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
[ 90, 42, 41, 30 ]
55
[ "90/30=3", "42/3=14", "41+14=55" ]
Current State: 55:[90, 42, 41, 30], Operations: [] Exploring Operation: 90/30=3, Resulting Numbers: [42, 41, 3] Generated Node #2: [42, 41, 3] from Operation: 90/30=3 Current State: 55:[42, 41, 3], Operations: ['90/30=3'] Exploring Operation: 42/3=14, Resulting Numbers: [41, 14] Generated Node #3: [41, 14] from Operation: 42/3=14 Current State: 55:[41, 14], Operations: ['90/30=3', '42/3=14'] Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[90, 42, 41, 30], Operations: [] Exploring Operation: 90/30=3, Resulting Numbers: [42, 41, 3] Generated Node #0,0: 55:[42, 41, 3] Operation: 90/30=3 Moving to Node #0,0 Current State: 55:[42, 41, 3], Operations: ['90/30=3'] Exploring Operation: 42-41=1, Resulting Numbers: [3, 1] Generated Node #0,0,0: 55:[3, 1] Operation: 42-41=1 Moving to Node #0,0,0 Current State: 55:[3, 1], Operations: ['90/30=3', '42-41=1'] Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,55 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 31, 45, 64, 1 ]
96
[ "31-1=30", "45*64=2880", "2880/30=96" ]
Current State: 96:[31, 45, 64, 1], Operations: [] Exploring Operation: 31-1=30, Resulting Numbers: [45, 64, 30] Generated Node #2: [45, 64, 30] from Operation: 31-1=30 Current State: 96:[45, 64, 30], Operations: ['31-1=30'] Exploring Operation: 45*64=2880, Resulting Numbers: [30, 2880] Generated Node #3: [30, 2880] from Operation: 45*64=2880 Current State: 96:[30, 2880], Operations: ['31-1=30', '45*64=2880'] Exploring Operation: 2880/30=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[31, 45, 64, 1], Operations: [] Exploring Operation: 64-31=33, Resulting Numbers: [45, 1, 33] Generated Node #0,0: 96:[45, 1, 33] Operation: 64-31=33 Exploring Operation: 64-45=19, Resulting Numbers: [31, 1, 19] Generated Node #0,1: 96:[31, 1, 19] Operation: 64-45=19 Exploring Operation: 31+64=95, Resulting Numbers: [45, 1, 95] Generated Node #0,2: 96:[45, 1, 95] Operation: 31+64=95 Moving to Node #0,0 Current State: 96:[45, 1, 33], Operations: ['64-31=33'] Exploring Operation: 33-1=32, Resulting Numbers: [45, 32] Generated Node #0,0,0: 96:[45, 32] Operation: 33-1=32 Exploring Operation: 45-33=12, Resulting Numbers: [1, 12] Generated Node #0,0,1: 96:[1, 12] Operation: 45-33=12 Exploring Operation: 45+1=46, Resulting Numbers: [33, 46] Generated Node #0,0,2: 96:[33, 46] Operation: 45+1=46 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 96:[1, 12], Operations: ['64-31=33', '45-33=12'] Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 1+12=13, Resulting Numbers: [13] 13,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[45, 32], Operations: ['64-31=33', '33-1=32'] Exploring Operation: 45+32=77, Resulting Numbers: [77] 77,96 unequal: No Solution Exploring Operation: 45-32=13, Resulting Numbers: [13] 13,96 unequal: No Solution Exploring Operation: 45*32=1440, Resulting Numbers: [1440] 1440,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 96:[33, 46], Operations: ['64-31=33', '45+1=46'] Exploring Operation: 33+46=79, Resulting Numbers: [79] 79,96 unequal: No Solution Exploring Operation: 46-33=13, Resulting Numbers: [13] 13,96 unequal: No Solution Exploring Operation: 33*46=1518, Resulting Numbers: [1518] 1518,96 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: 96:[31, 1, 19], Operations: ['64-45=19'] Exploring Operation: 31-19=12, Resulting Numbers: [1, 12] Generated Node #0,1,0: 96:[1, 12] Operation: 31-19=12 Exploring Operation: 31+19=50, Resulting Numbers: [1, 50] Generated Node #0,1,1: 96:[1, 50] Operation: 31+19=50 Exploring Operation: 31+1=32, Resulting Numbers: [19, 32] Generated Node #0,1,2: 96:[19, 32] Operation: 31+1=32 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 96:[1, 12], Operations: ['64-45=19', '31-19=12'] Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 1+12=13, Resulting Numbers: [13] 13,96 unequal: No Solution Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 96:[1, 50], Operations: ['64-45=19', '31+19=50'] Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,96 unequal: No Solution Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,96 unequal: No Solution Exploring Operation: 1*50=50, Resulting Numbers: [50] 50,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 96:[19, 32], Operations: ['64-45=19', '31+1=32'] Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,96 unequal: No Solution Exploring Operation: 19*32=608, Resulting Numbers: [608] 608,96 unequal: No Solution Exploring Operation: 19+32=51, Resulting Numbers: [51] 51,96 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: 96:[45, 1, 95], Operations: ['31+64=95'] Exploring Operation: 95-45=50, Resulting Numbers: [1, 50] Generated Node #0,2,0: 96:[1, 50] Operation: 95-45=50 Exploring Operation: 45+1=46, Resulting Numbers: [95, 46] Generated Node #0,2,1: 96:[95, 46] Operation: 45+1=46 Exploring Operation: 1+95=96, Resulting Numbers: [45, 96] Generated Node #0,2,2: 96:[45, 96] Operation: 1+95=96 Moving to Node #0,2,0 Current State: 96:[1, 50], Operations: ['31+64=95', '95-45=50'] Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,96 unequal: No Solution Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,96 unequal: No Solution Exploring Operation: 1*50=50, Resulting Numbers: [50] 50,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[95, 46], Operations: ['31+64=95', '45+1=46'] Exploring Operation: 95+46=141, Resulting Numbers: [141] 141,96 unequal: No Solution Exploring Operation: 95*46=4370, Resulting Numbers: [4370] 4370,96 unequal: No Solution Exploring Operation: 95-46=49, Resulting Numbers: [49] 49,96 unequal: No Solution Moving to Node #0,2,2 Current State: 96:[45, 96], Operations: ['31+64=95', '1+95=96'] Exploring Operation: 96-45=51, Resulting Numbers: [51] 51,96 unequal: No Solution Exploring Operation: 45+96=141, Resulting Numbers: [141] 141,96 unequal: No Solution Exploring Operation: 45*96=4320, Resulting Numbers: [4320] 4320,96 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 6, 3, 70, 2 ]
85
[ "6*2=12", "3+70=73", "12+73=85" ]
Current State: 85:[6, 3, 70, 2], Operations: [] Exploring Operation: 6*2=12, Resulting Numbers: [3, 70, 12] Generated Node #2: [3, 70, 12] from Operation: 6*2=12 Current State: 85:[3, 70, 12], Operations: ['6*2=12'] Exploring Operation: 3+70=73, Resulting Numbers: [12, 73] Generated Node #3: [12, 73] from Operation: 3+70=73 Current State: 85:[12, 73], Operations: ['6*2=12', '3+70=73'] Exploring Operation: 12+73=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[6, 3, 70, 2], Operations: [] Exploring Operation: 3+70=73, Resulting Numbers: [6, 2, 73] Generated Node #0,0: 85:[6, 2, 73] Operation: 3+70=73 Exploring Operation: 70+2=72, Resulting Numbers: [6, 3, 72] Generated Node #0,1: 85:[6, 3, 72] Operation: 70+2=72 Exploring Operation: 3*2=6, Resulting Numbers: [6, 70, 6] Generated Node #0,2: 85:[6, 70, 6] Operation: 3*2=6 Exploring Operation: 6+70=76, Resulting Numbers: [3, 2, 76] Generated Node #0,3: 85:[3, 2, 76] Operation: 6+70=76 Exploring Operation: 3+2=5, Resulting Numbers: [6, 70, 5] Generated Node #0,4: 85:[6, 70, 5] Operation: 3+2=5 Start Sub Search at level 1: Moving to Node #0,3 Current State: 85:[3, 2, 76], Operations: ['6+70=76'] Exploring Operation: 3+76=79, Resulting Numbers: [2, 79] Generated Node #0,3,0: 85:[2, 79] Operation: 3+76=79 Exploring Operation: 2+76=78, Resulting Numbers: [3, 78] Generated Node #0,3,1: 85:[3, 78] Operation: 2+76=78 Exploring Operation: 3+2=5, Resulting Numbers: [76, 5] Generated Node #0,3,2: 85:[76, 5] Operation: 3+2=5 Exploring Operation: 3*2=6, Resulting Numbers: [76, 6] Generated Node #0,3,3: 85:[76, 6] Operation: 3*2=6 Exploring Operation: 3-2=1, Resulting Numbers: [76, 1] Generated Node #0,3,4: 85:[76, 1] Operation: 3-2=1 Moving to Node #0,3,0 Current State: 85:[2, 79], Operations: ['6+70=76', '3+76=79'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,85 unequal: No Solution Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 2*79=158, Resulting Numbers: [158] 158,85 unequal: No Solution Moving to Node #0,3,2 Current State: 85:[76, 5], Operations: ['6+70=76', '3+2=5'] Exploring Operation: 76*5=380, Resulting Numbers: [380] 380,85 unequal: No Solution Exploring Operation: 76+5=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 76-5=71, Resulting Numbers: [71] 71,85 unequal: No Solution Moving to Node #0,3,1 Current State: 85:[3, 78], Operations: ['6+70=76', '2+76=78'] Exploring Operation: 3+78=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,85 unequal: No Solution Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 3*78=234, Resulting Numbers: [234] 234,85 unequal: No Solution Moving to Node #0,3,3 Current State: 85:[76, 6], Operations: ['6+70=76', '3*2=6'] Exploring Operation: 76+6=82, Resulting Numbers: [82] 82,85 unequal: No Solution Exploring Operation: 76*6=456, Resulting Numbers: [456] 456,85 unequal: No Solution Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,85 unequal: No Solution Moving to Node #0,3,4 Current State: 85:[76, 1], Operations: ['6+70=76', '3-2=1'] Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,85 unequal: No Solution Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,85 unequal: No Solution Exploring Operation: 76*1=76, Resulting Numbers: [76] 76,85 unequal: No Solution Exploring Operation: 76+1=77, Resulting Numbers: [77] 77,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[6, 2, 73], Operations: ['3+70=73'] Exploring Operation: 6/2=3, Resulting Numbers: [73, 3] Generated Node #0,0,0: 85:[73, 3] Operation: 6/2=3 Exploring Operation: 6-2=4, Resulting Numbers: [73, 4] Generated Node #0,0,1: 85:[73, 4] Operation: 6-2=4 Exploring Operation: 6+2=8, Resulting Numbers: [73, 8] Generated Node #0,0,2: 85:[73, 8] Operation: 6+2=8 Exploring Operation: 6+73=79, Resulting Numbers: [2, 79] Generated Node #0,0,3: 85:[2, 79] Operation: 6+73=79 Exploring Operation: 2+73=75, Resulting Numbers: [6, 75] Generated Node #0,0,4: 85:[6, 75] Operation: 2+73=75 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 85:[2, 79], Operations: ['3+70=73', '6+73=79'] Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,85 unequal: No Solution Exploring Operation: 2*79=158, Resulting Numbers: [158] 158,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 85:[6, 75], Operations: ['3+70=73', '2+73=75'] Exploring Operation: 6+75=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 6*75=450, Resulting Numbers: [450] 450,85 unequal: No Solution Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 85:[73, 4], Operations: ['3+70=73', '6-2=4'] Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,85 unequal: No Solution Exploring Operation: 73*4=292, Resulting Numbers: [292] 292,85 unequal: No Solution Exploring Operation: 73+4=77, Resulting Numbers: [77] 77,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[73, 3], Operations: ['3+70=73', '6/2=3'] Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,85 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,85 unequal: No Solution Exploring Operation: 73*3=219, Resulting Numbers: [219] 219,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 85:[73, 8], Operations: ['3+70=73', '6+2=8'] Exploring Operation: 73*8=584, Resulting Numbers: [584] 584,85 unequal: No Solution 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 No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[6, 3, 72], Operations: ['70+2=72'] Exploring Operation: 72/6=12, Resulting Numbers: [3, 12] Generated Node #0,1,0: 85:[3, 12] Operation: 72/6=12 Exploring Operation: 6*3=18, Resulting Numbers: [72, 18] Generated Node #0,1,1: 85:[72, 18] Operation: 6*3=18 Exploring Operation: 72/3=24, Resulting Numbers: [6, 24] Generated Node #0,1,2: 85:[6, 24] Operation: 72/3=24 Exploring Operation: 3+72=75, Resulting Numbers: [6, 75] Generated Node #0,1,3: 85:[6, 75] Operation: 3+72=75 Exploring Operation: 6+72=78, Resulting Numbers: [3, 78] Generated Node #0,1,4: 85:[3, 78] Operation: 6+72=78 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 85:[3, 12], Operations: ['70+2=72', '72/6=12'] Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,85 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,85 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 85:[6, 24], Operations: ['70+2=72', '72/3=24'] Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,85 unequal: No Solution Exploring Operation: 6*24=144, Resulting Numbers: [144] 144,85 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 85:[3, 78], Operations: ['70+2=72', '6+72=78'] Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 3+78=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,85 unequal: No Solution Exploring Operation: 3*78=234, Resulting Numbers: [234] 234,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 85:[6, 75], Operations: ['70+2=72', '3+72=75'] Exploring Operation: 6*75=450, Resulting Numbers: [450] 450,85 unequal: No Solution Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,85 unequal: No Solution Exploring Operation: 6+75=81, Resulting Numbers: [81] 81,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 85:[72, 18], Operations: ['70+2=72', '6*3=18'] Exploring Operation: 72/18=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 72-18=54, Resulting Numbers: [54] 54,85 unequal: No Solution Exploring Operation: 72+18=90, Resulting Numbers: [90] 90,85 unequal: No Solution Exploring Operation: 72*18=1296, Resulting Numbers: [1296] 1296,85 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 #0,4 Current State: 85:[6, 70, 5], Operations: ['3+2=5'] Exploring Operation: 6-5=1, Resulting Numbers: [70, 1] Generated Node #0,4,0: 85:[70, 1] Operation: 6-5=1 Exploring Operation: 70+5=75, Resulting Numbers: [6, 75] Generated Node #0,4,1: 85:[6, 75] Operation: 70+5=75 Exploring Operation: 6+70=76, Resulting Numbers: [5, 76] Generated Node #0,4,2: 85:[5, 76] Operation: 6+70=76 Exploring Operation: 70-6=64, Resulting Numbers: [5, 64] Generated Node #0,4,3: 85:[5, 64] Operation: 70-6=64 Exploring Operation: 70/5=14, Resulting Numbers: [6, 14] Generated Node #0,4,4: 85:[6, 14] Operation: 70/5=14 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 85:[6, 14], Operations: ['3+2=5', '70/5=14'] Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,85 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 #0,4,2 Current State: 85:[5, 76], Operations: ['3+2=5', '6+70=76'] Exploring Operation: 5*76=380, Resulting Numbers: [380] 380,85 unequal: No Solution Exploring Operation: 5+76=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 76-5=71, Resulting Numbers: [71] 71,85 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 #0,4,1 Current State: 85:[6, 75], Operations: ['3+2=5', '70+5=75'] Exploring Operation: 6*75=450, Resulting Numbers: [450] 450,85 unequal: No Solution Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,85 unequal: No Solution Exploring Operation: 6+75=81, Resulting Numbers: [81] 81,85 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 #0,4,0 Current State: 85:[70, 1], Operations: ['3+2=5', '6-5=1'] Exploring Operation: 70*1=70, Resulting Numbers: [70] 70,85 unequal: No Solution Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,85 unequal: No Solution Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,85 unequal: No Solution Exploring Operation: 70+1=71, Resulting Numbers: [71] 71,85 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 #0,4,3 Current State: 85:[5, 64], Operations: ['3+2=5', '70-6=64'] Exploring Operation: 64-5=59, Resulting Numbers: [59] 59,85 unequal: No Solution Exploring Operation: 5+64=69, Resulting Numbers: [69] 69,85 unequal: No Solution Exploring Operation: 5*64=320, Resulting Numbers: [320] 320,85 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 #0,2 Current State: 85:[6, 70, 6], Operations: ['3*2=6'] Exploring Operation: 6/6=1, Resulting Numbers: [70, 1] Generated Node #0,2,0: 85:[70, 1] Operation: 6/6=1 Exploring Operation: 6-6=0, Resulting Numbers: [70, 0] Generated Node #0,2,1: 85:[70, 0] Operation: 6-6=0 Exploring Operation: 6+70=76, Resulting Numbers: [6, 76] Generated Node #0,2,2: 85:[6, 76] Operation: 6+70=76 Exploring Operation: 70+6=76, Resulting Numbers: [6, 76] Generated Node #0,2,3: 85:[6, 76] Operation: 70+6=76 Exploring Operation: 6+6=12, Resulting Numbers: [70, 12] Generated Node #0,2,4: 85:[70, 12] Operation: 6+6=12 Moving to Node #0,2,2 Current State: 85:[6, 76], Operations: ['3*2=6', '6+70=76'] Exploring Operation: 6*76=456, Resulting Numbers: [456] 456,85 unequal: No Solution Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,85 unequal: No Solution Exploring Operation: 6+76=82, Resulting Numbers: [82] 82,85 unequal: No Solution Moving to Node #0,2,3 Current State: 85:[6, 76], Operations: ['3*2=6', '70+6=76'] Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,85 unequal: No Solution Exploring Operation: 6+76=82, Resulting Numbers: [82] 82,85 unequal: No Solution Exploring Operation: 6*76=456, Resulting Numbers: [456] 456,85 unequal: No Solution Moving to Node #0,2,0 Current State: 85:[70, 1], Operations: ['3*2=6', '6/6=1'] Exploring Operation: 70+1=71, Resulting Numbers: [71] 71,85 unequal: No Solution Exploring Operation: 70*1=70, Resulting Numbers: [70] 70,85 unequal: No Solution Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,85 unequal: No Solution Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[70, 0], Operations: ['3*2=6', '6-6=0'] Exploring Operation: 70-0=70, Resulting Numbers: [70] 70,85 unequal: No Solution Exploring Operation: 70*0=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 70+0=70, Resulting Numbers: [70] 70,85 unequal: No Solution Moving to Node #0,2,4 Current State: 85:[70, 12], Operations: ['3*2=6', '6+6=12'] Exploring Operation: 70+12=82, Resulting Numbers: [82] 82,85 unequal: No Solution Exploring Operation: 70*12=840, Resulting Numbers: [840] 840,85 unequal: No Solution Exploring Operation: 70-12=58, Resulting Numbers: [58] 58,85 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
[ 8, 42, 6, 75 ]
90
[ "8+75=83", "42/6=7", "83+7=90" ]
Current State: 90:[8, 42, 6, 75], Operations: [] Exploring Operation: 8+75=83, Resulting Numbers: [42, 6, 83] Generated Node #2: [42, 6, 83] from Operation: 8+75=83 Current State: 90:[42, 6, 83], Operations: ['8+75=83'] Exploring Operation: 42/6=7, Resulting Numbers: [83, 7] Generated Node #3: [83, 7] from Operation: 42/6=7 Current State: 90:[83, 7], Operations: ['8+75=83', '42/6=7'] Exploring Operation: 83+7=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[8, 42, 6, 75], Operations: [] Exploring Operation: 8+75=83, Resulting Numbers: [42, 6, 83] Generated Node #0,0: 90:[42, 6, 83] Operation: 8+75=83 Exploring Operation: 42/6=7, Resulting Numbers: [8, 75, 7] Generated Node #0,1: 90:[8, 75, 7] Operation: 42/6=7 Exploring Operation: 6+75=81, Resulting Numbers: [8, 42, 81] Generated Node #0,2: 90:[8, 42, 81] Operation: 6+75=81 Exploring Operation: 75-42=33, Resulting Numbers: [8, 6, 33] Generated Node #0,3: 90:[8, 6, 33] Operation: 75-42=33 Moving to Node #0,3 Current State: 90:[8, 6, 33], Operations: ['75-42=33'] Exploring Operation: 33-6=27, Resulting Numbers: [8, 27] Generated Node #0,3,0: 90:[8, 27] Operation: 33-6=27 Exploring Operation: 8-6=2, Resulting Numbers: [33, 2] Generated Node #0,3,1: 90:[33, 2] Operation: 8-6=2 Exploring Operation: 8+6=14, Resulting Numbers: [33, 14] Generated Node #0,3,2: 90:[33, 14] Operation: 8+6=14 Exploring Operation: 8+33=41, Resulting Numbers: [6, 41] Generated Node #0,3,3: 90:[6, 41] Operation: 8+33=41 Moving to Node #0,0 Current State: 90:[42, 6, 83], Operations: ['8+75=83'] Exploring Operation: 42/6=7, Resulting Numbers: [83, 7] Generated Node #0,0,0: 90:[83, 7] Operation: 42/6=7 Exploring Operation: 6+83=89, Resulting Numbers: [42, 89] Generated Node #0,0,1: 90:[42, 89] Operation: 6+83=89 Exploring Operation: 42+6=48, Resulting Numbers: [83, 48] Generated Node #0,0,2: 90:[83, 48] Operation: 42+6=48 Exploring Operation: 83-42=41, Resulting Numbers: [6, 41] Generated Node #0,0,3: 90:[6, 41] Operation: 83-42=41 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[42, 89], Operations: ['8+75=83', '6+83=89'] Exploring Operation: 42*89=3738, Resulting Numbers: [3738] 3738,90 unequal: No Solution Exploring Operation: 89-42=47, Resulting Numbers: [47] 47,90 unequal: No Solution Exploring Operation: 42+89=131, Resulting Numbers: [131] 131,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 90:[6, 41], Operations: ['8+75=83', '83-42=41'] Exploring Operation: 6*41=246, Resulting Numbers: [246] 246,90 unequal: No Solution Exploring Operation: 6+41=47, Resulting Numbers: [47] 47,90 unequal: No Solution Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[83, 7], Operations: ['8+75=83', '42/6=7'] Exploring Operation: 83*7=581, Resulting Numbers: [581] 581,90 unequal: No Solution Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,90 unequal: No Solution Exploring Operation: 83+7=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[8, 42, 6, 75], Operations: [] Exploring Operation: 8+75=83, Resulting Numbers: [42, 6, 83] Generated Node #0,0: 90:[42, 6, 83] Operation: 8+75=83 Moving to Node #0,0 Current State: 90:[42, 6, 83], Operations: ['8+75=83'] Exploring Operation: 42/6=7, Resulting Numbers: [83, 7] Generated Node #0,0,0: 90:[83, 7] Operation: 42/6=7 Moving to Node #0,0,0 Current State: 90:[83, 7], Operations: ['8+75=83', '42/6=7'] Exploring Operation: 83+7=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_4
sum_heuristic
[ 24, 23, 95, 9 ]
98
[ "24*9=216", "23+95=118", "216-118=98" ]
Current State: 98:[24, 23, 95, 9], Operations: [] Exploring Operation: 24*9=216, Resulting Numbers: [23, 95, 216] Generated Node #2: [23, 95, 216] from Operation: 24*9=216 Current State: 98:[23, 95, 216], Operations: ['24*9=216'] Exploring Operation: 23+95=118, Resulting Numbers: [216, 118] Generated Node #3: [216, 118] from Operation: 23+95=118 Current State: 98:[216, 118], Operations: ['24*9=216', '23+95=118'] Exploring Operation: 216-118=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[24, 23, 95, 9], Operations: [] Exploring Operation: 24-9=15, Resulting Numbers: [23, 95, 15] Generated Node #0,0: 98:[23, 95, 15] Operation: 24-9=15 Exploring Operation: 24+23=47, Resulting Numbers: [95, 9, 47] Generated Node #0,1: 98:[95, 9, 47] Operation: 24+23=47 Exploring Operation: 24-23=1, Resulting Numbers: [95, 9, 1] Generated Node #0,2: 98:[95, 9, 1] Operation: 24-23=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[95, 9, 1], Operations: ['24-23=1'] Exploring Operation: 9-1=8, Resulting Numbers: [95, 8] Generated Node #0,2,0: 98:[95, 8] Operation: 9-1=8 Exploring Operation: 95+1=96, Resulting Numbers: [9, 96] Generated Node #0,2,1: 98:[9, 96] Operation: 95+1=96 Exploring Operation: 95*1=95, Resulting Numbers: [9, 95] Generated Node #0,2,2: 98:[9, 95] Operation: 95*1=95 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 98:[95, 8], Operations: ['24-23=1', '9-1=8'] Exploring Operation: 95*8=760, Resulting Numbers: [760] 760,98 unequal: No Solution Exploring Operation: 95-8=87, Resulting Numbers: [87] 87,98 unequal: No Solution Exploring Operation: 95+8=103, Resulting Numbers: [103] 103,98 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 #0,2,1 Current State: 98:[9, 96], Operations: ['24-23=1', '95+1=96'] Exploring Operation: 9*96=864, Resulting Numbers: [864] 864,98 unequal: No Solution Exploring Operation: 9+96=105, Resulting Numbers: [105] 105,98 unequal: No Solution Exploring Operation: 96-9=87, Resulting Numbers: [87] 87,98 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 #0,2,2 Current State: 98:[9, 95], Operations: ['24-23=1', '95*1=95'] Exploring Operation: 9+95=104, Resulting Numbers: [104] 104,98 unequal: No Solution Exploring Operation: 95-9=86, Resulting Numbers: [86] 86,98 unequal: No Solution Exploring Operation: 9*95=855, Resulting Numbers: [855] 855,98 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[95, 9, 47], Operations: ['24+23=47'] Exploring Operation: 95+9=104, Resulting Numbers: [47, 104] Generated Node #0,1,0: 98:[47, 104] Operation: 95+9=104 Exploring Operation: 9+47=56, Resulting Numbers: [95, 56] Generated Node #0,1,1: 98:[95, 56] Operation: 9+47=56 Exploring Operation: 95-47=48, Resulting Numbers: [9, 48] Generated Node #0,1,2: 98:[9, 48] Operation: 95-47=48 Moving to Node #0,1,2 Current State: 98:[9, 48], Operations: ['24+23=47', '95-47=48'] Exploring Operation: 9*48=432, Resulting Numbers: [432] 432,98 unequal: No Solution Exploring Operation: 9+48=57, Resulting Numbers: [57] 57,98 unequal: No Solution Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[47, 104], Operations: ['24+23=47', '95+9=104'] Exploring Operation: 47+104=151, Resulting Numbers: [151] 151,98 unequal: No Solution Exploring Operation: 104-47=57, Resulting Numbers: [57] 57,98 unequal: No Solution Exploring Operation: 47*104=4888, Resulting Numbers: [4888] 4888,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[95, 56], Operations: ['24+23=47', '9+47=56'] Exploring Operation: 95+56=151, Resulting Numbers: [151] 151,98 unequal: No Solution Exploring Operation: 95-56=39, Resulting Numbers: [39] 39,98 unequal: No Solution Exploring Operation: 95*56=5320, Resulting Numbers: [5320] 5320,98 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:[23, 95, 15], Operations: ['24-9=15'] Exploring Operation: 23+95=118, Resulting Numbers: [15, 118] Generated Node #0,0,0: 98:[15, 118] Operation: 23+95=118 Exploring Operation: 23+15=38, Resulting Numbers: [95, 38] Generated Node #0,0,1: 98:[95, 38] Operation: 23+15=38 Exploring Operation: 23-15=8, Resulting Numbers: [95, 8] Generated Node #0,0,2: 98:[95, 8] Operation: 23-15=8 Moving to Node #0,0,2 Current State: 98:[95, 8], Operations: ['24-9=15', '23-15=8'] Exploring Operation: 95*8=760, Resulting Numbers: [760] 760,98 unequal: No Solution Exploring Operation: 95-8=87, Resulting Numbers: [87] 87,98 unequal: No Solution Exploring Operation: 95+8=103, Resulting Numbers: [103] 103,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[95, 38], Operations: ['24-9=15', '23+15=38'] Exploring Operation: 95-38=57, Resulting Numbers: [57] 57,98 unequal: No Solution Exploring Operation: 95+38=133, Resulting Numbers: [133] 133,98 unequal: No Solution Exploring Operation: 95*38=3610, Resulting Numbers: [3610] 3610,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[15, 118], Operations: ['24-9=15', '23+95=118'] Exploring Operation: 15+118=133, Resulting Numbers: [133] 133,98 unequal: No Solution Exploring Operation: 15*118=1770, Resulting Numbers: [1770] 1770,98 unequal: No Solution Exploring Operation: 118-15=103, Resulting Numbers: [103] 103,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 52, 3, 5, 4 ]
69
[ "52-3=49", "5*4=20", "49+20=69" ]
Current State: 69:[52, 3, 5, 4], Operations: [] Exploring Operation: 52-3=49, Resulting Numbers: [5, 4, 49] Generated Node #2: [5, 4, 49] from Operation: 52-3=49 Current State: 69:[5, 4, 49], Operations: ['52-3=49'] Exploring Operation: 5*4=20, Resulting Numbers: [49, 20] Generated Node #3: [49, 20] from Operation: 5*4=20 Current State: 69:[49, 20], Operations: ['52-3=49', '5*4=20'] Exploring Operation: 49+20=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[52, 3, 5, 4], Operations: [] Exploring Operation: 52+5=57, Resulting Numbers: [3, 4, 57] Generated Node #0,0: 69:[3, 4, 57] Operation: 52+5=57 Exploring Operation: 5-3=2, Resulting Numbers: [52, 4, 2] Generated Node #0,1: 69:[52, 4, 2] Operation: 5-3=2 Exploring Operation: 52+3=55, Resulting Numbers: [5, 4, 55] Generated Node #0,2: 69:[5, 4, 55] Operation: 52+3=55 Exploring Operation: 52/4=13, Resulting Numbers: [3, 5, 13] Generated Node #0,3: 69:[3, 5, 13] Operation: 52/4=13 Exploring Operation: 52+4=56, Resulting Numbers: [3, 5, 56] Generated Node #0,4: 69:[3, 5, 56] Operation: 52+4=56 Start Sub Search at level 1: Moving to Node #0,3 Current State: 69:[3, 5, 13], Operations: ['52/4=13'] Exploring Operation: 5*13=65, Resulting Numbers: [3, 65] Generated Node #0,3,0: 69:[3, 65] Operation: 5*13=65 Exploring Operation: 13-3=10, Resulting Numbers: [5, 10] Generated Node #0,3,1: 69:[5, 10] Operation: 13-3=10 Exploring Operation: 13-5=8, Resulting Numbers: [3, 8] Generated Node #0,3,2: 69:[3, 8] Operation: 13-5=8 Exploring Operation: 3+13=16, Resulting Numbers: [5, 16] Generated Node #0,3,3: 69:[5, 16] Operation: 3+13=16 Exploring Operation: 5+13=18, Resulting Numbers: [3, 18] Generated Node #0,3,4: 69:[3, 18] Operation: 5+13=18 Moving to Node #0,3,0 Current State: 69:[3, 65], Operations: ['52/4=13', '5*13=65'] Exploring Operation: 3*65=195, Resulting Numbers: [195] 195,69 unequal: No Solution Exploring Operation: 3+65=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,69 unequal: No Solution Moving to Node #0,3,4 Current State: 69:[3, 18], Operations: ['52/4=13', '5+13=18'] Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,69 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,69 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[3, 8], Operations: ['52/4=13', '13-5=8'] Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,69 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,69 unequal: No Solution Moving to Node #0,3,1 Current State: 69:[5, 10], Operations: ['52/4=13', '13-3=10'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[5, 16], Operations: ['52/4=13', '3+13=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,69 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,69 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[3, 4, 57], Operations: ['52+5=57'] Exploring Operation: 4-3=1, Resulting Numbers: [57, 1] Generated Node #0,0,0: 69:[57, 1] Operation: 4-3=1 Exploring Operation: 57/3=19, Resulting Numbers: [4, 19] Generated Node #0,0,1: 69:[4, 19] Operation: 57/3=19 Exploring Operation: 3+4=7, Resulting Numbers: [57, 7] Generated Node #0,0,2: 69:[57, 7] Operation: 3+4=7 Exploring Operation: 3+57=60, Resulting Numbers: [4, 60] Generated Node #0,0,3: 69:[4, 60] Operation: 3+57=60 Exploring Operation: 4+57=61, Resulting Numbers: [3, 61] Generated Node #0,0,4: 69:[3, 61] Operation: 4+57=61 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 69:[4, 19], Operations: ['52+5=57', '57/3=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,69 unequal: No Solution Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 69:[3, 61], Operations: ['52+5=57', '4+57=61'] Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,69 unequal: No Solution Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,69 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 69:[4, 60], Operations: ['52+5=57', '3+57=60'] Exploring Operation: 60-4=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 4*60=240, Resulting Numbers: [240] 240,69 unequal: No Solution Exploring Operation: 4+60=64, Resulting Numbers: [64] 64,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[57, 1], Operations: ['52+5=57', '4-3=1'] Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,69 unequal: No Solution Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,69 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 69:[57, 7], Operations: ['52+5=57', '3+4=7'] Exploring Operation: 57*7=399, Resulting Numbers: [399] 399,69 unequal: No Solution Exploring Operation: 57+7=64, Resulting Numbers: [64] 64,69 unequal: No Solution Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 69:[3, 5, 56], Operations: ['52+4=56'] Exploring Operation: 3+56=59, Resulting Numbers: [5, 59] Generated Node #0,4,0: 69:[5, 59] Operation: 3+56=59 Exploring Operation: 5-3=2, Resulting Numbers: [56, 2] Generated Node #0,4,1: 69:[56, 2] Operation: 5-3=2 Exploring Operation: 5+56=61, Resulting Numbers: [3, 61] Generated Node #0,4,2: 69:[3, 61] Operation: 5+56=61 Exploring Operation: 56-3=53, Resulting Numbers: [5, 53] Generated Node #0,4,3: 69:[5, 53] Operation: 56-3=53 Exploring Operation: 3+5=8, Resulting Numbers: [56, 8] Generated Node #0,4,4: 69:[56, 8] Operation: 3+5=8 Moving to Node #0,4,2 Current State: 69:[3, 61], Operations: ['52+4=56', '5+56=61'] Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,69 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,69 unequal: No Solution Moving to Node #0,4,0 Current State: 69:[5, 59], Operations: ['52+4=56', '3+56=59'] Exploring Operation: 5*59=295, Resulting Numbers: [295] 295,69 unequal: No Solution Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,69 unequal: No Solution Exploring Operation: 5+59=64, Resulting Numbers: [64] 64,69 unequal: No Solution Moving to Node #0,4,1 Current State: 69:[56, 2], Operations: ['52+4=56', '5-3=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,69 unequal: No Solution Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 56*2=112, Resulting Numbers: [112] 112,69 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,69 unequal: No Solution Moving to Node #0,4,3 Current State: 69:[5, 53], Operations: ['52+4=56', '56-3=53'] Exploring Operation: 5+53=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 5*53=265, Resulting Numbers: [265] 265,69 unequal: No Solution Moving to Node #0,4,4 Current State: 69:[56, 8], Operations: ['52+4=56', '3+5=8'] Exploring Operation: 56*8=448, Resulting Numbers: [448] 448,69 unequal: No Solution Exploring Operation: 56-8=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 56+8=64, Resulting Numbers: [64] 64,69 unequal: No Solution Exploring Operation: 56/8=7, Resulting Numbers: [7] 7,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[5, 4, 55], Operations: ['52+3=55'] Exploring Operation: 5-4=1, Resulting Numbers: [55, 1] Generated Node #0,2,0: 69:[55, 1] Operation: 5-4=1 Exploring Operation: 55/5=11, Resulting Numbers: [4, 11] Generated Node #0,2,1: 69:[4, 11] Operation: 55/5=11 Exploring Operation: 4+55=59, Resulting Numbers: [5, 59] Generated Node #0,2,2: 69:[5, 59] Operation: 4+55=59 Exploring Operation: 5*4=20, Resulting Numbers: [55, 20] Generated Node #0,2,3: 69:[55, 20] Operation: 5*4=20 Exploring Operation: 5+55=60, Resulting Numbers: [4, 60] Generated Node #0,2,4: 69:[4, 60] Operation: 5+55=60 Moving to Node #0,2,1 Current State: 69:[4, 11], Operations: ['52+3=55', '55/5=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,69 unequal: No Solution Moving to Node #0,2,4 Current State: 69:[4, 60], Operations: ['52+3=55', '5+55=60'] Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 4+60=64, Resulting Numbers: [64] 64,69 unequal: No Solution Exploring Operation: 60-4=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 4*60=240, Resulting Numbers: [240] 240,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[5, 59], Operations: ['52+3=55', '4+55=59'] Exploring Operation: 5+59=64, Resulting Numbers: [64] 64,69 unequal: No Solution Exploring Operation: 5*59=295, Resulting Numbers: [295] 295,69 unequal: No Solution Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[55, 1], Operations: ['52+3=55', '5-4=1'] Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[55, 20], Operations: ['52+3=55', '5*4=20'] Exploring Operation: 55*20=1100, Resulting Numbers: [1100] 1100,69 unequal: No Solution Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,69 unequal: No Solution Exploring Operation: 55+20=75, Resulting Numbers: [75] 75,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[52, 4, 2], Operations: ['5-3=2'] Exploring Operation: 52/2=26, Resulting Numbers: [4, 26] Generated Node #0,1,0: 69:[4, 26] Operation: 52/2=26 Exploring Operation: 52+4=56, Resulting Numbers: [2, 56] Generated Node #0,1,1: 69:[2, 56] Operation: 52+4=56 Exploring Operation: 52+2=54, Resulting Numbers: [4, 54] Generated Node #0,1,2: 69:[4, 54] Operation: 52+2=54 Exploring Operation: 52/4=13, Resulting Numbers: [2, 13] Generated Node #0,1,3: 69:[2, 13] Operation: 52/4=13 Exploring Operation: 4-2=2, Resulting Numbers: [52, 2] Generated Node #0,1,4: 69:[52, 2] Operation: 4-2=2 Moving to Node #0,1,0 Current State: 69:[4, 26], Operations: ['5-3=2', '52/2=26'] Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,69 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,69 unequal: No Solution Moving to Node #0,1,3 Current State: 69:[2, 13], Operations: ['5-3=2', '52/4=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,69 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[2, 56], Operations: ['5-3=2', '52+4=56'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,69 unequal: No Solution Exploring Operation: 2+56=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,69 unequal: No Solution Exploring Operation: 2*56=112, Resulting Numbers: [112] 112,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[4, 54], Operations: ['5-3=2', '52+2=54'] Exploring Operation: 4*54=216, Resulting Numbers: [216] 216,69 unequal: No Solution Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,69 unequal: No Solution Moving to Node #0,1,4 Current State: 69:[52, 2], Operations: ['5-3=2', '4-2=2'] Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,69 unequal: No Solution Exploring Operation: 52*2=104, Resulting Numbers: [104] 104,69 unequal: No Solution Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,69 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
[ 6, 47, 56, 8 ]
55
[ "6*8=48", "47+56=103", "103-48=55" ]
Current State: 55:[6, 47, 56, 8], Operations: [] Exploring Operation: 6*8=48, Resulting Numbers: [47, 56, 48] Generated Node #2: [47, 56, 48] from Operation: 6*8=48 Current State: 55:[47, 56, 48], Operations: ['6*8=48'] Exploring Operation: 47+56=103, Resulting Numbers: [48, 103] Generated Node #3: [48, 103] from Operation: 47+56=103 Current State: 55:[48, 103], Operations: ['6*8=48', '47+56=103'] Exploring Operation: 103-48=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[6, 47, 56, 8], Operations: [] Exploring Operation: 47+8=55, Resulting Numbers: [6, 56, 55] Generated Node #0,0: 55:[6, 56, 55] Operation: 47+8=55 Exploring Operation: 56-47=9, Resulting Numbers: [6, 8, 9] Generated Node #0,1: 55:[6, 8, 9] Operation: 56-47=9 Exploring Operation: 6+47=53, Resulting Numbers: [56, 8, 53] Generated Node #0,2: 55:[56, 8, 53] Operation: 6+47=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[6, 56, 55], Operations: ['47+8=55'] Exploring Operation: 6+56=62, Resulting Numbers: [55, 62] Generated Node #0,0,0: 55:[55, 62] Operation: 6+56=62 Exploring Operation: 56-6=50, Resulting Numbers: [55, 50] Generated Node #0,0,1: 55:[55, 50] Operation: 56-6=50 Exploring Operation: 56-55=1, Resulting Numbers: [6, 1] Generated Node #0,0,2: 55:[6, 1] Operation: 56-55=1 Moving to Node #0,0,1 Current State: 55:[55, 50], Operations: ['47+8=55', '56-6=50'] Exploring Operation: 55+50=105, Resulting Numbers: [105] 105,55 unequal: No Solution Exploring Operation: 55*50=2750, Resulting Numbers: [2750] 2750,55 unequal: No Solution Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[6, 1], Operations: ['47+8=55', '56-55=1'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,55 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[55, 62], Operations: ['47+8=55', '6+56=62'] Exploring Operation: 62-55=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 55+62=117, Resulting Numbers: [117] 117,55 unequal: No Solution Exploring Operation: 55*62=3410, Resulting Numbers: [3410] 3410,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[6, 8, 9], Operations: ['56-47=9'] Exploring Operation: 6*9=54, Resulting Numbers: [8, 54] Generated Node #0,1,0: 55:[8, 54] Operation: 6*9=54 Exploring Operation: 8-6=2, Resulting Numbers: [9, 2] Generated Node #0,1,1: 55:[9, 2] Operation: 8-6=2 Exploring Operation: 6+8=14, Resulting Numbers: [9, 14] Generated Node #0,1,2: 55:[9, 14] Operation: 6+8=14 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[8, 54], Operations: ['56-47=9', '6*9=54'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,55 unequal: No Solution Exploring Operation: 8*54=432, Resulting Numbers: [432] 432,55 unequal: No Solution Exploring Operation: 8+54=62, Resulting Numbers: [62] 62,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 55:[9, 2], Operations: ['56-47=9', '8-6=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,55 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 55:[9, 14], Operations: ['56-47=9', '6+8=14'] Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,55 unequal: No Solution Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,55 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[56, 8, 53], Operations: ['6+47=53'] Exploring Operation: 8+53=61, Resulting Numbers: [56, 61] Generated Node #0,2,0: 55:[56, 61] Operation: 8+53=61 Exploring Operation: 56/8=7, Resulting Numbers: [53, 7] Generated Node #0,2,1: 55:[53, 7] Operation: 56/8=7 Exploring Operation: 56-53=3, Resulting Numbers: [8, 3] Generated Node #0,2,2: 55:[8, 3] Operation: 56-53=3 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 55:[53, 7], Operations: ['6+47=53', '56/8=7'] Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,55 unequal: No Solution Exploring Operation: 53*7=371, Resulting Numbers: [371] 371,55 unequal: No Solution Exploring Operation: 53+7=60, Resulting Numbers: [60] 60,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 55:[8, 3], Operations: ['6+47=53', '56-53=3'] Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,55 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 55:[56, 61], Operations: ['6+47=53', '8+53=61'] Exploring Operation: 56+61=117, Resulting Numbers: [117] 117,55 unequal: No Solution Exploring Operation: 61-56=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 56*61=3416, Resulting Numbers: [3416] 3416,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 21, 45, 8, 40 ]
71
[ "21+45=66", "40/8=5", "66+5=71" ]
Current State: 71:[21, 45, 8, 40], Operations: [] Exploring Operation: 21+45=66, Resulting Numbers: [8, 40, 66] Generated Node #2: [8, 40, 66] from Operation: 21+45=66 Current State: 71:[8, 40, 66], Operations: ['21+45=66'] Exploring Operation: 40/8=5, Resulting Numbers: [66, 5] Generated Node #3: [66, 5] from Operation: 40/8=5 Current State: 71:[66, 5], Operations: ['21+45=66', '40/8=5'] Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[21, 45, 8, 40], Operations: [] Exploring Operation: 21+45=66, Resulting Numbers: [8, 40, 66] Generated Node #0,0: 71:[8, 40, 66] Operation: 21+45=66 Exploring Operation: 21+40=61, Resulting Numbers: [45, 8, 61] Generated Node #0,1: 71:[45, 8, 61] Operation: 21+40=61 Exploring Operation: 21+8=29, Resulting Numbers: [45, 40, 29] Generated Node #0,2: 71:[45, 40, 29] Operation: 21+8=29 Exploring Operation: 45+8=53, Resulting Numbers: [21, 40, 53] Generated Node #0,3: 71:[21, 40, 53] Operation: 45+8=53 Exploring Operation: 8+40=48, Resulting Numbers: [21, 45, 48] Generated Node #0,4: 71:[21, 45, 48] Operation: 8+40=48 Moving to Node #0,0 Current State: 71:[8, 40, 66], Operations: ['21+45=66'] Exploring Operation: 8+40=48, Resulting Numbers: [66, 48] Generated Node #0,0,0: 71:[66, 48] Operation: 8+40=48 Exploring Operation: 66-8=58, Resulting Numbers: [40, 58] Generated Node #0,0,1: 71:[40, 58] Operation: 66-8=58 Exploring Operation: 40/8=5, Resulting Numbers: [66, 5] Generated Node #0,0,2: 71:[66, 5] Operation: 40/8=5 Exploring Operation: 8+66=74, Resulting Numbers: [40, 74] Generated Node #0,0,3: 71:[40, 74] Operation: 8+66=74 Exploring Operation: 40-8=32, Resulting Numbers: [66, 32] Generated Node #0,0,4: 71:[66, 32] Operation: 40-8=32 Moving to Node #0,2 Current State: 71:[45, 40, 29], Operations: ['21+8=29'] Exploring Operation: 45+40=85, Resulting Numbers: [29, 85] Generated Node #0,2,0: 71:[29, 85] Operation: 45+40=85 Exploring Operation: 40+29=69, Resulting Numbers: [45, 69] Generated Node #0,2,1: 71:[45, 69] Operation: 40+29=69 Exploring Operation: 40-29=11, Resulting Numbers: [45, 11] Generated Node #0,2,2: 71:[45, 11] Operation: 40-29=11 Exploring Operation: 45-29=16, Resulting Numbers: [40, 16] Generated Node #0,2,3: 71:[40, 16] Operation: 45-29=16 Exploring Operation: 45+29=74, Resulting Numbers: [40, 74] Generated Node #0,2,4: 71:[40, 74] Operation: 45+29=74 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 71:[45, 69], Operations: ['21+8=29', '40+29=69'] Exploring Operation: 45*69=3105, Resulting Numbers: [3105] 3105,71 unequal: No Solution Exploring Operation: 69-45=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 45+69=114, Resulting Numbers: [114] 114,71 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 #0,2,4 Current State: 71:[40, 74], Operations: ['21+8=29', '45+29=74'] Exploring Operation: 40*74=2960, Resulting Numbers: [2960] 2960,71 unequal: No Solution Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,71 unequal: No Solution Exploring Operation: 40+74=114, Resulting Numbers: [114] 114,71 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 #0,2,0 Current State: 71:[29, 85], Operations: ['21+8=29', '45+40=85'] Exploring Operation: 85-29=56, Resulting Numbers: [56] 56,71 unequal: No Solution Exploring Operation: 29+85=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 29*85=2465, Resulting Numbers: [2465] 2465,71 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 #0,2,2 Current State: 71:[45, 11], Operations: ['21+8=29', '40-29=11'] Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,71 unequal: No Solution Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,71 unequal: No Solution Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,71 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 #0,2,3 Current State: 71:[40, 16], Operations: ['21+8=29', '45-29=16'] Exploring Operation: 40-16=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 40+16=56, Resulting Numbers: [56] 56,71 unequal: No Solution Exploring Operation: 40*16=640, Resulting Numbers: [640] 640,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 71:[21, 45, 48], Operations: ['8+40=48'] Exploring Operation: 21+48=69, Resulting Numbers: [45, 69] Generated Node #0,4,0: 71:[45, 69] Operation: 21+48=69 Exploring Operation: 45+48=93, Resulting Numbers: [21, 93] Generated Node #0,4,1: 71:[21, 93] Operation: 45+48=93 Exploring Operation: 45-21=24, Resulting Numbers: [48, 24] Generated Node #0,4,2: 71:[48, 24] Operation: 45-21=24 Exploring Operation: 48-21=27, Resulting Numbers: [45, 27] Generated Node #0,4,3: 71:[45, 27] Operation: 48-21=27 Exploring Operation: 21+45=66, Resulting Numbers: [48, 66] Generated Node #0,4,4: 71:[48, 66] Operation: 21+45=66 Moving to Node #0,1 Current State: 71:[45, 8, 61], Operations: ['21+40=61'] Exploring Operation: 8+61=69, Resulting Numbers: [45, 69] Generated Node #0,1,0: 71:[45, 69] Operation: 8+61=69 Exploring Operation: 45-8=37, Resulting Numbers: [61, 37] Generated Node #0,1,1: 71:[61, 37] Operation: 45-8=37 Exploring Operation: 61-8=53, Resulting Numbers: [45, 53] Generated Node #0,1,2: 71:[45, 53] Operation: 61-8=53 Exploring Operation: 45+8=53, Resulting Numbers: [61, 53] Generated Node #0,1,3: 71:[61, 53] Operation: 45+8=53 Exploring Operation: 45+61=106, Resulting Numbers: [8, 106] Generated Node #0,1,4: 71:[8, 106] Operation: 45+61=106 Moving to Node #0,3 Current State: 71:[21, 40, 53], Operations: ['45+8=53'] Exploring Operation: 21+53=74, Resulting Numbers: [40, 74] Generated Node #0,3,0: 71:[40, 74] Operation: 21+53=74 Exploring Operation: 40-21=19, Resulting Numbers: [53, 19] Generated Node #0,3,1: 71:[53, 19] Operation: 40-21=19 Exploring Operation: 21+40=61, Resulting Numbers: [53, 61] Generated Node #0,3,2: 71:[53, 61] Operation: 21+40=61 Exploring Operation: 40+53=93, Resulting Numbers: [21, 93] Generated Node #0,3,3: 71:[21, 93] Operation: 40+53=93 Exploring Operation: 53-21=32, Resulting Numbers: [40, 32] Generated Node #0,3,4: 71:[40, 32] Operation: 53-21=32 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 71:[53, 61], Operations: ['45+8=53', '21+40=61'] Exploring Operation: 61-53=8, Resulting Numbers: [8] 8,71 unequal: No Solution Exploring Operation: 53*61=3233, Resulting Numbers: [3233] 3233,71 unequal: No Solution Exploring Operation: 53+61=114, Resulting Numbers: [114] 114,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 71:[40, 74], Operations: ['45+8=53', '21+53=74'] Exploring Operation: 40*74=2960, Resulting Numbers: [2960] 2960,71 unequal: No Solution Exploring Operation: 40+74=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 71:[53, 19], Operations: ['45+8=53', '40-21=19'] Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,71 unequal: No Solution Exploring Operation: 53*19=1007, Resulting Numbers: [1007] 1007,71 unequal: No Solution Exploring Operation: 53+19=72, Resulting Numbers: [72] 72,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 71:[40, 32], Operations: ['45+8=53', '53-21=32'] Exploring Operation: 40+32=72, Resulting Numbers: [72] 72,71 unequal: No Solution Exploring Operation: 40*32=1280, Resulting Numbers: [1280] 1280,71 unequal: No Solution Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 71:[21, 93], Operations: ['45+8=53', '40+53=93'] Exploring Operation: 21+93=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 93-21=72, Resulting Numbers: [72] 72,71 unequal: No Solution Exploring Operation: 21*93=1953, Resulting Numbers: [1953] 1953,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 71:[66, 48], Operations: ['21+45=66', '8+40=48'] Exploring Operation: 66*48=3168, Resulting Numbers: [3168] 3168,71 unequal: No Solution Exploring Operation: 66+48=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 66-48=18, Resulting Numbers: [18] 18,71 unequal: No Solution Moving to Node #0,4,0 Current State: 71:[45, 69], Operations: ['8+40=48', '21+48=69'] Exploring Operation: 69-45=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 45*69=3105, Resulting Numbers: [3105] 3105,71 unequal: No Solution Exploring Operation: 45+69=114, Resulting Numbers: [114] 114,71 unequal: No Solution Moving to Node #0,4,4 Current State: 71:[48, 66], Operations: ['8+40=48', '21+45=66'] Exploring Operation: 48*66=3168, Resulting Numbers: [3168] 3168,71 unequal: No Solution Exploring Operation: 66-48=18, Resulting Numbers: [18] 18,71 unequal: No Solution Exploring Operation: 48+66=114, Resulting Numbers: [114] 114,71 unequal: No Solution Moving to Node #0,1,3 Current State: 71:[61, 53], Operations: ['21+40=61', '45+8=53'] Exploring Operation: 61*53=3233, Resulting Numbers: [3233] 3233,71 unequal: No Solution Exploring Operation: 61+53=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 61-53=8, Resulting Numbers: [8] 8,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[45, 69], Operations: ['21+40=61', '8+61=69'] Exploring Operation: 69-45=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 45*69=3105, Resulting Numbers: [3105] 3105,71 unequal: No Solution Exploring Operation: 45+69=114, Resulting Numbers: [114] 114,71 unequal: No Solution Moving to Node #0,0,3 Current State: 71:[40, 74], Operations: ['21+45=66', '8+66=74'] Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,71 unequal: No Solution Exploring Operation: 40+74=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 40*74=2960, Resulting Numbers: [2960] 2960,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[45, 53], Operations: ['21+40=61', '61-8=53'] Exploring Operation: 45*53=2385, Resulting Numbers: [2385] 2385,71 unequal: No Solution Exploring Operation: 53-45=8, Resulting Numbers: [8] 8,71 unequal: No Solution Exploring Operation: 45+53=98, Resulting Numbers: [98] 98,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[61, 37], Operations: ['21+40=61', '45-8=37'] Exploring Operation: 61-37=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 61*37=2257, Resulting Numbers: [2257] 2257,71 unequal: No Solution Exploring Operation: 61+37=98, Resulting Numbers: [98] 98,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[40, 58], Operations: ['21+45=66', '66-8=58'] Exploring Operation: 40+58=98, Resulting Numbers: [98] 98,71 unequal: No Solution Exploring Operation: 58-40=18, Resulting Numbers: [18] 18,71 unequal: No Solution Exploring Operation: 40*58=2320, Resulting Numbers: [2320] 2320,71 unequal: No Solution Moving to Node #0,0,4 Current State: 71:[66, 32], Operations: ['21+45=66', '40-8=32'] Exploring Operation: 66-32=34, Resulting Numbers: [34] 34,71 unequal: No Solution Exploring Operation: 66*32=2112, Resulting Numbers: [2112] 2112,71 unequal: No Solution Exploring Operation: 66+32=98, Resulting Numbers: [98] 98,71 unequal: No Solution Moving to Node #0,4,3 Current State: 71:[45, 27], Operations: ['8+40=48', '48-21=27'] Exploring Operation: 45*27=1215, Resulting Numbers: [1215] 1215,71 unequal: No Solution Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,71 unequal: No Solution Exploring Operation: 45+27=72, Resulting Numbers: [72] 72,71 unequal: No Solution Moving to Node #0,4,2 Current State: 71:[48, 24], Operations: ['8+40=48', '45-21=24'] Exploring Operation: 48*24=1152, Resulting Numbers: [1152] 1152,71 unequal: No Solution Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 48+24=72, Resulting Numbers: [72] 72,71 unequal: No Solution Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[66, 5], Operations: ['21+45=66', '40/8=5'] Exploring Operation: 66*5=330, Resulting Numbers: [330] 330,71 unequal: No Solution Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[21, 45, 8, 40], Operations: [] Exploring Operation: 21+45=66, Resulting Numbers: [8, 40, 66] Generated Node #0,0: 71:[8, 40, 66] Operation: 21+45=66 Moving to Node #0,0 Current State: 71:[8, 40, 66], Operations: ['21+45=66'] Exploring Operation: 40/8=5, Resulting Numbers: [66, 5] Generated Node #0,0,2: 71:[66, 5] Operation: 40/8=5 Moving to Node #0,0,2 Current State: 71:[66, 5], Operations: ['21+45=66', '40/8=5'] Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
0.91059
hs_5
mult_heuristic
[ 36, 20, 6, 40 ]
14
[ "36/6=6", "40-20=20", "20-6=14" ]
Current State: 14:[36, 20, 6, 40], Operations: [] Exploring Operation: 36/6=6, Resulting Numbers: [20, 40, 6] Generated Node #2: [20, 40, 6] from Operation: 36/6=6 Current State: 14:[20, 40, 6], Operations: ['36/6=6'] Exploring Operation: 40-20=20, Resulting Numbers: [6, 20] Generated Node #3: [6, 20] from Operation: 40-20=20 Current State: 14:[6, 20], Operations: ['36/6=6', '40-20=20'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[36, 20, 6, 40], Operations: [] Exploring Operation: 40-20=20, Resulting Numbers: [36, 6, 20] Generated Node #0,0: 14:[36, 6, 20] Operation: 40-20=20 Exploring Operation: 40/20=2, Resulting Numbers: [36, 6, 2] Generated Node #0,1: 14:[36, 6, 2] Operation: 40/20=2 Exploring Operation: 40-36=4, Resulting Numbers: [20, 6, 4] Generated Node #0,2: 14:[20, 6, 4] Operation: 40-36=4 Exploring Operation: 36-20=16, Resulting Numbers: [6, 40, 16] Generated Node #0,3: 14:[6, 40, 16] Operation: 36-20=16 Moving to Node #0,2 Current State: 14:[20, 6, 4], Operations: ['40-36=4'] Exploring Operation: 6-4=2, Resulting Numbers: [20, 2] Generated Node #0,2,0: 14:[20, 2] Operation: 6-4=2 Exploring Operation: 20/4=5, Resulting Numbers: [6, 5] Generated Node #0,2,1: 14:[6, 5] Operation: 20/4=5 Exploring Operation: 20-4=16, Resulting Numbers: [6, 16] Generated Node #0,2,2: 14:[6, 16] Operation: 20-4=16 Exploring Operation: 20-6=14, Resulting Numbers: [4, 14] Generated Node #0,2,3: 14:[4, 14] Operation: 20-6=14 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 14:[4, 14], Operations: ['40-36=4', '20-6=14'] Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,14 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 14:[6, 5], Operations: ['40-36=4', '20/4=5'] Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,14 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 14:[6, 16], Operations: ['40-36=4', '20-4=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,14 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 14:[20, 2], Operations: ['40-36=4', '6-4=2'] Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,14 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,14 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: 14:[36, 6, 2], Operations: ['40/20=2'] Exploring Operation: 36-2=34, Resulting Numbers: [6, 34] Generated Node #0,1,0: 14:[6, 34] Operation: 36-2=34 Exploring Operation: 36/2=18, Resulting Numbers: [6, 18] Generated Node #0,1,1: 14:[6, 18] Operation: 36/2=18 Exploring Operation: 36-6=30, Resulting Numbers: [2, 30] Generated Node #0,1,2: 14:[2, 30] Operation: 36-6=30 Exploring Operation: 36/6=6, Resulting Numbers: [2, 6] Generated Node #0,1,3: 14:[2, 6] Operation: 36/6=6 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 14:[2, 6], Operations: ['40/20=2', '36/6=6'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 14:[6, 18], Operations: ['40/20=2', '36/2=18'] Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 6*18=108, Resulting Numbers: [108] 108,14 unequal: No Solution Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 14:[2, 30], Operations: ['40/20=2', '36-6=30'] Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,14 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,14 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,14 unequal: No Solution Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[6, 34], Operations: ['40/20=2', '36-2=34'] Exploring Operation: 6*34=204, Resulting Numbers: [204] 204,14 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,14 unequal: No Solution Exploring Operation: 6+34=40, Resulting Numbers: [40] 40,14 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: 14:[6, 40, 16], Operations: ['36-20=16'] Exploring Operation: 40-6=34, Resulting Numbers: [16, 34] Generated Node #0,3,0: 14:[16, 34] Operation: 40-6=34 Exploring Operation: 16-6=10, Resulting Numbers: [40, 10] Generated Node #0,3,1: 14:[40, 10] Operation: 16-6=10 Exploring Operation: 6+40=46, Resulting Numbers: [16, 46] Generated Node #0,3,2: 14:[16, 46] Operation: 6+40=46 Exploring Operation: 40-16=24, Resulting Numbers: [6, 24] Generated Node #0,3,3: 14:[6, 24] Operation: 40-16=24 Moving to Node #0,0 Current State: 14:[36, 6, 20], Operations: ['40-20=20'] Exploring Operation: 20-6=14, Resulting Numbers: [36, 14] Generated Node #0,0,0: 14:[36, 14] Operation: 20-6=14 Exploring Operation: 36-20=16, Resulting Numbers: [6, 16] Generated Node #0,0,1: 14:[6, 16] Operation: 36-20=16 Exploring Operation: 36/6=6, Resulting Numbers: [20, 6] Generated Node #0,0,2: 14:[20, 6] Operation: 36/6=6 Exploring Operation: 36-6=30, Resulting Numbers: [20, 30] Generated Node #0,0,3: 14:[20, 30] Operation: 36-6=30 Moving to Node #0,0,1 Current State: 14:[6, 16], Operations: ['40-20=20', '36-20=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,14 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,14 unequal: No Solution Moving to Node #0,0,2 Current State: 14:[20, 6], Operations: ['40-20=20', '36/6=6'] Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,14 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[36, 20, 6, 40], Operations: [] Exploring Operation: 40-20=20, Resulting Numbers: [36, 6, 20] Generated Node #0,0: 14:[36, 6, 20] Operation: 40-20=20 Moving to Node #0,0 Current State: 14:[36, 6, 20], Operations: ['40-20=20'] Exploring Operation: 36/6=6, Resulting Numbers: [20, 6] Generated Node #0,0,2: 14:[20, 6] Operation: 36/6=6 Moving to Node #0,0,2 Current State: 14:[20, 6], Operations: ['40-20=20', '36/6=6'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
0.949653
hs_4
mult_heuristic
[ 26, 52, 13, 23 ]
94
[ "52*23=1196", "26+1196=1222", "1222/13=94" ]
Current State: 94:[26, 52, 13, 23], Operations: [] Exploring Operation: 52*23=1196, Resulting Numbers: [26, 13, 1196] Generated Node #2: [26, 13, 1196] from Operation: 52*23=1196 Current State: 94:[26, 13, 1196], Operations: ['52*23=1196'] Exploring Operation: 26+1196=1222, Resulting Numbers: [13, 1222] Generated Node #3: [13, 1222] from Operation: 26+1196=1222 Current State: 94:[13, 1222], Operations: ['52*23=1196', '26+1196=1222'] Exploring Operation: 1222/13=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[26, 52, 13, 23], Operations: [] Exploring Operation: 26+23=49, Resulting Numbers: [52, 13, 49] Generated Node #0,0: 94:[52, 13, 49] Operation: 26+23=49 Exploring Operation: 52/26=2, Resulting Numbers: [13, 23, 2] Generated Node #0,1: 94:[13, 23, 2] Operation: 52/26=2 Exploring Operation: 26-23=3, Resulting Numbers: [52, 13, 3] Generated Node #0,2: 94:[52, 13, 3] Operation: 26-23=3 Exploring Operation: 26+13=39, Resulting Numbers: [52, 23, 39] Generated Node #0,3: 94:[52, 23, 39] Operation: 26+13=39 Exploring Operation: 26/13=2, Resulting Numbers: [52, 23, 2] Generated Node #0,4: 94:[52, 23, 2] Operation: 26/13=2 Moving to Node #0,2 Current State: 94:[52, 13, 3], Operations: ['26-23=3'] Exploring Operation: 13-3=10, Resulting Numbers: [52, 10] Generated Node #0,2,0: 94:[52, 10] Operation: 13-3=10 Exploring Operation: 52-13=39, Resulting Numbers: [3, 39] Generated Node #0,2,1: 94:[3, 39] Operation: 52-13=39 Exploring Operation: 52-3=49, Resulting Numbers: [13, 49] Generated Node #0,2,2: 94:[13, 49] Operation: 52-3=49 Exploring Operation: 13*3=39, Resulting Numbers: [52, 39] Generated Node #0,2,3: 94:[52, 39] Operation: 13*3=39 Exploring Operation: 52/13=4, Resulting Numbers: [3, 4] Generated Node #0,2,4: 94:[3, 4] Operation: 52/13=4 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 94:[3, 4], Operations: ['26-23=3', '52/13=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,94 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 94:[3, 39], Operations: ['26-23=3', '52-13=39'] Exploring Operation: 3*39=117, Resulting Numbers: [117] 117,94 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,94 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,94 unequal: No Solution Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 94:[52, 10], Operations: ['26-23=3', '13-3=10'] Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 52*10=520, Resulting Numbers: [520] 520,94 unequal: No Solution Exploring Operation: 52+10=62, Resulting Numbers: [62] 62,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 94:[13, 49], Operations: ['26-23=3', '52-3=49'] Exploring Operation: 13*49=637, Resulting Numbers: [637] 637,94 unequal: No Solution Exploring Operation: 13+49=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 94:[52, 39], Operations: ['26-23=3', '13*3=39'] Exploring Operation: 52*39=2028, Resulting Numbers: [2028] 2028,94 unequal: No Solution Exploring Operation: 52-39=13, Resulting Numbers: [13] 13,94 unequal: No Solution Exploring Operation: 52+39=91, Resulting Numbers: [91] 91,94 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: 94:[52, 13, 49], Operations: ['26+23=49'] Exploring Operation: 52+49=101, Resulting Numbers: [13, 101] Generated Node #0,0,0: 94:[13, 101] Operation: 52+49=101 Exploring Operation: 49-13=36, Resulting Numbers: [52, 36] Generated Node #0,0,1: 94:[52, 36] Operation: 49-13=36 Exploring Operation: 52-49=3, Resulting Numbers: [13, 3] Generated Node #0,0,2: 94:[13, 3] Operation: 52-49=3 Exploring Operation: 52-13=39, Resulting Numbers: [49, 39] Generated Node #0,0,3: 94:[49, 39] Operation: 52-13=39 Exploring Operation: 52/13=4, Resulting Numbers: [49, 4] Generated Node #0,0,4: 94:[49, 4] Operation: 52/13=4 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 94:[49, 4], Operations: ['26+23=49', '52/13=4'] Exploring Operation: 49*4=196, Resulting Numbers: [196] 196,94 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 49+4=53, Resulting Numbers: [53] 53,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 94:[49, 39], Operations: ['26+23=49', '52-13=39'] Exploring Operation: 49+39=88, Resulting Numbers: [88] 88,94 unequal: No Solution Exploring Operation: 49*39=1911, Resulting Numbers: [1911] 1911,94 unequal: No Solution Exploring Operation: 49-39=10, Resulting Numbers: [10] 10,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 94:[13, 3], Operations: ['26+23=49', '52-49=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,94 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,94 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 94:[52, 36], Operations: ['26+23=49', '49-13=36'] Exploring Operation: 52*36=1872, Resulting Numbers: [1872] 1872,94 unequal: No Solution Exploring Operation: 52-36=16, Resulting Numbers: [16] 16,94 unequal: No Solution Exploring Operation: 52+36=88, Resulting Numbers: [88] 88,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[13, 101], Operations: ['26+23=49', '52+49=101'] Exploring Operation: 13*101=1313, Resulting Numbers: [1313] 1313,94 unequal: No Solution Exploring Operation: 101-13=88, Resulting Numbers: [88] 88,94 unequal: No Solution Exploring Operation: 13+101=114, Resulting Numbers: [114] 114,94 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: 94:[52, 23, 2], Operations: ['26/13=2'] Exploring Operation: 52+23=75, Resulting Numbers: [2, 75] Generated Node #0,4,0: 94:[2, 75] Operation: 52+23=75 Exploring Operation: 52-2=50, Resulting Numbers: [23, 50] Generated Node #0,4,1: 94:[23, 50] Operation: 52-2=50 Exploring Operation: 23-2=21, Resulting Numbers: [52, 21] Generated Node #0,4,2: 94:[52, 21] Operation: 23-2=21 Exploring Operation: 52-23=29, Resulting Numbers: [2, 29] Generated Node #0,4,3: 94:[2, 29] Operation: 52-23=29 Exploring Operation: 23*2=46, Resulting Numbers: [52, 46] Generated Node #0,4,4: 94:[52, 46] Operation: 23*2=46 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 94:[52, 46], Operations: ['26/13=2', '23*2=46'] Exploring Operation: 52+46=98, Resulting Numbers: [98] 98,94 unequal: No Solution Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,94 unequal: No Solution Exploring Operation: 52*46=2392, Resulting Numbers: [2392] 2392,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 94:[2, 29], Operations: ['26/13=2', '52-23=29'] Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,94 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,94 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 94:[2, 75], Operations: ['26/13=2', '52+23=75'] Exploring Operation: 2+75=77, Resulting Numbers: [77] 77,94 unequal: No Solution Exploring Operation: 2*75=150, Resulting Numbers: [150] 150,94 unequal: No Solution Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 94:[23, 50], Operations: ['26/13=2', '52-2=50'] Exploring Operation: 23+50=73, Resulting Numbers: [73] 73,94 unequal: No Solution Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,94 unequal: No Solution Exploring Operation: 23*50=1150, Resulting Numbers: [1150] 1150,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 94:[52, 21], Operations: ['26/13=2', '23-2=21'] Exploring Operation: 52*21=1092, Resulting Numbers: [1092] 1092,94 unequal: No Solution Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,94 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,94 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: 94:[13, 23, 2], Operations: ['52/26=2'] Exploring Operation: 13+23=36, Resulting Numbers: [2, 36] Generated Node #0,1,0: 94:[2, 36] Operation: 13+23=36 Exploring Operation: 23-2=21, Resulting Numbers: [13, 21] Generated Node #0,1,1: 94:[13, 21] Operation: 23-2=21 Exploring Operation: 23*2=46, Resulting Numbers: [13, 46] Generated Node #0,1,2: 94:[13, 46] Operation: 23*2=46 Exploring Operation: 13-2=11, Resulting Numbers: [23, 11] Generated Node #0,1,3: 94:[23, 11] Operation: 13-2=11 Exploring Operation: 23-13=10, Resulting Numbers: [2, 10] Generated Node #0,1,4: 94:[2, 10] Operation: 23-13=10 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 94:[2, 10], Operations: ['52/26=2', '23-13=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,94 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 94:[2, 36], Operations: ['52/26=2', '13+23=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,94 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,94 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 94:[13, 46], Operations: ['52/26=2', '23*2=46'] Exploring Operation: 13+46=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 46-13=33, Resulting Numbers: [33] 33,94 unequal: No Solution Exploring Operation: 13*46=598, Resulting Numbers: [598] 598,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 94:[13, 21], Operations: ['52/26=2', '23-2=21'] Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,94 unequal: No Solution Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,94 unequal: No Solution Exploring Operation: 13*21=273, Resulting Numbers: [273] 273,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 94:[23, 11], Operations: ['52/26=2', '13-2=11'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 23*11=253, Resulting Numbers: [253] 253,94 unequal: No Solution Exploring Operation: 23+11=34, Resulting Numbers: [34] 34,94 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: 94:[52, 23, 39], Operations: ['26+13=39'] Exploring Operation: 39-23=16, Resulting Numbers: [52, 16] Generated Node #0,3,0: 94:[52, 16] Operation: 39-23=16 Exploring Operation: 52+39=91, Resulting Numbers: [23, 91] Generated Node #0,3,1: 94:[23, 91] Operation: 52+39=91 Exploring Operation: 23+39=62, Resulting Numbers: [52, 62] Generated Node #0,3,2: 94:[52, 62] Operation: 23+39=62 Exploring Operation: 52+23=75, Resulting Numbers: [39, 75] Generated Node #0,3,3: 94:[39, 75] Operation: 52+23=75 Exploring Operation: 52-23=29, Resulting Numbers: [39, 29] Generated Node #0,3,4: 94:[39, 29] Operation: 52-23=29 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 94:[52, 16], Operations: ['26+13=39', '39-23=16'] Exploring Operation: 52-16=36, Resulting Numbers: [36] 36,94 unequal: No Solution Exploring Operation: 52*16=832, Resulting Numbers: [832] 832,94 unequal: No Solution Exploring Operation: 52+16=68, Resulting Numbers: [68] 68,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 94:[52, 62], Operations: ['26+13=39', '23+39=62'] Exploring Operation: 52+62=114, Resulting Numbers: [114] 114,94 unequal: No Solution Exploring Operation: 62-52=10, Resulting Numbers: [10] 10,94 unequal: No Solution Exploring Operation: 52*62=3224, Resulting Numbers: [3224] 3224,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 94:[23, 91], Operations: ['26+13=39', '52+39=91'] Exploring Operation: 23+91=114, Resulting Numbers: [114] 114,94 unequal: No Solution Exploring Operation: 91-23=68, Resulting Numbers: [68] 68,94 unequal: No Solution Exploring Operation: 23*91=2093, Resulting Numbers: [2093] 2093,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 94:[39, 29], Operations: ['26+13=39', '52-23=29'] Exploring Operation: 39+29=68, Resulting Numbers: [68] 68,94 unequal: No Solution Exploring Operation: 39*29=1131, Resulting Numbers: [1131] 1131,94 unequal: No Solution Exploring Operation: 39-29=10, Resulting Numbers: [10] 10,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 94:[39, 75], Operations: ['26+13=39', '52+23=75'] Exploring Operation: 39+75=114, Resulting Numbers: [114] 114,94 unequal: No Solution Exploring Operation: 75-39=36, Resulting Numbers: [36] 36,94 unequal: No Solution Exploring Operation: 39*75=2925, Resulting Numbers: [2925] 2925,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 50, 45, 22, 3 ]
70
[ "50+45=95", "22+3=25", "95-25=70" ]
Current State: 70:[50, 45, 22, 3], Operations: [] Exploring Operation: 50+45=95, Resulting Numbers: [22, 3, 95] Generated Node #2: [22, 3, 95] from Operation: 50+45=95 Current State: 70:[22, 3, 95], Operations: ['50+45=95'] Exploring Operation: 22+3=25, Resulting Numbers: [95, 25] Generated Node #3: [95, 25] from Operation: 22+3=25 Current State: 70:[95, 25], Operations: ['50+45=95', '22+3=25'] Exploring Operation: 95-25=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[50, 45, 22, 3], Operations: [] Exploring Operation: 50-45=5, Resulting Numbers: [22, 3, 5] Generated Node #0,0: 70:[22, 3, 5] Operation: 50-45=5 Exploring Operation: 50+22=72, Resulting Numbers: [45, 3, 72] Generated Node #0,1: 70:[45, 3, 72] Operation: 50+22=72 Exploring Operation: 45/3=15, Resulting Numbers: [50, 22, 15] Generated Node #0,2: 70:[50, 22, 15] Operation: 45/3=15 Exploring Operation: 50-22=28, Resulting Numbers: [45, 3, 28] Generated Node #0,3: 70:[45, 3, 28] Operation: 50-22=28 Exploring Operation: 45+22=67, Resulting Numbers: [50, 3, 67] Generated Node #0,4: 70:[50, 3, 67] Operation: 45+22=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[22, 3, 5], Operations: ['50-45=5'] Exploring Operation: 22-5=17, Resulting Numbers: [3, 17] Generated Node #0,0,0: 70:[3, 17] Operation: 22-5=17 Exploring Operation: 22-3=19, Resulting Numbers: [5, 19] Generated Node #0,0,1: 70:[5, 19] Operation: 22-3=19 Exploring Operation: 22+5=27, Resulting Numbers: [3, 27] Generated Node #0,0,2: 70:[3, 27] Operation: 22+5=27 Exploring Operation: 22*3=66, Resulting Numbers: [5, 66] Generated Node #0,0,3: 70:[5, 66] Operation: 22*3=66 Exploring Operation: 5-3=2, Resulting Numbers: [22, 2] Generated Node #0,0,4: 70:[22, 2] Operation: 5-3=2 Moving to Node #0,0,0 Current State: 70:[3, 17], Operations: ['50-45=5', '22-5=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,70 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,70 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,70 unequal: No Solution Moving to Node #0,0,3 Current State: 70:[5, 66], Operations: ['50-45=5', '22*3=66'] Exploring Operation: 5*66=330, Resulting Numbers: [330] 330,70 unequal: No Solution Exploring Operation: 5+66=71, Resulting Numbers: [71] 71,70 unequal: No Solution Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[5, 19], Operations: ['50-45=5', '22-3=19'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,70 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,70 unequal: No Solution Moving to Node #0,0,4 Current State: 70:[22, 2], Operations: ['50-45=5', '5-3=2'] Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,70 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,70 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[3, 27], Operations: ['50-45=5', '22+5=27'] Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,70 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,70 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[45, 3, 72], Operations: ['50+22=72'] Exploring Operation: 45/3=15, Resulting Numbers: [72, 15] Generated Node #0,1,0: 70:[72, 15] Operation: 45/3=15 Exploring Operation: 72-3=69, Resulting Numbers: [45, 69] Generated Node #0,1,1: 70:[45, 69] Operation: 72-3=69 Exploring Operation: 45-3=42, Resulting Numbers: [72, 42] Generated Node #0,1,2: 70:[72, 42] Operation: 45-3=42 Exploring Operation: 45+3=48, Resulting Numbers: [72, 48] Generated Node #0,1,3: 70:[72, 48] Operation: 45+3=48 Exploring Operation: 72-45=27, Resulting Numbers: [3, 27] Generated Node #0,1,4: 70:[3, 27] Operation: 72-45=27 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 70:[72, 15], Operations: ['50+22=72', '45/3=15'] Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 72+15=87, Resulting Numbers: [87] 87,70 unequal: No Solution Exploring Operation: 72*15=1080, Resulting Numbers: [1080] 1080,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 70:[72, 42], Operations: ['50+22=72', '45-3=42'] Exploring Operation: 72*42=3024, Resulting Numbers: [3024] 3024,70 unequal: No Solution Exploring Operation: 72+42=114, Resulting Numbers: [114] 114,70 unequal: No Solution Exploring Operation: 72-42=30, Resulting Numbers: [30] 30,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 70:[3, 27], Operations: ['50+22=72', '72-45=27'] Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,70 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 70:[45, 69], Operations: ['50+22=72', '72-3=69'] Exploring Operation: 69-45=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 45+69=114, Resulting Numbers: [114] 114,70 unequal: No Solution Exploring Operation: 45*69=3105, Resulting Numbers: [3105] 3105,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 70:[72, 48], Operations: ['50+22=72', '45+3=48'] Exploring Operation: 72*48=3456, Resulting Numbers: [3456] 3456,70 unequal: No Solution Exploring Operation: 72-48=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 72+48=120, Resulting Numbers: [120] 120,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 70:[45, 3, 28], Operations: ['50-22=28'] Exploring Operation: 45-28=17, Resulting Numbers: [3, 17] Generated Node #0,3,0: 70:[3, 17] Operation: 45-28=17 Exploring Operation: 45-3=42, Resulting Numbers: [28, 42] Generated Node #0,3,1: 70:[28, 42] Operation: 45-3=42 Exploring Operation: 3+28=31, Resulting Numbers: [45, 31] Generated Node #0,3,2: 70:[45, 31] Operation: 3+28=31 Exploring Operation: 45+28=73, Resulting Numbers: [3, 73] Generated Node #0,3,3: 70:[3, 73] Operation: 45+28=73 Exploring Operation: 45/3=15, Resulting Numbers: [28, 15] Generated Node #0,3,4: 70:[28, 15] Operation: 45/3=15 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 70:[3, 17], Operations: ['50-22=28', '45-28=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,70 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,70 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 70:[3, 73], Operations: ['50-22=28', '45+28=73'] Exploring Operation: 3+73=76, Resulting Numbers: [76] 76,70 unequal: No Solution Exploring Operation: 3*73=219, Resulting Numbers: [219] 219,70 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[50, 45, 22, 3], Operations: [] Exploring Operation: 50-22=28, Resulting Numbers: [45, 3, 28] Generated Node #0,3: 70:[45, 3, 28] Operation: 50-22=28 Moving to Node #0,3 Current State: 70:[45, 3, 28], Operations: ['50-22=28'] Exploring Operation: 45+28=73, Resulting Numbers: [3, 73] Generated Node #0,3,3: 70:[3, 73] Operation: 45+28=73 Moving to Node #0,3,3 Current State: 70:[3, 73], Operations: ['50-22=28', '45+28=73'] Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.945313
hs_5
mult_heuristic
[ 51, 2, 14, 82 ]
38
[ "82-51=31", "14/2=7", "31+7=38" ]
Current State: 38:[51, 2, 14, 82], Operations: [] Exploring Operation: 82-51=31, Resulting Numbers: [2, 14, 31] Generated Node #2: [2, 14, 31] from Operation: 82-51=31 Current State: 38:[2, 14, 31], Operations: ['82-51=31'] Exploring Operation: 14/2=7, Resulting Numbers: [31, 7] Generated Node #3: [31, 7] from Operation: 14/2=7 Current State: 38:[31, 7], Operations: ['82-51=31', '14/2=7'] Exploring Operation: 31+7=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[51, 2, 14, 82], Operations: [] Exploring Operation: 82-51=31, Resulting Numbers: [2, 14, 31] Generated Node #0,0: 38:[2, 14, 31] Operation: 82-51=31 Exploring Operation: 82/2=41, Resulting Numbers: [51, 14, 41] Generated Node #0,1: 38:[51, 14, 41] Operation: 82/2=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[2, 14, 31], Operations: ['82-51=31'] Exploring Operation: 31-14=17, Resulting Numbers: [2, 17] Generated Node #0,0,0: 38:[2, 17] Operation: 31-14=17 Exploring Operation: 14+31=45, Resulting Numbers: [2, 45] Generated Node #0,0,1: 38:[2, 45] Operation: 14+31=45 Moving to Node #0,0,0 Current State: 38:[2, 17], Operations: ['82-51=31', '31-14=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,38 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[2, 45], Operations: ['82-51=31', '14+31=45'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,38 unequal: No Solution Exploring Operation: 2+45=47, Resulting Numbers: [47] 47,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[51, 14, 41], Operations: ['82/2=41'] Exploring Operation: 51-41=10, Resulting Numbers: [14, 10] Generated Node #0,1,0: 38:[14, 10] Operation: 51-41=10 Exploring Operation: 51-14=37, Resulting Numbers: [41, 37] Generated Node #0,1,1: 38:[41, 37] Operation: 51-14=37 Moving to Node #0,1,1 Current State: 38:[41, 37], Operations: ['82/2=41', '51-14=37'] Exploring Operation: 41-37=4, Resulting Numbers: [4] 4,38 unequal: No Solution Exploring Operation: 41+37=78, Resulting Numbers: [78] 78,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[14, 10], Operations: ['82/2=41', '51-41=10'] Exploring Operation: 14+10=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,38 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
[ 54, 55, 18, 1 ]
17
[ "55-54=1", "18*1=18", "18-1=17" ]
Current State: 17:[54, 55, 18, 1], Operations: [] Exploring Operation: 55-54=1, Resulting Numbers: [18, 1, 1] Generated Node #2: [18, 1, 1] from Operation: 55-54=1 Current State: 17:[18, 1, 1], Operations: ['55-54=1'] Exploring Operation: 18*1=18, Resulting Numbers: [18] 18,17 equal: Goal Reached Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[54, 55, 18, 1], Operations: [] Exploring Operation: 54-1=53, Resulting Numbers: [55, 18, 53] Generated Node #0,0: 17:[55, 18, 53] Operation: 54-1=53 Exploring Operation: 54/18=3, Resulting Numbers: [55, 1, 3] Generated Node #0,1: 17:[55, 1, 3] Operation: 54/18=3 Exploring Operation: 55-18=37, Resulting Numbers: [54, 1, 37] Generated Node #0,2: 17:[54, 1, 37] Operation: 55-18=37 Exploring Operation: 55-54=1, Resulting Numbers: [18, 1, 1] Generated Node #0,3: 17:[18, 1, 1] Operation: 55-54=1 Exploring Operation: 54-18=36, Resulting Numbers: [55, 1, 36] Generated Node #0,4: 17:[55, 1, 36] Operation: 54-18=36 Moving to Node #0,3 Current State: 17:[18, 1, 1], Operations: ['55-54=1'] Exploring Operation: 18*1=18, Resulting Numbers: [1, 18] Generated Node #0,3,0: 17:[1, 18] Operation: 18*1=18 Exploring Operation: 1+1=2, Resulting Numbers: [18, 2] Generated Node #0,3,1: 17:[18, 2] Operation: 1+1=2 Exploring Operation: 18-1=17, Resulting Numbers: [1, 17] Generated Node #0,3,2: 17:[1, 17] Operation: 18-1=17 Exploring Operation: 18/1=18, Resulting Numbers: [1, 18] Generated Node #0,3,3: 17:[1, 18] Operation: 18/1=18 Exploring Operation: 18-1=17, Resulting Numbers: [1, 17] Generated Node #0,3,4: 17:[1, 17] Operation: 18-1=17 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 17:[18, 2], Operations: ['55-54=1', '1+1=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,17 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 17:[1, 17], Operations: ['55-54=1', '18-1=17'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[54, 55, 18, 1], Operations: [] Exploring Operation: 55-54=1, Resulting Numbers: [18, 1, 1] Generated Node #0,3: 17:[18, 1, 1] Operation: 55-54=1 Moving to Node #0,3 Current State: 17:[18, 1, 1], Operations: ['55-54=1'] Exploring Operation: 18-1=17, Resulting Numbers: [1, 17] Generated Node #0,3,2: 17:[1, 17] Operation: 18-1=17 Moving to Node #0,3,2 Current State: 17:[1, 17], Operations: ['55-54=1', '18-1=17'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 77, 15, 3, 8 ]
51
[ "77-15=62", "3+8=11", "62-11=51" ]
Current State: 51:[77, 15, 3, 8], Operations: [] Exploring Operation: 77-15=62, Resulting Numbers: [3, 8, 62] Generated Node #2: [3, 8, 62] from Operation: 77-15=62 Current State: 51:[3, 8, 62], Operations: ['77-15=62'] Exploring Operation: 3+8=11, Resulting Numbers: [62, 11] Generated Node #3: [62, 11] from Operation: 3+8=11 Current State: 51:[62, 11], Operations: ['77-15=62', '3+8=11'] Exploring Operation: 62-11=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[77, 15, 3, 8], Operations: [] Exploring Operation: 77-15=62, Resulting Numbers: [3, 8, 62] Generated Node #0,0: 51:[3, 8, 62] Operation: 77-15=62 Moving to Node #0,0 Current State: 51:[3, 8, 62], Operations: ['77-15=62'] Exploring Operation: 62-8=54, Resulting Numbers: [3, 54] Generated Node #0,0,0: 51:[3, 54] Operation: 62-8=54 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[3, 54], Operations: ['77-15=62', '62-8=54'] Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[77, 15, 3, 8], Operations: [] Exploring Operation: 77-15=62, Resulting Numbers: [3, 8, 62] Generated Node #0,0: 51:[3, 8, 62] Operation: 77-15=62 Moving to Node #0,0 Current State: 51:[3, 8, 62], Operations: ['77-15=62'] Exploring Operation: 62-8=54, Resulting Numbers: [3, 54] Generated Node #0,0,0: 51:[3, 54] Operation: 62-8=54 Moving to Node #0,0,0 Current State: 51:[3, 54], Operations: ['77-15=62', '62-8=54'] Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 72, 42, 21, 77 ]
39
[ "72*42=3024", "3024-21=3003", "3003/77=39" ]
Current State: 39:[72, 42, 21, 77], Operations: [] Exploring Operation: 72*42=3024, Resulting Numbers: [21, 77, 3024] Generated Node #2: [21, 77, 3024] from Operation: 72*42=3024 Current State: 39:[21, 77, 3024], Operations: ['72*42=3024'] Exploring Operation: 3024-21=3003, Resulting Numbers: [77, 3003] Generated Node #3: [77, 3003] from Operation: 3024-21=3003 Current State: 39:[77, 3003], Operations: ['72*42=3024', '3024-21=3003'] Exploring Operation: 3003/77=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[72, 42, 21, 77], Operations: [] Exploring Operation: 72-21=51, Resulting Numbers: [42, 77, 51] Generated Node #0,0: 39:[42, 77, 51] Operation: 72-21=51 Exploring Operation: 77-21=56, Resulting Numbers: [72, 42, 56] Generated Node #0,1: 39:[72, 42, 56] Operation: 77-21=56 Exploring Operation: 77-72=5, Resulting Numbers: [42, 21, 5] Generated Node #0,2: 39:[42, 21, 5] Operation: 77-72=5 Exploring Operation: 77-42=35, Resulting Numbers: [72, 21, 35] Generated Node #0,3: 39:[72, 21, 35] Operation: 77-42=35 Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[42, 21, 5], Operations: ['77-72=5'] Exploring Operation: 42-5=37, Resulting Numbers: [21, 37] Generated Node #0,2,0: 39:[21, 37] Operation: 42-5=37 Exploring Operation: 42/21=2, Resulting Numbers: [5, 2] Generated Node #0,2,1: 39:[5, 2] Operation: 42/21=2 Exploring Operation: 21-5=16, Resulting Numbers: [42, 16] Generated Node #0,2,2: 39:[42, 16] Operation: 21-5=16 Exploring Operation: 42-21=21, Resulting Numbers: [5, 21] Generated Node #0,2,3: 39:[5, 21] Operation: 42-21=21 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 39:[5, 2], Operations: ['77-72=5', '42/21=2'] Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 39:[42, 16], Operations: ['77-72=5', '21-5=16'] Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 42*16=672, Resulting Numbers: [672] 672,39 unequal: No Solution Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 39:[21, 37], Operations: ['77-72=5', '42-5=37'] Exploring Operation: 21+37=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 21*37=777, Resulting Numbers: [777] 777,39 unequal: No Solution Exploring Operation: 37-21=16, Resulting Numbers: [16] 16,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 39:[5, 21], Operations: ['77-72=5', '42-21=21'] Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,39 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,39 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 39:[72, 21, 35], Operations: ['77-42=35'] Exploring Operation: 21+35=56, Resulting Numbers: [72, 56] Generated Node #0,3,0: 39:[72, 56] Operation: 21+35=56 Exploring Operation: 72-21=51, Resulting Numbers: [35, 51] Generated Node #0,3,1: 39:[35, 51] Operation: 72-21=51 Exploring Operation: 35-21=14, Resulting Numbers: [72, 14] Generated Node #0,3,2: 39:[72, 14] Operation: 35-21=14 Exploring Operation: 72-35=37, Resulting Numbers: [21, 37] Generated Node #0,3,3: 39:[21, 37] Operation: 72-35=37 Moving to Node #0,3,3 Current State: 39:[21, 37], Operations: ['77-42=35', '72-35=37'] Exploring Operation: 21+37=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 37-21=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 21*37=777, Resulting Numbers: [777] 777,39 unequal: No Solution Moving to Node #0,3,1 Current State: 39:[35, 51], Operations: ['77-42=35', '72-21=51'] Exploring Operation: 35*51=1785, Resulting Numbers: [1785] 1785,39 unequal: No Solution Exploring Operation: 51-35=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 35+51=86, Resulting Numbers: [86] 86,39 unequal: No Solution Moving to Node #0,3,2 Current State: 39:[72, 14], Operations: ['77-42=35', '35-21=14'] Exploring Operation: 72-14=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 72+14=86, Resulting Numbers: [86] 86,39 unequal: No Solution Exploring Operation: 72*14=1008, Resulting Numbers: [1008] 1008,39 unequal: No Solution Moving to Node #0,3,0 Current State: 39:[72, 56], Operations: ['77-42=35', '21+35=56'] Exploring Operation: 72*56=4032, Resulting Numbers: [4032] 4032,39 unequal: No Solution Exploring Operation: 72-56=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 72+56=128, Resulting Numbers: [128] 128,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[42, 77, 51], Operations: ['72-21=51'] Exploring Operation: 42+77=119, Resulting Numbers: [51, 119] Generated Node #0,0,0: 39:[51, 119] Operation: 42+77=119 Exploring Operation: 77-42=35, Resulting Numbers: [51, 35] Generated Node #0,0,1: 39:[51, 35] Operation: 77-42=35 Exploring Operation: 77-51=26, Resulting Numbers: [42, 26] Generated Node #0,0,2: 39:[42, 26] Operation: 77-51=26 Exploring Operation: 51-42=9, Resulting Numbers: [77, 9] Generated Node #0,0,3: 39:[77, 9] Operation: 51-42=9 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 39:[51, 35], Operations: ['72-21=51', '77-42=35'] Exploring Operation: 51-35=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 51*35=1785, Resulting Numbers: [1785] 1785,39 unequal: No Solution Exploring Operation: 51+35=86, Resulting Numbers: [86] 86,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 39:[42, 26], Operations: ['72-21=51', '77-51=26'] Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 42+26=68, Resulting Numbers: [68] 68,39 unequal: No Solution Exploring Operation: 42*26=1092, Resulting Numbers: [1092] 1092,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 39:[77, 9], Operations: ['72-21=51', '51-42=9'] Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,39 unequal: No Solution Exploring Operation: 77+9=86, Resulting Numbers: [86] 86,39 unequal: No Solution Exploring Operation: 77*9=693, Resulting Numbers: [693] 693,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[51, 119], Operations: ['72-21=51', '42+77=119'] Exploring Operation: 51+119=170, Resulting Numbers: [170] 170,39 unequal: No Solution Exploring Operation: 51*119=6069, Resulting Numbers: [6069] 6069,39 unequal: No Solution Exploring Operation: 119-51=68, Resulting Numbers: [68] 68,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[72, 42, 56], Operations: ['77-21=56'] Exploring Operation: 72-56=16, Resulting Numbers: [42, 16] Generated Node #0,1,0: 39:[42, 16] Operation: 72-56=16 Exploring Operation: 56-42=14, Resulting Numbers: [72, 14] Generated Node #0,1,1: 39:[72, 14] Operation: 56-42=14 Exploring Operation: 72-42=30, Resulting Numbers: [56, 30] Generated Node #0,1,2: 39:[56, 30] Operation: 72-42=30 Exploring Operation: 72+42=114, Resulting Numbers: [56, 114] Generated Node #0,1,3: 39:[56, 114] Operation: 72+42=114 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 39:[42, 16], Operations: ['77-21=56', '72-56=16'] Exploring Operation: 42*16=672, Resulting Numbers: [672] 672,39 unequal: No Solution Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,39 unequal: No Solution Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 39:[56, 30], Operations: ['77-21=56', '72-42=30'] Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,39 unequal: No Solution Exploring Operation: 56*30=1680, Resulting Numbers: [1680] 1680,39 unequal: No Solution Exploring Operation: 56+30=86, Resulting Numbers: [86] 86,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 39:[72, 14], Operations: ['77-21=56', '56-42=14'] Exploring Operation: 72+14=86, Resulting Numbers: [86] 86,39 unequal: No Solution Exploring Operation: 72-14=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 72*14=1008, Resulting Numbers: [1008] 1008,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 39:[56, 114], Operations: ['77-21=56', '72+42=114'] Exploring Operation: 114-56=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 56*114=6384, Resulting Numbers: [6384] 6384,39 unequal: No Solution Exploring Operation: 56+114=170, Resulting Numbers: [170] 170,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 57, 64, 79, 72 ]
14
[ "64-57=7", "79-72=7", "7+7=14" ]
Current State: 14:[57, 64, 79, 72], Operations: [] Exploring Operation: 64-57=7, Resulting Numbers: [79, 72, 7] Generated Node #2: [79, 72, 7] from Operation: 64-57=7 Current State: 14:[79, 72, 7], Operations: ['64-57=7'] Exploring Operation: 79-72=7, Resulting Numbers: [7, 7] Generated Node #3: [7, 7] from Operation: 79-72=7 Current State: 14:[7, 7], Operations: ['64-57=7', '79-72=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[57, 64, 79, 72], Operations: [] Exploring Operation: 72-64=8, Resulting Numbers: [57, 79, 8] Generated Node #0,0: 14:[57, 79, 8] Operation: 72-64=8 Exploring Operation: 72-57=15, Resulting Numbers: [64, 79, 15] Generated Node #0,1: 14:[64, 79, 15] Operation: 72-57=15 Exploring Operation: 79-64=15, Resulting Numbers: [57, 72, 15] Generated Node #0,2: 14:[57, 72, 15] Operation: 79-64=15 Exploring Operation: 79-72=7, Resulting Numbers: [57, 64, 7] Generated Node #0,3: 14:[57, 64, 7] Operation: 79-72=7 Exploring Operation: 79-57=22, Resulting Numbers: [64, 72, 22] Generated Node #0,4: 14:[64, 72, 22] Operation: 79-57=22 Moving to Node #0,3 Current State: 14:[57, 64, 7], Operations: ['79-72=7'] Exploring Operation: 57-7=50, Resulting Numbers: [64, 50] Generated Node #0,3,0: 14:[64, 50] Operation: 57-7=50 Exploring Operation: 64-7=57, Resulting Numbers: [57, 57] Generated Node #0,3,1: 14:[57, 57] Operation: 64-7=57 Exploring Operation: 64-57=7, Resulting Numbers: [7, 7] Generated Node #0,3,2: 14:[7, 7] Operation: 64-57=7 Exploring Operation: 64+7=71, Resulting Numbers: [57, 71] Generated Node #0,3,3: 14:[57, 71] Operation: 64+7=71 Exploring Operation: 57+7=64, Resulting Numbers: [64, 64] Generated Node #0,3,4: 14:[64, 64] Operation: 57+7=64 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 14:[7, 7], Operations: ['79-72=7', '64-57=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[57, 64, 79, 72], Operations: [] Exploring Operation: 79-72=7, Resulting Numbers: [57, 64, 7] Generated Node #0,3: 14:[57, 64, 7] Operation: 79-72=7 Moving to Node #0,3 Current State: 14:[57, 64, 7], Operations: ['79-72=7'] Exploring Operation: 64-57=7, Resulting Numbers: [7, 7] Generated Node #0,3,2: 14:[7, 7] Operation: 64-57=7 Moving to Node #0,3,2 Current State: 14:[7, 7], Operations: ['79-72=7', '64-57=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 9, 63, 65, 20 ]
92
[ "63/9=7", "65+20=85", "7+85=92" ]
Current State: 92:[9, 63, 65, 20], Operations: [] Exploring Operation: 63/9=7, Resulting Numbers: [65, 20, 7] Generated Node #2: [65, 20, 7] from Operation: 63/9=7 Current State: 92:[65, 20, 7], Operations: ['63/9=7'] Exploring Operation: 65+20=85, Resulting Numbers: [7, 85] Generated Node #3: [7, 85] from Operation: 65+20=85 Current State: 92:[7, 85], Operations: ['63/9=7', '65+20=85'] Exploring Operation: 7+85=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[9, 63, 65, 20], Operations: [] Exploring Operation: 63-20=43, Resulting Numbers: [9, 65, 43] Generated Node #0,0: 92:[9, 65, 43] Operation: 63-20=43 Exploring Operation: 65+20=85, Resulting Numbers: [9, 63, 85] Generated Node #0,1: 92:[9, 63, 85] Operation: 65+20=85 Exploring Operation: 63/9=7, Resulting Numbers: [65, 20, 7] Generated Node #0,2: 92:[65, 20, 7] Operation: 63/9=7 Exploring Operation: 65-63=2, Resulting Numbers: [9, 20, 2] Generated Node #0,3: 92:[9, 20, 2] Operation: 65-63=2 Exploring Operation: 65-20=45, Resulting Numbers: [9, 63, 45] Generated Node #0,4: 92:[9, 63, 45] Operation: 65-20=45 Start Sub Search at level 1: Moving to Node #0,3 Current State: 92:[9, 20, 2], Operations: ['65-63=2'] Exploring Operation: 20+2=22, Resulting Numbers: [9, 22] Generated Node #0,3,0: 92:[9, 22] Operation: 20+2=22 Exploring Operation: 9*2=18, Resulting Numbers: [20, 18] Generated Node #0,3,1: 92:[20, 18] Operation: 9*2=18 Exploring Operation: 9+20=29, Resulting Numbers: [2, 29] Generated Node #0,3,2: 92:[2, 29] Operation: 9+20=29 Exploring Operation: 9-2=7, Resulting Numbers: [20, 7] Generated Node #0,3,3: 92:[20, 7] Operation: 9-2=7 Exploring Operation: 20-9=11, Resulting Numbers: [2, 11] Generated Node #0,3,4: 92:[2, 11] Operation: 20-9=11 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 92:[9, 22], Operations: ['65-63=2', '20+2=22'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,92 unequal: No Solution Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,92 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 92:[2, 29], Operations: ['65-63=2', '9+20=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,92 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 92:[20, 7], Operations: ['65-63=2', '9-2=7'] Exploring Operation: 20*7=140, Resulting Numbers: [140] 140,92 unequal: No Solution Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 92:[2, 11], Operations: ['65-63=2', '20-9=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,92 unequal: No Solution Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,92 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 92:[20, 18], Operations: ['65-63=2', '9*2=18'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,92 unequal: No Solution Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 92:[9, 63, 45], Operations: ['65-20=45'] Exploring Operation: 45/9=5, Resulting Numbers: [63, 5] Generated Node #0,4,0: 92:[63, 5] Operation: 45/9=5 Exploring Operation: 63-9=54, Resulting Numbers: [45, 54] Generated Node #0,4,1: 92:[45, 54] Operation: 63-9=54 Exploring Operation: 63/9=7, Resulting Numbers: [45, 7] Generated Node #0,4,2: 92:[45, 7] Operation: 63/9=7 Exploring Operation: 63-45=18, Resulting Numbers: [9, 18] Generated Node #0,4,3: 92:[9, 18] Operation: 63-45=18 Exploring Operation: 9+63=72, Resulting Numbers: [45, 72] Generated Node #0,4,4: 92:[45, 72] Operation: 9+63=72 Moving to Node #0,4,2 Current State: 92:[45, 7], Operations: ['65-20=45', '63/9=7'] Exploring Operation: 45+7=52, Resulting Numbers: [52] 52,92 unequal: No Solution Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,92 unequal: No Solution Exploring Operation: 45*7=315, Resulting Numbers: [315] 315,92 unequal: No Solution Moving to Node #0,4,1 Current State: 92:[45, 54], Operations: ['65-20=45', '63-9=54'] Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,92 unequal: No Solution Exploring Operation: 45+54=99, Resulting Numbers: [99] 99,92 unequal: No Solution Exploring Operation: 45*54=2430, Resulting Numbers: [2430] 2430,92 unequal: No Solution Moving to Node #0,4,3 Current State: 92:[9, 18], Operations: ['65-20=45', '63-45=18'] Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,92 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 9*18=162, Resulting Numbers: [162] 162,92 unequal: No Solution Moving to Node #0,4,0 Current State: 92:[63, 5], Operations: ['65-20=45', '45/9=5'] Exploring Operation: 63+5=68, Resulting Numbers: [68] 68,92 unequal: No Solution Exploring Operation: 63-5=58, Resulting Numbers: [58] 58,92 unequal: No Solution Exploring Operation: 63*5=315, Resulting Numbers: [315] 315,92 unequal: No Solution Moving to Node #0,4,4 Current State: 92:[45, 72], Operations: ['65-20=45', '9+63=72'] Exploring Operation: 45*72=3240, Resulting Numbers: [3240] 3240,92 unequal: No Solution Exploring Operation: 45+72=117, Resulting Numbers: [117] 117,92 unequal: No Solution Exploring Operation: 72-45=27, Resulting Numbers: [27] 27,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[65, 20, 7], Operations: ['63/9=7'] Exploring Operation: 20+7=27, Resulting Numbers: [65, 27] Generated Node #0,2,0: 92:[65, 27] Operation: 20+7=27 Exploring Operation: 65-20=45, Resulting Numbers: [7, 45] Generated Node #0,2,1: 92:[7, 45] Operation: 65-20=45 Exploring Operation: 65+7=72, Resulting Numbers: [20, 72] Generated Node #0,2,2: 92:[20, 72] Operation: 65+7=72 Exploring Operation: 65-7=58, Resulting Numbers: [20, 58] Generated Node #0,2,3: 92:[20, 58] Operation: 65-7=58 Exploring Operation: 65+20=85, Resulting Numbers: [7, 85] Generated Node #0,2,4: 92:[7, 85] Operation: 65+20=85 Moving to Node #0,2,1 Current State: 92:[7, 45], Operations: ['63/9=7', '65-20=45'] Exploring Operation: 7+45=52, Resulting Numbers: [52] 52,92 unequal: No Solution Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,92 unequal: No Solution Exploring Operation: 7*45=315, Resulting Numbers: [315] 315,92 unequal: No Solution Moving to Node #0,2,4 Current State: 92:[7, 85], Operations: ['63/9=7', '65+20=85'] Exploring Operation: 7*85=595, Resulting Numbers: [595] 595,92 unequal: No Solution Exploring Operation: 7+85=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[9, 63, 65, 20], Operations: [] Exploring Operation: 63/9=7, Resulting Numbers: [65, 20, 7] Generated Node #0,2: 92:[65, 20, 7] Operation: 63/9=7 Moving to Node #0,2 Current State: 92:[65, 20, 7], Operations: ['63/9=7'] Exploring Operation: 65+20=85, Resulting Numbers: [7, 85] Generated Node #0,2,4: 92:[7, 85] Operation: 65+20=85 Moving to Node #0,2,4 Current State: 92:[7, 85], Operations: ['63/9=7', '65+20=85'] Exploring Operation: 7+85=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.947917
hs_5
mult_heuristic
[ 65, 89, 34, 44 ]
14
[ "89-65=24", "44-34=10", "24-10=14" ]
Current State: 14:[65, 89, 34, 44], Operations: [] Exploring Operation: 89-65=24, Resulting Numbers: [34, 44, 24] Generated Node #2: [34, 44, 24] from Operation: 89-65=24 Current State: 14:[34, 44, 24], Operations: ['89-65=24'] Exploring Operation: 44-34=10, Resulting Numbers: [24, 10] Generated Node #3: [24, 10] from Operation: 44-34=10 Current State: 14:[24, 10], Operations: ['89-65=24', '44-34=10'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[65, 89, 34, 44], Operations: [] Exploring Operation: 89-34=55, Resulting Numbers: [65, 44, 55] Generated Node #0,0: 14:[65, 44, 55] Operation: 89-34=55 Exploring Operation: 89-44=45, Resulting Numbers: [65, 34, 45] Generated Node #0,1: 14:[65, 34, 45] Operation: 89-44=45 Exploring Operation: 89-65=24, Resulting Numbers: [34, 44, 24] Generated Node #0,2: 14:[34, 44, 24] Operation: 89-65=24 Exploring Operation: 65-44=21, Resulting Numbers: [89, 34, 21] Generated Node #0,3: 14:[89, 34, 21] Operation: 65-44=21 Exploring Operation: 65-34=31, Resulting Numbers: [89, 44, 31] Generated Node #0,4: 14:[89, 44, 31] Operation: 65-34=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[34, 44, 24], Operations: ['89-65=24'] Exploring Operation: 34+24=58, Resulting Numbers: [44, 58] Generated Node #0,2,0: 14:[44, 58] Operation: 34+24=58 Exploring Operation: 34-24=10, Resulting Numbers: [44, 10] Generated Node #0,2,1: 14:[44, 10] Operation: 34-24=10 Exploring Operation: 44-34=10, Resulting Numbers: [24, 10] Generated Node #0,2,2: 14:[24, 10] Operation: 44-34=10 Exploring Operation: 44-24=20, Resulting Numbers: [34, 20] Generated Node #0,2,3: 14:[34, 20] Operation: 44-24=20 Exploring Operation: 34+44=78, Resulting Numbers: [24, 78] Generated Node #0,2,4: 14:[24, 78] Operation: 34+44=78 Moving to Node #0,2,2 Current State: 14:[24, 10], Operations: ['89-65=24', '44-34=10'] Exploring Operation: 24*10=240, Resulting Numbers: [240] 240,14 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[65, 89, 34, 44], Operations: [] Exploring Operation: 89-65=24, Resulting Numbers: [34, 44, 24] Generated Node #0,2: 14:[34, 44, 24] Operation: 89-65=24 Moving to Node #0,2 Current State: 14:[34, 44, 24], Operations: ['89-65=24'] Exploring Operation: 44-34=10, Resulting Numbers: [24, 10] Generated Node #0,2,2: 14:[24, 10] Operation: 44-34=10 Moving to Node #0,2,2 Current State: 14:[24, 10], Operations: ['89-65=24', '44-34=10'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 57, 64, 61, 20 ]
69
[ "61-57=4", "20/4=5", "64+5=69" ]
Current State: 69:[57, 64, 61, 20], Operations: [] Exploring Operation: 61-57=4, Resulting Numbers: [64, 20, 4] Generated Node #2: [64, 20, 4] from Operation: 61-57=4 Current State: 69:[64, 20, 4], Operations: ['61-57=4'] Exploring Operation: 20/4=5, Resulting Numbers: [64, 5] Generated Node #3: [64, 5] from Operation: 20/4=5 Current State: 69:[64, 5], Operations: ['61-57=4', '20/4=5'] Exploring Operation: 64+5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[57, 64, 61, 20], Operations: [] Exploring Operation: 61-57=4, Resulting Numbers: [64, 20, 4] Generated Node #0,0: 69:[64, 20, 4] Operation: 61-57=4 Moving to Node #0,0 Current State: 69:[64, 20, 4], Operations: ['61-57=4'] Exploring Operation: 64+4=68, Resulting Numbers: [20, 68] Generated Node #0,0,0: 69:[20, 68] Operation: 64+4=68 Moving to Node #0,0,0 Current State: 69:[20, 68], Operations: ['61-57=4', '64+4=68'] Exploring Operation: 20+68=88, Resulting Numbers: [88] 88,69 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 49, 31, 38, 17 ]
59
[ "49+31=80", "38-17=21", "80-21=59" ]
Current State: 59:[49, 31, 38, 17], Operations: [] Exploring Operation: 49+31=80, Resulting Numbers: [38, 17, 80] Generated Node #2: [38, 17, 80] from Operation: 49+31=80 Current State: 59:[38, 17, 80], Operations: ['49+31=80'] Exploring Operation: 38-17=21, Resulting Numbers: [80, 21] Generated Node #3: [80, 21] from Operation: 38-17=21 Current State: 59:[80, 21], Operations: ['49+31=80', '38-17=21'] Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[49, 31, 38, 17], Operations: [] Exploring Operation: 31+17=48, Resulting Numbers: [49, 38, 48] Generated Node #0,0: 59:[49, 38, 48] Operation: 31+17=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[49, 38, 48], Operations: ['31+17=48'] Exploring Operation: 38+48=86, Resulting Numbers: [49, 86] Generated Node #0,0,0: 59:[49, 86] Operation: 38+48=86 Moving to Node #0,0,0 Current State: 59:[49, 86], Operations: ['31+17=48', '38+48=86'] Exploring Operation: 86-49=37, Resulting Numbers: [37] 37,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 84, 24, 40, 56 ]
82
[ "24+56=80", "80/40=2", "84-2=82" ]
Current State: 82:[84, 24, 40, 56], Operations: [] Exploring Operation: 24+56=80, Resulting Numbers: [84, 40, 80] Generated Node #2: [84, 40, 80] from Operation: 24+56=80 Current State: 82:[84, 40, 80], Operations: ['24+56=80'] Exploring Operation: 80/40=2, Resulting Numbers: [84, 2] Generated Node #3: [84, 2] from Operation: 80/40=2 Current State: 82:[84, 2], Operations: ['24+56=80', '80/40=2'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[84, 24, 40, 56], Operations: [] Exploring Operation: 56-24=32, Resulting Numbers: [84, 40, 32] Generated Node #0,0: 82:[84, 40, 32] Operation: 56-24=32 Exploring Operation: 24+56=80, Resulting Numbers: [84, 40, 80] Generated Node #0,1: 82:[84, 40, 80] Operation: 24+56=80 Moving to Node #0,1 Current State: 82:[84, 40, 80], Operations: ['24+56=80'] Exploring Operation: 80/40=2, Resulting Numbers: [84, 2] Generated Node #0,1,0: 82:[84, 2] Operation: 80/40=2 Exploring Operation: 84-80=4, Resulting Numbers: [40, 4] Generated Node #0,1,1: 82:[40, 4] Operation: 84-80=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 82:[84, 2], Operations: ['24+56=80', '80/40=2'] Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[84, 24, 40, 56], Operations: [] Exploring Operation: 24+56=80, Resulting Numbers: [84, 40, 80] Generated Node #0,1: 82:[84, 40, 80] Operation: 24+56=80 Moving to Node #0,1 Current State: 82:[84, 40, 80], Operations: ['24+56=80'] Exploring Operation: 80/40=2, Resulting Numbers: [84, 2] Generated Node #0,1,0: 82:[84, 2] Operation: 80/40=2 Moving to Node #0,1,0 Current State: 82:[84, 2], Operations: ['24+56=80', '80/40=2'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 30, 60, 6, 34 ]
56
[ "60/30=2", "34-6=28", "2*28=56" ]
Current State: 56:[30, 60, 6, 34], Operations: [] Exploring Operation: 60/30=2, Resulting Numbers: [6, 34, 2] Generated Node #2: [6, 34, 2] from Operation: 60/30=2 Current State: 56:[6, 34, 2], Operations: ['60/30=2'] Exploring Operation: 34-6=28, Resulting Numbers: [2, 28] Generated Node #3: [2, 28] from Operation: 34-6=28 Current State: 56:[2, 28], Operations: ['60/30=2', '34-6=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[30, 60, 6, 34], Operations: [] Exploring Operation: 34-30=4, Resulting Numbers: [60, 6, 4] Generated Node #0,0: 56:[60, 6, 4] Operation: 34-30=4 Moving to Node #0,0 Current State: 56:[60, 6, 4], Operations: ['34-30=4'] Exploring Operation: 60-4=56, Resulting Numbers: [6, 56] Generated Node #0,0,0: 56:[6, 56] Operation: 60-4=56 Moving to Node #0,0,0 Current State: 56:[6, 56], Operations: ['34-30=4', '60-4=56'] Exploring Operation: 6+56=62, Resulting Numbers: [62] 62,56 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 44, 82, 9, 64 ]
78
[ "44+82=126", "126/9=14", "64+14=78" ]
Current State: 78:[44, 82, 9, 64], Operations: [] Exploring Operation: 44+82=126, Resulting Numbers: [9, 64, 126] Generated Node #2: [9, 64, 126] from Operation: 44+82=126 Current State: 78:[9, 64, 126], Operations: ['44+82=126'] Exploring Operation: 126/9=14, Resulting Numbers: [64, 14] Generated Node #3: [64, 14] from Operation: 126/9=14 Current State: 78:[64, 14], Operations: ['44+82=126', '126/9=14'] Exploring Operation: 64+14=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[44, 82, 9, 64], Operations: [] Exploring Operation: 64-44=20, Resulting Numbers: [82, 9, 20] Generated Node #0,0: 78:[82, 9, 20] Operation: 64-44=20 Moving to Node #0,0 Current State: 78:[82, 9, 20], Operations: ['64-44=20'] Exploring Operation: 20-9=11, Resulting Numbers: [82, 11] Generated Node #0,0,0: 78:[82, 11] Operation: 20-9=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[82, 11], Operations: ['64-44=20', '20-9=11'] Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 2, 81, 6, 25 ]
68
[ "2*6=12", "81-25=56", "12+56=68" ]
Current State: 68:[2, 81, 6, 25], Operations: [] Exploring Operation: 2*6=12, Resulting Numbers: [81, 25, 12] Generated Node #2: [81, 25, 12] from Operation: 2*6=12 Current State: 68:[81, 25, 12], Operations: ['2*6=12'] Exploring Operation: 81-25=56, Resulting Numbers: [12, 56] Generated Node #3: [12, 56] from Operation: 81-25=56 Current State: 68:[12, 56], Operations: ['2*6=12', '81-25=56'] Exploring Operation: 12+56=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[2, 81, 6, 25], Operations: [] Exploring Operation: 81-25=56, Resulting Numbers: [2, 6, 56] Generated Node #0,0: 68:[2, 6, 56] Operation: 81-25=56 Exploring Operation: 25-6=19, Resulting Numbers: [2, 81, 19] Generated Node #0,1: 68:[2, 81, 19] Operation: 25-6=19 Exploring Operation: 81-6=75, Resulting Numbers: [2, 25, 75] Generated Node #0,2: 68:[2, 25, 75] Operation: 81-6=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[2, 6, 56], Operations: ['81-25=56'] Exploring Operation: 6+56=62, Resulting Numbers: [2, 62] Generated Node #0,0,0: 68:[2, 62] Operation: 6+56=62 Exploring Operation: 56/2=28, Resulting Numbers: [6, 28] Generated Node #0,0,1: 68:[6, 28] Operation: 56/2=28 Exploring Operation: 6-2=4, Resulting Numbers: [56, 4] Generated Node #0,0,2: 68:[56, 4] Operation: 6-2=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[2, 62], Operations: ['81-25=56', '6+56=62'] Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,68 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,68 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,68 unequal: No Solution No 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: 68:[6, 28], Operations: ['81-25=56', '56/2=28'] Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,68 unequal: No Solution Exploring Operation: 6+28=34, Resulting Numbers: [34] 34,68 unequal: No Solution Exploring Operation: 6*28=168, Resulting Numbers: [168] 168,68 unequal: No Solution No 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: 68:[56, 4], Operations: ['81-25=56', '6-2=4'] Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 56+4=60, Resulting Numbers: [60] 60,68 unequal: No Solution Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,68 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: 68:[2, 81, 19], Operations: ['25-6=19'] Exploring Operation: 19-2=17, Resulting Numbers: [81, 17] Generated Node #0,1,0: 68:[81, 17] Operation: 19-2=17 Exploring Operation: 81-19=62, Resulting Numbers: [2, 62] Generated Node #0,1,1: 68:[2, 62] Operation: 81-19=62 Exploring Operation: 81-2=79, Resulting Numbers: [19, 79] Generated Node #0,1,2: 68:[19, 79] Operation: 81-2=79 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 68:[2, 62], Operations: ['25-6=19', '81-19=62'] Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,68 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,68 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,68 unequal: No Solution No 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: 68:[81, 17], Operations: ['25-6=19', '19-2=17'] Exploring Operation: 81+17=98, Resulting Numbers: [98] 98,68 unequal: No Solution Exploring Operation: 81-17=64, Resulting Numbers: [64] 64,68 unequal: No Solution Exploring Operation: 81*17=1377, Resulting Numbers: [1377] 1377,68 unequal: No Solution No 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: 68:[19, 79], Operations: ['25-6=19', '81-2=79'] Exploring Operation: 79-19=60, Resulting Numbers: [60] 60,68 unequal: No Solution Exploring Operation: 19+79=98, Resulting Numbers: [98] 98,68 unequal: No Solution Exploring Operation: 19*79=1501, Resulting Numbers: [1501] 1501,68 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: 68:[2, 25, 75], Operations: ['81-6=75'] Exploring Operation: 75/25=3, Resulting Numbers: [2, 3] Generated Node #0,2,0: 68:[2, 3] Operation: 75/25=3 Exploring Operation: 75-2=73, Resulting Numbers: [25, 73] Generated Node #0,2,1: 68:[25, 73] Operation: 75-2=73 Exploring Operation: 25-2=23, Resulting Numbers: [75, 23] Generated Node #0,2,2: 68:[75, 23] Operation: 25-2=23 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 68:[2, 3], Operations: ['81-6=75', '75/25=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,68 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,68 unequal: No Solution No 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: 68:[25, 73], Operations: ['81-6=75', '75-2=73'] Exploring Operation: 25+73=98, Resulting Numbers: [98] 98,68 unequal: No Solution Exploring Operation: 25*73=1825, Resulting Numbers: [1825] 1825,68 unequal: No Solution Exploring Operation: 73-25=48, Resulting Numbers: [48] 48,68 unequal: No Solution No 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: 68:[75, 23], Operations: ['81-6=75', '25-2=23'] Exploring Operation: 75+23=98, Resulting Numbers: [98] 98,68 unequal: No Solution Exploring Operation: 75*23=1725, Resulting Numbers: [1725] 1725,68 unequal: No Solution Exploring Operation: 75-23=52, Resulting Numbers: [52] 52,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 92, 33, 50, 82 ]
88
[ "50+82=132", "132/33=4", "92-4=88" ]
Current State: 88:[92, 33, 50, 82], Operations: [] Exploring Operation: 50+82=132, Resulting Numbers: [92, 33, 132] Generated Node #2: [92, 33, 132] from Operation: 50+82=132 Current State: 88:[92, 33, 132], Operations: ['50+82=132'] Exploring Operation: 132/33=4, Resulting Numbers: [92, 4] Generated Node #3: [92, 4] from Operation: 132/33=4 Current State: 88:[92, 4], Operations: ['50+82=132', '132/33=4'] Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[92, 33, 50, 82], Operations: [] Exploring Operation: 92-50=42, Resulting Numbers: [33, 82, 42] Generated Node #0,0: 88:[33, 82, 42] Operation: 92-50=42 Exploring Operation: 82-33=49, Resulting Numbers: [92, 50, 49] Generated Node #0,1: 88:[92, 50, 49] Operation: 82-33=49 Exploring Operation: 50-33=17, Resulting Numbers: [92, 82, 17] Generated Node #0,2: 88:[92, 82, 17] Operation: 50-33=17 Exploring Operation: 92-82=10, Resulting Numbers: [33, 50, 10] Generated Node #0,3: 88:[33, 50, 10] Operation: 92-82=10 Exploring Operation: 33+50=83, Resulting Numbers: [92, 82, 83] Generated Node #0,4: 88:[92, 82, 83] Operation: 33+50=83 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[92, 50, 49], Operations: ['82-33=49'] Exploring Operation: 92-50=42, Resulting Numbers: [49, 42] Generated Node #0,1,0: 88:[49, 42] Operation: 92-50=42 Exploring Operation: 50-49=1, Resulting Numbers: [92, 1] Generated Node #0,1,1: 88:[92, 1] Operation: 50-49=1 Exploring Operation: 92-49=43, Resulting Numbers: [50, 43] Generated Node #0,1,2: 88:[50, 43] Operation: 92-49=43 Exploring Operation: 92+50=142, Resulting Numbers: [49, 142] Generated Node #0,1,3: 88:[49, 142] Operation: 92+50=142 Exploring Operation: 50+49=99, Resulting Numbers: [92, 99] Generated Node #0,1,4: 88:[92, 99] Operation: 50+49=99 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 88:[92, 1], Operations: ['82-33=49', '50-49=1'] Exploring Operation: 92*1=92, Resulting Numbers: [92] 92,88 unequal: No Solution Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,88 unequal: No Solution Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,88 unequal: No Solution Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,88 unequal: No Solution No 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: 88:[49, 42], Operations: ['82-33=49', '92-50=42'] Exploring Operation: 49*42=2058, Resulting Numbers: [2058] 2058,88 unequal: No Solution Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 49+42=91, Resulting Numbers: [91] 91,88 unequal: No Solution No 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: 88:[50, 43], Operations: ['82-33=49', '92-49=43'] Exploring Operation: 50*43=2150, Resulting Numbers: [2150] 2150,88 unequal: No Solution Exploring Operation: 50-43=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 50+43=93, Resulting Numbers: [93] 93,88 unequal: No Solution No 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: 88:[92, 99], Operations: ['82-33=49', '50+49=99'] Exploring Operation: 99-92=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 92*99=9108, Resulting Numbers: [9108] 9108,88 unequal: No Solution Exploring Operation: 92+99=191, Resulting Numbers: [191] 191,88 unequal: No Solution No 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: 88:[49, 142], Operations: ['82-33=49', '92+50=142'] Exploring Operation: 142-49=93, Resulting Numbers: [93] 93,88 unequal: No Solution Exploring Operation: 49+142=191, Resulting Numbers: [191] 191,88 unequal: No Solution Exploring Operation: 49*142=6958, Resulting Numbers: [6958] 6958,88 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: 88:[92, 82, 17], Operations: ['50-33=17'] Exploring Operation: 92+17=109, Resulting Numbers: [82, 109] Generated Node #0,2,0: 88:[82, 109] Operation: 92+17=109 Exploring Operation: 82+17=99, Resulting Numbers: [92, 99] Generated Node #0,2,1: 88:[92, 99] Operation: 82+17=99 Exploring Operation: 92-17=75, Resulting Numbers: [82, 75] Generated Node #0,2,2: 88:[82, 75] Operation: 92-17=75 Exploring Operation: 82-17=65, Resulting Numbers: [92, 65] Generated Node #0,2,3: 88:[92, 65] Operation: 82-17=65 Exploring Operation: 92-82=10, Resulting Numbers: [17, 10] Generated Node #0,2,4: 88:[17, 10] Operation: 92-82=10 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 88:[17, 10], Operations: ['50-33=17', '92-82=10'] Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,88 unequal: No Solution Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,88 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,88 unequal: No Solution No 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: 88:[92, 99], Operations: ['50-33=17', '82+17=99'] Exploring Operation: 99-92=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 92*99=9108, Resulting Numbers: [9108] 9108,88 unequal: No Solution Exploring Operation: 92+99=191, Resulting Numbers: [191] 191,88 unequal: No Solution No 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: 88:[82, 75], Operations: ['50-33=17', '92-17=75'] Exploring Operation: 82+75=157, Resulting Numbers: [157] 157,88 unequal: No Solution Exploring Operation: 82*75=6150, Resulting Numbers: [6150] 6150,88 unequal: No Solution Exploring Operation: 82-75=7, Resulting Numbers: [7] 7,88 unequal: No Solution No 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: 88:[92, 65], Operations: ['50-33=17', '82-17=65'] Exploring Operation: 92-65=27, Resulting Numbers: [27] 27,88 unequal: No Solution Exploring Operation: 92+65=157, Resulting Numbers: [157] 157,88 unequal: No Solution Exploring Operation: 92*65=5980, Resulting Numbers: [5980] 5980,88 unequal: No Solution No 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: 88:[82, 109], Operations: ['50-33=17', '92+17=109'] Exploring Operation: 82*109=8938, Resulting Numbers: [8938] 8938,88 unequal: No Solution Exploring Operation: 109-82=27, Resulting Numbers: [27] 27,88 unequal: No Solution Exploring Operation: 82+109=191, Resulting Numbers: [191] 191,88 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: 88:[92, 82, 83], Operations: ['33+50=83'] Exploring Operation: 92+82=174, Resulting Numbers: [83, 174] Generated Node #0,4,0: 88:[83, 174] Operation: 92+82=174 Exploring Operation: 92-83=9, Resulting Numbers: [82, 9] Generated Node #0,4,1: 88:[82, 9] Operation: 92-83=9 Exploring Operation: 92-82=10, Resulting Numbers: [83, 10] Generated Node #0,4,2: 88:[83, 10] Operation: 92-82=10 Exploring Operation: 82+83=165, Resulting Numbers: [92, 165] Generated Node #0,4,3: 88:[92, 165] Operation: 82+83=165 Exploring Operation: 83-82=1, Resulting Numbers: [92, 1] Generated Node #0,4,4: 88:[92, 1] Operation: 83-82=1 Moving to Node #0,4,4 Current State: 88:[92, 1], Operations: ['33+50=83', '83-82=1'] Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,88 unequal: No Solution Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,88 unequal: No Solution Exploring Operation: 92*1=92, Resulting Numbers: [92] 92,88 unequal: No Solution Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,88 unequal: No Solution Moving to Node #0,4,2 Current State: 88:[83, 10], Operations: ['33+50=83', '92-82=10'] Exploring Operation: 83*10=830, Resulting Numbers: [830] 830,88 unequal: No Solution Exploring Operation: 83-10=73, Resulting Numbers: [73] 73,88 unequal: No Solution Exploring Operation: 83+10=93, Resulting Numbers: [93] 93,88 unequal: No Solution Moving to Node #0,4,1 Current State: 88:[82, 9], Operations: ['33+50=83', '92-83=9'] Exploring Operation: 82+9=91, Resulting Numbers: [91] 91,88 unequal: No Solution Exploring Operation: 82-9=73, Resulting Numbers: [73] 73,88 unequal: No Solution Exploring Operation: 82*9=738, Resulting Numbers: [738] 738,88 unequal: No Solution Moving to Node #0,4,3 Current State: 88:[92, 165], Operations: ['33+50=83', '82+83=165'] Exploring Operation: 165-92=73, Resulting Numbers: [73] 73,88 unequal: No Solution Exploring Operation: 92*165=15180, Resulting Numbers: [15180] 15180,88 unequal: No Solution Exploring Operation: 92+165=257, Resulting Numbers: [257] 257,88 unequal: No Solution Moving to Node #0,4,0 Current State: 88:[83, 174], Operations: ['33+50=83', '92+82=174'] Exploring Operation: 83*174=14442, Resulting Numbers: [14442] 14442,88 unequal: No Solution Exploring Operation: 83+174=257, Resulting Numbers: [257] 257,88 unequal: No Solution Exploring Operation: 174-83=91, Resulting Numbers: [91] 91,88 unequal: No Solution No 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: 88:[33, 50, 10], Operations: ['92-82=10'] Exploring Operation: 33+10=43, Resulting Numbers: [50, 43] Generated Node #0,3,0: 88:[50, 43] Operation: 33+10=43 Exploring Operation: 33-10=23, Resulting Numbers: [50, 23] Generated Node #0,3,1: 88:[50, 23] Operation: 33-10=23 Exploring Operation: 33+50=83, Resulting Numbers: [10, 83] Generated Node #0,3,2: 88:[10, 83] Operation: 33+50=83 Exploring Operation: 50/10=5, Resulting Numbers: [33, 5] Generated Node #0,3,3: 88:[33, 5] Operation: 50/10=5 Exploring Operation: 50-33=17, Resulting Numbers: [10, 17] Generated Node #0,3,4: 88:[10, 17] Operation: 50-33=17 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 88:[10, 83], Operations: ['92-82=10', '33+50=83'] Exploring Operation: 83-10=73, Resulting Numbers: [73] 73,88 unequal: No Solution Exploring Operation: 10*83=830, Resulting Numbers: [830] 830,88 unequal: No Solution Exploring Operation: 10+83=93, Resulting Numbers: [93] 93,88 unequal: No Solution No 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: 88:[10, 17], Operations: ['92-82=10', '50-33=17'] Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 10*17=170, Resulting Numbers: [170] 170,88 unequal: No Solution Exploring Operation: 10+17=27, Resulting Numbers: [27] 27,88 unequal: No Solution No 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: 88:[50, 43], Operations: ['92-82=10', '33+10=43'] Exploring Operation: 50-43=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 50*43=2150, Resulting Numbers: [2150] 2150,88 unequal: No Solution Exploring Operation: 50+43=93, Resulting Numbers: [93] 93,88 unequal: No Solution No 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: 88:[50, 23], Operations: ['92-82=10', '33-10=23'] Exploring Operation: 50*23=1150, Resulting Numbers: [1150] 1150,88 unequal: No Solution Exploring Operation: 50+23=73, Resulting Numbers: [73] 73,88 unequal: No Solution Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,88 unequal: No Solution No 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: 88:[33, 5], Operations: ['92-82=10', '50/10=5'] Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,88 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,88 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,88 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: 88:[33, 82, 42], Operations: ['92-50=42'] Exploring Operation: 82-33=49, Resulting Numbers: [42, 49] Generated Node #0,0,0: 88:[42, 49] Operation: 82-33=49 Exploring Operation: 33+42=75, Resulting Numbers: [82, 75] Generated Node #0,0,1: 88:[82, 75] Operation: 33+42=75 Exploring Operation: 42-33=9, Resulting Numbers: [82, 9] Generated Node #0,0,2: 88:[82, 9] Operation: 42-33=9 Exploring Operation: 82-42=40, Resulting Numbers: [33, 40] Generated Node #0,0,3: 88:[33, 40] Operation: 82-42=40 Exploring Operation: 33+82=115, Resulting Numbers: [42, 115] Generated Node #0,0,4: 88:[42, 115] Operation: 33+82=115 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[42, 49], Operations: ['92-50=42', '82-33=49'] Exploring Operation: 42+49=91, Resulting Numbers: [91] 91,88 unequal: No Solution Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 42*49=2058, Resulting Numbers: [2058] 2058,88 unequal: No Solution No 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: 88:[82, 9], Operations: ['92-50=42', '42-33=9'] Exploring Operation: 82*9=738, Resulting Numbers: [738] 738,88 unequal: No Solution Exploring Operation: 82+9=91, Resulting Numbers: [91] 91,88 unequal: No Solution Exploring Operation: 82-9=73, Resulting Numbers: [73] 73,88 unequal: No Solution No 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: 88:[33, 40], Operations: ['92-50=42', '82-42=40'] Exploring Operation: 33+40=73, Resulting Numbers: [73] 73,88 unequal: No Solution Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 33*40=1320, Resulting Numbers: [1320] 1320,88 unequal: No Solution No 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: 88:[82, 75], Operations: ['92-50=42', '33+42=75'] Exploring Operation: 82-75=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 82*75=6150, Resulting Numbers: [6150] 6150,88 unequal: No Solution Exploring Operation: 82+75=157, Resulting Numbers: [157] 157,88 unequal: No Solution No 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: 88:[42, 115], Operations: ['92-50=42', '33+82=115'] Exploring Operation: 115-42=73, Resulting Numbers: [73] 73,88 unequal: No Solution Exploring Operation: 42*115=4830, Resulting Numbers: [4830] 4830,88 unequal: No Solution Exploring Operation: 42+115=157, Resulting Numbers: [157] 157,88 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
[ 61, 71, 22, 36 ]
30
[ "61+71=132", "132/22=6", "36-6=30" ]
Current State: 30:[61, 71, 22, 36], Operations: [] Exploring Operation: 61+71=132, Resulting Numbers: [22, 36, 132] Generated Node #2: [22, 36, 132] from Operation: 61+71=132 Current State: 30:[22, 36, 132], Operations: ['61+71=132'] Exploring Operation: 132/22=6, Resulting Numbers: [36, 6] Generated Node #3: [36, 6] from Operation: 132/22=6 Current State: 30:[36, 6], Operations: ['61+71=132', '132/22=6'] Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[61, 71, 22, 36], Operations: [] Exploring Operation: 71-61=10, Resulting Numbers: [22, 36, 10] Generated Node #0,0: 30:[22, 36, 10] Operation: 71-61=10 Exploring Operation: 71-36=35, Resulting Numbers: [61, 22, 35] Generated Node #0,1: 30:[61, 22, 35] Operation: 71-36=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[22, 36, 10], Operations: ['71-61=10'] Exploring Operation: 22+10=32, Resulting Numbers: [36, 32] Generated Node #0,0,0: 30:[36, 32] Operation: 22+10=32 Exploring Operation: 36-22=14, Resulting Numbers: [10, 14] Generated Node #0,0,1: 30:[10, 14] Operation: 36-22=14 Moving to Node #0,0,1 Current State: 30:[10, 14], Operations: ['71-61=10', '36-22=14'] Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[36, 32], Operations: ['71-61=10', '22+10=32'] Exploring Operation: 36-32=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 36+32=68, Resulting Numbers: [68] 68,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[61, 22, 35], Operations: ['71-36=35'] Exploring Operation: 61-35=26, Resulting Numbers: [22, 26] Generated Node #0,1,0: 30:[22, 26] Operation: 61-35=26 Exploring Operation: 61-22=39, Resulting Numbers: [35, 39] Generated Node #0,1,1: 30:[35, 39] Operation: 61-22=39 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[22, 26], Operations: ['71-36=35', '61-35=26'] Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 22+26=48, Resulting Numbers: [48] 48,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[35, 39], Operations: ['71-36=35', '61-22=39'] Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 35+39=74, Resulting Numbers: [74] 74,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 6, 2, 66, 69 ]
75
[ "6+66=72", "2*72=144", "144-69=75" ]
Current State: 75:[6, 2, 66, 69], Operations: [] Exploring Operation: 6+66=72, Resulting Numbers: [2, 69, 72] Generated Node #2: [2, 69, 72] from Operation: 6+66=72 Current State: 75:[2, 69, 72], Operations: ['6+66=72'] Exploring Operation: 2*72=144, Resulting Numbers: [69, 144] Generated Node #3: [69, 144] from Operation: 2*72=144 Current State: 75:[69, 144], Operations: ['6+66=72', '2*72=144'] Exploring Operation: 144-69=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[6, 2, 66, 69], Operations: [] Exploring Operation: 69-66=3, Resulting Numbers: [6, 2, 3] Generated Node #0,0: 75:[6, 2, 3] Operation: 69-66=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[6, 2, 3], Operations: ['69-66=3'] Exploring Operation: 6/2=3, Resulting Numbers: [3, 3] Generated Node #0,0,0: 75:[3, 3] Operation: 6/2=3 Moving to Node #0,0,0 Current State: 75:[3, 3], Operations: ['69-66=3', '6/2=3'] Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 29, 23, 93, 4 ]
95
[ "29-23=6", "93-4=89", "6+89=95" ]
Current State: 95:[29, 23, 93, 4], Operations: [] Exploring Operation: 29-23=6, Resulting Numbers: [93, 4, 6] Generated Node #2: [93, 4, 6] from Operation: 29-23=6 Current State: 95:[93, 4, 6], Operations: ['29-23=6'] Exploring Operation: 93-4=89, Resulting Numbers: [6, 89] Generated Node #3: [6, 89] from Operation: 93-4=89 Current State: 95:[6, 89], Operations: ['29-23=6', '93-4=89'] Exploring Operation: 6+89=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[29, 23, 93, 4], Operations: [] Exploring Operation: 29-4=25, Resulting Numbers: [23, 93, 25] Generated Node #0,0: 95:[23, 93, 25] Operation: 29-4=25 Exploring Operation: 29-23=6, Resulting Numbers: [93, 4, 6] Generated Node #0,1: 95:[93, 4, 6] Operation: 29-23=6 Exploring Operation: 23-4=19, Resulting Numbers: [29, 93, 19] Generated Node #0,2: 95:[29, 93, 19] Operation: 23-4=19 Exploring Operation: 23*4=92, Resulting Numbers: [29, 93, 92] Generated Node #0,3: 95:[29, 93, 92] Operation: 23*4=92 Moving to Node #0,1 Current State: 95:[93, 4, 6], Operations: ['29-23=6'] Exploring Operation: 93+6=99, Resulting Numbers: [4, 99] Generated Node #0,1,0: 95:[4, 99] Operation: 93+6=99 Exploring Operation: 93-4=89, Resulting Numbers: [6, 89] Generated Node #0,1,1: 95:[6, 89] Operation: 93-4=89 Exploring Operation: 93+4=97, Resulting Numbers: [6, 97] Generated Node #0,1,2: 95:[6, 97] Operation: 93+4=97 Exploring Operation: 6-4=2, Resulting Numbers: [93, 2] Generated Node #0,1,3: 95:[93, 2] Operation: 6-4=2 Moving to Node #0,2 Current State: 95:[29, 93, 19], Operations: ['23-4=19'] Exploring Operation: 29+93=122, Resulting Numbers: [19, 122] Generated Node #0,2,0: 95:[19, 122] Operation: 29+93=122 Exploring Operation: 93-29=64, Resulting Numbers: [19, 64] Generated Node #0,2,1: 95:[19, 64] Operation: 93-29=64 Exploring Operation: 93+19=112, Resulting Numbers: [29, 112] Generated Node #0,2,2: 95:[29, 112] Operation: 93+19=112 Exploring Operation: 29-19=10, Resulting Numbers: [93, 10] Generated Node #0,2,3: 95:[93, 10] Operation: 29-19=10 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 95:[93, 10], Operations: ['23-4=19', '29-19=10'] Exploring Operation: 93*10=930, Resulting Numbers: [930] 930,95 unequal: No Solution Exploring Operation: 93+10=103, Resulting Numbers: [103] 103,95 unequal: No Solution Exploring Operation: 93-10=83, Resulting Numbers: [83] 83,95 unequal: No Solution No 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: 95:[19, 122], Operations: ['23-4=19', '29+93=122'] Exploring Operation: 19+122=141, Resulting Numbers: [141] 141,95 unequal: No Solution Exploring Operation: 19*122=2318, Resulting Numbers: [2318] 2318,95 unequal: No Solution Exploring Operation: 122-19=103, Resulting Numbers: [103] 103,95 unequal: No Solution No 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: 95:[29, 112], Operations: ['23-4=19', '93+19=112'] Exploring Operation: 112-29=83, Resulting Numbers: [83] 83,95 unequal: No Solution Exploring Operation: 29*112=3248, Resulting Numbers: [3248] 3248,95 unequal: No Solution Exploring Operation: 29+112=141, Resulting Numbers: [141] 141,95 unequal: No Solution No 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: 95:[19, 64], Operations: ['23-4=19', '93-29=64'] Exploring Operation: 19+64=83, Resulting Numbers: [83] 83,95 unequal: No Solution Exploring Operation: 64-19=45, Resulting Numbers: [45] 45,95 unequal: No Solution Exploring Operation: 19*64=1216, Resulting Numbers: [1216] 1216,95 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: 95:[23, 93, 25], Operations: ['29-4=25'] Exploring Operation: 93-23=70, Resulting Numbers: [25, 70] Generated Node #0,0,0: 95:[25, 70] Operation: 93-23=70 Exploring Operation: 93+25=118, Resulting Numbers: [23, 118] Generated Node #0,0,1: 95:[23, 118] Operation: 93+25=118 Exploring Operation: 23+93=116, Resulting Numbers: [25, 116] Generated Node #0,0,2: 95:[25, 116] Operation: 23+93=116 Exploring Operation: 25-23=2, Resulting Numbers: [93, 2] Generated Node #0,0,3: 95:[93, 2] Operation: 25-23=2 Moving to Node #0,3 Current State: 95:[29, 93, 92], Operations: ['23*4=92'] Exploring Operation: 29+92=121, Resulting Numbers: [93, 121] Generated Node #0,3,0: 95:[93, 121] Operation: 29+92=121 Exploring Operation: 93-92=1, Resulting Numbers: [29, 1] Generated Node #0,3,1: 95:[29, 1] Operation: 93-92=1 Exploring Operation: 29+93=122, Resulting Numbers: [92, 122] Generated Node #0,3,2: 95:[92, 122] Operation: 29+93=122 Exploring Operation: 93-29=64, Resulting Numbers: [92, 64] Generated Node #0,3,3: 95:[92, 64] Operation: 93-29=64 Moving to Node #0,1,2 Current State: 95:[6, 97], Operations: ['29-23=6', '93+4=97'] Exploring Operation: 6+97=103, Resulting Numbers: [103] 103,95 unequal: No Solution Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,95 unequal: No Solution Exploring Operation: 6*97=582, Resulting Numbers: [582] 582,95 unequal: No Solution Moving to Node #0,1,3 Current State: 95:[93, 2], Operations: ['29-23=6', '6-4=2'] Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[29, 23, 93, 4], Operations: [] Exploring Operation: 29-23=6, Resulting Numbers: [93, 4, 6] Generated Node #0,1: 95:[93, 4, 6] Operation: 29-23=6 Moving to Node #0,1 Current State: 95:[93, 4, 6], Operations: ['29-23=6'] Exploring Operation: 6-4=2, Resulting Numbers: [93, 2] Generated Node #0,1,3: 95:[93, 2] Operation: 6-4=2 Moving to Node #0,1,3 Current State: 95:[93, 2], Operations: ['29-23=6', '6-4=2'] Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
0.965278
hs_4
mult_heuristic
[ 86, 36, 36, 21 ]
21
[ "36-36=0", "86*0=0", "21+0=21" ]
Current State: 21:[86, 36, 36, 21], Operations: [] Exploring Operation: 36-36=0, Resulting Numbers: [86, 21, 0] Generated Node #2: [86, 21, 0] from Operation: 36-36=0 Current State: 21:[86, 21, 0], Operations: ['36-36=0'] Exploring Operation: 86*0=0, Resulting Numbers: [21, 0] Generated Node #3: [21, 0] from Operation: 86*0=0 Current State: 21:[21, 0], Operations: ['36-36=0', '86*0=0'] Exploring Operation: 21+0=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[86, 36, 36, 21], Operations: [] Exploring Operation: 86-36=50, Resulting Numbers: [36, 21, 50] Generated Node #0,0: 21:[36, 21, 50] Operation: 86-36=50 Exploring Operation: 36-36=0, Resulting Numbers: [86, 21, 0] Generated Node #0,1: 21:[86, 21, 0] Operation: 36-36=0 Exploring Operation: 36/36=1, Resulting Numbers: [86, 21, 1] Generated Node #0,2: 21:[86, 21, 1] Operation: 36/36=1 Exploring Operation: 86-36=50, Resulting Numbers: [36, 21, 50] Generated Node #0,3: 21:[36, 21, 50] Operation: 86-36=50 Exploring Operation: 86-21=65, Resulting Numbers: [36, 36, 65] Generated Node #0,4: 21:[36, 36, 65] Operation: 86-21=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[36, 21, 50], Operations: ['86-36=50'] Exploring Operation: 36-21=15, Resulting Numbers: [50, 15] Generated Node #0,0,0: 21:[50, 15] Operation: 36-21=15 Exploring Operation: 50-21=29, Resulting Numbers: [36, 29] Generated Node #0,0,1: 21:[36, 29] Operation: 50-21=29 Exploring Operation: 36+21=57, Resulting Numbers: [50, 57] Generated Node #0,0,2: 21:[50, 57] Operation: 36+21=57 Exploring Operation: 50-36=14, Resulting Numbers: [21, 14] Generated Node #0,0,3: 21:[21, 14] Operation: 50-36=14 Exploring Operation: 36+50=86, Resulting Numbers: [21, 86] Generated Node #0,0,4: 21:[21, 86] Operation: 36+50=86 Moving to Node #0,0,3 Current State: 21:[21, 14], Operations: ['86-36=50', '50-36=14'] Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,21 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[36, 29], Operations: ['86-36=50', '50-21=29'] Exploring Operation: 36+29=65, Resulting Numbers: [65] 65,21 unequal: No Solution Exploring Operation: 36-29=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 36*29=1044, Resulting Numbers: [1044] 1044,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[50, 15], Operations: ['86-36=50', '36-21=15'] Exploring Operation: 50+15=65, Resulting Numbers: [65] 65,21 unequal: No Solution Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,21 unequal: No Solution Exploring Operation: 50*15=750, Resulting Numbers: [750] 750,21 unequal: No Solution Moving to Node #0,0,2 Current State: 21:[50, 57], Operations: ['86-36=50', '36+21=57'] Exploring Operation: 50+57=107, Resulting Numbers: [107] 107,21 unequal: No Solution Exploring Operation: 57-50=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 50*57=2850, Resulting Numbers: [2850] 2850,21 unequal: No Solution Moving to Node #0,0,4 Current State: 21:[21, 86], Operations: ['86-36=50', '36+50=86'] Exploring Operation: 21+86=107, Resulting Numbers: [107] 107,21 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,21 unequal: No Solution Exploring Operation: 21*86=1806, Resulting Numbers: [1806] 1806,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 21:[36, 21, 50], Operations: ['86-36=50'] Exploring Operation: 50-36=14, Resulting Numbers: [21, 14] Generated Node #0,3,0: 21:[21, 14] Operation: 50-36=14 Exploring Operation: 36-21=15, Resulting Numbers: [50, 15] Generated Node #0,3,1: 21:[50, 15] Operation: 36-21=15 Exploring Operation: 50-21=29, Resulting Numbers: [36, 29] Generated Node #0,3,2: 21:[36, 29] Operation: 50-21=29 Exploring Operation: 36+50=86, Resulting Numbers: [21, 86] Generated Node #0,3,3: 21:[21, 86] Operation: 36+50=86 Exploring Operation: 36+21=57, Resulting Numbers: [50, 57] Generated Node #0,3,4: 21:[50, 57] Operation: 36+21=57 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 21:[21, 14], Operations: ['86-36=50', '50-36=14'] Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,21 unequal: No Solution Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,21 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,21 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 #0,3,2 Current State: 21:[36, 29], Operations: ['86-36=50', '50-21=29'] Exploring Operation: 36*29=1044, Resulting Numbers: [1044] 1044,21 unequal: No Solution Exploring Operation: 36-29=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 36+29=65, Resulting Numbers: [65] 65,21 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 #0,3,1 Current State: 21:[50, 15], Operations: ['86-36=50', '36-21=15'] Exploring Operation: 50+15=65, Resulting Numbers: [65] 65,21 unequal: No Solution Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,21 unequal: No Solution Exploring Operation: 50*15=750, Resulting Numbers: [750] 750,21 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 #0,3,3 Current State: 21:[21, 86], Operations: ['86-36=50', '36+50=86'] Exploring Operation: 21+86=107, Resulting Numbers: [107] 107,21 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,21 unequal: No Solution Exploring Operation: 21*86=1806, Resulting Numbers: [1806] 1806,21 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 #0,3,4 Current State: 21:[50, 57], Operations: ['86-36=50', '36+21=57'] Exploring Operation: 50*57=2850, Resulting Numbers: [2850] 2850,21 unequal: No Solution Exploring Operation: 50+57=107, Resulting Numbers: [107] 107,21 unequal: No Solution Exploring Operation: 57-50=7, Resulting Numbers: [7] 7,21 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: 21:[86, 21, 1], Operations: ['36/36=1'] Exploring Operation: 21*1=21, Resulting Numbers: [86, 21] Generated Node #0,2,0: 21:[86, 21] Operation: 21*1=21 Exploring Operation: 86-1=85, Resulting Numbers: [21, 85] Generated Node #0,2,1: 21:[21, 85] Operation: 86-1=85 Exploring Operation: 86-21=65, Resulting Numbers: [1, 65] Generated Node #0,2,2: 21:[1, 65] Operation: 86-21=65 Exploring Operation: 86/1=86, Resulting Numbers: [21, 86] Generated Node #0,2,3: 21:[21, 86] Operation: 86/1=86 Exploring Operation: 86*1=86, Resulting Numbers: [21, 86] Generated Node #0,2,4: 21:[21, 86] Operation: 86*1=86 Moving to Node #0,2,2 Current State: 21:[1, 65], Operations: ['36/36=1', '86-21=65'] Exploring Operation: 1+65=66, Resulting Numbers: [66] 66,21 unequal: No Solution Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,21 unequal: No Solution Exploring Operation: 1*65=65, Resulting Numbers: [65] 65,21 unequal: No Solution Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,21 unequal: No Solution Moving to Node #0,2,1 Current State: 21:[21, 85], Operations: ['36/36=1', '86-1=85'] Exploring Operation: 21+85=106, Resulting Numbers: [106] 106,21 unequal: No Solution Exploring Operation: 21*85=1785, Resulting Numbers: [1785] 1785,21 unequal: No Solution Exploring Operation: 85-21=64, Resulting Numbers: [64] 64,21 unequal: No Solution Moving to Node #0,2,0 Current State: 21:[86, 21], Operations: ['36/36=1', '21*1=21'] Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,21 unequal: No Solution Exploring Operation: 86*21=1806, Resulting Numbers: [1806] 1806,21 unequal: No Solution Exploring Operation: 86+21=107, Resulting Numbers: [107] 107,21 unequal: No Solution Moving to Node #0,2,3 Current State: 21:[21, 86], Operations: ['36/36=1', '86/1=86'] Exploring Operation: 21+86=107, Resulting Numbers: [107] 107,21 unequal: No Solution Exploring Operation: 21*86=1806, Resulting Numbers: [1806] 1806,21 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,21 unequal: No Solution Moving to Node #0,2,4 Current State: 21:[21, 86], Operations: ['36/36=1', '86*1=86'] Exploring Operation: 21+86=107, Resulting Numbers: [107] 107,21 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,21 unequal: No Solution Exploring Operation: 21*86=1806, Resulting Numbers: [1806] 1806,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[86, 21, 0], Operations: ['36-36=0'] Exploring Operation: 86+0=86, Resulting Numbers: [21, 86] Generated Node #0,1,0: 21:[21, 86] Operation: 86+0=86 Exploring Operation: 21+0=21, Resulting Numbers: [86, 21] Generated Node #0,1,1: 21:[86, 21] Operation: 21+0=21 Exploring Operation: 86-21=65, Resulting Numbers: [0, 65] Generated Node #0,1,2: 21:[0, 65] Operation: 86-21=65 Exploring Operation: 86-0=86, Resulting Numbers: [21, 86] Generated Node #0,1,3: 21:[21, 86] Operation: 86-0=86 Exploring Operation: 86*0=0, Resulting Numbers: [21, 0] Generated Node #0,1,4: 21:[21, 0] Operation: 86*0=0 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 21:[21, 0], Operations: ['36-36=0', '86*0=0'] Exploring Operation: 21+0=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[86, 36, 36, 21], Operations: [] Exploring Operation: 36-36=0, Resulting Numbers: [86, 21, 0] Generated Node #0,1: 21:[86, 21, 0] Operation: 36-36=0 Moving to Node #0,1 Current State: 21:[86, 21, 0], Operations: ['36-36=0'] Exploring Operation: 86*0=0, Resulting Numbers: [21, 0] Generated Node #0,1,4: 21:[21, 0] Operation: 86*0=0 Moving to Node #0,1,4 Current State: 21:[21, 0], Operations: ['36-36=0', '86*0=0'] Exploring Operation: 21+0=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.934028
hs_5
sum_heuristic
[ 9, 8, 80, 2 ]
40
[ "9-8=1", "80/2=40", "1*40=40" ]
Current State: 40:[9, 8, 80, 2], Operations: [] Exploring Operation: 9-8=1, Resulting Numbers: [80, 2, 1] Generated Node #2: [80, 2, 1] from Operation: 9-8=1 Current State: 40:[80, 2, 1], Operations: ['9-8=1'] Exploring Operation: 80/2=40, Resulting Numbers: [1, 40] Generated Node #3: [1, 40] from Operation: 80/2=40 Current State: 40:[1, 40], Operations: ['9-8=1', '80/2=40'] Exploring Operation: 1*40=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[9, 8, 80, 2], Operations: [] Exploring Operation: 80-8=72, Resulting Numbers: [9, 2, 72] Generated Node #0,0: 40:[9, 2, 72] Operation: 80-8=72 Exploring Operation: 80/8=10, Resulting Numbers: [9, 2, 10] Generated Node #0,1: 40:[9, 2, 10] Operation: 80/8=10 Exploring Operation: 80/2=40, Resulting Numbers: [9, 8, 40] Generated Node #0,2: 40:[9, 8, 40] Operation: 80/2=40 Exploring Operation: 80-2=78, Resulting Numbers: [9, 8, 78] Generated Node #0,3: 40:[9, 8, 78] Operation: 80-2=78 Exploring Operation: 80-9=71, Resulting Numbers: [8, 2, 71] Generated Node #0,4: 40:[8, 2, 71] Operation: 80-9=71 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[9, 2, 10], Operations: ['80/8=10'] Exploring Operation: 2*10=20, Resulting Numbers: [9, 20] Generated Node #0,1,0: 40:[9, 20] Operation: 2*10=20 Exploring Operation: 10-9=1, Resulting Numbers: [2, 1] Generated Node #0,1,1: 40:[2, 1] Operation: 10-9=1 Exploring Operation: 9+10=19, Resulting Numbers: [2, 19] Generated Node #0,1,2: 40:[2, 19] Operation: 9+10=19 Exploring Operation: 9-2=7, Resulting Numbers: [10, 7] Generated Node #0,1,3: 40:[10, 7] Operation: 9-2=7 Exploring Operation: 9+2=11, Resulting Numbers: [10, 11] Generated Node #0,1,4: 40:[10, 11] Operation: 9+2=11 Moving to Node #0,1,0 Current State: 40:[9, 20], Operations: ['80/8=10', '2*10=20'] Exploring Operation: 9*20=180, Resulting Numbers: [180] 180,40 unequal: No Solution Exploring Operation: 9+20=29, Resulting Numbers: [29] 29,40 unequal: No Solution Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,40 unequal: No Solution Moving to Node #0,1,2 Current State: 40:[2, 19], Operations: ['80/8=10', '9+10=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,40 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,40 unequal: No Solution Moving to Node #0,1,4 Current State: 40:[10, 11], Operations: ['80/8=10', '9+2=11'] Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,40 unequal: No Solution Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,40 unequal: No Solution Moving to Node #0,1,1 Current State: 40:[2, 1], Operations: ['80/8=10', '10-9=1'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,40 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,40 unequal: No Solution Moving to Node #0,1,3 Current State: 40:[10, 7], Operations: ['80/8=10', '9-2=7'] Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,40 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[9, 8, 40], Operations: ['80/2=40'] Exploring Operation: 9+40=49, Resulting Numbers: [8, 49] Generated Node #0,2,0: 40:[8, 49] Operation: 9+40=49 Exploring Operation: 9+8=17, Resulting Numbers: [40, 17] Generated Node #0,2,1: 40:[40, 17] Operation: 9+8=17 Exploring Operation: 9-8=1, Resulting Numbers: [40, 1] Generated Node #0,2,2: 40:[40, 1] Operation: 9-8=1 Exploring Operation: 40/8=5, Resulting Numbers: [9, 5] Generated Node #0,2,3: 40:[9, 5] Operation: 40/8=5 Exploring Operation: 40-9=31, Resulting Numbers: [8, 31] Generated Node #0,2,4: 40:[8, 31] Operation: 40-9=31 Moving to Node #0,2,2 Current State: 40:[40, 1], Operations: ['80/2=40', '9-8=1'] Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[9, 8, 80, 2], Operations: [] Exploring Operation: 80/2=40, Resulting Numbers: [9, 8, 40] Generated Node #0,2: 40:[9, 8, 40] Operation: 80/2=40 Moving to Node #0,2 Current State: 40:[9, 8, 40], Operations: ['80/2=40'] Exploring Operation: 9-8=1, Resulting Numbers: [40, 1] Generated Node #0,2,2: 40:[40, 1] Operation: 9-8=1 Moving to Node #0,2,2 Current State: 40:[40, 1], Operations: ['80/2=40', '9-8=1'] Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 53, 93, 51, 33 ]
96
[ "53*93=4929", "4929-33=4896", "4896/51=96" ]
Current State: 96:[53, 93, 51, 33], Operations: [] Exploring Operation: 53*93=4929, Resulting Numbers: [51, 33, 4929] Generated Node #2: [51, 33, 4929] from Operation: 53*93=4929 Current State: 96:[51, 33, 4929], Operations: ['53*93=4929'] Exploring Operation: 4929-33=4896, Resulting Numbers: [51, 4896] Generated Node #3: [51, 4896] from Operation: 4929-33=4896 Current State: 96:[51, 4896], Operations: ['53*93=4929', '4929-33=4896'] Exploring Operation: 4896/51=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[53, 93, 51, 33], Operations: [] Exploring Operation: 53-33=20, Resulting Numbers: [93, 51, 20] Generated Node #0,0: 96:[93, 51, 20] Operation: 53-33=20 Exploring Operation: 53-51=2, Resulting Numbers: [93, 33, 2] Generated Node #0,1: 96:[93, 33, 2] Operation: 53-51=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[93, 33, 2], Operations: ['53-51=2'] Exploring Operation: 93+2=95, Resulting Numbers: [33, 95] Generated Node #0,1,0: 96:[33, 95] Operation: 93+2=95 Exploring Operation: 33-2=31, Resulting Numbers: [93, 31] Generated Node #0,1,1: 96:[93, 31] Operation: 33-2=31 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[33, 95], Operations: ['53-51=2', '93+2=95'] Exploring Operation: 33+95=128, Resulting Numbers: [128] 128,96 unequal: No Solution Exploring Operation: 95-33=62, Resulting Numbers: [62] 62,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[93, 31], Operations: ['53-51=2', '33-2=31'] Exploring Operation: 93-31=62, Resulting Numbers: [62] 62,96 unequal: No Solution Exploring Operation: 93/31=3, Resulting Numbers: [3] 3,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[93, 51, 20], Operations: ['53-33=20'] Exploring Operation: 51-20=31, Resulting Numbers: [93, 31] Generated Node #0,0,0: 96:[93, 31] Operation: 51-20=31 Exploring Operation: 93-51=42, Resulting Numbers: [20, 42] Generated Node #0,0,1: 96:[20, 42] Operation: 93-51=42 Moving to Node #0,0,0 Current State: 96:[93, 31], Operations: ['53-33=20', '51-20=31'] Exploring Operation: 93-31=62, Resulting Numbers: [62] 62,96 unequal: No Solution Exploring Operation: 93/31=3, Resulting Numbers: [3] 3,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[20, 42], Operations: ['53-33=20', '93-51=42'] Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 20+42=62, Resulting Numbers: [62] 62,96 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
[ 19, 68, 67, 89 ]
27
[ "68-19=49", "89-67=22", "49-22=27" ]
Current State: 27:[19, 68, 67, 89], Operations: [] Exploring Operation: 68-19=49, Resulting Numbers: [67, 89, 49] Generated Node #2: [67, 89, 49] from Operation: 68-19=49 Current State: 27:[67, 89, 49], Operations: ['68-19=49'] Exploring Operation: 89-67=22, Resulting Numbers: [49, 22] Generated Node #3: [49, 22] from Operation: 89-67=22 Current State: 27:[49, 22], Operations: ['68-19=49', '89-67=22'] Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[19, 68, 67, 89], Operations: [] Exploring Operation: 89-68=21, Resulting Numbers: [19, 67, 21] Generated Node #0,0: 27:[19, 67, 21] Operation: 89-68=21 Moving to Node #0,0 Current State: 27:[19, 67, 21], Operations: ['89-68=21'] Exploring Operation: 67-19=48, Resulting Numbers: [21, 48] Generated Node #0,0,0: 27:[21, 48] Operation: 67-19=48 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[21, 48], Operations: ['89-68=21', '67-19=48'] Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[19, 68, 67, 89], Operations: [] Exploring Operation: 89-68=21, Resulting Numbers: [19, 67, 21] Generated Node #0,0: 27:[19, 67, 21] Operation: 89-68=21 Moving to Node #0,0 Current State: 27:[19, 67, 21], Operations: ['89-68=21'] Exploring Operation: 67-19=48, Resulting Numbers: [21, 48] Generated Node #0,0,0: 27:[21, 48] Operation: 67-19=48 Moving to Node #0,0,0 Current State: 27:[21, 48], Operations: ['89-68=21', '67-19=48'] Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 28, 84, 70, 98 ]
23
[ "98-84=14", "70/14=5", "28-5=23" ]
Current State: 23:[28, 84, 70, 98], Operations: [] Exploring Operation: 98-84=14, Resulting Numbers: [28, 70, 14] Generated Node #2: [28, 70, 14] from Operation: 98-84=14 Current State: 23:[28, 70, 14], Operations: ['98-84=14'] Exploring Operation: 70/14=5, Resulting Numbers: [28, 5] Generated Node #3: [28, 5] from Operation: 70/14=5 Current State: 23:[28, 5], Operations: ['98-84=14', '70/14=5'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[28, 84, 70, 98], Operations: [] Exploring Operation: 98-84=14, Resulting Numbers: [28, 70, 14] Generated Node #0,0: 23:[28, 70, 14] Operation: 98-84=14 Exploring Operation: 98-70=28, Resulting Numbers: [28, 84, 28] Generated Node #0,1: 23:[28, 84, 28] Operation: 98-70=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[28, 70, 14], Operations: ['98-84=14'] Exploring Operation: 70-28=42, Resulting Numbers: [14, 42] Generated Node #0,0,0: 23:[14, 42] Operation: 70-28=42 Exploring Operation: 70/14=5, Resulting Numbers: [28, 5] Generated Node #0,0,1: 23:[28, 5] Operation: 70/14=5 Moving to Node #0,0,1 Current State: 23:[28, 5], Operations: ['98-84=14', '70/14=5'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[28, 84, 70, 98], Operations: [] Exploring Operation: 98-84=14, Resulting Numbers: [28, 70, 14] Generated Node #0,0: 23:[28, 70, 14] Operation: 98-84=14 Moving to Node #0,0 Current State: 23:[28, 70, 14], Operations: ['98-84=14'] Exploring Operation: 70/14=5, Resulting Numbers: [28, 5] Generated Node #0,0,1: 23:[28, 5] Operation: 70/14=5 Moving to Node #0,0,1 Current State: 23:[28, 5], Operations: ['98-84=14', '70/14=5'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 63, 5, 4, 10 ]
73
[ "63+10=73", "5-4=1", "73*1=73" ]
Current State: 73:[63, 5, 4, 10], Operations: [] Exploring Operation: 63+10=73, Resulting Numbers: [5, 4, 73] Generated Node #2: [5, 4, 73] from Operation: 63+10=73 Current State: 73:[5, 4, 73], Operations: ['63+10=73'] Exploring Operation: 5-4=1, Resulting Numbers: [73, 1] Generated Node #3: [73, 1] from Operation: 5-4=1 Current State: 73:[73, 1], Operations: ['63+10=73', '5-4=1'] Exploring Operation: 73*1=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[63, 5, 4, 10], Operations: [] Exploring Operation: 4*10=40, Resulting Numbers: [63, 5, 40] Generated Node #0,0: 73:[63, 5, 40] Operation: 4*10=40 Exploring Operation: 5*10=50, Resulting Numbers: [63, 4, 50] Generated Node #0,1: 73:[63, 4, 50] Operation: 5*10=50 Moving to Node #0,1 Current State: 73:[63, 4, 50], Operations: ['5*10=50'] Exploring Operation: 4+50=54, Resulting Numbers: [63, 54] Generated Node #0,1,0: 73:[63, 54] Operation: 4+50=54 Exploring Operation: 63+4=67, Resulting Numbers: [50, 67] Generated Node #0,1,1: 73:[50, 67] Operation: 63+4=67 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[63, 54], Operations: ['5*10=50', '4+50=54'] Exploring Operation: 63+54=117, Resulting Numbers: [117] 117,73 unequal: No Solution Exploring Operation: 63-54=9, Resulting Numbers: [9] 9,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[50, 67], Operations: ['5*10=50', '63+4=67'] Exploring Operation: 67-50=17, Resulting Numbers: [17] 17,73 unequal: No Solution Exploring Operation: 50+67=117, Resulting Numbers: [117] 117,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 73:[63, 5, 40], Operations: ['4*10=40'] Exploring Operation: 63+5=68, Resulting Numbers: [40, 68] Generated Node #0,0,0: 73:[40, 68] Operation: 63+5=68 Exploring Operation: 5+40=45, Resulting Numbers: [63, 45] Generated Node #0,0,1: 73:[63, 45] Operation: 5+40=45 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[40, 68], Operations: ['4*10=40', '63+5=68'] Exploring Operation: 68-40=28, Resulting Numbers: [28] 28,73 unequal: No Solution Exploring Operation: 40+68=108, Resulting Numbers: [108] 108,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[63, 45], Operations: ['4*10=40', '5+40=45'] Exploring Operation: 63+45=108, Resulting Numbers: [108] 108,73 unequal: No Solution Exploring Operation: 63-45=18, Resulting Numbers: [18] 18,73 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
[ 86, 52, 4, 96 ]
38
[ "86+52=138", "4+96=100", "138-100=38" ]
Current State: 38:[86, 52, 4, 96], Operations: [] Exploring Operation: 86+52=138, Resulting Numbers: [4, 96, 138] Generated Node #2: [4, 96, 138] from Operation: 86+52=138 Current State: 38:[4, 96, 138], Operations: ['86+52=138'] Exploring Operation: 4+96=100, Resulting Numbers: [138, 100] Generated Node #3: [138, 100] from Operation: 4+96=100 Current State: 38:[138, 100], Operations: ['86+52=138', '4+96=100'] Exploring Operation: 138-100=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[86, 52, 4, 96], Operations: [] Exploring Operation: 96/4=24, Resulting Numbers: [86, 52, 24] Generated Node #0,0: 38:[86, 52, 24] Operation: 96/4=24 Exploring Operation: 96-86=10, Resulting Numbers: [52, 4, 10] Generated Node #0,1: 38:[52, 4, 10] Operation: 96-86=10 Exploring Operation: 96-52=44, Resulting Numbers: [86, 4, 44] Generated Node #0,2: 38:[86, 4, 44] Operation: 96-52=44 Exploring Operation: 86-52=34, Resulting Numbers: [4, 96, 34] Generated Node #0,3: 38:[4, 96, 34] Operation: 86-52=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[52, 4, 10], Operations: ['96-86=10'] Exploring Operation: 4*10=40, Resulting Numbers: [52, 40] Generated Node #0,1,0: 38:[52, 40] Operation: 4*10=40 Exploring Operation: 52-10=42, Resulting Numbers: [4, 42] Generated Node #0,1,1: 38:[4, 42] Operation: 52-10=42 Exploring Operation: 52-4=48, Resulting Numbers: [10, 48] Generated Node #0,1,2: 38:[10, 48] Operation: 52-4=48 Exploring Operation: 52/4=13, Resulting Numbers: [10, 13] Generated Node #0,1,3: 38:[10, 13] Operation: 52/4=13 Moving to Node #0,1,1 Current State: 38:[4, 42], Operations: ['96-86=10', '52-10=42'] Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,38 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[86, 52, 4, 96], Operations: [] Exploring Operation: 96-86=10, Resulting Numbers: [52, 4, 10] Generated Node #0,1: 38:[52, 4, 10] Operation: 96-86=10 Moving to Node #0,1 Current State: 38:[52, 4, 10], Operations: ['96-86=10'] Exploring Operation: 52-10=42, Resulting Numbers: [4, 42] Generated Node #0,1,1: 38:[4, 42] Operation: 52-10=42 Moving to Node #0,1,1 Current State: 38:[4, 42], Operations: ['96-86=10', '52-10=42'] Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 3, 77, 6, 3 ]
80
[ "3+6=9", "9/3=3", "77+3=80" ]
Current State: 80:[3, 77, 6, 3], Operations: [] Exploring Operation: 3+6=9, Resulting Numbers: [77, 9] Generated Node #2: [77, 9] from Operation: 3+6=9 Current State: 80:[77, 9], Operations: ['3+6=9'] Exploring Operation: 9/3=3, Resulting Numbers: [77, 3] Generated Node #3: [77, 3] from Operation: 9/3=3 Current State: 80:[77, 3], Operations: ['3+6=9', '9/3=3'] Exploring Operation: 77+3=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[3, 77, 6, 3], Operations: [] Exploring Operation: 3+77=80, Resulting Numbers: [6, 3, 80] Generated Node #0,0: 80:[6, 3, 80] Operation: 3+77=80 Exploring Operation: 6/3=2, Resulting Numbers: [3, 77, 2] Generated Node #0,1: 80:[3, 77, 2] Operation: 6/3=2 Exploring Operation: 6/3=2, Resulting Numbers: [77, 3, 2] Generated Node #0,2: 80:[77, 3, 2] Operation: 6/3=2 Exploring Operation: 77+3=80, Resulting Numbers: [3, 6, 80] Generated Node #0,3: 80:[3, 6, 80] Operation: 77+3=80 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[6, 3, 80], Operations: ['3+77=80'] Exploring Operation: 6-3=3, Resulting Numbers: [80, 3] Generated Node #0,0,0: 80:[80, 3] Operation: 6-3=3 Exploring Operation: 6/3=2, Resulting Numbers: [80, 2] Generated Node #0,0,1: 80:[80, 2] Operation: 6/3=2 Exploring Operation: 6*3=18, Resulting Numbers: [80, 18] Generated Node #0,0,2: 80:[80, 18] Operation: 6*3=18 Exploring Operation: 6+3=9, Resulting Numbers: [80, 9] Generated Node #0,0,3: 80:[80, 9] Operation: 6+3=9 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 80:[80, 2], Operations: ['3+77=80', '6/3=2'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,80 unequal: No Solution Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,80 unequal: No Solution Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,80 unequal: No Solution No 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: 80:[80, 3], Operations: ['3+77=80', '6-3=3'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 80+3=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 80*3=240, Resulting Numbers: [240] 240,80 unequal: No Solution No 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: 80:[80, 9], Operations: ['3+77=80', '6+3=9'] Exploring Operation: 80+9=89, Resulting Numbers: [89] 89,80 unequal: No Solution Exploring Operation: 80*9=720, Resulting Numbers: [720] 720,80 unequal: No Solution Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,80 unequal: No Solution No 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: 80:[80, 18], Operations: ['3+77=80', '6*3=18'] Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 80*18=1440, Resulting Numbers: [1440] 1440,80 unequal: No Solution Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,80 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: 80:[3, 6, 80], Operations: ['77+3=80'] Exploring Operation: 6/3=2, Resulting Numbers: [80, 2] Generated Node #0,3,0: 80:[80, 2] Operation: 6/3=2 Exploring Operation: 6-3=3, Resulting Numbers: [80, 3] Generated Node #0,3,1: 80:[80, 3] Operation: 6-3=3 Exploring Operation: 3*6=18, Resulting Numbers: [80, 18] Generated Node #0,3,2: 80:[80, 18] Operation: 3*6=18 Exploring Operation: 3+6=9, Resulting Numbers: [80, 9] Generated Node #0,3,3: 80:[80, 9] Operation: 3+6=9 Moving to Node #0,3,0 Current State: 80:[80, 2], Operations: ['77+3=80', '6/3=2'] Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,80 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,80 unequal: No Solution Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,80 unequal: No Solution Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,80 unequal: No Solution Moving to Node #0,3,3 Current State: 80:[80, 9], Operations: ['77+3=80', '3+6=9'] Exploring Operation: 80*9=720, Resulting Numbers: [720] 720,80 unequal: No Solution Exploring Operation: 80+9=89, Resulting Numbers: [89] 89,80 unequal: No Solution Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[80, 3], Operations: ['77+3=80', '6-3=3'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 80+3=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 80*3=240, Resulting Numbers: [240] 240,80 unequal: No Solution Moving to Node #0,3,2 Current State: 80:[80, 18], Operations: ['77+3=80', '3*6=18'] Exploring Operation: 80*18=1440, Resulting Numbers: [1440] 1440,80 unequal: No Solution Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,80 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,80 unequal: No Solution No 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: 80:[3, 77, 2], Operations: ['6/3=2'] Exploring Operation: 3+77=80, Resulting Numbers: [2, 80] Generated Node #0,1,0: 80:[2, 80] Operation: 3+77=80 Exploring Operation: 3*2=6, Resulting Numbers: [77, 6] Generated Node #0,1,1: 80:[77, 6] Operation: 3*2=6 Exploring Operation: 3+2=5, Resulting Numbers: [77, 5] Generated Node #0,1,2: 80:[77, 5] Operation: 3+2=5 Exploring Operation: 77+2=79, Resulting Numbers: [3, 79] Generated Node #0,1,3: 80:[3, 79] Operation: 77+2=79 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 80:[2, 80], Operations: ['6/3=2', '3+77=80'] Exploring Operation: 2+80=82, Resulting Numbers: [82] 82,80 unequal: No Solution Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 2*80=160, Resulting Numbers: [160] 160,80 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,80 unequal: No Solution No 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: 80:[3, 79], Operations: ['6/3=2', '77+2=79'] Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,80 unequal: No Solution Exploring Operation: 3*79=237, Resulting Numbers: [237] 237,80 unequal: No Solution Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,80 unequal: No Solution No 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: 80:[77, 5], Operations: ['6/3=2', '3+2=5'] Exploring Operation: 77+5=82, Resulting Numbers: [82] 82,80 unequal: No Solution Exploring Operation: 77*5=385, Resulting Numbers: [385] 385,80 unequal: No Solution Exploring Operation: 77-5=72, Resulting Numbers: [72] 72,80 unequal: No Solution No 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: 80:[77, 6], Operations: ['6/3=2', '3*2=6'] Exploring Operation: 77-6=71, Resulting Numbers: [71] 71,80 unequal: No Solution Exploring Operation: 77*6=462, Resulting Numbers: [462] 462,80 unequal: No Solution Exploring Operation: 77+6=83, Resulting Numbers: [83] 83,80 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: 80:[77, 3, 2], Operations: ['6/3=2'] Exploring Operation: 77+3=80, Resulting Numbers: [2, 80] Generated Node #0,2,0: 80:[2, 80] Operation: 77+3=80 Exploring Operation: 3+2=5, Resulting Numbers: [77, 5] Generated Node #0,2,1: 80:[77, 5] Operation: 3+2=5 Exploring Operation: 3*2=6, Resulting Numbers: [77, 6] Generated Node #0,2,2: 80:[77, 6] Operation: 3*2=6 Exploring Operation: 77+2=79, Resulting Numbers: [3, 79] Generated Node #0,2,3: 80:[3, 79] Operation: 77+2=79 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 80:[2, 80], Operations: ['6/3=2', '77+3=80'] Exploring Operation: 2+80=82, Resulting Numbers: [82] 82,80 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,80 unequal: No Solution Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 2*80=160, Resulting Numbers: [160] 160,80 unequal: No Solution No 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: 80:[3, 79], Operations: ['6/3=2', '77+2=79'] Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,80 unequal: No Solution Exploring Operation: 3*79=237, Resulting Numbers: [237] 237,80 unequal: No Solution Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,80 unequal: No Solution No 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: 80:[77, 5], Operations: ['6/3=2', '3+2=5'] Exploring Operation: 77-5=72, Resulting Numbers: [72] 72,80 unequal: No Solution Exploring Operation: 77*5=385, Resulting Numbers: [385] 385,80 unequal: No Solution Exploring Operation: 77+5=82, Resulting Numbers: [82] 82,80 unequal: No Solution No 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: 80:[77, 6], Operations: ['6/3=2', '3*2=6'] Exploring Operation: 77-6=71, Resulting Numbers: [71] 71,80 unequal: No Solution Exploring Operation: 77+6=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 77*6=462, Resulting Numbers: [462] 462,80 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
[ 8, 55, 60, 43 ]
13
[ "55-43=12", "60/12=5", "8+5=13" ]
Current State: 13:[8, 55, 60, 43], Operations: [] Exploring Operation: 55-43=12, Resulting Numbers: [8, 60, 12] Generated Node #2: [8, 60, 12] from Operation: 55-43=12 Current State: 13:[8, 60, 12], Operations: ['55-43=12'] Exploring Operation: 60/12=5, Resulting Numbers: [8, 5] Generated Node #3: [8, 5] from Operation: 60/12=5 Current State: 13:[8, 5], Operations: ['55-43=12', '60/12=5'] Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[8, 55, 60, 43], Operations: [] Exploring Operation: 60-55=5, Resulting Numbers: [8, 43, 5] Generated Node #0,0: 13:[8, 43, 5] Operation: 60-55=5 Exploring Operation: 60-43=17, Resulting Numbers: [8, 55, 17] Generated Node #0,1: 13:[8, 55, 17] Operation: 60-43=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[8, 43, 5], Operations: ['60-55=5'] Exploring Operation: 8+5=13, Resulting Numbers: [43, 13] Generated Node #0,0,0: 13:[43, 13] Operation: 8+5=13 Exploring Operation: 43-8=35, Resulting Numbers: [5, 35] Generated Node #0,0,1: 13:[5, 35] Operation: 43-8=35 Moving to Node #0,0,0 Current State: 13:[43, 13], Operations: ['60-55=5', '8+5=13'] Exploring Operation: 43+13=56, Resulting Numbers: [56] 56,13 unequal: No Solution Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[5, 35], Operations: ['60-55=5', '43-8=35'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,13 unequal: No Solution No 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:[8, 55, 17], Operations: ['60-43=17'] Exploring Operation: 55-17=38, Resulting Numbers: [8, 38] Generated Node #0,1,0: 13:[8, 38] Operation: 55-17=38 Exploring Operation: 55-8=47, Resulting Numbers: [17, 47] Generated Node #0,1,1: 13:[17, 47] Operation: 55-8=47 Moving to Node #0,1,0 Current State: 13:[8, 38], Operations: ['60-43=17', '55-17=38'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 8+38=46, Resulting Numbers: [46] 46,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[17, 47], Operations: ['60-43=17', '55-8=47'] Exploring Operation: 17+47=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,13 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
[ 32, 26, 83, 74 ]
99
[ "32+26=58", "83+74=157", "157-58=99" ]
Current State: 99:[32, 26, 83, 74], Operations: [] Exploring Operation: 32+26=58, Resulting Numbers: [83, 74, 58] Generated Node #2: [83, 74, 58] from Operation: 32+26=58 Current State: 99:[83, 74, 58], Operations: ['32+26=58'] Exploring Operation: 83+74=157, Resulting Numbers: [58, 157] Generated Node #3: [58, 157] from Operation: 83+74=157 Current State: 99:[58, 157], Operations: ['32+26=58', '83+74=157'] Exploring Operation: 157-58=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[32, 26, 83, 74], Operations: [] Exploring Operation: 83-74=9, Resulting Numbers: [32, 26, 9] Generated Node #0,0: 99:[32, 26, 9] Operation: 83-74=9 Exploring Operation: 32+74=106, Resulting Numbers: [26, 83, 106] Generated Node #0,1: 99:[26, 83, 106] Operation: 32+74=106 Exploring Operation: 26+74=100, Resulting Numbers: [32, 83, 100] Generated Node #0,2: 99:[32, 83, 100] Operation: 26+74=100 Moving to Node #0,0 Current State: 99:[32, 26, 9], Operations: ['83-74=9'] Exploring Operation: 26+9=35, Resulting Numbers: [32, 35] Generated Node #0,0,0: 99:[32, 35] Operation: 26+9=35 Exploring Operation: 32-26=6, Resulting Numbers: [9, 6] Generated Node #0,0,1: 99:[9, 6] Operation: 32-26=6 Exploring Operation: 26-9=17, Resulting Numbers: [32, 17] Generated Node #0,0,2: 99:[32, 17] Operation: 26-9=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[32, 35], Operations: ['83-74=9', '26+9=35'] Exploring Operation: 32*35=1120, Resulting Numbers: [1120] 1120,99 unequal: No Solution Exploring Operation: 32+35=67, Resulting Numbers: [67] 67,99 unequal: No Solution Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[9, 6], Operations: ['83-74=9', '32-26=6'] Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 99:[32, 17], Operations: ['83-74=9', '26-9=17'] Exploring Operation: 32+17=49, Resulting Numbers: [49] 49,99 unequal: No Solution Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 32*17=544, Resulting Numbers: [544] 544,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 99:[32, 83, 100], Operations: ['26+74=100'] Exploring Operation: 100-83=17, Resulting Numbers: [32, 17] Generated Node #0,2,0: 99:[32, 17] Operation: 100-83=17 Exploring Operation: 83-32=51, Resulting Numbers: [100, 51] Generated Node #0,2,1: 99:[100, 51] Operation: 83-32=51 Exploring Operation: 32+83=115, Resulting Numbers: [100, 115] Generated Node #0,2,2: 99:[100, 115] Operation: 32+83=115 Moving to Node #0,1 Current State: 99:[26, 83, 106], Operations: ['32+74=106'] Exploring Operation: 106-83=23, Resulting Numbers: [26, 23] Generated Node #0,1,0: 99:[26, 23] Operation: 106-83=23 Exploring Operation: 26+83=109, Resulting Numbers: [106, 109] Generated Node #0,1,1: 99:[106, 109] Operation: 26+83=109 Exploring Operation: 83-26=57, Resulting Numbers: [106, 57] Generated Node #0,1,2: 99:[106, 57] Operation: 83-26=57 Moving to Node #0,2,0 Current State: 99:[32, 17], Operations: ['26+74=100', '100-83=17'] Exploring Operation: 32+17=49, Resulting Numbers: [49] 49,99 unequal: No Solution Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 32*17=544, Resulting Numbers: [544] 544,99 unequal: No Solution Moving to Node #0,2,2 Current State: 99:[100, 115], Operations: ['26+74=100', '32+83=115'] Exploring Operation: 100*115=11500, Resulting Numbers: [11500] 11500,99 unequal: No Solution Exploring Operation: 115-100=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 100+115=215, Resulting Numbers: [215] 215,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[106, 109], Operations: ['32+74=106', '26+83=109'] Exploring Operation: 109-106=3, Resulting Numbers: [3] 3,99 unequal: No Solution Exploring Operation: 106+109=215, Resulting Numbers: [215] 215,99 unequal: No Solution Exploring Operation: 106*109=11554, Resulting Numbers: [11554] 11554,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[26, 23], Operations: ['32+74=106', '106-83=23'] Exploring Operation: 26*23=598, Resulting Numbers: [598] 598,99 unequal: No Solution Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,99 unequal: No Solution Exploring Operation: 26+23=49, Resulting Numbers: [49] 49,99 unequal: No Solution Moving to Node #0,2,1 Current State: 99:[100, 51], Operations: ['26+74=100', '83-32=51'] Exploring Operation: 100*51=5100, Resulting Numbers: [5100] 5100,99 unequal: No Solution Exploring Operation: 100+51=151, Resulting Numbers: [151] 151,99 unequal: No Solution Exploring Operation: 100-51=49, Resulting Numbers: [49] 49,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[106, 57], Operations: ['32+74=106', '83-26=57'] Exploring Operation: 106*57=6042, Resulting Numbers: [6042] 6042,99 unequal: No Solution Exploring Operation: 106-57=49, Resulting Numbers: [49] 49,99 unequal: No Solution Exploring Operation: 106+57=163, Resulting Numbers: [163] 163,99 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 50, 22, 93, 84 ]
75
[ "50*93=4650", "84-22=62", "4650/62=75" ]
Current State: 75:[50, 22, 93, 84], Operations: [] Exploring Operation: 50*93=4650, Resulting Numbers: [22, 84, 4650] Generated Node #2: [22, 84, 4650] from Operation: 50*93=4650 Current State: 75:[22, 84, 4650], Operations: ['50*93=4650'] Exploring Operation: 84-22=62, Resulting Numbers: [4650, 62] Generated Node #3: [4650, 62] from Operation: 84-22=62 Current State: 75:[4650, 62], Operations: ['50*93=4650', '84-22=62'] Exploring Operation: 4650/62=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[50, 22, 93, 84], Operations: [] Exploring Operation: 93-84=9, Resulting Numbers: [50, 22, 9] Generated Node #0,0: 75:[50, 22, 9] Operation: 93-84=9 Exploring Operation: 50+22=72, Resulting Numbers: [93, 84, 72] Generated Node #0,1: 75:[93, 84, 72] Operation: 50+22=72 Exploring Operation: 50-22=28, Resulting Numbers: [93, 84, 28] Generated Node #0,2: 75:[93, 84, 28] Operation: 50-22=28 Exploring Operation: 93-50=43, Resulting Numbers: [22, 84, 43] Generated Node #0,3: 75:[22, 84, 43] Operation: 93-50=43 Exploring Operation: 84-50=34, Resulting Numbers: [22, 93, 34] Generated Node #0,4: 75:[22, 93, 34] Operation: 84-50=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[93, 84, 72], Operations: ['50+22=72'] Exploring Operation: 93-72=21, Resulting Numbers: [84, 21] Generated Node #0,1,0: 75:[84, 21] Operation: 93-72=21 Exploring Operation: 93+72=165, Resulting Numbers: [84, 165] Generated Node #0,1,1: 75:[84, 165] Operation: 93+72=165 Exploring Operation: 93-84=9, Resulting Numbers: [72, 9] Generated Node #0,1,2: 75:[72, 9] Operation: 93-84=9 Exploring Operation: 84+72=156, Resulting Numbers: [93, 156] Generated Node #0,1,3: 75:[93, 156] Operation: 84+72=156 Exploring Operation: 84-72=12, Resulting Numbers: [93, 12] Generated Node #0,1,4: 75:[93, 12] Operation: 84-72=12 Moving to Node #0,1,2 Current State: 75:[72, 9], Operations: ['50+22=72', '93-84=9'] Exploring Operation: 72/9=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 72*9=648, Resulting Numbers: [648] 648,75 unequal: No Solution Exploring Operation: 72+9=81, Resulting Numbers: [81] 81,75 unequal: No Solution Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[84, 21], Operations: ['50+22=72', '93-72=21'] Exploring Operation: 84-21=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 84+21=105, Resulting Numbers: [105] 105,75 unequal: No Solution Exploring Operation: 84*21=1764, Resulting Numbers: [1764] 1764,75 unequal: No Solution Exploring Operation: 84/21=4, Resulting Numbers: [4] 4,75 unequal: No Solution Moving to Node #0,1,4 Current State: 75:[93, 12], Operations: ['50+22=72', '84-72=12'] Exploring Operation: 93*12=1116, Resulting Numbers: [1116] 1116,75 unequal: No Solution Exploring Operation: 93-12=81, Resulting Numbers: [81] 81,75 unequal: No Solution Exploring Operation: 93+12=105, Resulting Numbers: [105] 105,75 unequal: No Solution Moving to Node #0,1,1 Current State: 75:[84, 165], Operations: ['50+22=72', '93+72=165'] Exploring Operation: 84+165=249, Resulting Numbers: [249] 249,75 unequal: No Solution Exploring Operation: 84*165=13860, Resulting Numbers: [13860] 13860,75 unequal: No Solution Exploring Operation: 165-84=81, Resulting Numbers: [81] 81,75 unequal: No Solution Moving to Node #0,1,3 Current State: 75:[93, 156], Operations: ['50+22=72', '84+72=156'] Exploring Operation: 93*156=14508, Resulting Numbers: [14508] 14508,75 unequal: No Solution Exploring Operation: 156-93=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 93+156=249, Resulting Numbers: [249] 249,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[93, 84, 28], Operations: ['50-22=28'] Exploring Operation: 93+28=121, Resulting Numbers: [84, 121] Generated Node #0,2,0: 75:[84, 121] Operation: 93+28=121 Exploring Operation: 84-28=56, Resulting Numbers: [93, 56] Generated Node #0,2,1: 75:[93, 56] Operation: 84-28=56 Exploring Operation: 84/28=3, Resulting Numbers: [93, 3] Generated Node #0,2,2: 75:[93, 3] Operation: 84/28=3 Exploring Operation: 93-28=65, Resulting Numbers: [84, 65] Generated Node #0,2,3: 75:[84, 65] Operation: 93-28=65 Exploring Operation: 93-84=9, Resulting Numbers: [28, 9] Generated Node #0,2,4: 75:[28, 9] Operation: 93-84=9 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 75:[28, 9], Operations: ['50-22=28', '93-84=9'] Exploring Operation: 28+9=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 28*9=252, Resulting Numbers: [252] 252,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 75:[93, 3], Operations: ['50-22=28', '84/28=3'] Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,75 unequal: No Solution Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,75 unequal: No Solution Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 93*3=279, Resulting Numbers: [279] 279,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 75:[84, 65], Operations: ['50-22=28', '93-28=65'] Exploring Operation: 84-65=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 84+65=149, Resulting Numbers: [149] 149,75 unequal: No Solution Exploring Operation: 84*65=5460, Resulting Numbers: [5460] 5460,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 75:[93, 56], Operations: ['50-22=28', '84-28=56'] Exploring Operation: 93*56=5208, Resulting Numbers: [5208] 5208,75 unequal: No Solution Exploring Operation: 93-56=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 93+56=149, Resulting Numbers: [149] 149,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 75:[84, 121], Operations: ['50-22=28', '93+28=121'] Exploring Operation: 121-84=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 84+121=205, Resulting Numbers: [205] 205,75 unequal: No Solution Exploring Operation: 84*121=10164, Resulting Numbers: [10164] 10164,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 75:[22, 84, 43], Operations: ['93-50=43'] Exploring Operation: 22+84=106, Resulting Numbers: [43, 106] Generated Node #0,3,0: 75:[43, 106] Operation: 22+84=106 Exploring Operation: 22+43=65, Resulting Numbers: [84, 65] Generated Node #0,3,1: 75:[84, 65] Operation: 22+43=65 Exploring Operation: 43-22=21, Resulting Numbers: [84, 21] Generated Node #0,3,2: 75:[84, 21] Operation: 43-22=21 Exploring Operation: 84-43=41, Resulting Numbers: [22, 41] Generated Node #0,3,3: 75:[22, 41] Operation: 84-43=41 Exploring Operation: 84-22=62, Resulting Numbers: [43, 62] Generated Node #0,3,4: 75:[43, 62] Operation: 84-22=62 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 75:[84, 21], Operations: ['93-50=43', '43-22=21'] Exploring Operation: 84-21=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 84*21=1764, Resulting Numbers: [1764] 1764,75 unequal: No Solution Exploring Operation: 84+21=105, Resulting Numbers: [105] 105,75 unequal: No Solution Exploring Operation: 84/21=4, Resulting Numbers: [4] 4,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 75:[84, 65], Operations: ['93-50=43', '22+43=65'] Exploring Operation: 84-65=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 84*65=5460, Resulting Numbers: [5460] 5460,75 unequal: No Solution Exploring Operation: 84+65=149, Resulting Numbers: [149] 149,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 75:[22, 41], Operations: ['93-50=43', '84-43=41'] Exploring Operation: 22*41=902, Resulting Numbers: [902] 902,75 unequal: No Solution Exploring Operation: 22+41=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 75:[43, 62], Operations: ['93-50=43', '84-22=62'] Exploring Operation: 43+62=105, Resulting Numbers: [105] 105,75 unequal: No Solution Exploring Operation: 62-43=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 43*62=2666, Resulting Numbers: [2666] 2666,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 75:[43, 106], Operations: ['93-50=43', '22+84=106'] Exploring Operation: 106-43=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 43+106=149, Resulting Numbers: [149] 149,75 unequal: No Solution Exploring Operation: 43*106=4558, Resulting Numbers: [4558] 4558,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 75:[22, 93, 34], Operations: ['84-50=34'] Exploring Operation: 93-22=71, Resulting Numbers: [34, 71] Generated Node #0,4,0: 75:[34, 71] Operation: 93-22=71 Exploring Operation: 93-34=59, Resulting Numbers: [22, 59] Generated Node #0,4,1: 75:[22, 59] Operation: 93-34=59 Exploring Operation: 22+93=115, Resulting Numbers: [34, 115] Generated Node #0,4,2: 75:[34, 115] Operation: 22+93=115 Exploring Operation: 22+34=56, Resulting Numbers: [93, 56] Generated Node #0,4,3: 75:[93, 56] Operation: 22+34=56 Exploring Operation: 34-22=12, Resulting Numbers: [93, 12] Generated Node #0,4,4: 75:[93, 12] Operation: 34-22=12 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 75:[34, 71], Operations: ['84-50=34', '93-22=71'] Exploring Operation: 34+71=105, Resulting Numbers: [105] 105,75 unequal: No Solution Exploring Operation: 34*71=2414, Resulting Numbers: [2414] 2414,75 unequal: No Solution Exploring Operation: 71-34=37, Resulting Numbers: [37] 37,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 75:[22, 59], Operations: ['84-50=34', '93-34=59'] Exploring Operation: 22*59=1298, Resulting Numbers: [1298] 1298,75 unequal: No Solution Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 22+59=81, Resulting Numbers: [81] 81,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 75:[93, 12], Operations: ['84-50=34', '34-22=12'] Exploring Operation: 93+12=105, Resulting Numbers: [105] 105,75 unequal: No Solution Exploring Operation: 93-12=81, Resulting Numbers: [81] 81,75 unequal: No Solution Exploring Operation: 93*12=1116, Resulting Numbers: [1116] 1116,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 75:[93, 56], Operations: ['84-50=34', '22+34=56'] Exploring Operation: 93*56=5208, Resulting Numbers: [5208] 5208,75 unequal: No Solution Exploring Operation: 93+56=149, Resulting Numbers: [149] 149,75 unequal: No Solution Exploring Operation: 93-56=37, Resulting Numbers: [37] 37,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 75:[34, 115], Operations: ['84-50=34', '22+93=115'] Exploring Operation: 34+115=149, Resulting Numbers: [149] 149,75 unequal: No Solution Exploring Operation: 115-34=81, Resulting Numbers: [81] 81,75 unequal: No Solution Exploring Operation: 34*115=3910, Resulting Numbers: [3910] 3910,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[50, 22, 9], Operations: ['93-84=9'] Exploring Operation: 50+22=72, Resulting Numbers: [9, 72] Generated Node #0,0,0: 75:[9, 72] Operation: 50+22=72 Exploring Operation: 50-9=41, Resulting Numbers: [22, 41] Generated Node #0,0,1: 75:[22, 41] Operation: 50-9=41 Exploring Operation: 50+9=59, Resulting Numbers: [22, 59] Generated Node #0,0,2: 75:[22, 59] Operation: 50+9=59 Exploring Operation: 22-9=13, Resulting Numbers: [50, 13] Generated Node #0,0,3: 75:[50, 13] Operation: 22-9=13 Exploring Operation: 50-22=28, Resulting Numbers: [9, 28] Generated Node #0,0,4: 75:[9, 28] Operation: 50-22=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[9, 72], Operations: ['93-84=9', '50+22=72'] Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 72/9=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 9*72=648, Resulting Numbers: [648] 648,75 unequal: No Solution Exploring Operation: 9+72=81, Resulting Numbers: [81] 81,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 75:[9, 28], Operations: ['93-84=9', '50-22=28'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 9*28=252, Resulting Numbers: [252] 252,75 unequal: No Solution Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 75:[22, 41], Operations: ['93-84=9', '50-9=41'] Exploring Operation: 22*41=902, Resulting Numbers: [902] 902,75 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 22+41=63, Resulting Numbers: [63] 63,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 75:[22, 59], Operations: ['93-84=9', '50+9=59'] Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 22+59=81, Resulting Numbers: [81] 81,75 unequal: No Solution Exploring Operation: 22*59=1298, Resulting Numbers: [1298] 1298,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 75:[50, 13], Operations: ['93-84=9', '22-9=13'] Exploring Operation: 50+13=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 50-13=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 50*13=650, Resulting Numbers: [650] 650,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 35, 53, 77, 2 ]
68
[ "53-35=18", "18/2=9", "77-9=68" ]
Current State: 68:[35, 53, 77, 2], Operations: [] Exploring Operation: 53-35=18, Resulting Numbers: [77, 2, 18] Generated Node #2: [77, 2, 18] from Operation: 53-35=18 Current State: 68:[77, 2, 18], Operations: ['53-35=18'] Exploring Operation: 18/2=9, Resulting Numbers: [77, 9] Generated Node #3: [77, 9] from Operation: 18/2=9 Current State: 68:[77, 9], Operations: ['53-35=18', '18/2=9'] Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[35, 53, 77, 2], Operations: [] Exploring Operation: 77-53=24, Resulting Numbers: [35, 2, 24] Generated Node #0,0: 68:[35, 2, 24] Operation: 77-53=24 Exploring Operation: 53-35=18, Resulting Numbers: [77, 2, 18] Generated Node #0,1: 68:[77, 2, 18] Operation: 53-35=18 Exploring Operation: 77-35=42, Resulting Numbers: [53, 2, 42] Generated Node #0,2: 68:[53, 2, 42] Operation: 77-35=42 Exploring Operation: 53+2=55, Resulting Numbers: [35, 77, 55] Generated Node #0,3: 68:[35, 77, 55] Operation: 53+2=55 Moving to Node #0,0 Current State: 68:[35, 2, 24], Operations: ['77-53=24'] Exploring Operation: 24-2=22, Resulting Numbers: [35, 22] Generated Node #0,0,0: 68:[35, 22] Operation: 24-2=22 Exploring Operation: 35-2=33, Resulting Numbers: [24, 33] Generated Node #0,0,1: 68:[24, 33] Operation: 35-2=33 Exploring Operation: 35-24=11, Resulting Numbers: [2, 11] Generated Node #0,0,2: 68:[2, 11] Operation: 35-24=11 Exploring Operation: 24/2=12, Resulting Numbers: [35, 12] Generated Node #0,0,3: 68:[35, 12] Operation: 24/2=12 Moving to Node #0,1 Current State: 68:[77, 2, 18], Operations: ['53-35=18'] Exploring Operation: 18-2=16, Resulting Numbers: [77, 16] Generated Node #0,1,0: 68:[77, 16] Operation: 18-2=16 Exploring Operation: 77-18=59, Resulting Numbers: [2, 59] Generated Node #0,1,1: 68:[2, 59] Operation: 77-18=59 Exploring Operation: 77-2=75, Resulting Numbers: [18, 75] Generated Node #0,1,2: 68:[18, 75] Operation: 77-2=75 Exploring Operation: 2*18=36, Resulting Numbers: [77, 36] Generated Node #0,1,3: 68:[77, 36] Operation: 2*18=36 Moving to Node #0,3 Current State: 68:[35, 77, 55], Operations: ['53+2=55'] Exploring Operation: 77-35=42, Resulting Numbers: [55, 42] Generated Node #0,3,0: 68:[55, 42] Operation: 77-35=42 Exploring Operation: 77-55=22, Resulting Numbers: [35, 22] Generated Node #0,3,1: 68:[35, 22] Operation: 77-55=22 Exploring Operation: 35+55=90, Resulting Numbers: [77, 90] Generated Node #0,3,2: 68:[77, 90] Operation: 35+55=90 Exploring Operation: 55-35=20, Resulting Numbers: [77, 20] Generated Node #0,3,3: 68:[77, 20] Operation: 55-35=20 Moving to Node #0,2 Current State: 68:[53, 2, 42], Operations: ['77-35=42'] Exploring Operation: 53+2=55, Resulting Numbers: [42, 55] Generated Node #0,2,0: 68:[42, 55] Operation: 53+2=55 Exploring Operation: 42/2=21, Resulting Numbers: [53, 21] Generated Node #0,2,1: 68:[53, 21] Operation: 42/2=21 Exploring Operation: 42-2=40, Resulting Numbers: [53, 40] Generated Node #0,2,2: 68:[53, 40] Operation: 42-2=40 Exploring Operation: 53-42=11, Resulting Numbers: [2, 11] Generated Node #0,2,3: 68:[2, 11] Operation: 53-42=11 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 68:[2, 11], Operations: ['77-35=42', '53-42=11'] Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,68 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 68:[53, 21], Operations: ['77-35=42', '42/2=21'] Exploring Operation: 53+21=74, Resulting Numbers: [74] 74,68 unequal: No Solution Exploring Operation: 53-21=32, Resulting Numbers: [32] 32,68 unequal: No Solution Exploring Operation: 53*21=1113, Resulting Numbers: [1113] 1113,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 68:[42, 55], Operations: ['77-35=42', '53+2=55'] Exploring Operation: 42*55=2310, Resulting Numbers: [2310] 2310,68 unequal: No Solution Exploring Operation: 42+55=97, Resulting Numbers: [97] 97,68 unequal: No Solution Exploring Operation: 55-42=13, Resulting Numbers: [13] 13,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 68:[53, 40], Operations: ['77-35=42', '42-2=40'] Exploring Operation: 53-40=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 53*40=2120, Resulting Numbers: [2120] 2120,68 unequal: No Solution Exploring Operation: 53+40=93, Resulting Numbers: [93] 93,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 68:[35, 22], Operations: ['77-53=24', '24-2=22'] Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 35*22=770, Resulting Numbers: [770] 770,68 unequal: No Solution Moving to Node #0,0,3 Current State: 68:[35, 12], Operations: ['77-53=24', '24/2=12'] Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,68 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,68 unequal: No Solution Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[2, 11], Operations: ['77-53=24', '35-24=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,68 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,68 unequal: No Solution Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,68 unequal: No Solution Moving to Node #0,3,1 Current State: 68:[35, 22], Operations: ['53+2=55', '77-55=22'] Exploring Operation: 35*22=770, Resulting Numbers: [770] 770,68 unequal: No Solution Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[18, 75], Operations: ['53-35=18', '77-2=75'] Exploring Operation: 75-18=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 18+75=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 18*75=1350, Resulting Numbers: [1350] 1350,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[24, 33], Operations: ['77-53=24', '35-2=33'] Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,68 unequal: No Solution Exploring Operation: 24*33=792, Resulting Numbers: [792] 792,68 unequal: No Solution Exploring Operation: 24+33=57, Resulting Numbers: [57] 57,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[2, 59], Operations: ['53-35=18', '77-18=59'] Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,68 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[77, 16], Operations: ['53-35=18', '18-2=16'] Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,68 unequal: No Solution Exploring Operation: 77*16=1232, Resulting Numbers: [1232] 1232,68 unequal: No Solution Exploring Operation: 77+16=93, Resulting Numbers: [93] 93,68 unequal: No Solution Moving to Node #0,1,3 Current State: 68:[77, 36], Operations: ['53-35=18', '2*18=36'] Exploring Operation: 77-36=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 77*36=2772, Resulting Numbers: [2772] 2772,68 unequal: No Solution Exploring Operation: 77+36=113, Resulting Numbers: [113] 113,68 unequal: No Solution Moving to Node #0,3,3 Current State: 68:[77, 20], Operations: ['53+2=55', '55-35=20'] Exploring Operation: 77+20=97, Resulting Numbers: [97] 97,68 unequal: No Solution Exploring Operation: 77*20=1540, Resulting Numbers: [1540] 1540,68 unequal: No Solution Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,68 unequal: No Solution Moving to Node #0,3,0 Current State: 68:[55, 42], Operations: ['53+2=55', '77-35=42'] Exploring Operation: 55*42=2310, Resulting Numbers: [2310] 2310,68 unequal: No Solution Exploring Operation: 55+42=97, Resulting Numbers: [97] 97,68 unequal: No Solution Exploring Operation: 55-42=13, Resulting Numbers: [13] 13,68 unequal: No Solution Moving to Node #0,3,2 Current State: 68:[77, 90], Operations: ['53+2=55', '35+55=90'] Exploring Operation: 77+90=167, Resulting Numbers: [167] 167,68 unequal: No Solution Exploring Operation: 90-77=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 77*90=6930, Resulting Numbers: [6930] 6930,68 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 8, 44, 31, 20 ]
47
[ "44-8=36", "31-20=11", "36+11=47" ]
Current State: 47:[8, 44, 31, 20], Operations: [] Exploring Operation: 44-8=36, Resulting Numbers: [31, 20, 36] Generated Node #2: [31, 20, 36] from Operation: 44-8=36 Current State: 47:[31, 20, 36], Operations: ['44-8=36'] Exploring Operation: 31-20=11, Resulting Numbers: [36, 11] Generated Node #3: [36, 11] from Operation: 31-20=11 Current State: 47:[36, 11], Operations: ['44-8=36', '31-20=11'] Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[8, 44, 31, 20], Operations: [] Exploring Operation: 8+31=39, Resulting Numbers: [44, 20, 39] Generated Node #0,0: 47:[44, 20, 39] Operation: 8+31=39 Exploring Operation: 8+20=28, Resulting Numbers: [44, 31, 28] Generated Node #0,1: 47:[44, 31, 28] Operation: 8+20=28 Moving to Node #0,0 Current State: 47:[44, 20, 39], Operations: ['8+31=39'] Exploring Operation: 44+20=64, Resulting Numbers: [39, 64] Generated Node #0,0,0: 47:[39, 64] Operation: 44+20=64 Exploring Operation: 20+39=59, Resulting Numbers: [44, 59] Generated Node #0,0,1: 47:[44, 59] Operation: 20+39=59 Moving to Node #0,1 Current State: 47:[44, 31, 28], Operations: ['8+20=28'] Exploring Operation: 31+28=59, Resulting Numbers: [44, 59] Generated Node #0,1,0: 47:[44, 59] Operation: 31+28=59 Exploring Operation: 44+28=72, Resulting Numbers: [31, 72] Generated Node #0,1,1: 47:[31, 72] Operation: 44+28=72 Moving to Node #0,0,1 Current State: 47:[44, 59], Operations: ['8+31=39', '20+39=59'] Exploring Operation: 59-44=15, Resulting Numbers: [15] 15,47 unequal: No Solution Exploring Operation: 44+59=103, Resulting Numbers: [103] 103,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[44, 59], Operations: ['8+20=28', '31+28=59'] Exploring Operation: 59-44=15, Resulting Numbers: [15] 15,47 unequal: No Solution Exploring Operation: 44+59=103, Resulting Numbers: [103] 103,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[39, 64], Operations: ['8+31=39', '44+20=64'] Exploring Operation: 64-39=25, Resulting Numbers: [25] 25,47 unequal: No Solution Exploring Operation: 39+64=103, Resulting Numbers: [103] 103,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[31, 72], Operations: ['8+20=28', '44+28=72'] Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 31+72=103, Resulting Numbers: [103] 103,47 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 51, 61, 25, 34 ]
19
[ "61-51=10", "34-25=9", "10+9=19" ]
Current State: 19:[51, 61, 25, 34], Operations: [] Exploring Operation: 61-51=10, Resulting Numbers: [25, 34, 10] Generated Node #2: [25, 34, 10] from Operation: 61-51=10 Current State: 19:[25, 34, 10], Operations: ['61-51=10'] Exploring Operation: 34-25=9, Resulting Numbers: [10, 9] Generated Node #3: [10, 9] from Operation: 34-25=9 Current State: 19:[10, 9], Operations: ['61-51=10', '34-25=9'] Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[51, 61, 25, 34], Operations: [] Exploring Operation: 61-51=10, Resulting Numbers: [25, 34, 10] Generated Node #0,0: 19:[25, 34, 10] Operation: 61-51=10 Exploring Operation: 61-34=27, Resulting Numbers: [51, 25, 27] Generated Node #0,1: 19:[51, 25, 27] Operation: 61-34=27 Exploring Operation: 61-25=36, Resulting Numbers: [51, 34, 36] Generated Node #0,2: 19:[51, 34, 36] Operation: 61-25=36 Exploring Operation: 51-25=26, Resulting Numbers: [61, 34, 26] Generated Node #0,3: 19:[61, 34, 26] Operation: 51-25=26 Exploring Operation: 51-34=17, Resulting Numbers: [61, 25, 17] Generated Node #0,4: 19:[61, 25, 17] Operation: 51-34=17 Moving to Node #0,0 Current State: 19:[25, 34, 10], Operations: ['61-51=10'] Exploring Operation: 34-25=9, Resulting Numbers: [10, 9] Generated Node #0,0,0: 19:[10, 9] Operation: 34-25=9 Exploring Operation: 34+10=44, Resulting Numbers: [25, 44] Generated Node #0,0,1: 19:[25, 44] Operation: 34+10=44 Exploring Operation: 25-10=15, Resulting Numbers: [34, 15] Generated Node #0,0,2: 19:[34, 15] Operation: 25-10=15 Exploring Operation: 34-10=24, Resulting Numbers: [25, 24] Generated Node #0,0,3: 19:[25, 24] Operation: 34-10=24 Exploring Operation: 25+10=35, Resulting Numbers: [34, 35] Generated Node #0,0,4: 19:[34, 35] Operation: 25+10=35 Moving to Node #0,1 Current State: 19:[51, 25, 27], Operations: ['61-34=27'] Exploring Operation: 51-25=26, Resulting Numbers: [27, 26] Generated Node #0,1,0: 19:[27, 26] Operation: 51-25=26 Exploring Operation: 51-27=24, Resulting Numbers: [25, 24] Generated Node #0,1,1: 19:[25, 24] Operation: 51-27=24 Exploring Operation: 27-25=2, Resulting Numbers: [51, 2] Generated Node #0,1,2: 19:[51, 2] Operation: 27-25=2 Exploring Operation: 51+27=78, Resulting Numbers: [25, 78] Generated Node #0,1,3: 19:[25, 78] Operation: 51+27=78 Exploring Operation: 51+25=76, Resulting Numbers: [27, 76] Generated Node #0,1,4: 19:[27, 76] Operation: 51+25=76 Moving to Node #0,4 Current State: 19:[61, 25, 17], Operations: ['51-34=17'] Exploring Operation: 61-25=36, Resulting Numbers: [17, 36] Generated Node #0,4,0: 19:[17, 36] Operation: 61-25=36 Exploring Operation: 61+17=78, Resulting Numbers: [25, 78] Generated Node #0,4,1: 19:[25, 78] Operation: 61+17=78 Exploring Operation: 25+17=42, Resulting Numbers: [61, 42] Generated Node #0,4,2: 19:[61, 42] Operation: 25+17=42 Exploring Operation: 25-17=8, Resulting Numbers: [61, 8] Generated Node #0,4,3: 19:[61, 8] Operation: 25-17=8 Exploring Operation: 61-17=44, Resulting Numbers: [25, 44] Generated Node #0,4,4: 19:[25, 44] Operation: 61-17=44 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 19:[17, 36], Operations: ['51-34=17', '61-25=36'] Exploring Operation: 17+36=53, Resulting Numbers: [53] 53,19 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[51, 61, 25, 34], Operations: [] Exploring Operation: 51-34=17, Resulting Numbers: [61, 25, 17] Generated Node #0,4: 19:[61, 25, 17] Operation: 51-34=17 Moving to Node #0,4 Current State: 19:[61, 25, 17], Operations: ['51-34=17'] Exploring Operation: 61-25=36, Resulting Numbers: [17, 36] Generated Node #0,4,0: 19:[17, 36] Operation: 61-25=36 Moving to Node #0,4,0 Current State: 19:[17, 36], Operations: ['51-34=17', '61-25=36'] Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
sum_heuristic
[ 56, 46, 19, 3 ]
21
[ "56+19=75", "75/3=25", "46-25=21" ]
Current State: 21:[56, 46, 19, 3], Operations: [] Exploring Operation: 56+19=75, Resulting Numbers: [46, 3, 75] Generated Node #2: [46, 3, 75] from Operation: 56+19=75 Current State: 21:[46, 3, 75], Operations: ['56+19=75'] Exploring Operation: 75/3=25, Resulting Numbers: [46, 25] Generated Node #3: [46, 25] from Operation: 75/3=25 Current State: 21:[46, 25], Operations: ['56+19=75', '75/3=25'] Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[56, 46, 19, 3], Operations: [] Exploring Operation: 56-19=37, Resulting Numbers: [46, 3, 37] Generated Node #0,0: 21:[46, 3, 37] Operation: 56-19=37 Exploring Operation: 56-46=10, Resulting Numbers: [19, 3, 10] Generated Node #0,1: 21:[19, 3, 10] Operation: 56-46=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[19, 3, 10], Operations: ['56-46=10'] Exploring Operation: 10-3=7, Resulting Numbers: [19, 7] Generated Node #0,1,0: 21:[19, 7] Operation: 10-3=7 Exploring Operation: 19-10=9, Resulting Numbers: [3, 9] Generated Node #0,1,1: 21:[3, 9] Operation: 19-10=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 21:[19, 7], Operations: ['56-46=10', '10-3=7'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,21 unequal: No Solution Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,21 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 #0,1,1 Current State: 21:[3, 9], Operations: ['56-46=10', '19-10=9'] Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,21 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: 21:[46, 3, 37], Operations: ['56-19=37'] Exploring Operation: 46-3=43, Resulting Numbers: [37, 43] Generated Node #0,0,0: 21:[37, 43] Operation: 46-3=43 Exploring Operation: 46-37=9, Resulting Numbers: [3, 9] Generated Node #0,0,1: 21:[3, 9] Operation: 46-37=9 Moving to Node #0,0,1 Current State: 21:[3, 9], Operations: ['56-19=37', '46-37=9'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[37, 43], Operations: ['56-19=37', '46-3=43'] Exploring Operation: 37+43=80, Resulting Numbers: [80] 80,21 unequal: No Solution Exploring Operation: 43-37=6, Resulting Numbers: [6] 6,21 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
[ 72, 42, 97, 69 ]
83
[ "72-69=3", "42/3=14", "97-14=83" ]
Current State: 83:[72, 42, 97, 69], Operations: [] Exploring Operation: 72-69=3, Resulting Numbers: [42, 97, 3] Generated Node #2: [42, 97, 3] from Operation: 72-69=3 Current State: 83:[42, 97, 3], Operations: ['72-69=3'] Exploring Operation: 42/3=14, Resulting Numbers: [97, 14] Generated Node #3: [97, 14] from Operation: 42/3=14 Current State: 83:[97, 14], Operations: ['72-69=3', '42/3=14'] Exploring Operation: 97-14=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[72, 42, 97, 69], Operations: [] Exploring Operation: 72-42=30, Resulting Numbers: [97, 69, 30] Generated Node #0,0: 83:[97, 69, 30] Operation: 72-42=30 Exploring Operation: 72+42=114, Resulting Numbers: [97, 69, 114] Generated Node #0,1: 83:[97, 69, 114] Operation: 72+42=114 Exploring Operation: 97-42=55, Resulting Numbers: [72, 69, 55] Generated Node #0,2: 83:[72, 69, 55] Operation: 97-42=55 Exploring Operation: 42+97=139, Resulting Numbers: [72, 69, 139] Generated Node #0,3: 83:[72, 69, 139] Operation: 42+97=139 Exploring Operation: 42+69=111, Resulting Numbers: [72, 97, 111] Generated Node #0,4: 83:[72, 97, 111] Operation: 42+69=111 Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[72, 69, 55], Operations: ['97-42=55'] Exploring Operation: 72+69=141, Resulting Numbers: [55, 141] Generated Node #0,2,0: 83:[55, 141] Operation: 72+69=141 Exploring Operation: 72-55=17, Resulting Numbers: [69, 17] Generated Node #0,2,1: 83:[69, 17] Operation: 72-55=17 Exploring Operation: 72+55=127, Resulting Numbers: [69, 127] Generated Node #0,2,2: 83:[69, 127] Operation: 72+55=127 Exploring Operation: 69+55=124, Resulting Numbers: [72, 124] Generated Node #0,2,3: 83:[72, 124] Operation: 69+55=124 Exploring Operation: 69-55=14, Resulting Numbers: [72, 14] Generated Node #0,2,4: 83:[72, 14] Operation: 69-55=14 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 83:[72, 124], Operations: ['97-42=55', '69+55=124'] Exploring Operation: 72*124=8928, Resulting Numbers: [8928] 8928,83 unequal: No Solution Exploring Operation: 124-72=52, Resulting Numbers: [52] 52,83 unequal: No Solution Exploring Operation: 72+124=196, Resulting Numbers: [196] 196,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 83:[69, 127], Operations: ['97-42=55', '72+55=127'] Exploring Operation: 69*127=8763, Resulting Numbers: [8763] 8763,83 unequal: No Solution Exploring Operation: 69+127=196, Resulting Numbers: [196] 196,83 unequal: No Solution Exploring Operation: 127-69=58, Resulting Numbers: [58] 58,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[69, 17], Operations: ['97-42=55', '72-55=17'] Exploring Operation: 69-17=52, Resulting Numbers: [52] 52,83 unequal: No Solution Exploring Operation: 69+17=86, Resulting Numbers: [86] 86,83 unequal: No Solution Exploring Operation: 69*17=1173, Resulting Numbers: [1173] 1173,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 83:[72, 14], Operations: ['97-42=55', '69-55=14'] Exploring Operation: 72+14=86, Resulting Numbers: [86] 86,83 unequal: No Solution Exploring Operation: 72*14=1008, Resulting Numbers: [1008] 1008,83 unequal: No Solution Exploring Operation: 72-14=58, Resulting Numbers: [58] 58,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[55, 141], Operations: ['97-42=55', '72+69=141'] Exploring Operation: 141-55=86, Resulting Numbers: [86] 86,83 unequal: No Solution Exploring Operation: 55*141=7755, Resulting Numbers: [7755] 7755,83 unequal: No Solution Exploring Operation: 55+141=196, Resulting Numbers: [196] 196,83 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: 83:[72, 97, 111], Operations: ['42+69=111'] Exploring Operation: 97-72=25, Resulting Numbers: [111, 25] Generated Node #0,4,0: 83:[111, 25] Operation: 97-72=25 Exploring Operation: 72+111=183, Resulting Numbers: [97, 183] Generated Node #0,4,1: 83:[97, 183] Operation: 72+111=183 Exploring Operation: 111-97=14, Resulting Numbers: [72, 14] Generated Node #0,4,2: 83:[72, 14] Operation: 111-97=14 Exploring Operation: 111-72=39, Resulting Numbers: [97, 39] Generated Node #0,4,3: 83:[97, 39] Operation: 111-72=39 Exploring Operation: 72+97=169, Resulting Numbers: [111, 169] Generated Node #0,4,4: 83:[111, 169] Operation: 72+97=169 Moving to Node #0,4,3 Current State: 83:[97, 39], Operations: ['42+69=111', '111-72=39'] Exploring Operation: 97-39=58, Resulting Numbers: [58] 58,83 unequal: No Solution Exploring Operation: 97*39=3783, Resulting Numbers: [3783] 3783,83 unequal: No Solution Exploring Operation: 97+39=136, Resulting Numbers: [136] 136,83 unequal: No Solution Moving to Node #0,4,2 Current State: 83:[72, 14], Operations: ['42+69=111', '111-97=14'] Exploring Operation: 72*14=1008, Resulting Numbers: [1008] 1008,83 unequal: No Solution Exploring Operation: 72-14=58, Resulting Numbers: [58] 58,83 unequal: No Solution Exploring Operation: 72+14=86, Resulting Numbers: [86] 86,83 unequal: No Solution Moving to Node #0,4,0 Current State: 83:[111, 25], Operations: ['42+69=111', '97-72=25'] Exploring Operation: 111+25=136, Resulting Numbers: [136] 136,83 unequal: No Solution Exploring Operation: 111-25=86, Resulting Numbers: [86] 86,83 unequal: No Solution Exploring Operation: 111*25=2775, Resulting Numbers: [2775] 2775,83 unequal: No Solution Moving to Node #0,4,1 Current State: 83:[97, 183], Operations: ['42+69=111', '72+111=183'] Exploring Operation: 97*183=17751, Resulting Numbers: [17751] 17751,83 unequal: No Solution Exploring Operation: 183-97=86, Resulting Numbers: [86] 86,83 unequal: No Solution Exploring Operation: 97+183=280, Resulting Numbers: [280] 280,83 unequal: No Solution Moving to Node #0,4,4 Current State: 83:[111, 169], Operations: ['42+69=111', '72+97=169'] Exploring Operation: 111+169=280, Resulting Numbers: [280] 280,83 unequal: No Solution Exploring Operation: 111*169=18759, Resulting Numbers: [18759] 18759,83 unequal: No Solution Exploring Operation: 169-111=58, Resulting Numbers: [58] 58,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[97, 69, 114], Operations: ['72+42=114'] Exploring Operation: 97-69=28, Resulting Numbers: [114, 28] Generated Node #0,1,0: 83:[114, 28] Operation: 97-69=28 Exploring Operation: 114-97=17, Resulting Numbers: [69, 17] Generated Node #0,1,1: 83:[69, 17] Operation: 114-97=17 Exploring Operation: 114-69=45, Resulting Numbers: [97, 45] Generated Node #0,1,2: 83:[97, 45] Operation: 114-69=45 Exploring Operation: 97+69=166, Resulting Numbers: [114, 166] Generated Node #0,1,3: 83:[114, 166] Operation: 97+69=166 Exploring Operation: 69+114=183, Resulting Numbers: [97, 183] Generated Node #0,1,4: 83:[97, 183] Operation: 69+114=183 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 83:[97, 45], Operations: ['72+42=114', '114-69=45'] Exploring Operation: 97+45=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 97*45=4365, Resulting Numbers: [4365] 4365,83 unequal: No Solution Exploring Operation: 97-45=52, Resulting Numbers: [52] 52,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[69, 17], Operations: ['72+42=114', '114-97=17'] Exploring Operation: 69*17=1173, Resulting Numbers: [1173] 1173,83 unequal: No Solution Exploring Operation: 69+17=86, Resulting Numbers: [86] 86,83 unequal: No Solution Exploring Operation: 69-17=52, Resulting Numbers: [52] 52,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[114, 28], Operations: ['72+42=114', '97-69=28'] Exploring Operation: 114*28=3192, Resulting Numbers: [3192] 3192,83 unequal: No Solution Exploring Operation: 114-28=86, Resulting Numbers: [86] 86,83 unequal: No Solution Exploring Operation: 114+28=142, Resulting Numbers: [142] 142,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 83:[114, 166], Operations: ['72+42=114', '97+69=166'] Exploring Operation: 166-114=52, Resulting Numbers: [52] 52,83 unequal: No Solution Exploring Operation: 114*166=18924, Resulting Numbers: [18924] 18924,83 unequal: No Solution Exploring Operation: 114+166=280, Resulting Numbers: [280] 280,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 83:[97, 183], Operations: ['72+42=114', '69+114=183'] Exploring Operation: 97*183=17751, Resulting Numbers: [17751] 17751,83 unequal: No Solution Exploring Operation: 183-97=86, Resulting Numbers: [86] 86,83 unequal: No Solution Exploring Operation: 97+183=280, Resulting Numbers: [280] 280,83 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: 83:[97, 69, 30], Operations: ['72-42=30'] Exploring Operation: 97-69=28, Resulting Numbers: [30, 28] Generated Node #0,0,0: 83:[30, 28] Operation: 97-69=28 Exploring Operation: 69+30=99, Resulting Numbers: [97, 99] Generated Node #0,0,1: 83:[97, 99] Operation: 69+30=99 Exploring Operation: 97-30=67, Resulting Numbers: [69, 67] Generated Node #0,0,2: 83:[69, 67] Operation: 97-30=67 Exploring Operation: 69-30=39, Resulting Numbers: [97, 39] Generated Node #0,0,3: 83:[97, 39] Operation: 69-30=39 Exploring Operation: 97+30=127, Resulting Numbers: [69, 127] Generated Node #0,0,4: 83:[69, 127] Operation: 97+30=127 Moving to Node #0,0,1 Current State: 83:[97, 99], Operations: ['72-42=30', '69+30=99'] Exploring Operation: 99-97=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 97+99=196, Resulting Numbers: [196] 196,83 unequal: No Solution Exploring Operation: 97*99=9603, Resulting Numbers: [9603] 9603,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[69, 67], Operations: ['72-42=30', '97-30=67'] Exploring Operation: 69-67=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 69*67=4623, Resulting Numbers: [4623] 4623,83 unequal: No Solution Exploring Operation: 69+67=136, Resulting Numbers: [136] 136,83 unequal: No Solution Moving to Node #0,0,3 Current State: 83:[97, 39], Operations: ['72-42=30', '69-30=39'] Exploring Operation: 97*39=3783, Resulting Numbers: [3783] 3783,83 unequal: No Solution Exploring Operation: 97-39=58, Resulting Numbers: [58] 58,83 unequal: No Solution Exploring Operation: 97+39=136, Resulting Numbers: [136] 136,83 unequal: No Solution Moving to Node #0,0,4 Current State: 83:[69, 127], Operations: ['72-42=30', '97+30=127'] Exploring Operation: 69+127=196, Resulting Numbers: [196] 196,83 unequal: No Solution Exploring Operation: 127-69=58, Resulting Numbers: [58] 58,83 unequal: No Solution Exploring Operation: 69*127=8763, Resulting Numbers: [8763] 8763,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[30, 28], Operations: ['72-42=30', '97-69=28'] Exploring Operation: 30*28=840, Resulting Numbers: [840] 840,83 unequal: No Solution Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,83 unequal: No Solution Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,83 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 Current State: 83:[72, 69, 139], Operations: ['42+97=139'] Exploring Operation: 72+69=141, Resulting Numbers: [139, 141] Generated Node #0,3,0: 83:[139, 141] Operation: 72+69=141 Exploring Operation: 139-72=67, Resulting Numbers: [69, 67] Generated Node #0,3,1: 83:[69, 67] Operation: 139-72=67 Exploring Operation: 139-69=70, Resulting Numbers: [72, 70] Generated Node #0,3,2: 83:[72, 70] Operation: 139-69=70 Exploring Operation: 69+139=208, Resulting Numbers: [72, 208] Generated Node #0,3,3: 83:[72, 208] Operation: 69+139=208 Exploring Operation: 72-69=3, Resulting Numbers: [139, 3] Generated Node #0,3,4: 83:[139, 3] Operation: 72-69=3 Moving to Node #0,3,2 Current State: 83:[72, 70], Operations: ['42+97=139', '139-69=70'] Exploring Operation: 72-70=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 72+70=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 72*70=5040, Resulting Numbers: [5040] 5040,83 unequal: No Solution Moving to Node #0,3,1 Current State: 83:[69, 67], Operations: ['42+97=139', '139-72=67'] Exploring Operation: 69-67=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 69*67=4623, Resulting Numbers: [4623] 4623,83 unequal: No Solution Exploring Operation: 69+67=136, Resulting Numbers: [136] 136,83 unequal: No Solution Moving to Node #0,3,0 Current State: 83:[139, 141], Operations: ['42+97=139', '72+69=141'] Exploring Operation: 139*141=19599, Resulting Numbers: [19599] 19599,83 unequal: No Solution Exploring Operation: 141-139=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 139+141=280, Resulting Numbers: [280] 280,83 unequal: No Solution Moving to Node #0,3,3 Current State: 83:[72, 208], Operations: ['42+97=139', '69+139=208'] Exploring Operation: 72*208=14976, Resulting Numbers: [14976] 14976,83 unequal: No Solution Exploring Operation: 208-72=136, Resulting Numbers: [136] 136,83 unequal: No Solution Exploring Operation: 72+208=280, Resulting Numbers: [280] 280,83 unequal: No Solution Moving to Node #0,3,4 Current State: 83:[139, 3], Operations: ['42+97=139', '72-69=3'] Exploring Operation: 139+3=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 139*3=417, Resulting Numbers: [417] 417,83 unequal: No Solution Exploring Operation: 139-3=136, Resulting Numbers: [136] 136,83 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
[ 77, 72, 61, 22 ]
99
[ "77-61=16", "72*22=1584", "1584/16=99" ]
Current State: 99:[77, 72, 61, 22], Operations: [] Exploring Operation: 77-61=16, Resulting Numbers: [72, 22, 16] Generated Node #2: [72, 22, 16] from Operation: 77-61=16 Current State: 99:[72, 22, 16], Operations: ['77-61=16'] Exploring Operation: 72*22=1584, Resulting Numbers: [16, 1584] Generated Node #3: [16, 1584] from Operation: 72*22=1584 Current State: 99:[16, 1584], Operations: ['77-61=16', '72*22=1584'] Exploring Operation: 1584/16=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[77, 72, 61, 22], Operations: [] Exploring Operation: 72-61=11, Resulting Numbers: [77, 22, 11] Generated Node #0,0: 99:[77, 22, 11] Operation: 72-61=11 Exploring Operation: 77-72=5, Resulting Numbers: [61, 22, 5] Generated Node #0,1: 99:[61, 22, 5] Operation: 77-72=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[77, 22, 11], Operations: ['72-61=11'] Exploring Operation: 77+22=99, Resulting Numbers: [11, 99] Generated Node #0,0,0: 99:[11, 99] Operation: 77+22=99 Exploring Operation: 77/11=7, Resulting Numbers: [22, 7] Generated Node #0,0,1: 99:[22, 7] Operation: 77/11=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[11, 99], Operations: ['72-61=11', '77+22=99'] Exploring Operation: 11+99=110, Resulting Numbers: [110] 110,99 unequal: No Solution Exploring Operation: 99/11=9, Resulting Numbers: [9] 9,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 99:[22, 7], Operations: ['72-61=11', '77/11=7'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 22+7=29, Resulting Numbers: [29] 29,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[61, 22, 5], Operations: ['77-72=5'] Exploring Operation: 61+22=83, Resulting Numbers: [5, 83] Generated Node #0,1,0: 99:[5, 83] Operation: 61+22=83 Exploring Operation: 61-22=39, Resulting Numbers: [5, 39] Generated Node #0,1,1: 99:[5, 39] Operation: 61-22=39 Moving to Node #0,1,1 Current State: 99:[5, 39], Operations: ['77-72=5', '61-22=39'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[5, 83], Operations: ['77-72=5', '61+22=83'] Exploring Operation: 5+83=88, Resulting Numbers: [88] 88,99 unequal: No Solution Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,99 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
[ 76, 47, 29, 11 ]
44
[ "76+11=87", "87/29=3", "47-3=44" ]
Current State: 44:[76, 47, 29, 11], Operations: [] Exploring Operation: 76+11=87, Resulting Numbers: [47, 29, 87] Generated Node #2: [47, 29, 87] from Operation: 76+11=87 Current State: 44:[47, 29, 87], Operations: ['76+11=87'] Exploring Operation: 87/29=3, Resulting Numbers: [47, 3] Generated Node #3: [47, 3] from Operation: 87/29=3 Current State: 44:[47, 3], Operations: ['76+11=87', '87/29=3'] Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[76, 47, 29, 11], Operations: [] Exploring Operation: 76-47=29, Resulting Numbers: [29, 11, 29] Generated Node #0,0: 44:[29, 11, 29] Operation: 76-47=29 Exploring Operation: 47-29=18, Resulting Numbers: [76, 11, 18] Generated Node #0,1: 44:[76, 11, 18] Operation: 47-29=18 Exploring Operation: 76-11=65, Resulting Numbers: [47, 29, 65] Generated Node #0,2: 44:[47, 29, 65] Operation: 76-11=65 Exploring Operation: 76-29=47, Resulting Numbers: [47, 11, 47] Generated Node #0,3: 44:[47, 11, 47] Operation: 76-29=47 Moving to Node #0,3 Current State: 44:[47, 11, 47], Operations: ['76-29=47'] Exploring Operation: 47-11=36, Resulting Numbers: [47, 36] Generated Node #0,3,0: 44:[47, 36] Operation: 47-11=36 Exploring Operation: 47-11=36, Resulting Numbers: [47, 36] Generated Node #0,3,1: 44:[47, 36] Operation: 47-11=36 Exploring Operation: 47-47=0, Resulting Numbers: [11, 0] Generated Node #0,3,2: 44:[11, 0] Operation: 47-47=0 Exploring Operation: 47/47=1, Resulting Numbers: [11, 1] Generated Node #0,3,3: 44:[11, 1] Operation: 47/47=1 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 44:[11, 1], Operations: ['76-29=47', '47/47=1'] Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 44:[11, 0], Operations: ['76-29=47', '47-47=0'] Exploring Operation: 11+0=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 11-0=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 11*0=0, Resulting Numbers: [0] 0,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 44:[47, 36], Operations: ['76-29=47', '47-11=36'] Exploring Operation: 47+36=83, Resulting Numbers: [83] 83,44 unequal: No Solution Exploring Operation: 47-36=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 47*36=1692, Resulting Numbers: [1692] 1692,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 44:[47, 36], Operations: ['76-29=47', '47-11=36'] Exploring Operation: 47-36=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 47*36=1692, Resulting Numbers: [1692] 1692,44 unequal: No Solution Exploring Operation: 47+36=83, Resulting Numbers: [83] 83,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 44:[29, 11, 29], Operations: ['76-47=29'] Exploring Operation: 29/29=1, Resulting Numbers: [11, 1] Generated Node #0,0,0: 44:[11, 1] Operation: 29/29=1 Exploring Operation: 29+11=40, Resulting Numbers: [29, 40] Generated Node #0,0,1: 44:[29, 40] Operation: 29+11=40 Exploring Operation: 29-29=0, Resulting Numbers: [11, 0] Generated Node #0,0,2: 44:[11, 0] Operation: 29-29=0 Exploring Operation: 29-11=18, Resulting Numbers: [29, 18] Generated Node #0,0,3: 44:[29, 18] Operation: 29-11=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[11, 1], Operations: ['76-47=29', '29/29=1'] Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 44:[11, 0], Operations: ['76-47=29', '29-29=0'] Exploring Operation: 11+0=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 11*0=0, Resulting Numbers: [0] 0,44 unequal: No Solution Exploring Operation: 11-0=11, Resulting Numbers: [11] 11,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 44:[29, 40], Operations: ['76-47=29', '29+11=40'] Exploring Operation: 29*40=1160, Resulting Numbers: [1160] 1160,44 unequal: No Solution Exploring Operation: 29+40=69, Resulting Numbers: [69] 69,44 unequal: No Solution Exploring Operation: 40-29=11, Resulting Numbers: [11] 11,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 44:[29, 18], Operations: ['76-47=29', '29-11=18'] Exploring Operation: 29*18=522, Resulting Numbers: [522] 522,44 unequal: No Solution Exploring Operation: 29+18=47, Resulting Numbers: [47] 47,44 unequal: No Solution Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 44:[47, 29, 65], Operations: ['76-11=65'] Exploring Operation: 65-47=18, Resulting Numbers: [29, 18] Generated Node #0,2,0: 44:[29, 18] Operation: 65-47=18 Exploring Operation: 65-29=36, Resulting Numbers: [47, 36] Generated Node #0,2,1: 44:[47, 36] Operation: 65-29=36 Exploring Operation: 47+29=76, Resulting Numbers: [65, 76] Generated Node #0,2,2: 44:[65, 76] Operation: 47+29=76 Exploring Operation: 47-29=18, Resulting Numbers: [65, 18] Generated Node #0,2,3: 44:[65, 18] Operation: 47-29=18 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 44:[29, 18], Operations: ['76-11=65', '65-47=18'] Exploring Operation: 29*18=522, Resulting Numbers: [522] 522,44 unequal: No Solution Exploring Operation: 29+18=47, Resulting Numbers: [47] 47,44 unequal: No Solution Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 44:[47, 36], Operations: ['76-11=65', '65-29=36'] Exploring Operation: 47-36=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 47+36=83, Resulting Numbers: [83] 83,44 unequal: No Solution Exploring Operation: 47*36=1692, Resulting Numbers: [1692] 1692,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 44:[65, 18], Operations: ['76-11=65', '47-29=18'] Exploring Operation: 65-18=47, Resulting Numbers: [47] 47,44 unequal: No Solution Exploring Operation: 65*18=1170, Resulting Numbers: [1170] 1170,44 unequal: No Solution Exploring Operation: 65+18=83, Resulting Numbers: [83] 83,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 44:[65, 76], Operations: ['76-11=65', '47+29=76'] Exploring Operation: 65+76=141, Resulting Numbers: [141] 141,44 unequal: No Solution Exploring Operation: 65*76=4940, Resulting Numbers: [4940] 4940,44 unequal: No Solution Exploring Operation: 76-65=11, Resulting Numbers: [11] 11,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 44:[76, 11, 18], Operations: ['47-29=18'] Exploring Operation: 76-18=58, Resulting Numbers: [11, 58] Generated Node #0,1,0: 44:[11, 58] Operation: 76-18=58 Exploring Operation: 11+18=29, Resulting Numbers: [76, 29] Generated Node #0,1,1: 44:[76, 29] Operation: 11+18=29 Exploring Operation: 18-11=7, Resulting Numbers: [76, 7] Generated Node #0,1,2: 44:[76, 7] Operation: 18-11=7 Exploring Operation: 76-11=65, Resulting Numbers: [18, 65] Generated Node #0,1,3: 44:[18, 65] Operation: 76-11=65 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 44:[11, 58], Operations: ['47-29=18', '76-18=58'] Exploring Operation: 11+58=69, Resulting Numbers: [69] 69,44 unequal: No Solution Exploring Operation: 11*58=638, Resulting Numbers: [638] 638,44 unequal: No Solution Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 44:[18, 65], Operations: ['47-29=18', '76-11=65'] Exploring Operation: 18+65=83, Resulting Numbers: [83] 83,44 unequal: No Solution Exploring Operation: 18*65=1170, Resulting Numbers: [1170] 1170,44 unequal: No Solution Exploring Operation: 65-18=47, Resulting Numbers: [47] 47,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 44:[76, 7], Operations: ['47-29=18', '18-11=7'] Exploring Operation: 76+7=83, Resulting Numbers: [83] 83,44 unequal: No Solution Exploring Operation: 76*7=532, Resulting Numbers: [532] 532,44 unequal: No Solution Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 44:[76, 29], Operations: ['47-29=18', '11+18=29'] Exploring Operation: 76*29=2204, Resulting Numbers: [2204] 2204,44 unequal: No Solution Exploring Operation: 76-29=47, Resulting Numbers: [47] 47,44 unequal: No Solution Exploring Operation: 76+29=105, Resulting Numbers: [105] 105,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 98, 80, 99, 6 ]
85
[ "98+80=178", "99-6=93", "178-93=85" ]
Current State: 85:[98, 80, 99, 6], Operations: [] Exploring Operation: 98+80=178, Resulting Numbers: [99, 6, 178] Generated Node #2: [99, 6, 178] from Operation: 98+80=178 Current State: 85:[99, 6, 178], Operations: ['98+80=178'] Exploring Operation: 99-6=93, Resulting Numbers: [178, 93] Generated Node #3: [178, 93] from Operation: 99-6=93 Current State: 85:[178, 93], Operations: ['98+80=178', '99-6=93'] Exploring Operation: 178-93=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[98, 80, 99, 6], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [80, 6, 1] Generated Node #0,0: 85:[80, 6, 1] Operation: 99-98=1 Exploring Operation: 98-6=92, Resulting Numbers: [80, 99, 92] Generated Node #0,1: 85:[80, 99, 92] Operation: 98-6=92 Exploring Operation: 99-80=19, Resulting Numbers: [98, 6, 19] Generated Node #0,2: 85:[98, 6, 19] Operation: 99-80=19 Exploring Operation: 98-80=18, Resulting Numbers: [99, 6, 18] Generated Node #0,3: 85:[99, 6, 18] Operation: 98-80=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[80, 6, 1], Operations: ['99-98=1'] Exploring Operation: 80*1=80, Resulting Numbers: [6, 80] Generated Node #0,0,0: 85:[6, 80] Operation: 80*1=80 Exploring Operation: 80+6=86, Resulting Numbers: [1, 86] Generated Node #0,0,1: 85:[1, 86] Operation: 80+6=86 Exploring Operation: 80+1=81, Resulting Numbers: [6, 81] Generated Node #0,0,2: 85:[6, 81] Operation: 80+1=81 Exploring Operation: 6-1=5, Resulting Numbers: [80, 5] Generated Node #0,0,3: 85:[80, 5] Operation: 6-1=5 Moving to Node #0,0,1 Current State: 85:[1, 86], Operations: ['99-98=1', '80+6=86'] Exploring Operation: 1+86=87, Resulting Numbers: [87] 87,85 unequal: No Solution Exploring Operation: 86-1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[98, 80, 99, 6], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [80, 6, 1] Generated Node #0,0: 85:[80, 6, 1] Operation: 99-98=1 Moving to Node #0,0 Current State: 85:[80, 6, 1], Operations: ['99-98=1'] Exploring Operation: 80+6=86, Resulting Numbers: [1, 86] Generated Node #0,0,1: 85:[1, 86] Operation: 80+6=86 Moving to Node #0,0,1 Current State: 85:[1, 86], Operations: ['99-98=1', '80+6=86'] Exploring Operation: 86-1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 97, 39, 8, 27 ]
93
[ "97-39=58", "8+27=35", "58+35=93" ]
Current State: 93:[97, 39, 8, 27], Operations: [] Exploring Operation: 97-39=58, Resulting Numbers: [8, 27, 58] Generated Node #2: [8, 27, 58] from Operation: 97-39=58 Current State: 93:[8, 27, 58], Operations: ['97-39=58'] Exploring Operation: 8+27=35, Resulting Numbers: [58, 35] Generated Node #3: [58, 35] from Operation: 8+27=35 Current State: 93:[58, 35], Operations: ['97-39=58', '8+27=35'] Exploring Operation: 58+35=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[97, 39, 8, 27], Operations: [] Exploring Operation: 39-8=31, Resulting Numbers: [97, 27, 31] Generated Node #0,0: 93:[97, 27, 31] Operation: 39-8=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[97, 27, 31], Operations: ['39-8=31'] Exploring Operation: 31-27=4, Resulting Numbers: [97, 4] Generated Node #0,0,0: 93:[97, 4] Operation: 31-27=4 Moving to Node #0,0,0 Current State: 93:[97, 4], Operations: ['39-8=31', '31-27=4'] Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[97, 39, 8, 27], Operations: [] Exploring Operation: 39-8=31, Resulting Numbers: [97, 27, 31] Generated Node #0,0: 93:[97, 27, 31] Operation: 39-8=31 Moving to Node #0,0 Current State: 93:[97, 27, 31], Operations: ['39-8=31'] Exploring Operation: 31-27=4, Resulting Numbers: [97, 4] Generated Node #0,0,0: 93:[97, 4] Operation: 31-27=4 Moving to Node #0,0,0 Current State: 93:[97, 4], Operations: ['39-8=31', '31-27=4'] Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 4, 84, 21, 73 ]
57
[ "4*84=336", "336/21=16", "73-16=57" ]
Current State: 57:[4, 84, 21, 73], Operations: [] Exploring Operation: 4*84=336, Resulting Numbers: [21, 73, 336] Generated Node #2: [21, 73, 336] from Operation: 4*84=336 Current State: 57:[21, 73, 336], Operations: ['4*84=336'] Exploring Operation: 336/21=16, Resulting Numbers: [73, 16] Generated Node #3: [73, 16] from Operation: 336/21=16 Current State: 57:[73, 16], Operations: ['4*84=336', '336/21=16'] Exploring Operation: 73-16=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[4, 84, 21, 73], Operations: [] Exploring Operation: 84/21=4, Resulting Numbers: [4, 73, 4] Generated Node #0,0: 57:[4, 73, 4] Operation: 84/21=4 Exploring Operation: 84-73=11, Resulting Numbers: [4, 21, 11] Generated Node #0,1: 57:[4, 21, 11] Operation: 84-73=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[4, 21, 11], Operations: ['84-73=11'] Exploring Operation: 11-4=7, Resulting Numbers: [21, 7] Generated Node #0,1,0: 57:[21, 7] Operation: 11-4=7 Exploring Operation: 4+11=15, Resulting Numbers: [21, 15] Generated Node #0,1,1: 57:[21, 15] Operation: 4+11=15 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 57:[21, 7], Operations: ['84-73=11', '11-4=7'] Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,57 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, 15], Operations: ['84-73=11', '4+11=15'] Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,57 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[4, 73, 4], Operations: ['84/21=4'] Exploring Operation: 73-4=69, Resulting Numbers: [4, 69] Generated Node #0,0,0: 57:[4, 69] Operation: 73-4=69 Exploring Operation: 73-4=69, Resulting Numbers: [4, 69] Generated Node #0,0,1: 57:[4, 69] Operation: 73-4=69 Moving to Node #0,0,0 Current State: 57:[4, 69], Operations: ['84/21=4', '73-4=69'] Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,57 unequal: No Solution Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[4, 69], Operations: ['84/21=4', '73-4=69'] Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,57 unequal: No Solution Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,57 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
[ 10, 10, 8, 35 ]
45
[ "10*35=350", "10+350=360", "360/8=45" ]
Current State: 45:[10, 10, 8, 35], Operations: [] Exploring Operation: 10*35=350, Resulting Numbers: [8, 350] Generated Node #2: [8, 350] from Operation: 10*35=350 Current State: 45:[8, 350], Operations: ['10*35=350'] Exploring Operation: 10+350=360, Resulting Numbers: [8, 360] Generated Node #3: [8, 360] from Operation: 10+350=360 Current State: 45:[8, 360], Operations: ['10*35=350', '10+350=360'] Exploring Operation: 360/8=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[10, 10, 8, 35], Operations: [] Exploring Operation: 10+35=45, Resulting Numbers: [10, 8, 45] Generated Node #0,0: 45:[10, 8, 45] Operation: 10+35=45 Exploring Operation: 10+35=45, Resulting Numbers: [10, 8, 45] Generated Node #0,1: 45:[10, 8, 45] Operation: 10+35=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[10, 8, 45], Operations: ['10+35=45'] Exploring Operation: 10+8=18, Resulting Numbers: [45, 18] Generated Node #0,0,0: 45:[45, 18] Operation: 10+8=18 Exploring Operation: 10-8=2, Resulting Numbers: [45, 2] Generated Node #0,0,1: 45:[45, 2] Operation: 10-8=2 Moving to Node #0,0,1 Current State: 45:[45, 2], Operations: ['10+35=45', '10-8=2'] Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,45 unequal: No Solution Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[45, 18], Operations: ['10+35=45', '10+8=18'] Exploring Operation: 45-18=27, Resulting Numbers: [27] 27,45 unequal: No Solution Exploring Operation: 45+18=63, Resulting Numbers: [63] 63,45 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 #0,1 Current State: 45:[10, 8, 45], Operations: ['10+35=45'] Exploring Operation: 10-8=2, Resulting Numbers: [45, 2] Generated Node #0,1,0: 45:[45, 2] Operation: 10-8=2 Exploring Operation: 10+8=18, Resulting Numbers: [45, 18] Generated Node #0,1,1: 45:[45, 18] Operation: 10+8=18 Moving to Node #0,1,0 Current State: 45:[45, 2], Operations: ['10+35=45', '10-8=2'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,45 unequal: No Solution Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[45, 18], Operations: ['10+35=45', '10+8=18'] Exploring Operation: 45+18=63, Resulting Numbers: [63] 63,45 unequal: No Solution Exploring Operation: 45-18=27, Resulting Numbers: [27] 27,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 33, 36, 7, 37 ]
58
[ "36-33=3", "7*3=21", "37+21=58" ]
Current State: 58:[33, 36, 7, 37], Operations: [] Exploring Operation: 36-33=3, Resulting Numbers: [7, 37, 3] Generated Node #2: [7, 37, 3] from Operation: 36-33=3 Current State: 58:[7, 37, 3], Operations: ['36-33=3'] Exploring Operation: 7*3=21, Resulting Numbers: [37, 21] Generated Node #3: [37, 21] from Operation: 7*3=21 Current State: 58:[37, 21], Operations: ['36-33=3', '7*3=21'] Exploring Operation: 37+21=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[33, 36, 7, 37], Operations: [] Exploring Operation: 36-33=3, Resulting Numbers: [7, 37, 3] Generated Node #0,0: 58:[7, 37, 3] Operation: 36-33=3 Exploring Operation: 36-7=29, Resulting Numbers: [33, 37, 29] Generated Node #0,1: 58:[33, 37, 29] Operation: 36-7=29 Exploring Operation: 37-7=30, Resulting Numbers: [33, 36, 30] Generated Node #0,2: 58:[33, 36, 30] Operation: 37-7=30 Exploring Operation: 37-36=1, Resulting Numbers: [33, 7, 1] Generated Node #0,3: 58:[33, 7, 1] Operation: 37-36=1 Moving to Node #0,3 Current State: 58:[33, 7, 1], Operations: ['37-36=1'] Exploring Operation: 33-7=26, Resulting Numbers: [1, 26] Generated Node #0,3,0: 58:[1, 26] Operation: 33-7=26 Exploring Operation: 33-1=32, Resulting Numbers: [7, 32] Generated Node #0,3,1: 58:[7, 32] Operation: 33-1=32 Exploring Operation: 33*1=33, Resulting Numbers: [7, 33] Generated Node #0,3,2: 58:[7, 33] Operation: 33*1=33 Exploring Operation: 7-1=6, Resulting Numbers: [33, 6] Generated Node #0,3,3: 58:[33, 6] Operation: 7-1=6 Moving to Node #0,2 Current State: 58:[33, 36, 30], Operations: ['37-7=30'] Exploring Operation: 36-33=3, Resulting Numbers: [30, 3] Generated Node #0,2,0: 58:[30, 3] Operation: 36-33=3 Exploring Operation: 33-30=3, Resulting Numbers: [36, 3] Generated Node #0,2,1: 58:[36, 3] Operation: 33-30=3 Exploring Operation: 36-30=6, Resulting Numbers: [33, 6] Generated Node #0,2,2: 58:[33, 6] Operation: 36-30=6 Exploring Operation: 33+36=69, Resulting Numbers: [30, 69] Generated Node #0,2,3: 58:[30, 69] Operation: 33+36=69 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 58:[30, 3], Operations: ['37-7=30', '36-33=3'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 30*3=90, Resulting Numbers: [90] 90,58 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,58 unequal: No Solution Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,58 unequal: No Solution No 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: 58:[36, 3], Operations: ['37-7=30', '33-30=3'] Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,58 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 36+3=39, Resulting Numbers: [39] 39,58 unequal: No Solution Exploring Operation: 36*3=108, Resulting Numbers: [108] 108,58 unequal: No Solution No 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: 58:[33, 6], Operations: ['37-7=30', '36-30=6'] Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 33*6=198, Resulting Numbers: [198] 198,58 unequal: No Solution Exploring Operation: 33+6=39, Resulting Numbers: [39] 39,58 unequal: No Solution No 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: 58:[30, 69], Operations: ['37-7=30', '33+36=69'] Exploring Operation: 30+69=99, Resulting Numbers: [99] 99,58 unequal: No Solution Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,58 unequal: No Solution Exploring Operation: 30*69=2070, Resulting Numbers: [2070] 2070,58 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: 58:[33, 37, 29], Operations: ['36-7=29'] Exploring Operation: 33+37=70, Resulting Numbers: [29, 70] Generated Node #0,1,0: 58:[29, 70] Operation: 33+37=70 Exploring Operation: 33-29=4, Resulting Numbers: [37, 4] Generated Node #0,1,1: 58:[37, 4] Operation: 33-29=4 Exploring Operation: 37-29=8, Resulting Numbers: [33, 8] Generated Node #0,1,2: 58:[33, 8] Operation: 37-29=8 Exploring Operation: 37-33=4, Resulting Numbers: [29, 4] Generated Node #0,1,3: 58:[29, 4] Operation: 37-33=4 Moving to Node #0,0 Current State: 58:[7, 37, 3], Operations: ['36-33=3'] Exploring Operation: 37-3=34, Resulting Numbers: [7, 34] Generated Node #0,0,0: 58:[7, 34] Operation: 37-3=34 Exploring Operation: 7-3=4, Resulting Numbers: [37, 4] Generated Node #0,0,1: 58:[37, 4] Operation: 7-3=4 Exploring Operation: 37-7=30, Resulting Numbers: [3, 30] Generated Node #0,0,2: 58:[3, 30] Operation: 37-7=30 Exploring Operation: 7+37=44, Resulting Numbers: [3, 44] Generated Node #0,0,3: 58:[3, 44] Operation: 7+37=44 Moving to Node #0,1,3 Current State: 58:[29, 4], Operations: ['36-7=29', '37-33=4'] Exploring Operation: 29+4=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 29*4=116, Resulting Numbers: [116] 116,58 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,58 unequal: No Solution Moving to Node #0,0,2 Current State: 58:[3, 30], Operations: ['36-33=3', '37-7=30'] Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,58 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,58 unequal: No Solution Moving to Node #0,3,0 Current State: 58:[1, 26], Operations: ['37-36=1', '33-7=26'] Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,58 unequal: No Solution Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,58 unequal: No Solution Exploring Operation: 1*26=26, Resulting Numbers: [26] 26,58 unequal: No Solution Moving to Node #0,3,3 Current State: 58:[33, 6], Operations: ['37-36=1', '7-1=6'] Exploring Operation: 33+6=39, Resulting Numbers: [39] 39,58 unequal: No Solution Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 33*6=198, Resulting Numbers: [198] 198,58 unequal: No Solution Moving to Node #0,3,1 Current State: 58:[7, 32], Operations: ['37-36=1', '33-1=32'] Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,58 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,58 unequal: No Solution Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,58 unequal: No Solution Moving to Node #0,3,2 Current State: 58:[7, 33], Operations: ['37-36=1', '33*1=33'] Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,58 unequal: No Solution Exploring Operation: 7*33=231, Resulting Numbers: [231] 231,58 unequal: No Solution Exploring Operation: 7+33=40, Resulting Numbers: [40] 40,58 unequal: No Solution Moving to Node #0,1,2 Current State: 58:[33, 8], Operations: ['36-7=29', '37-29=8'] Exploring Operation: 33*8=264, Resulting Numbers: [264] 264,58 unequal: No Solution Exploring Operation: 33+8=41, Resulting Numbers: [41] 41,58 unequal: No Solution Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[37, 4], Operations: ['36-7=29', '33-29=4'] Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,58 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 37*4=148, Resulting Numbers: [148] 148,58 unequal: No Solution Moving to Node #0,0,1 Current State: 58:[37, 4], Operations: ['36-33=3', '7-3=4'] Exploring Operation: 37*4=148, Resulting Numbers: [148] 148,58 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,58 unequal: No Solution Moving to Node #0,0,0 Current State: 58:[7, 34], Operations: ['36-33=3', '37-3=34'] Exploring Operation: 7*34=238, Resulting Numbers: [238] 238,58 unequal: No Solution Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,58 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,58 unequal: No Solution Moving to Node #0,1,0 Current State: 58:[29, 70], Operations: ['36-7=29', '33+37=70'] Exploring Operation: 70-29=41, Resulting Numbers: [41] 41,58 unequal: No Solution Exploring Operation: 29+70=99, Resulting Numbers: [99] 99,58 unequal: No Solution Exploring Operation: 29*70=2030, Resulting Numbers: [2030] 2030,58 unequal: No Solution Moving to Node #0,0,3 Current State: 58:[3, 44], Operations: ['36-33=3', '7+37=44'] Exploring Operation: 3*44=132, Resulting Numbers: [132] 132,58 unequal: No Solution Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,58 unequal: No Solution Exploring Operation: 3+44=47, Resulting Numbers: [47] 47,58 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 43, 5, 13, 5 ]
43
[ "5-5=0", "13*0=0", "43+0=43" ]
Current State: 43:[43, 5, 13, 5], Operations: [] Exploring Operation: 5-5=0, Resulting Numbers: [43, 13, 0] Generated Node #2: [43, 13, 0] from Operation: 5-5=0 Current State: 43:[43, 13, 0], Operations: ['5-5=0'] Exploring Operation: 13*0=0, Resulting Numbers: [43, 0] Generated Node #3: [43, 0] from Operation: 13*0=0 Current State: 43:[43, 0], Operations: ['5-5=0', '13*0=0'] Exploring Operation: 43+0=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[43, 5, 13, 5], Operations: [] Exploring Operation: 5*5=25, Resulting Numbers: [43, 13, 25] Generated Node #0,0: 43:[43, 13, 25] Operation: 5*5=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[43, 13, 25], Operations: ['5*5=25'] Exploring Operation: 13+25=38, Resulting Numbers: [43, 38] Generated Node #0,0,0: 43:[43, 38] Operation: 13+25=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[43, 38], Operations: ['5*5=25', '13+25=38'] Exploring Operation: 43+38=81, Resulting Numbers: [81] 81,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 35, 69, 23, 43 ]
11
[ "43-35=8", "69/23=3", "8+3=11" ]
Current State: 11:[35, 69, 23, 43], Operations: [] Exploring Operation: 43-35=8, Resulting Numbers: [69, 23, 8] Generated Node #2: [69, 23, 8] from Operation: 43-35=8 Current State: 11:[69, 23, 8], Operations: ['43-35=8'] Exploring Operation: 69/23=3, Resulting Numbers: [8, 3] Generated Node #3: [8, 3] from Operation: 69/23=3 Current State: 11:[8, 3], Operations: ['43-35=8', '69/23=3'] Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[35, 69, 23, 43], Operations: [] Exploring Operation: 69-43=26, Resulting Numbers: [35, 23, 26] Generated Node #0,0: 11:[35, 23, 26] Operation: 69-43=26 Exploring Operation: 69-35=34, Resulting Numbers: [23, 43, 34] Generated Node #0,1: 11:[23, 43, 34] Operation: 69-35=34 Exploring Operation: 43-35=8, Resulting Numbers: [69, 23, 8] Generated Node #0,2: 11:[69, 23, 8] Operation: 43-35=8 Exploring Operation: 69/23=3, Resulting Numbers: [35, 43, 3] Generated Node #0,3: 11:[35, 43, 3] Operation: 69/23=3 Exploring Operation: 35-23=12, Resulting Numbers: [69, 43, 12] Generated Node #0,4: 11:[69, 43, 12] Operation: 35-23=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[35, 23, 26], Operations: ['69-43=26'] Exploring Operation: 35-23=12, Resulting Numbers: [26, 12] Generated Node #0,0,0: 11:[26, 12] Operation: 35-23=12 Exploring Operation: 35+23=58, Resulting Numbers: [26, 58] Generated Node #0,0,1: 11:[26, 58] Operation: 35+23=58 Exploring Operation: 35-26=9, Resulting Numbers: [23, 9] Generated Node #0,0,2: 11:[23, 9] Operation: 35-26=9 Exploring Operation: 35+26=61, Resulting Numbers: [23, 61] Generated Node #0,0,3: 11:[23, 61] Operation: 35+26=61 Exploring Operation: 26-23=3, Resulting Numbers: [35, 3] Generated Node #0,0,4: 11:[35, 3] Operation: 26-23=3 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 11:[23, 9], Operations: ['69-43=26', '35-26=9'] Exploring Operation: 23*9=207, Resulting Numbers: [207] 207,11 unequal: No Solution Exploring Operation: 23+9=32, Resulting Numbers: [32] 32,11 unequal: No Solution Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[26, 12], Operations: ['69-43=26', '35-23=12'] Exploring Operation: 26*12=312, Resulting Numbers: [312] 312,11 unequal: No Solution Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 26+12=38, Resulting Numbers: [38] 38,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 11:[35, 3], Operations: ['69-43=26', '26-23=3'] Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,11 unequal: No Solution Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,11 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 11:[26, 58], Operations: ['69-43=26', '35+23=58'] Exploring Operation: 26*58=1508, Resulting Numbers: [1508] 1508,11 unequal: No Solution Exploring Operation: 58-26=32, Resulting Numbers: [32] 32,11 unequal: No Solution Exploring Operation: 26+58=84, Resulting Numbers: [84] 84,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 11:[23, 61], Operations: ['69-43=26', '35+26=61'] Exploring Operation: 61-23=38, Resulting Numbers: [38] 38,11 unequal: No Solution Exploring Operation: 23*61=1403, Resulting Numbers: [1403] 1403,11 unequal: No Solution Exploring Operation: 23+61=84, Resulting Numbers: [84] 84,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 11:[35, 43, 3], Operations: ['69/23=3'] Exploring Operation: 35-3=32, Resulting Numbers: [43, 32] Generated Node #0,3,0: 11:[43, 32] Operation: 35-3=32 Exploring Operation: 43-3=40, Resulting Numbers: [35, 40] Generated Node #0,3,1: 11:[35, 40] Operation: 43-3=40 Exploring Operation: 43+3=46, Resulting Numbers: [35, 46] Generated Node #0,3,2: 11:[35, 46] Operation: 43+3=46 Exploring Operation: 35+3=38, Resulting Numbers: [43, 38] Generated Node #0,3,3: 11:[43, 38] Operation: 35+3=38 Exploring Operation: 43-35=8, Resulting Numbers: [3, 8] Generated Node #0,3,4: 11:[3, 8] Operation: 43-35=8 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 11:[3, 8], Operations: ['69/23=3', '43-35=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,11 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[35, 69, 23, 43], Operations: [] Exploring Operation: 69/23=3, Resulting Numbers: [35, 43, 3] Generated Node #0,3: 11:[35, 43, 3] Operation: 69/23=3 Moving to Node #0,3 Current State: 11:[35, 43, 3], Operations: ['69/23=3'] Exploring Operation: 43-35=8, Resulting Numbers: [3, 8] Generated Node #0,3,4: 11:[3, 8] Operation: 43-35=8 Moving to Node #0,3,4 Current State: 11:[3, 8], Operations: ['69/23=3', '43-35=8'] Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_5
mult_heuristic
[ 9, 19, 18, 5 ]
29
[ "18/9=2", "5*2=10", "19+10=29" ]
Current State: 29:[9, 19, 18, 5], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [19, 5, 2] Generated Node #2: [19, 5, 2] from Operation: 18/9=2 Current State: 29:[19, 5, 2], Operations: ['18/9=2'] Exploring Operation: 5*2=10, Resulting Numbers: [19, 10] Generated Node #3: [19, 10] from Operation: 5*2=10 Current State: 29:[19, 10], Operations: ['18/9=2', '5*2=10'] Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[9, 19, 18, 5], Operations: [] Exploring Operation: 9+18=27, Resulting Numbers: [19, 5, 27] Generated Node #0,0: 29:[19, 5, 27] Operation: 9+18=27 Exploring Operation: 9+19=28, Resulting Numbers: [18, 5, 28] Generated Node #0,1: 29:[18, 5, 28] Operation: 9+19=28 Moving to Node #0,0 Current State: 29:[19, 5, 27], Operations: ['9+18=27'] Exploring Operation: 19+5=24, Resulting Numbers: [27, 24] Generated Node #0,0,0: 29:[27, 24] Operation: 19+5=24 Exploring Operation: 5+27=32, Resulting Numbers: [19, 32] Generated Node #0,0,1: 29:[19, 32] Operation: 5+27=32 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[27, 24], Operations: ['9+18=27', '19+5=24'] Exploring Operation: 27+24=51, Resulting Numbers: [51] 51,29 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,29 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:[19, 32], Operations: ['9+18=27', '5+27=32'] Exploring Operation: 19+32=51, Resulting Numbers: [51] 51,29 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,29 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: 29:[18, 5, 28], Operations: ['9+19=28'] Exploring Operation: 18+5=23, Resulting Numbers: [28, 23] Generated Node #0,1,0: 29:[28, 23] Operation: 18+5=23 Exploring Operation: 5+28=33, Resulting Numbers: [18, 33] Generated Node #0,1,1: 29:[18, 33] Operation: 5+28=33 Moving to Node #0,1,0 Current State: 29:[28, 23], Operations: ['9+19=28', '18+5=23'] Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,29 unequal: No Solution Exploring Operation: 28+23=51, Resulting Numbers: [51] 51,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[18, 33], Operations: ['9+19=28', '5+28=33'] Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,29 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,29 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 14, 15, 40, 24 ]
63
[ "15-14=1", "40+24=64", "64-1=63" ]
Current State: 63:[14, 15, 40, 24], Operations: [] Exploring Operation: 15-14=1, Resulting Numbers: [40, 24, 1] Generated Node #2: [40, 24, 1] from Operation: 15-14=1 Current State: 63:[40, 24, 1], Operations: ['15-14=1'] Exploring Operation: 40+24=64, Resulting Numbers: [1, 64] Generated Node #3: [1, 64] from Operation: 40+24=64 Current State: 63:[1, 64], Operations: ['15-14=1', '40+24=64'] Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[14, 15, 40, 24], Operations: [] Exploring Operation: 15+40=55, Resulting Numbers: [14, 24, 55] Generated Node #0,0: 63:[14, 24, 55] Operation: 15+40=55 Exploring Operation: 40-14=26, Resulting Numbers: [15, 24, 26] Generated Node #0,1: 63:[15, 24, 26] Operation: 40-14=26 Exploring Operation: 40-24=16, Resulting Numbers: [14, 15, 16] Generated Node #0,2: 63:[14, 15, 16] Operation: 40-24=16 Exploring Operation: 40+24=64, Resulting Numbers: [14, 15, 64] Generated Node #0,3: 63:[14, 15, 64] Operation: 40+24=64 Exploring Operation: 40-15=25, Resulting Numbers: [14, 24, 25] Generated Node #0,4: 63:[14, 24, 25] Operation: 40-15=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 63:[14, 15, 64], Operations: ['40+24=64'] Exploring Operation: 14+15=29, Resulting Numbers: [64, 29] Generated Node #0,3,0: 63:[64, 29] Operation: 14+15=29 Exploring Operation: 15-14=1, Resulting Numbers: [64, 1] Generated Node #0,3,1: 63:[64, 1] Operation: 15-14=1 Exploring Operation: 14+64=78, Resulting Numbers: [15, 78] Generated Node #0,3,2: 63:[15, 78] Operation: 14+64=78 Exploring Operation: 64-14=50, Resulting Numbers: [15, 50] Generated Node #0,3,3: 63:[15, 50] Operation: 64-14=50 Exploring Operation: 64-15=49, Resulting Numbers: [14, 49] Generated Node #0,3,4: 63:[14, 49] Operation: 64-15=49 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 63:[64, 1], Operations: ['40+24=64', '15-14=1'] Exploring Operation: 64+1=65, Resulting Numbers: [65] 65,63 unequal: No Solution Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[14, 15, 40, 24], Operations: [] Exploring Operation: 40+24=64, Resulting Numbers: [14, 15, 64] Generated Node #0,3: 63:[14, 15, 64] Operation: 40+24=64 Moving to Node #0,3 Current State: 63:[14, 15, 64], Operations: ['40+24=64'] Exploring Operation: 15-14=1, Resulting Numbers: [64, 1] Generated Node #0,3,1: 63:[64, 1] Operation: 15-14=1 Moving to Node #0,3,1 Current State: 63:[64, 1], Operations: ['40+24=64', '15-14=1'] Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 6, 37, 15, 2 ]
41
[ "15-2=13", "6*13=78", "78-37=41" ]
Current State: 41:[6, 37, 15, 2], Operations: [] Exploring Operation: 15-2=13, Resulting Numbers: [6, 37, 13] Generated Node #2: [6, 37, 13] from Operation: 15-2=13 Current State: 41:[6, 37, 13], Operations: ['15-2=13'] Exploring Operation: 6*13=78, Resulting Numbers: [37, 78] Generated Node #3: [37, 78] from Operation: 6*13=78 Current State: 41:[37, 78], Operations: ['15-2=13', '6*13=78'] Exploring Operation: 78-37=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[6, 37, 15, 2], Operations: [] Exploring Operation: 6*2=12, Resulting Numbers: [37, 15, 12] Generated Node #0,0: 41:[37, 15, 12] Operation: 6*2=12 Exploring Operation: 37+2=39, Resulting Numbers: [6, 15, 39] Generated Node #0,1: 41:[6, 15, 39] Operation: 37+2=39 Exploring Operation: 6+2=8, Resulting Numbers: [37, 15, 8] Generated Node #0,2: 41:[37, 15, 8] Operation: 6+2=8 Exploring Operation: 15*2=30, Resulting Numbers: [6, 37, 30] Generated Node #0,3: 41:[6, 37, 30] Operation: 15*2=30 Exploring Operation: 6+15=21, Resulting Numbers: [37, 2, 21] Generated Node #0,4: 41:[37, 2, 21] Operation: 6+15=21 Moving to Node #0,3 Current State: 41:[6, 37, 30], Operations: ['15*2=30'] Exploring Operation: 6+30=36, Resulting Numbers: [37, 36] Generated Node #0,3,0: 41:[37, 36] Operation: 6+30=36 Exploring Operation: 37-6=31, Resulting Numbers: [30, 31] Generated Node #0,3,1: 41:[30, 31] Operation: 37-6=31 Exploring Operation: 6+37=43, Resulting Numbers: [30, 43] Generated Node #0,3,2: 41:[30, 43] Operation: 6+37=43 Exploring Operation: 30-6=24, Resulting Numbers: [37, 24] Generated Node #0,3,3: 41:[37, 24] Operation: 30-6=24 Exploring Operation: 30/6=5, Resulting Numbers: [37, 5] Generated Node #0,3,4: 41:[37, 5] Operation: 30/6=5 Moving to Node #0,0 Current State: 41:[37, 15, 12], Operations: ['6*2=12'] Exploring Operation: 15-12=3, Resulting Numbers: [37, 3] Generated Node #0,0,0: 41:[37, 3] Operation: 15-12=3 Exploring Operation: 37+12=49, Resulting Numbers: [15, 49] Generated Node #0,0,1: 41:[15, 49] Operation: 37+12=49 Exploring Operation: 37-12=25, Resulting Numbers: [15, 25] Generated Node #0,0,2: 41:[15, 25] Operation: 37-12=25 Exploring Operation: 15+12=27, Resulting Numbers: [37, 27] Generated Node #0,0,3: 41:[37, 27] Operation: 15+12=27 Exploring Operation: 37+15=52, Resulting Numbers: [12, 52] Generated Node #0,0,4: 41:[12, 52] Operation: 37+15=52 Moving to Node #0,1 Current State: 41:[6, 15, 39], Operations: ['37+2=39'] Exploring Operation: 15-6=9, Resulting Numbers: [39, 9] Generated Node #0,1,0: 41:[39, 9] Operation: 15-6=9 Exploring Operation: 39-6=33, Resulting Numbers: [15, 33] Generated Node #0,1,1: 41:[15, 33] Operation: 39-6=33 Exploring Operation: 6+39=45, Resulting Numbers: [15, 45] Generated Node #0,1,2: 41:[15, 45] Operation: 6+39=45 Exploring Operation: 6+15=21, Resulting Numbers: [39, 21] Generated Node #0,1,3: 41:[39, 21] Operation: 6+15=21 Exploring Operation: 15+39=54, Resulting Numbers: [6, 54] Generated Node #0,1,4: 41:[6, 54] Operation: 15+39=54 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 41:[39, 21], Operations: ['37+2=39', '6+15=21'] Exploring Operation: 39*21=819, Resulting Numbers: [819] 819,41 unequal: No Solution Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 39+21=60, Resulting Numbers: [60] 60,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 41:[15, 45], Operations: ['37+2=39', '6+39=45'] Exploring Operation: 15*45=675, Resulting Numbers: [675] 675,41 unequal: No Solution Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,41 unequal: No Solution Exploring Operation: 15+45=60, Resulting Numbers: [60] 60,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[39, 9], Operations: ['37+2=39', '15-6=9'] Exploring Operation: 39-9=30, Resulting Numbers: [30] 30,41 unequal: No Solution Exploring Operation: 39+9=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 39*9=351, Resulting Numbers: [351] 351,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[15, 33], Operations: ['37+2=39', '39-6=33'] Exploring Operation: 15*33=495, Resulting Numbers: [495] 495,41 unequal: No Solution Exploring Operation: 15+33=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 41:[6, 54], Operations: ['37+2=39', '15+39=54'] Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,41 unequal: No Solution Exploring Operation: 6*54=324, Resulting Numbers: [324] 324,41 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: 41:[37, 15, 8], Operations: ['6+2=8'] Exploring Operation: 37+8=45, Resulting Numbers: [15, 45] Generated Node #0,2,0: 41:[15, 45] Operation: 37+8=45 Exploring Operation: 37+15=52, Resulting Numbers: [8, 52] Generated Node #0,2,1: 41:[8, 52] Operation: 37+15=52 Exploring Operation: 15-8=7, Resulting Numbers: [37, 7] Generated Node #0,2,2: 41:[37, 7] Operation: 15-8=7 Exploring Operation: 15+8=23, Resulting Numbers: [37, 23] Generated Node #0,2,3: 41:[37, 23] Operation: 15+8=23 Exploring Operation: 37-8=29, Resulting Numbers: [15, 29] Generated Node #0,2,4: 41:[15, 29] Operation: 37-8=29 Moving to Node #0,4 Current State: 41:[37, 2, 21], Operations: ['6+15=21'] Exploring Operation: 2*21=42, Resulting Numbers: [37, 42] Generated Node #0,4,0: 41:[37, 42] Operation: 2*21=42 Exploring Operation: 37-2=35, Resulting Numbers: [21, 35] Generated Node #0,4,1: 41:[21, 35] Operation: 37-2=35 Exploring Operation: 37+2=39, Resulting Numbers: [21, 39] Generated Node #0,4,2: 41:[21, 39] Operation: 37+2=39 Exploring Operation: 2+21=23, Resulting Numbers: [37, 23] Generated Node #0,4,3: 41:[37, 23] Operation: 2+21=23 Exploring Operation: 21-2=19, Resulting Numbers: [37, 19] Generated Node #0,4,4: 41:[37, 19] Operation: 21-2=19 Moving to Node #0,4,0 Current State: 41:[37, 42], Operations: ['6+15=21', '2*21=42'] Exploring Operation: 42-37=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 37*42=1554, Resulting Numbers: [1554] 1554,41 unequal: No Solution Exploring Operation: 37+42=79, Resulting Numbers: [79] 79,41 unequal: No Solution Moving to Node #0,3,0 Current State: 41:[37, 36], Operations: ['15*2=30', '6+30=36'] Exploring Operation: 37+36=73, Resulting Numbers: [73] 73,41 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 37*36=1332, Resulting Numbers: [1332] 1332,41 unequal: No Solution Moving to Node #0,3,2 Current State: 41:[30, 43], Operations: ['15*2=30', '6+37=43'] Exploring Operation: 43-30=13, Resulting Numbers: [13] 13,41 unequal: No Solution Exploring Operation: 30+43=73, Resulting Numbers: [73] 73,41 unequal: No Solution Exploring Operation: 30*43=1290, Resulting Numbers: [1290] 1290,41 unequal: No Solution Moving to Node #0,0,3 Current State: 41:[37, 27], Operations: ['6*2=12', '15+12=27'] Exploring Operation: 37*27=999, Resulting Numbers: [999] 999,41 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,41 unequal: No Solution Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,41 unequal: No Solution Moving to Node #0,3,1 Current State: 41:[30, 31], Operations: ['15*2=30', '37-6=31'] Exploring Operation: 30*31=930, Resulting Numbers: [930] 930,41 unequal: No Solution Exploring Operation: 30+31=61, Resulting Numbers: [61] 61,41 unequal: No Solution Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,41 unequal: No Solution Moving to Node #0,3,3 Current State: 41:[37, 24], Operations: ['15*2=30', '30-6=24'] Exploring Operation: 37*24=888, Resulting Numbers: [888] 888,41 unequal: No Solution Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,41 unequal: No Solution Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[37, 23], Operations: ['6+2=8', '15+8=23'] Exploring Operation: 37*23=851, Resulting Numbers: [851] 851,41 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,41 unequal: No Solution Exploring Operation: 37+23=60, Resulting Numbers: [60] 60,41 unequal: No Solution Moving to Node #0,4,3 Current State: 41:[37, 23], Operations: ['6+15=21', '2+21=23'] Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,41 unequal: No Solution Exploring Operation: 37*23=851, Resulting Numbers: [851] 851,41 unequal: No Solution Exploring Operation: 37+23=60, Resulting Numbers: [60] 60,41 unequal: No Solution Moving to Node #0,4,2 Current State: 41:[21, 39], Operations: ['6+15=21', '37+2=39'] Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 21*39=819, Resulting Numbers: [819] 819,41 unequal: No Solution Exploring Operation: 21+39=60, Resulting Numbers: [60] 60,41 unequal: No Solution Moving to Node #0,4,4 Current State: 41:[37, 19], Operations: ['6+15=21', '21-2=19'] Exploring Operation: 37+19=56, Resulting Numbers: [56] 56,41 unequal: No Solution Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 37*19=703, Resulting Numbers: [703] 703,41 unequal: No Solution Moving to Node #0,4,1 Current State: 41:[21, 35], Operations: ['6+15=21', '37-2=35'] Exploring Operation: 21*35=735, Resulting Numbers: [735] 735,41 unequal: No Solution Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,41 unequal: No Solution Exploring Operation: 21+35=56, Resulting Numbers: [56] 56,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[15, 45], Operations: ['6+2=8', '37+8=45'] Exploring Operation: 15*45=675, Resulting Numbers: [675] 675,41 unequal: No Solution Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,41 unequal: No Solution Exploring Operation: 15+45=60, Resulting Numbers: [60] 60,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[15, 49], Operations: ['6*2=12', '37+12=49'] Exploring Operation: 49-15=34, Resulting Numbers: [34] 34,41 unequal: No Solution Exploring Operation: 15+49=64, Resulting Numbers: [64] 64,41 unequal: No Solution Exploring Operation: 15*49=735, Resulting Numbers: [735] 735,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[37, 7], Operations: ['6+2=8', '15-8=7'] Exploring Operation: 37+7=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 37*7=259, Resulting Numbers: [259] 259,41 unequal: No Solution Exploring Operation: 37-7=30, Resulting Numbers: [30] 30,41 unequal: No Solution Moving to Node #0,2,4 Current State: 41:[15, 29], Operations: ['6+2=8', '37-8=29'] Exploring Operation: 15*29=435, Resulting Numbers: [435] 435,41 unequal: No Solution Exploring Operation: 15+29=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,41 unequal: No Solution Moving to Node #0,0,4 Current State: 41:[12, 52], Operations: ['6*2=12', '37+15=52'] Exploring Operation: 12+52=64, Resulting Numbers: [64] 64,41 unequal: No Solution Exploring Operation: 12*52=624, Resulting Numbers: [624] 624,41 unequal: No Solution Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,41 unequal: No Solution Moving to Node #0,3,4 Current State: 41:[37, 5], Operations: ['15*2=30', '30/6=5'] Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,41 unequal: No Solution Exploring Operation: 37*5=185, Resulting Numbers: [185] 185,41 unequal: No Solution Exploring Operation: 37+5=42, Resulting Numbers: [42] 42,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[15, 25], Operations: ['6*2=12', '37-12=25'] Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,41 unequal: No Solution Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 15*25=375, Resulting Numbers: [375] 375,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[37, 3], Operations: ['6*2=12', '15-12=3'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,41 unequal: No Solution Exploring Operation: 37+3=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 37*3=111, Resulting Numbers: [111] 111,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[8, 52], Operations: ['6+2=8', '37+15=52'] Exploring Operation: 8*52=416, Resulting Numbers: [416] 416,41 unequal: No Solution Exploring Operation: 8+52=60, Resulting Numbers: [60] 60,41 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,41 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 77, 73, 11, 81 ]
22
[ "77/11=7", "73+81=154", "154/7=22" ]
Current State: 22:[77, 73, 11, 81], Operations: [] Exploring Operation: 77/11=7, Resulting Numbers: [73, 81, 7] Generated Node #2: [73, 81, 7] from Operation: 77/11=7 Current State: 22:[73, 81, 7], Operations: ['77/11=7'] Exploring Operation: 73+81=154, Resulting Numbers: [7, 154] Generated Node #3: [7, 154] from Operation: 73+81=154 Current State: 22:[7, 154], Operations: ['77/11=7', '73+81=154'] Exploring Operation: 154/7=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[77, 73, 11, 81], Operations: [] Exploring Operation: 81-73=8, Resulting Numbers: [77, 11, 8] Generated Node #0,0: 22:[77, 11, 8] Operation: 81-73=8 Exploring Operation: 77-11=66, Resulting Numbers: [73, 81, 66] Generated Node #0,1: 22:[73, 81, 66] Operation: 77-11=66 Exploring Operation: 77-73=4, Resulting Numbers: [11, 81, 4] Generated Node #0,2: 22:[11, 81, 4] Operation: 77-73=4 Exploring Operation: 81-77=4, Resulting Numbers: [73, 11, 4] Generated Node #0,3: 22:[73, 11, 4] Operation: 81-77=4 Exploring Operation: 77/11=7, Resulting Numbers: [73, 81, 7] Generated Node #0,4: 22:[73, 81, 7] Operation: 77/11=7 Start Sub Search at level 1: Moving to Node #0,3 Current State: 22:[73, 11, 4], Operations: ['81-77=4'] Exploring Operation: 11+4=15, Resulting Numbers: [73, 15] Generated Node #0,3,0: 22:[73, 15] Operation: 11+4=15 Exploring Operation: 73-11=62, Resulting Numbers: [4, 62] Generated Node #0,3,1: 22:[4, 62] Operation: 73-11=62 Exploring Operation: 73-4=69, Resulting Numbers: [11, 69] Generated Node #0,3,2: 22:[11, 69] Operation: 73-4=69 Exploring Operation: 73+4=77, Resulting Numbers: [11, 77] Generated Node #0,3,3: 22:[11, 77] Operation: 73+4=77 Exploring Operation: 11-4=7, Resulting Numbers: [73, 7] Generated Node #0,3,4: 22:[73, 7] Operation: 11-4=7 Moving to Node #0,3,1 Current State: 22:[4, 62], Operations: ['81-77=4', '73-11=62'] Exploring Operation: 4*62=248, Resulting Numbers: [248] 248,22 unequal: No Solution Exploring Operation: 4+62=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,22 unequal: No Solution Moving to Node #0,3,2 Current State: 22:[11, 69], Operations: ['81-77=4', '73-4=69'] Exploring Operation: 69-11=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 11*69=759, Resulting Numbers: [759] 759,22 unequal: No Solution Exploring Operation: 11+69=80, Resulting Numbers: [80] 80,22 unequal: No Solution Moving to Node #0,3,0 Current State: 22:[73, 15], Operations: ['81-77=4', '11+4=15'] Exploring Operation: 73+15=88, Resulting Numbers: [88] 88,22 unequal: No Solution Exploring Operation: 73-15=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 73*15=1095, Resulting Numbers: [1095] 1095,22 unequal: No Solution Moving to Node #0,3,3 Current State: 22:[11, 77], Operations: ['81-77=4', '73+4=77'] Exploring Operation: 77/11=7, Resulting Numbers: [7] 7,22 unequal: No Solution Exploring Operation: 11*77=847, Resulting Numbers: [847] 847,22 unequal: No Solution Exploring Operation: 77-11=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 11+77=88, Resulting Numbers: [88] 88,22 unequal: No Solution Moving to Node #0,3,4 Current State: 22:[73, 7], Operations: ['81-77=4', '11-4=7'] Exploring Operation: 73+7=80, Resulting Numbers: [80] 80,22 unequal: No Solution Exploring Operation: 73-7=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 73*7=511, Resulting Numbers: [511] 511,22 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 Current State: 22:[77, 11, 8], Operations: ['81-73=8'] Exploring Operation: 77/11=7, Resulting Numbers: [8, 7] Generated Node #0,0,0: 22:[8, 7] Operation: 77/11=7 Exploring Operation: 11-8=3, Resulting Numbers: [77, 3] Generated Node #0,0,1: 22:[77, 3] Operation: 11-8=3 Exploring Operation: 77-8=69, Resulting Numbers: [11, 69] Generated Node #0,0,2: 22:[11, 69] Operation: 77-8=69 Exploring Operation: 77-11=66, Resulting Numbers: [8, 66] Generated Node #0,0,3: 22:[8, 66] Operation: 77-11=66 Exploring Operation: 11+8=19, Resulting Numbers: [77, 19] Generated Node #0,0,4: 22:[77, 19] Operation: 11+8=19 Moving to Node #0,0,0 Current State: 22:[8, 7], Operations: ['81-73=8', '77/11=7'] Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,22 unequal: No Solution Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,22 unequal: No Solution Moving to Node #0,0,3 Current State: 22:[8, 66], Operations: ['81-73=8', '77-11=66'] Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 8+66=74, Resulting Numbers: [74] 74,22 unequal: No Solution Exploring Operation: 8*66=528, Resulting Numbers: [528] 528,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[11, 69], Operations: ['81-73=8', '77-8=69'] Exploring Operation: 69-11=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 11+69=80, Resulting Numbers: [80] 80,22 unequal: No Solution Exploring Operation: 11*69=759, Resulting Numbers: [759] 759,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[77, 3], Operations: ['81-73=8', '11-8=3'] Exploring Operation: 77*3=231, Resulting Numbers: [231] 231,22 unequal: No Solution Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,22 unequal: No Solution Exploring Operation: 77+3=80, Resulting Numbers: [80] 80,22 unequal: No Solution Moving to Node #0,0,4 Current State: 22:[77, 19], Operations: ['81-73=8', '11+8=19'] Exploring Operation: 77-19=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 77+19=96, Resulting Numbers: [96] 96,22 unequal: No Solution Exploring Operation: 77*19=1463, Resulting Numbers: [1463] 1463,22 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 Current State: 22:[11, 81, 4], Operations: ['77-73=4'] Exploring Operation: 81-4=77, Resulting Numbers: [11, 77] Generated Node #0,2,0: 22:[11, 77] Operation: 81-4=77 Exploring Operation: 11-4=7, Resulting Numbers: [81, 7] Generated Node #0,2,1: 22:[81, 7] Operation: 11-4=7 Exploring Operation: 11+4=15, Resulting Numbers: [81, 15] Generated Node #0,2,2: 22:[81, 15] Operation: 11+4=15 Exploring Operation: 81-11=70, Resulting Numbers: [4, 70] Generated Node #0,2,3: 22:[4, 70] Operation: 81-11=70 Exploring Operation: 81+4=85, Resulting Numbers: [11, 85] Generated Node #0,2,4: 22:[11, 85] Operation: 81+4=85 Moving to Node #0,2,3 Current State: 22:[4, 70], Operations: ['77-73=4', '81-11=70'] Exploring Operation: 4+70=74, Resulting Numbers: [74] 74,22 unequal: No Solution Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 4*70=280, Resulting Numbers: [280] 280,22 unequal: No Solution Moving to Node #0,2,0 Current State: 22:[11, 77], Operations: ['77-73=4', '81-4=77'] Exploring Operation: 77-11=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 11+77=88, Resulting Numbers: [88] 88,22 unequal: No Solution Exploring Operation: 77/11=7, Resulting Numbers: [7] 7,22 unequal: No Solution Exploring Operation: 11*77=847, Resulting Numbers: [847] 847,22 unequal: No Solution Moving to Node #0,2,1 Current State: 22:[81, 7], Operations: ['77-73=4', '11-4=7'] Exploring Operation: 81-7=74, Resulting Numbers: [74] 74,22 unequal: No Solution Exploring Operation: 81+7=88, Resulting Numbers: [88] 88,22 unequal: No Solution Exploring Operation: 81*7=567, Resulting Numbers: [567] 567,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[81, 15], Operations: ['77-73=4', '11+4=15'] Exploring Operation: 81-15=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 81*15=1215, Resulting Numbers: [1215] 1215,22 unequal: No Solution Exploring Operation: 81+15=96, Resulting Numbers: [96] 96,22 unequal: No Solution Moving to Node #0,2,4 Current State: 22:[11, 85], Operations: ['77-73=4', '81+4=85'] Exploring Operation: 85-11=74, Resulting Numbers: [74] 74,22 unequal: No Solution Exploring Operation: 11+85=96, Resulting Numbers: [96] 96,22 unequal: No Solution Exploring Operation: 11*85=935, Resulting Numbers: [935] 935,22 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 #0,4 Current State: 22:[73, 81, 7], Operations: ['77/11=7'] Exploring Operation: 81+7=88, Resulting Numbers: [73, 88] Generated Node #0,4,0: 22:[73, 88] Operation: 81+7=88 Exploring Operation: 81-7=74, Resulting Numbers: [73, 74] Generated Node #0,4,1: 22:[73, 74] Operation: 81-7=74 Exploring Operation: 73-7=66, Resulting Numbers: [81, 66] Generated Node #0,4,2: 22:[81, 66] Operation: 73-7=66 Exploring Operation: 81-73=8, Resulting Numbers: [7, 8] Generated Node #0,4,3: 22:[7, 8] Operation: 81-73=8 Exploring Operation: 73+7=80, Resulting Numbers: [81, 80] Generated Node #0,4,4: 22:[81, 80] Operation: 73+7=80 Moving to Node #0,4,3 Current State: 22:[7, 8], Operations: ['77/11=7', '81-73=8'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,22 unequal: No Solution Moving to Node #0,4,2 Current State: 22:[81, 66], Operations: ['77/11=7', '73-7=66'] Exploring Operation: 81*66=5346, Resulting Numbers: [5346] 5346,22 unequal: No Solution Exploring Operation: 81-66=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 81+66=147, Resulting Numbers: [147] 147,22 unequal: No Solution Moving to Node #0,4,1 Current State: 22:[73, 74], Operations: ['77/11=7', '81-7=74'] Exploring Operation: 73*74=5402, Resulting Numbers: [5402] 5402,22 unequal: No Solution Exploring Operation: 74-73=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 73+74=147, Resulting Numbers: [147] 147,22 unequal: No Solution Moving to Node #0,4,0 Current State: 22:[73, 88], Operations: ['77/11=7', '81+7=88'] Exploring Operation: 88-73=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 73+88=161, Resulting Numbers: [161] 161,22 unequal: No Solution Exploring Operation: 73*88=6424, Resulting Numbers: [6424] 6424,22 unequal: No Solution Moving to Node #0,4,4 Current State: 22:[81, 80], Operations: ['77/11=7', '73+7=80'] Exploring Operation: 81*80=6480, Resulting Numbers: [6480] 6480,22 unequal: No Solution Exploring Operation: 81-80=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 81+80=161, Resulting Numbers: [161] 161,22 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 #0,1 Current State: 22:[73, 81, 66], Operations: ['77-11=66'] Exploring Operation: 81-66=15, Resulting Numbers: [73, 15] Generated Node #0,1,0: 22:[73, 15] Operation: 81-66=15 Exploring Operation: 73+81=154, Resulting Numbers: [66, 154] Generated Node #0,1,1: 22:[66, 154] Operation: 73+81=154 Exploring Operation: 73+66=139, Resulting Numbers: [81, 139] Generated Node #0,1,2: 22:[81, 139] Operation: 73+66=139 Exploring Operation: 81-73=8, Resulting Numbers: [66, 8] Generated Node #0,1,3: 22:[66, 8] Operation: 81-73=8 Exploring Operation: 73-66=7, Resulting Numbers: [81, 7] Generated Node #0,1,4: 22:[81, 7] Operation: 73-66=7 Moving to Node #0,1,3 Current State: 22:[66, 8], Operations: ['77-11=66', '81-73=8'] Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 66*8=528, Resulting Numbers: [528] 528,22 unequal: No Solution Exploring Operation: 66+8=74, Resulting Numbers: [74] 74,22 unequal: No Solution Moving to Node #0,1,0 Current State: 22:[73, 15], Operations: ['77-11=66', '81-66=15'] Exploring Operation: 73-15=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 73+15=88, Resulting Numbers: [88] 88,22 unequal: No Solution Exploring Operation: 73*15=1095, Resulting Numbers: [1095] 1095,22 unequal: No Solution Moving to Node #0,1,4 Current State: 22:[81, 7], Operations: ['77-11=66', '73-66=7'] Exploring Operation: 81*7=567, Resulting Numbers: [567] 567,22 unequal: No Solution Exploring Operation: 81-7=74, Resulting Numbers: [74] 74,22 unequal: No Solution Exploring Operation: 81+7=88, Resulting Numbers: [88] 88,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[66, 154], Operations: ['77-11=66', '73+81=154'] Exploring Operation: 66*154=10164, Resulting Numbers: [10164] 10164,22 unequal: No Solution Exploring Operation: 66+154=220, Resulting Numbers: [220] 220,22 unequal: No Solution Exploring Operation: 154-66=88, Resulting Numbers: [88] 88,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[81, 139], Operations: ['77-11=66', '73+66=139'] Exploring Operation: 81+139=220, Resulting Numbers: [220] 220,22 unequal: No Solution Exploring Operation: 139-81=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 81*139=11259, Resulting Numbers: [11259] 11259,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 70, 39, 34, 91 ]
52
[ "70+39=109", "91-34=57", "109-57=52" ]
Current State: 52:[70, 39, 34, 91], Operations: [] Exploring Operation: 70+39=109, Resulting Numbers: [34, 91, 109] Generated Node #2: [34, 91, 109] from Operation: 70+39=109 Current State: 52:[34, 91, 109], Operations: ['70+39=109'] Exploring Operation: 91-34=57, Resulting Numbers: [109, 57] Generated Node #3: [109, 57] from Operation: 91-34=57 Current State: 52:[109, 57], Operations: ['70+39=109', '91-34=57'] Exploring Operation: 109-57=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[70, 39, 34, 91], Operations: [] Exploring Operation: 39-34=5, Resulting Numbers: [70, 91, 5] Generated Node #0,0: 52:[70, 91, 5] Operation: 39-34=5 Exploring Operation: 70-39=31, Resulting Numbers: [34, 91, 31] Generated Node #0,1: 52:[34, 91, 31] Operation: 70-39=31 Exploring Operation: 91-70=21, Resulting Numbers: [39, 34, 21] Generated Node #0,2: 52:[39, 34, 21] Operation: 91-70=21 Exploring Operation: 91-39=52, Resulting Numbers: [70, 34, 52] Generated Node #0,3: 52:[70, 34, 52] Operation: 91-39=52 Exploring Operation: 91-34=57, Resulting Numbers: [70, 39, 57] Generated Node #0,4: 52:[70, 39, 57] Operation: 91-34=57 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[39, 34, 21], Operations: ['91-70=21'] Exploring Operation: 34+21=55, Resulting Numbers: [39, 55] Generated Node #0,2,0: 52:[39, 55] Operation: 34+21=55 Exploring Operation: 34-21=13, Resulting Numbers: [39, 13] Generated Node #0,2,1: 52:[39, 13] Operation: 34-21=13 Exploring Operation: 39-34=5, Resulting Numbers: [21, 5] Generated Node #0,2,2: 52:[21, 5] Operation: 39-34=5 Exploring Operation: 39-21=18, Resulting Numbers: [34, 18] Generated Node #0,2,3: 52:[34, 18] Operation: 39-21=18 Exploring Operation: 39+21=60, Resulting Numbers: [34, 60] Generated Node #0,2,4: 52:[34, 60] Operation: 39+21=60 Moving to Node #0,2,2 Current State: 52:[21, 5], Operations: ['91-70=21', '39-34=5'] Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,52 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,52 unequal: No Solution Moving to Node #0,2,3 Current State: 52:[34, 18], Operations: ['91-70=21', '39-21=18'] Exploring Operation: 34+18=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[70, 39, 34, 91], Operations: [] Exploring Operation: 91-70=21, Resulting Numbers: [39, 34, 21] Generated Node #0,2: 52:[39, 34, 21] Operation: 91-70=21 Moving to Node #0,2 Current State: 52:[39, 34, 21], Operations: ['91-70=21'] Exploring Operation: 39-21=18, Resulting Numbers: [34, 18] Generated Node #0,2,3: 52:[34, 18] Operation: 39-21=18 Moving to Node #0,2,3 Current State: 52:[34, 18], Operations: ['91-70=21', '39-21=18'] Exploring Operation: 34+18=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 9, 4, 40, 76 ]
41
[ "9-4=5", "76-40=36", "5+36=41" ]
Current State: 41:[9, 4, 40, 76], Operations: [] Exploring Operation: 9-4=5, Resulting Numbers: [40, 76, 5] Generated Node #2: [40, 76, 5] from Operation: 9-4=5 Current State: 41:[40, 76, 5], Operations: ['9-4=5'] Exploring Operation: 76-40=36, Resulting Numbers: [5, 36] Generated Node #3: [5, 36] from Operation: 76-40=36 Current State: 41:[5, 36], Operations: ['9-4=5', '76-40=36'] Exploring Operation: 5+36=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[9, 4, 40, 76], Operations: [] Exploring Operation: 76/4=19, Resulting Numbers: [9, 40, 19] Generated Node #0,0: 41:[9, 40, 19] Operation: 76/4=19 Exploring Operation: 9*4=36, Resulting Numbers: [40, 76, 36] Generated Node #0,1: 41:[40, 76, 36] Operation: 9*4=36 Exploring Operation: 9+4=13, Resulting Numbers: [40, 76, 13] Generated Node #0,2: 41:[40, 76, 13] Operation: 9+4=13 Moving to Node #0,1 Current State: 41:[40, 76, 36], Operations: ['9*4=36'] Exploring Operation: 40+36=76, Resulting Numbers: [76, 76] Generated Node #0,1,0: 41:[76, 76] Operation: 40+36=76 Exploring Operation: 76-36=40, Resulting Numbers: [40, 40] Generated Node #0,1,1: 41:[40, 40] Operation: 76-36=40 Exploring Operation: 76-40=36, Resulting Numbers: [36, 36] Generated Node #0,1,2: 41:[36, 36] Operation: 76-40=36 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[40, 40], Operations: ['9*4=36', '76-36=40'] Exploring Operation: 40/40=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 40+40=80, Resulting Numbers: [80] 80,41 unequal: No Solution Exploring Operation: 40-40=0, Resulting Numbers: [0] 0,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 41:[36, 36], Operations: ['9*4=36', '76-40=36'] Exploring Operation: 36+36=72, Resulting Numbers: [72] 72,41 unequal: No Solution Exploring Operation: 36/36=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 36-36=0, Resulting Numbers: [0] 0,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[76, 76], Operations: ['9*4=36', '40+36=76'] Exploring Operation: 76/76=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 76+76=152, Resulting Numbers: [152] 152,41 unequal: No Solution Exploring Operation: 76-76=0, Resulting Numbers: [0] 0,41 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: 41:[9, 40, 19], Operations: ['76/4=19'] Exploring Operation: 9+19=28, Resulting Numbers: [40, 28] Generated Node #0,0,0: 41:[40, 28] Operation: 9+19=28 Exploring Operation: 9+40=49, Resulting Numbers: [19, 49] Generated Node #0,0,1: 41:[19, 49] Operation: 9+40=49 Exploring Operation: 40-9=31, Resulting Numbers: [19, 31] Generated Node #0,0,2: 41:[19, 31] Operation: 40-9=31 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[40, 28], Operations: ['76/4=19', '9+19=28'] Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 40*28=1120, Resulting Numbers: [1120] 1120,41 unequal: No Solution Exploring Operation: 40+28=68, Resulting Numbers: [68] 68,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[19, 49], Operations: ['76/4=19', '9+40=49'] Exploring Operation: 19+49=68, Resulting Numbers: [68] 68,41 unequal: No Solution Exploring Operation: 49-19=30, Resulting Numbers: [30] 30,41 unequal: No Solution Exploring Operation: 19*49=931, Resulting Numbers: [931] 931,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 41:[19, 31], Operations: ['76/4=19', '40-9=31'] Exploring Operation: 19*31=589, Resulting Numbers: [589] 589,41 unequal: No Solution Exploring Operation: 31-19=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 19+31=50, Resulting Numbers: [50] 50,41 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: 41:[40, 76, 13], Operations: ['9+4=13'] Exploring Operation: 40+13=53, Resulting Numbers: [76, 53] Generated Node #0,2,0: 41:[76, 53] Operation: 40+13=53 Exploring Operation: 76-13=63, Resulting Numbers: [40, 63] Generated Node #0,2,1: 41:[40, 63] Operation: 76-13=63 Exploring Operation: 76-40=36, Resulting Numbers: [13, 36] Generated Node #0,2,2: 41:[13, 36] Operation: 76-40=36 Moving to Node #0,2,1 Current State: 41:[40, 63], Operations: ['9+4=13', '76-13=63'] Exploring Operation: 40+63=103, Resulting Numbers: [103] 103,41 unequal: No Solution Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 40*63=2520, Resulting Numbers: [2520] 2520,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[13, 36], Operations: ['9+4=13', '76-40=36'] Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,41 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 13*36=468, Resulting Numbers: [468] 468,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[76, 53], Operations: ['9+4=13', '40+13=53'] Exploring Operation: 76*53=4028, Resulting Numbers: [4028] 4028,41 unequal: No Solution Exploring Operation: 76+53=129, Resulting Numbers: [129] 129,41 unequal: No Solution Exploring Operation: 76-53=23, Resulting Numbers: [23] 23,41 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 11, 65, 63, 52 ]
93
[ "65-63=2", "52*2=104", "104-11=93" ]
Current State: 93:[11, 65, 63, 52], Operations: [] Exploring Operation: 65-63=2, Resulting Numbers: [11, 52, 2] Generated Node #2: [11, 52, 2] from Operation: 65-63=2 Current State: 93:[11, 52, 2], Operations: ['65-63=2'] Exploring Operation: 52*2=104, Resulting Numbers: [11, 104] Generated Node #3: [11, 104] from Operation: 52*2=104 Current State: 93:[11, 104], Operations: ['65-63=2', '52*2=104'] Exploring Operation: 104-11=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[11, 65, 63, 52], Operations: [] Exploring Operation: 65-63=2, Resulting Numbers: [11, 52, 2] Generated Node #0,0: 93:[11, 52, 2] Operation: 65-63=2 Exploring Operation: 63-52=11, Resulting Numbers: [11, 65, 11] Generated Node #0,1: 93:[11, 65, 11] Operation: 63-52=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[11, 52, 2], Operations: ['65-63=2'] Exploring Operation: 52/2=26, Resulting Numbers: [11, 26] Generated Node #0,0,0: 93:[11, 26] Operation: 52/2=26 Exploring Operation: 52-11=41, Resulting Numbers: [2, 41] Generated Node #0,0,1: 93:[2, 41] Operation: 52-11=41 Moving to Node #0,0,1 Current State: 93:[2, 41], Operations: ['65-63=2', '52-11=41'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,93 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[11, 26], Operations: ['65-63=2', '52/2=26'] Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,93 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,93 unequal: No Solution No 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: 93:[11, 65, 11], Operations: ['63-52=11'] Exploring Operation: 11+65=76, Resulting Numbers: [11, 76] Generated Node #0,1,0: 93:[11, 76] Operation: 11+65=76 Exploring Operation: 65+11=76, Resulting Numbers: [11, 76] Generated Node #0,1,1: 93:[11, 76] Operation: 65+11=76 Moving to Node #0,1,0 Current State: 93:[11, 76], Operations: ['63-52=11', '11+65=76'] Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,93 unequal: No Solution Exploring Operation: 11+76=87, Resulting Numbers: [87] 87,93 unequal: No Solution Moving to Node #0,1,1 Current State: 93:[11, 76], Operations: ['63-52=11', '65+11=76'] Exploring Operation: 11+76=87, Resulting Numbers: [87] 87,93 unequal: No Solution Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,93 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
[ 26, 59, 62, 53 ]
76
[ "26+59=85", "62-53=9", "85-9=76" ]
Current State: 76:[26, 59, 62, 53], Operations: [] Exploring Operation: 26+59=85, Resulting Numbers: [62, 53, 85] Generated Node #2: [62, 53, 85] from Operation: 26+59=85 Current State: 76:[62, 53, 85], Operations: ['26+59=85'] Exploring Operation: 62-53=9, Resulting Numbers: [85, 9] Generated Node #3: [85, 9] from Operation: 62-53=9 Current State: 76:[85, 9], Operations: ['26+59=85', '62-53=9'] Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[26, 59, 62, 53], Operations: [] Exploring Operation: 59-53=6, Resulting Numbers: [26, 62, 6] Generated Node #0,0: 76:[26, 62, 6] Operation: 59-53=6 Exploring Operation: 62-59=3, Resulting Numbers: [26, 53, 3] Generated Node #0,1: 76:[26, 53, 3] Operation: 62-59=3 Exploring Operation: 62-53=9, Resulting Numbers: [26, 59, 9] Generated Node #0,2: 76:[26, 59, 9] Operation: 62-53=9 Moving to Node #0,0 Current State: 76:[26, 62, 6], Operations: ['59-53=6'] Exploring Operation: 26+62=88, Resulting Numbers: [6, 88] Generated Node #0,0,0: 76:[6, 88] Operation: 26+62=88 Exploring Operation: 62-26=36, Resulting Numbers: [6, 36] Generated Node #0,0,1: 76:[6, 36] Operation: 62-26=36 Exploring Operation: 26-6=20, Resulting Numbers: [62, 20] Generated Node #0,0,2: 76:[62, 20] Operation: 26-6=20 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 76:[6, 36], Operations: ['59-53=6', '62-26=36'] Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 6+36=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[6, 88], Operations: ['59-53=6', '26+62=88'] Exploring Operation: 88-6=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 6*88=528, Resulting Numbers: [528] 528,76 unequal: No Solution Exploring Operation: 6+88=94, Resulting Numbers: [94] 94,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 76:[62, 20], Operations: ['59-53=6', '26-6=20'] Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 62*20=1240, Resulting Numbers: [1240] 1240,76 unequal: No Solution Exploring Operation: 62+20=82, Resulting Numbers: [82] 82,76 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: 76:[26, 53, 3], Operations: ['62-59=3'] Exploring Operation: 53-26=27, Resulting Numbers: [3, 27] Generated Node #0,1,0: 76:[3, 27] Operation: 53-26=27 Exploring Operation: 26+53=79, Resulting Numbers: [3, 79] Generated Node #0,1,1: 76:[3, 79] Operation: 26+53=79 Exploring Operation: 26*3=78, Resulting Numbers: [53, 78] Generated Node #0,1,2: 76:[53, 78] Operation: 26*3=78 Moving to Node #0,2 Current State: 76:[26, 59, 9], Operations: ['62-53=9'] Exploring Operation: 59-26=33, Resulting Numbers: [9, 33] Generated Node #0,2,0: 76:[9, 33] Operation: 59-26=33 Exploring Operation: 59+9=68, Resulting Numbers: [26, 68] Generated Node #0,2,1: 76:[26, 68] Operation: 59+9=68 Exploring Operation: 26+59=85, Resulting Numbers: [9, 85] Generated Node #0,2,2: 76:[9, 85] Operation: 26+59=85 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 76:[9, 33], Operations: ['62-53=9', '59-26=33'] Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,76 unequal: No Solution Exploring Operation: 9+33=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 9*33=297, Resulting Numbers: [297] 297,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 76:[9, 85], Operations: ['62-53=9', '26+59=85'] Exploring Operation: 9*85=765, Resulting Numbers: [765] 765,76 unequal: No Solution Exploring Operation: 9+85=94, Resulting Numbers: [94] 94,76 unequal: No Solution Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[26, 59, 62, 53], Operations: [] Exploring Operation: 62-53=9, Resulting Numbers: [26, 59, 9] Generated Node #0,2: 76:[26, 59, 9] Operation: 62-53=9 Moving to Node #0,2 Current State: 76:[26, 59, 9], Operations: ['62-53=9'] Exploring Operation: 26+59=85, Resulting Numbers: [9, 85] Generated Node #0,2,2: 76:[9, 85] Operation: 26+59=85 Moving to Node #0,2,2 Current State: 76:[9, 85], Operations: ['62-53=9', '26+59=85'] Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_3
sum_heuristic
[ 96, 17, 24, 92 ]
24
[ "96*17=1632", "92-24=68", "1632/68=24" ]
Current State: 24:[96, 17, 24, 92], Operations: [] Exploring Operation: 96*17=1632, Resulting Numbers: [24, 92, 1632] Generated Node #2: [24, 92, 1632] from Operation: 96*17=1632 Current State: 24:[24, 92, 1632], Operations: ['96*17=1632'] Exploring Operation: 92-24=68, Resulting Numbers: [1632, 68] Generated Node #3: [1632, 68] from Operation: 92-24=68 Current State: 24:[1632, 68], Operations: ['96*17=1632', '92-24=68'] Exploring Operation: 1632/68=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[96, 17, 24, 92], Operations: [] Exploring Operation: 96/24=4, Resulting Numbers: [17, 92, 4] Generated Node #0,0: 24:[17, 92, 4] Operation: 96/24=4 Exploring Operation: 96-24=72, Resulting Numbers: [17, 92, 72] Generated Node #0,1: 24:[17, 92, 72] Operation: 96-24=72 Exploring Operation: 96-92=4, Resulting Numbers: [17, 24, 4] Generated Node #0,2: 24:[17, 24, 4] Operation: 96-92=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[17, 24, 4], Operations: ['96-92=4'] Exploring Operation: 17-4=13, Resulting Numbers: [24, 13] Generated Node #0,2,0: 24:[24, 13] Operation: 17-4=13 Exploring Operation: 24-17=7, Resulting Numbers: [4, 7] Generated Node #0,2,1: 24:[4, 7] Operation: 24-17=7 Exploring Operation: 17+4=21, Resulting Numbers: [24, 21] Generated Node #0,2,2: 24:[24, 21] Operation: 17+4=21 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 24:[24, 13], Operations: ['96-92=4', '17-4=13'] Exploring Operation: 24*13=312, Resulting Numbers: [312] 312,24 unequal: No Solution Exploring Operation: 24+13=37, Resulting Numbers: [37] 37,24 unequal: No Solution Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 24:[4, 7], Operations: ['96-92=4', '24-17=7'] Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 24:[24, 21], Operations: ['96-92=4', '17+4=21'] Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[17, 92, 4], Operations: ['96/24=4'] Exploring Operation: 92/4=23, Resulting Numbers: [17, 23] Generated Node #0,0,0: 24:[17, 23] Operation: 92/4=23 Exploring Operation: 17-4=13, Resulting Numbers: [92, 13] Generated Node #0,0,1: 24:[92, 13] Operation: 17-4=13 Exploring Operation: 92-17=75, Resulting Numbers: [4, 75] Generated Node #0,0,2: 24:[4, 75] Operation: 92-17=75 Moving to Node #0,0,0 Current State: 24:[17, 23], Operations: ['96/24=4', '92/4=23'] Exploring Operation: 17*23=391, Resulting Numbers: [391] 391,24 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,24 unequal: No Solution Exploring Operation: 17+23=40, Resulting Numbers: [40] 40,24 unequal: No Solution Moving to Node #0,0,2 Current State: 24:[4, 75], Operations: ['96/24=4', '92-17=75'] Exploring Operation: 4+75=79, Resulting Numbers: [79] 79,24 unequal: No Solution Exploring Operation: 75-4=71, Resulting Numbers: [71] 71,24 unequal: No Solution Exploring Operation: 4*75=300, Resulting Numbers: [300] 300,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[92, 13], Operations: ['96/24=4', '17-4=13'] Exploring Operation: 92+13=105, Resulting Numbers: [105] 105,24 unequal: No Solution Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,24 unequal: No Solution Exploring Operation: 92*13=1196, Resulting Numbers: [1196] 1196,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[17, 92, 72], Operations: ['96-24=72'] Exploring Operation: 92-72=20, Resulting Numbers: [17, 20] Generated Node #0,1,0: 24:[17, 20] Operation: 92-72=20 Exploring Operation: 72-17=55, Resulting Numbers: [92, 55] Generated Node #0,1,1: 24:[92, 55] Operation: 72-17=55 Exploring Operation: 92-17=75, Resulting Numbers: [72, 75] Generated Node #0,1,2: 24:[72, 75] Operation: 92-17=75 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 24:[17, 20], Operations: ['96-24=72', '92-72=20'] Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 17*20=340, Resulting Numbers: [340] 340,24 unequal: No Solution Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 24:[92, 55], Operations: ['96-24=72', '72-17=55'] Exploring Operation: 92*55=5060, Resulting Numbers: [5060] 5060,24 unequal: No Solution Exploring Operation: 92+55=147, Resulting Numbers: [147] 147,24 unequal: No Solution Exploring Operation: 92-55=37, Resulting Numbers: [37] 37,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 24:[72, 75], Operations: ['96-24=72', '92-17=75'] Exploring Operation: 72+75=147, Resulting Numbers: [147] 147,24 unequal: No Solution Exploring Operation: 75-72=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 72*75=5400, Resulting Numbers: [5400] 5400,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 97, 81, 2, 7 ]
82
[ "97+81=178", "178/2=89", "89-7=82" ]
Current State: 82:[97, 81, 2, 7], Operations: [] Exploring Operation: 97+81=178, Resulting Numbers: [2, 7, 178] Generated Node #2: [2, 7, 178] from Operation: 97+81=178 Current State: 82:[2, 7, 178], Operations: ['97+81=178'] Exploring Operation: 178/2=89, Resulting Numbers: [7, 89] Generated Node #3: [7, 89] from Operation: 178/2=89 Current State: 82:[7, 89], Operations: ['97+81=178', '178/2=89'] Exploring Operation: 89-7=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[97, 81, 2, 7], Operations: [] Exploring Operation: 97-7=90, Resulting Numbers: [81, 2, 90] Generated Node #0,0: 82:[81, 2, 90] Operation: 97-7=90 Exploring Operation: 97-81=16, Resulting Numbers: [2, 7, 16] Generated Node #0,1: 82:[2, 7, 16] Operation: 97-81=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[81, 2, 90], Operations: ['97-7=90'] Exploring Operation: 90-81=9, Resulting Numbers: [2, 9] Generated Node #0,0,0: 82:[2, 9] Operation: 90-81=9 Exploring Operation: 90/2=45, Resulting Numbers: [81, 45] Generated Node #0,0,1: 82:[81, 45] Operation: 90/2=45 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[81, 45], Operations: ['97-7=90', '90/2=45'] Exploring Operation: 81+45=126, Resulting Numbers: [126] 126,82 unequal: No Solution Exploring Operation: 81-45=36, Resulting Numbers: [36] 36,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[2, 9], Operations: ['97-7=90', '90-81=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,82 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[2, 7, 16], Operations: ['97-81=16'] Exploring Operation: 16-7=9, Resulting Numbers: [2, 9] Generated Node #0,1,0: 82:[2, 9] Operation: 16-7=9 Exploring Operation: 16/2=8, Resulting Numbers: [7, 8] Generated Node #0,1,1: 82:[7, 8] Operation: 16/2=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[2, 9], Operations: ['97-81=16', '16-7=9'] Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[7, 8], Operations: ['97-81=16', '16/2=8'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,82 unequal: No Solution Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 60, 3, 16, 56 ]
23
[ "60+3=63", "56-16=40", "63-40=23" ]
Current State: 23:[60, 3, 16, 56], Operations: [] Exploring Operation: 60+3=63, Resulting Numbers: [16, 56, 63] Generated Node #2: [16, 56, 63] from Operation: 60+3=63 Current State: 23:[16, 56, 63], Operations: ['60+3=63'] Exploring Operation: 56-16=40, Resulting Numbers: [63, 40] Generated Node #3: [63, 40] from Operation: 56-16=40 Current State: 23:[63, 40], Operations: ['60+3=63', '56-16=40'] Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[60, 3, 16, 56], Operations: [] Exploring Operation: 60/3=20, Resulting Numbers: [16, 56, 20] Generated Node #0,0: 23:[16, 56, 20] Operation: 60/3=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[16, 56, 20], Operations: ['60/3=20'] Exploring Operation: 56-16=40, Resulting Numbers: [20, 40] Generated Node #0,0,0: 23:[20, 40] Operation: 56-16=40 Moving to Node #0,0,0 Current State: 23:[20, 40], Operations: ['60/3=20', '56-16=40'] Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,23 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
[ 35, 14, 15, 87 ]
53
[ "35+14=49", "15+87=102", "102-49=53" ]
Current State: 53:[35, 14, 15, 87], Operations: [] Exploring Operation: 35+14=49, Resulting Numbers: [15, 87, 49] Generated Node #2: [15, 87, 49] from Operation: 35+14=49 Current State: 53:[15, 87, 49], Operations: ['35+14=49'] Exploring Operation: 15+87=102, Resulting Numbers: [49, 102] Generated Node #3: [49, 102] from Operation: 15+87=102 Current State: 53:[49, 102], Operations: ['35+14=49', '15+87=102'] Exploring Operation: 102-49=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[35, 14, 15, 87], Operations: [] Exploring Operation: 35+14=49, Resulting Numbers: [15, 87, 49] Generated Node #0,0: 53:[15, 87, 49] Operation: 35+14=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[15, 87, 49], Operations: ['35+14=49'] Exploring Operation: 87-15=72, Resulting Numbers: [49, 72] Generated Node #0,0,0: 53:[49, 72] Operation: 87-15=72 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 53:[49, 72], Operations: ['35+14=49', '87-15=72'] Exploring Operation: 72-49=23, Resulting Numbers: [23] 23,53 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
[ 13, 28, 31, 44 ]
27
[ "13+31=44", "44/44=1", "28-1=27" ]
Current State: 27:[13, 28, 31, 44], Operations: [] Exploring Operation: 13+31=44, Resulting Numbers: [28, 44, 44] Generated Node #2: [28, 44, 44] from Operation: 13+31=44 Current State: 27:[28, 44, 44], Operations: ['13+31=44'] Exploring Operation: 44/44=1, Resulting Numbers: [28, 1] Generated Node #3: [28, 1] from Operation: 44/44=1 Current State: 27:[28, 1], Operations: ['13+31=44', '44/44=1'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[13, 28, 31, 44], Operations: [] Exploring Operation: 44-31=13, Resulting Numbers: [13, 28, 13] Generated Node #0,0: 27:[13, 28, 13] Operation: 44-31=13 Exploring Operation: 44-28=16, Resulting Numbers: [13, 31, 16] Generated Node #0,1: 27:[13, 31, 16] Operation: 44-28=16 Exploring Operation: 44-13=31, Resulting Numbers: [28, 31, 31] Generated Node #0,2: 27:[28, 31, 31] Operation: 44-13=31 Exploring Operation: 31-28=3, Resulting Numbers: [13, 44, 3] Generated Node #0,3: 27:[13, 44, 3] Operation: 31-28=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[13, 28, 13], Operations: ['44-31=13'] Exploring Operation: 28-13=15, Resulting Numbers: [13, 15] Generated Node #0,0,0: 27:[13, 15] Operation: 28-13=15 Exploring Operation: 13/13=1, Resulting Numbers: [28, 1] Generated Node #0,0,1: 27:[28, 1] Operation: 13/13=1 Exploring Operation: 13+13=26, Resulting Numbers: [28, 26] Generated Node #0,0,2: 27:[28, 26] Operation: 13+13=26 Exploring Operation: 13-13=0, Resulting Numbers: [28, 0] Generated Node #0,0,3: 27:[28, 0] Operation: 13-13=0 Moving to Node #0,0,2 Current State: 27:[28, 26], Operations: ['44-31=13', '13+13=26'] Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 28+26=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 28*26=728, Resulting Numbers: [728] 728,27 unequal: No Solution Moving to Node #0,0,1 Current State: 27:[28, 1], Operations: ['44-31=13', '13/13=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[13, 28, 31, 44], Operations: [] Exploring Operation: 44-31=13, Resulting Numbers: [13, 28, 13] Generated Node #0,0: 27:[13, 28, 13] Operation: 44-31=13 Moving to Node #0,0 Current State: 27:[13, 28, 13], Operations: ['44-31=13'] Exploring Operation: 13/13=1, Resulting Numbers: [28, 1] Generated Node #0,0,1: 27:[28, 1] Operation: 13/13=1 Moving to Node #0,0,1 Current State: 27:[28, 1], Operations: ['44-31=13', '13/13=1'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 2, 29, 87, 21 ]
77
[ "2+29=31", "87+21=108", "108-31=77" ]
Current State: 77:[2, 29, 87, 21], Operations: [] Exploring Operation: 2+29=31, Resulting Numbers: [87, 21, 31] Generated Node #2: [87, 21, 31] from Operation: 2+29=31 Current State: 77:[87, 21, 31], Operations: ['2+29=31'] Exploring Operation: 87+21=108, Resulting Numbers: [31, 108] Generated Node #3: [31, 108] from Operation: 87+21=108 Current State: 77:[31, 108], Operations: ['2+29=31', '87+21=108'] Exploring Operation: 108-31=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[2, 29, 87, 21], Operations: [] Exploring Operation: 29-21=8, Resulting Numbers: [2, 87, 8] Generated Node #0,0: 77:[2, 87, 8] Operation: 29-21=8 Exploring Operation: 87/29=3, Resulting Numbers: [2, 21, 3] Generated Node #0,1: 77:[2, 21, 3] Operation: 87/29=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[2, 87, 8], Operations: ['29-21=8'] Exploring Operation: 87-2=85, Resulting Numbers: [8, 85] Generated Node #0,0,0: 77:[8, 85] Operation: 87-2=85 Exploring Operation: 87-8=79, Resulting Numbers: [2, 79] Generated Node #0,0,1: 77:[2, 79] Operation: 87-8=79 Moving to Node #0,0,1 Current State: 77:[2, 79], Operations: ['29-21=8', '87-8=79'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[2, 29, 87, 21], Operations: [] Exploring Operation: 29-21=8, Resulting Numbers: [2, 87, 8] Generated Node #0,0: 77:[2, 87, 8] Operation: 29-21=8 Moving to Node #0,0 Current State: 77:[2, 87, 8], Operations: ['29-21=8'] Exploring Operation: 87-8=79, Resulting Numbers: [2, 79] Generated Node #0,0,1: 77:[2, 79] Operation: 87-8=79 Moving to Node #0,0,1 Current State: 77:[2, 79], Operations: ['29-21=8', '87-8=79'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 60, 12, 70, 75 ]
25
[ "60/12=5", "75-70=5", "5*5=25" ]
Current State: 25:[60, 12, 70, 75], Operations: [] Exploring Operation: 60/12=5, Resulting Numbers: [70, 75, 5] Generated Node #2: [70, 75, 5] from Operation: 60/12=5 Current State: 25:[70, 75, 5], Operations: ['60/12=5'] Exploring Operation: 75-70=5, Resulting Numbers: [5, 5] Generated Node #3: [5, 5] from Operation: 75-70=5 Current State: 25:[5, 5], Operations: ['60/12=5', '75-70=5'] Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[60, 12, 70, 75], Operations: [] Exploring Operation: 75-70=5, Resulting Numbers: [60, 12, 5] Generated Node #0,0: 25:[60, 12, 5] Operation: 75-70=5 Exploring Operation: 70-60=10, Resulting Numbers: [12, 75, 10] Generated Node #0,1: 25:[12, 75, 10] Operation: 70-60=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[60, 12, 5], Operations: ['75-70=5'] Exploring Operation: 60/5=12, Resulting Numbers: [12, 12] Generated Node #0,0,0: 25:[12, 12] Operation: 60/5=12 Exploring Operation: 60/12=5, Resulting Numbers: [5, 5] Generated Node #0,0,1: 25:[5, 5] Operation: 60/12=5 Moving to Node #0,0,1 Current State: 25:[5, 5], Operations: ['75-70=5', '60/12=5'] Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[60, 12, 70, 75], Operations: [] Exploring Operation: 75-70=5, Resulting Numbers: [60, 12, 5] Generated Node #0,0: 25:[60, 12, 5] Operation: 75-70=5 Moving to Node #0,0 Current State: 25:[60, 12, 5], Operations: ['75-70=5'] Exploring Operation: 60/12=5, Resulting Numbers: [5, 5] Generated Node #0,0,1: 25:[5, 5] Operation: 60/12=5 Moving to Node #0,0,1 Current State: 25:[5, 5], Operations: ['75-70=5', '60/12=5'] Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 42, 68, 5, 79 ]
66
[ "5+79=84", "84/42=2", "68-2=66" ]
Current State: 66:[42, 68, 5, 79], Operations: [] Exploring Operation: 5+79=84, Resulting Numbers: [42, 68, 84] Generated Node #2: [42, 68, 84] from Operation: 5+79=84 Current State: 66:[42, 68, 84], Operations: ['5+79=84'] Exploring Operation: 84/42=2, Resulting Numbers: [68, 2] Generated Node #3: [68, 2] from Operation: 84/42=2 Current State: 66:[68, 2], Operations: ['5+79=84', '84/42=2'] Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[42, 68, 5, 79], Operations: [] Exploring Operation: 79-42=37, Resulting Numbers: [68, 5, 37] Generated Node #0,0: 66:[68, 5, 37] Operation: 79-42=37 Exploring Operation: 79-68=11, Resulting Numbers: [42, 5, 11] Generated Node #0,1: 66:[42, 5, 11] Operation: 79-68=11 Exploring Operation: 68-42=26, Resulting Numbers: [5, 79, 26] Generated Node #0,2: 66:[5, 79, 26] Operation: 68-42=26 Moving to Node #0,0 Current State: 66:[68, 5, 37], Operations: ['79-42=37'] Exploring Operation: 68-5=63, Resulting Numbers: [37, 63] Generated Node #0,0,0: 66:[37, 63] Operation: 68-5=63 Exploring Operation: 37-5=32, Resulting Numbers: [68, 32] Generated Node #0,0,1: 66:[68, 32] Operation: 37-5=32 Exploring Operation: 68-37=31, Resulting Numbers: [5, 31] Generated Node #0,0,2: 66:[5, 31] Operation: 68-37=31 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 66:[68, 32], Operations: ['79-42=37', '37-5=32'] Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,66 unequal: No Solution Exploring Operation: 68+32=100, Resulting Numbers: [100] 100,66 unequal: No Solution Exploring Operation: 68*32=2176, Resulting Numbers: [2176] 2176,66 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 #0,0,2 Current State: 66:[5, 31], Operations: ['79-42=37', '68-37=31'] Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,66 unequal: No Solution Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,66 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 66:[37, 63], Operations: ['79-42=37', '68-5=63'] Exploring Operation: 63-37=26, Resulting Numbers: [26] 26,66 unequal: No Solution Exploring Operation: 37*63=2331, Resulting Numbers: [2331] 2331,66 unequal: No Solution Exploring Operation: 37+63=100, Resulting Numbers: [100] 100,66 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: 66:[42, 5, 11], Operations: ['79-68=11'] Exploring Operation: 11-5=6, Resulting Numbers: [42, 6] Generated Node #0,1,0: 66:[42, 6] Operation: 11-5=6 Exploring Operation: 42-5=37, Resulting Numbers: [11, 37] Generated Node #0,1,1: 66:[11, 37] Operation: 42-5=37 Exploring Operation: 42-11=31, Resulting Numbers: [5, 31] Generated Node #0,1,2: 66:[5, 31] Operation: 42-11=31 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 66:[5, 31], Operations: ['79-68=11', '42-11=31'] Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,66 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,66 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 66:[11, 37], Operations: ['79-68=11', '42-5=37'] Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,66 unequal: No Solution Exploring Operation: 11*37=407, Resulting Numbers: [407] 407,66 unequal: No Solution Exploring Operation: 11+37=48, Resulting Numbers: [48] 48,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 66:[42, 6], Operations: ['79-68=11', '11-5=6'] Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,66 unequal: No Solution Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 66:[5, 79, 26], Operations: ['68-42=26'] Exploring Operation: 79-5=74, Resulting Numbers: [26, 74] Generated Node #0,2,0: 66:[26, 74] Operation: 79-5=74 Exploring Operation: 79-26=53, Resulting Numbers: [5, 53] Generated Node #0,2,1: 66:[5, 53] Operation: 79-26=53 Exploring Operation: 26-5=21, Resulting Numbers: [79, 21] Generated Node #0,2,2: 66:[79, 21] Operation: 26-5=21 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 66:[26, 74], Operations: ['68-42=26', '79-5=74'] Exploring Operation: 74-26=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 26+74=100, Resulting Numbers: [100] 100,66 unequal: No Solution Exploring Operation: 26*74=1924, Resulting Numbers: [1924] 1924,66 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 #0,2,1 Current State: 66:[5, 53], Operations: ['68-42=26', '79-26=53'] Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 5+53=58, Resulting Numbers: [58] 58,66 unequal: No Solution Exploring Operation: 5*53=265, Resulting Numbers: [265] 265,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 66:[79, 21], Operations: ['68-42=26', '26-5=21'] Exploring Operation: 79*21=1659, Resulting Numbers: [1659] 1659,66 unequal: No Solution Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,66 unequal: No Solution Exploring Operation: 79+21=100, Resulting Numbers: [100] 100,66 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
[ 39, 49, 64, 60 ]
22
[ "39+49=88", "64-60=4", "88/4=22" ]
Current State: 22:[39, 49, 64, 60], Operations: [] Exploring Operation: 39+49=88, Resulting Numbers: [64, 60, 88] Generated Node #2: [64, 60, 88] from Operation: 39+49=88 Current State: 22:[64, 60, 88], Operations: ['39+49=88'] Exploring Operation: 64-60=4, Resulting Numbers: [88, 4] Generated Node #3: [88, 4] from Operation: 64-60=4 Current State: 22:[88, 4], Operations: ['39+49=88', '64-60=4'] Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[39, 49, 64, 60], Operations: [] Exploring Operation: 64-60=4, Resulting Numbers: [39, 49, 4] Generated Node #0,0: 22:[39, 49, 4] Operation: 64-60=4 Exploring Operation: 64-49=15, Resulting Numbers: [39, 60, 15] Generated Node #0,1: 22:[39, 60, 15] Operation: 64-49=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[39, 49, 4], Operations: ['64-60=4'] Exploring Operation: 49-39=10, Resulting Numbers: [4, 10] Generated Node #0,0,0: 22:[4, 10] Operation: 49-39=10 Exploring Operation: 39-4=35, Resulting Numbers: [49, 35] Generated Node #0,0,1: 22:[49, 35] Operation: 39-4=35 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 22:[4, 10], Operations: ['64-60=4', '49-39=10'] Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,22 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 22:[49, 35], Operations: ['64-60=4', '39-4=35'] Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,22 unequal: No Solution Exploring Operation: 49+35=84, Resulting Numbers: [84] 84,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[39, 60, 15], Operations: ['64-49=15'] Exploring Operation: 60-39=21, Resulting Numbers: [15, 21] Generated Node #0,1,0: 22:[15, 21] Operation: 60-39=21 Exploring Operation: 60/15=4, Resulting Numbers: [39, 4] Generated Node #0,1,1: 22:[39, 4] Operation: 60/15=4 Moving to Node #0,1,0 Current State: 22:[15, 21], Operations: ['64-49=15', '60-39=21'] Exploring Operation: 15+21=36, Resulting Numbers: [36] 36,22 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[39, 4], Operations: ['64-49=15', '60/15=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,22 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,22 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
[ 85, 5, 13, 53 ]
33
[ "85-53=32", "5*13=65", "65-32=33" ]
Current State: 33:[85, 5, 13, 53], Operations: [] Exploring Operation: 85-53=32, Resulting Numbers: [5, 13, 32] Generated Node #2: [5, 13, 32] from Operation: 85-53=32 Current State: 33:[5, 13, 32], Operations: ['85-53=32'] Exploring Operation: 5*13=65, Resulting Numbers: [32, 65] Generated Node #3: [32, 65] from Operation: 5*13=65 Current State: 33:[32, 65], Operations: ['85-53=32', '5*13=65'] Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[85, 5, 13, 53], Operations: [] Exploring Operation: 85/5=17, Resulting Numbers: [13, 53, 17] Generated Node #0,0: 33:[13, 53, 17] Operation: 85/5=17 Exploring Operation: 85-53=32, Resulting Numbers: [5, 13, 32] Generated Node #0,1: 33:[5, 13, 32] Operation: 85-53=32 Moving to Node #0,1 Current State: 33:[5, 13, 32], Operations: ['85-53=32'] Exploring Operation: 5+32=37, Resulting Numbers: [13, 37] Generated Node #0,1,0: 33:[13, 37] Operation: 5+32=37 Exploring Operation: 13-5=8, Resulting Numbers: [32, 8] Generated Node #0,1,1: 33:[32, 8] Operation: 13-5=8 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 33:[32, 8], Operations: ['85-53=32', '13-5=8'] Exploring Operation: 32+8=40, Resulting Numbers: [40] 40,33 unequal: No Solution Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,33 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:[13, 37], Operations: ['85-53=32', '5+32=37'] Exploring Operation: 37-13=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 13+37=50, Resulting Numbers: [50] 50,33 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: 33:[13, 53, 17], Operations: ['85/5=17'] Exploring Operation: 53-13=40, Resulting Numbers: [17, 40] Generated Node #0,0,0: 33:[17, 40] Operation: 53-13=40 Exploring Operation: 53-17=36, Resulting Numbers: [13, 36] Generated Node #0,0,1: 33:[13, 36] Operation: 53-17=36 Moving to Node #0,0,1 Current State: 33:[13, 36], Operations: ['85/5=17', '53-17=36'] Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,33 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,33 unequal: No Solution Moving to Node #0,0,0 Current State: 33:[17, 40], Operations: ['85/5=17', '53-13=40'] Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,33 unequal: No Solution Exploring Operation: 17+40=57, Resulting Numbers: [57] 57,33 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 40, 61, 29, 23 ]
31
[ "61-40=21", "29+23=52", "52-21=31" ]
Current State: 31:[40, 61, 29, 23], Operations: [] Exploring Operation: 61-40=21, Resulting Numbers: [29, 23, 21] Generated Node #2: [29, 23, 21] from Operation: 61-40=21 Current State: 31:[29, 23, 21], Operations: ['61-40=21'] Exploring Operation: 29+23=52, Resulting Numbers: [21, 52] Generated Node #3: [21, 52] from Operation: 29+23=52 Current State: 31:[21, 52], Operations: ['61-40=21', '29+23=52'] Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[40, 61, 29, 23], Operations: [] Exploring Operation: 61-29=32, Resulting Numbers: [40, 23, 32] Generated Node #0,0: 31:[40, 23, 32] Operation: 61-29=32 Moving to Node #0,0 Current State: 31:[40, 23, 32], Operations: ['61-29=32'] Exploring Operation: 40-23=17, Resulting Numbers: [32, 17] Generated Node #0,0,0: 31:[32, 17] Operation: 40-23=17 Moving to Node #0,0,0 Current State: 31:[32, 17], Operations: ['61-29=32', '40-23=17'] Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,31 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 28, 2, 53, 43 ]
23
[ "43-28=15", "2*15=30", "53-30=23" ]
Current State: 23:[28, 2, 53, 43], Operations: [] Exploring Operation: 43-28=15, Resulting Numbers: [2, 53, 15] Generated Node #2: [2, 53, 15] from Operation: 43-28=15 Current State: 23:[2, 53, 15], Operations: ['43-28=15'] Exploring Operation: 2*15=30, Resulting Numbers: [53, 30] Generated Node #3: [53, 30] from Operation: 2*15=30 Current State: 23:[53, 30], Operations: ['43-28=15', '2*15=30'] Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[28, 2, 53, 43], Operations: [] Exploring Operation: 53-28=25, Resulting Numbers: [2, 43, 25] Generated Node #0,0: 23:[2, 43, 25] Operation: 53-28=25 Exploring Operation: 28-2=26, Resulting Numbers: [53, 43, 26] Generated Node #0,1: 23:[53, 43, 26] Operation: 28-2=26 Exploring Operation: 53-2=51, Resulting Numbers: [28, 43, 51] Generated Node #0,2: 23:[28, 43, 51] Operation: 53-2=51 Exploring Operation: 53-43=10, Resulting Numbers: [28, 2, 10] Generated Node #0,3: 23:[28, 2, 10] Operation: 53-43=10 Start Sub Search at level 1: Moving to Node #0,3 Current State: 23:[28, 2, 10], Operations: ['53-43=10'] Exploring Operation: 2+10=12, Resulting Numbers: [28, 12] Generated Node #0,3,0: 23:[28, 12] Operation: 2+10=12 Exploring Operation: 28-2=26, Resulting Numbers: [10, 26] Generated Node #0,3,1: 23:[10, 26] Operation: 28-2=26 Exploring Operation: 2*10=20, Resulting Numbers: [28, 20] Generated Node #0,3,2: 23:[28, 20] Operation: 2*10=20 Exploring Operation: 28+2=30, Resulting Numbers: [10, 30] Generated Node #0,3,3: 23:[10, 30] Operation: 28+2=30 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 23:[28, 20], Operations: ['53-43=10', '2*10=20'] Exploring Operation: 28*20=560, Resulting Numbers: [560] 560,23 unequal: No Solution Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,23 unequal: No Solution Exploring Operation: 28+20=48, Resulting Numbers: [48] 48,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 23:[28, 12], Operations: ['53-43=10', '2+10=12'] Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,23 unequal: No Solution Exploring Operation: 28*12=336, Resulting Numbers: [336] 336,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 23:[10, 26], Operations: ['53-43=10', '28-2=26'] Exploring Operation: 10*26=260, Resulting Numbers: [260] 260,23 unequal: No Solution Exploring Operation: 10+26=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 23:[10, 30], Operations: ['53-43=10', '28+2=30'] Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,23 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 10*30=300, Resulting Numbers: [300] 300,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[2, 43, 25], Operations: ['53-28=25'] Exploring Operation: 2+43=45, Resulting Numbers: [25, 45] Generated Node #0,0,0: 23:[25, 45] Operation: 2+43=45 Exploring Operation: 25-2=23, Resulting Numbers: [43, 23] Generated Node #0,0,1: 23:[43, 23] Operation: 25-2=23 Exploring Operation: 2+25=27, Resulting Numbers: [43, 27] Generated Node #0,0,2: 23:[43, 27] Operation: 2+25=27 Exploring Operation: 43-2=41, Resulting Numbers: [25, 41] Generated Node #0,0,3: 23:[25, 41] Operation: 43-2=41 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 23:[43, 23], Operations: ['53-28=25', '25-2=23'] Exploring Operation: 43*23=989, Resulting Numbers: [989] 989,23 unequal: No Solution Exploring Operation: 43+23=66, Resulting Numbers: [66] 66,23 unequal: No Solution Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 23:[25, 41], Operations: ['53-28=25', '43-2=41'] Exploring Operation: 25*41=1025, Resulting Numbers: [1025] 1025,23 unequal: No Solution Exploring Operation: 41-25=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 25+41=66, Resulting Numbers: [66] 66,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[25, 45], Operations: ['53-28=25', '2+43=45'] Exploring Operation: 25*45=1125, Resulting Numbers: [1125] 1125,23 unequal: No Solution Exploring Operation: 25+45=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 23:[43, 27], Operations: ['53-28=25', '2+25=27'] Exploring Operation: 43-27=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 43+27=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 43*27=1161, Resulting Numbers: [1161] 1161,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[53, 43, 26], Operations: ['28-2=26'] Exploring Operation: 53+43=96, Resulting Numbers: [26, 96] Generated Node #0,1,0: 23:[26, 96] Operation: 53+43=96 Exploring Operation: 53-43=10, Resulting Numbers: [26, 10] Generated Node #0,1,1: 23:[26, 10] Operation: 53-43=10 Exploring Operation: 43-26=17, Resulting Numbers: [53, 17] Generated Node #0,1,2: 23:[53, 17] Operation: 43-26=17 Exploring Operation: 53-26=27, Resulting Numbers: [43, 27] Generated Node #0,1,3: 23:[43, 27] Operation: 53-26=27 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 23:[26, 10], Operations: ['28-2=26', '53-43=10'] Exploring Operation: 26*10=260, Resulting Numbers: [260] 260,23 unequal: No Solution Exploring Operation: 26+10=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 23:[43, 27], Operations: ['28-2=26', '53-26=27'] Exploring Operation: 43-27=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 43+27=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 43*27=1161, Resulting Numbers: [1161] 1161,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 23:[53, 17], Operations: ['28-2=26', '43-26=17'] Exploring Operation: 53*17=901, Resulting Numbers: [901] 901,23 unequal: No Solution Exploring Operation: 53+17=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 53-17=36, Resulting Numbers: [36] 36,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 23:[26, 96], Operations: ['28-2=26', '53+43=96'] Exploring Operation: 26+96=122, Resulting Numbers: [122] 122,23 unequal: No Solution Exploring Operation: 96-26=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 26*96=2496, Resulting Numbers: [2496] 2496,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[28, 43, 51], Operations: ['53-2=51'] Exploring Operation: 51-43=8, Resulting Numbers: [28, 8] Generated Node #0,2,0: 23:[28, 8] Operation: 51-43=8 Exploring Operation: 28+43=71, Resulting Numbers: [51, 71] Generated Node #0,2,1: 23:[51, 71] Operation: 28+43=71 Exploring Operation: 51-28=23, Resulting Numbers: [43, 23] Generated Node #0,2,2: 23:[43, 23] Operation: 51-28=23 Exploring Operation: 43-28=15, Resulting Numbers: [51, 15] Generated Node #0,2,3: 23:[51, 15] Operation: 43-28=15 Moving to Node #0,2,0 Current State: 23:[28, 8], Operations: ['53-2=51', '51-43=8'] Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 28*8=224, Resulting Numbers: [224] 224,23 unequal: No Solution Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[43, 23], Operations: ['53-2=51', '51-28=23'] Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 43*23=989, Resulting Numbers: [989] 989,23 unequal: No Solution Exploring Operation: 43+23=66, Resulting Numbers: [66] 66,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[51, 15], Operations: ['53-2=51', '43-28=15'] Exploring Operation: 51-15=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 51*15=765, Resulting Numbers: [765] 765,23 unequal: No Solution Exploring Operation: 51+15=66, Resulting Numbers: [66] 66,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[51, 71], Operations: ['53-2=51', '28+43=71'] Exploring Operation: 51+71=122, Resulting Numbers: [122] 122,23 unequal: No Solution Exploring Operation: 51*71=3621, Resulting Numbers: [3621] 3621,23 unequal: No Solution Exploring Operation: 71-51=20, Resulting Numbers: [20] 20,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 61, 38, 56, 2 ]
14
[ "61-56=5", "38/2=19", "19-5=14" ]
Current State: 14:[61, 38, 56, 2], Operations: [] Exploring Operation: 61-56=5, Resulting Numbers: [38, 2, 5] Generated Node #2: [38, 2, 5] from Operation: 61-56=5 Current State: 14:[38, 2, 5], Operations: ['61-56=5'] Exploring Operation: 38/2=19, Resulting Numbers: [5, 19] Generated Node #3: [5, 19] from Operation: 38/2=19 Current State: 14:[5, 19], Operations: ['61-56=5', '38/2=19'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[61, 38, 56, 2], Operations: [] Exploring Operation: 61-56=5, Resulting Numbers: [38, 2, 5] Generated Node #0,0: 14:[38, 2, 5] Operation: 61-56=5 Exploring Operation: 61-38=23, Resulting Numbers: [56, 2, 23] Generated Node #0,1: 14:[56, 2, 23] Operation: 61-38=23 Moving to Node #0,0 Current State: 14:[38, 2, 5], Operations: ['61-56=5'] Exploring Operation: 38-5=33, Resulting Numbers: [2, 33] Generated Node #0,0,0: 14:[2, 33] Operation: 38-5=33 Exploring Operation: 38/2=19, Resulting Numbers: [5, 19] Generated Node #0,0,1: 14:[5, 19] Operation: 38/2=19 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 14:[5, 19], Operations: ['61-56=5', '38/2=19'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[61, 38, 56, 2], Operations: [] Exploring Operation: 61-56=5, Resulting Numbers: [38, 2, 5] Generated Node #0,0: 14:[38, 2, 5] Operation: 61-56=5 Moving to Node #0,0 Current State: 14:[38, 2, 5], Operations: ['61-56=5'] Exploring Operation: 38/2=19, Resulting Numbers: [5, 19] Generated Node #0,0,1: 14:[5, 19] Operation: 38/2=19 Moving to Node #0,0,1 Current State: 14:[5, 19], Operations: ['61-56=5', '38/2=19'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 2, 27, 59, 59 ]
25
[ "27-2=25", "59-59=0", "25+0=25" ]
Current State: 25:[2, 27, 59, 59], Operations: [] Exploring Operation: 27-2=25, Resulting Numbers: [59, 59, 25] Generated Node #2: [59, 59, 25] from Operation: 27-2=25 Current State: 25:[59, 59, 25], Operations: ['27-2=25'] Exploring Operation: 59-59=0, Resulting Numbers: [25, 0] Generated Node #3: [25, 0] from Operation: 59-59=0 Current State: 25:[25, 0], Operations: ['27-2=25', '59-59=0'] Exploring Operation: 25+0=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[2, 27, 59, 59], Operations: [] Exploring Operation: 59-27=32, Resulting Numbers: [2, 59, 32] Generated Node #0,0: 25:[2, 59, 32] Operation: 59-27=32 Exploring Operation: 27-2=25, Resulting Numbers: [59, 59, 25] Generated Node #0,1: 25:[59, 59, 25] Operation: 27-2=25 Exploring Operation: 59-27=32, Resulting Numbers: [2, 59, 32] Generated Node #0,2: 25:[2, 59, 32] Operation: 59-27=32 Exploring Operation: 59/59=1, Resulting Numbers: [2, 27, 1] Generated Node #0,3: 25:[2, 27, 1] Operation: 59/59=1 Exploring Operation: 59-59=0, Resulting Numbers: [2, 27, 0] Generated Node #0,4: 25:[2, 27, 0] Operation: 59-59=0 Moving to Node #0,3 Current State: 25:[2, 27, 1], Operations: ['59/59=1'] Exploring Operation: 27-1=26, Resulting Numbers: [2, 26] Generated Node #0,3,0: 25:[2, 26] Operation: 27-1=26 Exploring Operation: 2+1=3, Resulting Numbers: [27, 3] Generated Node #0,3,1: 25:[27, 3] Operation: 2+1=3 Exploring Operation: 2/1=2, Resulting Numbers: [27, 2] Generated Node #0,3,2: 25:[27, 2] Operation: 2/1=2 Exploring Operation: 27-2=25, Resulting Numbers: [1, 25] Generated Node #0,3,3: 25:[1, 25] Operation: 27-2=25 Exploring Operation: 2*1=2, Resulting Numbers: [27, 2] Generated Node #0,3,4: 25:[27, 2] Operation: 2*1=2 Moving to Node #0,4 Current State: 25:[2, 27, 0], Operations: ['59-59=0'] Exploring Operation: 27+0=27, Resulting Numbers: [2, 27] Generated Node #0,4,0: 25:[2, 27] Operation: 27+0=27 Exploring Operation: 2+0=2, Resulting Numbers: [27, 2] Generated Node #0,4,1: 25:[27, 2] Operation: 2+0=2 Exploring Operation: 27-0=27, Resulting Numbers: [2, 27] Generated Node #0,4,2: 25:[2, 27] Operation: 27-0=27 Exploring Operation: 2-0=2, Resulting Numbers: [27, 2] Generated Node #0,4,3: 25:[27, 2] Operation: 2-0=2 Exploring Operation: 27-2=25, Resulting Numbers: [0, 25] Generated Node #0,4,4: 25:[0, 25] Operation: 27-2=25 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 25:[2, 27], Operations: ['59-59=0', '27+0=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,25 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,25 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[2, 27, 59, 59], Operations: [] Exploring Operation: 59-59=0, Resulting Numbers: [2, 27, 0] Generated Node #0,4: 25:[2, 27, 0] Operation: 59-59=0 Moving to Node #0,4 Current State: 25:[2, 27, 0], Operations: ['59-59=0'] Exploring Operation: 27+0=27, Resulting Numbers: [2, 27] Generated Node #0,4,0: 25:[2, 27] Operation: 27+0=27 Moving to Node #0,4,0 Current State: 25:[2, 27], Operations: ['59-59=0', '27+0=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 85, 13, 31, 7 ]
48
[ "85-13=72", "31-7=24", "72-24=48" ]
Current State: 48:[85, 13, 31, 7], Operations: [] Exploring Operation: 85-13=72, Resulting Numbers: [31, 7, 72] Generated Node #2: [31, 7, 72] from Operation: 85-13=72 Current State: 48:[31, 7, 72], Operations: ['85-13=72'] Exploring Operation: 31-7=24, Resulting Numbers: [72, 24] Generated Node #3: [72, 24] from Operation: 31-7=24 Current State: 48:[72, 24], Operations: ['85-13=72', '31-7=24'] Exploring Operation: 72-24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[85, 13, 31, 7], Operations: [] Exploring Operation: 85-31=54, Resulting Numbers: [13, 7, 54] Generated Node #0,0: 48:[13, 7, 54] Operation: 85-31=54 Moving to Node #0,0 Current State: 48:[13, 7, 54], Operations: ['85-31=54'] Exploring Operation: 54-7=47, Resulting Numbers: [13, 47] Generated Node #0,0,0: 48:[13, 47] Operation: 54-7=47 Moving to Node #0,0,0 Current State: 48:[13, 47], Operations: ['85-31=54', '54-7=47'] Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,48 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 4, 28, 14, 69 ]
41
[ "4*14=56", "28+69=97", "97-56=41" ]
Current State: 41:[4, 28, 14, 69], Operations: [] Exploring Operation: 4*14=56, Resulting Numbers: [28, 69, 56] Generated Node #2: [28, 69, 56] from Operation: 4*14=56 Current State: 41:[28, 69, 56], Operations: ['4*14=56'] Exploring Operation: 28+69=97, Resulting Numbers: [56, 97] Generated Node #3: [56, 97] from Operation: 28+69=97 Current State: 41:[56, 97], Operations: ['4*14=56', '28+69=97'] Exploring Operation: 97-56=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[4, 28, 14, 69], Operations: [] Exploring Operation: 4*14=56, Resulting Numbers: [28, 69, 56] Generated Node #0,0: 41:[28, 69, 56] Operation: 4*14=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[28, 69, 56], Operations: ['4*14=56'] Exploring Operation: 69-28=41, Resulting Numbers: [56, 41] Generated Node #0,0,0: 41:[56, 41] Operation: 69-28=41 Moving to Node #0,0,0 Current State: 41:[56, 41], Operations: ['4*14=56', '69-28=41'] Exploring Operation: 56-41=15, Resulting Numbers: [15] 15,41 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
[ 68, 1, 44, 26 ]
85
[ "68-1=67", "44-26=18", "67+18=85" ]
Current State: 85:[68, 1, 44, 26], Operations: [] Exploring Operation: 68-1=67, Resulting Numbers: [44, 26, 67] Generated Node #2: [44, 26, 67] from Operation: 68-1=67 Current State: 85:[44, 26, 67], Operations: ['68-1=67'] Exploring Operation: 44-26=18, Resulting Numbers: [67, 18] Generated Node #3: [67, 18] from Operation: 44-26=18 Current State: 85:[67, 18], Operations: ['68-1=67', '44-26=18'] Exploring Operation: 67+18=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[68, 1, 44, 26], Operations: [] Exploring Operation: 68-44=24, Resulting Numbers: [1, 26, 24] Generated Node #0,0: 85:[1, 26, 24] Operation: 68-44=24 Exploring Operation: 44-26=18, Resulting Numbers: [68, 1, 18] Generated Node #0,1: 85:[68, 1, 18] Operation: 44-26=18 Moving to Node #0,0 Current State: 85:[1, 26, 24], Operations: ['68-44=24'] Exploring Operation: 26-1=25, Resulting Numbers: [24, 25] Generated Node #0,0,0: 85:[24, 25] Operation: 26-1=25 Exploring Operation: 26-24=2, Resulting Numbers: [1, 2] Generated Node #0,0,1: 85:[1, 2] Operation: 26-24=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[1, 2], Operations: ['68-44=24', '26-24=2'] Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[24, 25], Operations: ['68-44=24', '26-1=25'] Exploring Operation: 24+25=49, Resulting Numbers: [49] 49,85 unequal: No Solution Exploring Operation: 25-24=1, Resulting Numbers: [1] 1,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 85:[68, 1, 18], Operations: ['44-26=18'] Exploring Operation: 68+1=69, Resulting Numbers: [18, 69] Generated Node #0,1,0: 85:[18, 69] Operation: 68+1=69 Exploring Operation: 68+18=86, Resulting Numbers: [1, 86] Generated Node #0,1,1: 85:[1, 86] Operation: 68+18=86 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 85:[1, 86], Operations: ['44-26=18', '68+18=86'] Exploring Operation: 86-1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[68, 1, 44, 26], Operations: [] Exploring Operation: 44-26=18, Resulting Numbers: [68, 1, 18] Generated Node #0,1: 85:[68, 1, 18] Operation: 44-26=18 Moving to Node #0,1 Current State: 85:[68, 1, 18], Operations: ['44-26=18'] Exploring Operation: 68+18=86, Resulting Numbers: [1, 86] Generated Node #0,1,1: 85:[1, 86] Operation: 68+18=86 Moving to Node #0,1,1 Current State: 85:[1, 86], Operations: ['44-26=18', '68+18=86'] Exploring Operation: 86-1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 65, 60, 6, 35 ]
20
[ "65-35=30", "60/6=10", "30-10=20" ]
Current State: 20:[65, 60, 6, 35], Operations: [] Exploring Operation: 65-35=30, Resulting Numbers: [60, 6, 30] Generated Node #2: [60, 6, 30] from Operation: 65-35=30 Current State: 20:[60, 6, 30], Operations: ['65-35=30'] Exploring Operation: 60/6=10, Resulting Numbers: [30, 10] Generated Node #3: [30, 10] from Operation: 60/6=10 Current State: 20:[30, 10], Operations: ['65-35=30', '60/6=10'] Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[65, 60, 6, 35], Operations: [] Exploring Operation: 65-60=5, Resulting Numbers: [6, 35, 5] Generated Node #0,0: 20:[6, 35, 5] Operation: 65-60=5 Exploring Operation: 65-35=30, Resulting Numbers: [60, 6, 30] Generated Node #0,1: 20:[60, 6, 30] Operation: 65-35=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[6, 35, 5], Operations: ['65-60=5'] Exploring Operation: 35/5=7, Resulting Numbers: [6, 7] Generated Node #0,0,0: 20:[6, 7] Operation: 35/5=7 Exploring Operation: 35-6=29, Resulting Numbers: [5, 29] Generated Node #0,0,1: 20:[5, 29] Operation: 35-6=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 20:[6, 7], Operations: ['65-60=5', '35/5=7'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,20 unequal: No Solution Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 20:[5, 29], Operations: ['65-60=5', '35-6=29'] Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,20 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: 20:[60, 6, 30], Operations: ['65-35=30'] Exploring Operation: 60/30=2, Resulting Numbers: [6, 2] Generated Node #0,1,0: 20:[6, 2] Operation: 60/30=2 Exploring Operation: 60/6=10, Resulting Numbers: [30, 10] Generated Node #0,1,1: 20:[30, 10] Operation: 60/6=10 Moving to Node #0,1,0 Current State: 20:[6, 2], Operations: ['65-35=30', '60/30=2'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[30, 10], Operations: ['65-35=30', '60/6=10'] Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[65, 60, 6, 35], Operations: [] Exploring Operation: 65-35=30, Resulting Numbers: [60, 6, 30] Generated Node #0,1: 20:[60, 6, 30] Operation: 65-35=30 Moving to Node #0,1 Current State: 20:[60, 6, 30], Operations: ['65-35=30'] Exploring Operation: 60/6=10, Resulting Numbers: [30, 10] Generated Node #0,1,1: 20:[30, 10] Operation: 60/6=10 Moving to Node #0,1,1 Current State: 20:[30, 10], Operations: ['65-35=30', '60/6=10'] Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_2
mult_heuristic
[ 77, 79, 14, 84 ]
68
[ "79-77=2", "84-14=70", "70-2=68" ]
Current State: 68:[77, 79, 14, 84], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [14, 84, 2] Generated Node #2: [14, 84, 2] from Operation: 79-77=2 Current State: 68:[14, 84, 2], Operations: ['79-77=2'] Exploring Operation: 84-14=70, Resulting Numbers: [2, 70] Generated Node #3: [2, 70] from Operation: 84-14=70 Current State: 68:[2, 70], Operations: ['79-77=2', '84-14=70'] Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[77, 79, 14, 84], Operations: [] Exploring Operation: 84-79=5, Resulting Numbers: [77, 14, 5] Generated Node #0,0: 68:[77, 14, 5] Operation: 84-79=5 Exploring Operation: 79-77=2, Resulting Numbers: [14, 84, 2] Generated Node #0,1: 68:[14, 84, 2] Operation: 79-77=2 Exploring Operation: 84-14=70, Resulting Numbers: [77, 79, 70] Generated Node #0,2: 68:[77, 79, 70] Operation: 84-14=70 Exploring Operation: 84-77=7, Resulting Numbers: [79, 14, 7] Generated Node #0,3: 68:[79, 14, 7] Operation: 84-77=7 Exploring Operation: 84/14=6, Resulting Numbers: [77, 79, 6] Generated Node #0,4: 68:[77, 79, 6] Operation: 84/14=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[77, 14, 5], Operations: ['84-79=5'] Exploring Operation: 14-5=9, Resulting Numbers: [77, 9] Generated Node #0,0,0: 68:[77, 9] Operation: 14-5=9 Exploring Operation: 14+5=19, Resulting Numbers: [77, 19] Generated Node #0,0,1: 68:[77, 19] Operation: 14+5=19 Exploring Operation: 77-14=63, Resulting Numbers: [5, 63] Generated Node #0,0,2: 68:[5, 63] Operation: 77-14=63 Exploring Operation: 14*5=70, Resulting Numbers: [77, 70] Generated Node #0,0,3: 68:[77, 70] Operation: 14*5=70 Exploring Operation: 77-5=72, Resulting Numbers: [14, 72] Generated Node #0,0,4: 68:[14, 72] Operation: 77-5=72 Moving to Node #0,0,2 Current State: 68:[5, 63], Operations: ['84-79=5', '77-14=63'] Exploring Operation: 63-5=58, Resulting Numbers: [58] 58,68 unequal: No Solution Exploring Operation: 5+63=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[77, 79, 14, 84], Operations: [] Exploring Operation: 84-79=5, Resulting Numbers: [77, 14, 5] Generated Node #0,0: 68:[77, 14, 5] Operation: 84-79=5 Moving to Node #0,0 Current State: 68:[77, 14, 5], Operations: ['84-79=5'] Exploring Operation: 77-14=63, Resulting Numbers: [5, 63] Generated Node #0,0,2: 68:[5, 63] Operation: 77-14=63 Moving to Node #0,0,2 Current State: 68:[5, 63], Operations: ['84-79=5', '77-14=63'] Exploring Operation: 5+63=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 49, 39, 61, 46 ]
19
[ "49+39=88", "61+46=107", "107-88=19" ]
Current State: 19:[49, 39, 61, 46], Operations: [] Exploring Operation: 49+39=88, Resulting Numbers: [61, 46, 88] Generated Node #2: [61, 46, 88] from Operation: 49+39=88 Current State: 19:[61, 46, 88], Operations: ['49+39=88'] Exploring Operation: 61+46=107, Resulting Numbers: [88, 107] Generated Node #3: [88, 107] from Operation: 61+46=107 Current State: 19:[88, 107], Operations: ['49+39=88', '61+46=107'] Exploring Operation: 107-88=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[49, 39, 61, 46], Operations: [] Exploring Operation: 61-39=22, Resulting Numbers: [49, 46, 22] Generated Node #0,0: 19:[49, 46, 22] Operation: 61-39=22 Exploring Operation: 61-46=15, Resulting Numbers: [49, 39, 15] Generated Node #0,1: 19:[49, 39, 15] Operation: 61-46=15 Exploring Operation: 61-49=12, Resulting Numbers: [39, 46, 12] Generated Node #0,2: 19:[39, 46, 12] Operation: 61-49=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[49, 39, 15], Operations: ['61-46=15'] Exploring Operation: 49-39=10, Resulting Numbers: [15, 10] Generated Node #0,1,0: 19:[15, 10] Operation: 49-39=10 Exploring Operation: 39-15=24, Resulting Numbers: [49, 24] Generated Node #0,1,1: 19:[49, 24] Operation: 39-15=24 Exploring Operation: 49-15=34, Resulting Numbers: [39, 34] Generated Node #0,1,2: 19:[39, 34] Operation: 49-15=34 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 19:[15, 10], Operations: ['61-46=15', '49-39=10'] Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,19 unequal: No Solution Exploring Operation: 15+10=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 15*10=150, Resulting Numbers: [150] 150,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 19:[49, 24], Operations: ['61-46=15', '39-15=24'] Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,19 unequal: No Solution Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 49*24=1176, Resulting Numbers: [1176] 1176,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 19:[39, 34], Operations: ['61-46=15', '49-15=34'] Exploring Operation: 39+34=73, Resulting Numbers: [73] 73,19 unequal: No Solution Exploring Operation: 39*34=1326, Resulting Numbers: [1326] 1326,19 unequal: No Solution Exploring Operation: 39-34=5, Resulting Numbers: [5] 5,19 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: 19:[39, 46, 12], Operations: ['61-49=12'] Exploring Operation: 39-12=27, Resulting Numbers: [46, 27] Generated Node #0,2,0: 19:[46, 27] Operation: 39-12=27 Exploring Operation: 46-39=7, Resulting Numbers: [12, 7] Generated Node #0,2,1: 19:[12, 7] Operation: 46-39=7 Exploring Operation: 46-12=34, Resulting Numbers: [39, 34] Generated Node #0,2,2: 19:[39, 34] Operation: 46-12=34 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 19:[12, 7], Operations: ['61-49=12', '46-39=7'] Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[49, 39, 61, 46], Operations: [] Exploring Operation: 61-49=12, Resulting Numbers: [39, 46, 12] Generated Node #0,2: 19:[39, 46, 12] Operation: 61-49=12 Moving to Node #0,2 Current State: 19:[39, 46, 12], Operations: ['61-49=12'] Exploring Operation: 46-39=7, Resulting Numbers: [12, 7] Generated Node #0,2,1: 19:[12, 7] Operation: 46-39=7 Moving to Node #0,2,1 Current State: 19:[12, 7], Operations: ['61-49=12', '46-39=7'] Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 88, 60, 95, 83 ]
30
[ "88+60=148", "95+83=178", "178-148=30" ]
Current State: 30:[88, 60, 95, 83], Operations: [] Exploring Operation: 88+60=148, Resulting Numbers: [95, 83, 148] Generated Node #2: [95, 83, 148] from Operation: 88+60=148 Current State: 30:[95, 83, 148], Operations: ['88+60=148'] Exploring Operation: 95+83=178, Resulting Numbers: [148, 178] Generated Node #3: [148, 178] from Operation: 95+83=178 Current State: 30:[148, 178], Operations: ['88+60=148', '95+83=178'] Exploring Operation: 178-148=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[88, 60, 95, 83], Operations: [] Exploring Operation: 95-60=35, Resulting Numbers: [88, 83, 35] Generated Node #0,0: 30:[88, 83, 35] Operation: 95-60=35 Exploring Operation: 95-83=12, Resulting Numbers: [88, 60, 12] Generated Node #0,1: 30:[88, 60, 12] Operation: 95-83=12 Exploring Operation: 95-88=7, Resulting Numbers: [60, 83, 7] Generated Node #0,2: 30:[60, 83, 7] Operation: 95-88=7 Exploring Operation: 88-83=5, Resulting Numbers: [60, 95, 5] Generated Node #0,3: 30:[60, 95, 5] Operation: 88-83=5 Moving to Node #0,2 Current State: 30:[60, 83, 7], Operations: ['95-88=7'] Exploring Operation: 60-7=53, Resulting Numbers: [83, 53] Generated Node #0,2,0: 30:[83, 53] Operation: 60-7=53 Exploring Operation: 83-60=23, Resulting Numbers: [7, 23] Generated Node #0,2,1: 30:[7, 23] Operation: 83-60=23 Exploring Operation: 60+7=67, Resulting Numbers: [83, 67] Generated Node #0,2,2: 30:[83, 67] Operation: 60+7=67 Exploring Operation: 83-7=76, Resulting Numbers: [60, 76] Generated Node #0,2,3: 30:[60, 76] Operation: 83-7=76 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 30:[7, 23], Operations: ['95-88=7', '83-60=23'] Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[88, 60, 95, 83], Operations: [] Exploring Operation: 95-88=7, Resulting Numbers: [60, 83, 7] Generated Node #0,2: 30:[60, 83, 7] Operation: 95-88=7 Moving to Node #0,2 Current State: 30:[60, 83, 7], Operations: ['95-88=7'] Exploring Operation: 83-60=23, Resulting Numbers: [7, 23] Generated Node #0,2,1: 30:[7, 23] Operation: 83-60=23 Moving to Node #0,2,1 Current State: 30:[7, 23], Operations: ['95-88=7', '83-60=23'] Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 8, 88, 17, 39 ]
11
[ "88/8=11", "39-17=22", "22-11=11" ]
Current State: 11:[8, 88, 17, 39], Operations: [] Exploring Operation: 88/8=11, Resulting Numbers: [17, 39, 11] Generated Node #2: [17, 39, 11] from Operation: 88/8=11 Current State: 11:[17, 39, 11], Operations: ['88/8=11'] Exploring Operation: 39-17=22, Resulting Numbers: [11, 22] Generated Node #3: [11, 22] from Operation: 39-17=22 Current State: 11:[11, 22], Operations: ['88/8=11', '39-17=22'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[8, 88, 17, 39], Operations: [] Exploring Operation: 88-39=49, Resulting Numbers: [8, 17, 49] Generated Node #0,0: 11:[8, 17, 49] Operation: 88-39=49 Exploring Operation: 88/8=11, Resulting Numbers: [17, 39, 11] Generated Node #0,1: 11:[17, 39, 11] Operation: 88/8=11 Exploring Operation: 88-17=71, Resulting Numbers: [8, 39, 71] Generated Node #0,2: 11:[8, 39, 71] Operation: 88-17=71 Moving to Node #0,1 Current State: 11:[17, 39, 11], Operations: ['88/8=11'] Exploring Operation: 39-11=28, Resulting Numbers: [17, 28] Generated Node #0,1,0: 11:[17, 28] Operation: 39-11=28 Exploring Operation: 17-11=6, Resulting Numbers: [39, 6] Generated Node #0,1,1: 11:[39, 6] Operation: 17-11=6 Exploring Operation: 39-17=22, Resulting Numbers: [11, 22] Generated Node #0,1,2: 11:[11, 22] Operation: 39-17=22 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 11:[11, 22], Operations: ['88/8=11', '39-17=22'] Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[8, 88, 17, 39], Operations: [] Exploring Operation: 88/8=11, Resulting Numbers: [17, 39, 11] Generated Node #0,1: 11:[17, 39, 11] Operation: 88/8=11 Moving to Node #0,1 Current State: 11:[17, 39, 11], Operations: ['88/8=11'] Exploring Operation: 39-17=22, Resulting Numbers: [11, 22] Generated Node #0,1,2: 11:[11, 22] Operation: 39-17=22 Moving to Node #0,1,2 Current State: 11:[11, 22], Operations: ['88/8=11', '39-17=22'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 33, 8, 15, 35 ]
45
[ "33-8=25", "35-15=20", "25+20=45" ]
Current State: 45:[33, 8, 15, 35], Operations: [] Exploring Operation: 33-8=25, Resulting Numbers: [15, 35, 25] Generated Node #2: [15, 35, 25] from Operation: 33-8=25 Current State: 45:[15, 35, 25], Operations: ['33-8=25'] Exploring Operation: 35-15=20, Resulting Numbers: [25, 20] Generated Node #3: [25, 20] from Operation: 35-15=20 Current State: 45:[25, 20], Operations: ['33-8=25', '35-15=20'] Exploring Operation: 25+20=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[33, 8, 15, 35], Operations: [] Exploring Operation: 33+15=48, Resulting Numbers: [8, 35, 48] Generated Node #0,0: 45:[8, 35, 48] Operation: 33+15=48 Exploring Operation: 33+8=41, Resulting Numbers: [15, 35, 41] Generated Node #0,1: 45:[15, 35, 41] Operation: 33+8=41 Exploring Operation: 35-33=2, Resulting Numbers: [8, 15, 2] Generated Node #0,2: 45:[8, 15, 2] Operation: 35-33=2 Moving to Node #0,2 Current State: 45:[8, 15, 2], Operations: ['35-33=2'] Exploring Operation: 8-2=6, Resulting Numbers: [15, 6] Generated Node #0,2,0: 45:[15, 6] Operation: 8-2=6 Exploring Operation: 8*2=16, Resulting Numbers: [15, 16] Generated Node #0,2,1: 45:[15, 16] Operation: 8*2=16 Exploring Operation: 8+2=10, Resulting Numbers: [15, 10] Generated Node #0,2,2: 45:[15, 10] Operation: 8+2=10 Moving to Node #0,0 Current State: 45:[8, 35, 48], Operations: ['33+15=48'] Exploring Operation: 8+35=43, Resulting Numbers: [48, 43] Generated Node #0,0,0: 45:[48, 43] Operation: 8+35=43 Exploring Operation: 48-35=13, Resulting Numbers: [8, 13] Generated Node #0,0,1: 45:[8, 13] Operation: 48-35=13 Exploring Operation: 48/8=6, Resulting Numbers: [35, 6] Generated Node #0,0,2: 45:[35, 6] Operation: 48/8=6 Moving to Node #0,1 Current State: 45:[15, 35, 41], Operations: ['33+8=41'] Exploring Operation: 35-15=20, Resulting Numbers: [41, 20] Generated Node #0,1,0: 45:[41, 20] Operation: 35-15=20 Exploring Operation: 15+35=50, Resulting Numbers: [41, 50] Generated Node #0,1,1: 45:[41, 50] Operation: 15+35=50 Exploring Operation: 41-35=6, Resulting Numbers: [15, 6] Generated Node #0,1,2: 45:[15, 6] Operation: 41-35=6 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[15, 6], Operations: ['33+8=41', '41-35=6'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,45 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,45 unequal: No Solution Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,45 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 #0,1,0 Current State: 45:[41, 20], Operations: ['33+8=41', '35-15=20'] Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,45 unequal: No Solution Exploring Operation: 41+20=61, Resulting Numbers: [61] 61,45 unequal: No Solution Exploring Operation: 41*20=820, Resulting Numbers: [820] 820,45 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 #0,1,1 Current State: 45:[41, 50], Operations: ['33+8=41', '15+35=50'] Exploring Operation: 41*50=2050, Resulting Numbers: [2050] 2050,45 unequal: No Solution Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,45 unequal: No Solution Exploring Operation: 41+50=91, Resulting Numbers: [91] 91,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 45:[15, 6], Operations: ['35-33=2', '8-2=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,45 unequal: No Solution Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,45 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,45 unequal: No Solution Moving to Node #0,2,2 Current State: 45:[15, 10], Operations: ['35-33=2', '8+2=10'] 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 Exploring Operation: 15*10=150, Resulting Numbers: [150] 150,45 unequal: No Solution Moving to Node #0,2,1 Current State: 45:[15, 16], Operations: ['35-33=2', '8*2=16'] Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,45 unequal: No Solution Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,45 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[8, 13], Operations: ['33+15=48', '48-35=13'] Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,45 unequal: No Solution Exploring Operation: 8*13=104, Resulting Numbers: [104] 104,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[48, 43], Operations: ['33+15=48', '8+35=43'] Exploring Operation: 48*43=2064, Resulting Numbers: [2064] 2064,45 unequal: No Solution Exploring Operation: 48-43=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 48+43=91, Resulting Numbers: [91] 91,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[35, 6], Operations: ['33+15=48', '48/8=6'] Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,45 unequal: No Solution Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,45 unequal: No Solution Exploring Operation: 35*6=210, Resulting Numbers: [210] 210,45 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 23, 45, 13, 32 ]
19
[ "45*13=585", "23+585=608", "608/32=19" ]
Current State: 19:[23, 45, 13, 32], Operations: [] Exploring Operation: 45*13=585, Resulting Numbers: [23, 32, 585] Generated Node #2: [23, 32, 585] from Operation: 45*13=585 Current State: 19:[23, 32, 585], Operations: ['45*13=585'] Exploring Operation: 23+585=608, Resulting Numbers: [32, 608] Generated Node #3: [32, 608] from Operation: 23+585=608 Current State: 19:[32, 608], Operations: ['45*13=585', '23+585=608'] Exploring Operation: 608/32=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[23, 45, 13, 32], Operations: [] Exploring Operation: 45-13=32, Resulting Numbers: [23, 32, 32] Generated Node #0,0: 19:[23, 32, 32] Operation: 45-13=32 Exploring Operation: 45-23=22, Resulting Numbers: [13, 32, 22] Generated Node #0,1: 19:[13, 32, 22] Operation: 45-23=22 Exploring Operation: 32-13=19, Resulting Numbers: [23, 45, 19] Generated Node #0,2: 19:[23, 45, 19] Operation: 32-13=19 Exploring Operation: 32-23=9, Resulting Numbers: [45, 13, 9] Generated Node #0,3: 19:[45, 13, 9] Operation: 32-23=9 Exploring Operation: 45-32=13, Resulting Numbers: [23, 13, 13] Generated Node #0,4: 19:[23, 13, 13] Operation: 45-32=13 Start Sub Search at level 1: Moving to Node #0,4 Current State: 19:[23, 13, 13], Operations: ['45-32=13'] Exploring Operation: 23+13=36, Resulting Numbers: [13, 36] Generated Node #0,4,0: 19:[13, 36] Operation: 23+13=36 Exploring Operation: 23-13=10, Resulting Numbers: [13, 10] Generated Node #0,4,1: 19:[13, 10] Operation: 23-13=10 Exploring Operation: 23-13=10, Resulting Numbers: [13, 10] Generated Node #0,4,2: 19:[13, 10] Operation: 23-13=10 Exploring Operation: 13/13=1, Resulting Numbers: [23, 1] Generated Node #0,4,3: 19:[23, 1] Operation: 13/13=1 Exploring Operation: 13+13=26, Resulting Numbers: [23, 26] Generated Node #0,4,4: 19:[23, 26] Operation: 13+13=26 Moving to Node #0,4,4 Current State: 19:[23, 26], Operations: ['45-32=13', '13+13=26'] Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,19 unequal: No Solution Exploring Operation: 23*26=598, Resulting Numbers: [598] 598,19 unequal: No Solution Moving to Node #0,4,2 Current State: 19:[13, 10], Operations: ['45-32=13', '23-13=10'] Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,19 unequal: No Solution Moving to Node #0,4,1 Current State: 19:[13, 10], Operations: ['45-32=13', '23-13=10'] Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,19 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,19 unequal: No Solution Moving to Node #0,4,3 Current State: 19:[23, 1], Operations: ['45-32=13', '13/13=1'] Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,19 unequal: No Solution Moving to Node #0,4,0 Current State: 19:[13, 36], Operations: ['45-32=13', '23+13=36'] Exploring Operation: 13*36=468, Resulting Numbers: [468] 468,19 unequal: No Solution Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,19 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,19 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:[13, 32, 22], Operations: ['45-23=22'] Exploring Operation: 13+32=45, Resulting Numbers: [22, 45] Generated Node #0,1,0: 19:[22, 45] Operation: 13+32=45 Exploring Operation: 13+22=35, Resulting Numbers: [32, 35] Generated Node #0,1,1: 19:[32, 35] Operation: 13+22=35 Exploring Operation: 22-13=9, Resulting Numbers: [32, 9] Generated Node #0,1,2: 19:[32, 9] Operation: 22-13=9 Exploring Operation: 32-13=19, Resulting Numbers: [22, 19] Generated Node #0,1,3: 19:[22, 19] Operation: 32-13=19 Exploring Operation: 32-22=10, Resulting Numbers: [13, 10] Generated Node #0,1,4: 19:[13, 10] Operation: 32-22=10 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 19:[22, 19], Operations: ['45-23=22', '32-13=19'] Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,19 unequal: No Solution Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 19:[13, 10], Operations: ['45-23=22', '32-22=10'] Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 19:[32, 9], Operations: ['45-23=22', '22-13=9'] Exploring Operation: 32*9=288, Resulting Numbers: [288] 288,19 unequal: No Solution Exploring Operation: 32+9=41, Resulting Numbers: [41] 41,19 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 19:[22, 45], Operations: ['45-23=22', '13+32=45'] Exploring Operation: 22*45=990, Resulting Numbers: [990] 990,19 unequal: No Solution Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 22+45=67, Resulting Numbers: [67] 67,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 19:[32, 35], Operations: ['45-23=22', '13+22=35'] Exploring Operation: 32+35=67, Resulting Numbers: [67] 67,19 unequal: No Solution Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 32*35=1120, Resulting Numbers: [1120] 1120,19 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: 19:[23, 32, 32], Operations: ['45-13=32'] Exploring Operation: 32-32=0, Resulting Numbers: [23, 0] Generated Node #0,0,0: 19:[23, 0] Operation: 32-32=0 Exploring Operation: 23+32=55, Resulting Numbers: [32, 55] Generated Node #0,0,1: 19:[32, 55] Operation: 23+32=55 Exploring Operation: 32/32=1, Resulting Numbers: [23, 1] Generated Node #0,0,2: 19:[23, 1] Operation: 32/32=1 Exploring Operation: 32-23=9, Resulting Numbers: [32, 9] Generated Node #0,0,3: 19:[32, 9] Operation: 32-23=9 Exploring Operation: 32-23=9, Resulting Numbers: [32, 9] Generated Node #0,0,4: 19:[32, 9] Operation: 32-23=9 Moving to Node #0,0,2 Current State: 19:[23, 1], Operations: ['45-13=32', '32/32=1'] Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,19 unequal: No Solution Moving to Node #0,0,3 Current State: 19:[32, 9], Operations: ['45-13=32', '32-23=9'] Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 32+9=41, Resulting Numbers: [41] 41,19 unequal: No Solution Exploring Operation: 32*9=288, Resulting Numbers: [288] 288,19 unequal: No Solution Moving to Node #0,0,0 Current State: 19:[23, 0], Operations: ['45-13=32', '32-32=0'] Exploring Operation: 23+0=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 23-0=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 23*0=0, Resulting Numbers: [0] 0,19 unequal: No Solution Moving to Node #0,0,4 Current State: 19:[32, 9], Operations: ['45-13=32', '32-23=9'] Exploring Operation: 32*9=288, Resulting Numbers: [288] 288,19 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 32+9=41, Resulting Numbers: [41] 41,19 unequal: No Solution Moving to Node #0,0,1 Current State: 19:[32, 55], Operations: ['45-13=32', '23+32=55'] Exploring Operation: 32*55=1760, Resulting Numbers: [1760] 1760,19 unequal: No Solution Exploring Operation: 32+55=87, Resulting Numbers: [87] 87,19 unequal: No Solution Exploring Operation: 55-32=23, Resulting Numbers: [23] 23,19 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:[23, 45, 19], Operations: ['32-13=19'] Exploring Operation: 23+45=68, Resulting Numbers: [19, 68] Generated Node #0,2,0: 19:[19, 68] Operation: 23+45=68 Exploring Operation: 23-19=4, Resulting Numbers: [45, 4] Generated Node #0,2,1: 19:[45, 4] Operation: 23-19=4 Exploring Operation: 45-19=26, Resulting Numbers: [23, 26] Generated Node #0,2,2: 19:[23, 26] Operation: 45-19=26 Exploring Operation: 45-23=22, Resulting Numbers: [19, 22] Generated Node #0,2,3: 19:[19, 22] Operation: 45-23=22 Exploring Operation: 23+19=42, Resulting Numbers: [45, 42] Generated Node #0,2,4: 19:[45, 42] Operation: 23+19=42 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 19:[19, 22], Operations: ['32-13=19', '45-23=22'] Exploring Operation: 19*22=418, Resulting Numbers: [418] 418,19 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 19:[23, 26], Operations: ['32-13=19', '45-19=26'] Exploring Operation: 23*26=598, Resulting Numbers: [598] 598,19 unequal: No Solution Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 19:[45, 4], Operations: ['32-13=19', '23-19=4'] Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,19 unequal: No Solution Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,19 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 19:[19, 68], Operations: ['32-13=19', '23+45=68'] Exploring Operation: 19+68=87, Resulting Numbers: [87] 87,19 unequal: No Solution Exploring Operation: 19*68=1292, Resulting Numbers: [1292] 1292,19 unequal: No Solution Exploring Operation: 68-19=49, Resulting Numbers: [49] 49,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 19:[45, 42], Operations: ['32-13=19', '23+19=42'] Exploring Operation: 45*42=1890, Resulting Numbers: [1890] 1890,19 unequal: No Solution Exploring Operation: 45+42=87, Resulting Numbers: [87] 87,19 unequal: No Solution Exploring Operation: 45-42=3, Resulting Numbers: [3] 3,19 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: 19:[45, 13, 9], Operations: ['32-23=9'] Exploring Operation: 45-13=32, Resulting Numbers: [9, 32] Generated Node #0,3,0: 19:[9, 32] Operation: 45-13=32 Exploring Operation: 45-9=36, Resulting Numbers: [13, 36] Generated Node #0,3,1: 19:[13, 36] Operation: 45-9=36 Exploring Operation: 45+9=54, Resulting Numbers: [13, 54] Generated Node #0,3,2: 19:[13, 54] Operation: 45+9=54 Exploring Operation: 13+9=22, Resulting Numbers: [45, 22] Generated Node #0,3,3: 19:[45, 22] Operation: 13+9=22 Exploring Operation: 45/9=5, Resulting Numbers: [13, 5] Generated Node #0,3,4: 19:[13, 5] Operation: 45/9=5 Moving to Node #0,3,4 Current State: 19:[13, 5], Operations: ['32-23=9', '45/9=5'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,19 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,19 unequal: No Solution Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,19 unequal: No Solution Moving to Node #0,3,1 Current State: 19:[13, 36], Operations: ['32-23=9', '45-9=36'] Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,19 unequal: No Solution Exploring Operation: 13*36=468, Resulting Numbers: [468] 468,19 unequal: No Solution Moving to Node #0,3,0 Current State: 19:[9, 32], Operations: ['32-23=9', '45-13=32'] Exploring Operation: 9*32=288, Resulting Numbers: [288] 288,19 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,19 unequal: No Solution Exploring Operation: 9+32=41, Resulting Numbers: [41] 41,19 unequal: No Solution Moving to Node #0,3,3 Current State: 19:[45, 22], Operations: ['32-23=9', '13+9=22'] Exploring Operation: 45*22=990, Resulting Numbers: [990] 990,19 unequal: No Solution Exploring Operation: 45+22=67, Resulting Numbers: [67] 67,19 unequal: No Solution Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,19 unequal: No Solution Moving to Node #0,3,2 Current State: 19:[13, 54], Operations: ['32-23=9', '45+9=54'] Exploring Operation: 13+54=67, Resulting Numbers: [67] 67,19 unequal: No Solution Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,19 unequal: No Solution Exploring Operation: 13*54=702, Resulting Numbers: [702] 702,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 24, 89, 52, 93 ]
72
[ "24+89=113", "93-52=41", "113-41=72" ]
Current State: 72:[24, 89, 52, 93], Operations: [] Exploring Operation: 24+89=113, Resulting Numbers: [52, 93, 113] Generated Node #2: [52, 93, 113] from Operation: 24+89=113 Current State: 72:[52, 93, 113], Operations: ['24+89=113'] Exploring Operation: 93-52=41, Resulting Numbers: [113, 41] Generated Node #3: [113, 41] from Operation: 93-52=41 Current State: 72:[113, 41], Operations: ['24+89=113', '93-52=41'] Exploring Operation: 113-41=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[24, 89, 52, 93], Operations: [] Exploring Operation: 93-52=41, Resulting Numbers: [24, 89, 41] Generated Node #0,0: 72:[24, 89, 41] Operation: 93-52=41 Exploring Operation: 89-52=37, Resulting Numbers: [24, 93, 37] Generated Node #0,1: 72:[24, 93, 37] Operation: 89-52=37 Exploring Operation: 93-89=4, Resulting Numbers: [24, 52, 4] Generated Node #0,2: 72:[24, 52, 4] Operation: 93-89=4 Exploring Operation: 24+52=76, Resulting Numbers: [89, 93, 76] Generated Node #0,3: 72:[89, 93, 76] Operation: 24+52=76 Exploring Operation: 93-24=69, Resulting Numbers: [89, 52, 69] Generated Node #0,4: 72:[89, 52, 69] Operation: 93-24=69 Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[24, 52, 4], Operations: ['93-89=4'] Exploring Operation: 24+52=76, Resulting Numbers: [4, 76] Generated Node #0,2,0: 72:[4, 76] Operation: 24+52=76 Exploring Operation: 52/4=13, Resulting Numbers: [24, 13] Generated Node #0,2,1: 72:[24, 13] Operation: 52/4=13 Exploring Operation: 52-4=48, Resulting Numbers: [24, 48] Generated Node #0,2,2: 72:[24, 48] Operation: 52-4=48 Exploring Operation: 24/4=6, Resulting Numbers: [52, 6] Generated Node #0,2,3: 72:[52, 6] Operation: 24/4=6 Exploring Operation: 52-24=28, Resulting Numbers: [4, 28] Generated Node #0,2,4: 72:[4, 28] Operation: 52-24=28 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 72:[24, 13], Operations: ['93-89=4', '52/4=13'] Exploring Operation: 24+13=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 24*13=312, Resulting Numbers: [312] 312,72 unequal: No Solution Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,72 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 #0,2,0 Current State: 72:[4, 76], Operations: ['93-89=4', '24+52=76'] Exploring Operation: 76/4=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 76-4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[24, 89, 52, 93], Operations: [] Exploring Operation: 93-89=4, Resulting Numbers: [24, 52, 4] Generated Node #0,2: 72:[24, 52, 4] Operation: 93-89=4 Moving to Node #0,2 Current State: 72:[24, 52, 4], Operations: ['93-89=4'] Exploring Operation: 24+52=76, Resulting Numbers: [4, 76] Generated Node #0,2,0: 72:[4, 76] Operation: 24+52=76 Moving to Node #0,2,0 Current State: 72:[4, 76], Operations: ['93-89=4', '24+52=76'] Exploring Operation: 76-4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 93, 94, 26, 90 ]
71
[ "93+94=187", "26+90=116", "187-116=71" ]
Current State: 71:[93, 94, 26, 90], Operations: [] Exploring Operation: 93+94=187, Resulting Numbers: [26, 90, 187] Generated Node #2: [26, 90, 187] from Operation: 93+94=187 Current State: 71:[26, 90, 187], Operations: ['93+94=187'] Exploring Operation: 26+90=116, Resulting Numbers: [187, 116] Generated Node #3: [187, 116] from Operation: 26+90=116 Current State: 71:[187, 116], Operations: ['93+94=187', '26+90=116'] Exploring Operation: 187-116=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[93, 94, 26, 90], Operations: [] Exploring Operation: 93-26=67, Resulting Numbers: [94, 90, 67] Generated Node #0,0: 71:[94, 90, 67] Operation: 93-26=67 Exploring Operation: 90-26=64, Resulting Numbers: [93, 94, 64] Generated Node #0,1: 71:[93, 94, 64] Operation: 90-26=64 Exploring Operation: 94-26=68, Resulting Numbers: [93, 90, 68] Generated Node #0,2: 71:[93, 90, 68] Operation: 94-26=68 Exploring Operation: 93+26=119, Resulting Numbers: [94, 90, 119] Generated Node #0,3: 71:[94, 90, 119] Operation: 93+26=119 Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[93, 90, 68], Operations: ['94-26=68'] Exploring Operation: 93+68=161, Resulting Numbers: [90, 161] Generated Node #0,2,0: 71:[90, 161] Operation: 93+68=161 Exploring Operation: 93-90=3, Resulting Numbers: [68, 3] Generated Node #0,2,1: 71:[68, 3] Operation: 93-90=3 Exploring Operation: 90-68=22, Resulting Numbers: [93, 22] Generated Node #0,2,2: 71:[93, 22] Operation: 90-68=22 Exploring Operation: 93-68=25, Resulting Numbers: [90, 25] Generated Node #0,2,3: 71:[90, 25] Operation: 93-68=25 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 71:[90, 25], Operations: ['94-26=68', '93-68=25'] Exploring Operation: 90*25=2250, Resulting Numbers: [2250] 2250,71 unequal: No Solution Exploring Operation: 90-25=65, Resulting Numbers: [65] 65,71 unequal: No Solution Exploring Operation: 90+25=115, Resulting Numbers: [115] 115,71 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:[68, 3], Operations: ['94-26=68', '93-90=3'] Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[93, 94, 26, 90], Operations: [] Exploring Operation: 94-26=68, Resulting Numbers: [93, 90, 68] Generated Node #0,2: 71:[93, 90, 68] Operation: 94-26=68 Moving to Node #0,2 Current State: 71:[93, 90, 68], Operations: ['94-26=68'] Exploring Operation: 93-90=3, Resulting Numbers: [68, 3] Generated Node #0,2,1: 71:[68, 3] Operation: 93-90=3 Moving to Node #0,2,1 Current State: 71:[68, 3], Operations: ['94-26=68', '93-90=3'] Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 42, 94, 2, 46 ]
20
[ "94-42=52", "52/2=26", "46-26=20" ]
Current State: 20:[42, 94, 2, 46], Operations: [] Exploring Operation: 94-42=52, Resulting Numbers: [2, 46, 52] Generated Node #2: [2, 46, 52] from Operation: 94-42=52 Current State: 20:[2, 46, 52], Operations: ['94-42=52'] Exploring Operation: 52/2=26, Resulting Numbers: [46, 26] Generated Node #3: [46, 26] from Operation: 52/2=26 Current State: 20:[46, 26], Operations: ['94-42=52', '52/2=26'] Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[42, 94, 2, 46], Operations: [] Exploring Operation: 46/2=23, Resulting Numbers: [42, 94, 23] Generated Node #0,0: 20:[42, 94, 23] Operation: 46/2=23 Exploring Operation: 94-46=48, Resulting Numbers: [42, 2, 48] Generated Node #0,1: 20:[42, 2, 48] Operation: 94-46=48 Exploring Operation: 94/2=47, Resulting Numbers: [42, 46, 47] Generated Node #0,2: 20:[42, 46, 47] Operation: 94/2=47 Exploring Operation: 94-42=52, Resulting Numbers: [2, 46, 52] Generated Node #0,3: 20:[2, 46, 52] Operation: 94-42=52 Exploring Operation: 46-42=4, Resulting Numbers: [94, 2, 4] Generated Node #0,4: 20:[94, 2, 4] Operation: 46-42=4 Moving to Node #0,1 Current State: 20:[42, 2, 48], Operations: ['94-46=48'] Exploring Operation: 42/2=21, Resulting Numbers: [48, 21] Generated Node #0,1,0: 20:[48, 21] Operation: 42/2=21 Exploring Operation: 42-2=40, Resulting Numbers: [48, 40] Generated Node #0,1,1: 20:[48, 40] Operation: 42-2=40 Exploring Operation: 48/2=24, Resulting Numbers: [42, 24] Generated Node #0,1,2: 20:[42, 24] Operation: 48/2=24 Exploring Operation: 48-2=46, Resulting Numbers: [42, 46] Generated Node #0,1,3: 20:[42, 46] Operation: 48-2=46 Exploring Operation: 48-42=6, Resulting Numbers: [2, 6] Generated Node #0,1,4: 20:[2, 6] Operation: 48-42=6 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 20:[2, 6], Operations: ['94-46=48', '48-42=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,20 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 20:[42, 24], Operations: ['94-46=48', '48/2=24'] Exploring Operation: 42*24=1008, Resulting Numbers: [1008] 1008,20 unequal: No Solution Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,20 unequal: No Solution Exploring Operation: 42+24=66, Resulting Numbers: [66] 66,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 20:[48, 21], Operations: ['94-46=48', '42/2=21'] Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,20 unequal: No Solution Exploring Operation: 48+21=69, Resulting Numbers: [69] 69,20 unequal: No Solution Exploring Operation: 48*21=1008, Resulting Numbers: [1008] 1008,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 20:[48, 40], Operations: ['94-46=48', '42-2=40'] Exploring Operation: 48+40=88, Resulting Numbers: [88] 88,20 unequal: No Solution Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 48*40=1920, Resulting Numbers: [1920] 1920,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 20:[42, 46], Operations: ['94-46=48', '48-2=46'] Exploring Operation: 42*46=1932, Resulting Numbers: [1932] 1932,20 unequal: No Solution Exploring Operation: 42+46=88, Resulting Numbers: [88] 88,20 unequal: No Solution Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,20 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: 20:[2, 46, 52], Operations: ['94-42=52'] Exploring Operation: 52-2=50, Resulting Numbers: [46, 50] Generated Node #0,3,0: 20:[46, 50] Operation: 52-2=50 Exploring Operation: 46/2=23, Resulting Numbers: [52, 23] Generated Node #0,3,1: 20:[52, 23] Operation: 46/2=23 Exploring Operation: 52/2=26, Resulting Numbers: [46, 26] Generated Node #0,3,2: 20:[46, 26] Operation: 52/2=26 Exploring Operation: 52-46=6, Resulting Numbers: [2, 6] Generated Node #0,3,3: 20:[2, 6] Operation: 52-46=6 Exploring Operation: 46-2=44, Resulting Numbers: [52, 44] Generated Node #0,3,4: 20:[52, 44] Operation: 46-2=44 Moving to Node #0,4 Current State: 20:[94, 2, 4], Operations: ['46-42=4'] Exploring Operation: 4/2=2, Resulting Numbers: [94, 2] Generated Node #0,4,0: 20:[94, 2] Operation: 4/2=2 Exploring Operation: 94-4=90, Resulting Numbers: [2, 90] Generated Node #0,4,1: 20:[2, 90] Operation: 94-4=90 Exploring Operation: 4-2=2, Resulting Numbers: [94, 2] Generated Node #0,4,2: 20:[94, 2] Operation: 4-2=2 Exploring Operation: 94-2=92, Resulting Numbers: [4, 92] Generated Node #0,4,3: 20:[4, 92] Operation: 94-2=92 Exploring Operation: 94/2=47, Resulting Numbers: [4, 47] Generated Node #0,4,4: 20:[4, 47] Operation: 94/2=47 Moving to Node #0,2 Current State: 20:[42, 46, 47], Operations: ['94/2=47'] Exploring Operation: 46-42=4, Resulting Numbers: [47, 4] Generated Node #0,2,0: 20:[47, 4] Operation: 46-42=4 Exploring Operation: 42+46=88, Resulting Numbers: [47, 88] Generated Node #0,2,1: 20:[47, 88] Operation: 42+46=88 Exploring Operation: 47-46=1, Resulting Numbers: [42, 1] Generated Node #0,2,2: 20:[42, 1] Operation: 47-46=1 Exploring Operation: 47-42=5, Resulting Numbers: [46, 5] Generated Node #0,2,3: 20:[46, 5] Operation: 47-42=5 Exploring Operation: 42+47=89, Resulting Numbers: [46, 89] Generated Node #0,2,4: 20:[46, 89] Operation: 42+47=89 Moving to Node #0,0 Current State: 20:[42, 94, 23], Operations: ['46/2=23'] Exploring Operation: 94-42=52, Resulting Numbers: [23, 52] Generated Node #0,0,0: 20:[23, 52] Operation: 94-42=52 Exploring Operation: 42+94=136, Resulting Numbers: [23, 136] Generated Node #0,0,1: 20:[23, 136] Operation: 42+94=136 Exploring Operation: 42-23=19, Resulting Numbers: [94, 19] Generated Node #0,0,2: 20:[94, 19] Operation: 42-23=19 Exploring Operation: 42+23=65, Resulting Numbers: [94, 65] Generated Node #0,0,3: 20:[94, 65] Operation: 42+23=65 Exploring Operation: 94-23=71, Resulting Numbers: [42, 71] Generated Node #0,0,4: 20:[42, 71] Operation: 94-23=71 Moving to Node #0,3,3 Current State: 20:[2, 6], Operations: ['94-42=52', '52-46=6'] Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,20 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,20 unequal: No Solution Moving to Node #0,2,2 Current State: 20:[42, 1], Operations: ['94/2=47', '47-46=1'] Exploring Operation: 42+1=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 42-1=41, Resulting Numbers: [41] 41,20 unequal: No Solution Exploring Operation: 42/1=42, Resulting Numbers: [42] 42,20 unequal: No Solution Exploring Operation: 42*1=42, Resulting Numbers: [42] 42,20 unequal: No Solution Moving to Node #0,2,3 Current State: 20:[46, 5], Operations: ['94/2=47', '47-42=5'] Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,20 unequal: No Solution Exploring Operation: 46+5=51, Resulting Numbers: [51] 51,20 unequal: No Solution Exploring Operation: 46*5=230, Resulting Numbers: [230] 230,20 unequal: No Solution Moving to Node #0,4,4 Current State: 20:[4, 47], Operations: ['46-42=4', '94/2=47'] Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,20 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,20 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,20 unequal: No Solution Moving to Node #0,2,0 Current State: 20:[47, 4], Operations: ['94/2=47', '46-42=4'] Exploring Operation: 47*4=188, Resulting Numbers: [188] 188,20 unequal: No Solution Exploring Operation: 47+4=51, Resulting Numbers: [51] 51,20 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,20 unequal: No Solution Moving to Node #0,3,2 Current State: 20:[46, 26], Operations: ['94-42=52', '52/2=26'] Exploring Operation: 46+26=72, Resulting Numbers: [72] 72,20 unequal: No Solution Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[42, 94, 2, 46], Operations: [] Exploring Operation: 94-42=52, Resulting Numbers: [2, 46, 52] Generated Node #0,3: 20:[2, 46, 52] Operation: 94-42=52 Moving to Node #0,3 Current State: 20:[2, 46, 52], Operations: ['94-42=52'] Exploring Operation: 52/2=26, Resulting Numbers: [46, 26] Generated Node #0,3,2: 20:[46, 26] Operation: 52/2=26 Moving to Node #0,3,2 Current State: 20:[46, 26], Operations: ['94-42=52', '52/2=26'] Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
0.940104
hs_5
sum_heuristic
[ 44, 36, 72, 90 ]
48
[ "90-44=46", "72/36=2", "46+2=48" ]
Current State: 48:[44, 36, 72, 90], Operations: [] Exploring Operation: 90-44=46, Resulting Numbers: [36, 72, 46] Generated Node #2: [36, 72, 46] from Operation: 90-44=46 Current State: 48:[36, 72, 46], Operations: ['90-44=46'] Exploring Operation: 72/36=2, Resulting Numbers: [46, 2] Generated Node #3: [46, 2] from Operation: 72/36=2 Current State: 48:[46, 2], Operations: ['90-44=46', '72/36=2'] Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[44, 36, 72, 90], Operations: [] Exploring Operation: 90-72=18, Resulting Numbers: [44, 36, 18] Generated Node #0,0: 48:[44, 36, 18] Operation: 90-72=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[44, 36, 18], Operations: ['90-72=18'] Exploring Operation: 44-36=8, Resulting Numbers: [18, 8] Generated Node #0,0,0: 48:[18, 8] Operation: 44-36=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[18, 8], Operations: ['90-72=18', '44-36=8'] Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 29, 36, 16, 78 ]
55
[ "36-29=7", "78-16=62", "62-7=55" ]
Current State: 55:[29, 36, 16, 78], Operations: [] Exploring Operation: 36-29=7, Resulting Numbers: [16, 78, 7] Generated Node #2: [16, 78, 7] from Operation: 36-29=7 Current State: 55:[16, 78, 7], Operations: ['36-29=7'] Exploring Operation: 78-16=62, Resulting Numbers: [7, 62] Generated Node #3: [7, 62] from Operation: 78-16=62 Current State: 55:[7, 62], Operations: ['36-29=7', '78-16=62'] Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[29, 36, 16, 78], Operations: [] Exploring Operation: 78-36=42, Resulting Numbers: [29, 16, 42] Generated Node #0,0: 55:[29, 16, 42] Operation: 78-36=42 Exploring Operation: 36-29=7, Resulting Numbers: [16, 78, 7] Generated Node #0,1: 55:[16, 78, 7] Operation: 36-29=7 Exploring Operation: 78-29=49, Resulting Numbers: [36, 16, 49] Generated Node #0,2: 55:[36, 16, 49] Operation: 78-29=49 Moving to Node #0,1 Current State: 55:[16, 78, 7], Operations: ['36-29=7'] Exploring Operation: 78-16=62, Resulting Numbers: [7, 62] Generated Node #0,1,0: 55:[7, 62] Operation: 78-16=62 Exploring Operation: 16-7=9, Resulting Numbers: [78, 9] Generated Node #0,1,1: 55:[78, 9] Operation: 16-7=9 Exploring Operation: 78-7=71, Resulting Numbers: [16, 71] Generated Node #0,1,2: 55:[16, 71] Operation: 78-7=71 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[7, 62], Operations: ['36-29=7', '78-16=62'] Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[29, 36, 16, 78], Operations: [] Exploring Operation: 36-29=7, Resulting Numbers: [16, 78, 7] Generated Node #0,1: 55:[16, 78, 7] Operation: 36-29=7 Moving to Node #0,1 Current State: 55:[16, 78, 7], Operations: ['36-29=7'] Exploring Operation: 78-16=62, Resulting Numbers: [7, 62] Generated Node #0,1,0: 55:[7, 62] Operation: 78-16=62 Moving to Node #0,1,0 Current State: 55:[7, 62], Operations: ['36-29=7', '78-16=62'] Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 8, 10, 62, 70 ]
61
[ "62-8=54", "70/10=7", "54+7=61" ]
Current State: 61:[8, 10, 62, 70], Operations: [] Exploring Operation: 62-8=54, Resulting Numbers: [10, 70, 54] Generated Node #2: [10, 70, 54] from Operation: 62-8=54 Current State: 61:[10, 70, 54], Operations: ['62-8=54'] Exploring Operation: 70/10=7, Resulting Numbers: [54, 7] Generated Node #3: [54, 7] from Operation: 70/10=7 Current State: 61:[54, 7], Operations: ['62-8=54', '70/10=7'] Exploring Operation: 54+7=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[8, 10, 62, 70], Operations: [] Exploring Operation: 8+10=18, Resulting Numbers: [62, 70, 18] Generated Node #0,0: 61:[62, 70, 18] Operation: 8+10=18 Exploring Operation: 70-8=62, Resulting Numbers: [10, 62, 62] Generated Node #0,1: 61:[10, 62, 62] Operation: 70-8=62 Exploring Operation: 8*10=80, Resulting Numbers: [62, 70, 80] Generated Node #0,2: 61:[62, 70, 80] Operation: 8*10=80 Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[62, 70, 80], Operations: ['8*10=80'] Exploring Operation: 80-70=10, Resulting Numbers: [62, 10] Generated Node #0,2,0: 61:[62, 10] Operation: 80-70=10 Exploring Operation: 80-62=18, Resulting Numbers: [70, 18] Generated Node #0,2,1: 61:[70, 18] Operation: 80-62=18 Exploring Operation: 70-62=8, Resulting Numbers: [80, 8] Generated Node #0,2,2: 61:[80, 8] Operation: 70-62=8 Moving to Node #0,2,0 Current State: 61:[62, 10], Operations: ['8*10=80', '80-70=10'] Exploring Operation: 62*10=620, Resulting Numbers: [620] 620,61 unequal: No Solution Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,61 unequal: No Solution Exploring Operation: 62+10=72, Resulting Numbers: [72] 72,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[70, 18], Operations: ['8*10=80', '80-62=18'] Exploring Operation: 70*18=1260, Resulting Numbers: [1260] 1260,61 unequal: No Solution Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,61 unequal: No Solution Exploring Operation: 70+18=88, Resulting Numbers: [88] 88,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[80, 8], Operations: ['8*10=80', '70-62=8'] Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 80+8=88, Resulting Numbers: [88] 88,61 unequal: No Solution Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[62, 70, 18], Operations: ['8+10=18'] Exploring Operation: 62+18=80, Resulting Numbers: [70, 80] Generated Node #0,0,0: 61:[70, 80] Operation: 62+18=80 Exploring Operation: 62-18=44, Resulting Numbers: [70, 44] Generated Node #0,0,1: 61:[70, 44] Operation: 62-18=44 Exploring Operation: 70-18=52, Resulting Numbers: [62, 52] Generated Node #0,0,2: 61:[62, 52] Operation: 70-18=52 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 61:[62, 52], Operations: ['8+10=18', '70-18=52'] Exploring Operation: 62-52=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 62*52=3224, Resulting Numbers: [3224] 3224,61 unequal: No Solution Exploring Operation: 62+52=114, Resulting Numbers: [114] 114,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 61:[70, 44], Operations: ['8+10=18', '62-18=44'] Exploring Operation: 70+44=114, Resulting Numbers: [114] 114,61 unequal: No Solution Exploring Operation: 70-44=26, Resulting Numbers: [26] 26,61 unequal: No Solution Exploring Operation: 70*44=3080, Resulting Numbers: [3080] 3080,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[70, 80], Operations: ['8+10=18', '62+18=80'] Exploring Operation: 70+80=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 70*80=5600, Resulting Numbers: [5600] 5600,61 unequal: No Solution Exploring Operation: 80-70=10, Resulting Numbers: [10] 10,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[10, 62, 62], Operations: ['70-8=62'] Exploring Operation: 62-10=52, Resulting Numbers: [62, 52] Generated Node #0,1,0: 61:[62, 52] Operation: 62-10=52 Exploring Operation: 10+62=72, Resulting Numbers: [62, 72] Generated Node #0,1,1: 61:[62, 72] Operation: 10+62=72 Exploring Operation: 62-10=52, Resulting Numbers: [62, 52] Generated Node #0,1,2: 61:[62, 52] Operation: 62-10=52 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[62, 52], Operations: ['70-8=62', '62-10=52'] Exploring Operation: 62-52=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 62+52=114, Resulting Numbers: [114] 114,61 unequal: No Solution Exploring Operation: 62*52=3224, Resulting Numbers: [3224] 3224,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 61:[62, 52], Operations: ['70-8=62', '62-10=52'] Exploring Operation: 62*52=3224, Resulting Numbers: [3224] 3224,61 unequal: No Solution Exploring Operation: 62-52=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 62+52=114, Resulting Numbers: [114] 114,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[62, 72], Operations: ['70-8=62', '10+62=72'] Exploring Operation: 62*72=4464, Resulting Numbers: [4464] 4464,61 unequal: No Solution Exploring Operation: 62+72=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 25, 3, 29, 13 ]
85
[ "25+13=38", "3*38=114", "114-29=85" ]
Current State: 85:[25, 3, 29, 13], Operations: [] Exploring Operation: 25+13=38, Resulting Numbers: [3, 29, 38] Generated Node #2: [3, 29, 38] from Operation: 25+13=38 Current State: 85:[3, 29, 38], Operations: ['25+13=38'] Exploring Operation: 3*38=114, Resulting Numbers: [29, 114] Generated Node #3: [29, 114] from Operation: 3*38=114 Current State: 85:[29, 114], Operations: ['25+13=38', '3*38=114'] Exploring Operation: 114-29=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[25, 3, 29, 13], Operations: [] Exploring Operation: 3*29=87, Resulting Numbers: [25, 13, 87] Generated Node #0,0: 85:[25, 13, 87] Operation: 3*29=87 Exploring Operation: 25-13=12, Resulting Numbers: [3, 29, 12] Generated Node #0,1: 85:[3, 29, 12] Operation: 25-13=12 Exploring Operation: 29-13=16, Resulting Numbers: [25, 3, 16] Generated Node #0,2: 85:[25, 3, 16] Operation: 29-13=16 Exploring Operation: 29-25=4, Resulting Numbers: [3, 13, 4] Generated Node #0,3: 85:[3, 13, 4] Operation: 29-25=4 Moving to Node #0,3 Current State: 85:[3, 13, 4], Operations: ['29-25=4'] Exploring Operation: 3+4=7, Resulting Numbers: [13, 7] Generated Node #0,3,0: 85:[13, 7] Operation: 3+4=7 Exploring Operation: 3+13=16, Resulting Numbers: [4, 16] Generated Node #0,3,1: 85:[4, 16] Operation: 3+13=16 Exploring Operation: 13+4=17, Resulting Numbers: [3, 17] Generated Node #0,3,2: 85:[3, 17] Operation: 13+4=17 Exploring Operation: 13-3=10, Resulting Numbers: [4, 10] Generated Node #0,3,3: 85:[4, 10] Operation: 13-3=10 Moving to Node #0,2 Current State: 85:[25, 3, 16], Operations: ['29-13=16'] Exploring Operation: 25*3=75, Resulting Numbers: [16, 75] Generated Node #0,2,0: 85:[16, 75] Operation: 25*3=75 Exploring Operation: 25-3=22, Resulting Numbers: [16, 22] Generated Node #0,2,1: 85:[16, 22] Operation: 25-3=22 Exploring Operation: 3+16=19, Resulting Numbers: [25, 19] Generated Node #0,2,2: 85:[25, 19] Operation: 3+16=19 Exploring Operation: 25-16=9, Resulting Numbers: [3, 9] Generated Node #0,2,3: 85:[3, 9] Operation: 25-16=9 Moving to Node #0,0 Current State: 85:[25, 13, 87], Operations: ['3*29=87'] Exploring Operation: 13+87=100, Resulting Numbers: [25, 100] Generated Node #0,0,0: 85:[25, 100] Operation: 13+87=100 Exploring Operation: 25+13=38, Resulting Numbers: [87, 38] Generated Node #0,0,1: 85:[87, 38] Operation: 25+13=38 Exploring Operation: 25-13=12, Resulting Numbers: [87, 12] Generated Node #0,0,2: 85:[87, 12] Operation: 25-13=12 Exploring Operation: 87-13=74, Resulting Numbers: [25, 74] Generated Node #0,0,3: 85:[25, 74] Operation: 87-13=74 Moving to Node #0,1 Current State: 85:[3, 29, 12], Operations: ['25-13=12'] Exploring Operation: 3*29=87, Resulting Numbers: [12, 87] Generated Node #0,1,0: 85:[12, 87] Operation: 3*29=87 Exploring Operation: 12/3=4, Resulting Numbers: [29, 4] Generated Node #0,1,1: 85:[29, 4] Operation: 12/3=4 Exploring Operation: 29-12=17, Resulting Numbers: [3, 17] Generated Node #0,1,2: 85:[3, 17] Operation: 29-12=17 Exploring Operation: 29-3=26, Resulting Numbers: [12, 26] Generated Node #0,1,3: 85:[12, 26] Operation: 29-3=26 Moving to Node #0,3,1 Current State: 85:[4, 16], Operations: ['29-25=4', '3+13=16'] Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[3, 17], Operations: ['25-13=12', '29-12=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,85 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,85 unequal: No Solution Moving to Node #0,3,2 Current State: 85:[3, 17], Operations: ['29-25=4', '13+4=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,85 unequal: No Solution Moving to Node #0,3,0 Current State: 85:[13, 7], Operations: ['29-25=4', '3+4=7'] Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,85 unequal: No Solution Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,85 unequal: No Solution Moving to Node #0,2,3 Current State: 85:[3, 9], Operations: ['29-13=16', '25-16=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,85 unequal: No Solution Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[16, 22], Operations: ['29-13=16', '25-3=22'] Exploring Operation: 16*22=352, Resulting Numbers: [352] 352,85 unequal: No Solution Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,85 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,85 unequal: No Solution Moving to Node #0,3,3 Current State: 85:[4, 10], Operations: ['29-25=4', '13-3=10'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[12, 87], Operations: ['25-13=12', '3*29=87'] Exploring Operation: 12+87=99, Resulting Numbers: [99] 99,85 unequal: No Solution Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,85 unequal: No Solution Exploring Operation: 12*87=1044, Resulting Numbers: [1044] 1044,85 unequal: No Solution Moving to Node #0,0,2 Current State: 85:[87, 12], Operations: ['3*29=87', '25-13=12'] Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,85 unequal: No Solution Exploring Operation: 87+12=99, Resulting Numbers: [99] 99,85 unequal: No Solution Exploring Operation: 87*12=1044, Resulting Numbers: [1044] 1044,85 unequal: No Solution Moving to Node #0,2,2 Current State: 85:[25, 19], Operations: ['29-13=16', '3+16=19'] Exploring Operation: 25*19=475, Resulting Numbers: [475] 475,85 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,85 unequal: No Solution Moving to Node #0,2,0 Current State: 85:[16, 75], Operations: ['29-13=16', '25*3=75'] Exploring Operation: 16*75=1200, Resulting Numbers: [1200] 1200,85 unequal: No Solution Exploring Operation: 16+75=91, Resulting Numbers: [91] 91,85 unequal: No Solution Exploring Operation: 75-16=59, Resulting Numbers: [59] 59,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[29, 4], Operations: ['25-13=12', '12/3=4'] Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 29*4=116, Resulting Numbers: [116] 116,85 unequal: No Solution Exploring Operation: 29+4=33, Resulting Numbers: [33] 33,85 unequal: No Solution Moving to Node #0,1,3 Current State: 85:[12, 26], Operations: ['25-13=12', '29-3=26'] Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 12*26=312, Resulting Numbers: [312] 312,85 unequal: No Solution Exploring Operation: 12+26=38, Resulting Numbers: [38] 38,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[25, 74], Operations: ['3*29=87', '87-13=74'] Exploring Operation: 25*74=1850, Resulting Numbers: [1850] 1850,85 unequal: No Solution Exploring Operation: 74-25=49, Resulting Numbers: [49] 49,85 unequal: No Solution Exploring Operation: 25+74=99, Resulting Numbers: [99] 99,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[25, 100], Operations: ['3*29=87', '13+87=100'] Exploring Operation: 25*100=2500, Resulting Numbers: [2500] 2500,85 unequal: No Solution Exploring Operation: 25+100=125, Resulting Numbers: [125] 125,85 unequal: No Solution Exploring Operation: 100-25=75, Resulting Numbers: [75] 75,85 unequal: No Solution Exploring Operation: 100/25=4, Resulting Numbers: [4] 4,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[87, 38], Operations: ['3*29=87', '25+13=38'] Exploring Operation: 87+38=125, Resulting Numbers: [125] 125,85 unequal: No Solution Exploring Operation: 87-38=49, Resulting Numbers: [49] 49,85 unequal: No Solution Exploring Operation: 87*38=3306, Resulting Numbers: [3306] 3306,85 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 26, 38, 25, 14 ]
26
[ "38-25=13", "14-13=1", "26*1=26" ]
Current State: 26:[26, 38, 25, 14], Operations: [] Exploring Operation: 38-25=13, Resulting Numbers: [26, 14, 13] Generated Node #2: [26, 14, 13] from Operation: 38-25=13 Current State: 26:[26, 14, 13], Operations: ['38-25=13'] Exploring Operation: 14-13=1, Resulting Numbers: [26, 1] Generated Node #3: [26, 1] from Operation: 14-13=1 Current State: 26:[26, 1], Operations: ['38-25=13', '14-13=1'] Exploring Operation: 26*1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[26, 38, 25, 14], Operations: [] Exploring Operation: 38-14=24, Resulting Numbers: [26, 25, 24] Generated Node #0,0: 26:[26, 25, 24] Operation: 38-14=24 Exploring Operation: 38-26=12, Resulting Numbers: [25, 14, 12] Generated Node #0,1: 26:[25, 14, 12] Operation: 38-26=12 Exploring Operation: 38-25=13, Resulting Numbers: [26, 14, 13] Generated Node #0,2: 26:[26, 14, 13] Operation: 38-25=13 Moving to Node #0,2 Current State: 26:[26, 14, 13], Operations: ['38-25=13'] Exploring Operation: 26-13=13, Resulting Numbers: [14, 13] Generated Node #0,2,0: 26:[14, 13] Operation: 26-13=13 Exploring Operation: 26/13=2, Resulting Numbers: [14, 2] Generated Node #0,2,1: 26:[14, 2] Operation: 26/13=2 Exploring Operation: 26-14=12, Resulting Numbers: [13, 12] Generated Node #0,2,2: 26:[13, 12] Operation: 26-14=12 Moving to Node #0,0 Current State: 26:[26, 25, 24], Operations: ['38-14=24'] Exploring Operation: 25-24=1, Resulting Numbers: [26, 1] Generated Node #0,0,0: 26:[26, 1] Operation: 25-24=1 Exploring Operation: 26-25=1, Resulting Numbers: [24, 1] Generated Node #0,0,1: 26:[24, 1] Operation: 26-25=1 Exploring Operation: 26-24=2, Resulting Numbers: [25, 2] Generated Node #0,0,2: 26:[25, 2] Operation: 26-24=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[26, 1], Operations: ['38-14=24', '25-24=1'] Exploring Operation: 26*1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[26, 38, 25, 14], Operations: [] Exploring Operation: 38-14=24, Resulting Numbers: [26, 25, 24] Generated Node #0,0: 26:[26, 25, 24] Operation: 38-14=24 Moving to Node #0,0 Current State: 26:[26, 25, 24], Operations: ['38-14=24'] Exploring Operation: 25-24=1, Resulting Numbers: [26, 1] Generated Node #0,0,0: 26:[26, 1] Operation: 25-24=1 Moving to Node #0,0,0 Current State: 26:[26, 1], Operations: ['38-14=24', '25-24=1'] Exploring Operation: 26*1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 90, 6, 68, 83 ]
68
[ "90-6=84", "84-83=1", "68*1=68" ]
Current State: 68:[90, 6, 68, 83], Operations: [] Exploring Operation: 90-6=84, Resulting Numbers: [68, 83, 84] Generated Node #2: [68, 83, 84] from Operation: 90-6=84 Current State: 68:[68, 83, 84], Operations: ['90-6=84'] Exploring Operation: 84-83=1, Resulting Numbers: [68, 1] Generated Node #3: [68, 1] from Operation: 84-83=1 Current State: 68:[68, 1], Operations: ['90-6=84', '84-83=1'] Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[90, 6, 68, 83], Operations: [] Exploring Operation: 90/6=15, Resulting Numbers: [68, 83, 15] Generated Node #0,0: 68:[68, 83, 15] Operation: 90/6=15 Exploring Operation: 83-68=15, Resulting Numbers: [90, 6, 15] Generated Node #0,1: 68:[90, 6, 15] Operation: 83-68=15 Exploring Operation: 90-83=7, Resulting Numbers: [6, 68, 7] Generated Node #0,2: 68:[6, 68, 7] Operation: 90-83=7 Exploring Operation: 90-68=22, Resulting Numbers: [6, 83, 22] Generated Node #0,3: 68:[6, 83, 22] Operation: 90-68=22 Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[6, 68, 7], Operations: ['90-83=7'] Exploring Operation: 6+68=74, Resulting Numbers: [7, 74] Generated Node #0,2,0: 68:[7, 74] Operation: 6+68=74 Exploring Operation: 6+7=13, Resulting Numbers: [68, 13] Generated Node #0,2,1: 68:[68, 13] Operation: 6+7=13 Exploring Operation: 7-6=1, Resulting Numbers: [68, 1] Generated Node #0,2,2: 68:[68, 1] Operation: 7-6=1 Exploring Operation: 6*7=42, Resulting Numbers: [68, 42] Generated Node #0,2,3: 68:[68, 42] Operation: 6*7=42 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 68:[68, 1], Operations: ['90-83=7', '7-6=1'] Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[90, 6, 68, 83], Operations: [] Exploring Operation: 90-83=7, Resulting Numbers: [6, 68, 7] Generated Node #0,2: 68:[6, 68, 7] Operation: 90-83=7 Moving to Node #0,2 Current State: 68:[6, 68, 7], Operations: ['90-83=7'] Exploring Operation: 7-6=1, Resulting Numbers: [68, 1] Generated Node #0,2,2: 68:[68, 1] Operation: 7-6=1 Moving to Node #0,2,2 Current State: 68:[68, 1], Operations: ['90-83=7', '7-6=1'] Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 7, 12, 79, 21 ]
83
[ "7*12=84", "84/21=4", "79+4=83" ]
Current State: 83:[7, 12, 79, 21], Operations: [] Exploring Operation: 7*12=84, Resulting Numbers: [79, 21, 84] Generated Node #2: [79, 21, 84] from Operation: 7*12=84 Current State: 83:[79, 21, 84], Operations: ['7*12=84'] Exploring Operation: 84/21=4, Resulting Numbers: [79, 4] Generated Node #3: [79, 4] from Operation: 84/21=4 Current State: 83:[79, 4], Operations: ['7*12=84', '84/21=4'] Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[7, 12, 79, 21], Operations: [] Exploring Operation: 7+12=19, Resulting Numbers: [79, 21, 19] Generated Node #0,0: 83:[79, 21, 19] Operation: 7+12=19 Exploring Operation: 7*12=84, Resulting Numbers: [79, 21, 84] Generated Node #0,1: 83:[79, 21, 84] Operation: 7*12=84 Moving to Node #0,1 Current State: 83:[79, 21, 84], Operations: ['7*12=84'] Exploring Operation: 79+21=100, Resulting Numbers: [84, 100] Generated Node #0,1,0: 83:[84, 100] Operation: 79+21=100 Exploring Operation: 84-21=63, Resulting Numbers: [79, 63] Generated Node #0,1,1: 83:[79, 63] Operation: 84-21=63 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 83:[84, 100], Operations: ['7*12=84', '79+21=100'] Exploring Operation: 84+100=184, Resulting Numbers: [184] 184,83 unequal: No Solution Exploring Operation: 100-84=16, Resulting Numbers: [16] 16,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 83:[79, 63], Operations: ['7*12=84', '84-21=63'] Exploring Operation: 79+63=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 79-63=16, Resulting Numbers: [16] 16,83 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:[79, 21, 19], Operations: ['7+12=19'] Exploring Operation: 79+19=98, Resulting Numbers: [21, 98] Generated Node #0,0,0: 83:[21, 98] Operation: 79+19=98 Exploring Operation: 21+19=40, Resulting Numbers: [79, 40] Generated Node #0,0,1: 83:[79, 40] Operation: 21+19=40 Moving to Node #0,0,1 Current State: 83:[79, 40], Operations: ['7+12=19', '21+19=40'] Exploring Operation: 79+40=119, Resulting Numbers: [119] 119,83 unequal: No Solution Exploring Operation: 79-40=39, Resulting Numbers: [39] 39,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[21, 98], Operations: ['7+12=19', '79+19=98'] Exploring Operation: 98-21=77, Resulting Numbers: [77] 77,83 unequal: No Solution Exploring Operation: 21+98=119, Resulting Numbers: [119] 119,83 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 50, 42, 1, 72 ]
64
[ "50-42=8", "1*72=72", "72-8=64" ]
Current State: 64:[50, 42, 1, 72], Operations: [] Exploring Operation: 50-42=8, Resulting Numbers: [1, 72, 8] Generated Node #2: [1, 72, 8] from Operation: 50-42=8 Current State: 64:[1, 72, 8], Operations: ['50-42=8'] Exploring Operation: 1*72=72, Resulting Numbers: [8, 72] Generated Node #3: [8, 72] from Operation: 1*72=72 Current State: 64:[8, 72], Operations: ['50-42=8', '1*72=72'] Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[50, 42, 1, 72], Operations: [] Exploring Operation: 72-50=22, Resulting Numbers: [42, 1, 22] Generated Node #0,0: 64:[42, 1, 22] Operation: 72-50=22 Exploring Operation: 50-42=8, Resulting Numbers: [1, 72, 8] Generated Node #0,1: 64:[1, 72, 8] Operation: 50-42=8 Exploring Operation: 42-1=41, Resulting Numbers: [50, 72, 41] Generated Node #0,2: 64:[50, 72, 41] Operation: 42-1=41 Exploring Operation: 50+1=51, Resulting Numbers: [42, 72, 51] Generated Node #0,3: 64:[42, 72, 51] Operation: 50+1=51 Exploring Operation: 72-42=30, Resulting Numbers: [50, 1, 30] Generated Node #0,4: 64:[50, 1, 30] Operation: 72-42=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[1, 72, 8], Operations: ['50-42=8'] Exploring Operation: 72-8=64, Resulting Numbers: [1, 64] Generated Node #0,1,0: 64:[1, 64] Operation: 72-8=64 Exploring Operation: 1*72=72, Resulting Numbers: [8, 72] Generated Node #0,1,1: 64:[8, 72] Operation: 1*72=72 Exploring Operation: 72/1=72, Resulting Numbers: [8, 72] Generated Node #0,1,2: 64:[8, 72] Operation: 72/1=72 Exploring Operation: 72/8=9, Resulting Numbers: [1, 9] Generated Node #0,1,3: 64:[1, 9] Operation: 72/8=9 Exploring Operation: 72-1=71, Resulting Numbers: [8, 71] Generated Node #0,1,4: 64:[8, 71] Operation: 72-1=71 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 64:[1, 64], Operations: ['50-42=8', '72-8=64'] Exploring Operation: 1+64=65, Resulting Numbers: [65] 65,64 unequal: No Solution Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,64 unequal: No Solution Exploring Operation: 64/1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[50, 42, 1, 72], Operations: [] Exploring Operation: 50-42=8, Resulting Numbers: [1, 72, 8] Generated Node #0,1: 64:[1, 72, 8] Operation: 50-42=8 Moving to Node #0,1 Current State: 64:[1, 72, 8], Operations: ['50-42=8'] Exploring Operation: 72-8=64, Resulting Numbers: [1, 64] Generated Node #0,1,0: 64:[1, 64] Operation: 72-8=64 Moving to Node #0,1,0 Current State: 64:[1, 64], Operations: ['50-42=8', '72-8=64'] Exploring Operation: 64/1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 31, 52, 16, 2 ]
65
[ "31+52=83", "16+2=18", "83-18=65" ]
Current State: 65:[31, 52, 16, 2], Operations: [] Exploring Operation: 31+52=83, Resulting Numbers: [16, 2, 83] Generated Node #2: [16, 2, 83] from Operation: 31+52=83 Current State: 65:[16, 2, 83], Operations: ['31+52=83'] Exploring Operation: 16+2=18, Resulting Numbers: [83, 18] Generated Node #3: [83, 18] from Operation: 16+2=18 Current State: 65:[83, 18], Operations: ['31+52=83', '16+2=18'] Exploring Operation: 83-18=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[31, 52, 16, 2], Operations: [] Exploring Operation: 52-31=21, Resulting Numbers: [16, 2, 21] Generated Node #0,0: 65:[16, 2, 21] Operation: 52-31=21 Moving to Node #0,0 Current State: 65:[16, 2, 21], Operations: ['52-31=21'] Exploring Operation: 21-16=5, Resulting Numbers: [2, 5] Generated Node #0,0,0: 65:[2, 5] Operation: 21-16=5 Moving to Node #0,0,0 Current State: 65:[2, 5], Operations: ['52-31=21', '21-16=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,65 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 69, 30, 86, 1 ]
47
[ "69-30=39", "86*1=86", "86-39=47" ]
Current State: 47:[69, 30, 86, 1], Operations: [] Exploring Operation: 69-30=39, Resulting Numbers: [86, 1, 39] Generated Node #2: [86, 1, 39] from Operation: 69-30=39 Current State: 47:[86, 1, 39], Operations: ['69-30=39'] Exploring Operation: 86*1=86, Resulting Numbers: [39, 86] Generated Node #3: [39, 86] from Operation: 86*1=86 Current State: 47:[39, 86], Operations: ['69-30=39', '86*1=86'] Exploring Operation: 86-39=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[69, 30, 86, 1], Operations: [] Exploring Operation: 69-1=68, Resulting Numbers: [30, 86, 68] Generated Node #0,0: 47:[30, 86, 68] Operation: 69-1=68 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[30, 86, 68], Operations: ['69-1=68'] Exploring Operation: 86-30=56, Resulting Numbers: [68, 56] Generated Node #0,0,0: 47:[68, 56] Operation: 86-30=56 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[68, 56], Operations: ['69-1=68', '86-30=56'] Exploring Operation: 68-56=12, Resulting Numbers: [12] 12,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 46, 97, 38, 7 ]
13
[ "46-38=8", "97+7=104", "104/8=13" ]
Current State: 13:[46, 97, 38, 7], Operations: [] Exploring Operation: 46-38=8, Resulting Numbers: [97, 7, 8] Generated Node #2: [97, 7, 8] from Operation: 46-38=8 Current State: 13:[97, 7, 8], Operations: ['46-38=8'] Exploring Operation: 97+7=104, Resulting Numbers: [8, 104] Generated Node #3: [8, 104] from Operation: 97+7=104 Current State: 13:[8, 104], Operations: ['46-38=8', '97+7=104'] Exploring Operation: 104/8=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[46, 97, 38, 7], Operations: [] Exploring Operation: 97-46=51, Resulting Numbers: [38, 7, 51] Generated Node #0,0: 13:[38, 7, 51] Operation: 97-46=51 Exploring Operation: 97-38=59, Resulting Numbers: [46, 7, 59] Generated Node #0,1: 13:[46, 7, 59] Operation: 97-38=59 Exploring Operation: 46-38=8, Resulting Numbers: [97, 7, 8] Generated Node #0,2: 13:[97, 7, 8] Operation: 46-38=8 Moving to Node #0,0 Current State: 13:[38, 7, 51], Operations: ['97-46=51'] Exploring Operation: 38-7=31, Resulting Numbers: [51, 31] Generated Node #0,0,0: 13:[51, 31] Operation: 38-7=31 Exploring Operation: 51-7=44, Resulting Numbers: [38, 44] Generated Node #0,0,1: 13:[38, 44] Operation: 51-7=44 Exploring Operation: 51-38=13, Resulting Numbers: [7, 13] Generated Node #0,0,2: 13:[7, 13] Operation: 51-38=13 Moving to Node #0,1 Current State: 13:[46, 7, 59], Operations: ['97-38=59'] Exploring Operation: 46-7=39, Resulting Numbers: [59, 39] Generated Node #0,1,0: 13:[59, 39] Operation: 46-7=39 Exploring Operation: 59-46=13, Resulting Numbers: [7, 13] Generated Node #0,1,1: 13:[7, 13] Operation: 59-46=13 Exploring Operation: 59-7=52, Resulting Numbers: [46, 52] Generated Node #0,1,2: 13:[46, 52] Operation: 59-7=52 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 13:[7, 13], Operations: ['97-38=59', '59-46=13'] Exploring Operation: 7*13=91, Resulting Numbers: [91] 91,13 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,13 unequal: No Solution No 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: 13:[59, 39], Operations: ['97-38=59', '46-7=39'] Exploring Operation: 59*39=2301, Resulting Numbers: [2301] 2301,13 unequal: No Solution Exploring Operation: 59+39=98, Resulting Numbers: [98] 98,13 unequal: No Solution Exploring Operation: 59-39=20, Resulting Numbers: [20] 20,13 unequal: No Solution No 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: 13:[46, 52], Operations: ['97-38=59', '59-7=52'] Exploring Operation: 46*52=2392, Resulting Numbers: [2392] 2392,13 unequal: No Solution Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 46+52=98, Resulting Numbers: [98] 98,13 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: 13:[97, 7, 8], Operations: ['46-38=8'] Exploring Operation: 97-8=89, Resulting Numbers: [7, 89] Generated Node #0,2,0: 13:[7, 89] Operation: 97-8=89 Exploring Operation: 7+8=15, Resulting Numbers: [97, 15] Generated Node #0,2,1: 13:[97, 15] Operation: 7+8=15 Exploring Operation: 97-7=90, Resulting Numbers: [8, 90] Generated Node #0,2,2: 13:[8, 90] Operation: 97-7=90 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 13:[7, 89], Operations: ['46-38=8', '97-8=89'] Exploring Operation: 7+89=96, Resulting Numbers: [96] 96,13 unequal: No Solution Exploring Operation: 7*89=623, Resulting Numbers: [623] 623,13 unequal: No Solution Exploring Operation: 89-7=82, Resulting Numbers: [82] 82,13 unequal: No Solution No 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: 13:[8, 90], Operations: ['46-38=8', '97-7=90'] Exploring Operation: 8+90=98, Resulting Numbers: [98] 98,13 unequal: No Solution Exploring Operation: 8*90=720, Resulting Numbers: [720] 720,13 unequal: No Solution Exploring Operation: 90-8=82, Resulting Numbers: [82] 82,13 unequal: No Solution No 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: 13:[97, 15], Operations: ['46-38=8', '7+8=15'] Exploring Operation: 97*15=1455, Resulting Numbers: [1455] 1455,13 unequal: No Solution Exploring Operation: 97-15=82, Resulting Numbers: [82] 82,13 unequal: No Solution Exploring Operation: 97+15=112, Resulting Numbers: [112] 112,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 13:[7, 13], Operations: ['97-46=51', '51-38=13'] Exploring Operation: 7*13=91, Resulting Numbers: [91] 91,13 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[51, 31], Operations: ['97-46=51', '38-7=31'] Exploring Operation: 51-31=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 51*31=1581, Resulting Numbers: [1581] 1581,13 unequal: No Solution Exploring Operation: 51+31=82, Resulting Numbers: [82] 82,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[38, 44], Operations: ['97-46=51', '51-7=44'] Exploring Operation: 38*44=1672, Resulting Numbers: [1672] 1672,13 unequal: No Solution Exploring Operation: 44-38=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 38+44=82, Resulting Numbers: [82] 82,13 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 14, 87, 87, 50 ]
36
[ "14+87=101", "87+50=137", "137-101=36" ]
Current State: 36:[14, 87, 87, 50], Operations: [] Exploring Operation: 14+87=101, Resulting Numbers: [50, 101] Generated Node #2: [50, 101] from Operation: 14+87=101 Current State: 36:[50, 101], Operations: ['14+87=101'] Exploring Operation: 87+50=137, Resulting Numbers: [101, 137] Generated Node #3: [101, 137] from Operation: 87+50=137 Current State: 36:[101, 137], Operations: ['14+87=101', '87+50=137'] Exploring Operation: 137-101=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[14, 87, 87, 50], Operations: [] Exploring Operation: 87-50=37, Resulting Numbers: [14, 87, 37] Generated Node #0,0: 36:[14, 87, 37] Operation: 87-50=37 Exploring Operation: 87/87=1, Resulting Numbers: [14, 50, 1] Generated Node #0,1: 36:[14, 50, 1] Operation: 87/87=1 Exploring Operation: 87-50=37, Resulting Numbers: [14, 87, 37] Generated Node #0,2: 36:[14, 87, 37] Operation: 87-50=37 Exploring Operation: 87-87=0, Resulting Numbers: [14, 50, 0] Generated Node #0,3: 36:[14, 50, 0] Operation: 87-87=0 Exploring Operation: 87-14=73, Resulting Numbers: [87, 50, 73] Generated Node #0,4: 36:[87, 50, 73] Operation: 87-14=73 Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[14, 50, 1], Operations: ['87/87=1'] Exploring Operation: 14/1=14, Resulting Numbers: [50, 14] Generated Node #0,1,0: 36:[50, 14] Operation: 14/1=14 Exploring Operation: 50-14=36, Resulting Numbers: [1, 36] Generated Node #0,1,1: 36:[1, 36] Operation: 50-14=36 Exploring Operation: 14*1=14, Resulting Numbers: [50, 14] Generated Node #0,1,2: 36:[50, 14] Operation: 14*1=14 Exploring Operation: 50-1=49, Resulting Numbers: [14, 49] Generated Node #0,1,3: 36:[14, 49] Operation: 50-1=49 Exploring Operation: 14-1=13, Resulting Numbers: [50, 13] Generated Node #0,1,4: 36:[50, 13] Operation: 14-1=13 Moving to Node #0,1,1 Current State: 36:[1, 36], Operations: ['87/87=1', '50-14=36'] Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[14, 87, 87, 50], Operations: [] Exploring Operation: 87/87=1, Resulting Numbers: [14, 50, 1] Generated Node #0,1: 36:[14, 50, 1] Operation: 87/87=1 Moving to Node #0,1 Current State: 36:[14, 50, 1], Operations: ['87/87=1'] Exploring Operation: 50-14=36, Resulting Numbers: [1, 36] Generated Node #0,1,1: 36:[1, 36] Operation: 50-14=36 Moving to Node #0,1,1 Current State: 36:[1, 36], Operations: ['87/87=1', '50-14=36'] Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic