 13] Operation: 94-81=13 Moving to Node #0,0 Current State: 29:[8, 24, 13], Operations: ['94-81=13'] Exploring Operation: 8+13=21, Resulting Numbers: [24, 21] Generated Node #0,0,0: 29:[24, 21] Operation: 8+13=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[24, 21], Operations: ['94-81=13', '8+13=21'] Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,29 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
[ 17, 53, 48, 96 ]
87
[ "17*96=1632", "1632/48=34", "53+34=87" ]
Current State: 87:[17, 53, 48, 96], Operations: [] Exploring Operation: 17*96=1632, Resulting Numbers: [53, 48, 1632] Generated Node #2: [53, 48, 1632] from Operation: 17*96=1632 Current State: 87:[53, 48, 1632], Operations: ['17*96=1632'] Exploring Operation: 1632/48=34, Resulting Numbers: [53, 34] Generated Node #3: [53, 34] from Operation: 1632/48=34 Current State: 87:[53, 34], Operations: ['17*96=1632', '1632/48=34'] Exploring Operation: 53+34=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[17, 53, 48, 96], Operations: [] Exploring Operation: 53-48=5, Resulting Numbers: [17, 96, 5] Generated Node #0,0: 87:[17, 96, 5] Operation: 53-48=5 Exploring Operation: 53-17=36, Resulting Numbers: [48, 96, 36] Generated Node #0,1: 87:[48, 96, 36] Operation: 53-17=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[17, 96, 5], Operations: ['53-48=5'] Exploring Operation: 96-17=79, Resulting Numbers: [5, 79] Generated Node #0,0,0: 87:[5, 79] Operation: 96-17=79 Exploring Operation: 17*5=85, Resulting Numbers: [96, 85] Generated Node #0,0,1: 87:[96, 85] Operation: 17*5=85 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[5, 79], Operations: ['53-48=5', '96-17=79'] Exploring Operation: 79-5=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 5+79=84, Resulting Numbers: [84] 84,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[96, 85], Operations: ['53-48=5', '17*5=85'] Exploring Operation: 96+85=181, Resulting Numbers: [181] 181,87 unequal: No Solution Exploring Operation: 96-85=11, Resulting Numbers: [11] 11,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[48, 96, 36], Operations: ['53-17=36'] Exploring Operation: 48+36=84, Resulting Numbers: [96, 84] Generated Node #0,1,0: 87:[96, 84] Operation: 48+36=84 Exploring Operation: 96/48=2, Resulting Numbers: [36, 2] Generated Node #0,1,1: 87:[36, 2] Operation: 96/48=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[36, 2], Operations: ['53-17=36', '96/48=2'] Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,87 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[96, 84], Operations: ['53-17=36', '48+36=84'] Exploring Operation: 96-84=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 96+84=180, Resulting Numbers: [180] 180,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 80, 73, 32, 51 ]
26
[ "80-73=7", "51-32=19", "7+19=26" ]
Current State: 26:[80, 73, 32, 51], Operations: [] Exploring Operation: 80-73=7, Resulting Numbers: [32, 51, 7] Generated Node #2: [32, 51, 7] from Operation: 80-73=7 Current State: 26:[32, 51, 7], Operations: ['80-73=7'] Exploring Operation: 51-32=19, Resulting Numbers: [7, 19] Generated Node #3: [7, 19] from Operation: 51-32=19 Current State: 26:[7, 19], Operations: ['80-73=7', '51-32=19'] Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[80, 73, 32, 51], Operations: [] Exploring Operation: 80-32=48, Resulting Numbers: [73, 51, 48] Generated Node #0,0: 26:[73, 51, 48] Operation: 80-32=48 Exploring Operation: 73-51=22, Resulting Numbers: [80, 32, 22] Generated Node #0,1: 26:[80, 32, 22] Operation: 73-51=22 Exploring Operation: 80-51=29, Resulting Numbers: [73, 32, 29] Generated Node #0,2: 26:[73, 32, 29] Operation: 80-51=29 Exploring Operation: 80-73=7, Resulting Numbers: [32, 51, 7] Generated Node #0,3: 26:[32, 51, 7] Operation: 80-73=7 Moving to Node #0,3 Current State: 26:[32, 51, 7], Operations: ['80-73=7'] Exploring Operation: 32-7=25, Resulting Numbers: [51, 25] Generated Node #0,3,0: 26:[51, 25] Operation: 32-7=25 Exploring Operation: 51-7=44, Resulting Numbers: [32, 44] Generated Node #0,3,1: 26:[32, 44] Operation: 51-7=44 Exploring Operation: 51-32=19, Resulting Numbers: [7, 19] Generated Node #0,3,2: 26:[7, 19] Operation: 51-32=19 Exploring Operation: 32+7=39, Resulting Numbers: [51, 39] Generated Node #0,3,3: 26:[51, 39] Operation: 32+7=39 Moving to Node #0,2 Current State: 26:[73, 32, 29], Operations: ['80-51=29'] Exploring Operation: 73-32=41, Resulting Numbers: [29, 41] Generated Node #0,2,0: 26:[29, 41] Operation: 73-32=41 Exploring Operation: 32-29=3, Resulting Numbers: [73, 3] Generated Node #0,2,1: 26:[73, 3] Operation: 32-29=3 Exploring Operation: 73-29=44, Resulting Numbers: [32, 44] Generated Node #0,2,2: 26:[32, 44] Operation: 73-29=44 Exploring Operation: 73+32=105, Resulting Numbers: [29, 105] Generated Node #0,2,3: 26:[29, 105] Operation: 73+32=105 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 26:[29, 41], Operations: ['80-51=29', '73-32=41'] Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,26 unequal: No Solution Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,26 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 26:[32, 44], Operations: ['80-51=29', '73-29=44'] Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,26 unequal: No Solution Exploring Operation: 32*44=1408, Resulting Numbers: [1408] 1408,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 26:[73, 3], Operations: ['80-51=29', '32-29=3'] Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,26 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,26 unequal: No Solution Exploring Operation: 73*3=219, Resulting Numbers: [219] 219,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 26:[29, 105], Operations: ['80-51=29', '73+32=105'] Exploring Operation: 29+105=134, Resulting Numbers: [134] 134,26 unequal: No Solution Exploring Operation: 29*105=3045, Resulting Numbers: [3045] 3045,26 unequal: No Solution Exploring Operation: 105-29=76, Resulting Numbers: [76] 76,26 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: 26:[80, 32, 22], Operations: ['73-51=22'] Exploring Operation: 80-22=58, Resulting Numbers: [32, 58] Generated Node #0,1,0: 26:[32, 58] Operation: 80-22=58 Exploring Operation: 80+22=102, Resulting Numbers: [32, 102] Generated Node #0,1,1: 26:[32, 102] Operation: 80+22=102 Exploring Operation: 32-22=10, Resulting Numbers: [80, 10] Generated Node #0,1,2: 26:[80, 10] Operation: 32-22=10 Exploring Operation: 80-32=48, Resulting Numbers: [22, 48] Generated Node #0,1,3: 26:[22, 48] Operation: 80-32=48 Moving to Node #0,0 Current State: 26:[73, 51, 48], Operations: ['80-32=48'] Exploring Operation: 51-48=3, Resulting Numbers: [73, 3] Generated Node #0,0,0: 26:[73, 3] Operation: 51-48=3 Exploring Operation: 73-48=25, Resulting Numbers: [51, 25] Generated Node #0,0,1: 26:[51, 25] Operation: 73-48=25 Exploring Operation: 73+51=124, Resulting Numbers: [48, 124] Generated Node #0,0,2: 26:[48, 124] Operation: 73+51=124 Exploring Operation: 73-51=22, Resulting Numbers: [48, 22] Generated Node #0,0,3: 26:[48, 22] Operation: 73-51=22 Moving to Node #0,3,2 Current State: 26:[7, 19], Operations: ['80-73=7', '51-32=19'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[80, 73, 32, 51], Operations: [] Exploring Operation: 80-73=7, Resulting Numbers: [32, 51, 7] Generated Node #0,3: 26:[32, 51, 7] Operation: 80-73=7 Moving to Node #0,3 Current State: 26:[32, 51, 7], Operations: ['80-73=7'] Exploring Operation: 51-32=19, Resulting Numbers: [7, 19] Generated Node #0,3,2: 26:[7, 19] Operation: 51-32=19 Moving to Node #0,3,2 Current State: 26:[7, 19], Operations: ['80-73=7', '51-32=19'] Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
0.967014
hs_4
mult_heuristic
[ 63, 17, 56, 32 ]
72
[ "63*56=3528", "17+32=49", "3528/49=72" ]
Current State: 72:[63, 17, 56, 32], Operations: [] Exploring Operation: 63*56=3528, Resulting Numbers: [17, 32, 3528] Generated Node #2: [17, 32, 3528] from Operation: 63*56=3528 Current State: 72:[17, 32, 3528], Operations: ['63*56=3528'] Exploring Operation: 17+32=49, Resulting Numbers: [3528, 49] Generated Node #3: [3528, 49] from Operation: 17+32=49 Current State: 72:[3528, 49], Operations: ['63*56=3528', '17+32=49'] Exploring Operation: 3528/49=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[63, 17, 56, 32], Operations: [] Exploring Operation: 63-56=7, Resulting Numbers: [17, 32, 7] Generated Node #0,0: 72:[17, 32, 7] Operation: 63-56=7 Exploring Operation: 56-32=24, Resulting Numbers: [63, 17, 24] Generated Node #0,1: 72:[63, 17, 24] Operation: 56-32=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[17, 32, 7], Operations: ['63-56=7'] Exploring Operation: 32-17=15, Resulting Numbers: [7, 15] Generated Node #0,0,0: 72:[7, 15] Operation: 32-17=15 Exploring Operation: 32-7=25, Resulting Numbers: [17, 25] Generated Node #0,0,1: 72:[17, 25] Operation: 32-7=25 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 72:[17, 25], Operations: ['63-56=7', '32-7=25'] Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,72 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[7, 15], Operations: ['63-56=7', '32-17=15'] Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,72 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: 72:[63, 17, 24], Operations: ['56-32=24'] Exploring Operation: 63-24=39, Resulting Numbers: [17, 39] Generated Node #0,1,0: 72:[17, 39] Operation: 63-24=39 Exploring Operation: 63+17=80, Resulting Numbers: [24, 80] Generated Node #0,1,1: 72:[24, 80] Operation: 63+17=80 Moving to Node #0,1,0 Current State: 72:[17, 39], Operations: ['56-32=24', '63-24=39'] Exploring Operation: 17+39=56, Resulting Numbers: [56] 56,72 unequal: No Solution Exploring Operation: 39-17=22, Resulting Numbers: [22] 22,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[24, 80], Operations: ['56-32=24', '63+17=80'] Exploring Operation: 24+80=104, Resulting Numbers: [104] 104,72 unequal: No Solution Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,72 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
[ 50, 16, 53, 44 ]
92
[ "53-50=3", "16*3=48", "44+48=92" ]
Current State: 92:[50, 16, 53, 44], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [16, 44, 3] Generated Node #2: [16, 44, 3] from Operation: 53-50=3 Current State: 92:[16, 44, 3], Operations: ['53-50=3'] Exploring Operation: 16*3=48, Resulting Numbers: [44, 48] Generated Node #3: [44, 48] from Operation: 16*3=48 Current State: 92:[44, 48], Operations: ['53-50=3', '16*3=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[50, 16, 53, 44], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [16, 44, 3] Generated Node #0,0: 92:[16, 44, 3] Operation: 53-50=3 Exploring Operation: 53-16=37, Resulting Numbers: [50, 44, 37] Generated Node #0,1: 92:[50, 44, 37] Operation: 53-16=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[16, 44, 3], Operations: ['53-50=3'] Exploring Operation: 16*3=48, Resulting Numbers: [44, 48] Generated Node #0,0,0: 92:[44, 48] Operation: 16*3=48 Exploring Operation: 44-16=28, Resulting Numbers: [3, 28] Generated Node #0,0,1: 92:[3, 28] Operation: 44-16=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[44, 48], Operations: ['53-50=3', '16*3=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[50, 16, 53, 44], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [16, 44, 3] Generated Node #0,0: 92:[16, 44, 3] Operation: 53-50=3 Moving to Node #0,0 Current State: 92:[16, 44, 3], Operations: ['53-50=3'] Exploring Operation: 16*3=48, Resulting Numbers: [44, 48] Generated Node #0,0,0: 92:[44, 48] Operation: 16*3=48 Moving to Node #0,0,0 Current State: 92:[44, 48], Operations: ['53-50=3', '16*3=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 49, 55, 19, 61 ]
38
[ "49+61=110", "110/55=2", "19*2=38" ]
Current State: 38:[49, 55, 19, 61], Operations: [] Exploring Operation: 49+61=110, Resulting Numbers: [55, 19, 110] Generated Node #2: [55, 19, 110] from Operation: 49+61=110 Current State: 38:[55, 19, 110], Operations: ['49+61=110'] Exploring Operation: 110/55=2, Resulting Numbers: [19, 2] Generated Node #3: [19, 2] from Operation: 110/55=2 Current State: 38:[19, 2], Operations: ['49+61=110', '110/55=2'] Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[49, 55, 19, 61], Operations: [] Exploring Operation: 61-49=12, Resulting Numbers: [55, 19, 12] Generated Node #0,0: 38:[55, 19, 12] Operation: 61-49=12 Exploring Operation: 61-19=42, Resulting Numbers: [49, 55, 42] Generated Node #0,1: 38:[49, 55, 42] Operation: 61-19=42 Exploring Operation: 55-49=6, Resulting Numbers: [19, 61, 6] Generated Node #0,2: 38:[19, 61, 6] Operation: 55-49=6 Exploring Operation: 61-55=6, Resulting Numbers: [49, 19, 6] Generated Node #0,3: 38:[49, 19, 6] Operation: 61-55=6 Exploring Operation: 55-19=36, Resulting Numbers: [49, 61, 36] Generated Node #0,4: 38:[49, 61, 36] Operation: 55-19=36 Moving to Node #0,3 Current State: 38:[49, 19, 6], Operations: ['61-55=6'] Exploring Operation: 49-6=43, Resulting Numbers: [19, 43] Generated Node #0,3,0: 38:[19, 43] Operation: 49-6=43 Exploring Operation: 49-19=30, Resulting Numbers: [6, 30] Generated Node #0,3,1: 38:[6, 30] Operation: 49-19=30 Exploring Operation: 49+6=55, Resulting Numbers: [19, 55] Generated Node #0,3,2: 38:[19, 55] Operation: 49+6=55 Exploring Operation: 19+6=25, Resulting Numbers: [49, 25] Generated Node #0,3,3: 38:[49, 25] Operation: 19+6=25 Exploring Operation: 19-6=13, Resulting Numbers: [49, 13] Generated Node #0,3,4: 38:[49, 13] Operation: 19-6=13 Moving to Node #0,0 Current State: 38:[55, 19, 12], Operations: ['61-49=12'] Exploring Operation: 19+12=31, Resulting Numbers: [55, 31] Generated Node #0,0,0: 38:[55, 31] Operation: 19+12=31 Exploring Operation: 19-12=7, Resulting Numbers: [55, 7] Generated Node #0,0,1: 38:[55, 7] Operation: 19-12=7 Exploring Operation: 55-12=43, Resulting Numbers: [19, 43] Generated Node #0,0,2: 38:[19, 43] Operation: 55-12=43 Exploring Operation: 55-19=36, Resulting Numbers: [12, 36] Generated Node #0,0,3: 38:[12, 36] Operation: 55-19=36 Exploring Operation: 55+12=67, Resulting Numbers: [19, 67] Generated Node #0,0,4: 38:[19, 67] Operation: 55+12=67 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 38:[19, 43], Operations: ['61-49=12', '55-12=43'] Exploring Operation: 19*43=817, Resulting Numbers: [817] 817,38 unequal: No Solution Exploring Operation: 43-19=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 19+43=62, Resulting Numbers: [62] 62,38 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 #0,0,3 Current State: 38:[12, 36], Operations: ['61-49=12', '55-19=36'] Exploring Operation: 12*36=432, Resulting Numbers: [432] 432,38 unequal: No Solution Exploring Operation: 12+36=48, Resulting Numbers: [48] 48,38 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,38 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 #0,0,1 Current State: 38:[55, 7], Operations: ['61-49=12', '19-12=7'] Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,38 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,38 unequal: No Solution Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,38 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 #0,0,0 Current State: 38:[55, 31], Operations: ['61-49=12', '19+12=31'] Exploring Operation: 55+31=86, Resulting Numbers: [86] 86,38 unequal: No Solution Exploring Operation: 55-31=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 55*31=1705, Resulting Numbers: [1705] 1705,38 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 #0,0,4 Current State: 38:[19, 67], Operations: ['61-49=12', '55+12=67'] Exploring Operation: 19*67=1273, Resulting Numbers: [1273] 1273,38 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,38 unequal: No Solution Exploring Operation: 19+67=86, Resulting Numbers: [86] 86,38 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: 38:[19, 61, 6], Operations: ['55-49=6'] Exploring Operation: 61+6=67, Resulting Numbers: [19, 67] Generated Node #0,2,0: 38:[19, 67] Operation: 61+6=67 Exploring Operation: 61-6=55, Resulting Numbers: [19, 55] Generated Node #0,2,1: 38:[19, 55] Operation: 61-6=55 Exploring Operation: 61-19=42, Resulting Numbers: [6, 42] Generated Node #0,2,2: 38:[6, 42] Operation: 61-19=42 Exploring Operation: 19-6=13, Resulting Numbers: [61, 13] Generated Node #0,2,3: 38:[61, 13] Operation: 19-6=13 Exploring Operation: 19+6=25, Resulting Numbers: [61, 25] Generated Node #0,2,4: 38:[61, 25] Operation: 19+6=25 Moving to Node #0,1 Current State: 38:[49, 55, 42], Operations: ['61-19=42'] Exploring Operation: 49+55=104, Resulting Numbers: [42, 104] Generated Node #0,1,0: 38:[42, 104] Operation: 49+55=104 Exploring Operation: 49+42=91, Resulting Numbers: [55, 91] Generated Node #0,1,1: 38:[55, 91] Operation: 49+42=91 Exploring Operation: 55-49=6, Resulting Numbers: [42, 6] Generated Node #0,1,2: 38:[42, 6] Operation: 55-49=6 Exploring Operation: 49-42=7, Resulting Numbers: [55, 7] Generated Node #0,1,3: 38:[55, 7] Operation: 49-42=7 Exploring Operation: 55-42=13, Resulting Numbers: [49, 13] Generated Node #0,1,4: 38:[49, 13] Operation: 55-42=13 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 38:[42, 6], Operations: ['61-19=42', '55-49=6'] Exploring Operation: 42*6=252, Resulting Numbers: [252] 252,38 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,38 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 #0,1,4 Current State: 38:[49, 13], Operations: ['61-19=42', '55-42=13'] Exploring Operation: 49+13=62, Resulting Numbers: [62] 62,38 unequal: No Solution Exploring Operation: 49*13=637, Resulting Numbers: [637] 637,38 unequal: No Solution Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,38 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 #0,1,3 Current State: 38:[55, 7], Operations: ['61-19=42', '49-42=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,38 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,38 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,38 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 #0,1,0 Current State: 38:[42, 104], Operations: ['61-19=42', '49+55=104'] Exploring Operation: 42*104=4368, Resulting Numbers: [4368] 4368,38 unequal: No Solution Exploring Operation: 42+104=146, Resulting Numbers: [146] 146,38 unequal: No Solution Exploring Operation: 104-42=62, Resulting Numbers: [62] 62,38 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 #0,1,1 Current State: 38:[55, 91], Operations: ['61-19=42', '49+42=91'] Exploring Operation: 55*91=5005, Resulting Numbers: [5005] 5005,38 unequal: No Solution Exploring Operation: 91-55=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 55+91=146, Resulting Numbers: [146] 146,38 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: 38:[49, 61, 36], Operations: ['55-19=36'] Exploring Operation: 61-49=12, Resulting Numbers: [36, 12] Generated Node #0,4,0: 38:[36, 12] Operation: 61-49=12 Exploring Operation: 61+36=97, Resulting Numbers: [49, 97] Generated Node #0,4,1: 38:[49, 97] Operation: 61+36=97 Exploring Operation: 49+36=85, Resulting Numbers: [61, 85] Generated Node #0,4,2: 38:[61, 85] Operation: 49+36=85 Exploring Operation: 49-36=13, Resulting Numbers: [61, 13] Generated Node #0,4,3: 38:[61, 13] Operation: 49-36=13 Exploring Operation: 61-36=25, Resulting Numbers: [49, 25] Generated Node #0,4,4: 38:[49, 25] Operation: 61-36=25 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 38:[36, 12], Operations: ['55-19=36', '61-49=12'] Exploring Operation: 36*12=432, Resulting Numbers: [432] 432,38 unequal: No Solution Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 36+12=48, Resulting Numbers: [48] 48,38 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 #0,4,4 Current State: 38:[49, 25], Operations: ['55-19=36', '61-36=25'] Exploring Operation: 49*25=1225, Resulting Numbers: [1225] 1225,38 unequal: No Solution Exploring Operation: 49+25=74, Resulting Numbers: [74] 74,38 unequal: No Solution Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,38 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 #0,4,3 Current State: 38:[61, 13], Operations: ['55-19=36', '49-36=13'] Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,38 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,38 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,38 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 #0,4,1 Current State: 38:[49, 97], Operations: ['55-19=36', '61+36=97'] Exploring Operation: 49+97=146, Resulting Numbers: [146] 146,38 unequal: No Solution Exploring Operation: 49*97=4753, Resulting Numbers: [4753] 4753,38 unequal: No Solution Exploring Operation: 97-49=48, Resulting Numbers: [48] 48,38 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 #0,4,2 Current State: 38:[61, 85], Operations: ['55-19=36', '49+36=85'] Exploring Operation: 61*85=5185, Resulting Numbers: [5185] 5185,38 unequal: No Solution Exploring Operation: 61+85=146, Resulting Numbers: [146] 146,38 unequal: No Solution Exploring Operation: 85-61=24, Resulting Numbers: [24] 24,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 38:[19, 43], Operations: ['61-55=6', '49-6=43'] Exploring Operation: 19*43=817, Resulting Numbers: [817] 817,38 unequal: No Solution Exploring Operation: 43-19=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 19+43=62, Resulting Numbers: [62] 62,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[6, 42], Operations: ['55-49=6', '61-19=42'] Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 6*42=252, Resulting Numbers: [252] 252,38 unequal: No Solution Exploring Operation: 6+42=48, Resulting Numbers: [48] 48,38 unequal: No Solution Moving to Node #0,3,1 Current State: 38:[6, 30], Operations: ['61-55=6', '49-19=30'] Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 6+30=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 6*30=180, Resulting Numbers: [180] 180,38 unequal: No Solution Moving to Node #0,2,1 Current State: 38:[19, 55], Operations: ['55-49=6', '61-6=55'] Exploring Operation: 55-19=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 19*55=1045, Resulting Numbers: [1045] 1045,38 unequal: No Solution Exploring Operation: 19+55=74, Resulting Numbers: [74] 74,38 unequal: No Solution Moving to Node #0,3,2 Current State: 38:[19, 55], Operations: ['61-55=6', '49+6=55'] Exploring Operation: 19+55=74, Resulting Numbers: [74] 74,38 unequal: No Solution Exploring Operation: 55-19=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 19*55=1045, Resulting Numbers: [1045] 1045,38 unequal: No Solution Moving to Node #0,3,4 Current State: 38:[49, 13], Operations: ['61-55=6', '19-6=13'] Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 49+13=62, Resulting Numbers: [62] 62,38 unequal: No Solution Exploring Operation: 49*13=637, Resulting Numbers: [637] 637,38 unequal: No Solution Moving to Node #0,3,3 Current State: 38:[49, 25], Operations: ['61-55=6', '19+6=25'] Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 49*25=1225, Resulting Numbers: [1225] 1225,38 unequal: No Solution Exploring Operation: 49+25=74, Resulting Numbers: [74] 74,38 unequal: No Solution Moving to Node #0,2,0 Current State: 38:[19, 67], Operations: ['55-49=6', '61+6=67'] Exploring Operation: 19+67=86, Resulting Numbers: [86] 86,38 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,38 unequal: No Solution Exploring Operation: 19*67=1273, Resulting Numbers: [1273] 1273,38 unequal: No Solution Moving to Node #0,2,4 Current State: 38:[61, 25], Operations: ['55-49=6', '19+6=25'] Exploring Operation: 61+25=86, Resulting Numbers: [86] 86,38 unequal: No Solution Exploring Operation: 61*25=1525, Resulting Numbers: [1525] 1525,38 unequal: No Solution Exploring Operation: 61-25=36, Resulting Numbers: [36] 36,38 unequal: No Solution Moving to Node #0,2,3 Current State: 38:[61, 13], Operations: ['55-49=6', '19-6=13'] Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,38 unequal: No Solution Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,38 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,38 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 41, 66, 84, 48 ]
61
[ "66-41=25", "84-48=36", "25+36=61" ]
Current State: 61:[41, 66, 84, 48], Operations: [] Exploring Operation: 66-41=25, Resulting Numbers: [84, 48, 25] Generated Node #2: [84, 48, 25] from Operation: 66-41=25 Current State: 61:[84, 48, 25], Operations: ['66-41=25'] Exploring Operation: 84-48=36, Resulting Numbers: [25, 36] Generated Node #3: [25, 36] from Operation: 84-48=36 Current State: 61:[25, 36], Operations: ['66-41=25', '84-48=36'] Exploring Operation: 25+36=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[41, 66, 84, 48], Operations: [] Exploring Operation: 84-66=18, Resulting Numbers: [41, 48, 18] Generated Node #0,0: 61:[41, 48, 18] Operation: 84-66=18 Exploring Operation: 84-48=36, Resulting Numbers: [41, 66, 36] Generated Node #0,1: 61:[41, 66, 36] Operation: 84-48=36 Exploring Operation: 41+48=89, Resulting Numbers: [66, 84, 89] Generated Node #0,2: 61:[66, 84, 89] Operation: 41+48=89 Exploring Operation: 66-41=25, Resulting Numbers: [84, 48, 25] Generated Node #0,3: 61:[84, 48, 25] Operation: 66-41=25 Exploring Operation: 84-41=43, Resulting Numbers: [66, 48, 43] Generated Node #0,4: 61:[66, 48, 43] Operation: 84-41=43 Moving to Node #0,4 Current State: 61:[66, 48, 43], Operations: ['84-41=43'] Exploring Operation: 66+43=109, Resulting Numbers: [48, 109] Generated Node #0,4,0: 61:[48, 109] Operation: 66+43=109 Exploring Operation: 66-48=18, Resulting Numbers: [43, 18] Generated Node #0,4,1: 61:[43, 18] Operation: 66-48=18 Exploring Operation: 48-43=5, Resulting Numbers: [66, 5] Generated Node #0,4,2: 61:[66, 5] Operation: 48-43=5 Exploring Operation: 66-43=23, Resulting Numbers: [48, 23] Generated Node #0,4,3: 61:[48, 23] Operation: 66-43=23 Exploring Operation: 48+43=91, Resulting Numbers: [66, 91] Generated Node #0,4,4: 61:[66, 91] Operation: 48+43=91 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 61:[66, 91], Operations: ['84-41=43', '48+43=91'] Exploring Operation: 66*91=6006, Resulting Numbers: [6006] 6006,61 unequal: No Solution Exploring Operation: 91-66=25, Resulting Numbers: [25] 25,61 unequal: No Solution Exploring Operation: 66+91=157, Resulting Numbers: [157] 157,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 61:[48, 23], Operations: ['84-41=43', '66-43=23'] Exploring Operation: 48*23=1104, Resulting Numbers: [1104] 1104,61 unequal: No Solution Exploring Operation: 48+23=71, Resulting Numbers: [71] 71,61 unequal: No Solution Exploring Operation: 48-23=25, Resulting Numbers: [25] 25,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 61:[48, 109], Operations: ['84-41=43', '66+43=109'] Exploring Operation: 48*109=5232, Resulting Numbers: [5232] 5232,61 unequal: No Solution Exploring Operation: 48+109=157, Resulting Numbers: [157] 157,61 unequal: No Solution Exploring Operation: 109-48=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[41, 66, 84, 48], Operations: [] Exploring Operation: 84-41=43, Resulting Numbers: [66, 48, 43] Generated Node #0,4: 61:[66, 48, 43] Operation: 84-41=43 Moving to Node #0,4 Current State: 61:[66, 48, 43], Operations: ['84-41=43'] Exploring Operation: 66+43=109, Resulting Numbers: [48, 109] Generated Node #0,4,0: 61:[48, 109] Operation: 66+43=109 Moving to Node #0,4,0 Current State: 61:[48, 109], Operations: ['84-41=43', '66+43=109'] Exploring Operation: 109-48=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 14, 4, 13, 32 ]
54
[ "14*13=182", "4*32=128", "182-128=54" ]
Current State: 54:[14, 4, 13, 32], Operations: [] Exploring Operation: 14*13=182, Resulting Numbers: [4, 32, 182] Generated Node #2: [4, 32, 182] from Operation: 14*13=182 Current State: 54:[4, 32, 182], Operations: ['14*13=182'] Exploring Operation: 4*32=128, Resulting Numbers: [182, 128] Generated Node #3: [182, 128] from Operation: 4*32=128 Current State: 54:[182, 128], Operations: ['14*13=182', '4*32=128'] Exploring Operation: 182-128=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[14, 4, 13, 32], Operations: [] Exploring Operation: 32-14=18, Resulting Numbers: [4, 13, 18] Generated Node #0,0: 54:[4, 13, 18] Operation: 32-14=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[4, 13, 18], Operations: ['32-14=18'] Exploring Operation: 13-4=9, Resulting Numbers: [18, 9] Generated Node #0,0,0: 54:[18, 9] Operation: 13-4=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[18, 9], Operations: ['32-14=18', '13-4=9'] Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 52, 95, 72, 12 ]
57
[ "72-52=20", "95*12=1140", "1140/20=57" ]
Current State: 57:[52, 95, 72, 12], Operations: [] Exploring Operation: 72-52=20, Resulting Numbers: [95, 12, 20] Generated Node #2: [95, 12, 20] from Operation: 72-52=20 Current State: 57:[95, 12, 20], Operations: ['72-52=20'] Exploring Operation: 95*12=1140, Resulting Numbers: [20, 1140] Generated Node #3: [20, 1140] from Operation: 95*12=1140 Current State: 57:[20, 1140], Operations: ['72-52=20', '95*12=1140'] Exploring Operation: 1140/20=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[52, 95, 72, 12], Operations: [] Exploring Operation: 95-72=23, Resulting Numbers: [52, 12, 23] Generated Node #0,0: 57:[52, 12, 23] Operation: 95-72=23 Exploring Operation: 72-52=20, Resulting Numbers: [95, 12, 20] Generated Node #0,1: 57:[95, 12, 20] Operation: 72-52=20 Exploring Operation: 95-52=43, Resulting Numbers: [72, 12, 43] Generated Node #0,2: 57:[72, 12, 43] Operation: 95-52=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[52, 12, 23], Operations: ['95-72=23'] Exploring Operation: 23-12=11, Resulting Numbers: [52, 11] Generated Node #0,0,0: 57:[52, 11] Operation: 23-12=11 Exploring Operation: 52-23=29, Resulting Numbers: [12, 29] Generated Node #0,0,1: 57:[12, 29] Operation: 52-23=29 Exploring Operation: 52+12=64, Resulting Numbers: [23, 64] Generated Node #0,0,2: 57:[23, 64] Operation: 52+12=64 Moving to Node #0,0,2 Current State: 57:[23, 64], Operations: ['95-72=23', '52+12=64'] Exploring Operation: 23+64=87, Resulting Numbers: [87] 87,57 unequal: No Solution Exploring Operation: 64-23=41, Resulting Numbers: [41] 41,57 unequal: No Solution Exploring Operation: 23*64=1472, Resulting Numbers: [1472] 1472,57 unequal: No Solution Moving to Node #0,0,0 Current State: 57:[52, 11], Operations: ['95-72=23', '23-12=11'] Exploring Operation: 52*11=572, Resulting Numbers: [572] 572,57 unequal: No Solution Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,57 unequal: No Solution Exploring Operation: 52+11=63, Resulting Numbers: [63] 63,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[12, 29], Operations: ['95-72=23', '52-23=29'] Exploring Operation: 12+29=41, Resulting Numbers: [41] 41,57 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,57 unequal: No Solution Exploring Operation: 12*29=348, Resulting Numbers: [348] 348,57 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:[72, 12, 43], Operations: ['95-52=43'] Exploring Operation: 72/12=6, Resulting Numbers: [43, 6] Generated Node #0,2,0: 57:[43, 6] Operation: 72/12=6 Exploring Operation: 72-12=60, Resulting Numbers: [43, 60] Generated Node #0,2,1: 57:[43, 60] Operation: 72-12=60 Exploring Operation: 72-43=29, Resulting Numbers: [12, 29] Generated Node #0,2,2: 57:[12, 29] Operation: 72-43=29 Moving to Node #0,2,0 Current State: 57:[43, 6], Operations: ['95-52=43', '72/12=6'] Exploring Operation: 43*6=258, Resulting Numbers: [258] 258,57 unequal: No Solution Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,57 unequal: No Solution Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[43, 60], Operations: ['95-52=43', '72-12=60'] Exploring Operation: 43+60=103, Resulting Numbers: [103] 103,57 unequal: No Solution Exploring Operation: 43*60=2580, Resulting Numbers: [2580] 2580,57 unequal: No Solution Exploring Operation: 60-43=17, Resulting Numbers: [17] 17,57 unequal: No Solution Moving to Node #0,2,2 Current State: 57:[12, 29], Operations: ['95-52=43', '72-43=29'] Exploring Operation: 12+29=41, Resulting Numbers: [41] 41,57 unequal: No Solution Exploring Operation: 12*29=348, Resulting Numbers: [348] 348,57 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,57 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 #0,1 Current State: 57:[95, 12, 20], Operations: ['72-52=20'] Exploring Operation: 20-12=8, Resulting Numbers: [95, 8] Generated Node #0,1,0: 57:[95, 8] Operation: 20-12=8 Exploring Operation: 95-20=75, Resulting Numbers: [12, 75] Generated Node #0,1,1: 57:[12, 75] Operation: 95-20=75 Exploring Operation: 95-12=83, Resulting Numbers: [20, 83] Generated Node #0,1,2: 57:[20, 83] Operation: 95-12=83 Moving to Node #0,1,1 Current State: 57:[12, 75], Operations: ['72-52=20', '95-20=75'] Exploring Operation: 75-12=63, Resulting Numbers: [63] 63,57 unequal: No Solution Exploring Operation: 12+75=87, Resulting Numbers: [87] 87,57 unequal: No Solution Exploring Operation: 12*75=900, Resulting Numbers: [900] 900,57 unequal: No Solution Moving to Node #0,1,2 Current State: 57:[20, 83], Operations: ['72-52=20', '95-12=83'] Exploring Operation: 20*83=1660, Resulting Numbers: [1660] 1660,57 unequal: No Solution Exploring Operation: 20+83=103, Resulting Numbers: [103] 103,57 unequal: No Solution Exploring Operation: 83-20=63, Resulting Numbers: [63] 63,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[95, 8], Operations: ['72-52=20', '20-12=8'] Exploring Operation: 95-8=87, Resulting Numbers: [87] 87,57 unequal: No Solution Exploring Operation: 95+8=103, Resulting Numbers: [103] 103,57 unequal: No Solution Exploring Operation: 95*8=760, Resulting Numbers: [760] 760,57 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