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
[ 39, 82, 3, 36 ]
31
[ "82-39=43", "36/3=12", "43-12=31" ]
Current State: 31:[39, 82, 3, 36], Operations: [] Exploring Operation: 82-39=43, Resulting Numbers: [3, 36, 43] Generated Node #2: [3, 36, 43] from Operation: 82-39=43 Current State: 31:[3, 36, 43], Operations: ['82-39=43'] Exploring Operation: 36/3=12, Resulting Numbers: [43, 12] Generated Node #3: [43, 12] from Operation: 36/3=12 Current State: 31:[43, 12], Operations: ['82-39=43', '36/3=12'] Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[39, 82, 3, 36], Operations: [] Exploring Operation: 82-36=46, Resulting Numbers: [39, 3, 46] Generated Node #0,0: 31:[39, 3, 46] Operation: 82-36=46 Exploring Operation: 82-39=43, Resulting Numbers: [3, 36, 43] Generated Node #0,1: 31:[3, 36, 43] Operation: 82-39=43 Moving to Node #0,1 Current State: 31:[3, 36, 43], Operations: ['82-39=43'] Exploring Operation: 36-3=33, Resulting Numbers: [43, 33] Generated Node #0,1,0: 31:[43, 33] Operation: 36-3=33 Exploring Operation: 43-3=40, Resulting Numbers: [36, 40] Generated Node #0,1,1: 31:[36, 40] Operation: 43-3=40 Moving to Node #0,0 Current State: 31:[39, 3, 46], Operations: ['82-36=46'] Exploring Operation: 46-3=43, Resulting Numbers: [39, 43] Generated Node #0,0,0: 31:[39, 43] Operation: 46-3=43 Exploring Operation: 39-3=36, Resulting Numbers: [46, 36] Generated Node #0,0,1: 31:[46, 36] Operation: 39-3=36 Moving to Node #0,1,0 Current State: 31:[43, 33], Operations: ['82-39=43', '36-3=33'] Exploring Operation: 43+33=76, Resulting Numbers: [76] 76,31 unequal: No Solution Exploring Operation: 43-33=10, Resulting Numbers: [10] 10,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[36, 40], Operations: ['82-39=43', '43-3=40'] Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[46, 36], Operations: ['82-36=46', '39-3=36'] Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 46+36=82, Resulting Numbers: [82] 82,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[39, 43], Operations: ['82-36=46', '46-3=43'] Exploring Operation: 39+43=82, Resulting Numbers: [82] 82,31 unequal: No Solution Exploring Operation: 43-39=4, Resulting Numbers: [4] 4,31 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 89, 2, 68, 85 ]
55
[ "85-68=17", "2*17=34", "89-34=55" ]
Current State: 55:[89, 2, 68, 85], Operations: [] Exploring Operation: 85-68=17, Resulting Numbers: [89, 2, 17] Generated Node #2: [89, 2, 17] from Operation: 85-68=17 Current State: 55:[89, 2, 17], Operations: ['85-68=17'] Exploring Operation: 2*17=34, Resulting Numbers: [89, 34] Generated Node #3: [89, 34] from Operation: 2*17=34 Current State: 55:[89, 34], Operations: ['85-68=17', '2*17=34'] Exploring Operation: 89-34=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[89, 2, 68, 85], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [2, 68, 4] Generated Node #0,0: 55:[2, 68, 4] Operation: 89-85=4 Moving to Node #0,0 Current State: 55:[2, 68, 4], Operations: ['89-85=4'] Exploring Operation: 68/4=17, Resulting Numbers: [2, 17] Generated Node #0,0,0: 55:[2, 17] Operation: 68/4=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 55:[2, 17], Operations: ['89-85=4', '68/4=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,55 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
[ 40, 50, 5, 15 ]
14
[ "50*5=250", "250-40=210", "210/15=14" ]
Current State: 14:[40, 50, 5, 15], Operations: [] Exploring Operation: 50*5=250, Resulting Numbers: [40, 15, 250] Generated Node #2: [40, 15, 250] from Operation: 50*5=250 Current State: 14:[40, 15, 250], Operations: ['50*5=250'] Exploring Operation: 250-40=210, Resulting Numbers: [15, 210] Generated Node #3: [15, 210] from Operation: 250-40=210 Current State: 14:[15, 210], Operations: ['50*5=250', '250-40=210'] Exploring Operation: 210/15=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[40, 50, 5, 15], Operations: [] Exploring Operation: 40-15=25, Resulting Numbers: [50, 5, 25] Generated Node #0,0: 14:[50, 5, 25] Operation: 40-15=25 Exploring Operation: 50-15=35, Resulting Numbers: [40, 5, 35] Generated Node #0,1: 14:[40, 5, 35] Operation: 50-15=35 Exploring Operation: 50/5=10, Resulting Numbers: [40, 15, 10] Generated Node #0,2: 14:[40, 15, 10] Operation: 50/5=10 Exploring Operation: 50-40=10, Resulting Numbers: [5, 15, 10] Generated Node #0,3: 14:[5, 15, 10] Operation: 50-40=10 Exploring Operation: 40/5=8, Resulting Numbers: [50, 15, 8] Generated Node #0,4: 14:[50, 15, 8] Operation: 40/5=8 Moving to Node #0,3 Current State: 14:[5, 15, 10], Operations: ['50-40=10'] Exploring Operation: 15/5=3, Resulting Numbers: [10, 3] Generated Node #0,3,0: 14:[10, 3] Operation: 15/5=3 Exploring Operation: 5+10=15, Resulting Numbers: [15, 15] Generated Node #0,3,1: 14:[15, 15] Operation: 5+10=15 Exploring Operation: 15-10=5, Resulting Numbers: [5, 5] Generated Node #0,3,2: 14:[5, 5] Operation: 15-10=5 Exploring Operation: 10/5=2, Resulting Numbers: [15, 2] Generated Node #0,3,3: 14:[15, 2] Operation: 10/5=2 Exploring Operation: 10-5=5, Resulting Numbers: [15, 5] Generated Node #0,3,4: 14:[15, 5] Operation: 10-5=5 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 14:[15, 2], Operations: ['50-40=10', '10/5=2'] Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,14 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,14 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 14:[15, 15], Operations: ['50-40=10', '5+10=15'] Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,14 unequal: No Solution Exploring Operation: 15*15=225, Resulting Numbers: [225] 225,14 unequal: No Solution Exploring Operation: 15/15=1, Resulting Numbers: [1] 1,14 unequal: No Solution Exploring Operation: 15-15=0, Resulting Numbers: [0] 0,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 14:[15, 5], Operations: ['50-40=10', '10-5=5'] Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,14 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,14 unequal: No Solution Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,14 unequal: No Solution Exploring Operation: 15/5=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 #0,3,0 Current State: 14:[10, 3], Operations: ['50-40=10', '15/5=3'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,14 unequal: No Solution Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 14:[5, 5], Operations: ['50-40=10', '15-10=5'] Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,14 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,14 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,14 unequal: No Solution Exploring Operation: 5+5=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 #0,2 Current State: 14:[40, 15, 10], Operations: ['50/5=10'] Exploring Operation: 40-10=30, Resulting Numbers: [15, 30] Generated Node #0,2,0: 14:[15, 30] Operation: 40-10=30 Exploring Operation: 15-10=5, Resulting Numbers: [40, 5] Generated Node #0,2,1: 14:[40, 5] Operation: 15-10=5 Exploring Operation: 40/10=4, Resulting Numbers: [15, 4] Generated Node #0,2,2: 14:[15, 4] Operation: 40/10=4 Exploring Operation: 40-15=25, Resulting Numbers: [10, 25] Generated Node #0,2,3: 14:[10, 25] Operation: 40-15=25 Exploring Operation: 40+10=50, Resulting Numbers: [15, 50] Generated Node #0,2,4: 14:[15, 50] Operation: 40+10=50 Moving to Node #0,4 Current State: 14:[50, 15, 8], Operations: ['40/5=8'] Exploring Operation: 15-8=7, Resulting Numbers: [50, 7] Generated Node #0,4,0: 14:[50, 7] Operation: 15-8=7 Exploring Operation: 15+8=23, Resulting Numbers: [50, 23] Generated Node #0,4,1: 14:[50, 23] Operation: 15+8=23 Exploring Operation: 50-15=35, Resulting Numbers: [8, 35] Generated Node #0,4,2: 14:[8, 35] Operation: 50-15=35 Exploring Operation: 50+8=58, Resulting Numbers: [15, 58] Generated Node #0,4,3: 14:[15, 58] Operation: 50+8=58 Exploring Operation: 50-8=42, Resulting Numbers: [15, 42] Generated Node #0,4,4: 14:[15, 42] Operation: 50-8=42 Moving to Node #0,0 Current State: 14:[50, 5, 25], Operations: ['40-15=25'] Exploring Operation: 50-25=25, Resulting Numbers: [5, 25] Generated Node #0,0,0: 14:[5, 25] Operation: 50-25=25 Exploring Operation: 50/25=2, Resulting Numbers: [5, 2] Generated Node #0,0,1: 14:[5, 2] Operation: 50/25=2 Exploring Operation: 50/5=10, Resulting Numbers: [25, 10] Generated Node #0,0,2: 14:[25, 10] Operation: 50/5=10 Exploring Operation: 50-5=45, Resulting Numbers: [25, 45] Generated Node #0,0,3: 14:[25, 45] Operation: 50-5=45 Exploring Operation: 25/5=5, Resulting Numbers: [50, 5] Generated Node #0,0,4: 14:[50, 5] Operation: 25/5=5 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 14:[5, 2], Operations: ['40-15=25', '50/25=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,14 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,14 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 #0,0,0 Current State: 14:[5, 25], Operations: ['40-15=25', '50-25=25'] Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,14 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 5*25=125, Resulting Numbers: [125] 125,14 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,14 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 #0,0,2 Current State: 14:[25, 10], Operations: ['40-15=25', '50/5=10'] Exploring Operation: 25+10=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 25*10=250, Resulting Numbers: [250] 250,14 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,14 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 #0,0,4 Current State: 14:[50, 5], Operations: ['40-15=25', '25/5=5'] Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,14 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,14 unequal: No Solution Exploring Operation: 50*5=250, Resulting Numbers: [250] 250,14 unequal: No Solution Exploring Operation: 50+5=55, Resulting Numbers: [55] 55,14 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 #0,0,3 Current State: 14:[25, 45], Operations: ['40-15=25', '50-5=45'] Exploring Operation: 25+45=70, Resulting Numbers: [70] 70,14 unequal: No Solution Exploring Operation: 25*45=1125, Resulting Numbers: [1125] 1125,14 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,14 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:[40, 5, 35], Operations: ['50-15=35'] Exploring Operation: 35-5=30, Resulting Numbers: [40, 30] Generated Node #0,1,0: 14:[40, 30] Operation: 35-5=30 Exploring Operation: 35/5=7, Resulting Numbers: [40, 7] Generated Node #0,1,1: 14:[40, 7] Operation: 35/5=7 Exploring Operation: 40/5=8, Resulting Numbers: [35, 8] Generated Node #0,1,2: 14:[35, 8] Operation: 40/5=8 Exploring Operation: 40-5=35, Resulting Numbers: [35, 35] Generated Node #0,1,3: 14:[35, 35] Operation: 40-5=35 Exploring Operation: 40-35=5, Resulting Numbers: [5, 5] Generated Node #0,1,4: 14:[5, 5] Operation: 40-35=5 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 14:[5, 5], Operations: ['50-15=35', '40-35=5'] Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,14 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,14 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,14 unequal: No Solution Exploring Operation: 5+5=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 #0,1,2 Current State: 14:[35, 8], Operations: ['50-15=35', '40/5=8'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,14 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:[40, 7], Operations: ['50-15=35', '35/5=7'] Exploring Operation: 40+7=47, Resulting Numbers: [47] 47,14 unequal: No Solution Exploring Operation: 40*7=280, Resulting Numbers: [280] 280,14 unequal: No Solution Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,14 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:[40, 30], Operations: ['50-15=35', '35-5=30'] Exploring Operation: 40*30=1200, Resulting Numbers: [1200] 1200,14 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,14 unequal: No Solution Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,14 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 #0,1,3 Current State: 14:[35, 35], Operations: ['50-15=35', '40-5=35'] Exploring Operation: 35*35=1225, Resulting Numbers: [1225] 1225,14 unequal: No Solution Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,14 unequal: No Solution Exploring Operation: 35-35=0, Resulting Numbers: [0] 0,14 unequal: No Solution Exploring Operation: 35/35=1, Resulting Numbers: [1] 1,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 14:[15, 4], Operations: ['50/5=10', '40/10=4'] Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,14 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,14 unequal: No Solution Moving to Node #0,2,3 Current State: 14:[10, 25], Operations: ['50/5=10', '40-15=25'] Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,14 unequal: No Solution Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,14 unequal: No Solution Moving to Node #0,2,0 Current State: 14:[15, 30], Operations: ['50/5=10', '40-10=30'] Exploring Operation: 15+30=45, Resulting Numbers: [45] 45,14 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,14 unequal: No Solution Exploring Operation: 15*30=450, Resulting Numbers: [450] 450,14 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,14 unequal: No Solution Moving to Node #0,4,2 Current State: 14:[8, 35], Operations: ['40/5=8', '50-15=35'] Exploring Operation: 8*35=280, Resulting Numbers: [280] 280,14 unequal: No Solution Exploring Operation: 8+35=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[40, 5], Operations: ['50/5=10', '15-10=5'] Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 40+5=45, Resulting Numbers: [45] 45,14 unequal: No Solution Exploring Operation: 40*5=200, Resulting Numbers: [200] 200,14 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,14 unequal: No Solution Moving to Node #0,4,4 Current State: 14:[15, 42], Operations: ['40/5=8', '50-8=42'] Exploring Operation: 15+42=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 15*42=630, Resulting Numbers: [630] 630,14 unequal: No Solution Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,14 unequal: No Solution Moving to Node #0,4,0 Current State: 14:[50, 7], Operations: ['40/5=8', '15-8=7'] Exploring Operation: 50*7=350, Resulting Numbers: [350] 350,14 unequal: No Solution Exploring Operation: 50+7=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,14 unequal: No Solution Moving to Node #0,2,4 Current State: 14:[15, 50], Operations: ['50/5=10', '40+10=50'] Exploring Operation: 15*50=750, Resulting Numbers: [750] 750,14 unequal: No Solution Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 15+50=65, Resulting Numbers: [65] 65,14 unequal: No Solution Moving to Node #0,4,3 Current State: 14:[15, 58], Operations: ['40/5=8', '50+8=58'] Exploring Operation: 58-15=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 15*58=870, Resulting Numbers: [870] 870,14 unequal: No Solution Exploring Operation: 15+58=73, Resulting Numbers: [73] 73,14 unequal: No Solution Moving to Node #0,4,1 Current State: 14:[50, 23], Operations: ['40/5=8', '15+8=23'] Exploring Operation: 50+23=73, Resulting Numbers: [73] 73,14 unequal: No Solution Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 50*23=1150, Resulting Numbers: [1150] 1150,14 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 30, 46, 77, 67 ]
68
[ "30+46=76", "77+67=144", "144-76=68" ]
Current State: 68:[30, 46, 77, 67], Operations: [] Exploring Operation: 30+46=76, Resulting Numbers: [77, 67, 76] Generated Node #2: [77, 67, 76] from Operation: 30+46=76 Current State: 68:[77, 67, 76], Operations: ['30+46=76'] Exploring Operation: 77+67=144, Resulting Numbers: [76, 144] Generated Node #3: [76, 144] from Operation: 77+67=144 Current State: 68:[76, 144], Operations: ['30+46=76', '77+67=144'] Exploring Operation: 144-76=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[30, 46, 77, 67], Operations: [] Exploring Operation: 77-46=31, Resulting Numbers: [30, 67, 31] Generated Node #0,0: 68:[30, 67, 31] Operation: 77-46=31 Exploring Operation: 67-46=21, Resulting Numbers: [30, 77, 21] Generated Node #0,1: 68:[30, 77, 21] Operation: 67-46=21 Exploring Operation: 46-30=16, Resulting Numbers: [77, 67, 16] Generated Node #0,2: 68:[77, 67, 16] Operation: 46-30=16 Moving to Node #0,0 Current State: 68:[30, 67, 31], Operations: ['77-46=31'] Exploring Operation: 67-30=37, Resulting Numbers: [31, 37] Generated Node #0,0,0: 68:[31, 37] Operation: 67-30=37 Exploring Operation: 31-30=1, Resulting Numbers: [67, 1] Generated Node #0,0,1: 68:[67, 1] Operation: 31-30=1 Exploring Operation: 67-31=36, Resulting Numbers: [30, 36] Generated Node #0,0,2: 68:[30, 36] Operation: 67-31=36 Moving to Node #0,2 Current State: 68:[77, 67, 16], Operations: ['46-30=16'] Exploring Operation: 77-16=61, Resulting Numbers: [67, 61] Generated Node #0,2,0: 68:[67, 61] Operation: 77-16=61 Exploring Operation: 67+16=83, Resulting Numbers: [77, 83] Generated Node #0,2,1: 68:[77, 83] Operation: 67+16=83 Exploring Operation: 77-67=10, Resulting Numbers: [16, 10] Generated Node #0,2,2: 68:[16, 10] Operation: 77-67=10 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 68:[16, 10], Operations: ['46-30=16', '77-67=10'] Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,68 unequal: No Solution Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,68 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 68:[67, 61], Operations: ['46-30=16', '77-16=61'] Exploring Operation: 67*61=4087, Resulting Numbers: [4087] 4087,68 unequal: No Solution Exploring Operation: 67+61=128, Resulting Numbers: [128] 128,68 unequal: No Solution Exploring Operation: 67-61=6, Resulting Numbers: [6] 6,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 68:[77, 83], Operations: ['46-30=16', '67+16=83'] Exploring Operation: 77*83=6391, Resulting Numbers: [6391] 6391,68 unequal: No Solution Exploring Operation: 77+83=160, Resulting Numbers: [160] 160,68 unequal: No Solution Exploring Operation: 83-77=6, Resulting Numbers: [6] 6,68 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: 68:[30, 77, 21], Operations: ['67-46=21'] Exploring Operation: 77-21=56, Resulting Numbers: [30, 56] Generated Node #0,1,0: 68:[30, 56] Operation: 77-21=56 Exploring Operation: 30-21=9, Resulting Numbers: [77, 9] Generated Node #0,1,1: 68:[77, 9] Operation: 30-21=9 Exploring Operation: 77-30=47, Resulting Numbers: [21, 47] Generated Node #0,1,2: 68:[21, 47] Operation: 77-30=47 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 68:[77, 9], Operations: ['67-46=21', '30-21=9'] Exploring Operation: 77*9=693, Resulting Numbers: [693] 693,68 unequal: No Solution Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[30, 46, 77, 67], Operations: [] Exploring Operation: 67-46=21, Resulting Numbers: [30, 77, 21] Generated Node #0,1: 68:[30, 77, 21] Operation: 67-46=21 Moving to Node #0,1 Current State: 68:[30, 77, 21], Operations: ['67-46=21'] Exploring Operation: 30-21=9, Resulting Numbers: [77, 9] Generated Node #0,1,1: 68:[77, 9] Operation: 30-21=9 Moving to Node #0,1,1 Current State: 68:[77, 9], Operations: ['67-46=21', '30-21=9'] Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_3
mult_heuristic
[ 90, 33, 69, 45 ]
57
[ "90-33=57", "69+45=114", "114-57=57" ]
Current State: 57:[90, 33, 69, 45], Operations: [] Exploring Operation: 90-33=57, Resulting Numbers: [69, 45, 57] Generated Node #2: [69, 45, 57] from Operation: 90-33=57 Current State: 57:[69, 45, 57], Operations: ['90-33=57'] Exploring Operation: 69+45=114, Resulting Numbers: [57, 114] Generated Node #3: [57, 114] from Operation: 69+45=114 Current State: 57:[57, 114], Operations: ['90-33=57', '69+45=114'] Exploring Operation: 114-57=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[90, 33, 69, 45], Operations: [] Exploring Operation: 90-33=57, Resulting Numbers: [69, 45, 57] Generated Node #0,0: 57:[69, 45, 57] Operation: 90-33=57 Moving to Node #0,0 Current State: 57:[69, 45, 57], Operations: ['90-33=57'] Exploring Operation: 69-45=24, Resulting Numbers: [57, 24] Generated Node #0,0,0: 57:[57, 24] Operation: 69-45=24 Moving to Node #0,0,0 Current State: 57:[57, 24], Operations: ['90-33=57', '69-45=24'] Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,57 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 75, 78, 94, 49 ]
10
[ "75+78=153", "94+49=143", "153-143=10" ]
Current State: 10:[75, 78, 94, 49], Operations: [] Exploring Operation: 75+78=153, Resulting Numbers: [94, 49, 153] Generated Node #2: [94, 49, 153] from Operation: 75+78=153 Current State: 10:[94, 49, 153], Operations: ['75+78=153'] Exploring Operation: 94+49=143, Resulting Numbers: [153, 143] Generated Node #3: [153, 143] from Operation: 94+49=143 Current State: 10:[153, 143], Operations: ['75+78=153', '94+49=143'] Exploring Operation: 153-143=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[75, 78, 94, 49], Operations: [] Exploring Operation: 94-75=19, Resulting Numbers: [78, 49, 19] Generated Node #0,0: 10:[78, 49, 19] Operation: 94-75=19 Exploring Operation: 78-49=29, Resulting Numbers: [75, 94, 29] Generated Node #0,1: 10:[75, 94, 29] Operation: 78-49=29 Exploring Operation: 94-78=16, Resulting Numbers: [75, 49, 16] Generated Node #0,2: 10:[75, 49, 16] Operation: 94-78=16 Exploring Operation: 75-49=26, Resulting Numbers: [78, 94, 26] Generated Node #0,3: 10:[78, 94, 26] Operation: 75-49=26 Exploring Operation: 78-75=3, Resulting Numbers: [94, 49, 3] Generated Node #0,4: 10:[94, 49, 3] Operation: 78-75=3 Moving to Node #0,2 Current State: 10:[75, 49, 16], Operations: ['94-78=16'] Exploring Operation: 75-49=26, Resulting Numbers: [16, 26] Generated Node #0,2,0: 10:[16, 26] Operation: 75-49=26 Exploring Operation: 75+49=124, Resulting Numbers: [16, 124] Generated Node #0,2,1: 10:[16, 124] Operation: 75+49=124 Exploring Operation: 49-16=33, Resulting Numbers: [75, 33] Generated Node #0,2,2: 10:[75, 33] Operation: 49-16=33 Exploring Operation: 75-16=59, Resulting Numbers: [49, 59] Generated Node #0,2,3: 10:[49, 59] Operation: 75-16=59 Exploring Operation: 75+16=91, Resulting Numbers: [49, 91] Generated Node #0,2,4: 10:[49, 91] Operation: 75+16=91 Moving to Node #0,0 Current State: 10:[78, 49, 19], Operations: ['94-75=19'] Exploring Operation: 78-19=59, Resulting Numbers: [49, 59] Generated Node #0,0,0: 10:[49, 59] Operation: 78-19=59 Exploring Operation: 78+49=127, Resulting Numbers: [19, 127] Generated Node #0,0,1: 10:[19, 127] Operation: 78+49=127 Exploring Operation: 49-19=30, Resulting Numbers: [78, 30] Generated Node #0,0,2: 10:[78, 30] Operation: 49-19=30 Exploring Operation: 78+19=97, Resulting Numbers: [49, 97] Generated Node #0,0,3: 10:[49, 97] Operation: 78+19=97 Exploring Operation: 78-49=29, Resulting Numbers: [19, 29] Generated Node #0,0,4: 10:[19, 29] Operation: 78-49=29 Moving to Node #0,4 Current State: 10:[94, 49, 3], Operations: ['78-75=3'] Exploring Operation: 94-49=45, Resulting Numbers: [3, 45] Generated Node #0,4,0: 10:[3, 45] Operation: 94-49=45 Exploring Operation: 94+3=97, Resulting Numbers: [49, 97] Generated Node #0,4,1: 10:[49, 97] Operation: 94+3=97 Exploring Operation: 94-3=91, Resulting Numbers: [49, 91] Generated Node #0,4,2: 10:[49, 91] Operation: 94-3=91 Exploring Operation: 49-3=46, Resulting Numbers: [94, 46] Generated Node #0,4,3: 10:[94, 46] Operation: 49-3=46 Exploring Operation: 49+3=52, Resulting Numbers: [94, 52] Generated Node #0,4,4: 10:[94, 52] Operation: 49+3=52 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 10:[3, 45], Operations: ['78-75=3', '94-49=45'] Exploring Operation: 3+45=48, Resulting Numbers: [48] 48,10 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,10 unequal: No Solution Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 3*45=135, Resulting Numbers: [135] 135,10 unequal: No Solution No 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: 10:[49, 91], Operations: ['78-75=3', '94-3=91'] Exploring Operation: 49*91=4459, Resulting Numbers: [4459] 4459,10 unequal: No Solution Exploring Operation: 91-49=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 49+91=140, Resulting Numbers: [140] 140,10 unequal: No Solution No 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: 10:[94, 46], Operations: ['78-75=3', '49-3=46'] Exploring Operation: 94*46=4324, Resulting Numbers: [4324] 4324,10 unequal: No Solution Exploring Operation: 94+46=140, Resulting Numbers: [140] 140,10 unequal: No Solution Exploring Operation: 94-46=48, Resulting Numbers: [48] 48,10 unequal: No Solution No 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: 10:[49, 97], Operations: ['78-75=3', '94+3=97'] Exploring Operation: 97-49=48, Resulting Numbers: [48] 48,10 unequal: No Solution Exploring Operation: 49+97=146, Resulting Numbers: [146] 146,10 unequal: No Solution Exploring Operation: 49*97=4753, Resulting Numbers: [4753] 4753,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 10:[94, 52], Operations: ['78-75=3', '49+3=52'] Exploring Operation: 94*52=4888, Resulting Numbers: [4888] 4888,10 unequal: No Solution Exploring Operation: 94-52=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 94+52=146, Resulting Numbers: [146] 146,10 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: 10:[75, 94, 29], Operations: ['78-49=29'] Exploring Operation: 94-29=65, Resulting Numbers: [75, 65] Generated Node #0,1,0: 10:[75, 65] Operation: 94-29=65 Exploring Operation: 75-29=46, Resulting Numbers: [94, 46] Generated Node #0,1,1: 10:[94, 46] Operation: 75-29=46 Exploring Operation: 75+94=169, Resulting Numbers: [29, 169] Generated Node #0,1,2: 10:[29, 169] Operation: 75+94=169 Exploring Operation: 75+29=104, Resulting Numbers: [94, 104] Generated Node #0,1,3: 10:[94, 104] Operation: 75+29=104 Exploring Operation: 94-75=19, Resulting Numbers: [29, 19] Generated Node #0,1,4: 10:[29, 19] Operation: 94-75=19 Moving to Node #0,3 Current State: 10:[78, 94, 26], Operations: ['75-49=26'] Exploring Operation: 94-78=16, Resulting Numbers: [26, 16] Generated Node #0,3,0: 10:[26, 16] Operation: 94-78=16 Exploring Operation: 78+94=172, Resulting Numbers: [26, 172] Generated Node #0,3,1: 10:[26, 172] Operation: 78+94=172 Exploring Operation: 78/26=3, Resulting Numbers: [94, 3] Generated Node #0,3,2: 10:[94, 3] Operation: 78/26=3 Exploring Operation: 94-26=68, Resulting Numbers: [78, 68] Generated Node #0,3,3: 10:[78, 68] Operation: 94-26=68 Exploring Operation: 78-26=52, Resulting Numbers: [94, 52] Generated Node #0,3,4: 10:[94, 52] Operation: 78-26=52 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 10:[26, 16], Operations: ['75-49=26', '94-78=16'] Exploring Operation: 26*16=416, Resulting Numbers: [416] 416,10 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[75, 78, 94, 49], Operations: [] Exploring Operation: 75-49=26, Resulting Numbers: [78, 94, 26] Generated Node #0,3: 10:[78, 94, 26] Operation: 75-49=26 Moving to Node #0,3 Current State: 10:[78, 94, 26], Operations: ['75-49=26'] Exploring Operation: 94-78=16, Resulting Numbers: [26, 16] Generated Node #0,3,0: 10:[26, 16] Operation: 94-78=16 Moving to Node #0,3,0 Current State: 10:[26, 16], Operations: ['75-49=26', '94-78=16'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.954861
hs_5
sum_heuristic
[ 32, 42, 7, 60 ]
86
[ "32+60=92", "42/7=6", "92-6=86" ]
Current State: 86:[32, 42, 7, 60], Operations: [] Exploring Operation: 32+60=92, Resulting Numbers: [42, 7, 92] Generated Node #2: [42, 7, 92] from Operation: 32+60=92 Current State: 86:[42, 7, 92], Operations: ['32+60=92'] Exploring Operation: 42/7=6, Resulting Numbers: [92, 6] Generated Node #3: [92, 6] from Operation: 42/7=6 Current State: 86:[92, 6], Operations: ['32+60=92', '42/7=6'] Exploring Operation: 92-6=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[32, 42, 7, 60], Operations: [] Exploring Operation: 32+60=92, Resulting Numbers: [42, 7, 92] Generated Node #0,0: 86:[42, 7, 92] Operation: 32+60=92 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[42, 7, 92], Operations: ['32+60=92'] Exploring Operation: 92-7=85, Resulting Numbers: [42, 85] Generated Node #0,0,0: 86:[42, 85] Operation: 92-7=85 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[42, 85], Operations: ['32+60=92', '92-7=85'] Exploring Operation: 85-42=43, Resulting Numbers: [43] 43,86 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
[ 18, 19, 38, 26 ]
10
[ "18*38=684", "684/19=36", "36-26=10" ]
Current State: 10:[18, 19, 38, 26], Operations: [] Exploring Operation: 18*38=684, Resulting Numbers: [19, 26, 684] Generated Node #2: [19, 26, 684] from Operation: 18*38=684 Current State: 10:[19, 26, 684], Operations: ['18*38=684'] Exploring Operation: 684/19=36, Resulting Numbers: [26, 36] Generated Node #3: [26, 36] from Operation: 684/19=36 Current State: 10:[26, 36], Operations: ['18*38=684', '684/19=36'] Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[18, 19, 38, 26], Operations: [] Exploring Operation: 38-18=20, Resulting Numbers: [19, 26, 20] Generated Node #0,0: 10:[19, 26, 20] Operation: 38-18=20 Exploring Operation: 38-26=12, Resulting Numbers: [18, 19, 12] Generated Node #0,1: 10:[18, 19, 12] Operation: 38-26=12 Exploring Operation: 38/19=2, Resulting Numbers: [18, 26, 2] Generated Node #0,2: 10:[18, 26, 2] Operation: 38/19=2 Exploring Operation: 38-19=19, Resulting Numbers: [18, 26, 19] Generated Node #0,3: 10:[18, 26, 19] Operation: 38-19=19 Moving to Node #0,1 Current State: 10:[18, 19, 12], Operations: ['38-26=12'] Exploring Operation: 18-12=6, Resulting Numbers: [19, 6] Generated Node #0,1,0: 10:[19, 6] Operation: 18-12=6 Exploring Operation: 19-18=1, Resulting Numbers: [12, 1] Generated Node #0,1,1: 10:[12, 1] Operation: 19-18=1 Exploring Operation: 18+19=37, Resulting Numbers: [12, 37] Generated Node #0,1,2: 10:[12, 37] Operation: 18+19=37 Exploring Operation: 19-12=7, Resulting Numbers: [18, 7] Generated Node #0,1,3: 10:[18, 7] Operation: 19-12=7 Moving to Node #0,2 Current State: 10:[18, 26, 2], Operations: ['38/19=2'] Exploring Operation: 18-2=16, Resulting Numbers: [26, 16] Generated Node #0,2,0: 10:[26, 16] Operation: 18-2=16 Exploring Operation: 26-18=8, Resulting Numbers: [2, 8] Generated Node #0,2,1: 10:[2, 8] Operation: 26-18=8 Exploring Operation: 26/2=13, Resulting Numbers: [18, 13] Generated Node #0,2,2: 10:[18, 13] Operation: 26/2=13 Exploring Operation: 18/2=9, Resulting Numbers: [26, 9] Generated Node #0,2,3: 10:[26, 9] Operation: 18/2=9 Moving to Node #0,3 Current State: 10:[18, 26, 19], Operations: ['38-19=19'] Exploring Operation: 26-18=8, Resulting Numbers: [19, 8] Generated Node #0,3,0: 10:[19, 8] Operation: 26-18=8 Exploring Operation: 26-19=7, Resulting Numbers: [18, 7] Generated Node #0,3,1: 10:[18, 7] Operation: 26-19=7 Exploring Operation: 18+26=44, Resulting Numbers: [19, 44] Generated Node #0,3,2: 10:[19, 44] Operation: 18+26=44 Exploring Operation: 19-18=1, Resulting Numbers: [26, 1] Generated Node #0,3,3: 10:[26, 1] Operation: 19-18=1 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 10:[18, 7], Operations: ['38-19=19', '26-19=7'] Exploring Operation: 18+7=25, Resulting Numbers: [25] 25,10 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,10 unequal: No Solution Exploring Operation: 18*7=126, Resulting Numbers: [126] 126,10 unequal: No Solution No 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: 10:[19, 8], Operations: ['38-19=19', '26-18=8'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,10 unequal: No Solution Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,10 unequal: No Solution Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,10 unequal: No Solution No 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: 10:[26, 1], Operations: ['38-19=19', '19-18=1'] Exploring Operation: 26*1=26, Resulting Numbers: [26] 26,10 unequal: No Solution Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,10 unequal: No Solution Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,10 unequal: No Solution Exploring Operation: 26+1=27, Resulting Numbers: [27] 27,10 unequal: No Solution No 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: 10:[19, 44], Operations: ['38-19=19', '18+26=44'] Exploring Operation: 19*44=836, Resulting Numbers: [836] 836,10 unequal: No Solution Exploring Operation: 19+44=63, Resulting Numbers: [63] 63,10 unequal: No Solution Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,10 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: 10:[19, 26, 20], Operations: ['38-18=20'] Exploring Operation: 26-20=6, Resulting Numbers: [19, 6] Generated Node #0,0,0: 10:[19, 6] Operation: 26-20=6 Exploring Operation: 19+26=45, Resulting Numbers: [20, 45] Generated Node #0,0,1: 10:[20, 45] Operation: 19+26=45 Exploring Operation: 26-19=7, Resulting Numbers: [20, 7] Generated Node #0,0,2: 10:[20, 7] Operation: 26-19=7 Exploring Operation: 20-19=1, Resulting Numbers: [26, 1] Generated Node #0,0,3: 10:[26, 1] Operation: 20-19=1 Moving to Node #0,2,1 Current State: 10:[2, 8], Operations: ['38/19=2', '26-18=8'] Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,10 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[18, 19, 38, 26], Operations: [] Exploring Operation: 38/19=2, Resulting Numbers: [18, 26, 2] Generated Node #0,2: 10:[18, 26, 2] Operation: 38/19=2 Moving to Node #0,2 Current State: 10:[18, 26, 2], Operations: ['38/19=2'] Exploring Operation: 26-18=8, Resulting Numbers: [2, 8] Generated Node #0,2,1: 10:[2, 8] Operation: 26-18=8 Moving to Node #0,2,1 Current State: 10:[2, 8], Operations: ['38/19=2', '26-18=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.966146
hs_4
sum_heuristic
[ 78, 8, 82, 19 ]
39
[ "78+82=160", "160/8=20", "19+20=39" ]
Current State: 39:[78, 8, 82, 19], Operations: [] Exploring Operation: 78+82=160, Resulting Numbers: [8, 19, 160] Generated Node #2: [8, 19, 160] from Operation: 78+82=160 Current State: 39:[8, 19, 160], Operations: ['78+82=160'] Exploring Operation: 160/8=20, Resulting Numbers: [19, 20] Generated Node #3: [19, 20] from Operation: 160/8=20 Current State: 39:[19, 20], Operations: ['78+82=160', '160/8=20'] Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[78, 8, 82, 19], Operations: [] Exploring Operation: 78-19=59, Resulting Numbers: [8, 82, 59] Generated Node #0,0: 39:[8, 82, 59] Operation: 78-19=59 Exploring Operation: 82-78=4, Resulting Numbers: [8, 19, 4] Generated Node #0,1: 39:[8, 19, 4] Operation: 82-78=4 Moving to Node #0,1 Current State: 39:[8, 19, 4], Operations: ['82-78=4'] Exploring Operation: 8+4=12, Resulting Numbers: [19, 12] Generated Node #0,1,0: 39:[19, 12] Operation: 8+4=12 Exploring Operation: 19-8=11, Resulting Numbers: [4, 11] Generated Node #0,1,1: 39:[4, 11] Operation: 19-8=11 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[4, 11], Operations: ['82-78=4', '19-8=11'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,39 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 #0,1,0 Current State: 39:[19, 12], Operations: ['82-78=4', '8+4=12'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,39 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: 39:[8, 82, 59], Operations: ['78-19=59'] Exploring Operation: 82-8=74, Resulting Numbers: [59, 74] Generated Node #0,0,0: 39:[59, 74] Operation: 82-8=74 Exploring Operation: 82-59=23, Resulting Numbers: [8, 23] Generated Node #0,0,1: 39:[8, 23] Operation: 82-59=23 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 39:[8, 23], Operations: ['78-19=59', '82-59=23'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 8+23=31, Resulting Numbers: [31] 31,39 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 #0,0,0 Current State: 39:[59, 74], Operations: ['78-19=59', '82-8=74'] Exploring Operation: 59+74=133, Resulting Numbers: [133] 133,39 unequal: No Solution Exploring Operation: 74-59=15, Resulting Numbers: [15] 15,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 29, 12, 24, 6 ]
90
[ "29-24=5", "12+6=18", "5*18=90" ]
Current State: 90:[29, 12, 24, 6], Operations: [] Exploring Operation: 29-24=5, Resulting Numbers: [12, 6, 5] Generated Node #2: [12, 6, 5] from Operation: 29-24=5 Current State: 90:[12, 6, 5], Operations: ['29-24=5'] Exploring Operation: 12+6=18, Resulting Numbers: [5, 18] Generated Node #3: [5, 18] from Operation: 12+6=18 Current State: 90:[5, 18], Operations: ['29-24=5', '12+6=18'] Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[29, 12, 24, 6], Operations: [] Exploring Operation: 29-24=5, Resulting Numbers: [12, 6, 5] Generated Node #0,0: 90:[12, 6, 5] Operation: 29-24=5 Exploring Operation: 24+6=30, Resulting Numbers: [29, 12, 30] Generated Node #0,1: 90:[29, 12, 30] Operation: 24+6=30 Exploring Operation: 24/12=2, Resulting Numbers: [29, 6, 2] Generated Node #0,2: 90:[29, 6, 2] Operation: 24/12=2 Exploring Operation: 24-12=12, Resulting Numbers: [29, 6, 12] Generated Node #0,3: 90:[29, 6, 12] Operation: 24-12=12 Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[29, 6, 2], Operations: ['24/12=2'] Exploring Operation: 6-2=4, Resulting Numbers: [29, 4] Generated Node #0,2,0: 90:[29, 4] Operation: 6-2=4 Exploring Operation: 6+2=8, Resulting Numbers: [29, 8] Generated Node #0,2,1: 90:[29, 8] Operation: 6+2=8 Exploring Operation: 6/2=3, Resulting Numbers: [29, 3] Generated Node #0,2,2: 90:[29, 3] Operation: 6/2=3 Exploring Operation: 29+2=31, Resulting Numbers: [6, 31] Generated Node #0,2,3: 90:[6, 31] Operation: 29+2=31 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 90:[29, 3], Operations: ['24/12=2', '6/2=3'] Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,90 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,90 unequal: No Solution Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 90:[6, 31], Operations: ['24/12=2', '29+2=31'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,90 unequal: No Solution Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,90 unequal: No Solution Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 90:[29, 4], Operations: ['24/12=2', '6-2=4'] Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,90 unequal: No Solution Exploring Operation: 29*4=116, Resulting Numbers: [116] 116,90 unequal: No Solution Exploring Operation: 29+4=33, Resulting Numbers: [33] 33,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 90:[29, 8], Operations: ['24/12=2', '6+2=8'] Exploring Operation: 29*8=232, Resulting Numbers: [232] 232,90 unequal: No Solution Exploring Operation: 29+8=37, Resulting Numbers: [37] 37,90 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[12, 6, 5], Operations: ['29-24=5'] Exploring Operation: 12/6=2, Resulting Numbers: [5, 2] Generated Node #0,0,0: 90:[5, 2] Operation: 12/6=2 Exploring Operation: 12+5=17, Resulting Numbers: [6, 17] Generated Node #0,0,1: 90:[6, 17] Operation: 12+5=17 Exploring Operation: 12+6=18, Resulting Numbers: [5, 18] Generated Node #0,0,2: 90:[5, 18] Operation: 12+6=18 Exploring Operation: 12-6=6, Resulting Numbers: [5, 6] Generated Node #0,0,3: 90:[5, 6] Operation: 12-6=6 Moving to Node #0,0,0 Current State: 90:[5, 2], Operations: ['29-24=5', '12/6=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,90 unequal: No Solution Moving to Node #0,0,3 Current State: 90:[5, 6], Operations: ['29-24=5', '12-6=6'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,90 unequal: No Solution Moving to Node #0,0,2 Current State: 90:[5, 18], Operations: ['29-24=5', '12+6=18'] Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[29, 12, 24, 6], Operations: [] Exploring Operation: 29-24=5, Resulting Numbers: [12, 6, 5] Generated Node #0,0: 90:[12, 6, 5] Operation: 29-24=5 Moving to Node #0,0 Current State: 90:[12, 6, 5], Operations: ['29-24=5'] Exploring Operation: 12+6=18, Resulting Numbers: [5, 18] Generated Node #0,0,2: 90:[5, 18] Operation: 12+6=18 Moving to Node #0,0,2 Current State: 90:[5, 18], Operations: ['29-24=5', '12+6=18'] Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_4
sum_heuristic
[ 60, 11, 41, 8 ]
29
[ "60*8=480", "11*41=451", "480-451=29" ]
Current State: 29:[60, 11, 41, 8], Operations: [] Exploring Operation: 60*8=480, Resulting Numbers: [11, 41, 480] Generated Node #2: [11, 41, 480] from Operation: 60*8=480 Current State: 29:[11, 41, 480], Operations: ['60*8=480'] Exploring Operation: 11*41=451, Resulting Numbers: [480, 451] Generated Node #3: [480, 451] from Operation: 11*41=451 Current State: 29:[480, 451], Operations: ['60*8=480', '11*41=451'] Exploring Operation: 480-451=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[60, 11, 41, 8], Operations: [] Exploring Operation: 60-11=49, Resulting Numbers: [41, 8, 49] Generated Node #0,0: 29:[41, 8, 49] Operation: 60-11=49 Exploring Operation: 60-41=19, Resulting Numbers: [11, 8, 19] Generated Node #0,1: 29:[11, 8, 19] Operation: 60-41=19 Moving to Node #0,1 Current State: 29:[11, 8, 19], Operations: ['60-41=19'] Exploring Operation: 11+8=19, Resulting Numbers: [19, 19] Generated Node #0,1,0: 29:[19, 19] Operation: 11+8=19 Exploring Operation: 8+19=27, Resulting Numbers: [11, 27] Generated Node #0,1,1: 29:[11, 27] Operation: 8+19=27 Moving to Node #0,0 Current State: 29:[41, 8, 49], Operations: ['60-11=49'] Exploring Operation: 49-8=41, Resulting Numbers: [41, 41] Generated Node #0,0,0: 29:[41, 41] Operation: 49-8=41 Exploring Operation: 41-8=33, Resulting Numbers: [49, 33] Generated Node #0,0,1: 29:[49, 33] Operation: 41-8=33 Moving to Node #0,1,0 Current State: 29:[19, 19], Operations: ['60-41=19', '11+8=19'] Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[11, 27], Operations: ['60-41=19', '8+19=27'] Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,29 unequal: No Solution Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[49, 33], Operations: ['60-11=49', '41-8=33'] Exploring Operation: 49+33=82, Resulting Numbers: [82] 82,29 unequal: No Solution Exploring Operation: 49-33=16, Resulting Numbers: [16] 16,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[41, 41], Operations: ['60-11=49', '49-8=41'] Exploring Operation: 41/41=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 41-41=0, Resulting Numbers: [0] 0,29 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 74, 30, 15, 79 ]
40
[ "74+30=104", "79-15=64", "104-64=40" ]
Current State: 40:[74, 30, 15, 79], Operations: [] Exploring Operation: 74+30=104, Resulting Numbers: [15, 79, 104] Generated Node #2: [15, 79, 104] from Operation: 74+30=104 Current State: 40:[15, 79, 104], Operations: ['74+30=104'] Exploring Operation: 79-15=64, Resulting Numbers: [104, 64] Generated Node #3: [104, 64] from Operation: 79-15=64 Current State: 40:[104, 64], Operations: ['74+30=104', '79-15=64'] Exploring Operation: 104-64=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[74, 30, 15, 79], Operations: [] Exploring Operation: 79-74=5, Resulting Numbers: [30, 15, 5] Generated Node #0,0: 40:[30, 15, 5] Operation: 79-74=5 Moving to Node #0,0 Current State: 40:[30, 15, 5], Operations: ['79-74=5'] Exploring Operation: 30/15=2, Resulting Numbers: [5, 2] Generated Node #0,0,0: 40:[5, 2] Operation: 30/15=2 Moving to Node #0,0,0 Current State: 40:[5, 2], Operations: ['79-74=5', '30/15=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,40 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 68, 47, 4, 46 ]
65
[ "68+47=115", "4+46=50", "115-50=65" ]
Current State: 65:[68, 47, 4, 46], Operations: [] Exploring Operation: 68+47=115, Resulting Numbers: [4, 46, 115] Generated Node #2: [4, 46, 115] from Operation: 68+47=115 Current State: 65:[4, 46, 115], Operations: ['68+47=115'] Exploring Operation: 4+46=50, Resulting Numbers: [115, 50] Generated Node #3: [115, 50] from Operation: 4+46=50 Current State: 65:[115, 50], Operations: ['68+47=115', '4+46=50'] Exploring Operation: 115-50=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[68, 47, 4, 46], Operations: [] Exploring Operation: 47+46=93, Resulting Numbers: [68, 4, 93] Generated Node #0,0: 65:[68, 4, 93] Operation: 47+46=93 Exploring Operation: 68-46=22, Resulting Numbers: [47, 4, 22] Generated Node #0,1: 65:[47, 4, 22] Operation: 68-46=22 Exploring Operation: 47-46=1, Resulting Numbers: [68, 4, 1] Generated Node #0,2: 65:[68, 4, 1] Operation: 47-46=1 Exploring Operation: 68-47=21, Resulting Numbers: [4, 46, 21] Generated Node #0,3: 65:[4, 46, 21] Operation: 68-47=21 Moving to Node #0,2 Current State: 65:[68, 4, 1], Operations: ['47-46=1'] Exploring Operation: 68-1=67, Resulting Numbers: [4, 67] Generated Node #0,2,0: 65:[4, 67] Operation: 68-1=67 Exploring Operation: 68/1=68, Resulting Numbers: [4, 68] Generated Node #0,2,1: 65:[4, 68] Operation: 68/1=68 Exploring Operation: 68*1=68, Resulting Numbers: [4, 68] Generated Node #0,2,2: 65:[4, 68] Operation: 68*1=68 Exploring Operation: 4+1=5, Resulting Numbers: [68, 5] Generated Node #0,2,3: 65:[68, 5] Operation: 4+1=5 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 65:[4, 67], Operations: ['47-46=1', '68-1=67'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,65 unequal: No Solution Exploring Operation: 4*67=268, Resulting Numbers: [268] 268,65 unequal: No Solution Exploring Operation: 4+67=71, Resulting Numbers: [71] 71,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 65:[68, 5], Operations: ['47-46=1', '4+1=5'] Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,65 unequal: No Solution Exploring Operation: 68+5=73, Resulting Numbers: [73] 73,65 unequal: No Solution Exploring Operation: 68*5=340, Resulting Numbers: [340] 340,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 65:[4, 68], Operations: ['47-46=1', '68/1=68'] Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,65 unequal: No Solution Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,65 unequal: No Solution Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,65 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 65:[4, 68], Operations: ['47-46=1', '68*1=68'] Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,65 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,65 unequal: No Solution Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,65 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,65 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: 65:[4, 46, 21], Operations: ['68-47=21'] Exploring Operation: 4+46=50, Resulting Numbers: [21, 50] Generated Node #0,3,0: 65:[21, 50] Operation: 4+46=50 Exploring Operation: 46-21=25, Resulting Numbers: [4, 25] Generated Node #0,3,1: 65:[4, 25] Operation: 46-21=25 Exploring Operation: 21-4=17, Resulting Numbers: [46, 17] Generated Node #0,3,2: 65:[46, 17] Operation: 21-4=17 Exploring Operation: 46+21=67, Resulting Numbers: [4, 67] Generated Node #0,3,3: 65:[4, 67] Operation: 46+21=67 Moving to Node #0,1 Current State: 65:[47, 4, 22], Operations: ['68-46=22'] Exploring Operation: 47+4=51, Resulting Numbers: [22, 51] Generated Node #0,1,0: 65:[22, 51] Operation: 47+4=51 Exploring Operation: 22-4=18, Resulting Numbers: [47, 18] Generated Node #0,1,1: 65:[47, 18] Operation: 22-4=18 Exploring Operation: 47+22=69, Resulting Numbers: [4, 69] Generated Node #0,1,2: 65:[4, 69] Operation: 47+22=69 Exploring Operation: 47-22=25, Resulting Numbers: [4, 25] Generated Node #0,1,3: 65:[4, 25] Operation: 47-22=25 Moving to Node #0,0 Current State: 65:[68, 4, 93], Operations: ['47+46=93'] Exploring Operation: 68/4=17, Resulting Numbers: [93, 17] Generated Node #0,0,0: 65:[93, 17] Operation: 68/4=17 Exploring Operation: 93-68=25, Resulting Numbers: [4, 25] Generated Node #0,0,1: 65:[4, 25] Operation: 93-68=25 Exploring Operation: 68-4=64, Resulting Numbers: [93, 64] Generated Node #0,0,2: 65:[93, 64] Operation: 68-4=64 Exploring Operation: 93-4=89, Resulting Numbers: [68, 89] Generated Node #0,0,3: 65:[68, 89] Operation: 93-4=89 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 65:[4, 25], Operations: ['47+46=93', '93-68=25'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,65 unequal: No Solution Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 65:[68, 89], Operations: ['47+46=93', '93-4=89'] Exploring Operation: 68+89=157, Resulting Numbers: [157] 157,65 unequal: No Solution Exploring Operation: 89-68=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 68*89=6052, Resulting Numbers: [6052] 6052,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 65:[93, 64], Operations: ['47+46=93', '68-4=64'] Exploring Operation: 93-64=29, Resulting Numbers: [29] 29,65 unequal: No Solution Exploring Operation: 93*64=5952, Resulting Numbers: [5952] 5952,65 unequal: No Solution Exploring Operation: 93+64=157, Resulting Numbers: [157] 157,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[93, 17], Operations: ['47+46=93', '68/4=17'] Exploring Operation: 93*17=1581, Resulting Numbers: [1581] 1581,65 unequal: No Solution Exploring Operation: 93+17=110, Resulting Numbers: [110] 110,65 unequal: No Solution Exploring Operation: 93-17=76, Resulting Numbers: [76] 76,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,3 Current State: 65:[4, 67], Operations: ['68-47=21', '46+21=67'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,65 unequal: No Solution Exploring Operation: 4*67=268, Resulting Numbers: [268] 268,65 unequal: No Solution Exploring Operation: 4+67=71, Resulting Numbers: [71] 71,65 unequal: No Solution Moving to Node #0,1,2 Current State: 65:[4, 69], Operations: ['68-46=22', '47+22=69'] Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,65 unequal: No Solution Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[68, 47, 4, 46], Operations: [] Exploring Operation: 68-46=22, Resulting Numbers: [47, 4, 22] Generated Node #0,1: 65:[47, 4, 22] Operation: 68-46=22 Moving to Node #0,1 Current State: 65:[47, 4, 22], Operations: ['68-46=22'] Exploring Operation: 47+22=69, Resulting Numbers: [4, 69] Generated Node #0,1,2: 65:[4, 69] Operation: 47+22=69 Moving to Node #0,1,2 Current State: 65:[4, 69], Operations: ['68-46=22', '47+22=69'] Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
0.952257
hs_4
sum_heuristic
[ 46, 38, 55, 36 ]
37
[ "38-36=2", "46*2=92", "92-55=37" ]
Current State: 37:[46, 38, 55, 36], Operations: [] Exploring Operation: 38-36=2, Resulting Numbers: [46, 55, 2] Generated Node #2: [46, 55, 2] from Operation: 38-36=2 Current State: 37:[46, 55, 2], Operations: ['38-36=2'] Exploring Operation: 46*2=92, Resulting Numbers: [55, 92] Generated Node #3: [55, 92] from Operation: 46*2=92 Current State: 37:[55, 92], Operations: ['38-36=2', '46*2=92'] Exploring Operation: 92-55=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[46, 38, 55, 36], Operations: [] Exploring Operation: 55-36=19, Resulting Numbers: [46, 38, 19] Generated Node #0,0: 37:[46, 38, 19] Operation: 55-36=19 Exploring Operation: 55-38=17, Resulting Numbers: [46, 36, 17] Generated Node #0,1: 37:[46, 36, 17] Operation: 55-38=17 Exploring Operation: 46-36=10, Resulting Numbers: [38, 55, 10] Generated Node #0,2: 37:[38, 55, 10] Operation: 46-36=10 Exploring Operation: 55-46=9, Resulting Numbers: [38, 36, 9] Generated Node #0,3: 37:[38, 36, 9] Operation: 55-46=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[46, 38, 19], Operations: ['55-36=19'] Exploring Operation: 38-19=19, Resulting Numbers: [46, 19] Generated Node #0,0,0: 37:[46, 19] Operation: 38-19=19 Exploring Operation: 38+19=57, Resulting Numbers: [46, 57] Generated Node #0,0,1: 37:[46, 57] Operation: 38+19=57 Exploring Operation: 46+19=65, Resulting Numbers: [38, 65] Generated Node #0,0,2: 37:[38, 65] Operation: 46+19=65 Exploring Operation: 46-19=27, Resulting Numbers: [38, 27] Generated Node #0,0,3: 37:[38, 27] Operation: 46-19=27 Moving to Node #0,0,3 Current State: 37:[38, 27], Operations: ['55-36=19', '46-19=27'] Exploring Operation: 38+27=65, Resulting Numbers: [65] 65,37 unequal: No Solution Exploring Operation: 38*27=1026, Resulting Numbers: [1026] 1026,37 unequal: No Solution Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[46, 19], Operations: ['55-36=19', '38-19=19'] Exploring Operation: 46*19=874, Resulting Numbers: [874] 874,37 unequal: No Solution Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 46+19=65, Resulting Numbers: [65] 65,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[38, 65], Operations: ['55-36=19', '46+19=65'] Exploring Operation: 38*65=2470, Resulting Numbers: [2470] 2470,37 unequal: No Solution Exploring Operation: 65-38=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 38+65=103, Resulting Numbers: [103] 103,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[46, 57], Operations: ['55-36=19', '38+19=57'] Exploring Operation: 46+57=103, Resulting Numbers: [103] 103,37 unequal: No Solution Exploring Operation: 46*57=2622, Resulting Numbers: [2622] 2622,37 unequal: No Solution Exploring Operation: 57-46=11, Resulting Numbers: [11] 11,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[46, 36, 17], Operations: ['55-38=17'] Exploring Operation: 36-17=19, Resulting Numbers: [46, 19] Generated Node #0,1,0: 37:[46, 19] Operation: 36-17=19 Exploring Operation: 46-17=29, Resulting Numbers: [36, 29] Generated Node #0,1,1: 37:[36, 29] Operation: 46-17=29 Exploring Operation: 36+17=53, Resulting Numbers: [46, 53] Generated Node #0,1,2: 37:[46, 53] Operation: 36+17=53 Exploring Operation: 46+17=63, Resulting Numbers: [36, 63] Generated Node #0,1,3: 37:[36, 63] Operation: 46+17=63 Moving to Node #0,1,1 Current State: 37:[36, 29], Operations: ['55-38=17', '46-17=29'] Exploring Operation: 36+29=65, Resulting Numbers: [65] 65,37 unequal: No Solution Exploring Operation: 36*29=1044, Resulting Numbers: [1044] 1044,37 unequal: No Solution Exploring Operation: 36-29=7, Resulting Numbers: [7] 7,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[46, 53], Operations: ['55-38=17', '36+17=53'] Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 46+53=99, Resulting Numbers: [99] 99,37 unequal: No Solution Exploring Operation: 46*53=2438, Resulting Numbers: [2438] 2438,37 unequal: No Solution Moving to Node #0,1,3 Current State: 37:[36, 63], Operations: ['55-38=17', '46+17=63'] Exploring Operation: 36*63=2268, Resulting Numbers: [2268] 2268,37 unequal: No Solution Exploring Operation: 36+63=99, Resulting Numbers: [99] 99,37 unequal: No Solution Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[46, 19], Operations: ['55-38=17', '36-17=19'] Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 46+19=65, Resulting Numbers: [65] 65,37 unequal: No Solution Exploring Operation: 46*19=874, Resulting Numbers: [874] 874,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 37:[38, 36, 9], Operations: ['55-46=9'] Exploring Operation: 36+9=45, Resulting Numbers: [38, 45] Generated Node #0,3,0: 37:[38, 45] Operation: 36+9=45 Exploring Operation: 36-9=27, Resulting Numbers: [38, 27] Generated Node #0,3,1: 37:[38, 27] Operation: 36-9=27 Exploring Operation: 38-9=29, Resulting Numbers: [36, 29] Generated Node #0,3,2: 37:[36, 29] Operation: 38-9=29 Exploring Operation: 38+9=47, Resulting Numbers: [36, 47] Generated Node #0,3,3: 37:[36, 47] Operation: 38+9=47 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 37:[38, 45], Operations: ['55-46=9', '36+9=45'] Exploring Operation: 38*45=1710, Resulting Numbers: [1710] 1710,37 unequal: No Solution Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,37 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,37 unequal: No Solution No 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: 37:[36, 29], Operations: ['55-46=9', '38-9=29'] Exploring Operation: 36*29=1044, Resulting Numbers: [1044] 1044,37 unequal: No Solution Exploring Operation: 36-29=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 36+29=65, Resulting Numbers: [65] 65,37 unequal: No Solution No 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: 37:[38, 27], Operations: ['55-46=9', '36-9=27'] Exploring Operation: 38*27=1026, Resulting Numbers: [1026] 1026,37 unequal: No Solution Exploring Operation: 38+27=65, Resulting Numbers: [65] 65,37 unequal: No Solution Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,37 unequal: No Solution No 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: 37:[36, 47], Operations: ['55-46=9', '38+9=47'] Exploring Operation: 36*47=1692, Resulting Numbers: [1692] 1692,37 unequal: No Solution Exploring Operation: 47-36=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 36+47=83, Resulting Numbers: [83] 83,37 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: 37:[38, 55, 10], Operations: ['46-36=10'] Exploring Operation: 55+10=65, Resulting Numbers: [38, 65] Generated Node #0,2,0: 37:[38, 65] Operation: 55+10=65 Exploring Operation: 55-10=45, Resulting Numbers: [38, 45] Generated Node #0,2,1: 37:[38, 45] Operation: 55-10=45 Exploring Operation: 38-10=28, Resulting Numbers: [55, 28] Generated Node #0,2,2: 37:[55, 28] Operation: 38-10=28 Exploring Operation: 38+10=48, Resulting Numbers: [55, 48] Generated Node #0,2,3: 37:[55, 48] Operation: 38+10=48 Moving to Node #0,2,1 Current State: 37:[38, 45], Operations: ['46-36=10', '55-10=45'] Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,37 unequal: No Solution Exploring Operation: 38*45=1710, Resulting Numbers: [1710] 1710,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[55, 28], Operations: ['46-36=10', '38-10=28'] Exploring Operation: 55*28=1540, Resulting Numbers: [1540] 1540,37 unequal: No Solution Exploring Operation: 55+28=83, Resulting Numbers: [83] 83,37 unequal: No Solution Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[55, 48], Operations: ['46-36=10', '38+10=48'] Exploring Operation: 55*48=2640, Resulting Numbers: [2640] 2640,37 unequal: No Solution Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 55+48=103, Resulting Numbers: [103] 103,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[38, 65], Operations: ['46-36=10', '55+10=65'] Exploring Operation: 38+65=103, Resulting Numbers: [103] 103,37 unequal: No Solution Exploring Operation: 38*65=2470, Resulting Numbers: [2470] 2470,37 unequal: No Solution Exploring Operation: 65-38=27, Resulting Numbers: [27] 27,37 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
[ 34, 50, 14, 53 ]
51
[ "50-34=16", "14+53=67", "67-16=51" ]
Current State: 51:[34, 50, 14, 53], Operations: [] Exploring Operation: 50-34=16, Resulting Numbers: [14, 53, 16] Generated Node #2: [14, 53, 16] from Operation: 50-34=16 Current State: 51:[14, 53, 16], Operations: ['50-34=16'] Exploring Operation: 14+53=67, Resulting Numbers: [16, 67] Generated Node #3: [16, 67] from Operation: 14+53=67 Current State: 51:[16, 67], Operations: ['50-34=16', '14+53=67'] Exploring Operation: 67-16=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[34, 50, 14, 53], Operations: [] Exploring Operation: 34-14=20, Resulting Numbers: [50, 53, 20] Generated Node #0,0: 51:[50, 53, 20] Operation: 34-14=20 Exploring Operation: 34+14=48, Resulting Numbers: [50, 53, 48] Generated Node #0,1: 51:[50, 53, 48] Operation: 34+14=48 Exploring Operation: 50-34=16, Resulting Numbers: [14, 53, 16] Generated Node #0,2: 51:[14, 53, 16] Operation: 50-34=16 Exploring Operation: 53-34=19, Resulting Numbers: [50, 14, 19] Generated Node #0,3: 51:[50, 14, 19] Operation: 53-34=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[50, 53, 20], Operations: ['34-14=20'] Exploring Operation: 53-50=3, Resulting Numbers: [20, 3] Generated Node #0,0,0: 51:[20, 3] Operation: 53-50=3 Exploring Operation: 50-20=30, Resulting Numbers: [53, 30] Generated Node #0,0,1: 51:[53, 30] Operation: 50-20=30 Exploring Operation: 53-20=33, Resulting Numbers: [50, 33] Generated Node #0,0,2: 51:[50, 33] Operation: 53-20=33 Exploring Operation: 50+20=70, Resulting Numbers: [53, 70] Generated Node #0,0,3: 51:[53, 70] Operation: 50+20=70 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[20, 3], Operations: ['34-14=20', '53-50=3'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,51 unequal: No Solution Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,51 unequal: No Solution Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 51:[53, 30], Operations: ['34-14=20', '50-20=30'] Exploring Operation: 53*30=1590, Resulting Numbers: [1590] 1590,51 unequal: No Solution Exploring Operation: 53+30=83, Resulting Numbers: [83] 83,51 unequal: No Solution Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 51:[50, 33], Operations: ['34-14=20', '53-20=33'] Exploring Operation: 50*33=1650, Resulting Numbers: [1650] 1650,51 unequal: No Solution Exploring Operation: 50-33=17, Resulting Numbers: [17] 17,51 unequal: No Solution Exploring Operation: 50+33=83, Resulting Numbers: [83] 83,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 51:[53, 70], Operations: ['34-14=20', '50+20=70'] Exploring Operation: 53*70=3710, Resulting Numbers: [3710] 3710,51 unequal: No Solution Exploring Operation: 53+70=123, Resulting Numbers: [123] 123,51 unequal: No Solution Exploring Operation: 70-53=17, Resulting Numbers: [17] 17,51 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: 51:[50, 53, 48], Operations: ['34+14=48'] Exploring Operation: 50-48=2, Resulting Numbers: [53, 2] Generated Node #0,1,0: 51:[53, 2] Operation: 50-48=2 Exploring Operation: 53-50=3, Resulting Numbers: [48, 3] Generated Node #0,1,1: 51:[48, 3] Operation: 53-50=3 Exploring Operation: 53-48=5, Resulting Numbers: [50, 5] Generated Node #0,1,2: 51:[50, 5] Operation: 53-48=5 Exploring Operation: 50+48=98, Resulting Numbers: [53, 98] Generated Node #0,1,3: 51:[53, 98] Operation: 50+48=98 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 51:[53, 2], Operations: ['34+14=48', '50-48=2'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[34, 50, 14, 53], Operations: [] Exploring Operation: 34+14=48, Resulting Numbers: [50, 53, 48] Generated Node #0,1: 51:[50, 53, 48] Operation: 34+14=48 Moving to Node #0,1 Current State: 51:[50, 53, 48], Operations: ['34+14=48'] Exploring Operation: 50-48=2, Resulting Numbers: [53, 2] Generated Node #0,1,0: 51:[53, 2] Operation: 50-48=2 Moving to Node #0,1,0 Current State: 51:[53, 2], Operations: ['34+14=48', '50-48=2'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic
[ 30, 57, 63, 80 ]
76
[ "57+63=120", "120/30=4", "80-4=76" ]
Current State: 76:[30, 57, 63, 80], Operations: [] Exploring Operation: 57+63=120, Resulting Numbers: [30, 80, 120] Generated Node #2: [30, 80, 120] from Operation: 57+63=120 Current State: 76:[30, 80, 120], Operations: ['57+63=120'] Exploring Operation: 120/30=4, Resulting Numbers: [80, 4] Generated Node #3: [80, 4] from Operation: 120/30=4 Current State: 76:[80, 4], Operations: ['57+63=120', '120/30=4'] Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[30, 57, 63, 80], Operations: [] Exploring Operation: 57-30=27, Resulting Numbers: [63, 80, 27] Generated Node #0,0: 76:[63, 80, 27] Operation: 57-30=27 Exploring Operation: 80-57=23, Resulting Numbers: [30, 63, 23] Generated Node #0,1: 76:[30, 63, 23] Operation: 80-57=23 Exploring Operation: 30+57=87, Resulting Numbers: [63, 80, 87] Generated Node #0,2: 76:[63, 80, 87] Operation: 30+57=87 Exploring Operation: 63-57=6, Resulting Numbers: [30, 80, 6] Generated Node #0,3: 76:[30, 80, 6] Operation: 63-57=6 Moving to Node #0,3 Current State: 76:[30, 80, 6], Operations: ['63-57=6'] Exploring Operation: 80-6=74, Resulting Numbers: [30, 74] Generated Node #0,3,0: 76:[30, 74] Operation: 80-6=74 Exploring Operation: 30-6=24, Resulting Numbers: [80, 24] Generated Node #0,3,1: 76:[80, 24] Operation: 30-6=24 Exploring Operation: 30+6=36, Resulting Numbers: [80, 36] Generated Node #0,3,2: 76:[80, 36] Operation: 30+6=36 Exploring Operation: 30/6=5, Resulting Numbers: [80, 5] Generated Node #0,3,3: 76:[80, 5] Operation: 30/6=5 Moving to Node #0,1 Current State: 76:[30, 63, 23], Operations: ['80-57=23'] Exploring Operation: 30-23=7, Resulting Numbers: [63, 7] Generated Node #0,1,0: 76:[63, 7] Operation: 30-23=7 Exploring Operation: 63-23=40, Resulting Numbers: [30, 40] Generated Node #0,1,1: 76:[30, 40] Operation: 63-23=40 Exploring Operation: 63-30=33, Resulting Numbers: [23, 33] Generated Node #0,1,2: 76:[23, 33] Operation: 63-30=33 Exploring Operation: 63+23=86, Resulting Numbers: [30, 86] Generated Node #0,1,3: 76:[30, 86] Operation: 63+23=86 Moving to Node #0,0 Current State: 76:[63, 80, 27], Operations: ['57-30=27'] Exploring Operation: 63-27=36, Resulting Numbers: [80, 36] Generated Node #0,0,0: 76:[80, 36] Operation: 63-27=36 Exploring Operation: 63+27=90, Resulting Numbers: [80, 90] Generated Node #0,0,1: 76:[80, 90] Operation: 63+27=90 Exploring Operation: 80-63=17, Resulting Numbers: [27, 17] Generated Node #0,0,2: 76:[27, 17] Operation: 80-63=17 Exploring Operation: 80-27=53, Resulting Numbers: [63, 53] Generated Node #0,0,3: 76:[63, 53] Operation: 80-27=53 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[80, 36], Operations: ['57-30=27', '63-27=36'] Exploring Operation: 80*36=2880, Resulting Numbers: [2880] 2880,76 unequal: No Solution Exploring Operation: 80-36=44, Resulting Numbers: [44] 44,76 unequal: No Solution Exploring Operation: 80+36=116, Resulting Numbers: [116] 116,76 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:[27, 17], Operations: ['57-30=27', '80-63=17'] Exploring Operation: 27+17=44, Resulting Numbers: [44] 44,76 unequal: No Solution Exploring Operation: 27*17=459, Resulting Numbers: [459] 459,76 unequal: No Solution Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,76 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 #0,0,1 Current State: 76:[80, 90], Operations: ['57-30=27', '63+27=90'] Exploring Operation: 90-80=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 80+90=170, Resulting Numbers: [170] 170,76 unequal: No Solution Exploring Operation: 80*90=7200, Resulting Numbers: [7200] 7200,76 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 #0,0,3 Current State: 76:[63, 53], Operations: ['57-30=27', '80-27=53'] Exploring Operation: 63*53=3339, Resulting Numbers: [3339] 3339,76 unequal: No Solution Exploring Operation: 63-53=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 63+53=116, Resulting Numbers: [116] 116,76 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: 76:[63, 80, 87], Operations: ['30+57=87'] Exploring Operation: 80-63=17, Resulting Numbers: [87, 17] Generated Node #0,2,0: 76:[87, 17] Operation: 80-63=17 Exploring Operation: 87-80=7, Resulting Numbers: [63, 7] Generated Node #0,2,1: 76:[63, 7] Operation: 87-80=7 Exploring Operation: 87-63=24, Resulting Numbers: [80, 24] Generated Node #0,2,2: 76:[80, 24] Operation: 87-63=24 Exploring Operation: 63+80=143, Resulting Numbers: [87, 143] Generated Node #0,2,3: 76:[87, 143] Operation: 63+80=143 Moving to Node #0,3,3 Current State: 76:[80, 5], Operations: ['63-57=6', '30/6=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,76 unequal: No Solution Exploring Operation: 80*5=400, Resulting Numbers: [400] 400,76 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,76 unequal: No Solution Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[80, 36], Operations: ['63-57=6', '30+6=36'] Exploring Operation: 80+36=116, Resulting Numbers: [116] 116,76 unequal: No Solution Exploring Operation: 80-36=44, Resulting Numbers: [44] 44,76 unequal: No Solution Exploring Operation: 80*36=2880, Resulting Numbers: [2880] 2880,76 unequal: No Solution Moving to Node #0,3,1 Current State: 76:[80, 24], Operations: ['63-57=6', '30-6=24'] Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,76 unequal: No Solution Exploring Operation: 80+24=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 80*24=1920, Resulting Numbers: [1920] 1920,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[23, 33], Operations: ['80-57=23', '63-30=33'] Exploring Operation: 23*33=759, Resulting Numbers: [759] 759,76 unequal: No Solution Exploring Operation: 23+33=56, Resulting Numbers: [56] 56,76 unequal: No Solution Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[80, 24], Operations: ['30+57=87', '87-63=24'] Exploring Operation: 80*24=1920, Resulting Numbers: [1920] 1920,76 unequal: No Solution Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,76 unequal: No Solution Exploring Operation: 80+24=104, Resulting Numbers: [104] 104,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[30, 40], Operations: ['80-57=23', '63-23=40'] Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 30+40=70, Resulting Numbers: [70] 70,76 unequal: No Solution Exploring Operation: 30*40=1200, Resulting Numbers: [1200] 1200,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[30, 74], Operations: ['63-57=6', '80-6=74'] Exploring Operation: 30*74=2220, Resulting Numbers: [2220] 2220,76 unequal: No Solution Exploring Operation: 74-30=44, Resulting Numbers: [44] 44,76 unequal: No Solution Exploring Operation: 30+74=104, Resulting Numbers: [104] 104,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[87, 17], Operations: ['30+57=87', '80-63=17'] Exploring Operation: 87*17=1479, Resulting Numbers: [1479] 1479,76 unequal: No Solution Exploring Operation: 87+17=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 87-17=70, Resulting Numbers: [70] 70,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[63, 7], Operations: ['80-57=23', '30-23=7'] Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 63*7=441, Resulting Numbers: [441] 441,76 unequal: No Solution Exploring Operation: 63+7=70, Resulting Numbers: [70] 70,76 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,76 unequal: No Solution Moving to Node #0,2,1 Current State: 76:[63, 7], Operations: ['30+57=87', '87-80=7'] Exploring Operation: 63+7=70, Resulting Numbers: [70] 70,76 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,76 unequal: No Solution Exploring Operation: 63*7=441, Resulting Numbers: [441] 441,76 unequal: No Solution Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,76 unequal: No Solution Moving to Node #0,1,3 Current State: 76:[30, 86], Operations: ['80-57=23', '63+23=86'] Exploring Operation: 30+86=116, Resulting Numbers: [116] 116,76 unequal: No Solution Exploring Operation: 86-30=56, Resulting Numbers: [56] 56,76 unequal: No Solution Exploring Operation: 30*86=2580, Resulting Numbers: [2580] 2580,76 unequal: No Solution Moving to Node #0,2,3 Current State: 76:[87, 143], Operations: ['30+57=87', '63+80=143'] Exploring Operation: 143-87=56, Resulting Numbers: [56] 56,76 unequal: No Solution Exploring Operation: 87+143=230, Resulting Numbers: [230] 230,76 unequal: No Solution Exploring Operation: 87*143=12441, Resulting Numbers: [12441] 12441,76 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 33, 74, 16, 47 ]
69
[ "33+47=80", "80/16=5", "74-5=69" ]
Current State: 69:[33, 74, 16, 47], Operations: [] Exploring Operation: 33+47=80, Resulting Numbers: [74, 16, 80] Generated Node #2: [74, 16, 80] from Operation: 33+47=80 Current State: 69:[74, 16, 80], Operations: ['33+47=80'] Exploring Operation: 80/16=5, Resulting Numbers: [74, 5] Generated Node #3: [74, 5] from Operation: 80/16=5 Current State: 69:[74, 5], Operations: ['33+47=80', '80/16=5'] Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[33, 74, 16, 47], Operations: [] Exploring Operation: 47-33=14, Resulting Numbers: [74, 16, 14] Generated Node #0,0: 69:[74, 16, 14] Operation: 47-33=14 Moving to Node #0,0 Current State: 69:[74, 16, 14], Operations: ['47-33=14'] Exploring Operation: 16-14=2, Resulting Numbers: [74, 2] Generated Node #0,0,0: 69:[74, 2] Operation: 16-14=2 Moving to Node #0,0,0 Current State: 69:[74, 2], Operations: ['47-33=14', '16-14=2'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,69 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 80, 63, 34, 88 ]
89
[ "80+63=143", "88-34=54", "143-54=89" ]
Current State: 89:[80, 63, 34, 88], Operations: [] Exploring Operation: 80+63=143, Resulting Numbers: [34, 88, 143] Generated Node #2: [34, 88, 143] from Operation: 80+63=143 Current State: 89:[34, 88, 143], Operations: ['80+63=143'] Exploring Operation: 88-34=54, Resulting Numbers: [143, 54] Generated Node #3: [143, 54] from Operation: 88-34=54 Current State: 89:[143, 54], Operations: ['80+63=143', '88-34=54'] Exploring Operation: 143-54=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[80, 63, 34, 88], Operations: [] Exploring Operation: 63+34=97, Resulting Numbers: [80, 88, 97] Generated Node #0,0: 89:[80, 88, 97] Operation: 63+34=97 Exploring Operation: 80+34=114, Resulting Numbers: [63, 88, 114] Generated Node #0,1: 89:[63, 88, 114] Operation: 80+34=114 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[80, 88, 97], Operations: ['63+34=97'] Exploring Operation: 97-80=17, Resulting Numbers: [88, 17] Generated Node #0,0,0: 89:[88, 17] Operation: 97-80=17 Exploring Operation: 80+88=168, Resulting Numbers: [97, 168] Generated Node #0,0,1: 89:[97, 168] Operation: 80+88=168 Moving to Node #0,0,0 Current State: 89:[88, 17], Operations: ['63+34=97', '97-80=17'] Exploring Operation: 88+17=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[97, 168], Operations: ['63+34=97', '80+88=168'] Exploring Operation: 97+168=265, Resulting Numbers: [265] 265,89 unequal: No Solution Exploring Operation: 168-97=71, Resulting Numbers: [71] 71,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[63, 88, 114], Operations: ['80+34=114'] Exploring Operation: 114-63=51, Resulting Numbers: [88, 51] Generated Node #0,1,0: 89:[88, 51] Operation: 114-63=51 Exploring Operation: 63+88=151, Resulting Numbers: [114, 151] Generated Node #0,1,1: 89:[114, 151] Operation: 63+88=151 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[88, 51], Operations: ['80+34=114', '114-63=51'] Exploring Operation: 88+51=139, Resulting Numbers: [139] 139,89 unequal: No Solution Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 89:[114, 151], Operations: ['80+34=114', '63+88=151'] Exploring Operation: 114+151=265, Resulting Numbers: [265] 265,89 unequal: No Solution Exploring Operation: 151-114=37, Resulting Numbers: [37] 37,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 8, 32, 23, 29 ]
64
[ "8+23=31", "31-29=2", "32*2=64" ]
Current State: 64:[8, 32, 23, 29], Operations: [] Exploring Operation: 8+23=31, Resulting Numbers: [32, 29, 31] Generated Node #2: [32, 29, 31] from Operation: 8+23=31 Current State: 64:[32, 29, 31], Operations: ['8+23=31'] Exploring Operation: 31-29=2, Resulting Numbers: [32, 2] Generated Node #3: [32, 2] from Operation: 31-29=2 Current State: 64:[32, 2], Operations: ['8+23=31', '31-29=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[8, 32, 23, 29], Operations: [] Exploring Operation: 23-8=15, Resulting Numbers: [32, 29, 15] Generated Node #0,0: 64:[32, 29, 15] Operation: 23-8=15 Exploring Operation: 8+23=31, Resulting Numbers: [32, 29, 31] Generated Node #0,1: 64:[32, 29, 31] Operation: 8+23=31 Exploring Operation: 32-29=3, Resulting Numbers: [8, 23, 3] Generated Node #0,2: 64:[8, 23, 3] Operation: 32-29=3 Exploring Operation: 32-23=9, Resulting Numbers: [8, 29, 9] Generated Node #0,3: 64:[8, 29, 9] Operation: 32-23=9 Exploring Operation: 29-23=6, Resulting Numbers: [8, 32, 6] Generated Node #0,4: 64:[8, 32, 6] Operation: 29-23=6 Moving to Node #0,4 Current State: 64:[8, 32, 6], Operations: ['29-23=6'] Exploring Operation: 32-6=26, Resulting Numbers: [8, 26] Generated Node #0,4,0: 64:[8, 26] Operation: 32-6=26 Exploring Operation: 32/8=4, Resulting Numbers: [6, 4] Generated Node #0,4,1: 64:[6, 4] Operation: 32/8=4 Exploring Operation: 8+6=14, Resulting Numbers: [32, 14] Generated Node #0,4,2: 64:[32, 14] Operation: 8+6=14 Exploring Operation: 8-6=2, Resulting Numbers: [32, 2] Generated Node #0,4,3: 64:[32, 2] Operation: 8-6=2 Exploring Operation: 32+6=38, Resulting Numbers: [8, 38] Generated Node #0,4,4: 64:[8, 38] Operation: 32+6=38 Moving to Node #0,1 Current State: 64:[32, 29, 31], Operations: ['8+23=31'] Exploring Operation: 32-31=1, Resulting Numbers: [29, 1] Generated Node #0,1,0: 64:[29, 1] Operation: 32-31=1 Exploring Operation: 32+29=61, Resulting Numbers: [31, 61] Generated Node #0,1,1: 64:[31, 61] Operation: 32+29=61 Exploring Operation: 31-29=2, Resulting Numbers: [32, 2] Generated Node #0,1,2: 64:[32, 2] Operation: 31-29=2 Exploring Operation: 32-29=3, Resulting Numbers: [31, 3] Generated Node #0,1,3: 64:[31, 3] Operation: 32-29=3 Exploring Operation: 32+31=63, Resulting Numbers: [29, 63] Generated Node #0,1,4: 64:[29, 63] Operation: 32+31=63 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 64:[32, 2], Operations: ['8+23=31', '31-29=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,64 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,64 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[8, 32, 23, 29], Operations: [] Exploring Operation: 8+23=31, Resulting Numbers: [32, 29, 31] Generated Node #0,1: 64:[32, 29, 31] Operation: 8+23=31 Moving to Node #0,1 Current State: 64:[32, 29, 31], Operations: ['8+23=31'] Exploring Operation: 31-29=2, Resulting Numbers: [32, 2] Generated Node #0,1,2: 64:[32, 2] Operation: 31-29=2 Moving to Node #0,1,2 Current State: 64:[32, 2], Operations: ['8+23=31', '31-29=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 19, 76, 69, 62 ]
88
[ "19+76=95", "69-62=7", "95-7=88" ]
Current State: 88:[19, 76, 69, 62], Operations: [] Exploring Operation: 19+76=95, Resulting Numbers: [69, 62, 95] Generated Node #2: [69, 62, 95] from Operation: 19+76=95 Current State: 88:[69, 62, 95], Operations: ['19+76=95'] Exploring Operation: 69-62=7, Resulting Numbers: [95, 7] Generated Node #3: [95, 7] from Operation: 69-62=7 Current State: 88:[95, 7], Operations: ['19+76=95', '69-62=7'] Exploring Operation: 95-7=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[19, 76, 69, 62], Operations: [] Exploring Operation: 69-62=7, Resulting Numbers: [19, 76, 7] Generated Node #0,0: 88:[19, 76, 7] Operation: 69-62=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[19, 76, 7], Operations: ['69-62=7'] Exploring Operation: 76/19=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 88:[7, 4] Operation: 76/19=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[7, 4], Operations: ['69-62=7', '76/19=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,88 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_1
sum_heuristic
[ 74, 12, 87, 39 ]
36
[ "87-74=13", "12*39=468", "468/13=36" ]
Current State: 36:[74, 12, 87, 39], Operations: [] Exploring Operation: 87-74=13, Resulting Numbers: [12, 39, 13] Generated Node #2: [12, 39, 13] from Operation: 87-74=13 Current State: 36:[12, 39, 13], Operations: ['87-74=13'] Exploring Operation: 12*39=468, Resulting Numbers: [13, 468] Generated Node #3: [13, 468] from Operation: 12*39=468 Current State: 36:[13, 468], Operations: ['87-74=13', '12*39=468'] Exploring Operation: 468/13=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[74, 12, 87, 39], Operations: [] Exploring Operation: 87-74=13, Resulting Numbers: [12, 39, 13] Generated Node #0,0: 36:[12, 39, 13] Operation: 87-74=13 Exploring Operation: 87-39=48, Resulting Numbers: [74, 12, 48] Generated Node #0,1: 36:[74, 12, 48] Operation: 87-39=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[12, 39, 13], Operations: ['87-74=13'] Exploring Operation: 39/13=3, Resulting Numbers: [12, 3] Generated Node #0,0,0: 36:[12, 3] Operation: 39/13=3 Exploring Operation: 13-12=1, Resulting Numbers: [39, 1] Generated Node #0,0,1: 36:[39, 1] Operation: 13-12=1 Moving to Node #0,0,0 Current State: 36:[12, 3], Operations: ['87-74=13', '39/13=3'] Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[74, 12, 87, 39], Operations: [] Exploring Operation: 87-74=13, Resulting Numbers: [12, 39, 13] Generated Node #0,0: 36:[12, 39, 13] Operation: 87-74=13 Moving to Node #0,0 Current State: 36:[12, 39, 13], Operations: ['87-74=13'] Exploring Operation: 39/13=3, Resulting Numbers: [12, 3] Generated Node #0,0,0: 36:[12, 3] Operation: 39/13=3 Moving to Node #0,0,0 Current State: 36:[12, 3], Operations: ['87-74=13', '39/13=3'] Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 69, 91, 2, 7 ]
37
[ "91-69=22", "2*22=44", "44-7=37" ]
Current State: 37:[69, 91, 2, 7], Operations: [] Exploring Operation: 91-69=22, Resulting Numbers: [2, 7, 22] Generated Node #2: [2, 7, 22] from Operation: 91-69=22 Current State: 37:[2, 7, 22], Operations: ['91-69=22'] Exploring Operation: 2*22=44, Resulting Numbers: [7, 44] Generated Node #3: [7, 44] from Operation: 2*22=44 Current State: 37:[7, 44], Operations: ['91-69=22', '2*22=44'] Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[69, 91, 2, 7], Operations: [] Exploring Operation: 91/7=13, Resulting Numbers: [69, 2, 13] Generated Node #0,0: 37:[69, 2, 13] Operation: 91/7=13 Exploring Operation: 2*7=14, Resulting Numbers: [69, 91, 14] Generated Node #0,1: 37:[69, 91, 14] Operation: 2*7=14 Exploring Operation: 91-69=22, Resulting Numbers: [2, 7, 22] Generated Node #0,2: 37:[2, 7, 22] Operation: 91-69=22 Exploring Operation: 69-2=67, Resulting Numbers: [91, 7, 67] Generated Node #0,3: 37:[91, 7, 67] Operation: 69-2=67 Exploring Operation: 69-7=62, Resulting Numbers: [91, 2, 62] Generated Node #0,4: 37:[91, 2, 62] Operation: 69-7=62 Start Sub Search at level 1: Moving to Node #0,2 Current State: 37:[2, 7, 22], Operations: ['91-69=22'] Exploring Operation: 2+22=24, Resulting Numbers: [7, 24] Generated Node #0,2,0: 37:[7, 24] Operation: 2+22=24 Exploring Operation: 2+7=9, Resulting Numbers: [22, 9] Generated Node #0,2,1: 37:[22, 9] Operation: 2+7=9 Exploring Operation: 2*22=44, Resulting Numbers: [7, 44] Generated Node #0,2,2: 37:[7, 44] Operation: 2*22=44 Exploring Operation: 7+22=29, Resulting Numbers: [2, 29] Generated Node #0,2,3: 37:[2, 29] Operation: 7+22=29 Exploring Operation: 2*7=14, Resulting Numbers: [22, 14] Generated Node #0,2,4: 37:[22, 14] Operation: 2*7=14 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 37:[7, 44], Operations: ['91-69=22', '2*22=44'] Exploring Operation: 7+44=51, Resulting Numbers: [51] 51,37 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[69, 91, 2, 7], Operations: [] Exploring Operation: 91-69=22, Resulting Numbers: [2, 7, 22] Generated Node #0,2: 37:[2, 7, 22] Operation: 91-69=22 Moving to Node #0,2 Current State: 37:[2, 7, 22], Operations: ['91-69=22'] Exploring Operation: 2*22=44, Resulting Numbers: [7, 44] Generated Node #0,2,2: 37:[7, 44] Operation: 2*22=44 Moving to Node #0,2,2 Current State: 37:[7, 44], Operations: ['91-69=22', '2*22=44'] Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 53, 67, 26, 8 ]
86
[ "53+67=120", "26+8=34", "120-34=86" ]
Current State: 86:[53, 67, 26, 8], Operations: [] Exploring Operation: 53+67=120, Resulting Numbers: [26, 8, 120] Generated Node #2: [26, 8, 120] from Operation: 53+67=120 Current State: 86:[26, 8, 120], Operations: ['53+67=120'] Exploring Operation: 26+8=34, Resulting Numbers: [120, 34] Generated Node #3: [120, 34] from Operation: 26+8=34 Current State: 86:[120, 34], Operations: ['53+67=120', '26+8=34'] Exploring Operation: 120-34=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[53, 67, 26, 8], Operations: [] Exploring Operation: 67-53=14, Resulting Numbers: [26, 8, 14] Generated Node #0,0: 86:[26, 8, 14] Operation: 67-53=14 Exploring Operation: 67-26=41, Resulting Numbers: [53, 8, 41] Generated Node #0,1: 86:[53, 8, 41] Operation: 67-26=41 Exploring Operation: 67+26=93, Resulting Numbers: [53, 8, 93] Generated Node #0,2: 86:[53, 8, 93] Operation: 67+26=93 Exploring Operation: 53+26=79, Resulting Numbers: [67, 8, 79] Generated Node #0,3: 86:[67, 8, 79] Operation: 53+26=79 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[53, 8, 41], Operations: ['67-26=41'] Exploring Operation: 53+41=94, Resulting Numbers: [8, 94] Generated Node #0,1,0: 86:[8, 94] Operation: 53+41=94 Exploring Operation: 53-41=12, Resulting Numbers: [8, 12] Generated Node #0,1,1: 86:[8, 12] Operation: 53-41=12 Exploring Operation: 8+41=49, Resulting Numbers: [53, 49] Generated Node #0,1,2: 86:[53, 49] Operation: 8+41=49 Exploring Operation: 53-8=45, Resulting Numbers: [41, 45] Generated Node #0,1,3: 86:[41, 45] Operation: 53-8=45 Moving to Node #0,1,3 Current State: 86:[41, 45], Operations: ['67-26=41', '53-8=45'] Exploring Operation: 41+45=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[53, 67, 26, 8], Operations: [] Exploring Operation: 67-26=41, Resulting Numbers: [53, 8, 41] Generated Node #0,1: 86:[53, 8, 41] Operation: 67-26=41 Moving to Node #0,1 Current State: 86:[53, 8, 41], Operations: ['67-26=41'] Exploring Operation: 53-8=45, Resulting Numbers: [41, 45] Generated Node #0,1,3: 86:[41, 45] Operation: 53-8=45 Moving to Node #0,1,3 Current State: 86:[41, 45], Operations: ['67-26=41', '53-8=45'] Exploring Operation: 41+45=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 8, 76, 44, 93 ]
53
[ "8+76=84", "44+93=137", "137-84=53" ]
Current State: 53:[8, 76, 44, 93], Operations: [] Exploring Operation: 8+76=84, Resulting Numbers: [44, 93, 84] Generated Node #2: [44, 93, 84] from Operation: 8+76=84 Current State: 53:[44, 93, 84], Operations: ['8+76=84'] Exploring Operation: 44+93=137, Resulting Numbers: [84, 137] Generated Node #3: [84, 137] from Operation: 44+93=137 Current State: 53:[84, 137], Operations: ['8+76=84', '44+93=137'] Exploring Operation: 137-84=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[8, 76, 44, 93], Operations: [] Exploring Operation: 8+44=52, Resulting Numbers: [76, 93, 52] Generated Node #0,0: 53:[76, 93, 52] Operation: 8+44=52 Exploring Operation: 76-8=68, Resulting Numbers: [44, 93, 68] Generated Node #0,1: 53:[44, 93, 68] Operation: 76-8=68 Moving to Node #0,0 Current State: 53:[76, 93, 52], Operations: ['8+44=52'] Exploring Operation: 93-52=41, Resulting Numbers: [76, 41] Generated Node #0,0,0: 53:[76, 41] Operation: 93-52=41 Exploring Operation: 93-76=17, Resulting Numbers: [52, 17] Generated Node #0,0,1: 53:[52, 17] Operation: 93-76=17 Moving to Node #0,1 Current State: 53:[44, 93, 68], Operations: ['76-8=68'] Exploring Operation: 93-68=25, Resulting Numbers: [44, 25] Generated Node #0,1,0: 53:[44, 25] Operation: 93-68=25 Exploring Operation: 93-44=49, Resulting Numbers: [68, 49] Generated Node #0,1,1: 53:[68, 49] Operation: 93-44=49 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 53:[68, 49], Operations: ['76-8=68', '93-44=49'] Exploring Operation: 68+49=117, Resulting Numbers: [117] 117,53 unequal: No Solution Exploring Operation: 68-49=19, Resulting Numbers: [19] 19,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[44, 25], Operations: ['76-8=68', '93-68=25'] Exploring Operation: 44+25=69, Resulting Numbers: [69] 69,53 unequal: No Solution Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,53 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: 53:[76, 41], Operations: ['8+44=52', '93-52=41'] Exploring Operation: 76-41=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 76+41=117, Resulting Numbers: [117] 117,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[52, 17], Operations: ['8+44=52', '93-76=17'] Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 52+17=69, Resulting Numbers: [69] 69,53 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 41, 86, 45, 95 ]
95
[ "86-41=45", "45+95=140", "140-45=95" ]
Current State: 95:[41, 86, 45, 95], Operations: [] Exploring Operation: 86-41=45, Resulting Numbers: [45, 95, 45] Generated Node #2: [45, 95, 45] from Operation: 86-41=45 Current State: 95:[45, 95, 45], Operations: ['86-41=45'] Exploring Operation: 45+95=140, Resulting Numbers: [140] 140,95 equal: Goal Reached Exploring Operation: 140-45=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[41, 86, 45, 95], Operations: [] Exploring Operation: 41+45=86, Resulting Numbers: [86, 95, 86] Generated Node #0,0: 95:[86, 95, 86] Operation: 41+45=86 Exploring Operation: 45-41=4, Resulting Numbers: [86, 95, 4] Generated Node #0,1: 95:[86, 95, 4] Operation: 45-41=4 Exploring Operation: 86-41=45, Resulting Numbers: [45, 95, 45] Generated Node #0,2: 95:[45, 95, 45] Operation: 86-41=45 Exploring Operation: 86-45=41, Resulting Numbers: [41, 95, 41] Generated Node #0,3: 95:[41, 95, 41] Operation: 86-45=41 Moving to Node #0,1 Current State: 95:[86, 95, 4], Operations: ['45-41=4'] Exploring Operation: 95+4=99, Resulting Numbers: [86, 99] Generated Node #0,1,0: 95:[86, 99] Operation: 95+4=99 Exploring Operation: 95-86=9, Resulting Numbers: [4, 9] Generated Node #0,1,1: 95:[4, 9] Operation: 95-86=9 Exploring Operation: 86+4=90, Resulting Numbers: [95, 90] Generated Node #0,1,2: 95:[95, 90] Operation: 86+4=90 Exploring Operation: 86-4=82, Resulting Numbers: [95, 82] Generated Node #0,1,3: 95:[95, 82] Operation: 86-4=82 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 95:[4, 9], Operations: ['45-41=4', '95-86=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,95 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,95 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 #0,1,2 Current State: 95:[95, 90], Operations: ['45-41=4', '86+4=90'] Exploring Operation: 95*90=8550, Resulting Numbers: [8550] 8550,95 unequal: No Solution Exploring Operation: 95-90=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 95+90=185, Resulting Numbers: [185] 185,95 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 #0,1,0 Current State: 95:[86, 99], Operations: ['45-41=4', '95+4=99'] Exploring Operation: 99-86=13, Resulting Numbers: [13] 13,95 unequal: No Solution Exploring Operation: 86*99=8514, Resulting Numbers: [8514] 8514,95 unequal: No Solution Exploring Operation: 86+99=185, Resulting Numbers: [185] 185,95 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 #0,1,3 Current State: 95:[95, 82], Operations: ['45-41=4', '86-4=82'] Exploring Operation: 95-82=13, Resulting Numbers: [13] 13,95 unequal: No Solution Exploring Operation: 95+82=177, Resulting Numbers: [177] 177,95 unequal: No Solution Exploring Operation: 95*82=7790, Resulting Numbers: [7790] 7790,95 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:[86, 95, 86], Operations: ['41+45=86'] Exploring Operation: 86-86=0, Resulting Numbers: [95, 0] Generated Node #0,0,0: 95:[95, 0] Operation: 86-86=0 Exploring Operation: 86/86=1, Resulting Numbers: [95, 1] Generated Node #0,0,1: 95:[95, 1] Operation: 86/86=1 Exploring Operation: 95-86=9, Resulting Numbers: [86, 9] Generated Node #0,0,2: 95:[86, 9] Operation: 95-86=9 Exploring Operation: 95-86=9, Resulting Numbers: [86, 9] Generated Node #0,0,3: 95:[86, 9] Operation: 95-86=9 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 95:[95, 1], Operations: ['41+45=86', '86/86=1'] Exploring Operation: 95*1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[41, 86, 45, 95], Operations: [] Exploring Operation: 41+45=86, Resulting Numbers: [86, 95, 86] Generated Node #0,0: 95:[86, 95, 86] Operation: 41+45=86 Moving to Node #0,0 Current State: 95:[86, 95, 86], Operations: ['41+45=86'] Exploring Operation: 86/86=1, Resulting Numbers: [95, 1] Generated Node #0,0,1: 95:[95, 1] Operation: 86/86=1 Moving to Node #0,0,1 Current State: 95:[95, 1], Operations: ['41+45=86', '86/86=1'] Exploring Operation: 95*1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 72, 69, 56, 11 ]
96
[ "72+69=141", "56-11=45", "141-45=96" ]
Current State: 96:[72, 69, 56, 11], Operations: [] Exploring Operation: 72+69=141, Resulting Numbers: [56, 11, 141] Generated Node #2: [56, 11, 141] from Operation: 72+69=141 Current State: 96:[56, 11, 141], Operations: ['72+69=141'] Exploring Operation: 56-11=45, Resulting Numbers: [141, 45] Generated Node #3: [141, 45] from Operation: 56-11=45 Current State: 96:[141, 45], Operations: ['72+69=141', '56-11=45'] Exploring Operation: 141-45=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[72, 69, 56, 11], Operations: [] Exploring Operation: 72-69=3, Resulting Numbers: [56, 11, 3] Generated Node #0,0: 96:[56, 11, 3] Operation: 72-69=3 Moving to Node #0,0 Current State: 96:[56, 11, 3], Operations: ['72-69=3'] Exploring Operation: 56-11=45, Resulting Numbers: [3, 45] Generated Node #0,0,0: 96:[3, 45] Operation: 56-11=45 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[3, 45], Operations: ['72-69=3', '56-11=45'] Exploring Operation: 3+45=48, Resulting Numbers: [48] 48,96 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
[ 97, 85, 83, 82 ]
67
[ "85-83=2", "82*2=164", "164-97=67" ]
Current State: 67:[97, 85, 83, 82], Operations: [] Exploring Operation: 85-83=2, Resulting Numbers: [97, 82, 2] Generated Node #2: [97, 82, 2] from Operation: 85-83=2 Current State: 67:[97, 82, 2], Operations: ['85-83=2'] Exploring Operation: 82*2=164, Resulting Numbers: [97, 164] Generated Node #3: [97, 164] from Operation: 82*2=164 Current State: 67:[97, 164], Operations: ['85-83=2', '82*2=164'] Exploring Operation: 164-97=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[97, 85, 83, 82], Operations: [] Exploring Operation: 97-85=12, Resulting Numbers: [83, 82, 12] Generated Node #0,0: 67:[83, 82, 12] Operation: 97-85=12 Exploring Operation: 97-83=14, Resulting Numbers: [85, 82, 14] Generated Node #0,1: 67:[85, 82, 14] Operation: 97-83=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[83, 82, 12], Operations: ['97-85=12'] Exploring Operation: 83-12=71, Resulting Numbers: [82, 71] Generated Node #0,0,0: 67:[82, 71] Operation: 83-12=71 Exploring Operation: 82-12=70, Resulting Numbers: [83, 70] Generated Node #0,0,1: 67:[83, 70] Operation: 82-12=70 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[82, 71], Operations: ['97-85=12', '83-12=71'] Exploring Operation: 82-71=11, Resulting Numbers: [11] 11,67 unequal: No Solution Exploring Operation: 82+71=153, Resulting Numbers: [153] 153,67 unequal: No Solution No 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: 67:[83, 70], Operations: ['97-85=12', '82-12=70'] Exploring Operation: 83+70=153, Resulting Numbers: [153] 153,67 unequal: No Solution Exploring Operation: 83-70=13, Resulting Numbers: [13] 13,67 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: 67:[85, 82, 14], Operations: ['97-83=14'] Exploring Operation: 82-14=68, Resulting Numbers: [85, 68] Generated Node #0,1,0: 67:[85, 68] Operation: 82-14=68 Exploring Operation: 85-14=71, Resulting Numbers: [82, 71] Generated Node #0,1,1: 67:[82, 71] Operation: 85-14=71 Moving to Node #0,1,0 Current State: 67:[85, 68], Operations: ['97-83=14', '82-14=68'] Exploring Operation: 85+68=153, Resulting Numbers: [153] 153,67 unequal: No Solution Exploring Operation: 85-68=17, Resulting Numbers: [17] 17,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[82, 71], Operations: ['97-83=14', '85-14=71'] Exploring Operation: 82+71=153, Resulting Numbers: [153] 153,67 unequal: No Solution Exploring Operation: 82-71=11, Resulting Numbers: [11] 11,67 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
[ 20, 8, 10, 12 ]
44
[ "10-8=2", "12*2=24", "20+24=44" ]
Current State: 44:[20, 8, 10, 12], Operations: [] Exploring Operation: 10-8=2, Resulting Numbers: [20, 12, 2] Generated Node #2: [20, 12, 2] from Operation: 10-8=2 Current State: 44:[20, 12, 2], Operations: ['10-8=2'] Exploring Operation: 12*2=24, Resulting Numbers: [20, 24] Generated Node #3: [20, 24] from Operation: 12*2=24 Current State: 44:[20, 24], Operations: ['10-8=2', '12*2=24'] Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[20, 8, 10, 12], Operations: [] Exploring Operation: 12-8=4, Resulting Numbers: [20, 10, 4] Generated Node #0,0: 44:[20, 10, 4] Operation: 12-8=4 Exploring Operation: 20-10=10, Resulting Numbers: [8, 12, 10] Generated Node #0,1: 44:[8, 12, 10] Operation: 20-10=10 Exploring Operation: 10-8=2, Resulting Numbers: [20, 12, 2] Generated Node #0,2: 44:[20, 12, 2] Operation: 10-8=2 Exploring Operation: 20-8=12, Resulting Numbers: [10, 12, 12] Generated Node #0,3: 44:[10, 12, 12] Operation: 20-8=12 Exploring Operation: 20/10=2, Resulting Numbers: [8, 12, 2] Generated Node #0,4: 44:[8, 12, 2] Operation: 20/10=2 Moving to Node #0,0 Current State: 44:[20, 10, 4], Operations: ['12-8=4'] Exploring Operation: 20/4=5, Resulting Numbers: [10, 5] Generated Node #0,0,0: 44:[10, 5] Operation: 20/4=5 Exploring Operation: 20+4=24, Resulting Numbers: [10, 24] Generated Node #0,0,1: 44:[10, 24] Operation: 20+4=24 Exploring Operation: 20-10=10, Resulting Numbers: [4, 10] Generated Node #0,0,2: 44:[4, 10] Operation: 20-10=10 Exploring Operation: 20/10=2, Resulting Numbers: [4, 2] Generated Node #0,0,3: 44:[4, 2] Operation: 20/10=2 Exploring Operation: 10-4=6, Resulting Numbers: [20, 6] Generated Node #0,0,4: 44:[20, 6] Operation: 10-4=6 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 44:[4, 2], Operations: ['12-8=4', '20/10=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,44 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:[4, 10], Operations: ['12-8=4', '20-10=10'] Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,44 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[10, 5], Operations: ['12-8=4', '20/4=5'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 10+5=15, Resulting Numbers: [15] 15,44 unequal: No Solution Exploring Operation: 10*5=50, Resulting Numbers: [50] 50,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 44:[10, 24], Operations: ['12-8=4', '20+4=24'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 10*24=240, Resulting Numbers: [240] 240,44 unequal: No Solution Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,44 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 #0,0,4 Current State: 44:[20, 6], Operations: ['12-8=4', '10-4=6'] Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,44 unequal: No Solution Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,44 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: 44:[10, 12, 12], Operations: ['20-8=12'] Exploring Operation: 10+12=22, Resulting Numbers: [12, 22] Generated Node #0,3,0: 44:[12, 22] Operation: 10+12=22 Exploring Operation: 12-10=2, Resulting Numbers: [12, 2] Generated Node #0,3,1: 44:[12, 2] Operation: 12-10=2 Exploring Operation: 12/12=1, Resulting Numbers: [10, 1] Generated Node #0,3,2: 44:[10, 1] Operation: 12/12=1 Exploring Operation: 12-10=2, Resulting Numbers: [12, 2] Generated Node #0,3,3: 44:[12, 2] Operation: 12-10=2 Exploring Operation: 10+12=22, Resulting Numbers: [12, 22] Generated Node #0,3,4: 44:[12, 22] Operation: 10+12=22 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 44:[12, 22], Operations: ['20-8=12', '10+12=22'] Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,44 unequal: No Solution Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,44 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:[12, 2], Operations: ['20-8=12', '12-10=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,44 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 44:[12, 2], Operations: ['20-8=12', '12-10=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,44 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,44 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 #0,3,4 Current State: 44:[12, 22], Operations: ['20-8=12', '10+12=22'] Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,44 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:[10, 1], Operations: ['20-8=12', '12/12=1'] Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,44 unequal: No Solution Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,44 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:[20, 12, 2], Operations: ['10-8=2'] Exploring Operation: 20/2=10, Resulting Numbers: [12, 10] Generated Node #0,2,0: 44:[12, 10] Operation: 20/2=10 Exploring Operation: 20+2=22, Resulting Numbers: [12, 22] Generated Node #0,2,1: 44:[12, 22] Operation: 20+2=22 Exploring Operation: 20-12=8, Resulting Numbers: [2, 8] Generated Node #0,2,2: 44:[2, 8] Operation: 20-12=8 Exploring Operation: 12*2=24, Resulting Numbers: [20, 24] Generated Node #0,2,3: 44:[20, 24] Operation: 12*2=24 Exploring Operation: 12-2=10, Resulting Numbers: [20, 10] Generated Node #0,2,4: 44:[20, 10] Operation: 12-2=10 Moving to Node #0,4 Current State: 44:[8, 12, 2], Operations: ['20/10=2'] Exploring Operation: 8+12=20, Resulting Numbers: [2, 20] Generated Node #0,4,0: 44:[2, 20] Operation: 8+12=20 Exploring Operation: 8+2=10, Resulting Numbers: [12, 10] Generated Node #0,4,1: 44:[12, 10] Operation: 8+2=10 Exploring Operation: 8-2=6, Resulting Numbers: [12, 6] Generated Node #0,4,2: 44:[12, 6] Operation: 8-2=6 Exploring Operation: 8/2=4, Resulting Numbers: [12, 4] Generated Node #0,4,3: 44:[12, 4] Operation: 8/2=4 Exploring Operation: 12-8=4, Resulting Numbers: [2, 4] Generated Node #0,4,4: 44:[2, 4] Operation: 12-8=4 Moving to Node #0,1 Current State: 44:[8, 12, 10], Operations: ['20-10=10'] Exploring Operation: 10-8=2, Resulting Numbers: [12, 2] Generated Node #0,1,0: 44:[12, 2] Operation: 10-8=2 Exploring Operation: 12+10=22, Resulting Numbers: [8, 22] Generated Node #0,1,1: 44:[8, 22] Operation: 12+10=22 Exploring Operation: 12-10=2, Resulting Numbers: [8, 2] Generated Node #0,1,2: 44:[8, 2] Operation: 12-10=2 Exploring Operation: 12-8=4, Resulting Numbers: [10, 4] Generated Node #0,1,3: 44:[10, 4] Operation: 12-8=4 Exploring Operation: 8+12=20, Resulting Numbers: [10, 20] Generated Node #0,1,4: 44:[10, 20] Operation: 8+12=20 Moving to Node #0,4,4 Current State: 44:[2, 4], Operations: ['20/10=2', '12-8=4'] Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,44 unequal: No Solution Moving to Node #0,2,1 Current State: 44:[12, 22], Operations: ['10-8=2', '20+2=22'] Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,44 unequal: No Solution Moving to Node #0,4,3 Current State: 44:[12, 4], Operations: ['20/10=2', '8/2=4'] Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,44 unequal: No Solution Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,44 unequal: No Solution Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,44 unequal: No Solution Moving to Node #0,1,3 Current State: 44:[10, 4], Operations: ['20-10=10', '12-8=4'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[12, 2], Operations: ['20-10=10', '10-8=2'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,44 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,44 unequal: No Solution Moving to Node #0,2,0 Current State: 44:[12, 10], Operations: ['10-8=2', '20/2=10'] Exploring Operation: 12*10=120, Resulting Numbers: [120] 120,44 unequal: No Solution Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,44 unequal: No Solution Moving to Node #0,4,0 Current State: 44:[2, 20], Operations: ['20/10=2', '8+12=20'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,44 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,44 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,44 unequal: No Solution Moving to Node #0,4,1 Current State: 44:[12, 10], Operations: ['20/10=2', '8+2=10'] Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 12*10=120, Resulting Numbers: [120] 120,44 unequal: No Solution Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,44 unequal: No Solution Moving to Node #0,1,2 Current State: 44:[8, 2], Operations: ['20-10=10', '12-10=2'] Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,44 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,44 unequal: No Solution Moving to Node #0,1,4 Current State: 44:[10, 20], Operations: ['20-10=10', '8+12=20'] Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 10*20=200, Resulting Numbers: [200] 200,44 unequal: No Solution Exploring Operation: 10+20=30, Resulting Numbers: [30] 30,44 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[8, 22], Operations: ['20-10=10', '12+10=22'] Exploring Operation: 8+22=30, Resulting Numbers: [30] 30,44 unequal: No Solution Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 8*22=176, Resulting Numbers: [176] 176,44 unequal: No Solution Moving to Node #0,2,4 Current State: 44:[20, 10], Operations: ['10-8=2', '12-2=10'] Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,44 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,44 unequal: No Solution Moving to Node #0,4,2 Current State: 44:[12, 6], Operations: ['20/10=2', '8-2=6'] Exploring Operation: 12*6=72, Resulting Numbers: [72] 72,44 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 12+6=18, Resulting Numbers: [18] 18,44 unequal: No Solution Moving to Node #0,2,2 Current State: 44:[2, 8], Operations: ['10-8=2', '20-12=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,44 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,44 unequal: No Solution Moving to Node #0,2,3 Current State: 44:[20, 24], Operations: ['10-8=2', '12*2=24'] Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,44 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[20, 8, 10, 12], Operations: [] Exploring Operation: 10-8=2, Resulting Numbers: [20, 12, 2] Generated Node #0,2: 44:[20, 12, 2] Operation: 10-8=2 Moving to Node #0,2 Current State: 44:[20, 12, 2], Operations: ['10-8=2'] Exploring Operation: 12*2=24, Resulting Numbers: [20, 24] Generated Node #0,2,3: 44:[20, 24] Operation: 12*2=24 Moving to Node #0,2,3 Current State: 44:[20, 24], Operations: ['10-8=2', '12*2=24'] Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
0.893229
hs_5
sum_heuristic
[ 10, 43, 67, 71 ]
49
[ "10+43=53", "71-67=4", "53-4=49" ]
Current State: 49:[10, 43, 67, 71], Operations: [] Exploring Operation: 10+43=53, Resulting Numbers: [67, 71, 53] Generated Node #2: [67, 71, 53] from Operation: 10+43=53 Current State: 49:[67, 71, 53], Operations: ['10+43=53'] Exploring Operation: 71-67=4, Resulting Numbers: [53, 4] Generated Node #3: [53, 4] from Operation: 71-67=4 Current State: 49:[53, 4], Operations: ['10+43=53', '71-67=4'] Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[10, 43, 67, 71], Operations: [] Exploring Operation: 71-67=4, Resulting Numbers: [10, 43, 4] Generated Node #0,0: 49:[10, 43, 4] Operation: 71-67=4 Exploring Operation: 67-10=57, Resulting Numbers: [43, 71, 57] Generated Node #0,1: 49:[43, 71, 57] Operation: 67-10=57 Moving to Node #0,0 Current State: 49:[10, 43, 4], Operations: ['71-67=4'] Exploring Operation: 10+43=53, Resulting Numbers: [4, 53] Generated Node #0,0,0: 49:[4, 53] Operation: 10+43=53 Exploring Operation: 43+4=47, Resulting Numbers: [10, 47] Generated Node #0,0,1: 49:[10, 47] Operation: 43+4=47 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 49:[10, 47], Operations: ['71-67=4', '43+4=47'] Exploring Operation: 10+47=57, Resulting Numbers: [57] 57,49 unequal: No Solution Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 49:[4, 53], Operations: ['71-67=4', '10+43=53'] Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[10, 43, 67, 71], Operations: [] Exploring Operation: 71-67=4, Resulting Numbers: [10, 43, 4] Generated Node #0,0: 49:[10, 43, 4] Operation: 71-67=4 Moving to Node #0,0 Current State: 49:[10, 43, 4], Operations: ['71-67=4'] Exploring Operation: 10+43=53, Resulting Numbers: [4, 53] Generated Node #0,0,0: 49:[4, 53] Operation: 10+43=53 Moving to Node #0,0,0 Current State: 49:[4, 53], Operations: ['71-67=4', '10+43=53'] Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 39, 85, 89, 35 ]
78
[ "85-39=46", "89+35=124", "124-46=78" ]
Current State: 78:[39, 85, 89, 35], Operations: [] Exploring Operation: 85-39=46, Resulting Numbers: [89, 35, 46] Generated Node #2: [89, 35, 46] from Operation: 85-39=46 Current State: 78:[89, 35, 46], Operations: ['85-39=46'] Exploring Operation: 89+35=124, Resulting Numbers: [46, 124] Generated Node #3: [46, 124] from Operation: 89+35=124 Current State: 78:[46, 124], Operations: ['85-39=46', '89+35=124'] Exploring Operation: 124-46=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[39, 85, 89, 35], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [39, 35, 4] Generated Node #0,0: 78:[39, 35, 4] Operation: 89-85=4 Exploring Operation: 85-39=46, Resulting Numbers: [89, 35, 46] Generated Node #0,1: 78:[89, 35, 46] Operation: 85-39=46 Exploring Operation: 89-39=50, Resulting Numbers: [85, 35, 50] Generated Node #0,2: 78:[85, 35, 50] Operation: 89-39=50 Exploring Operation: 39-35=4, Resulting Numbers: [85, 89, 4] Generated Node #0,3: 78:[85, 89, 4] Operation: 39-35=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[39, 35, 4], Operations: ['89-85=4'] Exploring Operation: 39+35=74, Resulting Numbers: [4, 74] Generated Node #0,0,0: 78:[4, 74] Operation: 39+35=74 Exploring Operation: 35+4=39, Resulting Numbers: [39, 39] Generated Node #0,0,1: 78:[39, 39] Operation: 35+4=39 Exploring Operation: 39-35=4, Resulting Numbers: [4, 4] Generated Node #0,0,2: 78:[4, 4] Operation: 39-35=4 Exploring Operation: 35-4=31, Resulting Numbers: [39, 31] Generated Node #0,0,3: 78:[39, 31] Operation: 35-4=31 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 78:[39, 39], Operations: ['89-85=4', '35+4=39'] Exploring Operation: 39*39=1521, Resulting Numbers: [1521] 1521,78 unequal: No Solution Exploring Operation: 39+39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[39, 85, 89, 35], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [39, 35, 4] Generated Node #0,0: 78:[39, 35, 4] Operation: 89-85=4 Moving to Node #0,0 Current State: 78:[39, 35, 4], Operations: ['89-85=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39, 39] Generated Node #0,0,1: 78:[39, 39] Operation: 35+4=39 Moving to Node #0,0,1 Current State: 78:[39, 39], Operations: ['89-85=4', '35+4=39'] Exploring Operation: 39+39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 14, 79, 74, 9 ]
69
[ "79-9=70", "70/14=5", "74-5=69" ]
Current State: 69:[14, 79, 74, 9], Operations: [] Exploring Operation: 79-9=70, Resulting Numbers: [14, 74, 70] Generated Node #2: [14, 74, 70] from Operation: 79-9=70 Current State: 69:[14, 74, 70], Operations: ['79-9=70'] Exploring Operation: 70/14=5, Resulting Numbers: [74, 5] Generated Node #3: [74, 5] from Operation: 70/14=5 Current State: 69:[74, 5], Operations: ['79-9=70', '70/14=5'] Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[14, 79, 74, 9], Operations: [] Exploring Operation: 14-9=5, Resulting Numbers: [79, 74, 5] Generated Node #0,0: 69:[79, 74, 5] Operation: 14-9=5 Exploring Operation: 79-9=70, Resulting Numbers: [14, 74, 70] Generated Node #0,1: 69:[14, 74, 70] Operation: 79-9=70 Exploring Operation: 79-74=5, Resulting Numbers: [14, 9, 5] Generated Node #0,2: 69:[14, 9, 5] Operation: 79-74=5 Exploring Operation: 79-14=65, Resulting Numbers: [74, 9, 65] Generated Node #0,3: 69:[74, 9, 65] Operation: 79-14=65 Exploring Operation: 14+9=23, Resulting Numbers: [79, 74, 23] Generated Node #0,4: 69:[79, 74, 23] Operation: 14+9=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[14, 74, 70], Operations: ['79-9=70'] Exploring Operation: 74-14=60, Resulting Numbers: [70, 60] Generated Node #0,1,0: 69:[70, 60] Operation: 74-14=60 Exploring Operation: 70/14=5, Resulting Numbers: [74, 5] Generated Node #0,1,1: 69:[74, 5] Operation: 70/14=5 Exploring Operation: 14+74=88, Resulting Numbers: [70, 88] Generated Node #0,1,2: 69:[70, 88] Operation: 14+74=88 Exploring Operation: 70-14=56, Resulting Numbers: [74, 56] Generated Node #0,1,3: 69:[74, 56] Operation: 70-14=56 Exploring Operation: 74-70=4, Resulting Numbers: [14, 4] Generated Node #0,1,4: 69:[14, 4] Operation: 74-70=4 Moving to Node #0,1,1 Current State: 69:[74, 5], Operations: ['79-9=70', '70/14=5'] Exploring Operation: 74+5=79, Resulting Numbers: [79] 79,69 unequal: No Solution Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[14, 79, 74, 9], Operations: [] Exploring Operation: 79-9=70, Resulting Numbers: [14, 74, 70] Generated Node #0,1: 69:[14, 74, 70] Operation: 79-9=70 Moving to Node #0,1 Current State: 69:[14, 74, 70], Operations: ['79-9=70'] Exploring Operation: 70/14=5, Resulting Numbers: [74, 5] Generated Node #0,1,1: 69:[74, 5] Operation: 70/14=5 Moving to Node #0,1,1 Current State: 69:[74, 5], Operations: ['79-9=70', '70/14=5'] Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 69, 23, 20, 19 ]
36
[ "69/23=3", "20+19=39", "39-3=36" ]
Current State: 36:[69, 23, 20, 19], Operations: [] Exploring Operation: 69/23=3, Resulting Numbers: [20, 19, 3] Generated Node #2: [20, 19, 3] from Operation: 69/23=3 Current State: 36:[20, 19, 3], Operations: ['69/23=3'] Exploring Operation: 20+19=39, Resulting Numbers: [3, 39] Generated Node #3: [3, 39] from Operation: 20+19=39 Current State: 36:[3, 39], Operations: ['69/23=3', '20+19=39'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[69, 23, 20, 19], Operations: [] Exploring Operation: 69/23=3, Resulting Numbers: [20, 19, 3] Generated Node #0,0: 36:[20, 19, 3] Operation: 69/23=3 Exploring Operation: 69-23=46, Resulting Numbers: [20, 19, 46] Generated Node #0,1: 36:[20, 19, 46] Operation: 69-23=46 Exploring Operation: 69-20=49, Resulting Numbers: [23, 19, 49] Generated Node #0,2: 36:[23, 19, 49] Operation: 69-20=49 Exploring Operation: 69-19=50, Resulting Numbers: [23, 20, 50] Generated Node #0,3: 36:[23, 20, 50] Operation: 69-19=50 Moving to Node #0,0 Current State: 36:[20, 19, 3], Operations: ['69/23=3'] Exploring Operation: 20-19=1, Resulting Numbers: [3, 1] Generated Node #0,0,0: 36:[3, 1] Operation: 20-19=1 Exploring Operation: 20-3=17, Resulting Numbers: [19, 17] Generated Node #0,0,1: 36:[19, 17] Operation: 20-3=17 Exploring Operation: 19-3=16, Resulting Numbers: [20, 16] Generated Node #0,0,2: 36:[20, 16] Operation: 19-3=16 Exploring Operation: 20+19=39, Resulting Numbers: [3, 39] Generated Node #0,0,3: 36:[3, 39] Operation: 20+19=39 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[3, 1], Operations: ['69/23=3', '20-19=1'] Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[19, 17], Operations: ['69/23=3', '20-3=17'] Exploring Operation: 19+17=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[69, 23, 20, 19], Operations: [] Exploring Operation: 69/23=3, Resulting Numbers: [20, 19, 3] Generated Node #0,0: 36:[20, 19, 3] Operation: 69/23=3 Moving to Node #0,0 Current State: 36:[20, 19, 3], Operations: ['69/23=3'] Exploring Operation: 20-3=17, Resulting Numbers: [19, 17] Generated Node #0,0,1: 36:[19, 17] Operation: 20-3=17 Moving to Node #0,0,1 Current State: 36:[19, 17], Operations: ['69/23=3', '20-3=17'] Exploring Operation: 19+17=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 77, 49, 80, 77 ]
30
[ "77/77=1", "80-49=31", "31-1=30" ]
Current State: 30:[77, 49, 80, 77], Operations: [] Exploring Operation: 77/77=1, Resulting Numbers: [49, 80, 1] Generated Node #2: [49, 80, 1] from Operation: 77/77=1 Current State: 30:[49, 80, 1], Operations: ['77/77=1'] Exploring Operation: 80-49=31, Resulting Numbers: [1, 31] Generated Node #3: [1, 31] from Operation: 80-49=31 Current State: 30:[1, 31], Operations: ['77/77=1', '80-49=31'] Exploring Operation: 31-1=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[77, 49, 80, 77], Operations: [] Exploring Operation: 80-77=3, Resulting Numbers: [49, 77, 3] Generated Node #0,0: 30:[49, 77, 3] Operation: 80-77=3 Exploring Operation: 80-77=3, Resulting Numbers: [77, 49, 3] Generated Node #0,1: 30:[77, 49, 3] Operation: 80-77=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[49, 77, 3], Operations: ['80-77=3'] Exploring Operation: 77-49=28, Resulting Numbers: [3, 28] Generated Node #0,0,0: 30:[3, 28] Operation: 77-49=28 Exploring Operation: 49-3=46, Resulting Numbers: [77, 46] Generated Node #0,0,1: 30:[77, 46] Operation: 49-3=46 Moving to Node #0,0,0 Current State: 30:[3, 28], Operations: ['80-77=3', '77-49=28'] Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,30 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,30 unequal: No Solution Moving to Node #0,0,1 Current State: 30:[77, 46], Operations: ['80-77=3', '49-3=46'] Exploring Operation: 77+46=123, Resulting Numbers: [123] 123,30 unequal: No Solution Exploring Operation: 77-46=31, Resulting Numbers: [31] 31,30 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:[77, 49, 3], Operations: ['80-77=3'] Exploring Operation: 77-49=28, Resulting Numbers: [3, 28] Generated Node #0,1,0: 30:[3, 28] Operation: 77-49=28 Exploring Operation: 77-3=74, Resulting Numbers: [49, 74] Generated Node #0,1,1: 30:[49, 74] Operation: 77-3=74 Moving to Node #0,1,0 Current State: 30:[3, 28], Operations: ['80-77=3', '77-49=28'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,30 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[49, 74], Operations: ['80-77=3', '77-3=74'] Exploring Operation: 74-49=25, Resulting Numbers: [25] 25,30 unequal: No Solution Exploring Operation: 49+74=123, Resulting Numbers: [123] 123,30 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
[ 72, 60, 95, 19 ]
95
[ "72*95=6840", "6840/60=114", "114-19=95" ]
Current State: 95:[72, 60, 95, 19], Operations: [] Exploring Operation: 72*95=6840, Resulting Numbers: [60, 19, 6840] Generated Node #2: [60, 19, 6840] from Operation: 72*95=6840 Current State: 95:[60, 19, 6840], Operations: ['72*95=6840'] Exploring Operation: 6840/60=114, Resulting Numbers: [19, 114] Generated Node #3: [19, 114] from Operation: 6840/60=114 Current State: 95:[19, 114], Operations: ['72*95=6840', '6840/60=114'] Exploring Operation: 114-19=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[72, 60, 95, 19], Operations: [] Exploring Operation: 72-60=12, Resulting Numbers: [95, 19, 12] Generated Node #0,0: 95:[95, 19, 12] Operation: 72-60=12 Exploring Operation: 72+60=132, Resulting Numbers: [95, 19, 132] Generated Node #0,1: 95:[95, 19, 132] Operation: 72+60=132 Exploring Operation: 95-72=23, Resulting Numbers: [60, 19, 23] Generated Node #0,2: 95:[60, 19, 23] Operation: 95-72=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[95, 19, 12], Operations: ['72-60=12'] Exploring Operation: 19-12=7, Resulting Numbers: [95, 7] Generated Node #0,0,0: 95:[95, 7] Operation: 19-12=7 Exploring Operation: 95/19=5, Resulting Numbers: [12, 5] Generated Node #0,0,1: 95:[12, 5] Operation: 95/19=5 Exploring Operation: 95+12=107, Resulting Numbers: [19, 107] Generated Node #0,0,2: 95:[19, 107] Operation: 95+12=107 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 95:[95, 7], Operations: ['72-60=12', '19-12=7'] Exploring Operation: 95*7=665, Resulting Numbers: [665] 665,95 unequal: No Solution Exploring Operation: 95+7=102, Resulting Numbers: [102] 102,95 unequal: No Solution Exploring Operation: 95-7=88, Resulting Numbers: [88] 88,95 unequal: No Solution No 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: 95:[12, 5], Operations: ['72-60=12', '95/19=5'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,95 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,95 unequal: No Solution Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,95 unequal: No Solution No 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: 95:[19, 107], Operations: ['72-60=12', '95+12=107'] Exploring Operation: 19+107=126, Resulting Numbers: [126] 126,95 unequal: No Solution Exploring Operation: 19*107=2033, Resulting Numbers: [2033] 2033,95 unequal: No Solution Exploring Operation: 107-19=88, Resulting Numbers: [88] 88,95 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: 95:[95, 19, 132], Operations: ['72+60=132'] Exploring Operation: 132-95=37, Resulting Numbers: [19, 37] Generated Node #0,1,0: 95:[19, 37] Operation: 132-95=37 Exploring Operation: 132-19=113, Resulting Numbers: [95, 113] Generated Node #0,1,1: 95:[95, 113] Operation: 132-19=113 Exploring Operation: 95/19=5, Resulting Numbers: [132, 5] Generated Node #0,1,2: 95:[132, 5] Operation: 95/19=5 Moving to Node #0,1,0 Current State: 95:[19, 37], Operations: ['72+60=132', '132-95=37'] Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,95 unequal: No Solution Exploring Operation: 19*37=703, Resulting Numbers: [703] 703,95 unequal: No Solution Exploring Operation: 19+37=56, Resulting Numbers: [56] 56,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[95, 113], Operations: ['72+60=132', '132-19=113'] Exploring Operation: 95+113=208, Resulting Numbers: [208] 208,95 unequal: No Solution Exploring Operation: 95*113=10735, Resulting Numbers: [10735] 10735,95 unequal: No Solution Exploring Operation: 113-95=18, Resulting Numbers: [18] 18,95 unequal: No Solution Moving to Node #0,1,2 Current State: 95:[132, 5], Operations: ['72+60=132', '95/19=5'] Exploring Operation: 132-5=127, Resulting Numbers: [127] 127,95 unequal: No Solution Exploring Operation: 132*5=660, Resulting Numbers: [660] 660,95 unequal: No Solution Exploring Operation: 132+5=137, Resulting Numbers: [137] 137,95 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 Current State: 95:[60, 19, 23], Operations: ['95-72=23'] Exploring Operation: 60+23=83, Resulting Numbers: [19, 83] Generated Node #0,2,0: 95:[19, 83] Operation: 60+23=83 Exploring Operation: 60+19=79, Resulting Numbers: [23, 79] Generated Node #0,2,1: 95:[23, 79] Operation: 60+19=79 Exploring Operation: 60-23=37, Resulting Numbers: [19, 37] Generated Node #0,2,2: 95:[19, 37] Operation: 60-23=37 Moving to Node #0,2,0 Current State: 95:[19, 83], Operations: ['95-72=23', '60+23=83'] Exploring Operation: 19+83=102, Resulting Numbers: [102] 102,95 unequal: No Solution Exploring Operation: 83-19=64, Resulting Numbers: [64] 64,95 unequal: No Solution Exploring Operation: 19*83=1577, Resulting Numbers: [1577] 1577,95 unequal: No Solution Moving to Node #0,2,2 Current State: 95:[19, 37], Operations: ['95-72=23', '60-23=37'] Exploring Operation: 19*37=703, Resulting Numbers: [703] 703,95 unequal: No Solution Exploring Operation: 19+37=56, Resulting Numbers: [56] 56,95 unequal: No Solution Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,95 unequal: No Solution Moving to Node #0,2,1 Current State: 95:[23, 79], Operations: ['95-72=23', '60+19=79'] Exploring Operation: 23*79=1817, Resulting Numbers: [1817] 1817,95 unequal: No Solution Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,95 unequal: No Solution Exploring Operation: 23+79=102, Resulting Numbers: [102] 102,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 16, 42, 50, 43 ]
86
[ "16*43=688", "50-42=8", "688/8=86" ]
Current State: 86:[16, 42, 50, 43], Operations: [] Exploring Operation: 16*43=688, Resulting Numbers: [42, 50, 688] Generated Node #2: [42, 50, 688] from Operation: 16*43=688 Current State: 86:[42, 50, 688], Operations: ['16*43=688'] Exploring Operation: 50-42=8, Resulting Numbers: [688, 8] Generated Node #3: [688, 8] from Operation: 50-42=8 Current State: 86:[688, 8], Operations: ['16*43=688', '50-42=8'] Exploring Operation: 688/8=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[16, 42, 50, 43], Operations: [] Exploring Operation: 42+50=92, Resulting Numbers: [16, 43, 92] Generated Node #0,0: 86:[16, 43, 92] Operation: 42+50=92 Exploring Operation: 50-42=8, Resulting Numbers: [16, 43, 8] Generated Node #0,1: 86:[16, 43, 8] Operation: 50-42=8 Exploring Operation: 50-16=34, Resulting Numbers: [42, 43, 34] Generated Node #0,2: 86:[42, 43, 34] Operation: 50-16=34 Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[42, 43, 34], Operations: ['50-16=34'] Exploring Operation: 43-34=9, Resulting Numbers: [42, 9] Generated Node #0,2,0: 86:[42, 9] Operation: 43-34=9 Exploring Operation: 42+43=85, Resulting Numbers: [34, 85] Generated Node #0,2,1: 86:[34, 85] Operation: 42+43=85 Exploring Operation: 42-34=8, Resulting Numbers: [43, 8] Generated Node #0,2,2: 86:[43, 8] Operation: 42-34=8 Moving to Node #0,2,2 Current State: 86:[43, 8], Operations: ['50-16=34', '42-34=8'] Exploring Operation: 43+8=51, Resulting Numbers: [51] 51,86 unequal: No Solution Exploring Operation: 43*8=344, Resulting Numbers: [344] 344,86 unequal: No Solution Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,86 unequal: No Solution Moving to Node #0,2,0 Current State: 86:[42, 9], Operations: ['50-16=34', '43-34=9'] Exploring Operation: 42+9=51, Resulting Numbers: [51] 51,86 unequal: No Solution Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,86 unequal: No Solution Exploring Operation: 42*9=378, Resulting Numbers: [378] 378,86 unequal: No Solution Moving to Node #0,2,1 Current State: 86:[34, 85], Operations: ['50-16=34', '42+43=85'] Exploring Operation: 85-34=51, Resulting Numbers: [51] 51,86 unequal: No Solution Exploring Operation: 34*85=2890, Resulting Numbers: [2890] 2890,86 unequal: No Solution Exploring Operation: 34+85=119, Resulting Numbers: [119] 119,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[16, 43, 92], Operations: ['42+50=92'] Exploring Operation: 92-16=76, Resulting Numbers: [43, 76] Generated Node #0,0,0: 86:[43, 76] Operation: 92-16=76 Exploring Operation: 16+43=59, Resulting Numbers: [92, 59] Generated Node #0,0,1: 86:[92, 59] Operation: 16+43=59 Exploring Operation: 92-43=49, Resulting Numbers: [16, 49] Generated Node #0,0,2: 86:[16, 49] Operation: 92-43=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[43, 76], Operations: ['42+50=92', '92-16=76'] Exploring Operation: 43+76=119, Resulting Numbers: [119] 119,86 unequal: No Solution Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,86 unequal: No Solution Exploring Operation: 43*76=3268, Resulting Numbers: [3268] 3268,86 unequal: No Solution No 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: 86:[16, 49], Operations: ['42+50=92', '92-43=49'] Exploring Operation: 49-16=33, Resulting Numbers: [33] 33,86 unequal: No Solution Exploring Operation: 16+49=65, Resulting Numbers: [65] 65,86 unequal: No Solution Exploring Operation: 16*49=784, Resulting Numbers: [784] 784,86 unequal: No Solution No 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: 86:[92, 59], Operations: ['42+50=92', '16+43=59'] Exploring Operation: 92*59=5428, Resulting Numbers: [5428] 5428,86 unequal: No Solution Exploring Operation: 92+59=151, Resulting Numbers: [151] 151,86 unequal: No Solution Exploring Operation: 92-59=33, Resulting Numbers: [33] 33,86 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: 86:[16, 43, 8], Operations: ['50-42=8'] Exploring Operation: 16/8=2, Resulting Numbers: [43, 2] Generated Node #0,1,0: 86:[43, 2] Operation: 16/8=2 Exploring Operation: 16-8=8, Resulting Numbers: [43, 8] Generated Node #0,1,1: 86:[43, 8] Operation: 16-8=8 Exploring Operation: 16+8=24, Resulting Numbers: [43, 24] Generated Node #0,1,2: 86:[43, 24] Operation: 16+8=24 Moving to Node #0,1,0 Current State: 86:[43, 2], Operations: ['50-42=8', '16/8=2'] Exploring Operation: 43+2=45, Resulting Numbers: [45] 45,86 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,86 unequal: No Solution Exploring Operation: 43*2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[16, 42, 50, 43], Operations: [] Exploring Operation: 50-42=8, Resulting Numbers: [16, 43, 8] Generated Node #0,1: 86:[16, 43, 8] Operation: 50-42=8 Moving to Node #0,1 Current State: 86:[16, 43, 8], Operations: ['50-42=8'] Exploring Operation: 16/8=2, Resulting Numbers: [43, 2] Generated Node #0,1,0: 86:[43, 2] Operation: 16/8=2 Moving to Node #0,1,0 Current State: 86:[43, 2], Operations: ['50-42=8', '16/8=2'] Exploring Operation: 43*2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_3
mult_heuristic
[ 26, 82, 83, 41 ]
16
[ "26+82=108", "83+41=124", "124-108=16" ]
Current State: 16:[26, 82, 83, 41], Operations: [] Exploring Operation: 26+82=108, Resulting Numbers: [83, 41, 108] Generated Node #2: [83, 41, 108] from Operation: 26+82=108 Current State: 16:[83, 41, 108], Operations: ['26+82=108'] Exploring Operation: 83+41=124, Resulting Numbers: [108, 124] Generated Node #3: [108, 124] from Operation: 83+41=124 Current State: 16:[108, 124], Operations: ['26+82=108', '83+41=124'] Exploring Operation: 124-108=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[26, 82, 83, 41], Operations: [] Exploring Operation: 83-41=42, Resulting Numbers: [26, 82, 42] Generated Node #0,0: 16:[26, 82, 42] Operation: 83-41=42 Exploring Operation: 83-82=1, Resulting Numbers: [26, 41, 1] Generated Node #0,1: 16:[26, 41, 1] Operation: 83-82=1 Exploring Operation: 82-26=56, Resulting Numbers: [83, 41, 56] Generated Node #0,2: 16:[83, 41, 56] Operation: 82-26=56 Exploring Operation: 82/41=2, Resulting Numbers: [26, 83, 2] Generated Node #0,3: 16:[26, 83, 2] Operation: 82/41=2 Exploring Operation: 82-41=41, Resulting Numbers: [26, 83, 41] Generated Node #0,4: 16:[26, 83, 41] Operation: 82-41=41 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[26, 41, 1], Operations: ['83-82=1'] Exploring Operation: 41-26=15, Resulting Numbers: [1, 15] Generated Node #0,1,0: 16:[1, 15] Operation: 41-26=15 Exploring Operation: 26-1=25, Resulting Numbers: [41, 25] Generated Node #0,1,1: 16:[41, 25] Operation: 26-1=25 Exploring Operation: 26/1=26, Resulting Numbers: [41, 26] Generated Node #0,1,2: 16:[41, 26] Operation: 26/1=26 Exploring Operation: 26*1=26, Resulting Numbers: [41, 26] Generated Node #0,1,3: 16:[41, 26] Operation: 26*1=26 Exploring Operation: 41-1=40, Resulting Numbers: [26, 40] Generated Node #0,1,4: 16:[26, 40] Operation: 41-1=40 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[1, 15], Operations: ['83-82=1', '41-26=15'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,16 unequal: No Solution Exploring Operation: 1*15=15, Resulting Numbers: [15] 15,16 unequal: No Solution Exploring Operation: 1+15=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[26, 82, 83, 41], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [26, 41, 1] Generated Node #0,1: 16:[26, 41, 1] Operation: 83-82=1 Moving to Node #0,1 Current State: 16:[26, 41, 1], Operations: ['83-82=1'] Exploring Operation: 41-26=15, Resulting Numbers: [1, 15] Generated Node #0,1,0: 16:[1, 15] Operation: 41-26=15 Moving to Node #0,1,0 Current State: 16:[1, 15], Operations: ['83-82=1', '41-26=15'] Exploring Operation: 1+15=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 4, 32, 90, 82 ]
30
[ "90-82=8", "8/4=2", "32-2=30" ]
Current State: 30:[4, 32, 90, 82], Operations: [] Exploring Operation: 90-82=8, Resulting Numbers: [4, 32, 8] Generated Node #2: [4, 32, 8] from Operation: 90-82=8 Current State: 30:[4, 32, 8], Operations: ['90-82=8'] Exploring Operation: 8/4=2, Resulting Numbers: [32, 2] Generated Node #3: [32, 2] from Operation: 8/4=2 Current State: 30:[32, 2], Operations: ['90-82=8', '8/4=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[4, 32, 90, 82], Operations: [] Exploring Operation: 90-82=8, Resulting Numbers: [4, 32, 8] Generated Node #0,0: 30:[4, 32, 8] Operation: 90-82=8 Exploring Operation: 90-32=58, Resulting Numbers: [4, 82, 58] Generated Node #0,1: 30:[4, 82, 58] Operation: 90-32=58 Exploring Operation: 82-32=50, Resulting Numbers: [4, 90, 50] Generated Node #0,2: 30:[4, 90, 50] Operation: 82-32=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[4, 32, 8], Operations: ['90-82=8'] Exploring Operation: 8/4=2, Resulting Numbers: [32, 2] Generated Node #0,0,0: 30:[32, 2] Operation: 8/4=2 Exploring Operation: 8-4=4, Resulting Numbers: [32, 4] Generated Node #0,0,1: 30:[32, 4] Operation: 8-4=4 Exploring Operation: 32/8=4, Resulting Numbers: [4, 4] Generated Node #0,0,2: 30:[4, 4] Operation: 32/8=4 Moving to Node #0,0,0 Current State: 30:[32, 2], Operations: ['90-82=8', '8/4=2'] Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[4, 32, 90, 82], Operations: [] Exploring Operation: 90-82=8, Resulting Numbers: [4, 32, 8] Generated Node #0,0: 30:[4, 32, 8] Operation: 90-82=8 Moving to Node #0,0 Current State: 30:[4, 32, 8], Operations: ['90-82=8'] Exploring Operation: 8/4=2, Resulting Numbers: [32, 2] Generated Node #0,0,0: 30:[32, 2] Operation: 8/4=2 Moving to Node #0,0,0 Current State: 30:[32, 2], Operations: ['90-82=8', '8/4=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 8, 51, 78, 44 ]
78
[ "51-8=43", "44-43=1", "78*1=78" ]
Current State: 78:[8, 51, 78, 44], Operations: [] Exploring Operation: 51-8=43, Resulting Numbers: [78, 44, 43] Generated Node #2: [78, 44, 43] from Operation: 51-8=43 Current State: 78:[78, 44, 43], Operations: ['51-8=43'] Exploring Operation: 44-43=1, Resulting Numbers: [78, 1] Generated Node #3: [78, 1] from Operation: 44-43=1 Current State: 78:[78, 1], Operations: ['51-8=43', '44-43=1'] Exploring Operation: 78*1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[8, 51, 78, 44], Operations: [] Exploring Operation: 78-51=27, Resulting Numbers: [8, 44, 27] Generated Node #0,0: 78:[8, 44, 27] Operation: 78-51=27 Exploring Operation: 51-44=7, Resulting Numbers: [8, 78, 7] Generated Node #0,1: 78:[8, 78, 7] Operation: 51-44=7 Exploring Operation: 51-8=43, Resulting Numbers: [78, 44, 43] Generated Node #0,2: 78:[78, 44, 43] Operation: 51-8=43 Moving to Node #0,1 Current State: 78:[8, 78, 7], Operations: ['51-44=7'] Exploring Operation: 8+78=86, Resulting Numbers: [7, 86] Generated Node #0,1,0: 78:[7, 86] Operation: 8+78=86 Exploring Operation: 8-7=1, Resulting Numbers: [78, 1] Generated Node #0,1,1: 78:[78, 1] Operation: 8-7=1 Exploring Operation: 8+7=15, Resulting Numbers: [78, 15] Generated Node #0,1,2: 78:[78, 15] Operation: 8+7=15 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[78, 1], Operations: ['51-44=7', '8-7=1'] Exploring Operation: 78+1=79, Resulting Numbers: [79] 79,78 unequal: No Solution Exploring Operation: 78*1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[8, 51, 78, 44], Operations: [] Exploring Operation: 51-44=7, Resulting Numbers: [8, 78, 7] Generated Node #0,1: 78:[8, 78, 7] Operation: 51-44=7 Moving to Node #0,1 Current State: 78:[8, 78, 7], Operations: ['51-44=7'] Exploring Operation: 8-7=1, Resulting Numbers: [78, 1] Generated Node #0,1,1: 78:[78, 1] Operation: 8-7=1 Moving to Node #0,1,1 Current State: 78:[78, 1], Operations: ['51-44=7', '8-7=1'] Exploring Operation: 78*1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 2, 56, 51, 70 ]
30
[ "70/2=35", "56-51=5", "35-5=30" ]
Current State: 30:[2, 56, 51, 70], Operations: [] Exploring Operation: 70/2=35, Resulting Numbers: [56, 51, 35] Generated Node #2: [56, 51, 35] from Operation: 70/2=35 Current State: 30:[56, 51, 35], Operations: ['70/2=35'] Exploring Operation: 56-51=5, Resulting Numbers: [35, 5] Generated Node #3: [35, 5] from Operation: 56-51=5 Current State: 30:[35, 5], Operations: ['70/2=35', '56-51=5'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[2, 56, 51, 70], Operations: [] Exploring Operation: 70-56=14, Resulting Numbers: [2, 51, 14] Generated Node #0,0: 30:[2, 51, 14] Operation: 70-56=14 Exploring Operation: 70-51=19, Resulting Numbers: [2, 56, 19] Generated Node #0,1: 30:[2, 56, 19] Operation: 70-51=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[2, 51, 14], Operations: ['70-56=14'] Exploring Operation: 51-14=37, Resulting Numbers: [2, 37] Generated Node #0,0,0: 30:[2, 37] Operation: 51-14=37 Exploring Operation: 51-2=49, Resulting Numbers: [14, 49] Generated Node #0,0,1: 30:[14, 49] Operation: 51-2=49 Moving to Node #0,0,0 Current State: 30:[2, 37], Operations: ['70-56=14', '51-14=37'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,30 unequal: No Solution Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,30 unequal: No Solution Moving to Node #0,0,1 Current State: 30:[14, 49], Operations: ['70-56=14', '51-2=49'] Exploring Operation: 14+49=63, Resulting Numbers: [63] 63,30 unequal: No Solution Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,30 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:[2, 56, 19], Operations: ['70-51=19'] Exploring Operation: 56-19=37, Resulting Numbers: [2, 37] Generated Node #0,1,0: 30:[2, 37] Operation: 56-19=37 Exploring Operation: 56/2=28, Resulting Numbers: [19, 28] Generated Node #0,1,1: 30:[19, 28] Operation: 56/2=28 Moving to Node #0,1,1 Current State: 30:[19, 28], Operations: ['70-51=19', '56/2=28'] Exploring Operation: 19+28=47, Resulting Numbers: [47] 47,30 unequal: No Solution Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[2, 37], Operations: ['70-51=19', '56-19=37'] Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,30 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
[ 39, 54, 42, 21 ]
95
[ "39+54=93", "42/21=2", "93+2=95" ]
Current State: 95:[39, 54, 42, 21], Operations: [] Exploring Operation: 39+54=93, Resulting Numbers: [42, 21, 93] Generated Node #2: [42, 21, 93] from Operation: 39+54=93 Current State: 95:[42, 21, 93], Operations: ['39+54=93'] Exploring Operation: 42/21=2, Resulting Numbers: [93, 2] Generated Node #3: [93, 2] from Operation: 42/21=2 Current State: 95:[93, 2], Operations: ['39+54=93', '42/21=2'] Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[39, 54, 42, 21], Operations: [] Exploring Operation: 54+42=96, Resulting Numbers: [39, 21, 96] Generated Node #0,0: 95:[39, 21, 96] Operation: 54+42=96 Exploring Operation: 39+54=93, Resulting Numbers: [42, 21, 93] Generated Node #0,1: 95:[42, 21, 93] Operation: 39+54=93 Exploring Operation: 42-39=3, Resulting Numbers: [54, 21, 3] Generated Node #0,2: 95:[54, 21, 3] Operation: 42-39=3 Exploring Operation: 54-42=12, Resulting Numbers: [39, 21, 12] Generated Node #0,3: 95:[39, 21, 12] Operation: 54-42=12 Exploring Operation: 54-39=15, Resulting Numbers: [42, 21, 15] Generated Node #0,4: 95:[42, 21, 15] Operation: 54-39=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[39, 21, 96], Operations: ['54+42=96'] Exploring Operation: 96-21=75, Resulting Numbers: [39, 75] Generated Node #0,0,0: 95:[39, 75] Operation: 96-21=75 Exploring Operation: 39+96=135, Resulting Numbers: [21, 135] Generated Node #0,0,1: 95:[21, 135] Operation: 39+96=135 Exploring Operation: 39+21=60, Resulting Numbers: [96, 60] Generated Node #0,0,2: 95:[96, 60] Operation: 39+21=60 Exploring Operation: 39-21=18, Resulting Numbers: [96, 18] Generated Node #0,0,3: 95:[96, 18] Operation: 39-21=18 Exploring Operation: 96-39=57, Resulting Numbers: [21, 57] Generated Node #0,0,4: 95:[21, 57] Operation: 96-39=57 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 95:[96, 18], Operations: ['54+42=96', '39-21=18'] Exploring Operation: 96-18=78, Resulting Numbers: [78] 78,95 unequal: No Solution Exploring Operation: 96+18=114, Resulting Numbers: [114] 114,95 unequal: No Solution Exploring Operation: 96*18=1728, Resulting Numbers: [1728] 1728,95 unequal: No Solution No 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: 95:[96, 60], Operations: ['54+42=96', '39+21=60'] Exploring Operation: 96-60=36, Resulting Numbers: [36] 36,95 unequal: No Solution Exploring Operation: 96+60=156, Resulting Numbers: [156] 156,95 unequal: No Solution Exploring Operation: 96*60=5760, Resulting Numbers: [5760] 5760,95 unequal: No Solution No 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: 95:[39, 75], Operations: ['54+42=96', '96-21=75'] Exploring Operation: 75-39=36, Resulting Numbers: [36] 36,95 unequal: No Solution Exploring Operation: 39*75=2925, Resulting Numbers: [2925] 2925,95 unequal: No Solution Exploring Operation: 39+75=114, Resulting Numbers: [114] 114,95 unequal: No Solution No 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: 95:[21, 57], Operations: ['54+42=96', '96-39=57'] Exploring Operation: 21+57=78, Resulting Numbers: [78] 78,95 unequal: No Solution Exploring Operation: 57-21=36, Resulting Numbers: [36] 36,95 unequal: No Solution Exploring Operation: 21*57=1197, Resulting Numbers: [1197] 1197,95 unequal: No Solution No 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: 95:[21, 135], Operations: ['54+42=96', '39+96=135'] Exploring Operation: 135-21=114, Resulting Numbers: [114] 114,95 unequal: No Solution Exploring Operation: 21*135=2835, Resulting Numbers: [2835] 2835,95 unequal: No Solution Exploring Operation: 21+135=156, Resulting Numbers: [156] 156,95 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: 95:[42, 21, 93], Operations: ['39+54=93'] Exploring Operation: 42/21=2, Resulting Numbers: [93, 2] Generated Node #0,1,0: 95:[93, 2] Operation: 42/21=2 Exploring Operation: 42+21=63, Resulting Numbers: [93, 63] Generated Node #0,1,1: 95:[93, 63] Operation: 42+21=63 Exploring Operation: 42-21=21, Resulting Numbers: [93, 21] Generated Node #0,1,2: 95:[93, 21] Operation: 42-21=21 Exploring Operation: 93-42=51, Resulting Numbers: [21, 51] Generated Node #0,1,3: 95:[21, 51] Operation: 93-42=51 Exploring Operation: 42+93=135, Resulting Numbers: [21, 135] Generated Node #0,1,4: 95:[21, 135] Operation: 42+93=135 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 95:[93, 21], Operations: ['39+54=93', '42-21=21'] Exploring Operation: 93*21=1953, Resulting Numbers: [1953] 1953,95 unequal: No Solution Exploring Operation: 93-21=72, Resulting Numbers: [72] 72,95 unequal: No Solution Exploring Operation: 93+21=114, Resulting Numbers: [114] 114,95 unequal: No Solution No 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: 95:[93, 2], Operations: ['39+54=93', '42/21=2'] Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,95 unequal: No Solution Exploring Operation: 93*2=186, Resulting Numbers: [186] 186,95 unequal: No Solution Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[39, 54, 42, 21], Operations: [] Exploring Operation: 39+54=93, Resulting Numbers: [42, 21, 93] Generated Node #0,1: 95:[42, 21, 93] Operation: 39+54=93 Moving to Node #0,1 Current State: 95:[42, 21, 93], Operations: ['39+54=93'] Exploring Operation: 42/21=2, Resulting Numbers: [93, 2] Generated Node #0,1,0: 95:[93, 2] Operation: 42/21=2 Moving to Node #0,1,0 Current State: 95:[93, 2], Operations: ['39+54=93', '42/21=2'] Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_5
sum_heuristic
[ 19, 6, 23, 14 ]
22
[ "19-6=13", "23-14=9", "13+9=22" ]
Current State: 22:[19, 6, 23, 14], Operations: [] Exploring Operation: 19-6=13, Resulting Numbers: [23, 14, 13] Generated Node #2: [23, 14, 13] from Operation: 19-6=13 Current State: 22:[23, 14, 13], Operations: ['19-6=13'] Exploring Operation: 23-14=9, Resulting Numbers: [13, 9] Generated Node #3: [13, 9] from Operation: 23-14=9 Current State: 22:[13, 9], Operations: ['19-6=13', '23-14=9'] Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[19, 6, 23, 14], Operations: [] Exploring Operation: 19+6=25, Resulting Numbers: [23, 14, 25] Generated Node #0,0: 22:[23, 14, 25] Operation: 19+6=25 Exploring Operation: 6+14=20, Resulting Numbers: [19, 23, 20] Generated Node #0,1: 22:[19, 23, 20] Operation: 6+14=20 Exploring Operation: 14-6=8, Resulting Numbers: [19, 23, 8] Generated Node #0,2: 22:[19, 23, 8] Operation: 14-6=8 Exploring Operation: 19-6=13, Resulting Numbers: [23, 14, 13] Generated Node #0,3: 22:[23, 14, 13] Operation: 19-6=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[19, 23, 20], Operations: ['6+14=20'] Exploring Operation: 23-20=3, Resulting Numbers: [19, 3] Generated Node #0,1,0: 22:[19, 3] Operation: 23-20=3 Exploring Operation: 19+20=39, Resulting Numbers: [23, 39] Generated Node #0,1,1: 22:[23, 39] Operation: 19+20=39 Exploring Operation: 23-19=4, Resulting Numbers: [20, 4] Generated Node #0,1,2: 22:[20, 4] Operation: 23-19=4 Exploring Operation: 20-19=1, Resulting Numbers: [23, 1] Generated Node #0,1,3: 22:[23, 1] Operation: 20-19=1 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 22:[23, 1], Operations: ['6+14=20', '20-19=1'] Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[19, 6, 23, 14], Operations: [] Exploring Operation: 6+14=20, Resulting Numbers: [19, 23, 20] Generated Node #0,1: 22:[19, 23, 20] Operation: 6+14=20 Moving to Node #0,1 Current State: 22:[19, 23, 20], Operations: ['6+14=20'] Exploring Operation: 20-19=1, Resulting Numbers: [23, 1] Generated Node #0,1,3: 22:[23, 1] Operation: 20-19=1 Moving to Node #0,1,3 Current State: 22:[23, 1], Operations: ['6+14=20', '20-19=1'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 55, 29, 32, 18 ]
98
[ "55+29=84", "32-18=14", "84+14=98" ]
Current State: 98:[55, 29, 32, 18], Operations: [] Exploring Operation: 55+29=84, Resulting Numbers: [32, 18, 84] Generated Node #2: [32, 18, 84] from Operation: 55+29=84 Current State: 98:[32, 18, 84], Operations: ['55+29=84'] Exploring Operation: 32-18=14, Resulting Numbers: [84, 14] Generated Node #3: [84, 14] from Operation: 32-18=14 Current State: 98:[84, 14], Operations: ['55+29=84', '32-18=14'] Exploring Operation: 84+14=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[55, 29, 32, 18], Operations: [] Exploring Operation: 32-29=3, Resulting Numbers: [55, 18, 3] Generated Node #0,0: 98:[55, 18, 3] Operation: 32-29=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[55, 18, 3], Operations: ['32-29=3'] Exploring Operation: 55-3=52, Resulting Numbers: [18, 52] Generated Node #0,0,0: 98:[18, 52] Operation: 55-3=52 Moving to Node #0,0,0 Current State: 98:[18, 52], Operations: ['32-29=3', '55-3=52'] Exploring Operation: 52-18=34, Resulting Numbers: [34] 34,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 64, 6, 60, 74 ]
100
[ "74-64=10", "60/6=10", "10*10=100" ]
Current State: 100:[64, 6, 60, 74], Operations: [] Exploring Operation: 74-64=10, Resulting Numbers: [6, 60, 10] Generated Node #2: [6, 60, 10] from Operation: 74-64=10 Current State: 100:[6, 60, 10], Operations: ['74-64=10'] Exploring Operation: 60/6=10, Resulting Numbers: [10, 10] Generated Node #3: [10, 10] from Operation: 60/6=10 Current State: 100:[10, 10], Operations: ['74-64=10', '60/6=10'] Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[64, 6, 60, 74], Operations: [] Exploring Operation: 74-64=10, Resulting Numbers: [6, 60, 10] Generated Node #0,0: 100:[6, 60, 10] Operation: 74-64=10 Exploring Operation: 64-60=4, Resulting Numbers: [6, 74, 4] Generated Node #0,1: 100:[6, 74, 4] Operation: 64-60=4 Exploring Operation: 74-60=14, Resulting Numbers: [64, 6, 14] Generated Node #0,2: 100:[64, 6, 14] Operation: 74-60=14 Moving to Node #0,0 Current State: 100:[6, 60, 10], Operations: ['74-64=10'] Exploring Operation: 60/6=10, Resulting Numbers: [10, 10] Generated Node #0,0,0: 100:[10, 10] Operation: 60/6=10 Exploring Operation: 60-10=50, Resulting Numbers: [6, 50] Generated Node #0,0,1: 100:[6, 50] Operation: 60-10=50 Exploring Operation: 60/10=6, Resulting Numbers: [6, 6] Generated Node #0,0,2: 100:[6, 6] Operation: 60/10=6 Moving to Node #0,2 Current State: 100:[64, 6, 14], Operations: ['74-60=14'] Exploring Operation: 6+14=20, Resulting Numbers: [64, 20] Generated Node #0,2,0: 100:[64, 20] Operation: 6+14=20 Exploring Operation: 64-6=58, Resulting Numbers: [14, 58] Generated Node #0,2,1: 100:[14, 58] Operation: 64-6=58 Exploring Operation: 64-14=50, Resulting Numbers: [6, 50] Generated Node #0,2,2: 100:[6, 50] Operation: 64-14=50 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 100:[6, 50], Operations: ['74-60=14', '64-14=50'] Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 6*50=300, Resulting Numbers: [300] 300,100 unequal: No Solution Exploring Operation: 6+50=56, Resulting Numbers: [56] 56,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 100:[14, 58], Operations: ['74-60=14', '64-6=58'] Exploring Operation: 14*58=812, Resulting Numbers: [812] 812,100 unequal: No Solution Exploring Operation: 14+58=72, Resulting Numbers: [72] 72,100 unequal: No Solution Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 100:[64, 20], Operations: ['74-60=14', '6+14=20'] Exploring Operation: 64+20=84, Resulting Numbers: [84] 84,100 unequal: No Solution Exploring Operation: 64*20=1280, Resulting Numbers: [1280] 1280,100 unequal: No Solution Exploring Operation: 64-20=44, Resulting Numbers: [44] 44,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 100:[6, 74, 4], Operations: ['64-60=4'] Exploring Operation: 74-6=68, Resulting Numbers: [4, 68] Generated Node #0,1,0: 100:[4, 68] Operation: 74-6=68 Exploring Operation: 74-4=70, Resulting Numbers: [6, 70] Generated Node #0,1,1: 100:[6, 70] Operation: 74-4=70 Exploring Operation: 6+74=80, Resulting Numbers: [4, 80] Generated Node #0,1,2: 100:[4, 80] Operation: 6+74=80 Moving to Node #0,0,0 Current State: 100:[10, 10], Operations: ['74-64=10', '60/6=10'] Exploring Operation: 10+10=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 10/10=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[64, 6, 60, 74], Operations: [] Exploring Operation: 74-64=10, Resulting Numbers: [6, 60, 10] Generated Node #0,0: 100:[6, 60, 10] Operation: 74-64=10 Moving to Node #0,0 Current State: 100:[6, 60, 10], Operations: ['74-64=10'] Exploring Operation: 60/6=10, Resulting Numbers: [10, 10] Generated Node #0,0,0: 100:[10, 10] Operation: 60/6=10 Moving to Node #0,0,0 Current State: 100:[10, 10], Operations: ['74-64=10', '60/6=10'] Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.975694
hs_3
mult_heuristic
[ 13, 70, 66, 62 ]
87
[ "13+70=83", "66-62=4", "83+4=87" ]
Current State: 87:[13, 70, 66, 62], Operations: [] Exploring Operation: 13+70=83, Resulting Numbers: [66, 62, 83] Generated Node #2: [66, 62, 83] from Operation: 13+70=83 Current State: 87:[66, 62, 83], Operations: ['13+70=83'] Exploring Operation: 66-62=4, Resulting Numbers: [83, 4] Generated Node #3: [83, 4] from Operation: 66-62=4 Current State: 87:[83, 4], Operations: ['13+70=83', '66-62=4'] Exploring Operation: 83+4=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[13, 70, 66, 62], Operations: [] Exploring Operation: 70-62=8, Resulting Numbers: [13, 66, 8] Generated Node #0,0: 87:[13, 66, 8] Operation: 70-62=8 Exploring Operation: 66-62=4, Resulting Numbers: [13, 70, 4] Generated Node #0,1: 87:[13, 70, 4] Operation: 66-62=4 Exploring Operation: 70-66=4, Resulting Numbers: [13, 62, 4] Generated Node #0,2: 87:[13, 62, 4] Operation: 70-66=4 Moving to Node #0,1 Current State: 87:[13, 70, 4], Operations: ['66-62=4'] Exploring Operation: 13-4=9, Resulting Numbers: [70, 9] Generated Node #0,1,0: 87:[70, 9] Operation: 13-4=9 Exploring Operation: 70+4=74, Resulting Numbers: [13, 74] Generated Node #0,1,1: 87:[13, 74] Operation: 70+4=74 Exploring Operation: 13+70=83, Resulting Numbers: [4, 83] Generated Node #0,1,2: 87:[4, 83] Operation: 13+70=83 Moving to Node #0,0 Current State: 87:[13, 66, 8], Operations: ['70-62=8'] Exploring Operation: 13-8=5, Resulting Numbers: [66, 5] Generated Node #0,0,0: 87:[66, 5] Operation: 13-8=5 Exploring Operation: 66+8=74, Resulting Numbers: [13, 74] Generated Node #0,0,1: 87:[13, 74] Operation: 66+8=74 Exploring Operation: 13+66=79, Resulting Numbers: [8, 79] Generated Node #0,0,2: 87:[8, 79] Operation: 13+66=79 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 87:[8, 79], Operations: ['70-62=8', '13+66=79'] Exploring Operation: 8*79=632, Resulting Numbers: [632] 632,87 unequal: No Solution Exploring Operation: 8+79=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[13, 70, 66, 62], Operations: [] Exploring Operation: 70-62=8, Resulting Numbers: [13, 66, 8] Generated Node #0,0: 87:[13, 66, 8] Operation: 70-62=8 Moving to Node #0,0 Current State: 87:[13, 66, 8], Operations: ['70-62=8'] Exploring Operation: 13+66=79, Resulting Numbers: [8, 79] Generated Node #0,0,2: 87:[8, 79] Operation: 13+66=79 Moving to Node #0,0,2 Current State: 87:[8, 79], Operations: ['70-62=8', '13+66=79'] Exploring Operation: 8+79=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 58, 62, 2, 18 ]
72
[ "58*2=116", "62-18=44", "116-44=72" ]
Current State: 72:[58, 62, 2, 18], Operations: [] Exploring Operation: 58*2=116, Resulting Numbers: [62, 18, 116] Generated Node #2: [62, 18, 116] from Operation: 58*2=116 Current State: 72:[62, 18, 116], Operations: ['58*2=116'] Exploring Operation: 62-18=44, Resulting Numbers: [116, 44] Generated Node #3: [116, 44] from Operation: 62-18=44 Current State: 72:[116, 44], Operations: ['58*2=116', '62-18=44'] Exploring Operation: 116-44=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[58, 62, 2, 18], Operations: [] Exploring Operation: 58+18=76, Resulting Numbers: [62, 2, 76] Generated Node #0,0: 72:[62, 2, 76] Operation: 58+18=76 Exploring Operation: 62-58=4, Resulting Numbers: [2, 18, 4] Generated Node #0,1: 72:[2, 18, 4] Operation: 62-58=4 Exploring Operation: 58-18=40, Resulting Numbers: [62, 2, 40] Generated Node #0,2: 72:[62, 2, 40] Operation: 58-18=40 Moving to Node #0,1 Current State: 72:[2, 18, 4], Operations: ['62-58=4'] Exploring Operation: 2+4=6, Resulting Numbers: [18, 6] Generated Node #0,1,0: 72:[18, 6] Operation: 2+4=6 Exploring Operation: 18/2=9, Resulting Numbers: [4, 9] Generated Node #0,1,1: 72:[4, 9] Operation: 18/2=9 Exploring Operation: 2*18=36, Resulting Numbers: [4, 36] Generated Node #0,1,2: 72:[4, 36] Operation: 2*18=36 Moving to Node #0,0 Current State: 72:[62, 2, 76], Operations: ['58+18=76'] Exploring Operation: 76-62=14, Resulting Numbers: [2, 14] Generated Node #0,0,0: 72:[2, 14] Operation: 76-62=14 Exploring Operation: 62/2=31, Resulting Numbers: [76, 31] Generated Node #0,0,1: 72:[76, 31] Operation: 62/2=31 Exploring Operation: 62+2=64, Resulting Numbers: [76, 64] Generated Node #0,0,2: 72:[76, 64] Operation: 62+2=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[2, 14], Operations: ['58+18=76', '76-62=14'] Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[76, 31], Operations: ['58+18=76', '62/2=31'] Exploring Operation: 76+31=107, Resulting Numbers: [107] 107,72 unequal: No Solution Exploring Operation: 76*31=2356, Resulting Numbers: [2356] 2356,72 unequal: No Solution Exploring Operation: 76-31=45, Resulting Numbers: [45] 45,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 72:[76, 64], Operations: ['58+18=76', '62+2=64'] Exploring Operation: 76-64=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 76*64=4864, Resulting Numbers: [4864] 4864,72 unequal: No Solution Exploring Operation: 76+64=140, Resulting Numbers: [140] 140,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 72:[62, 2, 40], Operations: ['58-18=40'] Exploring Operation: 62+2=64, Resulting Numbers: [40, 64] Generated Node #0,2,0: 72:[40, 64] Operation: 62+2=64 Exploring Operation: 62/2=31, Resulting Numbers: [40, 31] Generated Node #0,2,1: 72:[40, 31] Operation: 62/2=31 Exploring Operation: 62-40=22, Resulting Numbers: [2, 22] Generated Node #0,2,2: 72:[2, 22] Operation: 62-40=22 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 72:[2, 22], Operations: ['58-18=40', '62-40=22'] Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,72 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,72 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 72:[40, 31], Operations: ['58-18=40', '62/2=31'] Exploring Operation: 40+31=71, Resulting Numbers: [71] 71,72 unequal: No Solution Exploring Operation: 40*31=1240, Resulting Numbers: [1240] 1240,72 unequal: No Solution Exploring Operation: 40-31=9, Resulting Numbers: [9] 9,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 72:[40, 64], Operations: ['58-18=40', '62+2=64'] Exploring Operation: 40*64=2560, Resulting Numbers: [2560] 2560,72 unequal: No Solution Exploring Operation: 64-40=24, Resulting Numbers: [24] 24,72 unequal: No Solution Exploring Operation: 40+64=104, Resulting Numbers: [104] 104,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 72:[18, 6], Operations: ['62-58=4', '2+4=6'] Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,72 unequal: No Solution Exploring Operation: 18+6=24, Resulting Numbers: [24] 24,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[4, 9], Operations: ['62-58=4', '18/2=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[4, 36], Operations: ['62-58=4', '2*18=36'] Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,72 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,72 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,72 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 82, 59, 50, 2 ]
14
[ "82+50=132", "59*2=118", "132-118=14" ]
Current State: 14:[82, 59, 50, 2], Operations: [] Exploring Operation: 82+50=132, Resulting Numbers: [59, 2, 132] Generated Node #2: [59, 2, 132] from Operation: 82+50=132 Current State: 14:[59, 2, 132], Operations: ['82+50=132'] Exploring Operation: 59*2=118, Resulting Numbers: [132, 118] Generated Node #3: [132, 118] from Operation: 59*2=118 Current State: 14:[132, 118], Operations: ['82+50=132', '59*2=118'] Exploring Operation: 132-118=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[82, 59, 50, 2], Operations: [] Exploring Operation: 82-59=23, Resulting Numbers: [50, 2, 23] Generated Node #0,0: 14:[50, 2, 23] Operation: 82-59=23 Exploring Operation: 82-50=32, Resulting Numbers: [59, 2, 32] Generated Node #0,1: 14:[59, 2, 32] Operation: 82-50=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[50, 2, 23], Operations: ['82-59=23'] Exploring Operation: 50-23=27, Resulting Numbers: [2, 27] Generated Node #0,0,0: 14:[2, 27] Operation: 50-23=27 Exploring Operation: 50/2=25, Resulting Numbers: [23, 25] Generated Node #0,0,1: 14:[23, 25] Operation: 50/2=25 Moving to Node #0,0,0 Current State: 14:[2, 27], Operations: ['82-59=23', '50-23=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,14 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[23, 25], Operations: ['82-59=23', '50/2=25'] Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,14 unequal: No Solution Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,14 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 Current State: 14:[59, 2, 32], Operations: ['82-50=32'] Exploring Operation: 32/2=16, Resulting Numbers: [59, 16] Generated Node #0,1,0: 14:[59, 16] Operation: 32/2=16 Exploring Operation: 59-32=27, Resulting Numbers: [2, 27] Generated Node #0,1,1: 14:[2, 27] Operation: 59-32=27 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 14:[2, 27], Operations: ['82-50=32', '59-32=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,14 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 14:[59, 16], Operations: ['82-50=32', '32/2=16'] Exploring Operation: 59+16=75, Resulting Numbers: [75] 75,14 unequal: No Solution Exploring Operation: 59-16=43, Resulting Numbers: [43] 43,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 9, 81, 56, 35 ]
100
[ "81/9=9", "56+35=91", "9+91=100" ]
Current State: 100:[9, 81, 56, 35], Operations: [] Exploring Operation: 81/9=9, Resulting Numbers: [56, 35, 9] Generated Node #2: [56, 35, 9] from Operation: 81/9=9 Current State: 100:[56, 35, 9], Operations: ['81/9=9'] Exploring Operation: 56+35=91, Resulting Numbers: [9, 91] Generated Node #3: [9, 91] from Operation: 56+35=91 Current State: 100:[9, 91], Operations: ['81/9=9', '56+35=91'] Exploring Operation: 9+91=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[9, 81, 56, 35], Operations: [] Exploring Operation: 56-35=21, Resulting Numbers: [9, 81, 21] Generated Node #0,0: 100:[9, 81, 21] Operation: 56-35=21 Exploring Operation: 81/9=9, Resulting Numbers: [56, 35, 9] Generated Node #0,1: 100:[56, 35, 9] Operation: 81/9=9 Exploring Operation: 81-56=25, Resulting Numbers: [9, 35, 25] Generated Node #0,2: 100:[9, 35, 25] Operation: 81-56=25 Exploring Operation: 81-35=46, Resulting Numbers: [9, 56, 46] Generated Node #0,3: 100:[9, 56, 46] Operation: 81-35=46 Moving to Node #0,2 Current State: 100:[9, 35, 25], Operations: ['81-56=25'] Exploring Operation: 9+35=44, Resulting Numbers: [25, 44] Generated Node #0,2,0: 100:[25, 44] Operation: 9+35=44 Exploring Operation: 35-25=10, Resulting Numbers: [9, 10] Generated Node #0,2,1: 100:[9, 10] Operation: 35-25=10 Exploring Operation: 35-9=26, Resulting Numbers: [25, 26] Generated Node #0,2,2: 100:[25, 26] Operation: 35-9=26 Exploring Operation: 35+25=60, Resulting Numbers: [9, 60] Generated Node #0,2,3: 100:[9, 60] Operation: 35+25=60 Moving to Node #0,3 Current State: 100:[9, 56, 46], Operations: ['81-35=46'] Exploring Operation: 56-46=10, Resulting Numbers: [9, 10] Generated Node #0,3,0: 100:[9, 10] Operation: 56-46=10 Exploring Operation: 9+46=55, Resulting Numbers: [56, 55] Generated Node #0,3,1: 100:[56, 55] Operation: 9+46=55 Exploring Operation: 56-9=47, Resulting Numbers: [46, 47] Generated Node #0,3,2: 100:[46, 47] Operation: 56-9=47 Exploring Operation: 56+46=102, Resulting Numbers: [9, 102] Generated Node #0,3,3: 100:[9, 102] Operation: 56+46=102 Moving to Node #0,1 Current State: 100:[56, 35, 9], Operations: ['81/9=9'] Exploring Operation: 35+9=44, Resulting Numbers: [56, 44] Generated Node #0,1,0: 100:[56, 44] Operation: 35+9=44 Exploring Operation: 56+35=91, Resulting Numbers: [9, 91] Generated Node #0,1,1: 100:[9, 91] Operation: 56+35=91 Exploring Operation: 56-35=21, Resulting Numbers: [9, 21] Generated Node #0,1,2: 100:[9, 21] Operation: 56-35=21 Exploring Operation: 35-9=26, Resulting Numbers: [56, 26] Generated Node #0,1,3: 100:[56, 26] Operation: 35-9=26 Moving to Node #0,0 Current State: 100:[9, 81, 21], Operations: ['56-35=21'] Exploring Operation: 81/9=9, Resulting Numbers: [21, 9] Generated Node #0,0,0: 100:[21, 9] Operation: 81/9=9 Exploring Operation: 81-21=60, Resulting Numbers: [9, 60] Generated Node #0,0,1: 100:[9, 60] Operation: 81-21=60 Exploring Operation: 9+81=90, Resulting Numbers: [21, 90] Generated Node #0,0,2: 100:[21, 90] Operation: 9+81=90 Exploring Operation: 81+21=102, Resulting Numbers: [9, 102] Generated Node #0,0,3: 100:[9, 102] Operation: 81+21=102 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[21, 9], Operations: ['56-35=21', '81/9=9'] Exploring Operation: 21*9=189, Resulting Numbers: [189] 189,100 unequal: No Solution Exploring Operation: 21+9=30, Resulting Numbers: [30] 30,100 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 100:[9, 102], Operations: ['56-35=21', '81+21=102'] Exploring Operation: 102-9=93, Resulting Numbers: [93] 93,100 unequal: No Solution Exploring Operation: 9*102=918, Resulting Numbers: [918] 918,100 unequal: No Solution Exploring Operation: 9+102=111, Resulting Numbers: [111] 111,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[9, 60], Operations: ['56-35=21', '81-21=60'] Exploring Operation: 9*60=540, Resulting Numbers: [540] 540,100 unequal: No Solution Exploring Operation: 9+60=69, Resulting Numbers: [69] 69,100 unequal: No Solution Exploring Operation: 60-9=51, Resulting Numbers: [51] 51,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 100:[21, 90], Operations: ['56-35=21', '9+81=90'] Exploring Operation: 21+90=111, Resulting Numbers: [111] 111,100 unequal: No Solution Exploring Operation: 21*90=1890, Resulting Numbers: [1890] 1890,100 unequal: No Solution Exploring Operation: 90-21=69, Resulting Numbers: [69] 69,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 100:[9, 10], Operations: ['81-56=25', '35-25=10'] Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,100 unequal: No Solution Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,100 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,100 unequal: No Solution Moving to Node #0,2,2 Current State: 100:[25, 26], Operations: ['81-56=25', '35-9=26'] Exploring Operation: 25+26=51, Resulting Numbers: [51] 51,100 unequal: No Solution Exploring Operation: 25*26=650, Resulting Numbers: [650] 650,100 unequal: No Solution Exploring Operation: 26-25=1, Resulting Numbers: [1] 1,100 unequal: No Solution Moving to Node #0,3,0 Current State: 100:[9, 10], Operations: ['81-35=46', '56-46=10'] Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,100 unequal: No Solution Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,100 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,100 unequal: No Solution Moving to Node #0,1,2 Current State: 100:[9, 21], Operations: ['81/9=9', '56-35=21'] Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,100 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 9*21=189, Resulting Numbers: [189] 189,100 unequal: No Solution Moving to Node #0,3,3 Current State: 100:[9, 102], Operations: ['81-35=46', '56+46=102'] Exploring Operation: 9*102=918, Resulting Numbers: [918] 918,100 unequal: No Solution Exploring Operation: 9+102=111, Resulting Numbers: [111] 111,100 unequal: No Solution Exploring Operation: 102-9=93, Resulting Numbers: [93] 93,100 unequal: No Solution Moving to Node #0,2,0 Current State: 100:[25, 44], Operations: ['81-56=25', '9+35=44'] Exploring Operation: 25+44=69, Resulting Numbers: [69] 69,100 unequal: No Solution Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,100 unequal: No Solution Exploring Operation: 25*44=1100, Resulting Numbers: [1100] 1100,100 unequal: No Solution Moving to Node #0,3,2 Current State: 100:[46, 47], Operations: ['81-35=46', '56-9=47'] Exploring Operation: 46*47=2162, Resulting Numbers: [2162] 2162,100 unequal: No Solution Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 46+47=93, Resulting Numbers: [93] 93,100 unequal: No Solution Moving to Node #0,1,3 Current State: 100:[56, 26], Operations: ['81/9=9', '35-9=26'] Exploring Operation: 56-26=30, Resulting Numbers: [30] 30,100 unequal: No Solution Exploring Operation: 56*26=1456, Resulting Numbers: [1456] 1456,100 unequal: No Solution Exploring Operation: 56+26=82, Resulting Numbers: [82] 82,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[9, 91], Operations: ['81/9=9', '56+35=91'] Exploring Operation: 9*91=819, Resulting Numbers: [819] 819,100 unequal: No Solution Exploring Operation: 9+91=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[9, 81, 56, 35], Operations: [] Exploring Operation: 81/9=9, Resulting Numbers: [56, 35, 9] Generated Node #0,1: 100:[56, 35, 9] Operation: 81/9=9 Moving to Node #0,1 Current State: 100:[56, 35, 9], Operations: ['81/9=9'] Exploring Operation: 56+35=91, Resulting Numbers: [9, 91] Generated Node #0,1,1: 100:[9, 91] Operation: 56+35=91 Moving to Node #0,1,1 Current State: 100:[9, 91], Operations: ['81/9=9', '56+35=91'] Exploring Operation: 9+91=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.946181
hs_4
sum_heuristic
[ 61, 92, 62, 63 ]
65
[ "92-61=31", "62/31=2", "63+2=65" ]
Current State: 65:[61, 92, 62, 63], Operations: [] Exploring Operation: 92-61=31, Resulting Numbers: [62, 63, 31] Generated Node #2: [62, 63, 31] from Operation: 92-61=31 Current State: 65:[62, 63, 31], Operations: ['92-61=31'] Exploring Operation: 62/31=2, Resulting Numbers: [63, 2] Generated Node #3: [63, 2] from Operation: 62/31=2 Current State: 65:[63, 2], Operations: ['92-61=31', '62/31=2'] Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[61, 92, 62, 63], Operations: [] Exploring Operation: 92-61=31, Resulting Numbers: [62, 63, 31] Generated Node #0,0: 65:[62, 63, 31] Operation: 92-61=31 Moving to Node #0,0 Current State: 65:[62, 63, 31], Operations: ['92-61=31'] Exploring Operation: 62/31=2, Resulting Numbers: [63, 2] Generated Node #0,0,0: 65:[63, 2] Operation: 62/31=2 Moving to Node #0,0,0 Current State: 65:[63, 2], Operations: ['92-61=31', '62/31=2'] Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[61, 92, 62, 63], Operations: [] Exploring Operation: 92-61=31, Resulting Numbers: [62, 63, 31] Generated Node #0,0: 65:[62, 63, 31] Operation: 92-61=31 Moving to Node #0,0 Current State: 65:[62, 63, 31], Operations: ['92-61=31'] Exploring Operation: 62/31=2, Resulting Numbers: [63, 2] Generated Node #0,0,0: 65:[63, 2] Operation: 62/31=2 Moving to Node #0,0,0 Current State: 65:[63, 2], Operations: ['92-61=31', '62/31=2'] Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 49, 99, 91, 16 ]
41
[ "49+99=148", "91+16=107", "148-107=41" ]
Current State: 41:[49, 99, 91, 16], Operations: [] Exploring Operation: 49+99=148, Resulting Numbers: [91, 16, 148] Generated Node #2: [91, 16, 148] from Operation: 49+99=148 Current State: 41:[91, 16, 148], Operations: ['49+99=148'] Exploring Operation: 91+16=107, Resulting Numbers: [148, 107] Generated Node #3: [148, 107] from Operation: 91+16=107 Current State: 41:[148, 107], Operations: ['49+99=148', '91+16=107'] Exploring Operation: 148-107=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[49, 99, 91, 16], Operations: [] Exploring Operation: 99-91=8, Resulting Numbers: [49, 16, 8] Generated Node #0,0: 41:[49, 16, 8] Operation: 99-91=8 Exploring Operation: 99-49=50, Resulting Numbers: [91, 16, 50] Generated Node #0,1: 41:[91, 16, 50] Operation: 99-49=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[49, 16, 8], Operations: ['99-91=8'] Exploring Operation: 49-8=41, Resulting Numbers: [16, 41] Generated Node #0,0,0: 41:[16, 41] Operation: 49-8=41 Exploring Operation: 16+8=24, Resulting Numbers: [49, 24] Generated Node #0,0,1: 41:[49, 24] Operation: 16+8=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[16, 41], Operations: ['99-91=8', '49-8=41'] Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 16+41=57, Resulting Numbers: [57] 57,41 unequal: No Solution No 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: 41:[49, 24], Operations: ['99-91=8', '16+8=24'] Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,41 unequal: No Solution Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,41 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: 41:[91, 16, 50], Operations: ['99-49=50'] Exploring Operation: 91-50=41, Resulting Numbers: [16, 41] Generated Node #0,1,0: 41:[16, 41] Operation: 91-50=41 Exploring Operation: 91-16=75, Resulting Numbers: [50, 75] Generated Node #0,1,1: 41:[50, 75] Operation: 91-16=75 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[16, 41], Operations: ['99-49=50', '91-50=41'] Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 16+41=57, Resulting Numbers: [57] 57,41 unequal: No Solution No 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: 41:[50, 75], Operations: ['99-49=50', '91-16=75'] Exploring Operation: 50+75=125, Resulting Numbers: [125] 125,41 unequal: No Solution Exploring Operation: 75-50=25, Resulting Numbers: [25] 25,41 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
[ 15, 45, 38, 65 ]
57
[ "45-15=30", "65-38=27", "30+27=57" ]
Current State: 57:[15, 45, 38, 65], Operations: [] Exploring Operation: 45-15=30, Resulting Numbers: [38, 65, 30] Generated Node #2: [38, 65, 30] from Operation: 45-15=30 Current State: 57:[38, 65, 30], Operations: ['45-15=30'] Exploring Operation: 65-38=27, Resulting Numbers: [30, 27] Generated Node #3: [30, 27] from Operation: 65-38=27 Current State: 57:[30, 27], Operations: ['45-15=30', '65-38=27'] Exploring Operation: 30+27=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[15, 45, 38, 65], Operations: [] Exploring Operation: 65-45=20, Resulting Numbers: [15, 38, 20] Generated Node #0,0: 57:[15, 38, 20] Operation: 65-45=20 Exploring Operation: 15+38=53, Resulting Numbers: [45, 65, 53] Generated Node #0,1: 57:[45, 65, 53] Operation: 15+38=53 Exploring Operation: 45-38=7, Resulting Numbers: [15, 65, 7] Generated Node #0,2: 57:[15, 65, 7] Operation: 45-38=7 Exploring Operation: 38-15=23, Resulting Numbers: [45, 65, 23] Generated Node #0,3: 57:[45, 65, 23] Operation: 38-15=23 Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[15, 65, 7], Operations: ['45-38=7'] Exploring Operation: 15+7=22, Resulting Numbers: [65, 22] Generated Node #0,2,0: 57:[65, 22] Operation: 15+7=22 Exploring Operation: 15-7=8, Resulting Numbers: [65, 8] Generated Node #0,2,1: 57:[65, 8] Operation: 15-7=8 Exploring Operation: 65-7=58, Resulting Numbers: [15, 58] Generated Node #0,2,2: 57:[15, 58] Operation: 65-7=58 Exploring Operation: 65-15=50, Resulting Numbers: [7, 50] Generated Node #0,2,3: 57:[7, 50] Operation: 65-15=50 Moving to Node #0,2,2 Current State: 57:[15, 58], Operations: ['45-38=7', '65-7=58'] Exploring Operation: 15*58=870, Resulting Numbers: [870] 870,57 unequal: No Solution Exploring Operation: 15+58=73, Resulting Numbers: [73] 73,57 unequal: No Solution Exploring Operation: 58-15=43, Resulting Numbers: [43] 43,57 unequal: No Solution Moving to Node #0,2,3 Current State: 57:[7, 50], Operations: ['45-38=7', '65-15=50'] Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[15, 45, 38, 65], Operations: [] Exploring Operation: 45-38=7, Resulting Numbers: [15, 65, 7] Generated Node #0,2: 57:[15, 65, 7] Operation: 45-38=7 Moving to Node #0,2 Current State: 57:[15, 65, 7], Operations: ['45-38=7'] Exploring Operation: 65-15=50, Resulting Numbers: [7, 50] Generated Node #0,2,3: 57:[7, 50] Operation: 65-15=50 Moving to Node #0,2,3 Current State: 57:[7, 50], Operations: ['45-38=7', '65-15=50'] Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 18, 7, 70, 23 ]
76
[ "18*23=414", "7*70=490", "490-414=76" ]
Current State: 76:[18, 7, 70, 23], Operations: [] Exploring Operation: 18*23=414, Resulting Numbers: [7, 70, 414] Generated Node #2: [7, 70, 414] from Operation: 18*23=414 Current State: 76:[7, 70, 414], Operations: ['18*23=414'] Exploring Operation: 7*70=490, Resulting Numbers: [414, 490] Generated Node #3: [414, 490] from Operation: 7*70=490 Current State: 76:[414, 490], Operations: ['18*23=414', '7*70=490'] Exploring Operation: 490-414=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[18, 7, 70, 23], Operations: [] Exploring Operation: 23-7=16, Resulting Numbers: [18, 70, 16] Generated Node #0,0: 76:[18, 70, 16] Operation: 23-7=16 Exploring Operation: 7+70=77, Resulting Numbers: [18, 23, 77] Generated Node #0,1: 76:[18, 23, 77] Operation: 7+70=77 Exploring Operation: 23-18=5, Resulting Numbers: [7, 70, 5] Generated Node #0,2: 76:[7, 70, 5] Operation: 23-18=5 Exploring Operation: 70/7=10, Resulting Numbers: [18, 23, 10] Generated Node #0,3: 76:[18, 23, 10] Operation: 70/7=10 Exploring Operation: 18+23=41, Resulting Numbers: [7, 70, 41] Generated Node #0,4: 76:[7, 70, 41] Operation: 18+23=41 Moving to Node #0,1 Current State: 76:[18, 23, 77], Operations: ['7+70=77'] Exploring Operation: 18+23=41, Resulting Numbers: [77, 41] Generated Node #0,1,0: 76:[77, 41] Operation: 18+23=41 Exploring Operation: 77-23=54, Resulting Numbers: [18, 54] Generated Node #0,1,1: 76:[18, 54] Operation: 77-23=54 Exploring Operation: 77-18=59, Resulting Numbers: [23, 59] Generated Node #0,1,2: 76:[23, 59] Operation: 77-18=59 Exploring Operation: 18+77=95, Resulting Numbers: [23, 95] Generated Node #0,1,3: 76:[23, 95] Operation: 18+77=95 Exploring Operation: 23-18=5, Resulting Numbers: [77, 5] Generated Node #0,1,4: 76:[77, 5] Operation: 23-18=5 Moving to Node #0,2 Current State: 76:[7, 70, 5], Operations: ['23-18=5'] Exploring Operation: 7+70=77, Resulting Numbers: [5, 77] Generated Node #0,2,0: 76:[5, 77] Operation: 7+70=77 Exploring Operation: 70+5=75, Resulting Numbers: [7, 75] Generated Node #0,2,1: 76:[7, 75] Operation: 70+5=75 Exploring Operation: 70/5=14, Resulting Numbers: [7, 14] Generated Node #0,2,2: 76:[7, 14] Operation: 70/5=14 Exploring Operation: 70/7=10, Resulting Numbers: [5, 10] Generated Node #0,2,3: 76:[5, 10] Operation: 70/7=10 Exploring Operation: 7-5=2, Resulting Numbers: [70, 2] Generated Node #0,2,4: 76:[70, 2] Operation: 7-5=2 Moving to Node #0,0 Current State: 76:[18, 70, 16], Operations: ['23-7=16'] Exploring Operation: 18-16=2, Resulting Numbers: [70, 2] Generated Node #0,0,0: 76:[70, 2] Operation: 18-16=2 Exploring Operation: 18+70=88, Resulting Numbers: [16, 88] Generated Node #0,0,1: 76:[16, 88] Operation: 18+70=88 Exploring Operation: 18+16=34, Resulting Numbers: [70, 34] Generated Node #0,0,2: 76:[70, 34] Operation: 18+16=34 Exploring Operation: 70+16=86, Resulting Numbers: [18, 86] Generated Node #0,0,3: 76:[18, 86] Operation: 70+16=86 Exploring Operation: 70-18=52, Resulting Numbers: [16, 52] Generated Node #0,0,4: 76:[16, 52] Operation: 70-18=52 Moving to Node #0,3 Current State: 76:[18, 23, 10], Operations: ['70/7=10'] Exploring Operation: 23-10=13, Resulting Numbers: [18, 13] Generated Node #0,3,0: 76:[18, 13] Operation: 23-10=13 Exploring Operation: 23+10=33, Resulting Numbers: [18, 33] Generated Node #0,3,1: 76:[18, 33] Operation: 23+10=33 Exploring Operation: 23-18=5, Resulting Numbers: [10, 5] Generated Node #0,3,2: 76:[10, 5] Operation: 23-18=5 Exploring Operation: 18+23=41, Resulting Numbers: [10, 41] Generated Node #0,3,3: 76:[10, 41] Operation: 18+23=41 Exploring Operation: 18-10=8, Resulting Numbers: [23, 8] Generated Node #0,3,4: 76:[23, 8] Operation: 18-10=8 Moving to Node #0,4 Current State: 76:[7, 70, 41], Operations: ['18+23=41'] Exploring Operation: 70-7=63, Resulting Numbers: [41, 63] Generated Node #0,4,0: 76:[41, 63] Operation: 70-7=63 Exploring Operation: 41-7=34, Resulting Numbers: [70, 34] Generated Node #0,4,1: 76:[70, 34] Operation: 41-7=34 Exploring Operation: 7+70=77, Resulting Numbers: [41, 77] Generated Node #0,4,2: 76:[41, 77] Operation: 7+70=77 Exploring Operation: 70-41=29, Resulting Numbers: [7, 29] Generated Node #0,4,3: 76:[7, 29] Operation: 70-41=29 Exploring Operation: 70/7=10, Resulting Numbers: [41, 10] Generated Node #0,4,4: 76:[41, 10] Operation: 70/7=10 Moving to Node #0,1,4 Current State: 76:[77, 5], Operations: ['7+70=77', '23-18=5'] Exploring Operation: 77-5=72, Resulting Numbers: [72] 72,76 unequal: No Solution Exploring Operation: 77+5=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 77*5=385, Resulting Numbers: [385] 385,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[5, 77], Operations: ['23-18=5', '7+70=77'] Exploring Operation: 5*77=385, Resulting Numbers: [385] 385,76 unequal: No Solution Exploring Operation: 5+77=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 77-5=72, Resulting Numbers: [72] 72,76 unequal: No Solution Moving to Node #0,2,1 Current State: 76:[7, 75], Operations: ['23-18=5', '70+5=75'] Exploring Operation: 7+75=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 7*75=525, Resulting Numbers: [525] 525,76 unequal: No Solution Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[77, 41], Operations: ['7+70=77', '18+23=41'] Exploring Operation: 77*41=3157, Resulting Numbers: [3157] 3157,76 unequal: No Solution Exploring Operation: 77+41=118, Resulting Numbers: [118] 118,76 unequal: No Solution Exploring Operation: 77-41=36, Resulting Numbers: [36] 36,76 unequal: No Solution Moving to Node #0,4,2 Current State: 76:[41, 77], Operations: ['18+23=41', '7+70=77'] Exploring Operation: 77-41=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 41+77=118, Resulting Numbers: [118] 118,76 unequal: No Solution Exploring Operation: 41*77=3157, Resulting Numbers: [3157] 3157,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[70, 2], Operations: ['23-7=16', '18-16=2'] Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,76 unequal: No Solution Exploring Operation: 70*2=140, Resulting Numbers: [140] 140,76 unequal: No Solution Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,76 unequal: No Solution Moving to Node #0,2,4 Current State: 76:[70, 2], Operations: ['23-18=5', '7-5=2'] Exploring Operation: 70*2=140, Resulting Numbers: [140] 140,76 unequal: No Solution Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,76 unequal: No Solution Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,76 unequal: No Solution Moving to Node #0,3,1 Current State: 76:[18, 33], Operations: ['70/7=10', '23+10=33'] Exploring Operation: 18*33=594, Resulting Numbers: [594] 594,76 unequal: No Solution Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,76 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,76 unequal: No Solution Moving to Node #0,2,3 Current State: 76:[5, 10], Operations: ['23-18=5', '70/7=10'] Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,76 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,76 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[10, 5], Operations: ['70/7=10', '23-18=5'] Exploring Operation: 10*5=50, Resulting Numbers: [50] 50,76 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 10+5=15, Resulting Numbers: [15] 15,76 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[18, 13], Operations: ['70/7=10', '23-10=13'] Exploring Operation: 18*13=234, Resulting Numbers: [234] 234,76 unequal: No Solution Exploring Operation: 18-13=5, Resulting Numbers: [5] 5,76 unequal: No Solution Exploring Operation: 18+13=31, Resulting Numbers: [31] 31,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[7, 14], Operations: ['23-18=5', '70/5=14'] Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,76 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,76 unequal: No Solution Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,76 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,76 unequal: No Solution Moving to Node #0,3,4 Current State: 76:[23, 8], Operations: ['70/7=10', '18-10=8'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,76 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,76 unequal: No Solution Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,76 unequal: No Solution Moving to Node #0,4,4 Current State: 76:[41, 10], Operations: ['18+23=41', '70/7=10'] Exploring Operation: 41+10=51, Resulting Numbers: [51] 51,76 unequal: No Solution Exploring Operation: 41*10=410, Resulting Numbers: [410] 410,76 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[10, 41], Operations: ['70/7=10', '18+23=41'] Exploring Operation: 10*41=410, Resulting Numbers: [410] 410,76 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,76 unequal: No Solution Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[70, 34], Operations: ['23-7=16', '18+16=34'] Exploring Operation: 70*34=2380, Resulting Numbers: [2380] 2380,76 unequal: No Solution Exploring Operation: 70+34=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,76 unequal: No Solution Moving to Node #0,4,1 Current State: 76:[70, 34], Operations: ['18+23=41', '41-7=34'] Exploring Operation: 70+34=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 70*34=2380, Resulting Numbers: [2380] 2380,76 unequal: No Solution Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,76 unequal: No Solution Moving to Node #0,0,3 Current State: 76:[18, 86], Operations: ['23-7=16', '70+16=86'] Exploring Operation: 86-18=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 18*86=1548, Resulting Numbers: [1548] 1548,76 unequal: No Solution Exploring Operation: 18+86=104, Resulting Numbers: [104] 104,76 unequal: No Solution Moving to Node #0,4,3 Current State: 76:[7, 29], Operations: ['18+23=41', '70-41=29'] Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,76 unequal: No Solution Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[16, 88], Operations: ['23-7=16', '18+70=88'] Exploring Operation: 16*88=1408, Resulting Numbers: [1408] 1408,76 unequal: No Solution Exploring Operation: 88-16=72, Resulting Numbers: [72] 72,76 unequal: No Solution Exploring Operation: 16+88=104, Resulting Numbers: [104] 104,76 unequal: No Solution Moving to Node #0,4,0 Current State: 76:[41, 63], Operations: ['18+23=41', '70-7=63'] Exploring Operation: 41+63=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 41*63=2583, Resulting Numbers: [2583] 2583,76 unequal: No Solution Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[18, 54], Operations: ['7+70=77', '77-23=54'] Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 18*54=972, Resulting Numbers: [972] 972,76 unequal: No Solution Exploring Operation: 18+54=72, Resulting Numbers: [72] 72,76 unequal: No Solution Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,76 unequal: No Solution Moving to Node #0,0,4 Current State: 76:[16, 52], Operations: ['23-7=16', '70-18=52'] Exploring Operation: 52-16=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 16*52=832, Resulting Numbers: [832] 832,76 unequal: No Solution Exploring Operation: 16+52=68, Resulting Numbers: [68] 68,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[23, 59], Operations: ['7+70=77', '77-18=59'] Exploring Operation: 23+59=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 59-23=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 23*59=1357, Resulting Numbers: [1357] 1357,76 unequal: No Solution Moving to Node #0,1,3 Current State: 76:[23, 95], Operations: ['7+70=77', '18+77=95'] Exploring Operation: 23+95=118, Resulting Numbers: [118] 118,76 unequal: No Solution Exploring Operation: 95-23=72, Resulting Numbers: [72] 72,76 unequal: No Solution Exploring Operation: 23*95=2185, Resulting Numbers: [2185] 2185,76 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 5, 79, 60, 40 ]
55
[ "79-60=19", "5*19=95", "95-40=55" ]
Current State: 55:[5, 79, 60, 40], Operations: [] Exploring Operation: 79-60=19, Resulting Numbers: [5, 40, 19] Generated Node #2: [5, 40, 19] from Operation: 79-60=19 Current State: 55:[5, 40, 19], Operations: ['79-60=19'] Exploring Operation: 5*19=95, Resulting Numbers: [40, 95] Generated Node #3: [40, 95] from Operation: 5*19=95 Current State: 55:[40, 95], Operations: ['79-60=19', '5*19=95'] Exploring Operation: 95-40=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[5, 79, 60, 40], Operations: [] Exploring Operation: 60-40=20, Resulting Numbers: [5, 79, 20] Generated Node #0,0: 55:[5, 79, 20] Operation: 60-40=20 Exploring Operation: 40/5=8, Resulting Numbers: [79, 60, 8] Generated Node #0,1: 55:[79, 60, 8] Operation: 40/5=8 Exploring Operation: 79-40=39, Resulting Numbers: [5, 60, 39] Generated Node #0,2: 55:[5, 60, 39] Operation: 79-40=39 Exploring Operation: 79-60=19, Resulting Numbers: [5, 40, 19] Generated Node #0,3: 55:[5, 40, 19] Operation: 79-60=19 Exploring Operation: 79-5=74, Resulting Numbers: [60, 40, 74] Generated Node #0,4: 55:[60, 40, 74] Operation: 79-5=74 Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[5, 60, 39], Operations: ['79-40=39'] Exploring Operation: 5+60=65, Resulting Numbers: [39, 65] Generated Node #0,2,0: 55:[39, 65] Operation: 5+60=65 Exploring Operation: 60/5=12, Resulting Numbers: [39, 12] Generated Node #0,2,1: 55:[39, 12] Operation: 60/5=12 Exploring Operation: 60-5=55, Resulting Numbers: [39, 55] Generated Node #0,2,2: 55:[39, 55] Operation: 60-5=55 Exploring Operation: 60-39=21, Resulting Numbers: [5, 21] Generated Node #0,2,3: 55:[5, 21] Operation: 60-39=21 Exploring Operation: 5+39=44, Resulting Numbers: [60, 44] Generated Node #0,2,4: 55:[60, 44] Operation: 5+39=44 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 55:[5, 21], Operations: ['79-40=39', '60-39=21'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,55 unequal: No Solution Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,55 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:[39, 55], Operations: ['79-40=39', '60-5=55'] Exploring Operation: 39*55=2145, Resulting Numbers: [2145] 2145,55 unequal: No Solution Exploring Operation: 55-39=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 39+55=94, Resulting Numbers: [94] 94,55 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 #0,2,4 Current State: 55:[60, 44], Operations: ['79-40=39', '5+39=44'] Exploring Operation: 60*44=2640, Resulting Numbers: [2640] 2640,55 unequal: No Solution Exploring Operation: 60-44=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 60+44=104, Resulting Numbers: [104] 104,55 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 #0,2,1 Current State: 55:[39, 12], Operations: ['79-40=39', '60/5=12'] Exploring Operation: 39+12=51, Resulting Numbers: [51] 51,55 unequal: No Solution Exploring Operation: 39*12=468, Resulting Numbers: [468] 468,55 unequal: No Solution Exploring Operation: 39-12=27, Resulting Numbers: [27] 27,55 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:[39, 65], Operations: ['79-40=39', '5+60=65'] Exploring Operation: 39+65=104, Resulting Numbers: [104] 104,55 unequal: No Solution Exploring Operation: 39*65=2535, Resulting Numbers: [2535] 2535,55 unequal: No Solution Exploring Operation: 65-39=26, Resulting Numbers: [26] 26,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 55:[5, 40, 19], Operations: ['79-60=19'] Exploring Operation: 40+19=59, Resulting Numbers: [5, 59] Generated Node #0,3,0: 55:[5, 59] Operation: 40+19=59 Exploring Operation: 40/5=8, Resulting Numbers: [19, 8] Generated Node #0,3,1: 55:[19, 8] Operation: 40/5=8 Exploring Operation: 19-5=14, Resulting Numbers: [40, 14] Generated Node #0,3,2: 55:[40, 14] Operation: 19-5=14 Exploring Operation: 40-19=21, Resulting Numbers: [5, 21] Generated Node #0,3,3: 55:[5, 21] Operation: 40-19=21 Exploring Operation: 5+40=45, Resulting Numbers: [19, 45] Generated Node #0,3,4: 55:[19, 45] Operation: 5+40=45 Moving to Node #0,3,0 Current State: 55:[5, 59], Operations: ['79-60=19', '40+19=59'] Exploring Operation: 5+59=64, Resulting Numbers: [64] 64,55 unequal: No Solution Exploring Operation: 5*59=295, Resulting Numbers: [295] 295,55 unequal: No Solution Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,55 unequal: No Solution Moving to Node #0,3,3 Current State: 55:[5, 21], Operations: ['79-60=19', '40-19=21'] Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,55 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,55 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,55 unequal: No Solution Moving to Node #0,3,1 Current State: 55:[19, 8], Operations: ['79-60=19', '40/5=8'] Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,55 unequal: No Solution Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,55 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,55 unequal: No Solution Moving to Node #0,3,2 Current State: 55:[40, 14], Operations: ['79-60=19', '19-5=14'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,55 unequal: No Solution Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,55 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,55 unequal: No Solution Moving to Node #0,3,4 Current State: 55:[19, 45], Operations: ['79-60=19', '5+40=45'] Exploring Operation: 19*45=855, Resulting Numbers: [855] 855,55 unequal: No Solution Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,55 unequal: No Solution Exploring Operation: 19+45=64, Resulting Numbers: [64] 64,55 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:[79, 60, 8], Operations: ['40/5=8'] Exploring Operation: 79-8=71, Resulting Numbers: [60, 71] Generated Node #0,1,0: 55:[60, 71] Operation: 79-8=71 Exploring Operation: 60+8=68, Resulting Numbers: [79, 68] Generated Node #0,1,1: 55:[79, 68] Operation: 60+8=68 Exploring Operation: 60-8=52, Resulting Numbers: [79, 52] Generated Node #0,1,2: 55:[79, 52] Operation: 60-8=52 Exploring Operation: 79+8=87, Resulting Numbers: [60, 87] Generated Node #0,1,3: 55:[60, 87] Operation: 79+8=87 Exploring Operation: 79-60=19, Resulting Numbers: [8, 19] Generated Node #0,1,4: 55:[8, 19] Operation: 79-60=19 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 55:[8, 19], Operations: ['40/5=8', '79-60=19'] Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,55 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,55 unequal: No Solution Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[60, 71], Operations: ['40/5=8', '79-8=71'] Exploring Operation: 60+71=131, Resulting Numbers: [131] 131,55 unequal: No Solution Exploring Operation: 60*71=4260, Resulting Numbers: [4260] 4260,55 unequal: No Solution Exploring Operation: 71-60=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:[79, 52], Operations: ['40/5=8', '60-8=52'] Exploring Operation: 79*52=4108, Resulting Numbers: [4108] 4108,55 unequal: No Solution Exploring Operation: 79+52=131, Resulting Numbers: [131] 131,55 unequal: No Solution Exploring Operation: 79-52=27, Resulting Numbers: [27] 27,55 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:[79, 68], Operations: ['40/5=8', '60+8=68'] Exploring Operation: 79-68=11, Resulting Numbers: [11] 11,55 unequal: No Solution Exploring Operation: 79+68=147, Resulting Numbers: [147] 147,55 unequal: No Solution Exploring Operation: 79*68=5372, Resulting Numbers: [5372] 5372,55 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 #0,1,3 Current State: 55:[60, 87], Operations: ['40/5=8', '79+8=87'] Exploring Operation: 87-60=27, Resulting Numbers: [27] 27,55 unequal: No Solution Exploring Operation: 60+87=147, Resulting Numbers: [147] 147,55 unequal: No Solution Exploring Operation: 60*87=5220, Resulting Numbers: [5220] 5220,55 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 #0,0 Current State: 55:[5, 79, 20], Operations: ['60-40=20'] Exploring Operation: 79-20=59, Resulting Numbers: [5, 59] Generated Node #0,0,0: 55:[5, 59] Operation: 79-20=59 Exploring Operation: 5+79=84, Resulting Numbers: [20, 84] Generated Node #0,0,1: 55:[20, 84] Operation: 5+79=84 Exploring Operation: 20-5=15, Resulting Numbers: [79, 15] Generated Node #0,0,2: 55:[79, 15] Operation: 20-5=15 Exploring Operation: 79-5=74, Resulting Numbers: [20, 74] Generated Node #0,0,3: 55:[20, 74] Operation: 79-5=74 Exploring Operation: 20/5=4, Resulting Numbers: [79, 4] Generated Node #0,0,4: 55:[79, 4] Operation: 20/5=4 Moving to Node #0,0,0 Current State: 55:[5, 59], Operations: ['60-40=20', '79-20=59'] Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 5*59=295, Resulting Numbers: [295] 295,55 unequal: No Solution Exploring Operation: 5+59=64, Resulting Numbers: [64] 64,55 unequal: No Solution Moving to Node #0,0,4 Current State: 55:[79, 4], Operations: ['60-40=20', '20/5=4'] Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,55 unequal: No Solution Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,55 unequal: No Solution Exploring Operation: 79*4=316, Resulting Numbers: [316] 316,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[79, 15], Operations: ['60-40=20', '20-5=15'] Exploring Operation: 79-15=64, Resulting Numbers: [64] 64,55 unequal: No Solution Exploring Operation: 79+15=94, Resulting Numbers: [94] 94,55 unequal: No Solution Exploring Operation: 79*15=1185, Resulting Numbers: [1185] 1185,55 unequal: No Solution Moving to Node #0,0,3 Current State: 55:[20, 74], Operations: ['60-40=20', '79-5=74'] Exploring Operation: 74-20=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 20+74=94, Resulting Numbers: [94] 94,55 unequal: No Solution Exploring Operation: 20*74=1480, Resulting Numbers: [1480] 1480,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[20, 84], Operations: ['60-40=20', '5+79=84'] Exploring Operation: 20*84=1680, Resulting Numbers: [1680] 1680,55 unequal: No Solution Exploring Operation: 20+84=104, Resulting Numbers: [104] 104,55 unequal: No Solution Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 55:[60, 40, 74], Operations: ['79-5=74'] Exploring Operation: 40+74=114, Resulting Numbers: [60, 114] Generated Node #0,4,0: 55:[60, 114] Operation: 40+74=114 Exploring Operation: 74-60=14, Resulting Numbers: [40, 14] Generated Node #0,4,1: 55:[40, 14] Operation: 74-60=14 Exploring Operation: 60+40=100, Resulting Numbers: [74, 100] Generated Node #0,4,2: 55:[74, 100] Operation: 60+40=100 Exploring Operation: 60-40=20, Resulting Numbers: [74, 20] Generated Node #0,4,3: 55:[74, 20] Operation: 60-40=20 Exploring Operation: 74-40=34, Resulting Numbers: [60, 34] Generated Node #0,4,4: 55:[60, 34] Operation: 74-40=34 Moving to Node #0,4,1 Current State: 55:[40, 14], Operations: ['79-5=74', '74-60=14'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,55 unequal: No Solution Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,55 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,55 unequal: No Solution Moving to Node #0,4,4 Current State: 55:[60, 34], Operations: ['79-5=74', '74-40=34'] Exploring Operation: 60*34=2040, Resulting Numbers: [2040] 2040,55 unequal: No Solution Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,55 unequal: No Solution Exploring Operation: 60+34=94, Resulting Numbers: [94] 94,55 unequal: No Solution Moving to Node #0,4,3 Current State: 55:[74, 20], Operations: ['79-5=74', '60-40=20'] Exploring Operation: 74*20=1480, Resulting Numbers: [1480] 1480,55 unequal: No Solution Exploring Operation: 74-20=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 74+20=94, Resulting Numbers: [94] 94,55 unequal: No Solution Moving to Node #0,4,0 Current State: 55:[60, 114], Operations: ['79-5=74', '40+74=114'] Exploring Operation: 60+114=174, Resulting Numbers: [174] 174,55 unequal: No Solution Exploring Operation: 60*114=6840, Resulting Numbers: [6840] 6840,55 unequal: No Solution Exploring Operation: 114-60=54, Resulting Numbers: [54] 54,55 unequal: No Solution Moving to Node #0,4,2 Current State: 55:[74, 100], Operations: ['79-5=74', '60+40=100'] Exploring Operation: 100-74=26, Resulting Numbers: [26] 26,55 unequal: No Solution Exploring Operation: 74+100=174, Resulting Numbers: [174] 174,55 unequal: No Solution Exploring Operation: 74*100=7400, Resulting Numbers: [7400] 7400,55 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
[ 2, 92, 97, 13 ]
20
[ "92-2=90", "97+13=110", "110-90=20" ]
Current State: 20:[2, 92, 97, 13], Operations: [] Exploring Operation: 92-2=90, Resulting Numbers: [97, 13, 90] Generated Node #2: [97, 13, 90] from Operation: 92-2=90 Current State: 20:[97, 13, 90], Operations: ['92-2=90'] Exploring Operation: 97+13=110, Resulting Numbers: [90, 110] Generated Node #3: [90, 110] from Operation: 97+13=110 Current State: 20:[90, 110], Operations: ['92-2=90', '97+13=110'] Exploring Operation: 110-90=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[2, 92, 97, 13], Operations: [] Exploring Operation: 92-13=79, Resulting Numbers: [2, 97, 79] Generated Node #0,0: 20:[2, 97, 79] Operation: 92-13=79 Exploring Operation: 92/2=46, Resulting Numbers: [97, 13, 46] Generated Node #0,1: 20:[97, 13, 46] Operation: 92/2=46 Exploring Operation: 97-92=5, Resulting Numbers: [2, 13, 5] Generated Node #0,2: 20:[2, 13, 5] Operation: 97-92=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 20:[2, 13, 5], Operations: ['97-92=5'] Exploring Operation: 13-5=8, Resulting Numbers: [2, 8] Generated Node #0,2,0: 20:[2, 8] Operation: 13-5=8 Exploring Operation: 13-2=11, Resulting Numbers: [5, 11] Generated Node #0,2,1: 20:[5, 11] Operation: 13-2=11 Exploring Operation: 13+5=18, Resulting Numbers: [2, 18] Generated Node #0,2,2: 20:[2, 18] Operation: 13+5=18 Moving to Node #0,2,1 Current State: 20:[5, 11], Operations: ['97-92=5', '13-2=11'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,20 unequal: No Solution Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,20 unequal: No Solution Moving to Node #0,2,0 Current State: 20:[2, 8], Operations: ['97-92=5', '13-5=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,20 unequal: No Solution Moving to Node #0,2,2 Current State: 20:[2, 18], Operations: ['97-92=5', '13+5=18'] Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[2, 92, 97, 13], Operations: [] Exploring Operation: 97-92=5, Resulting Numbers: [2, 13, 5] Generated Node #0,2: 20:[2, 13, 5] Operation: 97-92=5 Moving to Node #0,2 Current State: 20:[2, 13, 5], Operations: ['97-92=5'] Exploring Operation: 13+5=18, Resulting Numbers: [2, 18] Generated Node #0,2,2: 20:[2, 18] Operation: 13+5=18 Moving to Node #0,2,2 Current State: 20:[2, 18], Operations: ['97-92=5', '13+5=18'] Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 78, 13, 13, 12 ]
31
[ "78/13=6", "13+12=25", "6+25=31" ]
Current State: 31:[78, 13, 13, 12], Operations: [] Exploring Operation: 78/13=6, Resulting Numbers: [12, 6] Generated Node #2: [12, 6] from Operation: 78/13=6 Current State: 31:[12, 6], Operations: ['78/13=6'] Exploring Operation: 13+12=25, Resulting Numbers: [6, 25] Generated Node #3: [6, 25] from Operation: 13+12=25 Current State: 31:[6, 25], Operations: ['78/13=6', '13+12=25'] Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[78, 13, 13, 12], Operations: [] Exploring Operation: 78/13=6, Resulting Numbers: [13, 12, 6] Generated Node #0,0: 31:[13, 12, 6] Operation: 78/13=6 Exploring Operation: 78/13=6, Resulting Numbers: [13, 12, 6] Generated Node #0,1: 31:[13, 12, 6] Operation: 78/13=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[13, 12, 6], Operations: ['78/13=6'] Exploring Operation: 13+6=19, Resulting Numbers: [12, 19] Generated Node #0,0,0: 31:[12, 19] Operation: 13+6=19 Exploring Operation: 13+12=25, Resulting Numbers: [6, 25] Generated Node #0,0,1: 31:[6, 25] Operation: 13+12=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[12, 19], Operations: ['78/13=6', '13+6=19'] Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[78, 13, 13, 12], Operations: [] Exploring Operation: 78/13=6, Resulting Numbers: [13, 12, 6] Generated Node #0,0: 31:[13, 12, 6] Operation: 78/13=6 Moving to Node #0,0 Current State: 31:[13, 12, 6], Operations: ['78/13=6'] Exploring Operation: 13+6=19, Resulting Numbers: [12, 19] Generated Node #0,0,0: 31:[12, 19] Operation: 13+6=19 Moving to Node #0,0,0 Current State: 31:[12, 19], Operations: ['78/13=6', '13+6=19'] Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 81, 49, 78, 5 ]
64
[ "81-78=3", "5*3=15", "49+15=64" ]
Current State: 64:[81, 49, 78, 5], Operations: [] Exploring Operation: 81-78=3, Resulting Numbers: [49, 5, 3] Generated Node #2: [49, 5, 3] from Operation: 81-78=3 Current State: 64:[49, 5, 3], Operations: ['81-78=3'] Exploring Operation: 5*3=15, Resulting Numbers: [49, 15] Generated Node #3: [49, 15] from Operation: 5*3=15 Current State: 64:[49, 15], Operations: ['81-78=3', '5*3=15'] Exploring Operation: 49+15=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[81, 49, 78, 5], Operations: [] Exploring Operation: 78-49=29, Resulting Numbers: [81, 5, 29] Generated Node #0,0: 64:[81, 5, 29] Operation: 78-49=29 Exploring Operation: 81-5=76, Resulting Numbers: [49, 78, 76] Generated Node #0,1: 64:[49, 78, 76] Operation: 81-5=76 Exploring Operation: 81-78=3, Resulting Numbers: [49, 5, 3] Generated Node #0,2: 64:[49, 5, 3] Operation: 81-78=3 Exploring Operation: 81-49=32, Resulting Numbers: [78, 5, 32] Generated Node #0,3: 64:[78, 5, 32] Operation: 81-49=32 Moving to Node #0,3 Current State: 64:[78, 5, 32], Operations: ['81-49=32'] Exploring Operation: 78-5=73, Resulting Numbers: [32, 73] Generated Node #0,3,0: 64:[32, 73] Operation: 78-5=73 Exploring Operation: 78+5=83, Resulting Numbers: [32, 83] Generated Node #0,3,1: 64:[32, 83] Operation: 78+5=83 Exploring Operation: 78-32=46, Resulting Numbers: [5, 46] Generated Node #0,3,2: 64:[5, 46] Operation: 78-32=46 Exploring Operation: 5+32=37, Resulting Numbers: [78, 37] Generated Node #0,3,3: 64:[78, 37] Operation: 5+32=37 Moving to Node #0,2 Current State: 64:[49, 5, 3], Operations: ['81-78=3'] Exploring Operation: 49+5=54, Resulting Numbers: [3, 54] Generated Node #0,2,0: 64:[3, 54] Operation: 49+5=54 Exploring Operation: 49+3=52, Resulting Numbers: [5, 52] Generated Node #0,2,1: 64:[5, 52] Operation: 49+3=52 Exploring Operation: 49-5=44, Resulting Numbers: [3, 44] Generated Node #0,2,2: 64:[3, 44] Operation: 49-5=44 Exploring Operation: 49-3=46, Resulting Numbers: [5, 46] Generated Node #0,2,3: 64:[5, 46] Operation: 49-3=46 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 64:[3, 54], Operations: ['81-78=3', '49+5=54'] Exploring Operation: 3*54=162, Resulting Numbers: [162] 162,64 unequal: No Solution Exploring Operation: 3+54=57, Resulting Numbers: [57] 57,64 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,64 unequal: No Solution Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 64:[5, 52], Operations: ['81-78=3', '49+3=52'] Exploring Operation: 5*52=260, Resulting Numbers: [260] 260,64 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,64 unequal: No Solution Exploring Operation: 5+52=57, Resulting Numbers: [57] 57,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 64:[3, 44], Operations: ['81-78=3', '49-5=44'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,64 unequal: No Solution Exploring Operation: 3*44=132, Resulting Numbers: [132] 132,64 unequal: No Solution Exploring Operation: 3+44=47, Resulting Numbers: [47] 47,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 64:[5, 46], Operations: ['81-78=3', '49-3=46'] Exploring Operation: 5*46=230, Resulting Numbers: [230] 230,64 unequal: No Solution Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,64 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,64 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: 64:[81, 5, 29], Operations: ['78-49=29'] Exploring Operation: 81-29=52, Resulting Numbers: [5, 52] Generated Node #0,0,0: 64:[5, 52] Operation: 81-29=52 Exploring Operation: 5+29=34, Resulting Numbers: [81, 34] Generated Node #0,0,1: 64:[81, 34] Operation: 5+29=34 Exploring Operation: 81-5=76, Resulting Numbers: [29, 76] Generated Node #0,0,2: 64:[29, 76] Operation: 81-5=76 Exploring Operation: 81+5=86, Resulting Numbers: [29, 86] Generated Node #0,0,3: 64:[29, 86] Operation: 81+5=86 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[5, 52], Operations: ['78-49=29', '81-29=52'] Exploring Operation: 5+52=57, Resulting Numbers: [57] 57,64 unequal: No Solution Exploring Operation: 5*52=260, Resulting Numbers: [260] 260,64 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 64:[29, 76], Operations: ['78-49=29', '81-5=76'] Exploring Operation: 76-29=47, Resulting Numbers: [47] 47,64 unequal: No Solution Exploring Operation: 29+76=105, Resulting Numbers: [105] 105,64 unequal: No Solution Exploring Operation: 29*76=2204, Resulting Numbers: [2204] 2204,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 64:[81, 34], Operations: ['78-49=29', '5+29=34'] Exploring Operation: 81*34=2754, Resulting Numbers: [2754] 2754,64 unequal: No Solution Exploring Operation: 81+34=115, Resulting Numbers: [115] 115,64 unequal: No Solution Exploring Operation: 81-34=47, Resulting Numbers: [47] 47,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 64:[29, 86], Operations: ['78-49=29', '81+5=86'] Exploring Operation: 29*86=2494, Resulting Numbers: [2494] 2494,64 unequal: No Solution Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,64 unequal: No Solution Exploring Operation: 29+86=115, Resulting Numbers: [115] 115,64 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: 64:[49, 78, 76], Operations: ['81-5=76'] Exploring Operation: 78-76=2, Resulting Numbers: [49, 2] Generated Node #0,1,0: 64:[49, 2] Operation: 78-76=2 Exploring Operation: 49+78=127, Resulting Numbers: [76, 127] Generated Node #0,1,1: 64:[76, 127] Operation: 49+78=127 Exploring Operation: 78-49=29, Resulting Numbers: [76, 29] Generated Node #0,1,2: 64:[76, 29] Operation: 78-49=29 Exploring Operation: 76-49=27, Resulting Numbers: [78, 27] Generated Node #0,1,3: 64:[78, 27] Operation: 76-49=27 Moving to Node #0,3,0 Current State: 64:[32, 73], Operations: ['81-49=32', '78-5=73'] Exploring Operation: 32+73=105, Resulting Numbers: [105] 105,64 unequal: No Solution Exploring Operation: 32*73=2336, Resulting Numbers: [2336] 2336,64 unequal: No Solution Exploring Operation: 73-32=41, Resulting Numbers: [41] 41,64 unequal: No Solution Moving to Node #0,1,2 Current State: 64:[76, 29], Operations: ['81-5=76', '78-49=29'] Exploring Operation: 76*29=2204, Resulting Numbers: [2204] 2204,64 unequal: No Solution Exploring Operation: 76-29=47, Resulting Numbers: [47] 47,64 unequal: No Solution Exploring Operation: 76+29=105, Resulting Numbers: [105] 105,64 unequal: No Solution Moving to Node #0,3,2 Current State: 64:[5, 46], Operations: ['81-49=32', '78-32=46'] Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,64 unequal: No Solution Exploring Operation: 5*46=230, Resulting Numbers: [230] 230,64 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,64 unequal: No Solution Moving to Node #0,1,0 Current State: 64:[49, 2], Operations: ['81-5=76', '78-76=2'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,64 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,64 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,64 unequal: No Solution Moving to Node #0,1,3 Current State: 64:[78, 27], Operations: ['81-5=76', '76-49=27'] Exploring Operation: 78+27=105, Resulting Numbers: [105] 105,64 unequal: No Solution Exploring Operation: 78-27=51, Resulting Numbers: [51] 51,64 unequal: No Solution Exploring Operation: 78*27=2106, Resulting Numbers: [2106] 2106,64 unequal: No Solution Moving to Node #0,3,3 Current State: 64:[78, 37], Operations: ['81-49=32', '5+32=37'] Exploring Operation: 78*37=2886, Resulting Numbers: [2886] 2886,64 unequal: No Solution Exploring Operation: 78-37=41, Resulting Numbers: [41] 41,64 unequal: No Solution Exploring Operation: 78+37=115, Resulting Numbers: [115] 115,64 unequal: No Solution Moving to Node #0,3,1 Current State: 64:[32, 83], Operations: ['81-49=32', '78+5=83'] Exploring Operation: 32*83=2656, Resulting Numbers: [2656] 2656,64 unequal: No Solution Exploring Operation: 32+83=115, Resulting Numbers: [115] 115,64 unequal: No Solution Exploring Operation: 83-32=51, Resulting Numbers: [51] 51,64 unequal: No Solution Moving to Node #0,1,1 Current State: 64:[76, 127], Operations: ['81-5=76', '49+78=127'] Exploring Operation: 76*127=9652, Resulting Numbers: [9652] 9652,64 unequal: No Solution Exploring Operation: 127-76=51, Resulting Numbers: [51] 51,64 unequal: No Solution Exploring Operation: 76+127=203, Resulting Numbers: [203] 203,64 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 63, 20, 30, 58 ]
50
[ "63-58=5", "30-20=10", "5*10=50" ]
Current State: 50:[63, 20, 30, 58], Operations: [] Exploring Operation: 63-58=5, Resulting Numbers: [20, 30, 5] Generated Node #2: [20, 30, 5] from Operation: 63-58=5 Current State: 50:[20, 30, 5], Operations: ['63-58=5'] Exploring Operation: 30-20=10, Resulting Numbers: [5, 10] Generated Node #3: [5, 10] from Operation: 30-20=10 Current State: 50:[5, 10], Operations: ['63-58=5', '30-20=10'] Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[63, 20, 30, 58], Operations: [] Exploring Operation: 63-30=33, Resulting Numbers: [20, 58, 33] Generated Node #0,0: 50:[20, 58, 33] Operation: 63-30=33 Exploring Operation: 63-20=43, Resulting Numbers: [30, 58, 43] Generated Node #0,1: 50:[30, 58, 43] Operation: 63-20=43 Exploring Operation: 63-58=5, Resulting Numbers: [20, 30, 5] Generated Node #0,2: 50:[20, 30, 5] Operation: 63-58=5 Exploring Operation: 20+30=50, Resulting Numbers: [63, 58, 50] Generated Node #0,3: 50:[63, 58, 50] Operation: 20+30=50 Moving to Node #0,2 Current State: 50:[20, 30, 5], Operations: ['63-58=5'] Exploring Operation: 20+5=25, Resulting Numbers: [30, 25] Generated Node #0,2,0: 50:[30, 25] Operation: 20+5=25 Exploring Operation: 30-5=25, Resulting Numbers: [20, 25] Generated Node #0,2,1: 50:[20, 25] Operation: 30-5=25 Exploring Operation: 30-20=10, Resulting Numbers: [5, 10] Generated Node #0,2,2: 50:[5, 10] Operation: 30-20=10 Exploring Operation: 20+30=50, Resulting Numbers: [5, 50] Generated Node #0,2,3: 50:[5, 50] Operation: 20+30=50 Moving to Node #0,1 Current State: 50:[30, 58, 43], Operations: ['63-20=43'] Exploring Operation: 30+43=73, Resulting Numbers: [58, 73] Generated Node #0,1,0: 50:[58, 73] Operation: 30+43=73 Exploring Operation: 58-30=28, Resulting Numbers: [43, 28] Generated Node #0,1,1: 50:[43, 28] Operation: 58-30=28 Exploring Operation: 43-30=13, Resulting Numbers: [58, 13] Generated Node #0,1,2: 50:[58, 13] Operation: 43-30=13 Exploring Operation: 58-43=15, Resulting Numbers: [30, 15] Generated Node #0,1,3: 50:[30, 15] Operation: 58-43=15 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 50:[43, 28], Operations: ['63-20=43', '58-30=28'] Exploring Operation: 43*28=1204, Resulting Numbers: [1204] 1204,50 unequal: No Solution Exploring Operation: 43+28=71, Resulting Numbers: [71] 71,50 unequal: No Solution Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 50:[30, 15], Operations: ['63-20=43', '58-43=15'] Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,50 unequal: No Solution Exploring Operation: 30+15=45, Resulting Numbers: [45] 45,50 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 30*15=450, Resulting Numbers: [450] 450,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 50:[58, 13], Operations: ['63-20=43', '43-30=13'] Exploring Operation: 58+13=71, Resulting Numbers: [71] 71,50 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,50 unequal: No Solution Exploring Operation: 58*13=754, Resulting Numbers: [754] 754,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[58, 73], Operations: ['63-20=43', '30+43=73'] Exploring Operation: 58+73=131, Resulting Numbers: [131] 131,50 unequal: No Solution Exploring Operation: 73-58=15, Resulting Numbers: [15] 15,50 unequal: No Solution Exploring Operation: 58*73=4234, Resulting Numbers: [4234] 4234,50 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: 50:[63, 58, 50], Operations: ['20+30=50'] Exploring Operation: 63-50=13, Resulting Numbers: [58, 13] Generated Node #0,3,0: 50:[58, 13] Operation: 63-50=13 Exploring Operation: 63+58=121, Resulting Numbers: [50, 121] Generated Node #0,3,1: 50:[50, 121] Operation: 63+58=121 Exploring Operation: 63-58=5, Resulting Numbers: [50, 5] Generated Node #0,3,2: 50:[50, 5] Operation: 63-58=5 Exploring Operation: 58-50=8, Resulting Numbers: [63, 8] Generated Node #0,3,3: 50:[63, 8] Operation: 58-50=8 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 50:[50, 5], Operations: ['20+30=50', '63-58=5'] Exploring Operation: 50*5=250, Resulting Numbers: [250] 250,50 unequal: No Solution Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,50 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 50+5=55, Resulting Numbers: [55] 55,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 50:[58, 13], Operations: ['20+30=50', '63-50=13'] Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,50 unequal: No Solution Exploring Operation: 58+13=71, Resulting Numbers: [71] 71,50 unequal: No Solution Exploring Operation: 58*13=754, Resulting Numbers: [754] 754,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 50:[63, 8], Operations: ['20+30=50', '58-50=8'] Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,50 unequal: No Solution Exploring Operation: 63+8=71, Resulting Numbers: [71] 71,50 unequal: No Solution Exploring Operation: 63*8=504, Resulting Numbers: [504] 504,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 50:[50, 121], Operations: ['20+30=50', '63+58=121'] Exploring Operation: 121-50=71, Resulting Numbers: [71] 71,50 unequal: No Solution Exploring Operation: 50+121=171, Resulting Numbers: [171] 171,50 unequal: No Solution Exploring Operation: 50*121=6050, Resulting Numbers: [6050] 6050,50 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: 50:[20, 58, 33], Operations: ['63-30=33'] Exploring Operation: 58-33=25, Resulting Numbers: [20, 25] Generated Node #0,0,0: 50:[20, 25] Operation: 58-33=25 Exploring Operation: 58-20=38, Resulting Numbers: [33, 38] Generated Node #0,0,1: 50:[33, 38] Operation: 58-20=38 Exploring Operation: 33-20=13, Resulting Numbers: [58, 13] Generated Node #0,0,2: 50:[58, 13] Operation: 33-20=13 Exploring Operation: 20+33=53, Resulting Numbers: [58, 53] Generated Node #0,0,3: 50:[58, 53] Operation: 20+33=53 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[20, 25], Operations: ['63-30=33', '58-33=25'] Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,50 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,50 unequal: No Solution Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 50:[58, 13], Operations: ['63-30=33', '33-20=13'] Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,50 unequal: No Solution Exploring Operation: 58+13=71, Resulting Numbers: [71] 71,50 unequal: No Solution Exploring Operation: 58*13=754, Resulting Numbers: [754] 754,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 50:[58, 53], Operations: ['63-30=33', '20+33=53'] Exploring Operation: 58+53=111, Resulting Numbers: [111] 111,50 unequal: No Solution Exploring Operation: 58-53=5, Resulting Numbers: [5] 5,50 unequal: No Solution Exploring Operation: 58*53=3074, Resulting Numbers: [3074] 3074,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 50:[33, 38], Operations: ['63-30=33', '58-20=38'] Exploring Operation: 38-33=5, Resulting Numbers: [5] 5,50 unequal: No Solution Exploring Operation: 33*38=1254, Resulting Numbers: [1254] 1254,50 unequal: No Solution Exploring Operation: 33+38=71, Resulting Numbers: [71] 71,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 50:[5, 10], Operations: ['63-58=5', '30-20=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,50 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[63, 20, 30, 58], Operations: [] Exploring Operation: 63-58=5, Resulting Numbers: [20, 30, 5] Generated Node #0,2: 50:[20, 30, 5] Operation: 63-58=5 Moving to Node #0,2 Current State: 50:[20, 30, 5], Operations: ['63-58=5'] Exploring Operation: 30-20=10, Resulting Numbers: [5, 10] Generated Node #0,2,2: 50:[5, 10] Operation: 30-20=10 Moving to Node #0,2,2 Current State: 50:[5, 10], Operations: ['63-58=5', '30-20=10'] Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
0.943576
hs_4
sum_heuristic
[ 9, 50, 48, 44 ]
31
[ "50-48=2", "44/2=22", "9+22=31" ]
Current State: 31:[9, 50, 48, 44], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [9, 44, 2] Generated Node #2: [9, 44, 2] from Operation: 50-48=2 Current State: 31:[9, 44, 2], Operations: ['50-48=2'] Exploring Operation: 44/2=22, Resulting Numbers: [9, 22] Generated Node #3: [9, 22] from Operation: 44/2=22 Current State: 31:[9, 22], Operations: ['50-48=2', '44/2=22'] Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[9, 50, 48, 44], Operations: [] Exploring Operation: 48-9=39, Resulting Numbers: [50, 44, 39] Generated Node #0,0: 31:[50, 44, 39] Operation: 48-9=39 Exploring Operation: 50-9=41, Resulting Numbers: [48, 44, 41] Generated Node #0,1: 31:[48, 44, 41] Operation: 50-9=41 Moving to Node #0,0 Current State: 31:[50, 44, 39], Operations: ['48-9=39'] Exploring Operation: 50-44=6, Resulting Numbers: [39, 6] Generated Node #0,0,0: 31:[39, 6] Operation: 50-44=6 Exploring Operation: 50-39=11, Resulting Numbers: [44, 11] Generated Node #0,0,1: 31:[44, 11] Operation: 50-39=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[39, 6], Operations: ['48-9=39', '50-44=6'] Exploring Operation: 39+6=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[44, 11], Operations: ['48-9=39', '50-39=11'] Exploring Operation: 44+11=55, Resulting Numbers: [55] 55,31 unequal: No Solution Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 31:[48, 44, 41], Operations: ['50-9=41'] Exploring Operation: 48-41=7, Resulting Numbers: [44, 7] Generated Node #0,1,0: 31:[44, 7] Operation: 48-41=7 Exploring Operation: 48-44=4, Resulting Numbers: [41, 4] Generated Node #0,1,1: 31:[41, 4] Operation: 48-44=4 Moving to Node #0,1,0 Current State: 31:[44, 7], Operations: ['50-9=41', '48-41=7'] Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,31 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[41, 4], Operations: ['50-9=41', '48-44=4'] Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,31 unequal: No Solution Exploring Operation: 41+4=45, Resulting Numbers: [45] 45,31 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 14, 3, 21, 20 ]
12
[ "14-3=11", "21-20=1", "11+1=12" ]
Current State: 12:[14, 3, 21, 20], Operations: [] Exploring Operation: 14-3=11, Resulting Numbers: [21, 20, 11] Generated Node #2: [21, 20, 11] from Operation: 14-3=11 Current State: 12:[21, 20, 11], Operations: ['14-3=11'] Exploring Operation: 21-20=1, Resulting Numbers: [11, 1] Generated Node #3: [11, 1] from Operation: 21-20=1 Current State: 12:[11, 1], Operations: ['14-3=11', '21-20=1'] Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[14, 3, 21, 20], Operations: [] Exploring Operation: 21-14=7, Resulting Numbers: [3, 20, 7] Generated Node #0,0: 12:[3, 20, 7] Operation: 21-14=7 Exploring Operation: 21-20=1, Resulting Numbers: [14, 3, 1] Generated Node #0,1: 12:[14, 3, 1] Operation: 21-20=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[14, 3, 1], Operations: ['21-20=1'] Exploring Operation: 14-1=13, Resulting Numbers: [3, 13] Generated Node #0,1,0: 12:[3, 13] Operation: 14-1=13 Exploring Operation: 14-3=11, Resulting Numbers: [1, 11] Generated Node #0,1,1: 12:[1, 11] Operation: 14-3=11 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 12:[3, 13], Operations: ['21-20=1', '14-1=13'] Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,12 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,12 unequal: No Solution No 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: 12:[1, 11], Operations: ['21-20=1', '14-3=11'] Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[14, 3, 21, 20], Operations: [] Exploring Operation: 21-20=1, Resulting Numbers: [14, 3, 1] Generated Node #0,1: 12:[14, 3, 1] Operation: 21-20=1 Moving to Node #0,1 Current State: 12:[14, 3, 1], Operations: ['21-20=1'] Exploring Operation: 14-3=11, Resulting Numbers: [1, 11] Generated Node #0,1,1: 12:[1, 11] Operation: 14-3=11 Moving to Node #0,1,1 Current State: 12:[1, 11], Operations: ['21-20=1', '14-3=11'] Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 7, 12, 25, 93 ]
48
[ "7+93=100", "12*100=1200", "1200/25=48" ]
Current State: 48:[7, 12, 25, 93], Operations: [] Exploring Operation: 7+93=100, Resulting Numbers: [12, 25, 100] Generated Node #2: [12, 25, 100] from Operation: 7+93=100 Current State: 48:[12, 25, 100], Operations: ['7+93=100'] Exploring Operation: 12*100=1200, Resulting Numbers: [25, 1200] Generated Node #3: [25, 1200] from Operation: 12*100=1200 Current State: 48:[25, 1200], Operations: ['7+93=100', '12*100=1200'] Exploring Operation: 1200/25=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[7, 12, 25, 93], Operations: [] Exploring Operation: 93-12=81, Resulting Numbers: [7, 25, 81] Generated Node #0,0: 48:[7, 25, 81] Operation: 93-12=81 Exploring Operation: 93-25=68, Resulting Numbers: [7, 12, 68] Generated Node #0,1: 48:[7, 12, 68] Operation: 93-25=68 Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[7, 12, 68], Operations: ['93-25=68'] Exploring Operation: 68-12=56, Resulting Numbers: [7, 56] Generated Node #0,1,0: 48:[7, 56] Operation: 68-12=56 Exploring Operation: 68-7=61, Resulting Numbers: [12, 61] Generated Node #0,1,1: 48:[12, 61] Operation: 68-7=61 Moving to Node #0,1,0 Current State: 48:[7, 56], Operations: ['93-25=68', '68-12=56'] Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[12, 61], Operations: ['93-25=68', '68-7=61'] Exploring Operation: 12+61=73, Resulting Numbers: [73] 73,48 unequal: No Solution Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[7, 25, 81], Operations: ['93-12=81'] Exploring Operation: 81-25=56, Resulting Numbers: [7, 56] Generated Node #0,0,0: 48:[7, 56] Operation: 81-25=56 Exploring Operation: 81-7=74, Resulting Numbers: [25, 74] Generated Node #0,0,1: 48:[25, 74] Operation: 81-7=74 Moving to Node #0,0,0 Current State: 48:[7, 56], Operations: ['93-12=81', '81-25=56'] Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[25, 74], Operations: ['93-12=81', '81-7=74'] Exploring Operation: 74-25=49, Resulting Numbers: [49] 49,48 unequal: No Solution Exploring Operation: 25+74=99, Resulting Numbers: [99] 99,48 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
[ 14, 4, 8, 90 ]
18
[ "14*8=112", "4+90=94", "112-94=18" ]
Current State: 18:[14, 4, 8, 90], Operations: [] Exploring Operation: 14*8=112, Resulting Numbers: [4, 90, 112] Generated Node #2: [4, 90, 112] from Operation: 14*8=112 Current State: 18:[4, 90, 112], Operations: ['14*8=112'] Exploring Operation: 4+90=94, Resulting Numbers: [112, 94] Generated Node #3: [112, 94] from Operation: 4+90=94 Current State: 18:[112, 94], Operations: ['14*8=112', '4+90=94'] Exploring Operation: 112-94=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[14, 4, 8, 90], Operations: [] Exploring Operation: 90-14=76, Resulting Numbers: [4, 8, 76] Generated Node #0,0: 18:[4, 8, 76] Operation: 90-14=76 Exploring Operation: 90-8=82, Resulting Numbers: [14, 4, 82] Generated Node #0,1: 18:[14, 4, 82] Operation: 90-8=82 Exploring Operation: 14+4=18, Resulting Numbers: [8, 90, 18] Generated Node #0,2: 18:[8, 90, 18] Operation: 14+4=18 Exploring Operation: 14-8=6, Resulting Numbers: [4, 90, 6] Generated Node #0,3: 18:[4, 90, 6] Operation: 14-8=6 Moving to Node #0,0 Current State: 18:[4, 8, 76], Operations: ['90-14=76'] Exploring Operation: 76-4=72, Resulting Numbers: [8, 72] Generated Node #0,0,0: 18:[8, 72] Operation: 76-4=72 Exploring Operation: 76/4=19, Resulting Numbers: [8, 19] Generated Node #0,0,1: 18:[8, 19] Operation: 76/4=19 Exploring Operation: 8/4=2, Resulting Numbers: [76, 2] Generated Node #0,0,2: 18:[76, 2] Operation: 8/4=2 Exploring Operation: 76-8=68, Resulting Numbers: [4, 68] Generated Node #0,0,3: 18:[4, 68] Operation: 76-8=68 Moving to Node #0,1 Current State: 18:[14, 4, 82], Operations: ['90-8=82'] Exploring Operation: 14+4=18, Resulting Numbers: [82, 18] Generated Node #0,1,0: 18:[82, 18] Operation: 14+4=18 Exploring Operation: 14-4=10, Resulting Numbers: [82, 10] Generated Node #0,1,1: 18:[82, 10] Operation: 14-4=10 Exploring Operation: 82-4=78, Resulting Numbers: [14, 78] Generated Node #0,1,2: 18:[14, 78] Operation: 82-4=78 Exploring Operation: 82-14=68, Resulting Numbers: [4, 68] Generated Node #0,1,3: 18:[4, 68] Operation: 82-14=68 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[4, 68], Operations: ['90-8=82', '82-14=68'] Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,18 unequal: No Solution Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[82, 18], Operations: ['90-8=82', '14+4=18'] Exploring Operation: 82*18=1476, Resulting Numbers: [1476] 1476,18 unequal: No Solution Exploring Operation: 82-18=64, Resulting Numbers: [64] 64,18 unequal: No Solution Exploring Operation: 82+18=100, Resulting Numbers: [100] 100,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[14, 78], Operations: ['90-8=82', '82-4=78'] Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,18 unequal: No Solution Exploring Operation: 14*78=1092, Resulting Numbers: [1092] 1092,18 unequal: No Solution Exploring Operation: 14+78=92, Resulting Numbers: [92] 92,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[82, 10], Operations: ['90-8=82', '14-4=10'] Exploring Operation: 82+10=92, Resulting Numbers: [92] 92,18 unequal: No Solution Exploring Operation: 82-10=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 82*10=820, Resulting Numbers: [820] 820,18 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: 18:[4, 90, 6], Operations: ['14-8=6'] Exploring Operation: 90/6=15, Resulting Numbers: [4, 15] Generated Node #0,3,0: 18:[4, 15] Operation: 90/6=15 Exploring Operation: 90-4=86, Resulting Numbers: [6, 86] Generated Node #0,3,1: 18:[6, 86] Operation: 90-4=86 Exploring Operation: 90-6=84, Resulting Numbers: [4, 84] Generated Node #0,3,2: 18:[4, 84] Operation: 90-6=84 Exploring Operation: 6-4=2, Resulting Numbers: [90, 2] Generated Node #0,3,3: 18:[90, 2] Operation: 6-4=2 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 18:[4, 15], Operations: ['14-8=6', '90/6=15'] Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 18:[4, 84], Operations: ['14-8=6', '90-6=84'] Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 4+84=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 4*84=336, Resulting Numbers: [336] 336,18 unequal: No Solution Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 18:[6, 86], Operations: ['14-8=6', '90-4=86'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,18 unequal: No Solution Exploring Operation: 6+86=92, Resulting Numbers: [92] 92,18 unequal: No Solution Exploring Operation: 6*86=516, Resulting Numbers: [516] 516,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 18:[90, 2], Operations: ['14-8=6', '6-4=2'] Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 90*2=180, Resulting Numbers: [180] 180,18 unequal: No Solution Exploring Operation: 90+2=92, Resulting Numbers: [92] 92,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 18:[8, 90, 18], Operations: ['14+4=18'] Exploring Operation: 90/18=5, Resulting Numbers: [8, 5] Generated Node #0,2,0: 18:[8, 5] Operation: 90/18=5 Exploring Operation: 18-8=10, Resulting Numbers: [90, 10] Generated Node #0,2,1: 18:[90, 10] Operation: 18-8=10 Exploring Operation: 90-18=72, Resulting Numbers: [8, 72] Generated Node #0,2,2: 18:[8, 72] Operation: 90-18=72 Exploring Operation: 90-8=82, Resulting Numbers: [18, 82] Generated Node #0,2,3: 18:[18, 82] Operation: 90-8=82 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[8, 5], Operations: ['14+4=18', '90/18=5'] Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,18 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[8, 72], Operations: ['14+4=18', '90-18=72'] Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,18 unequal: No Solution Exploring Operation: 8*72=576, Resulting Numbers: [576] 576,18 unequal: No Solution Exploring Operation: 8+72=80, Resulting Numbers: [80] 80,18 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 18:[18, 82], Operations: ['14+4=18', '90-8=82'] Exploring Operation: 18+82=100, Resulting Numbers: [100] 100,18 unequal: No Solution Exploring Operation: 18*82=1476, Resulting Numbers: [1476] 1476,18 unequal: No Solution Exploring Operation: 82-18=64, Resulting Numbers: [64] 64,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[90, 10], Operations: ['14+4=18', '18-8=10'] Exploring Operation: 90+10=100, Resulting Numbers: [100] 100,18 unequal: No Solution Exploring Operation: 90*10=900, Resulting Numbers: [900] 900,18 unequal: No Solution Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,18 unequal: No Solution Exploring Operation: 90/10=9, Resulting Numbers: [9] 9,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 18:[8, 19], Operations: ['90-14=76', '76/4=19'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,18 unequal: No Solution Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[4, 68], Operations: ['90-14=76', '76-8=68'] Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,18 unequal: No Solution Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,18 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[8, 72], Operations: ['90-14=76', '76-4=72'] Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,18 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 8*72=576, Resulting Numbers: [576] 576,18 unequal: No Solution Exploring Operation: 8+72=80, Resulting Numbers: [80] 80,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[76, 2], Operations: ['90-14=76', '8/4=2'] Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,18 unequal: No Solution Exploring Operation: 76+2=78, Resulting Numbers: [78] 78,18 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 76*2=152, Resulting Numbers: [152] 152,18 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 21, 61, 28, 60 ]
19
[ "28*60=1680", "1680/21=80", "80-61=19" ]
Current State: 19:[21, 61, 28, 60], Operations: [] Exploring Operation: 28*60=1680, Resulting Numbers: [21, 61, 1680] Generated Node #2: [21, 61, 1680] from Operation: 28*60=1680 Current State: 19:[21, 61, 1680], Operations: ['28*60=1680'] Exploring Operation: 1680/21=80, Resulting Numbers: [61, 80] Generated Node #3: [61, 80] from Operation: 1680/21=80 Current State: 19:[61, 80], Operations: ['28*60=1680', '1680/21=80'] Exploring Operation: 80-61=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[21, 61, 28, 60], Operations: [] Exploring Operation: 61-28=33, Resulting Numbers: [21, 60, 33] Generated Node #0,0: 19:[21, 60, 33] Operation: 61-28=33 Exploring Operation: 60-28=32, Resulting Numbers: [21, 61, 32] Generated Node #0,1: 19:[21, 61, 32] Operation: 60-28=32 Exploring Operation: 60-21=39, Resulting Numbers: [61, 28, 39] Generated Node #0,2: 19:[61, 28, 39] Operation: 60-21=39 Exploring Operation: 61-60=1, Resulting Numbers: [21, 28, 1] Generated Node #0,3: 19:[21, 28, 1] Operation: 61-60=1 Exploring Operation: 61-21=40, Resulting Numbers: [28, 60, 40] Generated Node #0,4: 19:[28, 60, 40] Operation: 61-21=40 Start Sub Search at level 1: Moving to Node #0,3 Current State: 19:[21, 28, 1], Operations: ['61-60=1'] Exploring Operation: 21-1=20, Resulting Numbers: [28, 20] Generated Node #0,3,0: 19:[28, 20] Operation: 21-1=20 Exploring Operation: 28*1=28, Resulting Numbers: [21, 28] Generated Node #0,3,1: 19:[21, 28] Operation: 28*1=28 Exploring Operation: 28-1=27, Resulting Numbers: [21, 27] Generated Node #0,3,2: 19:[21, 27] Operation: 28-1=27 Exploring Operation: 21*1=21, Resulting Numbers: [28, 21] Generated Node #0,3,3: 19:[28, 21] Operation: 21*1=21 Exploring Operation: 21/1=21, Resulting Numbers: [28, 21] Generated Node #0,3,4: 19:[28, 21] Operation: 21/1=21 Moving to Node #0,3,0 Current State: 19:[28, 20], Operations: ['61-60=1', '21-1=20'] Exploring Operation: 28*20=560, Resulting Numbers: [560] 560,19 unequal: No Solution Exploring Operation: 28+20=48, Resulting Numbers: [48] 48,19 unequal: No Solution Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,19 unequal: No Solution Moving to Node #0,3,2 Current State: 19:[21, 27], Operations: ['61-60=1', '28-1=27'] Exploring Operation: 21*27=567, Resulting Numbers: [567] 567,19 unequal: No Solution Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,19 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,19 unequal: No Solution Moving to Node #0,3,1 Current State: 19:[21, 28], Operations: ['61-60=1', '28*1=28'] Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,19 unequal: No Solution Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,19 unequal: No Solution Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,19 unequal: No Solution Moving to Node #0,3,3 Current State: 19:[28, 21], Operations: ['61-60=1', '21*1=21'] Exploring Operation: 28*21=588, Resulting Numbers: [588] 588,19 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,19 unequal: No Solution Exploring Operation: 28+21=49, Resulting Numbers: [49] 49,19 unequal: No Solution Moving to Node #0,3,4 Current State: 19:[28, 21], Operations: ['61-60=1', '21/1=21'] Exploring Operation: 28+21=49, Resulting Numbers: [49] 49,19 unequal: No Solution Exploring Operation: 28*21=588, Resulting Numbers: [588] 588,19 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,19 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 #0,0 Current State: 19:[21, 60, 33], Operations: ['61-28=33'] Exploring Operation: 60-33=27, Resulting Numbers: [21, 27] Generated Node #0,0,0: 19:[21, 27] Operation: 60-33=27 Exploring Operation: 33-21=12, Resulting Numbers: [60, 12] Generated Node #0,0,1: 19:[60, 12] Operation: 33-21=12 Exploring Operation: 21+33=54, Resulting Numbers: [60, 54] Generated Node #0,0,2: 19:[60, 54] Operation: 21+33=54 Exploring Operation: 21+60=81, Resulting Numbers: [33, 81] Generated Node #0,0,3: 19:[33, 81] Operation: 21+60=81 Exploring Operation: 60-21=39, Resulting Numbers: [33, 39] Generated Node #0,0,4: 19:[33, 39] Operation: 60-21=39 Moving to Node #0,0,0 Current State: 19:[21, 27], Operations: ['61-28=33', '60-33=27'] Exploring Operation: 21*27=567, Resulting Numbers: [567] 567,19 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,19 unequal: No Solution Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,19 unequal: No Solution Moving to Node #0,0,4 Current State: 19:[33, 39], Operations: ['61-28=33', '60-21=39'] Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,19 unequal: No Solution Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,19 unequal: No Solution Moving to Node #0,0,1 Current State: 19:[60, 12], Operations: ['61-28=33', '33-21=12'] Exploring Operation: 60*12=720, Resulting Numbers: [720] 720,19 unequal: No Solution Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,19 unequal: No Solution Exploring Operation: 60+12=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,19 unequal: No Solution Moving to Node #0,0,2 Current State: 19:[60, 54], Operations: ['61-28=33', '21+33=54'] Exploring Operation: 60*54=3240, Resulting Numbers: [3240] 3240,19 unequal: No Solution Exploring Operation: 60-54=6, Resulting Numbers: [6] 6,19 unequal: No Solution Exploring Operation: 60+54=114, Resulting Numbers: [114] 114,19 unequal: No Solution Moving to Node #0,0,3 Current State: 19:[33, 81], Operations: ['61-28=33', '21+60=81'] Exploring Operation: 33+81=114, Resulting Numbers: [114] 114,19 unequal: No Solution Exploring Operation: 81-33=48, Resulting Numbers: [48] 48,19 unequal: No Solution Exploring Operation: 33*81=2673, Resulting Numbers: [2673] 2673,19 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:[21, 61, 32], Operations: ['60-28=32'] Exploring Operation: 61-32=29, Resulting Numbers: [21, 29] Generated Node #0,1,0: 19:[21, 29] Operation: 61-32=29 Exploring Operation: 21+61=82, Resulting Numbers: [32, 82] Generated Node #0,1,1: 19:[32, 82] Operation: 21+61=82 Exploring Operation: 61-21=40, Resulting Numbers: [32, 40] Generated Node #0,1,2: 19:[32, 40] Operation: 61-21=40 Exploring Operation: 21+32=53, Resulting Numbers: [61, 53] Generated Node #0,1,3: 19:[61, 53] Operation: 21+32=53 Exploring Operation: 32-21=11, Resulting Numbers: [61, 11] Generated Node #0,1,4: 19:[61, 11] Operation: 32-21=11 Moving to Node #0,1,0 Current State: 19:[21, 29], Operations: ['60-28=32', '61-32=29'] Exploring Operation: 21*29=609, Resulting Numbers: [609] 609,19 unequal: No Solution Exploring Operation: 21+29=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,19 unequal: No Solution Moving to Node #0,1,2 Current State: 19:[32, 40], Operations: ['60-28=32', '61-21=40'] Exploring Operation: 32+40=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 32*40=1280, Resulting Numbers: [1280] 1280,19 unequal: No Solution Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,19 unequal: No Solution Moving to Node #0,1,4 Current State: 19:[61, 11], Operations: ['60-28=32', '32-21=11'] Exploring Operation: 61*11=671, Resulting Numbers: [671] 671,19 unequal: No Solution Exploring Operation: 61-11=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 61+11=72, Resulting Numbers: [72] 72,19 unequal: No Solution Moving to Node #0,1,1 Current State: 19:[32, 82], Operations: ['60-28=32', '21+61=82'] Exploring Operation: 32*82=2624, Resulting Numbers: [2624] 2624,19 unequal: No Solution Exploring Operation: 32+82=114, Resulting Numbers: [114] 114,19 unequal: No Solution Exploring Operation: 82-32=50, Resulting Numbers: [50] 50,19 unequal: No Solution Moving to Node #0,1,3 Current State: 19:[61, 53], Operations: ['60-28=32', '21+32=53'] Exploring Operation: 61*53=3233, Resulting Numbers: [3233] 3233,19 unequal: No Solution Exploring Operation: 61-53=8, Resulting Numbers: [8] 8,19 unequal: No Solution Exploring Operation: 61+53=114, Resulting Numbers: [114] 114,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[61, 28, 39], Operations: ['60-21=39'] Exploring Operation: 39-28=11, Resulting Numbers: [61, 11] Generated Node #0,2,0: 19:[61, 11] Operation: 39-28=11 Exploring Operation: 61+28=89, Resulting Numbers: [39, 89] Generated Node #0,2,1: 19:[39, 89] Operation: 61+28=89 Exploring Operation: 61-39=22, Resulting Numbers: [28, 22] Generated Node #0,2,2: 19:[28, 22] Operation: 61-39=22 Exploring Operation: 61+39=100, Resulting Numbers: [28, 100] Generated Node #0,2,3: 19:[28, 100] Operation: 61+39=100 Exploring Operation: 61-28=33, Resulting Numbers: [39, 33] Generated Node #0,2,4: 19:[39, 33] Operation: 61-28=33 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 19:[28, 22], Operations: ['60-21=39', '61-39=22'] Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,19 unequal: No Solution Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,19 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:[39, 33], Operations: ['60-21=39', '61-28=33'] Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,19 unequal: No Solution Exploring Operation: 39+33=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 39*33=1287, Resulting Numbers: [1287] 1287,19 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:[61, 11], Operations: ['60-21=39', '39-28=11'] Exploring Operation: 61-11=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 61+11=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 61*11=671, Resulting Numbers: [671] 671,19 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:[39, 89], Operations: ['60-21=39', '61+28=89'] Exploring Operation: 89-39=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 39*89=3471, Resulting Numbers: [3471] 3471,19 unequal: No Solution Exploring Operation: 39+89=128, Resulting Numbers: [128] 128,19 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 #0,2,3 Current State: 19:[28, 100], Operations: ['60-21=39', '61+39=100'] Exploring Operation: 100-28=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 28*100=2800, Resulting Numbers: [2800] 2800,19 unequal: No Solution Exploring Operation: 28+100=128, Resulting Numbers: [128] 128,19 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 #0,4 Current State: 19:[28, 60, 40], Operations: ['61-21=40'] Exploring Operation: 28+60=88, Resulting Numbers: [40, 88] Generated Node #0,4,0: 19:[40, 88] Operation: 28+60=88 Exploring Operation: 28+40=68, Resulting Numbers: [60, 68] Generated Node #0,4,1: 19:[60, 68] Operation: 28+40=68 Exploring Operation: 60-28=32, Resulting Numbers: [40, 32] Generated Node #0,4,2: 19:[40, 32] Operation: 60-28=32 Exploring Operation: 40-28=12, Resulting Numbers: [60, 12] Generated Node #0,4,3: 19:[60, 12] Operation: 40-28=12 Exploring Operation: 60-40=20, Resulting Numbers: [28, 20] Generated Node #0,4,4: 19:[28, 20] Operation: 60-40=20 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 19:[28, 20], Operations: ['61-21=40', '60-40=20'] Exploring Operation: 28+20=48, Resulting Numbers: [48] 48,19 unequal: No Solution Exploring Operation: 28*20=560, Resulting Numbers: [560] 560,19 unequal: No Solution Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,19 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 #0,4,2 Current State: 19:[40, 32], Operations: ['61-21=40', '60-28=32'] Exploring Operation: 40*32=1280, Resulting Numbers: [1280] 1280,19 unequal: No Solution Exploring Operation: 40+32=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,19 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 #0,4,3 Current State: 19:[60, 12], Operations: ['61-21=40', '40-28=12'] Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,19 unequal: No Solution Exploring Operation: 60*12=720, Resulting Numbers: [720] 720,19 unequal: No Solution Exploring Operation: 60+12=72, Resulting Numbers: [72] 72,19 unequal: No Solution Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,19 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 #0,4,0 Current State: 19:[40, 88], Operations: ['61-21=40', '28+60=88'] Exploring Operation: 40+88=128, Resulting Numbers: [128] 128,19 unequal: No Solution Exploring Operation: 40*88=3520, Resulting Numbers: [3520] 3520,19 unequal: No Solution Exploring Operation: 88-40=48, Resulting Numbers: [48] 48,19 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 #0,4,1 Current State: 19:[60, 68], Operations: ['61-21=40', '28+40=68'] Exploring Operation: 68-60=8, Resulting Numbers: [8] 8,19 unequal: No Solution Exploring Operation: 60*68=4080, Resulting Numbers: [4080] 4080,19 unequal: No Solution Exploring Operation: 60+68=128, Resulting Numbers: [128] 128,19 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 No solution found.
0
hs_5
mult_heuristic
[ 94, 29, 36, 1 ]
88
[ "94+29=123", "36-1=35", "123-35=88" ]
Current State: 88:[94, 29, 36, 1], Operations: [] Exploring Operation: 94+29=123, Resulting Numbers: [36, 1, 123] Generated Node #2: [36, 1, 123] from Operation: 94+29=123 Current State: 88:[36, 1, 123], Operations: ['94+29=123'] Exploring Operation: 36-1=35, Resulting Numbers: [123, 35] Generated Node #3: [123, 35] from Operation: 36-1=35 Current State: 88:[123, 35], Operations: ['94+29=123', '36-1=35'] Exploring Operation: 123-35=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[94, 29, 36, 1], Operations: [] Exploring Operation: 94*1=94, Resulting Numbers: [29, 36, 94] Generated Node #0,0: 88:[29, 36, 94] Operation: 94*1=94 Exploring Operation: 36-29=7, Resulting Numbers: [94, 1, 7] Generated Node #0,1: 88:[94, 1, 7] Operation: 36-29=7 Exploring Operation: 29-1=28, Resulting Numbers: [94, 36, 28] Generated Node #0,2: 88:[94, 36, 28] Operation: 29-1=28 Exploring Operation: 94-1=93, Resulting Numbers: [29, 36, 93] Generated Node #0,3: 88:[29, 36, 93] Operation: 94-1=93 Exploring Operation: 36+1=37, Resulting Numbers: [94, 29, 37] Generated Node #0,4: 88:[94, 29, 37] Operation: 36+1=37 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[94, 1, 7], Operations: ['36-29=7'] Exploring Operation: 94-1=93, Resulting Numbers: [7, 93] Generated Node #0,1,0: 88:[7, 93] Operation: 94-1=93 Exploring Operation: 94*1=94, Resulting Numbers: [7, 94] Generated Node #0,1,1: 88:[7, 94] Operation: 94*1=94 Exploring Operation: 94/1=94, Resulting Numbers: [7, 94] Generated Node #0,1,2: 88:[7, 94] Operation: 94/1=94 Exploring Operation: 94-7=87, Resulting Numbers: [1, 87] Generated Node #0,1,3: 88:[1, 87] Operation: 94-7=87 Exploring Operation: 1+7=8, Resulting Numbers: [94, 8] Generated Node #0,1,4: 88:[94, 8] Operation: 1+7=8 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 88:[1, 87], Operations: ['36-29=7', '94-7=87'] Exploring Operation: 1*87=87, Resulting Numbers: [87] 87,88 unequal: No Solution Exploring Operation: 1+87=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[94, 29, 36, 1], Operations: [] Exploring Operation: 36-29=7, Resulting Numbers: [94, 1, 7] Generated Node #0,1: 88:[94, 1, 7] Operation: 36-29=7 Moving to Node #0,1 Current State: 88:[94, 1, 7], Operations: ['36-29=7'] Exploring Operation: 94-7=87, Resulting Numbers: [1, 87] Generated Node #0,1,3: 88:[1, 87] Operation: 94-7=87 Moving to Node #0,1,3 Current State: 88:[1, 87], Operations: ['36-29=7', '94-7=87'] Exploring Operation: 1+87=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 10, 76, 25, 12 ]
73
[ "10+76=86", "25-12=13", "86-13=73" ]
Current State: 73:[10, 76, 25, 12], Operations: [] Exploring Operation: 10+76=86, Resulting Numbers: [25, 12, 86] Generated Node #2: [25, 12, 86] from Operation: 10+76=86 Current State: 73:[25, 12, 86], Operations: ['10+76=86'] Exploring Operation: 25-12=13, Resulting Numbers: [86, 13] Generated Node #3: [86, 13] from Operation: 25-12=13 Current State: 73:[86, 13], Operations: ['10+76=86', '25-12=13'] Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[10, 76, 25, 12], Operations: [] Exploring Operation: 10+12=22, Resulting Numbers: [76, 25, 22] Generated Node #0,0: 73:[76, 25, 22] Operation: 10+12=22 Exploring Operation: 25+12=37, Resulting Numbers: [10, 76, 37] Generated Node #0,1: 73:[10, 76, 37] Operation: 25+12=37 Exploring Operation: 10+25=35, Resulting Numbers: [76, 12, 35] Generated Node #0,2: 73:[76, 12, 35] Operation: 10+25=35 Exploring Operation: 10*12=120, Resulting Numbers: [76, 25, 120] Generated Node #0,3: 73:[76, 25, 120] Operation: 10*12=120 Exploring Operation: 76-10=66, Resulting Numbers: [25, 12, 66] Generated Node #0,4: 73:[25, 12, 66] Operation: 76-10=66 Moving to Node #0,3 Current State: 73:[76, 25, 120], Operations: ['10*12=120'] Exploring Operation: 120-76=44, Resulting Numbers: [25, 44] Generated Node #0,3,0: 73:[25, 44] Operation: 120-76=44 Exploring Operation: 76-25=51, Resulting Numbers: [120, 51] Generated Node #0,3,1: 73:[120, 51] Operation: 76-25=51 Exploring Operation: 25+120=145, Resulting Numbers: [76, 145] Generated Node #0,3,2: 73:[76, 145] Operation: 25+120=145 Exploring Operation: 76+25=101, Resulting Numbers: [120, 101] Generated Node #0,3,3: 73:[120, 101] Operation: 76+25=101 Exploring Operation: 120-25=95, Resulting Numbers: [76, 95] Generated Node #0,3,4: 73:[76, 95] Operation: 120-25=95 Moving to Node #0,1 Current State: 73:[10, 76, 37], Operations: ['25+12=37'] Exploring Operation: 10+37=47, Resulting Numbers: [76, 47] Generated Node #0,1,0: 73:[76, 47] Operation: 10+37=47 Exploring Operation: 76-10=66, Resulting Numbers: [37, 66] Generated Node #0,1,1: 73:[37, 66] Operation: 76-10=66 Exploring Operation: 10+76=86, Resulting Numbers: [37, 86] Generated Node #0,1,2: 73:[37, 86] Operation: 10+76=86 Exploring Operation: 37-10=27, Resulting Numbers: [76, 27] Generated Node #0,1,3: 73:[76, 27] Operation: 37-10=27 Exploring Operation: 76-37=39, Resulting Numbers: [10, 39] Generated Node #0,1,4: 73:[10, 39] Operation: 76-37=39 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[76, 47], Operations: ['25+12=37', '10+37=47'] Exploring Operation: 76-47=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 76*47=3572, Resulting Numbers: [3572] 3572,73 unequal: No Solution Exploring Operation: 76+47=123, Resulting Numbers: [123] 123,73 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:[37, 66], Operations: ['25+12=37', '76-10=66'] Exploring Operation: 37+66=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 66-37=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 37*66=2442, Resulting Numbers: [2442] 2442,73 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 #0,1,2 Current State: 73:[37, 86], Operations: ['25+12=37', '10+76=86'] Exploring Operation: 37*86=3182, Resulting Numbers: [3182] 3182,73 unequal: No Solution Exploring Operation: 86-37=49, Resulting Numbers: [49] 49,73 unequal: No Solution Exploring Operation: 37+86=123, Resulting Numbers: [123] 123,73 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 #0,1,3 Current State: 73:[76, 27], Operations: ['25+12=37', '37-10=27'] Exploring Operation: 76*27=2052, Resulting Numbers: [2052] 2052,73 unequal: No Solution Exploring Operation: 76-27=49, Resulting Numbers: [49] 49,73 unequal: No Solution Exploring Operation: 76+27=103, Resulting Numbers: [103] 103,73 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 #0,1,4 Current State: 73:[10, 39], Operations: ['25+12=37', '76-37=39'] Exploring Operation: 10*39=390, Resulting Numbers: [390] 390,73 unequal: No Solution Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 10+39=49, Resulting Numbers: [49] 49,73 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:[76, 25, 22], Operations: ['10+12=22'] Exploring Operation: 25+22=47, Resulting Numbers: [76, 47] Generated Node #0,0,0: 73:[76, 47] Operation: 25+22=47 Exploring Operation: 76+22=98, Resulting Numbers: [25, 98] Generated Node #0,0,1: 73:[25, 98] Operation: 76+22=98 Exploring Operation: 76-25=51, Resulting Numbers: [22, 51] Generated Node #0,0,2: 73:[22, 51] Operation: 76-25=51 Exploring Operation: 76-22=54, Resulting Numbers: [25, 54] Generated Node #0,0,3: 73:[25, 54] Operation: 76-22=54 Exploring Operation: 25-22=3, Resulting Numbers: [76, 3] Generated Node #0,0,4: 73:[76, 3] Operation: 25-22=3 Moving to Node #0,2 Current State: 73:[76, 12, 35], Operations: ['10+25=35'] Exploring Operation: 76-12=64, Resulting Numbers: [35, 64] Generated Node #0,2,0: 73:[35, 64] Operation: 76-12=64 Exploring Operation: 35-12=23, Resulting Numbers: [76, 23] Generated Node #0,2,1: 73:[76, 23] Operation: 35-12=23 Exploring Operation: 12+35=47, Resulting Numbers: [76, 47] Generated Node #0,2,2: 73:[76, 47] Operation: 12+35=47 Exploring Operation: 76+12=88, Resulting Numbers: [35, 88] Generated Node #0,2,3: 73:[35, 88] Operation: 76+12=88 Exploring Operation: 76-35=41, Resulting Numbers: [12, 41] Generated Node #0,2,4: 73:[12, 41] Operation: 76-35=41 Moving to Node #0,4 Current State: 73:[25, 12, 66], Operations: ['76-10=66'] Exploring Operation: 25+12=37, Resulting Numbers: [66, 37] Generated Node #0,4,0: 73:[66, 37] Operation: 25+12=37 Exploring Operation: 12+66=78, Resulting Numbers: [25, 78] Generated Node #0,4,1: 73:[25, 78] Operation: 12+66=78 Exploring Operation: 25-12=13, Resulting Numbers: [66, 13] Generated Node #0,4,2: 73:[66, 13] Operation: 25-12=13 Exploring Operation: 25+66=91, Resulting Numbers: [12, 91] Generated Node #0,4,3: 73:[12, 91] Operation: 25+66=91 Exploring Operation: 66-12=54, Resulting Numbers: [25, 54] Generated Node #0,4,4: 73:[25, 54] Operation: 66-12=54 Moving to Node #0,3,4 Current State: 73:[76, 95], Operations: ['10*12=120', '120-25=95'] Exploring Operation: 76*95=7220, Resulting Numbers: [7220] 7220,73 unequal: No Solution Exploring Operation: 95-76=19, Resulting Numbers: [19] 19,73 unequal: No Solution Exploring Operation: 76+95=171, Resulting Numbers: [171] 171,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[76, 47], Operations: ['10+12=22', '25+22=47'] Exploring Operation: 76-47=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 76+47=123, Resulting Numbers: [123] 123,73 unequal: No Solution Exploring Operation: 76*47=3572, Resulting Numbers: [3572] 3572,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[76, 47], Operations: ['10+25=35', '12+35=47'] Exploring Operation: 76+47=123, Resulting Numbers: [123] 123,73 unequal: No Solution Exploring Operation: 76*47=3572, Resulting Numbers: [3572] 3572,73 unequal: No Solution Exploring Operation: 76-47=29, Resulting Numbers: [29] 29,73 unequal: No Solution Moving to Node #0,4,0 Current State: 73:[66, 37], Operations: ['76-10=66', '25+12=37'] Exploring Operation: 66+37=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 66-37=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 66*37=2442, Resulting Numbers: [2442] 2442,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[35, 64], Operations: ['10+25=35', '76-12=64'] Exploring Operation: 35*64=2240, Resulting Numbers: [2240] 2240,73 unequal: No Solution Exploring Operation: 64-35=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 35+64=99, Resulting Numbers: [99] 99,73 unequal: No Solution Moving to Node #0,2,3 Current State: 73:[35, 88], Operations: ['10+25=35', '76+12=88'] Exploring Operation: 88-35=53, Resulting Numbers: [53] 53,73 unequal: No Solution Exploring Operation: 35+88=123, Resulting Numbers: [123] 123,73 unequal: No Solution Exploring Operation: 35*88=3080, Resulting Numbers: [3080] 3080,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[76, 23], Operations: ['10+25=35', '35-12=23'] Exploring Operation: 76+23=99, Resulting Numbers: [99] 99,73 unequal: No Solution Exploring Operation: 76*23=1748, Resulting Numbers: [1748] 1748,73 unequal: No Solution Exploring Operation: 76-23=53, Resulting Numbers: [53] 53,73 unequal: No Solution Moving to Node #0,4,1 Current State: 73:[25, 78], Operations: ['76-10=66', '12+66=78'] Exploring Operation: 25+78=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 78-25=53, Resulting Numbers: [53] 53,73 unequal: No Solution Exploring Operation: 25*78=1950, Resulting Numbers: [1950] 1950,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[25, 54], Operations: ['10+12=22', '76-22=54'] Exploring Operation: 25*54=1350, Resulting Numbers: [1350] 1350,73 unequal: No Solution Exploring Operation: 25+54=79, Resulting Numbers: [79] 79,73 unequal: No Solution Exploring Operation: 54-25=29, Resulting Numbers: [29] 29,73 unequal: No Solution Moving to Node #0,4,2 Current State: 73:[66, 13], Operations: ['76-10=66', '25-12=13'] Exploring Operation: 66*13=858, Resulting Numbers: [858] 858,73 unequal: No Solution Exploring Operation: 66+13=79, Resulting Numbers: [79] 79,73 unequal: No Solution Exploring Operation: 66-13=53, Resulting Numbers: [53] 53,73 unequal: No Solution Moving to Node #0,4,4 Current State: 73:[25, 54], Operations: ['76-10=66', '66-12=54'] Exploring Operation: 54-25=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 25+54=79, Resulting Numbers: [79] 79,73 unequal: No Solution Exploring Operation: 25*54=1350, Resulting Numbers: [1350] 1350,73 unequal: No Solution Moving to Node #0,3,1 Current State: 73:[120, 51], Operations: ['10*12=120', '76-25=51'] Exploring Operation: 120-51=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 120*51=6120, Resulting Numbers: [6120] 6120,73 unequal: No Solution Exploring Operation: 120+51=171, Resulting Numbers: [171] 171,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[25, 98], Operations: ['10+12=22', '76+22=98'] Exploring Operation: 98-25=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[10, 76, 25, 12], Operations: [] Exploring Operation: 10+12=22, Resulting Numbers: [76, 25, 22] Generated Node #0,0: 73:[76, 25, 22] Operation: 10+12=22 Moving to Node #0,0 Current State: 73:[76, 25, 22], Operations: ['10+12=22'] Exploring Operation: 76+22=98, Resulting Numbers: [25, 98] Generated Node #0,0,1: 73:[25, 98] Operation: 76+22=98 Moving to Node #0,0,1 Current State: 73:[25, 98], Operations: ['10+12=22', '76+22=98'] Exploring Operation: 98-25=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
0.925347
hs_5
mult_heuristic
[ 46, 81, 91, 5 ]
13
[ "81-46=35", "91*5=455", "455/35=13" ]
Current State: 13:[46, 81, 91, 5], Operations: [] Exploring Operation: 81-46=35, Resulting Numbers: [91, 5, 35] Generated Node #2: [91, 5, 35] from Operation: 81-46=35 Current State: 13:[91, 5, 35], Operations: ['81-46=35'] Exploring Operation: 91*5=455, Resulting Numbers: [35, 455] Generated Node #3: [35, 455] from Operation: 91*5=455 Current State: 13:[35, 455], Operations: ['81-46=35', '91*5=455'] Exploring Operation: 455/35=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[46, 81, 91, 5], Operations: [] Exploring Operation: 91-81=10, Resulting Numbers: [46, 5, 10] Generated Node #0,0: 13:[46, 5, 10] Operation: 91-81=10 Exploring Operation: 81-46=35, Resulting Numbers: [91, 5, 35] Generated Node #0,1: 13:[91, 5, 35] Operation: 81-46=35 Exploring Operation: 91-46=45, Resulting Numbers: [81, 5, 45] Generated Node #0,2: 13:[81, 5, 45] Operation: 91-46=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[46, 5, 10], Operations: ['91-81=10'] Exploring Operation: 46-10=36, Resulting Numbers: [5, 36] Generated Node #0,0,0: 13:[5, 36] Operation: 46-10=36 Exploring Operation: 46-5=41, Resulting Numbers: [10, 41] Generated Node #0,0,1: 13:[10, 41] Operation: 46-5=41 Exploring Operation: 5+10=15, Resulting Numbers: [46, 15] Generated Node #0,0,2: 13:[46, 15] Operation: 5+10=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[5, 36], Operations: ['91-81=10', '46-10=36'] Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,13 unequal: No Solution Exploring Operation: 5*36=180, Resulting Numbers: [180] 180,13 unequal: No Solution Exploring Operation: 5+36=41, Resulting Numbers: [41] 41,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 13:[10, 41], Operations: ['91-81=10', '46-5=41'] Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,13 unequal: No Solution Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,13 unequal: No Solution Exploring Operation: 10*41=410, Resulting Numbers: [410] 410,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 13:[46, 15], Operations: ['91-81=10', '5+10=15'] Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,13 unequal: No Solution Exploring Operation: 46+15=61, Resulting Numbers: [61] 61,13 unequal: No Solution Exploring Operation: 46*15=690, Resulting Numbers: [690] 690,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[91, 5, 35], Operations: ['81-46=35'] Exploring Operation: 91-35=56, Resulting Numbers: [5, 56] Generated Node #0,1,0: 13:[5, 56] Operation: 91-35=56 Exploring Operation: 91-5=86, Resulting Numbers: [35, 86] Generated Node #0,1,1: 13:[35, 86] Operation: 91-5=86 Exploring Operation: 35/5=7, Resulting Numbers: [91, 7] Generated Node #0,1,2: 13:[91, 7] Operation: 35/5=7 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 13:[5, 56], Operations: ['81-46=35', '91-35=56'] Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,13 unequal: No Solution Exploring Operation: 5*56=280, Resulting Numbers: [280] 280,13 unequal: No Solution Exploring Operation: 5+56=61, Resulting Numbers: [61] 61,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 13:[91, 7], Operations: ['81-46=35', '35/5=7'] Exploring Operation: 91+7=98, Resulting Numbers: [98] 98,13 unequal: No Solution Exploring Operation: 91/7=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[46, 81, 91, 5], Operations: [] Exploring Operation: 81-46=35, Resulting Numbers: [91, 5, 35] Generated Node #0,1: 13:[91, 5, 35] Operation: 81-46=35 Moving to Node #0,1 Current State: 13:[91, 5, 35], Operations: ['81-46=35'] Exploring Operation: 35/5=7, Resulting Numbers: [91, 7] Generated Node #0,1,2: 13:[91, 7] Operation: 35/5=7 Moving to Node #0,1,2 Current State: 13:[91, 7], Operations: ['81-46=35', '35/5=7'] Exploring Operation: 91/7=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.976563
hs_3
sum_heuristic
[ 80, 4, 15, 30 ]
40
[ "80/4=20", "30/15=2", "20*2=40" ]
Current State: 40:[80, 4, 15, 30], Operations: [] Exploring Operation: 80/4=20, Resulting Numbers: [15, 30, 20] Generated Node #2: [15, 30, 20] from Operation: 80/4=20 Current State: 40:[15, 30, 20], Operations: ['80/4=20'] Exploring Operation: 30/15=2, Resulting Numbers: [20, 2] Generated Node #3: [20, 2] from Operation: 30/15=2 Current State: 40:[20, 2], Operations: ['80/4=20', '30/15=2'] Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[80, 4, 15, 30], Operations: [] Exploring Operation: 15+30=45, Resulting Numbers: [80, 4, 45] Generated Node #0,0: 40:[80, 4, 45] Operation: 15+30=45 Exploring Operation: 30/15=2, Resulting Numbers: [80, 4, 2] Generated Node #0,1: 40:[80, 4, 2] Operation: 30/15=2 Exploring Operation: 80-30=50, Resulting Numbers: [4, 15, 50] Generated Node #0,2: 40:[4, 15, 50] Operation: 80-30=50 Exploring Operation: 80/4=20, Resulting Numbers: [15, 30, 20] Generated Node #0,3: 40:[15, 30, 20] Operation: 80/4=20 Exploring Operation: 80-15=65, Resulting Numbers: [4, 30, 65] Generated Node #0,4: 40:[4, 30, 65] Operation: 80-15=65 Moving to Node #0,2 Current State: 40:[4, 15, 50], Operations: ['80-30=50'] Exploring Operation: 4+50=54, Resulting Numbers: [15, 54] Generated Node #0,2,0: 40:[15, 54] Operation: 4+50=54 Exploring Operation: 50-15=35, Resulting Numbers: [4, 35] Generated Node #0,2,1: 40:[4, 35] Operation: 50-15=35 Exploring Operation: 4+15=19, Resulting Numbers: [50, 19] Generated Node #0,2,2: 40:[50, 19] Operation: 4+15=19 Exploring Operation: 50-4=46, Resulting Numbers: [15, 46] Generated Node #0,2,3: 40:[15, 46] Operation: 50-4=46 Exploring Operation: 15-4=11, Resulting Numbers: [50, 11] Generated Node #0,2,4: 40:[50, 11] Operation: 15-4=11 Moving to Node #0,3 Current State: 40:[15, 30, 20], Operations: ['80/4=20'] Exploring Operation: 30/15=2, Resulting Numbers: [20, 2] Generated Node #0,3,0: 40:[20, 2] Operation: 30/15=2 Exploring Operation: 30-15=15, Resulting Numbers: [20, 15] Generated Node #0,3,1: 40:[20, 15] Operation: 30-15=15 Exploring Operation: 20-15=5, Resulting Numbers: [30, 5] Generated Node #0,3,2: 40:[30, 5] Operation: 20-15=5 Exploring Operation: 30-20=10, Resulting Numbers: [15, 10] Generated Node #0,3,3: 40:[15, 10] Operation: 30-20=10 Exploring Operation: 15+30=45, Resulting Numbers: [20, 45] Generated Node #0,3,4: 40:[20, 45] Operation: 15+30=45 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 40:[20, 2], Operations: ['80/4=20', '30/15=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[80, 4, 15, 30], Operations: [] Exploring Operation: 80/4=20, Resulting Numbers: [15, 30, 20] Generated Node #0,3: 40:[15, 30, 20] Operation: 80/4=20 Moving to Node #0,3 Current State: 40:[15, 30, 20], Operations: ['80/4=20'] Exploring Operation: 30/15=2, Resulting Numbers: [20, 2] Generated Node #0,3,0: 40:[20, 2] Operation: 30/15=2 Moving to Node #0,3,0 Current State: 40:[20, 2], Operations: ['80/4=20', '30/15=2'] Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 33, 28, 63, 69 ]
24
[ "63+69=132", "132/33=4", "28-4=24" ]
Current State: 24:[33, 28, 63, 69], Operations: [] Exploring Operation: 63+69=132, Resulting Numbers: [33, 28, 132] Generated Node #2: [33, 28, 132] from Operation: 63+69=132 Current State: 24:[33, 28, 132], Operations: ['63+69=132'] Exploring Operation: 132/33=4, Resulting Numbers: [28, 4] Generated Node #3: [28, 4] from Operation: 132/33=4 Current State: 24:[28, 4], Operations: ['63+69=132', '132/33=4'] Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[33, 28, 63, 69], Operations: [] Exploring Operation: 69-63=6, Resulting Numbers: [33, 28, 6] Generated Node #0,0: 24:[33, 28, 6] Operation: 69-63=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[33, 28, 6], Operations: ['69-63=6'] Exploring Operation: 33-28=5, Resulting Numbers: [6, 5] Generated Node #0,0,0: 24:[6, 5] Operation: 33-28=5 Moving to Node #0,0,0 Current State: 24:[6, 5], Operations: ['69-63=6', '33-28=5'] Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,24 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
[ 62, 40, 59, 59 ]
33
[ "62-59=3", "40+59=99", "99/3=33" ]
Current State: 33:[62, 40, 59, 59], Operations: [] Exploring Operation: 62-59=3, Resulting Numbers: [40, 3] Generated Node #2: [40, 3] from Operation: 62-59=3 Current State: 33:[40, 3], Operations: ['62-59=3'] Exploring Operation: 40+59=99, Resulting Numbers: [3, 99] Generated Node #3: [3, 99] from Operation: 40+59=99 Current State: 33:[3, 99], Operations: ['62-59=3', '40+59=99'] Exploring Operation: 99/3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[62, 40, 59, 59], Operations: [] Exploring Operation: 62-59=3, Resulting Numbers: [40, 59, 3] Generated Node #0,0: 33:[40, 59, 3] Operation: 62-59=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[40, 59, 3], Operations: ['62-59=3'] Exploring Operation: 59-40=19, Resulting Numbers: [3, 19] Generated Node #0,0,0: 33:[3, 19] Operation: 59-40=19 Moving to Node #0,0,0 Current State: 33:[3, 19], Operations: ['62-59=3', '59-40=19'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,33 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
[ 17, 33, 90, 12 ]
51
[ "17-12=5", "90/5=18", "33+18=51" ]
Current State: 51:[17, 33, 90, 12], Operations: [] Exploring Operation: 17-12=5, Resulting Numbers: [33, 90, 5] Generated Node #2: [33, 90, 5] from Operation: 17-12=5 Current State: 51:[33, 90, 5], Operations: ['17-12=5'] Exploring Operation: 90/5=18, Resulting Numbers: [33, 18] Generated Node #3: [33, 18] from Operation: 90/5=18 Current State: 51:[33, 18], Operations: ['17-12=5', '90/5=18'] Exploring Operation: 33+18=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[17, 33, 90, 12], Operations: [] Exploring Operation: 33-12=21, Resulting Numbers: [17, 90, 21] Generated Node #0,0: 51:[17, 90, 21] Operation: 33-12=21 Exploring Operation: 90-33=57, Resulting Numbers: [17, 12, 57] Generated Node #0,1: 51:[17, 12, 57] Operation: 90-33=57 Exploring Operation: 90-17=73, Resulting Numbers: [33, 12, 73] Generated Node #0,2: 51:[33, 12, 73] Operation: 90-17=73 Moving to Node #0,1 Current State: 51:[17, 12, 57], Operations: ['90-33=57'] Exploring Operation: 17-12=5, Resulting Numbers: [57, 5] Generated Node #0,1,0: 51:[57, 5] Operation: 17-12=5 Exploring Operation: 57-17=40, Resulting Numbers: [12, 40] Generated Node #0,1,1: 51:[12, 40] Operation: 57-17=40 Exploring Operation: 57-12=45, Resulting Numbers: [17, 45] Generated Node #0,1,2: 51:[17, 45] Operation: 57-12=45 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 51:[17, 45], Operations: ['90-33=57', '57-12=45'] Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,51 unequal: No Solution Exploring Operation: 17+45=62, Resulting Numbers: [62] 62,51 unequal: No Solution Exploring Operation: 17*45=765, Resulting Numbers: [765] 765,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 51:[57, 5], Operations: ['90-33=57', '17-12=5'] Exploring Operation: 57+5=62, Resulting Numbers: [62] 62,51 unequal: No Solution Exploring Operation: 57*5=285, Resulting Numbers: [285] 285,51 unequal: No Solution Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 51:[12, 40], Operations: ['90-33=57', '57-17=40'] Exploring Operation: 12+40=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 12*40=480, Resulting Numbers: [480] 480,51 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,51 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: 51:[17, 90, 21], Operations: ['33-12=21'] Exploring Operation: 21-17=4, Resulting Numbers: [90, 4] Generated Node #0,0,0: 51:[90, 4] Operation: 21-17=4 Exploring Operation: 90-17=73, Resulting Numbers: [21, 73] Generated Node #0,0,1: 51:[21, 73] Operation: 90-17=73 Exploring Operation: 90-21=69, Resulting Numbers: [17, 69] Generated Node #0,0,2: 51:[17, 69] Operation: 90-21=69 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 51:[17, 69], Operations: ['33-12=21', '90-21=69'] Exploring Operation: 17+69=86, Resulting Numbers: [86] 86,51 unequal: No Solution Exploring Operation: 17*69=1173, Resulting Numbers: [1173] 1173,51 unequal: No Solution Exploring Operation: 69-17=52, Resulting Numbers: [52] 52,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 51:[21, 73], Operations: ['33-12=21', '90-17=73'] Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 21+73=94, Resulting Numbers: [94] 94,51 unequal: No Solution Exploring Operation: 21*73=1533, Resulting Numbers: [1533] 1533,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[90, 4], Operations: ['33-12=21', '21-17=4'] Exploring Operation: 90+4=94, Resulting Numbers: [94] 94,51 unequal: No Solution Exploring Operation: 90*4=360, Resulting Numbers: [360] 360,51 unequal: No Solution Exploring Operation: 90-4=86, Resulting Numbers: [86] 86,51 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: 51:[33, 12, 73], Operations: ['90-17=73'] Exploring Operation: 73-12=61, Resulting Numbers: [33, 61] Generated Node #0,2,0: 51:[33, 61] Operation: 73-12=61 Exploring Operation: 73-33=40, Resulting Numbers: [12, 40] Generated Node #0,2,1: 51:[12, 40] Operation: 73-33=40 Exploring Operation: 33-12=21, Resulting Numbers: [73, 21] Generated Node #0,2,2: 51:[73, 21] Operation: 33-12=21 Moving to Node #0,2,1 Current State: 51:[12, 40], Operations: ['90-17=73', '73-33=40'] Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,51 unequal: No Solution Exploring Operation: 12*40=480, Resulting Numbers: [480] 480,51 unequal: No Solution Exploring Operation: 12+40=52, Resulting Numbers: [52] 52,51 unequal: No Solution Moving to Node #0,2,0 Current State: 51:[33, 61], Operations: ['90-17=73', '73-12=61'] Exploring Operation: 61-33=28, Resulting Numbers: [28] 28,51 unequal: No Solution Exploring Operation: 33+61=94, Resulting Numbers: [94] 94,51 unequal: No Solution Exploring Operation: 33*61=2013, Resulting Numbers: [2013] 2013,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[73, 21], Operations: ['90-17=73', '33-12=21'] Exploring Operation: 73+21=94, Resulting Numbers: [94] 94,51 unequal: No Solution Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 73*21=1533, Resulting Numbers: [1533] 1533,51 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 83, 4, 48, 41 ]
68
[ "83+41=124", "4*48=192", "192-124=68" ]
Current State: 68:[83, 4, 48, 41], Operations: [] Exploring Operation: 83+41=124, Resulting Numbers: [4, 48, 124] Generated Node #2: [4, 48, 124] from Operation: 83+41=124 Current State: 68:[4, 48, 124], Operations: ['83+41=124'] Exploring Operation: 4*48=192, Resulting Numbers: [124, 192] Generated Node #3: [124, 192] from Operation: 4*48=192 Current State: 68:[124, 192], Operations: ['83+41=124', '4*48=192'] Exploring Operation: 192-124=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[83, 4, 48, 41], Operations: [] Exploring Operation: 83-48=35, Resulting Numbers: [4, 41, 35] Generated Node #0,0: 68:[4, 41, 35] Operation: 83-48=35 Moving to Node #0,0 Current State: 68:[4, 41, 35], Operations: ['83-48=35'] Exploring Operation: 41-35=6, Resulting Numbers: [4, 6] Generated Node #0,0,0: 68:[4, 6] Operation: 41-35=6 Moving to Node #0,0,0 Current State: 68:[4, 6], Operations: ['83-48=35', '41-35=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,68 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 13, 94, 60, 44 ]
46
[ "60-13=47", "94/47=2", "44+2=46" ]
Current State: 46:[13, 94, 60, 44], Operations: [] Exploring Operation: 60-13=47, Resulting Numbers: [94, 44, 47] Generated Node #2: [94, 44, 47] from Operation: 60-13=47 Current State: 46:[94, 44, 47], Operations: ['60-13=47'] Exploring Operation: 94/47=2, Resulting Numbers: [44, 2] Generated Node #3: [44, 2] from Operation: 94/47=2 Current State: 46:[44, 2], Operations: ['60-13=47', '94/47=2'] Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[13, 94, 60, 44], Operations: [] Exploring Operation: 94-60=34, Resulting Numbers: [13, 44, 34] Generated Node #0,0: 46:[13, 44, 34] Operation: 94-60=34 Exploring Operation: 94-13=81, Resulting Numbers: [60, 44, 81] Generated Node #0,1: 46:[60, 44, 81] Operation: 94-13=81 Exploring Operation: 94-44=50, Resulting Numbers: [13, 60, 50] Generated Node #0,2: 46:[13, 60, 50] Operation: 94-44=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[13, 44, 34], Operations: ['94-60=34'] Exploring Operation: 13+34=47, Resulting Numbers: [44, 47] Generated Node #0,0,0: 46:[44, 47] Operation: 13+34=47 Exploring Operation: 44-34=10, Resulting Numbers: [13, 10] Generated Node #0,0,1: 46:[13, 10] Operation: 44-34=10 Exploring Operation: 34-13=21, Resulting Numbers: [44, 21] Generated Node #0,0,2: 46:[44, 21] Operation: 34-13=21 Moving to Node #0,0,0 Current State: 46:[44, 47], Operations: ['94-60=34', '13+34=47'] Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,46 unequal: No Solution Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 44*47=2068, Resulting Numbers: [2068] 2068,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[44, 21], Operations: ['94-60=34', '34-13=21'] Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 44+21=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 44*21=924, Resulting Numbers: [924] 924,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[13, 10], Operations: ['94-60=34', '44-34=10'] Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,46 unequal: No Solution No 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: 46:[13, 60, 50], Operations: ['94-44=50'] Exploring Operation: 50-13=37, Resulting Numbers: [60, 37] Generated Node #0,2,0: 46:[60, 37] Operation: 50-13=37 Exploring Operation: 60-13=47, Resulting Numbers: [50, 47] Generated Node #0,2,1: 46:[50, 47] Operation: 60-13=47 Exploring Operation: 60-50=10, Resulting Numbers: [13, 10] Generated Node #0,2,2: 46:[13, 10] Operation: 60-50=10 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 46:[50, 47], Operations: ['94-44=50', '60-13=47'] Exploring Operation: 50+47=97, Resulting Numbers: [97] 97,46 unequal: No Solution Exploring Operation: 50*47=2350, Resulting Numbers: [2350] 2350,46 unequal: No Solution Exploring Operation: 50-47=3, Resulting Numbers: [3] 3,46 unequal: No Solution No 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: 46:[13, 10], Operations: ['94-44=50', '60-50=10'] Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,46 unequal: No Solution No 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: 46:[60, 37], Operations: ['94-44=50', '50-13=37'] Exploring Operation: 60+37=97, Resulting Numbers: [97] 97,46 unequal: No Solution Exploring Operation: 60-37=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 60*37=2220, Resulting Numbers: [2220] 2220,46 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: 46:[60, 44, 81], Operations: ['94-13=81'] Exploring Operation: 60-44=16, Resulting Numbers: [81, 16] Generated Node #0,1,0: 46:[81, 16] Operation: 60-44=16 Exploring Operation: 81-44=37, Resulting Numbers: [60, 37] Generated Node #0,1,1: 46:[60, 37] Operation: 81-44=37 Exploring Operation: 81-60=21, Resulting Numbers: [44, 21] Generated Node #0,1,2: 46:[44, 21] Operation: 81-60=21 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 46:[44, 21], Operations: ['94-13=81', '81-60=21'] Exploring Operation: 44*21=924, Resulting Numbers: [924] 924,46 unequal: No Solution Exploring Operation: 44+21=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,46 unequal: No Solution No 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: 46:[60, 37], Operations: ['94-13=81', '81-44=37'] Exploring Operation: 60*37=2220, Resulting Numbers: [2220] 2220,46 unequal: No Solution Exploring Operation: 60+37=97, Resulting Numbers: [97] 97,46 unequal: No Solution Exploring Operation: 60-37=23, Resulting Numbers: [23] 23,46 unequal: No Solution No 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: 46:[81, 16], Operations: ['94-13=81', '60-44=16'] Exploring Operation: 81-16=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 81*16=1296, Resulting Numbers: [1296] 1296,46 unequal: No Solution Exploring Operation: 81+16=97, Resulting Numbers: [97] 97,46 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
[ 57, 86, 21, 67 ]
55
[ "57+86=143", "21+67=88", "143-88=55" ]
Current State: 55:[57, 86, 21, 67], Operations: [] Exploring Operation: 57+86=143, Resulting Numbers: [21, 67, 143] Generated Node #2: [21, 67, 143] from Operation: 57+86=143 Current State: 55:[21, 67, 143], Operations: ['57+86=143'] Exploring Operation: 21+67=88, Resulting Numbers: [143, 88] Generated Node #3: [143, 88] from Operation: 21+67=88 Current State: 55:[143, 88], Operations: ['57+86=143', '21+67=88'] Exploring Operation: 143-88=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[57, 86, 21, 67], Operations: [] Exploring Operation: 86-67=19, Resulting Numbers: [57, 21, 19] Generated Node #0,0: 55:[57, 21, 19] Operation: 86-67=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[57, 21, 19], Operations: ['86-67=19'] Exploring Operation: 21-19=2, Resulting Numbers: [57, 2] Generated Node #0,0,0: 55:[57, 2] Operation: 21-19=2 Moving to Node #0,0,0 Current State: 55:[57, 2], Operations: ['86-67=19', '21-19=2'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[57, 86, 21, 67], Operations: [] Exploring Operation: 86-67=19, Resulting Numbers: [57, 21, 19] Generated Node #0,0: 55:[57, 21, 19] Operation: 86-67=19 Moving to Node #0,0 Current State: 55:[57, 21, 19], Operations: ['86-67=19'] Exploring Operation: 21-19=2, Resulting Numbers: [57, 2] Generated Node #0,0,0: 55:[57, 2] Operation: 21-19=2 Moving to Node #0,0,0 Current State: 55:[57, 2], Operations: ['86-67=19', '21-19=2'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 86, 13, 24, 7 ]
68
[ "86+13=99", "24+7=31", "99-31=68" ]
Current State: 68:[86, 13, 24, 7], Operations: [] Exploring Operation: 86+13=99, Resulting Numbers: [24, 7, 99] Generated Node #2: [24, 7, 99] from Operation: 86+13=99 Current State: 68:[24, 7, 99], Operations: ['86+13=99'] Exploring Operation: 24+7=31, Resulting Numbers: [99, 31] Generated Node #3: [99, 31] from Operation: 24+7=31 Current State: 68:[99, 31], Operations: ['86+13=99', '24+7=31'] Exploring Operation: 99-31=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[86, 13, 24, 7], Operations: [] Exploring Operation: 86-24=62, Resulting Numbers: [13, 7, 62] Generated Node #0,0: 68:[13, 7, 62] Operation: 86-24=62 Exploring Operation: 86-7=79, Resulting Numbers: [13, 24, 79] Generated Node #0,1: 68:[13, 24, 79] Operation: 86-7=79 Exploring Operation: 86-13=73, Resulting Numbers: [24, 7, 73] Generated Node #0,2: 68:[24, 7, 73] Operation: 86-13=73 Moving to Node #0,0 Current State: 68:[13, 7, 62], Operations: ['86-24=62'] Exploring Operation: 13+7=20, Resulting Numbers: [62, 20] Generated Node #0,0,0: 68:[62, 20] Operation: 13+7=20 Exploring Operation: 13-7=6, Resulting Numbers: [62, 6] Generated Node #0,0,1: 68:[62, 6] Operation: 13-7=6 Exploring Operation: 7+62=69, Resulting Numbers: [13, 69] Generated Node #0,0,2: 68:[13, 69] Operation: 7+62=69 Moving to Node #0,2 Current State: 68:[24, 7, 73], Operations: ['86-13=73'] Exploring Operation: 24+7=31, Resulting Numbers: [73, 31] Generated Node #0,2,0: 68:[73, 31] Operation: 24+7=31 Exploring Operation: 73-7=66, Resulting Numbers: [24, 66] Generated Node #0,2,1: 68:[24, 66] Operation: 73-7=66 Exploring Operation: 24-7=17, Resulting Numbers: [73, 17] Generated Node #0,2,2: 68:[73, 17] Operation: 24-7=17 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 68:[73, 17], Operations: ['86-13=73', '24-7=17'] Exploring Operation: 73+17=90, Resulting Numbers: [90] 90,68 unequal: No Solution Exploring Operation: 73-17=56, Resulting Numbers: [56] 56,68 unequal: No Solution Exploring Operation: 73*17=1241, Resulting Numbers: [1241] 1241,68 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:[73, 31], Operations: ['86-13=73', '24+7=31'] Exploring Operation: 73*31=2263, Resulting Numbers: [2263] 2263,68 unequal: No Solution Exploring Operation: 73+31=104, Resulting Numbers: [104] 104,68 unequal: No Solution Exploring Operation: 73-31=42, Resulting Numbers: [42] 42,68 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:[24, 66], Operations: ['86-13=73', '73-7=66'] Exploring Operation: 24+66=90, Resulting Numbers: [90] 90,68 unequal: No Solution Exploring Operation: 24*66=1584, Resulting Numbers: [1584] 1584,68 unequal: No Solution Exploring Operation: 66-24=42, Resulting Numbers: [42] 42,68 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: 68:[13, 24, 79], Operations: ['86-7=79'] Exploring Operation: 13+24=37, Resulting Numbers: [79, 37] Generated Node #0,1,0: 68:[79, 37] Operation: 13+24=37 Exploring Operation: 79-13=66, Resulting Numbers: [24, 66] Generated Node #0,1,1: 68:[24, 66] Operation: 79-13=66 Exploring Operation: 24-13=11, Resulting Numbers: [79, 11] Generated Node #0,1,2: 68:[79, 11] Operation: 24-13=11 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 68:[24, 66], Operations: ['86-7=79', '79-13=66'] Exploring Operation: 66-24=42, Resulting Numbers: [42] 42,68 unequal: No Solution Exploring Operation: 24+66=90, Resulting Numbers: [90] 90,68 unequal: No Solution Exploring Operation: 24*66=1584, Resulting Numbers: [1584] 1584,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 68:[79, 37], Operations: ['86-7=79', '13+24=37'] Exploring Operation: 79+37=116, Resulting Numbers: [116] 116,68 unequal: No Solution Exploring Operation: 79*37=2923, Resulting Numbers: [2923] 2923,68 unequal: No Solution Exploring Operation: 79-37=42, Resulting Numbers: [42] 42,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 68:[79, 11], Operations: ['86-7=79', '24-13=11'] Exploring Operation: 79*11=869, Resulting Numbers: [869] 869,68 unequal: No Solution Exploring Operation: 79+11=90, Resulting Numbers: [90] 90,68 unequal: No Solution Exploring Operation: 79-11=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[86, 13, 24, 7], Operations: [] Exploring Operation: 86-7=79, Resulting Numbers: [13, 24, 79] Generated Node #0,1: 68:[13, 24, 79] Operation: 86-7=79 Moving to Node #0,1 Current State: 68:[13, 24, 79], Operations: ['86-7=79'] Exploring Operation: 24-13=11, Resulting Numbers: [79, 11] Generated Node #0,1,2: 68:[79, 11] Operation: 24-13=11 Moving to Node #0,1,2 Current State: 68:[79, 11], Operations: ['86-7=79', '24-13=11'] Exploring Operation: 79-11=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_3
mult_heuristic
[ 74, 4, 12, 84 ]
77
[ "74-4=70", "84/12=7", "70+7=77" ]
Current State: 77:[74, 4, 12, 84], Operations: [] Exploring Operation: 74-4=70, Resulting Numbers: [12, 84, 70] Generated Node #2: [12, 84, 70] from Operation: 74-4=70 Current State: 77:[12, 84, 70], Operations: ['74-4=70'] Exploring Operation: 84/12=7, Resulting Numbers: [70, 7] Generated Node #3: [70, 7] from Operation: 84/12=7 Current State: 77:[70, 7], Operations: ['74-4=70', '84/12=7'] Exploring Operation: 70+7=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[74, 4, 12, 84], Operations: [] Exploring Operation: 84/12=7, Resulting Numbers: [74, 4, 7] Generated Node #0,0: 77:[74, 4, 7] Operation: 84/12=7 Exploring Operation: 84-74=10, Resulting Numbers: [4, 12, 10] Generated Node #0,1: 77:[4, 12, 10] Operation: 84-74=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[4, 12, 10], Operations: ['84-74=10'] Exploring Operation: 10-4=6, Resulting Numbers: [12, 6] Generated Node #0,1,0: 77:[12, 6] Operation: 10-4=6 Exploring Operation: 12-4=8, Resulting Numbers: [10, 8] Generated Node #0,1,1: 77:[10, 8] Operation: 12-4=8 Moving to Node #0,1,0 Current State: 77:[12, 6], Operations: ['84-74=10', '10-4=6'] Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 12*6=72, Resulting Numbers: [72] 72,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[10, 8], Operations: ['84-74=10', '12-4=8'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,77 unequal: No Solution No 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: 77:[74, 4, 7], Operations: ['84/12=7'] Exploring Operation: 4+7=11, Resulting Numbers: [74, 11] Generated Node #0,0,0: 77:[74, 11] Operation: 4+7=11 Exploring Operation: 74+4=78, Resulting Numbers: [7, 78] Generated Node #0,0,1: 77:[7, 78] Operation: 74+4=78 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 77:[7, 78], Operations: ['84/12=7', '74+4=78'] Exploring Operation: 7+78=85, Resulting Numbers: [85] 85,77 unequal: No Solution Exploring Operation: 78-7=71, Resulting Numbers: [71] 71,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[74, 11], Operations: ['84/12=7', '4+7=11'] Exploring Operation: 74+11=85, Resulting Numbers: [85] 85,77 unequal: No Solution Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 88, 44, 61, 96 ]
97
[ "88+44=132", "96-61=35", "132-35=97" ]
Current State: 97:[88, 44, 61, 96], Operations: [] Exploring Operation: 88+44=132, Resulting Numbers: [61, 96, 132] Generated Node #2: [61, 96, 132] from Operation: 88+44=132 Current State: 97:[61, 96, 132], Operations: ['88+44=132'] Exploring Operation: 96-61=35, Resulting Numbers: [132, 35] Generated Node #3: [132, 35] from Operation: 96-61=35 Current State: 97:[132, 35], Operations: ['88+44=132', '96-61=35'] Exploring Operation: 132-35=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[88, 44, 61, 96], Operations: [] Exploring Operation: 44+96=140, Resulting Numbers: [88, 61, 140] Generated Node #0,0: 97:[88, 61, 140] Operation: 44+96=140 Exploring Operation: 44+61=105, Resulting Numbers: [88, 96, 105] Generated Node #0,1: 97:[88, 96, 105] Operation: 44+61=105 Exploring Operation: 88-44=44, Resulting Numbers: [61, 96, 44] Generated Node #0,2: 97:[61, 96, 44] Operation: 88-44=44 Exploring Operation: 88+44=132, Resulting Numbers: [61, 96, 132] Generated Node #0,3: 97:[61, 96, 132] Operation: 88+44=132 Moving to Node #0,1 Current State: 97:[88, 96, 105], Operations: ['44+61=105'] Exploring Operation: 88+105=193, Resulting Numbers: [96, 193] Generated Node #0,1,0: 97:[96, 193] Operation: 88+105=193 Exploring Operation: 88+96=184, Resulting Numbers: [105, 184] Generated Node #0,1,1: 97:[105, 184] Operation: 88+96=184 Exploring Operation: 96-88=8, Resulting Numbers: [105, 8] Generated Node #0,1,2: 97:[105, 8] Operation: 96-88=8 Exploring Operation: 105-88=17, Resulting Numbers: [96, 17] Generated Node #0,1,3: 97:[96, 17] Operation: 105-88=17 Moving to Node #0,3 Current State: 97:[61, 96, 132], Operations: ['88+44=132'] Exploring Operation: 61+132=193, Resulting Numbers: [96, 193] Generated Node #0,3,0: 97:[96, 193] Operation: 61+132=193 Exploring Operation: 132-61=71, Resulting Numbers: [96, 71] Generated Node #0,3,1: 97:[96, 71] Operation: 132-61=71 Exploring Operation: 61+96=157, Resulting Numbers: [132, 157] Generated Node #0,3,2: 97:[132, 157] Operation: 61+96=157 Exploring Operation: 96-61=35, Resulting Numbers: [132, 35] Generated Node #0,3,3: 97:[132, 35] Operation: 96-61=35 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 97:[96, 71], Operations: ['88+44=132', '132-61=71'] Exploring Operation: 96*71=6816, Resulting Numbers: [6816] 6816,97 unequal: No Solution Exploring Operation: 96-71=25, Resulting Numbers: [25] 25,97 unequal: No Solution Exploring Operation: 96+71=167, Resulting Numbers: [167] 167,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 97:[132, 157], Operations: ['88+44=132', '61+96=157'] Exploring Operation: 132*157=20724, Resulting Numbers: [20724] 20724,97 unequal: No Solution Exploring Operation: 132+157=289, Resulting Numbers: [289] 289,97 unequal: No Solution Exploring Operation: 157-132=25, Resulting Numbers: [25] 25,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 97:[96, 193], Operations: ['88+44=132', '61+132=193'] Exploring Operation: 193-96=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[88, 44, 61, 96], Operations: [] Exploring Operation: 88+44=132, Resulting Numbers: [61, 96, 132] Generated Node #0,3: 97:[61, 96, 132] Operation: 88+44=132 Moving to Node #0,3 Current State: 97:[61, 96, 132], Operations: ['88+44=132'] Exploring Operation: 61+132=193, Resulting Numbers: [96, 193] Generated Node #0,3,0: 97:[96, 193] Operation: 61+132=193 Moving to Node #0,3,0 Current State: 97:[96, 193], Operations: ['88+44=132', '61+132=193'] Exploring Operation: 193-96=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
mult_heuristic
[ 48, 54, 18, 40 ]
37
[ "54-48=6", "18/6=3", "40-3=37" ]
Current State: 37:[48, 54, 18, 40], Operations: [] Exploring Operation: 54-48=6, Resulting Numbers: [18, 40, 6] Generated Node #2: [18, 40, 6] from Operation: 54-48=6 Current State: 37:[18, 40, 6], Operations: ['54-48=6'] Exploring Operation: 18/6=3, Resulting Numbers: [40, 3] Generated Node #3: [40, 3] from Operation: 18/6=3 Current State: 37:[40, 3], Operations: ['54-48=6', '18/6=3'] Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[48, 54, 18, 40], Operations: [] Exploring Operation: 48-18=30, Resulting Numbers: [54, 40, 30] Generated Node #0,0: 37:[54, 40, 30] Operation: 48-18=30 Exploring Operation: 54-18=36, Resulting Numbers: [48, 40, 36] Generated Node #0,1: 37:[48, 40, 36] Operation: 54-18=36 Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[48, 40, 36], Operations: ['54-18=36'] Exploring Operation: 48-36=12, Resulting Numbers: [40, 12] Generated Node #0,1,0: 37:[40, 12] Operation: 48-36=12 Exploring Operation: 48-40=8, Resulting Numbers: [36, 8] Generated Node #0,1,1: 37:[36, 8] Operation: 48-40=8 Moving to Node #0,1,0 Current State: 37:[40, 12], Operations: ['54-18=36', '48-36=12'] Exploring Operation: 40+12=52, Resulting Numbers: [52] 52,37 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[36, 8], Operations: ['54-18=36', '48-40=8'] Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,37 unequal: No Solution Exploring Operation: 36+8=44, Resulting Numbers: [44] 44,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[54, 40, 30], Operations: ['48-18=30'] Exploring Operation: 54-40=14, Resulting Numbers: [30, 14] Generated Node #0,0,0: 37:[30, 14] Operation: 54-40=14 Exploring Operation: 54-30=24, Resulting Numbers: [40, 24] Generated Node #0,0,1: 37:[40, 24] Operation: 54-30=24 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 37:[40, 24], Operations: ['48-18=30', '54-30=24'] Exploring Operation: 40+24=64, Resulting Numbers: [64] 64,37 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,37 unequal: No Solution No 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: 37:[30, 14], Operations: ['48-18=30', '54-40=14'] Exploring Operation: 30+14=44, Resulting Numbers: [44] 44,37 unequal: No Solution Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,37 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
[ 59, 13, 88, 73 ]
87
[ "59+13=72", "88-73=15", "72+15=87" ]
Current State: 87:[59, 13, 88, 73], Operations: [] Exploring Operation: 59+13=72, Resulting Numbers: [88, 73, 72] Generated Node #2: [88, 73, 72] from Operation: 59+13=72 Current State: 87:[88, 73, 72], Operations: ['59+13=72'] Exploring Operation: 88-73=15, Resulting Numbers: [72, 15] Generated Node #3: [72, 15] from Operation: 88-73=15 Current State: 87:[72, 15], Operations: ['59+13=72', '88-73=15'] Exploring Operation: 72+15=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[59, 13, 88, 73], Operations: [] Exploring Operation: 13+73=86, Resulting Numbers: [59, 88, 86] Generated Node #0,0: 87:[59, 88, 86] Operation: 13+73=86 Exploring Operation: 73-59=14, Resulting Numbers: [13, 88, 14] Generated Node #0,1: 87:[13, 88, 14] Operation: 73-59=14 Exploring Operation: 88-59=29, Resulting Numbers: [13, 73, 29] Generated Node #0,2: 87:[13, 73, 29] Operation: 88-59=29 Exploring Operation: 59+13=72, Resulting Numbers: [88, 73, 72] Generated Node #0,3: 87:[88, 73, 72] Operation: 59+13=72 Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[13, 88, 14], Operations: ['73-59=14'] Exploring Operation: 14-13=1, Resulting Numbers: [88, 1] Generated Node #0,1,0: 87:[88, 1] Operation: 14-13=1 Exploring Operation: 13+14=27, Resulting Numbers: [88, 27] Generated Node #0,1,1: 87:[88, 27] Operation: 13+14=27 Exploring Operation: 88-13=75, Resulting Numbers: [14, 75] Generated Node #0,1,2: 87:[14, 75] Operation: 88-13=75 Exploring Operation: 88-14=74, Resulting Numbers: [13, 74] Generated Node #0,1,3: 87:[13, 74] Operation: 88-14=74 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[88, 1], Operations: ['73-59=14', '14-13=1'] Exploring Operation: 88/1=88, Resulting Numbers: [88] 88,87 unequal: No Solution Exploring Operation: 88+1=89, Resulting Numbers: [89] 89,87 unequal: No Solution Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[59, 13, 88, 73], Operations: [] Exploring Operation: 73-59=14, Resulting Numbers: [13, 88, 14] Generated Node #0,1: 87:[13, 88, 14] Operation: 73-59=14 Moving to Node #0,1 Current State: 87:[13, 88, 14], Operations: ['73-59=14'] Exploring Operation: 14-13=1, Resulting Numbers: [88, 1] Generated Node #0,1,0: 87:[88, 1] Operation: 14-13=1 Moving to Node #0,1,0 Current State: 87:[88, 1], Operations: ['73-59=14', '14-13=1'] Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 42, 28, 22, 76 ]
84
[ "42-28=14", "22+76=98", "98-14=84" ]
Current State: 84:[42, 28, 22, 76], Operations: [] Exploring Operation: 42-28=14, Resulting Numbers: [22, 76, 14] Generated Node #2: [22, 76, 14] from Operation: 42-28=14 Current State: 84:[22, 76, 14], Operations: ['42-28=14'] Exploring Operation: 22+76=98, Resulting Numbers: [14, 98] Generated Node #3: [14, 98] from Operation: 22+76=98 Current State: 84:[14, 98], Operations: ['42-28=14', '22+76=98'] Exploring Operation: 98-14=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[42, 28, 22, 76], Operations: [] Exploring Operation: 76-42=34, Resulting Numbers: [28, 22, 34] Generated Node #0,0: 84:[28, 22, 34] Operation: 76-42=34 Moving to Node #0,0 Current State: 84:[28, 22, 34], Operations: ['76-42=34'] Exploring Operation: 34-22=12, Resulting Numbers: [28, 12] Generated Node #0,0,0: 84:[28, 12] Operation: 34-22=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[28, 12], Operations: ['76-42=34', '34-22=12'] Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 22, 65, 74, 57 ]
13
[ "74-22=52", "57-52=5", "65/5=13" ]
Current State: 13:[22, 65, 74, 57], Operations: [] Exploring Operation: 74-22=52, Resulting Numbers: [65, 57, 52] Generated Node #2: [65, 57, 52] from Operation: 74-22=52 Current State: 13:[65, 57, 52], Operations: ['74-22=52'] Exploring Operation: 57-52=5, Resulting Numbers: [65, 5] Generated Node #3: [65, 5] from Operation: 57-52=5 Current State: 13:[65, 5], Operations: ['74-22=52', '57-52=5'] Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[22, 65, 74, 57], Operations: [] Exploring Operation: 74-65=9, Resulting Numbers: [22, 57, 9] Generated Node #0,0: 13:[22, 57, 9] Operation: 74-65=9 Moving to Node #0,0 Current State: 13:[22, 57, 9], Operations: ['74-65=9'] Exploring Operation: 57-22=35, Resulting Numbers: [9, 35] Generated Node #0,0,0: 13:[9, 35] Operation: 57-22=35 Moving to Node #0,0,0 Current State: 13:[9, 35], Operations: ['74-65=9', '57-22=35'] Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,13 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 55, 78, 17, 87 ]
51
[ "78+87=165", "165/55=3", "17*3=51" ]
Current State: 51:[55, 78, 17, 87], Operations: [] Exploring Operation: 78+87=165, Resulting Numbers: [55, 17, 165] Generated Node #2: [55, 17, 165] from Operation: 78+87=165 Current State: 51:[55, 17, 165], Operations: ['78+87=165'] Exploring Operation: 165/55=3, Resulting Numbers: [17, 3] Generated Node #3: [17, 3] from Operation: 165/55=3 Current State: 51:[17, 3], Operations: ['78+87=165', '165/55=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[55, 78, 17, 87], Operations: [] Exploring Operation: 87-17=70, Resulting Numbers: [55, 78, 70] Generated Node #0,0: 51:[55, 78, 70] Operation: 87-17=70 Exploring Operation: 78-17=61, Resulting Numbers: [55, 87, 61] Generated Node #0,1: 51:[55, 87, 61] Operation: 78-17=61 Exploring Operation: 87-55=32, Resulting Numbers: [78, 17, 32] Generated Node #0,2: 51:[78, 17, 32] Operation: 87-55=32 Exploring Operation: 78-55=23, Resulting Numbers: [17, 87, 23] Generated Node #0,3: 51:[17, 87, 23] Operation: 78-55=23 Exploring Operation: 87-78=9, Resulting Numbers: [55, 17, 9] Generated Node #0,4: 51:[55, 17, 9] Operation: 87-78=9 Start Sub Search at level 1: Moving to Node #0,4 Current State: 51:[55, 17, 9], Operations: ['87-78=9'] Exploring Operation: 17-9=8, Resulting Numbers: [55, 8] Generated Node #0,4,0: 51:[55, 8] Operation: 17-9=8 Exploring Operation: 55-9=46, Resulting Numbers: [17, 46] Generated Node #0,4,1: 51:[17, 46] Operation: 55-9=46 Exploring Operation: 55-17=38, Resulting Numbers: [9, 38] Generated Node #0,4,2: 51:[9, 38] Operation: 55-17=38 Exploring Operation: 55+9=64, Resulting Numbers: [17, 64] Generated Node #0,4,3: 51:[17, 64] Operation: 55+9=64 Exploring Operation: 17+9=26, Resulting Numbers: [55, 26] Generated Node #0,4,4: 51:[55, 26] Operation: 17+9=26 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 51:[17, 46], Operations: ['87-78=9', '55-9=46'] Exploring Operation: 17*46=782, Resulting Numbers: [782] 782,51 unequal: No Solution Exploring Operation: 17+46=63, Resulting Numbers: [63] 63,51 unequal: No Solution Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 51:[55, 8], Operations: ['87-78=9', '17-9=8'] Exploring Operation: 55*8=440, Resulting Numbers: [440] 440,51 unequal: No Solution Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,51 unequal: No Solution Exploring Operation: 55+8=63, Resulting Numbers: [63] 63,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 51:[17, 64], Operations: ['87-78=9', '55+9=64'] Exploring Operation: 17*64=1088, Resulting Numbers: [1088] 1088,51 unequal: No Solution Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,51 unequal: No Solution Exploring Operation: 17+64=81, Resulting Numbers: [81] 81,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 51:[55, 26], Operations: ['87-78=9', '17+9=26'] Exploring Operation: 55-26=29, Resulting Numbers: [29] 29,51 unequal: No Solution Exploring Operation: 55+26=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 55*26=1430, Resulting Numbers: [1430] 1430,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 51:[9, 38], Operations: ['87-78=9', '55-17=38'] Exploring Operation: 9*38=342, Resulting Numbers: [342] 342,51 unequal: No Solution Exploring Operation: 9+38=47, Resulting Numbers: [47] 47,51 unequal: No Solution Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,51 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: 51:[78, 17, 32], Operations: ['87-55=32'] Exploring Operation: 17+32=49, Resulting Numbers: [78, 49] Generated Node #0,2,0: 51:[78, 49] Operation: 17+32=49 Exploring Operation: 78-32=46, Resulting Numbers: [17, 46] Generated Node #0,2,1: 51:[17, 46] Operation: 78-32=46 Exploring Operation: 78+17=95, Resulting Numbers: [32, 95] Generated Node #0,2,2: 51:[32, 95] Operation: 78+17=95 Exploring Operation: 78-17=61, Resulting Numbers: [32, 61] Generated Node #0,2,3: 51:[32, 61] Operation: 78-17=61 Exploring Operation: 32-17=15, Resulting Numbers: [78, 15] Generated Node #0,2,4: 51:[78, 15] Operation: 32-17=15 Moving to Node #0,2,1 Current State: 51:[17, 46], Operations: ['87-55=32', '78-32=46'] Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,51 unequal: No Solution Exploring Operation: 17*46=782, Resulting Numbers: [782] 782,51 unequal: No Solution Exploring Operation: 17+46=63, Resulting Numbers: [63] 63,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[32, 61], Operations: ['87-55=32', '78-17=61'] Exploring Operation: 32+61=93, Resulting Numbers: [93] 93,51 unequal: No Solution Exploring Operation: 61-32=29, Resulting Numbers: [29] 29,51 unequal: No Solution Exploring Operation: 32*61=1952, Resulting Numbers: [1952] 1952,51 unequal: No Solution Moving to Node #0,2,0 Current State: 51:[78, 49], Operations: ['87-55=32', '17+32=49'] Exploring Operation: 78+49=127, Resulting Numbers: [127] 127,51 unequal: No Solution Exploring Operation: 78-49=29, Resulting Numbers: [29] 29,51 unequal: No Solution Exploring Operation: 78*49=3822, Resulting Numbers: [3822] 3822,51 unequal: No Solution Moving to Node #0,2,4 Current State: 51:[78, 15], Operations: ['87-55=32', '32-17=15'] Exploring Operation: 78-15=63, Resulting Numbers: [63] 63,51 unequal: No Solution Exploring Operation: 78*15=1170, Resulting Numbers: [1170] 1170,51 unequal: No Solution Exploring Operation: 78+15=93, Resulting Numbers: [93] 93,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[32, 95], Operations: ['87-55=32', '78+17=95'] Exploring Operation: 32+95=127, Resulting Numbers: [127] 127,51 unequal: No Solution Exploring Operation: 32*95=3040, Resulting Numbers: [3040] 3040,51 unequal: No Solution Exploring Operation: 95-32=63, Resulting Numbers: [63] 63,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[17, 87, 23], Operations: ['78-55=23'] Exploring Operation: 17+23=40, Resulting Numbers: [87, 40] Generated Node #0,3,0: 51:[87, 40] Operation: 17+23=40 Exploring Operation: 17+87=104, Resulting Numbers: [23, 104] Generated Node #0,3,1: 51:[23, 104] Operation: 17+87=104 Exploring Operation: 87-23=64, Resulting Numbers: [17, 64] Generated Node #0,3,2: 51:[17, 64] Operation: 87-23=64 Exploring Operation: 87-17=70, Resulting Numbers: [23, 70] Generated Node #0,3,3: 51:[23, 70] Operation: 87-17=70 Exploring Operation: 23-17=6, Resulting Numbers: [87, 6] Generated Node #0,3,4: 51:[87, 6] Operation: 23-17=6 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 51:[17, 64], Operations: ['78-55=23', '87-23=64'] Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,51 unequal: No Solution Exploring Operation: 17*64=1088, Resulting Numbers: [1088] 1088,51 unequal: No Solution Exploring Operation: 17+64=81, Resulting Numbers: [81] 81,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 51:[23, 70], Operations: ['78-55=23', '87-17=70'] Exploring Operation: 70-23=47, Resulting Numbers: [47] 47,51 unequal: No Solution Exploring Operation: 23*70=1610, Resulting Numbers: [1610] 1610,51 unequal: No Solution Exploring Operation: 23+70=93, Resulting Numbers: [93] 93,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 51:[87, 6], Operations: ['78-55=23', '23-17=6'] Exploring Operation: 87*6=522, Resulting Numbers: [522] 522,51 unequal: No Solution Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,51 unequal: No Solution Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 51:[87, 40], Operations: ['78-55=23', '17+23=40'] Exploring Operation: 87+40=127, Resulting Numbers: [127] 127,51 unequal: No Solution Exploring Operation: 87-40=47, Resulting Numbers: [47] 47,51 unequal: No Solution Exploring Operation: 87*40=3480, Resulting Numbers: [3480] 3480,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 51:[23, 104], Operations: ['78-55=23', '17+87=104'] Exploring Operation: 104-23=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 23+104=127, Resulting Numbers: [127] 127,51 unequal: No Solution Exploring Operation: 23*104=2392, Resulting Numbers: [2392] 2392,51 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: 51:[55, 78, 70], Operations: ['87-17=70'] Exploring Operation: 78-70=8, Resulting Numbers: [55, 8] Generated Node #0,0,0: 51:[55, 8] Operation: 78-70=8 Exploring Operation: 70-55=15, Resulting Numbers: [78, 15] Generated Node #0,0,1: 51:[78, 15] Operation: 70-55=15 Exploring Operation: 78-55=23, Resulting Numbers: [70, 23] Generated Node #0,0,2: 51:[70, 23] Operation: 78-55=23 Exploring Operation: 55+78=133, Resulting Numbers: [70, 133] Generated Node #0,0,3: 51:[70, 133] Operation: 55+78=133 Exploring Operation: 55+70=125, Resulting Numbers: [78, 125] Generated Node #0,0,4: 51:[78, 125] Operation: 55+70=125 Moving to Node #0,0,0 Current State: 51:[55, 8], Operations: ['87-17=70', '78-70=8'] Exploring Operation: 55+8=63, Resulting Numbers: [63] 63,51 unequal: No Solution Exploring Operation: 55*8=440, Resulting Numbers: [440] 440,51 unequal: No Solution Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[70, 23], Operations: ['87-17=70', '78-55=23'] Exploring Operation: 70+23=93, Resulting Numbers: [93] 93,51 unequal: No Solution Exploring Operation: 70-23=47, Resulting Numbers: [47] 47,51 unequal: No Solution Exploring Operation: 70*23=1610, Resulting Numbers: [1610] 1610,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[78, 15], Operations: ['87-17=70', '70-55=15'] Exploring Operation: 78+15=93, Resulting Numbers: [93] 93,51 unequal: No Solution Exploring Operation: 78*15=1170, Resulting Numbers: [1170] 1170,51 unequal: No Solution Exploring Operation: 78-15=63, Resulting Numbers: [63] 63,51 unequal: No Solution Moving to Node #0,0,3 Current State: 51:[70, 133], Operations: ['87-17=70', '55+78=133'] Exploring Operation: 70+133=203, Resulting Numbers: [203] 203,51 unequal: No Solution Exploring Operation: 133-70=63, Resulting Numbers: [63] 63,51 unequal: No Solution Exploring Operation: 70*133=9310, Resulting Numbers: [9310] 9310,51 unequal: No Solution Moving to Node #0,0,4 Current State: 51:[78, 125], Operations: ['87-17=70', '55+70=125'] Exploring Operation: 78+125=203, Resulting Numbers: [203] 203,51 unequal: No Solution Exploring Operation: 125-78=47, Resulting Numbers: [47] 47,51 unequal: No Solution Exploring Operation: 78*125=9750, Resulting Numbers: [9750] 9750,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[55, 87, 61], Operations: ['78-17=61'] Exploring Operation: 55+61=116, Resulting Numbers: [87, 116] Generated Node #0,1,0: 51:[87, 116] Operation: 55+61=116 Exploring Operation: 87-55=32, Resulting Numbers: [61, 32] Generated Node #0,1,1: 51:[61, 32] Operation: 87-55=32 Exploring Operation: 61-55=6, Resulting Numbers: [87, 6] Generated Node #0,1,2: 51:[87, 6] Operation: 61-55=6 Exploring Operation: 55+87=142, Resulting Numbers: [61, 142] Generated Node #0,1,3: 51:[61, 142] Operation: 55+87=142 Exploring Operation: 87-61=26, Resulting Numbers: [55, 26] Generated Node #0,1,4: 51:[55, 26] Operation: 87-61=26 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 51:[55, 26], Operations: ['78-17=61', '87-61=26'] Exploring Operation: 55+26=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 55-26=29, Resulting Numbers: [29] 29,51 unequal: No Solution Exploring Operation: 55*26=1430, Resulting Numbers: [1430] 1430,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[61, 32], Operations: ['78-17=61', '87-55=32'] Exploring Operation: 61-32=29, Resulting Numbers: [29] 29,51 unequal: No Solution Exploring Operation: 61+32=93, Resulting Numbers: [93] 93,51 unequal: No Solution Exploring Operation: 61*32=1952, Resulting Numbers: [1952] 1952,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 51:[87, 6], Operations: ['78-17=61', '61-55=6'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,51 unequal: No Solution Exploring Operation: 87*6=522, Resulting Numbers: [522] 522,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 51:[87, 116], Operations: ['78-17=61', '55+61=116'] Exploring Operation: 87*116=10092, Resulting Numbers: [10092] 10092,51 unequal: No Solution Exploring Operation: 87+116=203, Resulting Numbers: [203] 203,51 unequal: No Solution Exploring Operation: 116-87=29, Resulting Numbers: [29] 29,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 51:[61, 142], Operations: ['78-17=61', '55+87=142'] Exploring Operation: 61+142=203, Resulting Numbers: [203] 203,51 unequal: No Solution Exploring Operation: 142-61=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 61*142=8662, Resulting Numbers: [8662] 8662,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 14, 6, 85, 57 ]
58
[ "14*6=84", "85+57=142", "142-84=58" ]
Current State: 58:[14, 6, 85, 57], Operations: [] Exploring Operation: 14*6=84, Resulting Numbers: [85, 57, 84] Generated Node #2: [85, 57, 84] from Operation: 14*6=84 Current State: 58:[85, 57, 84], Operations: ['14*6=84'] Exploring Operation: 85+57=142, Resulting Numbers: [84, 142] Generated Node #3: [84, 142] from Operation: 85+57=142 Current State: 58:[84, 142], Operations: ['14*6=84', '85+57=142'] Exploring Operation: 142-84=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[14, 6, 85, 57], Operations: [] Exploring Operation: 85-57=28, Resulting Numbers: [14, 6, 28] Generated Node #0,0: 58:[14, 6, 28] Operation: 85-57=28 Exploring Operation: 85-14=71, Resulting Numbers: [6, 57, 71] Generated Node #0,1: 58:[6, 57, 71] Operation: 85-14=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[14, 6, 28], Operations: ['85-57=28'] Exploring Operation: 28/14=2, Resulting Numbers: [6, 2] Generated Node #0,0,0: 58:[6, 2] Operation: 28/14=2 Exploring Operation: 14-6=8, Resulting Numbers: [28, 8] Generated Node #0,0,1: 58:[28, 8] Operation: 14-6=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[6, 2], Operations: ['85-57=28', '28/14=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,58 unequal: No Solution No 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: 58:[28, 8], Operations: ['85-57=28', '14-6=8'] Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,58 unequal: No Solution Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,58 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: 58:[6, 57, 71], Operations: ['85-14=71'] Exploring Operation: 71-6=65, Resulting Numbers: [57, 65] Generated Node #0,1,0: 58:[57, 65] Operation: 71-6=65 Exploring Operation: 71-57=14, Resulting Numbers: [6, 14] Generated Node #0,1,1: 58:[6, 14] Operation: 71-57=14 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 58:[57, 65], Operations: ['85-14=71', '71-6=65'] Exploring Operation: 57+65=122, Resulting Numbers: [122] 122,58 unequal: No Solution Exploring Operation: 65-57=8, Resulting Numbers: [8] 8,58 unequal: No Solution No 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: 58:[6, 14], Operations: ['85-14=71', '71-57=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,58 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,58 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
[ 25, 63, 23, 81 ]
16
[ "25+63=88", "23+81=104", "104-88=16" ]
Current State: 16:[25, 63, 23, 81], Operations: [] Exploring Operation: 25+63=88, Resulting Numbers: [23, 81, 88] Generated Node #2: [23, 81, 88] from Operation: 25+63=88 Current State: 16:[23, 81, 88], Operations: ['25+63=88'] Exploring Operation: 23+81=104, Resulting Numbers: [88, 104] Generated Node #3: [88, 104] from Operation: 23+81=104 Current State: 16:[88, 104], Operations: ['25+63=88', '23+81=104'] Exploring Operation: 104-88=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[25, 63, 23, 81], Operations: [] Exploring Operation: 81-63=18, Resulting Numbers: [25, 23, 18] Generated Node #0,0: 16:[25, 23, 18] Operation: 81-63=18 Exploring Operation: 63-25=38, Resulting Numbers: [23, 81, 38] Generated Node #0,1: 16:[23, 81, 38] Operation: 63-25=38 Moving to Node #0,0 Current State: 16:[25, 23, 18], Operations: ['81-63=18'] Exploring Operation: 25-18=7, Resulting Numbers: [23, 7] Generated Node #0,0,0: 16:[23, 7] Operation: 25-18=7 Exploring Operation: 25-23=2, Resulting Numbers: [18, 2] Generated Node #0,0,1: 16:[18, 2] Operation: 25-23=2 Moving to Node #0,1 Current State: 16:[23, 81, 38], Operations: ['63-25=38'] Exploring Operation: 81-23=58, Resulting Numbers: [38, 58] Generated Node #0,1,0: 16:[38, 58] Operation: 81-23=58 Exploring Operation: 81-38=43, Resulting Numbers: [23, 43] Generated Node #0,1,1: 16:[23, 43] Operation: 81-38=43 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 16:[23, 43], Operations: ['63-25=38', '81-38=43'] Exploring Operation: 23+43=66, Resulting Numbers: [66] 66,16 unequal: No Solution Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[38, 58], Operations: ['63-25=38', '81-23=58'] Exploring Operation: 58-38=20, Resulting Numbers: [20] 20,16 unequal: No Solution Exploring Operation: 38+58=96, Resulting Numbers: [96] 96,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 16:[18, 2], Operations: ['81-63=18', '25-23=2'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[25, 63, 23, 81], Operations: [] Exploring Operation: 81-63=18, Resulting Numbers: [25, 23, 18] Generated Node #0,0: 16:[25, 23, 18] Operation: 81-63=18 Moving to Node #0,0 Current State: 16:[25, 23, 18], Operations: ['81-63=18'] Exploring Operation: 25-23=2, Resulting Numbers: [18, 2] Generated Node #0,0,1: 16:[18, 2] Operation: 25-23=2 Moving to Node #0,0,1 Current State: 16:[18, 2], Operations: ['81-63=18', '25-23=2'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 35, 40, 97, 34 ]
68
[ "40-35=5", "97-34=63", "5+63=68" ]
Current State: 68:[35, 40, 97, 34], Operations: [] Exploring Operation: 40-35=5, Resulting Numbers: [97, 34, 5] Generated Node #2: [97, 34, 5] from Operation: 40-35=5 Current State: 68:[97, 34, 5], Operations: ['40-35=5'] Exploring Operation: 97-34=63, Resulting Numbers: [5, 63] Generated Node #3: [5, 63] from Operation: 97-34=63 Current State: 68:[5, 63], Operations: ['40-35=5', '97-34=63'] Exploring Operation: 5+63=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[35, 40, 97, 34], Operations: [] Exploring Operation: 97-40=57, Resulting Numbers: [35, 34, 57] Generated Node #0,0: 68:[35, 34, 57] Operation: 97-40=57 Exploring Operation: 97-35=62, Resulting Numbers: [40, 34, 62] Generated Node #0,1: 68:[40, 34, 62] Operation: 97-35=62 Moving to Node #0,0 Current State: 68:[35, 34, 57], Operations: ['97-40=57'] Exploring Operation: 57-35=22, Resulting Numbers: [34, 22] Generated Node #0,0,0: 68:[34, 22] Operation: 57-35=22 Exploring Operation: 57-34=23, Resulting Numbers: [35, 23] Generated Node #0,0,1: 68:[35, 23] Operation: 57-34=23 Moving to Node #0,1 Current State: 68:[40, 34, 62], Operations: ['97-35=62'] Exploring Operation: 40-34=6, Resulting Numbers: [62, 6] Generated Node #0,1,0: 68:[62, 6] Operation: 40-34=6 Exploring Operation: 62-40=22, Resulting Numbers: [34, 22] Generated Node #0,1,1: 68:[34, 22] Operation: 62-40=22 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 68:[34, 22], Operations: ['97-35=62', '62-40=22'] Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 34+22=56, Resulting Numbers: [56] 56,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 68:[62, 6], Operations: ['97-35=62', '40-34=6'] Exploring Operation: 62+6=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[35, 40, 97, 34], Operations: [] Exploring Operation: 97-35=62, Resulting Numbers: [40, 34, 62] Generated Node #0,1: 68:[40, 34, 62] Operation: 97-35=62 Moving to Node #0,1 Current State: 68:[40, 34, 62], Operations: ['97-35=62'] Exploring Operation: 40-34=6, Resulting Numbers: [62, 6] Generated Node #0,1,0: 68:[62, 6] Operation: 40-34=6 Moving to Node #0,1,0 Current State: 68:[62, 6], Operations: ['97-35=62', '40-34=6'] Exploring Operation: 62+6=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_2
sum_heuristic
[ 18, 23, 60, 10 ]
69
[ "18*23=414", "60/10=6", "414/6=69" ]
Current State: 69:[18, 23, 60, 10], Operations: [] Exploring Operation: 18*23=414, Resulting Numbers: [60, 10, 414] Generated Node #2: [60, 10, 414] from Operation: 18*23=414 Current State: 69:[60, 10, 414], Operations: ['18*23=414'] Exploring Operation: 60/10=6, Resulting Numbers: [414, 6] Generated Node #3: [414, 6] from Operation: 60/10=6 Current State: 69:[414, 6], Operations: ['18*23=414', '60/10=6'] Exploring Operation: 414/6=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[18, 23, 60, 10], Operations: [] Exploring Operation: 60/10=6, Resulting Numbers: [18, 23, 6] Generated Node #0,0: 69:[18, 23, 6] Operation: 60/10=6 Exploring Operation: 18+10=28, Resulting Numbers: [23, 60, 28] Generated Node #0,1: 69:[23, 60, 28] Operation: 18+10=28 Exploring Operation: 60+10=70, Resulting Numbers: [18, 23, 70] Generated Node #0,2: 69:[18, 23, 70] Operation: 60+10=70 Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[18, 23, 70], Operations: ['60+10=70'] Exploring Operation: 18+23=41, Resulting Numbers: [70, 41] Generated Node #0,2,0: 69:[70, 41] Operation: 18+23=41 Exploring Operation: 23-18=5, Resulting Numbers: [70, 5] Generated Node #0,2,1: 69:[70, 5] Operation: 23-18=5 Exploring Operation: 70-18=52, Resulting Numbers: [23, 52] Generated Node #0,2,2: 69:[23, 52] Operation: 70-18=52 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 69:[70, 5], Operations: ['60+10=70', '23-18=5'] Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 70+5=75, Resulting Numbers: [75] 75,69 unequal: No Solution Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,69 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 #0,2,2 Current State: 69:[23, 52], Operations: ['60+10=70', '70-18=52'] Exploring Operation: 23+52=75, Resulting Numbers: [75] 75,69 unequal: No Solution Exploring Operation: 23*52=1196, Resulting Numbers: [1196] 1196,69 unequal: No Solution Exploring Operation: 52-23=29, Resulting Numbers: [29] 29,69 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 #0,2,0 Current State: 69:[70, 41], Operations: ['60+10=70', '18+23=41'] Exploring Operation: 70+41=111, Resulting Numbers: [111] 111,69 unequal: No Solution Exploring Operation: 70-41=29, Resulting Numbers: [29] 29,69 unequal: No Solution Exploring Operation: 70*41=2870, Resulting Numbers: [2870] 2870,69 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 #0,0 Current State: 69:[18, 23, 6], Operations: ['60/10=6'] Exploring Operation: 18+6=24, Resulting Numbers: [23, 24] Generated Node #0,0,0: 69:[23, 24] Operation: 18+6=24 Exploring Operation: 18/6=3, Resulting Numbers: [23, 3] Generated Node #0,0,1: 69:[23, 3] Operation: 18/6=3 Exploring Operation: 23-18=5, Resulting Numbers: [6, 5] Generated Node #0,0,2: 69:[6, 5] Operation: 23-18=5 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 69:[23, 3], Operations: ['60/10=6', '18/6=3'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[18, 23, 60, 10], Operations: [] Exploring Operation: 60/10=6, Resulting Numbers: [18, 23, 6] Generated Node #0,0: 69:[18, 23, 6] Operation: 60/10=6 Moving to Node #0,0 Current State: 69:[18, 23, 6], Operations: ['60/10=6'] Exploring Operation: 18/6=3, Resulting Numbers: [23, 3] Generated Node #0,0,1: 69:[23, 3] Operation: 18/6=3 Moving to Node #0,0,1 Current State: 69:[23, 3], Operations: ['60/10=6', '18/6=3'] Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 15, 69, 9, 7 ]
100
[ "15+69=84", "9+7=16", "84+16=100" ]
Current State: 100:[15, 69, 9, 7], Operations: [] Exploring Operation: 15+69=84, Resulting Numbers: [9, 7, 84] Generated Node #2: [9, 7, 84] from Operation: 15+69=84 Current State: 100:[9, 7, 84], Operations: ['15+69=84'] Exploring Operation: 9+7=16, Resulting Numbers: [84, 16] Generated Node #3: [84, 16] from Operation: 9+7=16 Current State: 100:[84, 16], Operations: ['15+69=84', '9+7=16'] Exploring Operation: 84+16=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[15, 69, 9, 7], Operations: [] Exploring Operation: 69-7=62, Resulting Numbers: [15, 9, 62] Generated Node #0,0: 100:[15, 9, 62] Operation: 69-7=62 Exploring Operation: 15+9=24, Resulting Numbers: [69, 7, 24] Generated Node #0,1: 100:[69, 7, 24] Operation: 15+9=24 Exploring Operation: 15+69=84, Resulting Numbers: [9, 7, 84] Generated Node #0,2: 100:[9, 7, 84] Operation: 15+69=84 Exploring Operation: 69-9=60, Resulting Numbers: [15, 7, 60] Generated Node #0,3: 100:[15, 7, 60] Operation: 69-9=60 Exploring Operation: 69-15=54, Resulting Numbers: [9, 7, 54] Generated Node #0,4: 100:[9, 7, 54] Operation: 69-15=54 Moving to Node #0,4 Current State: 100:[9, 7, 54], Operations: ['69-15=54'] Exploring Operation: 54-9=45, Resulting Numbers: [7, 45] Generated Node #0,4,0: 100:[7, 45] Operation: 54-9=45 Exploring Operation: 9-7=2, Resulting Numbers: [54, 2] Generated Node #0,4,1: 100:[54, 2] Operation: 9-7=2 Exploring Operation: 54/9=6, Resulting Numbers: [7, 6] Generated Node #0,4,2: 100:[7, 6] Operation: 54/9=6 Exploring Operation: 54-7=47, Resulting Numbers: [9, 47] Generated Node #0,4,3: 100:[9, 47] Operation: 54-7=47 Exploring Operation: 9+7=16, Resulting Numbers: [54, 16] Generated Node #0,4,4: 100:[54, 16] Operation: 9+7=16 Moving to Node #0,3 Current State: 100:[15, 7, 60], Operations: ['69-9=60'] Exploring Operation: 15-7=8, Resulting Numbers: [60, 8] Generated Node #0,3,0: 100:[60, 8] Operation: 15-7=8 Exploring Operation: 60-15=45, Resulting Numbers: [7, 45] Generated Node #0,3,1: 100:[7, 45] Operation: 60-15=45 Exploring Operation: 60-7=53, Resulting Numbers: [15, 53] Generated Node #0,3,2: 100:[15, 53] Operation: 60-7=53 Exploring Operation: 15+7=22, Resulting Numbers: [60, 22] Generated Node #0,3,3: 100:[60, 22] Operation: 15+7=22 Exploring Operation: 60/15=4, Resulting Numbers: [7, 4] Generated Node #0,3,4: 100:[7, 4] Operation: 60/15=4 Moving to Node #0,0 Current State: 100:[15, 9, 62], Operations: ['69-7=62'] Exploring Operation: 62-9=53, Resulting Numbers: [15, 53] Generated Node #0,0,0: 100:[15, 53] Operation: 62-9=53 Exploring Operation: 62-15=47, Resulting Numbers: [9, 47] Generated Node #0,0,1: 100:[9, 47] Operation: 62-15=47 Exploring Operation: 15-9=6, Resulting Numbers: [62, 6] Generated Node #0,0,2: 100:[62, 6] Operation: 15-9=6 Exploring Operation: 15+9=24, Resulting Numbers: [62, 24] Generated Node #0,0,3: 100:[62, 24] Operation: 15+9=24 Exploring Operation: 15+62=77, Resulting Numbers: [9, 77] Generated Node #0,0,4: 100:[9, 77] Operation: 15+62=77 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[9, 47], Operations: ['69-7=62', '62-15=47'] Exploring Operation: 9*47=423, Resulting Numbers: [423] 423,100 unequal: No Solution Exploring Operation: 9+47=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[15, 53], Operations: ['69-7=62', '62-9=53'] Exploring Operation: 53-15=38, Resulting Numbers: [38] 38,100 unequal: No Solution Exploring Operation: 15+53=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 15*53=795, Resulting Numbers: [795] 795,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 100:[62, 6], Operations: ['69-7=62', '15-9=6'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 62*6=372, Resulting Numbers: [372] 372,100 unequal: No Solution Exploring Operation: 62+6=68, Resulting Numbers: [68] 68,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 100:[62, 24], Operations: ['69-7=62', '15+9=24'] Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,100 unequal: No Solution Exploring Operation: 62*24=1488, Resulting Numbers: [1488] 1488,100 unequal: No Solution Exploring Operation: 62+24=86, Resulting Numbers: [86] 86,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 100:[9, 77], Operations: ['69-7=62', '15+62=77'] Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 9*77=693, Resulting Numbers: [693] 693,100 unequal: No Solution Exploring Operation: 9+77=86, Resulting Numbers: [86] 86,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 100:[9, 7, 84], Operations: ['15+69=84'] Exploring Operation: 7+84=91, Resulting Numbers: [9, 91] Generated Node #0,2,0: 100:[9, 91] Operation: 7+84=91 Exploring Operation: 9+84=93, Resulting Numbers: [7, 93] Generated Node #0,2,1: 100:[7, 93] Operation: 9+84=93 Exploring Operation: 9-7=2, Resulting Numbers: [84, 2] Generated Node #0,2,2: 100:[84, 2] Operation: 9-7=2 Exploring Operation: 9+7=16, Resulting Numbers: [84, 16] Generated Node #0,2,3: 100:[84, 16] Operation: 9+7=16 Exploring Operation: 84/7=12, Resulting Numbers: [9, 12] Generated Node #0,2,4: 100:[9, 12] Operation: 84/7=12 Moving to Node #0,1 Current State: 100:[69, 7, 24], Operations: ['15+9=24'] Exploring Operation: 69-24=45, Resulting Numbers: [7, 45] Generated Node #0,1,0: 100:[7, 45] Operation: 69-24=45 Exploring Operation: 69-7=62, Resulting Numbers: [24, 62] Generated Node #0,1,1: 100:[24, 62] Operation: 69-7=62 Exploring Operation: 24-7=17, Resulting Numbers: [69, 17] Generated Node #0,1,2: 100:[69, 17] Operation: 24-7=17 Exploring Operation: 69+24=93, Resulting Numbers: [7, 93] Generated Node #0,1,3: 100:[7, 93] Operation: 69+24=93 Exploring Operation: 69+7=76, Resulting Numbers: [24, 76] Generated Node #0,1,4: 100:[24, 76] Operation: 69+7=76 Moving to Node #0,3,4 Current State: 100:[7, 4], Operations: ['69-9=60', '60/15=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,100 unequal: No Solution Moving to Node #0,4,2 Current State: 100:[7, 6], Operations: ['69-15=54', '54/9=6'] Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,100 unequal: No Solution Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,100 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,100 unequal: No Solution Moving to Node #0,2,4 Current State: 100:[9, 12], Operations: ['15+69=84', '84/7=12'] Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 9+12=21, Resulting Numbers: [21] 21,100 unequal: No Solution Exploring Operation: 9*12=108, Resulting Numbers: [108] 108,100 unequal: No Solution Moving to Node #0,4,3 Current State: 100:[9, 47], Operations: ['69-15=54', '54-7=47'] Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,100 unequal: No Solution Exploring Operation: 9+47=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 9*47=423, Resulting Numbers: [423] 423,100 unequal: No Solution Moving to Node #0,4,1 Current State: 100:[54, 2], Operations: ['69-15=54', '9-7=2'] Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,100 unequal: No Solution Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 54*2=108, Resulting Numbers: [108] 108,100 unequal: No Solution Moving to Node #0,3,1 Current State: 100:[7, 45], Operations: ['69-9=60', '60-15=45'] Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,100 unequal: No Solution Exploring Operation: 7*45=315, Resulting Numbers: [315] 315,100 unequal: No Solution Exploring Operation: 7+45=52, Resulting Numbers: [52] 52,100 unequal: No Solution Moving to Node #0,4,0 Current State: 100:[7, 45], Operations: ['69-15=54', '54-9=45'] Exploring Operation: 7+45=52, Resulting Numbers: [52] 52,100 unequal: No Solution Exploring Operation: 7*45=315, Resulting Numbers: [315] 315,100 unequal: No Solution Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,100 unequal: No Solution Moving to Node #0,1,0 Current State: 100:[7, 45], Operations: ['15+9=24', '69-24=45'] Exploring Operation: 7+45=52, Resulting Numbers: [52] 52,100 unequal: No Solution Exploring Operation: 7*45=315, Resulting Numbers: [315] 315,100 unequal: No Solution Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,100 unequal: No Solution Moving to Node #0,4,4 Current State: 100:[54, 16], Operations: ['69-15=54', '9+7=16'] Exploring Operation: 54+16=70, Resulting Numbers: [70] 70,100 unequal: No Solution Exploring Operation: 54-16=38, Resulting Numbers: [38] 38,100 unequal: No Solution Exploring Operation: 54*16=864, Resulting Numbers: [864] 864,100 unequal: No Solution Moving to Node #0,3,2 Current State: 100:[15, 53], Operations: ['69-9=60', '60-7=53'] Exploring Operation: 53-15=38, Resulting Numbers: [38] 38,100 unequal: No Solution Exploring Operation: 15+53=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 15*53=795, Resulting Numbers: [795] 795,100 unequal: No Solution Moving to Node #0,2,1 Current State: 100:[7, 93], Operations: ['15+69=84', '9+84=93'] Exploring Operation: 7*93=651, Resulting Numbers: [651] 651,100 unequal: No Solution Exploring Operation: 7+93=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[15, 69, 9, 7], Operations: [] Exploring Operation: 15+69=84, Resulting Numbers: [9, 7, 84] Generated Node #0,2: 100:[9, 7, 84] Operation: 15+69=84 Moving to Node #0,2 Current State: 100:[9, 7, 84], Operations: ['15+69=84'] Exploring Operation: 9+84=93, Resulting Numbers: [7, 93] Generated Node #0,2,1: 100:[7, 93] Operation: 9+84=93 Moving to Node #0,2,1 Current State: 100:[7, 93], Operations: ['15+69=84', '9+84=93'] Exploring Operation: 7+93=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.928819
hs_5
sum_heuristic
[ 11, 8, 89, 59 ]
10
[ "11-8=3", "89-59=30", "30/3=10" ]
Current State: 10:[11, 8, 89, 59], Operations: [] Exploring Operation: 11-8=3, Resulting Numbers: [89, 59, 3] Generated Node #2: [89, 59, 3] from Operation: 11-8=3 Current State: 10:[89, 59, 3], Operations: ['11-8=3'] Exploring Operation: 89-59=30, Resulting Numbers: [3, 30] Generated Node #3: [3, 30] from Operation: 89-59=30 Current State: 10:[3, 30], Operations: ['11-8=3', '89-59=30'] Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[11, 8, 89, 59], Operations: [] Exploring Operation: 89-59=30, Resulting Numbers: [11, 8, 30] Generated Node #0,0: 10:[11, 8, 30] Operation: 89-59=30 Exploring Operation: 89-8=81, Resulting Numbers: [11, 59, 81] Generated Node #0,1: 10:[11, 59, 81] Operation: 89-8=81 Exploring Operation: 59-11=48, Resulting Numbers: [8, 89, 48] Generated Node #0,2: 10:[8, 89, 48] Operation: 59-11=48 Exploring Operation: 89-11=78, Resulting Numbers: [8, 59, 78] Generated Node #0,3: 10:[8, 59, 78] Operation: 89-11=78 Moving to Node #0,0 Current State: 10:[11, 8, 30], Operations: ['89-59=30'] Exploring Operation: 30-11=19, Resulting Numbers: [8, 19] Generated Node #0,0,0: 10:[8, 19] Operation: 30-11=19 Exploring Operation: 30-8=22, Resulting Numbers: [11, 22] Generated Node #0,0,1: 10:[11, 22] Operation: 30-8=22 Exploring Operation: 11+8=19, Resulting Numbers: [30, 19] Generated Node #0,0,2: 10:[30, 19] Operation: 11+8=19 Exploring Operation: 11-8=3, Resulting Numbers: [30, 3] Generated Node #0,0,3: 10:[30, 3] Operation: 11-8=3 Moving to Node #0,3 Current State: 10:[8, 59, 78], Operations: ['89-11=78'] Exploring Operation: 8+59=67, Resulting Numbers: [78, 67] Generated Node #0,3,0: 10:[78, 67] Operation: 8+59=67 Exploring Operation: 78-8=70, Resulting Numbers: [59, 70] Generated Node #0,3,1: 10:[59, 70] Operation: 78-8=70 Exploring Operation: 78-59=19, Resulting Numbers: [8, 19] Generated Node #0,3,2: 10:[8, 19] Operation: 78-59=19 Exploring Operation: 59-8=51, Resulting Numbers: [78, 51] Generated Node #0,3,3: 10:[78, 51] Operation: 59-8=51 Moving to Node #0,2 Current State: 10:[8, 89, 48], Operations: ['59-11=48'] Exploring Operation: 48-8=40, Resulting Numbers: [89, 40] Generated Node #0,2,0: 10:[89, 40] Operation: 48-8=40 Exploring Operation: 89-8=81, Resulting Numbers: [48, 81] Generated Node #0,2,1: 10:[48, 81] Operation: 89-8=81 Exploring Operation: 89-48=41, Resulting Numbers: [8, 41] Generated Node #0,2,2: 10:[8, 41] Operation: 89-48=41 Exploring Operation: 48/8=6, Resulting Numbers: [89, 6] Generated Node #0,2,3: 10:[89, 6] Operation: 48/8=6 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 10:[8, 41], Operations: ['59-11=48', '89-48=41'] Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,10 unequal: No Solution Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,10 unequal: No Solution Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,10 unequal: No Solution No 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: 10:[89, 6], Operations: ['59-11=48', '48/8=6'] Exploring Operation: 89*6=534, Resulting Numbers: [534] 534,10 unequal: No Solution Exploring Operation: 89-6=83, Resulting Numbers: [83] 83,10 unequal: No Solution Exploring Operation: 89+6=95, Resulting Numbers: [95] 95,10 unequal: No Solution No 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: 10:[89, 40], Operations: ['59-11=48', '48-8=40'] Exploring Operation: 89*40=3560, Resulting Numbers: [3560] 3560,10 unequal: No Solution Exploring Operation: 89+40=129, Resulting Numbers: [129] 129,10 unequal: No Solution Exploring Operation: 89-40=49, Resulting Numbers: [49] 49,10 unequal: No Solution No 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: 10:[48, 81], Operations: ['59-11=48', '89-8=81'] Exploring Operation: 48*81=3888, Resulting Numbers: [3888] 3888,10 unequal: No Solution Exploring Operation: 81-48=33, Resulting Numbers: [33] 33,10 unequal: No Solution Exploring Operation: 48+81=129, Resulting Numbers: [129] 129,10 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: 10:[11, 59, 81], Operations: ['89-8=81'] Exploring Operation: 81-59=22, Resulting Numbers: [11, 22] Generated Node #0,1,0: 10:[11, 22] Operation: 81-59=22 Exploring Operation: 81-11=70, Resulting Numbers: [59, 70] Generated Node #0,1,1: 10:[59, 70] Operation: 81-11=70 Exploring Operation: 11+59=70, Resulting Numbers: [81, 70] Generated Node #0,1,2: 10:[81, 70] Operation: 11+59=70 Exploring Operation: 59-11=48, Resulting Numbers: [81, 48] Generated Node #0,1,3: 10:[81, 48] Operation: 59-11=48 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 10:[11, 22], Operations: ['89-8=81', '81-59=22'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,10 unequal: No Solution Exploring Operation: 11+22=33, Resulting Numbers: [33] 33,10 unequal: No Solution Exploring Operation: 11*22=242, Resulting Numbers: [242] 242,10 unequal: No Solution Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,10 unequal: No Solution No 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: 10:[59, 70], Operations: ['89-8=81', '81-11=70'] Exploring Operation: 70-59=11, Resulting Numbers: [11] 11,10 unequal: No Solution Exploring Operation: 59*70=4130, Resulting Numbers: [4130] 4130,10 unequal: No Solution Exploring Operation: 59+70=129, Resulting Numbers: [129] 129,10 unequal: No Solution No 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: 10:[81, 48], Operations: ['89-8=81', '59-11=48'] Exploring Operation: 81*48=3888, Resulting Numbers: [3888] 3888,10 unequal: No Solution Exploring Operation: 81-48=33, Resulting Numbers: [33] 33,10 unequal: No Solution Exploring Operation: 81+48=129, Resulting Numbers: [129] 129,10 unequal: No Solution No 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: 10:[81, 70], Operations: ['89-8=81', '11+59=70'] Exploring Operation: 81*70=5670, Resulting Numbers: [5670] 5670,10 unequal: No Solution Exploring Operation: 81-70=11, Resulting Numbers: [11] 11,10 unequal: No Solution Exploring Operation: 81+70=151, Resulting Numbers: [151] 151,10 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: 10:[8, 19], Operations: ['89-59=30', '30-11=19'] Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,10 unequal: No Solution Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,10 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,10 unequal: No Solution Moving to Node #0,3,2 Current State: 10:[8, 19], Operations: ['89-11=78', '78-59=19'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,10 unequal: No Solution Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,10 unequal: No Solution Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,10 unequal: No Solution Moving to Node #0,0,1 Current State: 10:[11, 22], Operations: ['89-59=30', '30-8=22'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,10 unequal: No Solution Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 11+22=33, Resulting Numbers: [33] 33,10 unequal: No Solution Exploring Operation: 11*22=242, Resulting Numbers: [242] 242,10 unequal: No Solution Moving to Node #0,0,3 Current State: 10:[30, 3], Operations: ['89-59=30', '11-8=3'] Exploring Operation: 30*3=90, Resulting Numbers: [90] 90,10 unequal: No Solution Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,10 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,10 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[11, 8, 89, 59], Operations: [] Exploring Operation: 89-59=30, Resulting Numbers: [11, 8, 30] Generated Node #0,0: 10:[11, 8, 30] Operation: 89-59=30 Moving to Node #0,0 Current State: 10:[11, 8, 30], Operations: ['89-59=30'] Exploring Operation: 11-8=3, Resulting Numbers: [30, 3] Generated Node #0,0,3: 10:[30, 3] Operation: 11-8=3 Moving to Node #0,0,3 Current State: 10:[30, 3], Operations: ['89-59=30', '11-8=3'] Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.945313
hs_4
mult_heuristic
[ 50, 80, 23, 95 ]
30
[ "80-23=57", "50*57=2850", "2850/95=30" ]
Current State: 30:[50, 80, 23, 95], Operations: [] Exploring Operation: 80-23=57, Resulting Numbers: [50, 95, 57] Generated Node #2: [50, 95, 57] from Operation: 80-23=57 Current State: 30:[50, 95, 57], Operations: ['80-23=57'] Exploring Operation: 50*57=2850, Resulting Numbers: [95, 2850] Generated Node #3: [95, 2850] from Operation: 50*57=2850 Current State: 30:[95, 2850], Operations: ['80-23=57', '50*57=2850'] Exploring Operation: 2850/95=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[50, 80, 23, 95], Operations: [] Exploring Operation: 95-80=15, Resulting Numbers: [50, 23, 15] Generated Node #0,0: 30:[50, 23, 15] Operation: 95-80=15 Exploring Operation: 80-50=30, Resulting Numbers: [23, 95, 30] Generated Node #0,1: 30:[23, 95, 30] Operation: 80-50=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[50, 23, 15], Operations: ['95-80=15'] Exploring Operation: 50-15=35, Resulting Numbers: [23, 35] Generated Node #0,0,0: 30:[23, 35] Operation: 50-15=35 Exploring Operation: 50-23=27, Resulting Numbers: [15, 27] Generated Node #0,0,1: 30:[15, 27] Operation: 50-23=27 Moving to Node #0,0,1 Current State: 30:[15, 27], Operations: ['95-80=15', '50-23=27'] Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 15+27=42, Resulting Numbers: [42] 42,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[23, 35], Operations: ['95-80=15', '50-15=35'] Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 23+35=58, Resulting Numbers: [58] 58,30 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:[23, 95, 30], Operations: ['80-50=30'] Exploring Operation: 95-23=72, Resulting Numbers: [30, 72] Generated Node #0,1,0: 30:[30, 72] Operation: 95-23=72 Exploring Operation: 95-30=65, Resulting Numbers: [23, 65] Generated Node #0,1,1: 30:[23, 65] Operation: 95-30=65 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[30, 72], Operations: ['80-50=30', '95-23=72'] Exploring Operation: 30+72=102, Resulting Numbers: [102] 102,30 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,30 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:[23, 65], Operations: ['80-50=30', '95-30=65'] Exploring Operation: 23+65=88, Resulting Numbers: [88] 88,30 unequal: No Solution Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,30 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
[ 25, 60, 10, 40 ]
30
[ "25*60=1500", "10+40=50", "1500/50=30" ]
Current State: 30:[25, 60, 10, 40], Operations: [] Exploring Operation: 25*60=1500, Resulting Numbers: [10, 40, 1500] Generated Node #2: [10, 40, 1500] from Operation: 25*60=1500 Current State: 30:[10, 40, 1500], Operations: ['25*60=1500'] Exploring Operation: 10+40=50, Resulting Numbers: [1500, 50] Generated Node #3: [1500, 50] from Operation: 10+40=50 Current State: 30:[1500, 50], Operations: ['25*60=1500', '10+40=50'] Exploring Operation: 1500/50=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[25, 60, 10, 40], Operations: [] Exploring Operation: 60-40=20, Resulting Numbers: [25, 10, 20] Generated Node #0,0: 30:[25, 10, 20] Operation: 60-40=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[25, 10, 20], Operations: ['60-40=20'] Exploring Operation: 25-20=5, Resulting Numbers: [10, 5] Generated Node #0,0,0: 30:[10, 5] Operation: 25-20=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[10, 5], Operations: ['60-40=20', '25-20=5'] Exploring Operation: 10+5=15, Resulting Numbers: [15] 15,30 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_1
sum_heuristic
[ 54, 76, 93, 16 ]
91
[ "54-16=38", "76/38=2", "93-2=91" ]
Current State: 91:[54, 76, 93, 16], Operations: [] Exploring Operation: 54-16=38, Resulting Numbers: [76, 93, 38] Generated Node #2: [76, 93, 38] from Operation: 54-16=38 Current State: 91:[76, 93, 38], Operations: ['54-16=38'] Exploring Operation: 76/38=2, Resulting Numbers: [93, 2] Generated Node #3: [93, 2] from Operation: 76/38=2 Current State: 91:[93, 2], Operations: ['54-16=38', '76/38=2'] Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[54, 76, 93, 16], Operations: [] Exploring Operation: 76-54=22, Resulting Numbers: [93, 16, 22] Generated Node #0,0: 91:[93, 16, 22] Operation: 76-54=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[93, 16, 22], Operations: ['76-54=22'] Exploring Operation: 22-16=6, Resulting Numbers: [93, 6] Generated Node #0,0,0: 91:[93, 6] Operation: 22-16=6 Moving to Node #0,0,0 Current State: 91:[93, 6], Operations: ['76-54=22', '22-16=6'] Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,91 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
[ 39, 94, 39, 58 ]
94
[ "39-39=0", "58*0=0", "94+0=94" ]
Current State: 94:[39, 94, 39, 58], Operations: [] Exploring Operation: 39-39=0, Resulting Numbers: [94, 58, 0] Generated Node #2: [94, 58, 0] from Operation: 39-39=0 Current State: 94:[94, 58, 0], Operations: ['39-39=0'] Exploring Operation: 58*0=0, Resulting Numbers: [94, 0] Generated Node #3: [94, 0] from Operation: 58*0=0 Current State: 94:[94, 0], Operations: ['39-39=0', '58*0=0'] Exploring Operation: 94+0=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[39, 94, 39, 58], Operations: [] Exploring Operation: 39+58=97, Resulting Numbers: [39, 94, 97] Generated Node #0,0: 94:[39, 94, 97] Operation: 39+58=97 Exploring Operation: 39/39=1, Resulting Numbers: [94, 58, 1] Generated Node #0,1: 94:[94, 58, 1] Operation: 39/39=1 Exploring Operation: 39+58=97, Resulting Numbers: [94, 39, 97] Generated Node #0,2: 94:[94, 39, 97] Operation: 39+58=97 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[39, 94, 97], Operations: ['39+58=97'] Exploring Operation: 97-39=58, Resulting Numbers: [94, 58] Generated Node #0,0,0: 94:[94, 58] Operation: 97-39=58 Exploring Operation: 94-39=55, Resulting Numbers: [97, 55] Generated Node #0,0,1: 94:[97, 55] Operation: 94-39=55 Exploring Operation: 97-94=3, Resulting Numbers: [39, 3] Generated Node #0,0,2: 94:[39, 3] Operation: 97-94=3 Moving to Node #0,0,2 Current State: 94:[39, 3], Operations: ['39+58=97', '97-94=3'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,94 unequal: No Solution Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[94, 58], Operations: ['39+58=97', '97-39=58'] Exploring Operation: 94+58=152, Resulting Numbers: [152] 152,94 unequal: No Solution Exploring Operation: 94*58=5452, Resulting Numbers: [5452] 5452,94 unequal: No Solution Exploring Operation: 94-58=36, Resulting Numbers: [36] 36,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[97, 55], Operations: ['39+58=97', '94-39=55'] Exploring Operation: 97*55=5335, Resulting Numbers: [5335] 5335,94 unequal: No Solution Exploring Operation: 97-55=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 97+55=152, Resulting Numbers: [152] 152,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[94, 39, 97], Operations: ['39+58=97'] Exploring Operation: 94-39=55, Resulting Numbers: [97, 55] Generated Node #0,2,0: 94:[97, 55] Operation: 94-39=55 Exploring Operation: 97-94=3, Resulting Numbers: [39, 3] Generated Node #0,2,1: 94:[39, 3] Operation: 97-94=3 Exploring Operation: 97-39=58, Resulting Numbers: [94, 58] Generated Node #0,2,2: 94:[94, 58] Operation: 97-39=58 Moving to Node #0,2,1 Current State: 94:[39, 3], Operations: ['39+58=97', '97-94=3'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,94 unequal: No Solution Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,94 unequal: No Solution Moving to Node #0,2,0 Current State: 94:[97, 55], Operations: ['39+58=97', '94-39=55'] Exploring Operation: 97+55=152, Resulting Numbers: [152] 152,94 unequal: No Solution Exploring Operation: 97-55=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 97*55=5335, Resulting Numbers: [5335] 5335,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[94, 58], Operations: ['39+58=97', '97-39=58'] Exploring Operation: 94+58=152, Resulting Numbers: [152] 152,94 unequal: No Solution Exploring Operation: 94*58=5452, Resulting Numbers: [5452] 5452,94 unequal: No Solution Exploring Operation: 94-58=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 #0,1 Current State: 94:[94, 58, 1], Operations: ['39/39=1'] Exploring Operation: 58-1=57, Resulting Numbers: [94, 57] Generated Node #0,1,0: 94:[94, 57] Operation: 58-1=57 Exploring Operation: 94*1=94, Resulting Numbers: [58, 94] Generated Node #0,1,1: 94:[58, 94] Operation: 94*1=94 Exploring Operation: 94/1=94, Resulting Numbers: [58, 94] Generated Node #0,1,2: 94:[58, 94] Operation: 94/1=94 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[94, 57], Operations: ['39/39=1', '58-1=57'] Exploring Operation: 94-57=37, Resulting Numbers: [37] 37,94 unequal: No Solution Exploring Operation: 94+57=151, Resulting Numbers: [151] 151,94 unequal: No Solution Exploring Operation: 94*57=5358, Resulting Numbers: [5358] 5358,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[58, 94], Operations: ['39/39=1', '94*1=94'] Exploring Operation: 58+94=152, Resulting Numbers: [152] 152,94 unequal: No Solution Exploring Operation: 58*94=5452, Resulting Numbers: [5452] 5452,94 unequal: No Solution Exploring Operation: 94-58=36, Resulting Numbers: [36] 36,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 94:[58, 94], Operations: ['39/39=1', '94/1=94'] Exploring Operation: 94-58=36, Resulting Numbers: [36] 36,94 unequal: No Solution Exploring Operation: 58*94=5452, Resulting Numbers: [5452] 5452,94 unequal: No Solution Exploring Operation: 58+94=152, Resulting Numbers: [152] 152,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 24, 25, 75, 36 ]
39
[ "25-24=1", "75-36=39", "1*39=39" ]
Current State: 39:[24, 25, 75, 36], Operations: [] Exploring Operation: 25-24=1, Resulting Numbers: [75, 36, 1] Generated Node #2: [75, 36, 1] from Operation: 25-24=1 Current State: 39:[75, 36, 1], Operations: ['25-24=1'] Exploring Operation: 75-36=39, Resulting Numbers: [1, 39] Generated Node #3: [1, 39] from Operation: 75-36=39 Current State: 39:[1, 39], Operations: ['25-24=1', '75-36=39'] Exploring Operation: 1*39=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[24, 25, 75, 36], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [24, 36, 3] Generated Node #0,0: 39:[24, 36, 3] Operation: 75/25=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[24, 36, 3], Operations: ['75/25=3'] Exploring Operation: 36-24=12, Resulting Numbers: [3, 12] Generated Node #0,0,0: 39:[3, 12] Operation: 36-24=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[3, 12], Operations: ['75/25=3', '36-24=12'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,39 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_1
mult_heuristic
[ 19, 28, 19, 31 ]
31
[ "19-19=0", "28*0=0", "31+0=31" ]
Current State: 31:[19, 28, 19, 31], Operations: [] Exploring Operation: 19-19=0, Resulting Numbers: [28, 31, 0] Generated Node #2: [28, 31, 0] from Operation: 19-19=0 Current State: 31:[28, 31, 0], Operations: ['19-19=0'] Exploring Operation: 28*0=0, Resulting Numbers: [31, 0] Generated Node #3: [31, 0] from Operation: 28*0=0 Current State: 31:[31, 0], Operations: ['19-19=0', '28*0=0'] Exploring Operation: 31+0=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[19, 28, 19, 31], Operations: [] Exploring Operation: 19+19=38, Resulting Numbers: [28, 31, 38] Generated Node #0,0: 31:[28, 31, 38] Operation: 19+19=38 Exploring Operation: 19/19=1, Resulting Numbers: [28, 31, 1] Generated Node #0,1: 31:[28, 31, 1] Operation: 19/19=1 Exploring Operation: 19+28=47, Resulting Numbers: [19, 31, 47] Generated Node #0,2: 31:[19, 31, 47] Operation: 19+28=47 Exploring Operation: 28-19=9, Resulting Numbers: [19, 31, 9] Generated Node #0,3: 31:[19, 31, 9] Operation: 28-19=9 Exploring Operation: 28+19=47, Resulting Numbers: [19, 31, 47] Generated Node #0,4: 31:[19, 31, 47] Operation: 28+19=47 Moving to Node #0,0 Current State: 31:[28, 31, 38], Operations: ['19+19=38'] Exploring Operation: 31-28=3, Resulting Numbers: [38, 3] Generated Node #0,0,0: 31:[38, 3] Operation: 31-28=3 Exploring Operation: 28+31=59, Resulting Numbers: [38, 59] Generated Node #0,0,1: 31:[38, 59] Operation: 28+31=59 Exploring Operation: 38-28=10, Resulting Numbers: [31, 10] Generated Node #0,0,2: 31:[31, 10] Operation: 38-28=10 Exploring Operation: 28+38=66, Resulting Numbers: [31, 66] Generated Node #0,0,3: 31:[31, 66] Operation: 28+38=66 Exploring Operation: 38-31=7, Resulting Numbers: [28, 7] Generated Node #0,0,4: 31:[28, 7] Operation: 38-31=7 Moving to Node #0,4 Current State: 31:[19, 31, 47], Operations: ['28+19=47'] Exploring Operation: 19+47=66, Resulting Numbers: [31, 66] Generated Node #0,4,0: 31:[31, 66] Operation: 19+47=66 Exploring Operation: 47-19=28, Resulting Numbers: [31, 28] Generated Node #0,4,1: 31:[31, 28] Operation: 47-19=28 Exploring Operation: 47-31=16, Resulting Numbers: [19, 16] Generated Node #0,4,2: 31:[19, 16] Operation: 47-31=16 Exploring Operation: 31-19=12, Resulting Numbers: [47, 12] Generated Node #0,4,3: 31:[47, 12] Operation: 31-19=12 Exploring Operation: 19+31=50, Resulting Numbers: [47, 50] Generated Node #0,4,4: 31:[47, 50] Operation: 19+31=50 Moving to Node #0,2 Current State: 31:[19, 31, 47], Operations: ['19+28=47'] Exploring Operation: 47-19=28, Resulting Numbers: [31, 28] Generated Node #0,2,0: 31:[31, 28] Operation: 47-19=28 Exploring Operation: 19+31=50, Resulting Numbers: [47, 50] Generated Node #0,2,1: 31:[47, 50] Operation: 19+31=50 Exploring Operation: 31-19=12, Resulting Numbers: [47, 12] Generated Node #0,2,2: 31:[47, 12] Operation: 31-19=12 Exploring Operation: 47-31=16, Resulting Numbers: [19, 16] Generated Node #0,2,3: 31:[19, 16] Operation: 47-31=16 Exploring Operation: 19+47=66, Resulting Numbers: [31, 66] Generated Node #0,2,4: 31:[31, 66] Operation: 19+47=66 Moving to Node #0,1 Current State: 31:[28, 31, 1], Operations: ['19/19=1'] Exploring Operation: 31*1=31, Resulting Numbers: [28, 31] Generated Node #0,1,0: 31:[28, 31] Operation: 31*1=31 Exploring Operation: 31/1=31, Resulting Numbers: [28, 31] Generated Node #0,1,1: 31:[28, 31] Operation: 31/1=31 Exploring Operation: 28/1=28, Resulting Numbers: [31, 28] Generated Node #0,1,2: 31:[31, 28] Operation: 28/1=28 Exploring Operation: 28+1=29, Resulting Numbers: [31, 29] Generated Node #0,1,3: 31:[31, 29] Operation: 28+1=29 Exploring Operation: 28*1=28, Resulting Numbers: [31, 28] Generated Node #0,1,4: 31:[31, 28] Operation: 28*1=28 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 31:[31, 29], Operations: ['19/19=1', '28+1=29'] Exploring Operation: 31-29=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 31*29=899, Resulting Numbers: [899] 899,31 unequal: No Solution Exploring Operation: 31+29=60, Resulting Numbers: [60] 60,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[28, 31], Operations: ['19/19=1', '31*1=31'] Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 28+31=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 28*31=868, Resulting Numbers: [868] 868,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[28, 31], Operations: ['19/19=1', '31/1=31'] Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 28*31=868, Resulting Numbers: [868] 868,31 unequal: No Solution Exploring Operation: 28+31=59, Resulting Numbers: [59] 59,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[31, 28], Operations: ['19/19=1', '28/1=28'] Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,31 unequal: No Solution Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 31:[31, 28], Operations: ['19/19=1', '28*1=28'] Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,31 unequal: No Solution Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,31 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: 31:[19, 31, 9], Operations: ['28-19=9'] Exploring Operation: 19+31=50, Resulting Numbers: [9, 50] Generated Node #0,3,0: 31:[9, 50] Operation: 19+31=50 Exploring Operation: 19+9=28, Resulting Numbers: [31, 28] Generated Node #0,3,1: 31:[31, 28] Operation: 19+9=28 Exploring Operation: 19-9=10, Resulting Numbers: [31, 10] Generated Node #0,3,2: 31:[31, 10] Operation: 19-9=10 Exploring Operation: 31-9=22, Resulting Numbers: [19, 22] Generated Node #0,3,3: 31:[19, 22] Operation: 31-9=22 Exploring Operation: 31+9=40, Resulting Numbers: [19, 40] Generated Node #0,3,4: 31:[19, 40] Operation: 31+9=40 Moving to Node #0,4,1 Current State: 31:[31, 28], Operations: ['28+19=47', '47-19=28'] Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,31 unequal: No Solution Moving to Node #0,2,0 Current State: 31:[31, 28], Operations: ['19+28=47', '47-19=28'] Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,31 unequal: No Solution Moving to Node #0,3,1 Current State: 31:[31, 28], Operations: ['28-19=9', '19+9=28'] Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[31, 10], Operations: ['19+19=38', '38-28=10'] Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 31*10=310, Resulting Numbers: [310] 310,31 unequal: No Solution Exploring Operation: 31+10=41, Resulting Numbers: [41] 41,31 unequal: No Solution Moving to Node #0,3,3 Current State: 31:[19, 22], Operations: ['28-19=9', '31-9=22'] Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,31 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 19*22=418, Resulting Numbers: [418] 418,31 unequal: No Solution Moving to Node #0,3,4 Current State: 31:[19, 40], Operations: ['28-19=9', '31+9=40'] Exploring Operation: 19+40=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 19*40=760, Resulting Numbers: [760] 760,31 unequal: No Solution Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,31 unequal: No Solution Moving to Node #0,3,2 Current State: 31:[31, 10], Operations: ['28-19=9', '19-9=10'] Exploring Operation: 31*10=310, Resulting Numbers: [310] 310,31 unequal: No Solution Exploring Operation: 31+10=41, Resulting Numbers: [41] 41,31 unequal: No Solution Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,31 unequal: No Solution Moving to Node #0,4,2 Current State: 31:[19, 16], Operations: ['28+19=47', '47-31=16'] Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 19+16=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 19*16=304, Resulting Numbers: [304] 304,31 unequal: No Solution Moving to Node #0,2,3 Current State: 31:[19, 16], Operations: ['19+28=47', '47-31=16'] Exploring Operation: 19*16=304, Resulting Numbers: [304] 304,31 unequal: No Solution Exploring Operation: 19+16=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,31 unequal: No Solution Moving to Node #0,0,4 Current State: 31:[28, 7], Operations: ['19+19=38', '38-31=7'] Exploring Operation: 28+7=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 28*7=196, Resulting Numbers: [196] 196,31 unequal: No Solution Moving to Node #0,2,4 Current State: 31:[31, 66], Operations: ['19+28=47', '19+47=66'] Exploring Operation: 31+66=97, Resulting Numbers: [97] 97,31 unequal: No Solution Exploring Operation: 66-31=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 31*66=2046, Resulting Numbers: [2046] 2046,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[47, 12], Operations: ['19+28=47', '31-19=12'] Exploring Operation: 47+12=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 47*12=564, Resulting Numbers: [564] 564,31 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,31 unequal: No Solution Moving to Node #0,2,1 Current State: 31:[47, 50], Operations: ['19+28=47', '19+31=50'] Exploring Operation: 47+50=97, Resulting Numbers: [97] 97,31 unequal: No Solution Exploring Operation: 50-47=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 47*50=2350, Resulting Numbers: [2350] 2350,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[38, 3], Operations: ['19+19=38', '31-28=3'] Exploring Operation: 38*3=114, Resulting Numbers: [114] 114,31 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 38+3=41, Resulting Numbers: [41] 41,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[38, 59], Operations: ['19+19=38', '28+31=59'] Exploring Operation: 59-38=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 38*59=2242, Resulting Numbers: [2242] 2242,31 unequal: No Solution Exploring Operation: 38+59=97, Resulting Numbers: [97] 97,31 unequal: No Solution Moving to Node #0,4,0 Current State: 31:[31, 66], Operations: ['28+19=47', '19+47=66'] Exploring Operation: 66-31=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 31*66=2046, Resulting Numbers: [2046] 2046,31 unequal: No Solution Exploring Operation: 31+66=97, Resulting Numbers: [97] 97,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[31, 66], Operations: ['19+19=38', '28+38=66'] Exploring Operation: 31+66=97, Resulting Numbers: [97] 97,31 unequal: No Solution Exploring Operation: 31*66=2046, Resulting Numbers: [2046] 2046,31 unequal: No Solution Exploring Operation: 66-31=35, Resulting Numbers: [35] 35,31 unequal: No Solution Moving to Node #0,4,3 Current State: 31:[47, 12], Operations: ['28+19=47', '31-19=12'] Exploring Operation: 47*12=564, Resulting Numbers: [564] 564,31 unequal: No Solution Exploring Operation: 47+12=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,31 unequal: No Solution Moving to Node #0,4,4 Current State: 31:[47, 50], Operations: ['28+19=47', '19+31=50'] Exploring Operation: 47*50=2350, Resulting Numbers: [2350] 2350,31 unequal: No Solution Exploring Operation: 50-47=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 47+50=97, Resulting Numbers: [97] 97,31 unequal: No Solution Moving to Node #0,3,0 Current State: 31:[9, 50], Operations: ['28-19=9', '19+31=50'] Exploring Operation: 9*50=450, Resulting Numbers: [450] 450,31 unequal: No Solution Exploring Operation: 9+50=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 50-9=41, Resulting Numbers: [41] 41,31 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 94, 43, 7, 66 ]
29
[ "94+43=137", "66+137=203", "203/7=29" ]
Current State: 29:[94, 43, 7, 66], Operations: [] Exploring Operation: 94+43=137, Resulting Numbers: [7, 66, 137] Generated Node #2: [7, 66, 137] from Operation: 94+43=137 Current State: 29:[7, 66, 137], Operations: ['94+43=137'] Exploring Operation: 66+137=203, Resulting Numbers: [7, 203] Generated Node #3: [7, 203] from Operation: 66+137=203 Current State: 29:[7, 203], Operations: ['94+43=137', '66+137=203'] Exploring Operation: 203/7=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[94, 43, 7, 66], Operations: [] Exploring Operation: 43-7=36, Resulting Numbers: [94, 66, 36] Generated Node #0,0: 29:[94, 66, 36] Operation: 43-7=36 Exploring Operation: 66-43=23, Resulting Numbers: [94, 7, 23] Generated Node #0,1: 29:[94, 7, 23] Operation: 66-43=23 Exploring Operation: 94-66=28, Resulting Numbers: [43, 7, 28] Generated Node #0,2: 29:[43, 7, 28] Operation: 94-66=28 Exploring Operation: 94-43=51, Resulting Numbers: [7, 66, 51] Generated Node #0,3: 29:[7, 66, 51] Operation: 94-43=51 Exploring Operation: 94-7=87, Resulting Numbers: [43, 66, 87] Generated Node #0,4: 29:[43, 66, 87] Operation: 94-7=87 Start Sub Search at level 1: Moving to Node #0,2 Current State: 29:[43, 7, 28], Operations: ['94-66=28'] Exploring Operation: 43-28=15, Resulting Numbers: [7, 15] Generated Node #0,2,0: 29:[7, 15] Operation: 43-28=15 Exploring Operation: 43-7=36, Resulting Numbers: [28, 36] Generated Node #0,2,1: 29:[28, 36] Operation: 43-7=36 Exploring Operation: 28-7=21, Resulting Numbers: [43, 21] Generated Node #0,2,2: 29:[43, 21] Operation: 28-7=21 Exploring Operation: 43+7=50, Resulting Numbers: [28, 50] Generated Node #0,2,3: 29:[28, 50] Operation: 43+7=50 Exploring Operation: 7+28=35, Resulting Numbers: [43, 35] Generated Node #0,2,4: 29:[43, 35] Operation: 7+28=35 Moving to Node #0,2,1 Current State: 29:[28, 36], Operations: ['94-66=28', '43-7=36'] Exploring Operation: 28*36=1008, Resulting Numbers: [1008] 1008,29 unequal: No Solution Exploring Operation: 28+36=64, Resulting Numbers: [64] 64,29 unequal: No Solution Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,29 unequal: No Solution Moving to Node #0,2,4 Current State: 29:[43, 35], Operations: ['94-66=28', '7+28=35'] Exploring Operation: 43+35=78, Resulting Numbers: [78] 78,29 unequal: No Solution Exploring Operation: 43*35=1505, Resulting Numbers: [1505] 1505,29 unequal: No Solution Exploring Operation: 43-35=8, Resulting Numbers: [8] 8,29 unequal: No Solution Moving to Node #0,2,2 Current State: 29:[43, 21], Operations: ['94-66=28', '28-7=21'] Exploring Operation: 43*21=903, Resulting Numbers: [903] 903,29 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 43+21=64, Resulting Numbers: [64] 64,29 unequal: No Solution Moving to Node #0,2,3 Current State: 29:[28, 50], Operations: ['94-66=28', '43+7=50'] Exploring Operation: 28+50=78, Resulting Numbers: [78] 78,29 unequal: No Solution Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 28*50=1400, Resulting Numbers: [1400] 1400,29 unequal: No Solution Moving to Node #0,2,0 Current State: 29:[7, 15], Operations: ['94-66=28', '43-28=15'] Exploring Operation: 7*15=105, Resulting Numbers: [105] 105,29 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,29 unequal: No Solution Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,29 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 #0,3 Current State: 29:[7, 66, 51], Operations: ['94-43=51'] Exploring Operation: 7+66=73, Resulting Numbers: [51, 73] Generated Node #0,3,0: 29:[51, 73] Operation: 7+66=73 Exploring Operation: 51-7=44, Resulting Numbers: [66, 44] Generated Node #0,3,1: 29:[66, 44] Operation: 51-7=44 Exploring Operation: 7+51=58, Resulting Numbers: [66, 58] Generated Node #0,3,2: 29:[66, 58] Operation: 7+51=58 Exploring Operation: 66-7=59, Resulting Numbers: [51, 59] Generated Node #0,3,3: 29:[51, 59] Operation: 66-7=59 Exploring Operation: 66-51=15, Resulting Numbers: [7, 15] Generated Node #0,3,4: 29:[7, 15] Operation: 66-51=15 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 29:[7, 15], Operations: ['94-43=51', '66-51=15'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,29 unequal: No Solution Exploring Operation: 7*15=105, Resulting Numbers: [105] 105,29 unequal: No Solution Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,29 unequal: No Solution No 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: 29:[66, 44], Operations: ['94-43=51', '51-7=44'] Exploring Operation: 66+44=110, Resulting Numbers: [110] 110,29 unequal: No Solution Exploring Operation: 66-44=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 66*44=2904, Resulting Numbers: [2904] 2904,29 unequal: No Solution No 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: 29:[51, 59], Operations: ['94-43=51', '66-7=59'] Exploring Operation: 59-51=8, Resulting Numbers: [8] 8,29 unequal: No Solution Exploring Operation: 51+59=110, Resulting Numbers: [110] 110,29 unequal: No Solution Exploring Operation: 51*59=3009, Resulting Numbers: [3009] 3009,29 unequal: No Solution No 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: 29:[51, 73], Operations: ['94-43=51', '7+66=73'] Exploring Operation: 51*73=3723, Resulting Numbers: [3723] 3723,29 unequal: No Solution Exploring Operation: 73-51=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 51+73=124, Resulting Numbers: [124] 124,29 unequal: No Solution No 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: 29:[66, 58], Operations: ['94-43=51', '7+51=58'] Exploring Operation: 66+58=124, Resulting Numbers: [124] 124,29 unequal: No Solution Exploring Operation: 66*58=3828, Resulting Numbers: [3828] 3828,29 unequal: No Solution Exploring Operation: 66-58=8, Resulting Numbers: [8] 8,29 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: 29:[94, 7, 23], Operations: ['66-43=23'] Exploring Operation: 23-7=16, Resulting Numbers: [94, 16] Generated Node #0,1,0: 29:[94, 16] Operation: 23-7=16 Exploring Operation: 7+23=30, Resulting Numbers: [94, 30] Generated Node #0,1,1: 29:[94, 30] Operation: 7+23=30 Exploring Operation: 94-7=87, Resulting Numbers: [23, 87] Generated Node #0,1,2: 29:[23, 87] Operation: 94-7=87 Exploring Operation: 94+7=101, Resulting Numbers: [23, 101] Generated Node #0,1,3: 29:[23, 101] Operation: 94+7=101 Exploring Operation: 94-23=71, Resulting Numbers: [7, 71] Generated Node #0,1,4: 29:[7, 71] Operation: 94-23=71 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 29:[23, 87], Operations: ['66-43=23', '94-7=87'] Exploring Operation: 23+87=110, Resulting Numbers: [110] 110,29 unequal: No Solution Exploring Operation: 23*87=2001, Resulting Numbers: [2001] 2001,29 unequal: No Solution Exploring Operation: 87-23=64, Resulting Numbers: [64] 64,29 unequal: No Solution No 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: 29:[7, 71], Operations: ['66-43=23', '94-23=71'] Exploring Operation: 7*71=497, Resulting Numbers: [497] 497,29 unequal: No Solution Exploring Operation: 7+71=78, Resulting Numbers: [78] 78,29 unequal: No Solution Exploring Operation: 71-7=64, Resulting Numbers: [64] 64,29 unequal: No Solution No 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: 29:[94, 30], Operations: ['66-43=23', '7+23=30'] Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,29 unequal: No Solution Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,29 unequal: No Solution Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,29 unequal: No Solution No 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: 29:[94, 16], Operations: ['66-43=23', '23-7=16'] Exploring Operation: 94+16=110, Resulting Numbers: [110] 110,29 unequal: No Solution Exploring Operation: 94-16=78, Resulting Numbers: [78] 78,29 unequal: No Solution Exploring Operation: 94*16=1504, Resulting Numbers: [1504] 1504,29 unequal: No Solution No 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: 29:[23, 101], Operations: ['66-43=23', '94+7=101'] Exploring Operation: 101-23=78, Resulting Numbers: [78] 78,29 unequal: No Solution Exploring Operation: 23*101=2323, Resulting Numbers: [2323] 2323,29 unequal: No Solution Exploring Operation: 23+101=124, Resulting Numbers: [124] 124,29 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: 29:[94, 66, 36], Operations: ['43-7=36'] Exploring Operation: 94-36=58, Resulting Numbers: [66, 58] Generated Node #0,0,0: 29:[66, 58] Operation: 94-36=58 Exploring Operation: 94+66=160, Resulting Numbers: [36, 160] Generated Node #0,0,1: 29:[36, 160] Operation: 94+66=160 Exploring Operation: 94+36=130, Resulting Numbers: [66, 130] Generated Node #0,0,2: 29:[66, 130] Operation: 94+36=130 Exploring Operation: 94-66=28, Resulting Numbers: [36, 28] Generated Node #0,0,3: 29:[36, 28] Operation: 94-66=28 Exploring Operation: 66-36=30, Resulting Numbers: [94, 30] Generated Node #0,0,4: 29:[94, 30] Operation: 66-36=30 Moving to Node #0,0,3 Current State: 29:[36, 28], Operations: ['43-7=36', '94-66=28'] Exploring Operation: 36*28=1008, Resulting Numbers: [1008] 1008,29 unequal: No Solution Exploring Operation: 36+28=64, Resulting Numbers: [64] 64,29 unequal: No Solution Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,29 unequal: No Solution Moving to Node #0,0,4 Current State: 29:[94, 30], Operations: ['43-7=36', '66-36=30'] Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,29 unequal: No Solution Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,29 unequal: No Solution Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[66, 58], Operations: ['43-7=36', '94-36=58'] Exploring Operation: 66+58=124, Resulting Numbers: [124] 124,29 unequal: No Solution Exploring Operation: 66-58=8, Resulting Numbers: [8] 8,29 unequal: No Solution Exploring Operation: 66*58=3828, Resulting Numbers: [3828] 3828,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[36, 160], Operations: ['43-7=36', '94+66=160'] Exploring Operation: 36+160=196, Resulting Numbers: [196] 196,29 unequal: No Solution Exploring Operation: 36*160=5760, Resulting Numbers: [5760] 5760,29 unequal: No Solution Exploring Operation: 160-36=124, Resulting Numbers: [124] 124,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[66, 130], Operations: ['43-7=36', '94+36=130'] Exploring Operation: 66+130=196, Resulting Numbers: [196] 196,29 unequal: No Solution Exploring Operation: 66*130=8580, Resulting Numbers: [8580] 8580,29 unequal: No Solution Exploring Operation: 130-66=64, Resulting Numbers: [64] 64,29 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 #0,4 Current State: 29:[43, 66, 87], Operations: ['94-7=87'] Exploring Operation: 87-66=21, Resulting Numbers: [43, 21] Generated Node #0,4,0: 29:[43, 21] Operation: 87-66=21 Exploring Operation: 43+87=130, Resulting Numbers: [66, 130] Generated Node #0,4,1: 29:[66, 130] Operation: 43+87=130 Exploring Operation: 66-43=23, Resulting Numbers: [87, 23] Generated Node #0,4,2: 29:[87, 23] Operation: 66-43=23 Exploring Operation: 43+66=109, Resulting Numbers: [87, 109] Generated Node #0,4,3: 29:[87, 109] Operation: 43+66=109 Exploring Operation: 87-43=44, Resulting Numbers: [66, 44] Generated Node #0,4,4: 29:[66, 44] Operation: 87-43=44 Moving to Node #0,4,0 Current State: 29:[43, 21], Operations: ['94-7=87', '87-66=21'] Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 43*21=903, Resulting Numbers: [903] 903,29 unequal: No Solution Exploring Operation: 43+21=64, Resulting Numbers: [64] 64,29 unequal: No Solution Moving to Node #0,4,4 Current State: 29:[66, 44], Operations: ['94-7=87', '87-43=44'] Exploring Operation: 66-44=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 66+44=110, Resulting Numbers: [110] 110,29 unequal: No Solution Exploring Operation: 66*44=2904, Resulting Numbers: [2904] 2904,29 unequal: No Solution Moving to Node #0,4,2 Current State: 29:[87, 23], Operations: ['94-7=87', '66-43=23'] Exploring Operation: 87+23=110, Resulting Numbers: [110] 110,29 unequal: No Solution Exploring Operation: 87-23=64, Resulting Numbers: [64] 64,29 unequal: No Solution Exploring Operation: 87*23=2001, Resulting Numbers: [2001] 2001,29 unequal: No Solution Moving to Node #0,4,1 Current State: 29:[66, 130], Operations: ['94-7=87', '43+87=130'] Exploring Operation: 66*130=8580, Resulting Numbers: [8580] 8580,29 unequal: No Solution Exploring Operation: 66+130=196, Resulting Numbers: [196] 196,29 unequal: No Solution Exploring Operation: 130-66=64, Resulting Numbers: [64] 64,29 unequal: No Solution Moving to Node #0,4,3 Current State: 29:[87, 109], Operations: ['94-7=87', '43+66=109'] Exploring Operation: 109-87=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 87*109=9483, Resulting Numbers: [9483] 9483,29 unequal: No Solution Exploring Operation: 87+109=196, Resulting Numbers: [196] 196,29 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
[ 22, 38, 2, 68 ]
82
[ "38-22=16", "68-2=66", "16+66=82" ]
Current State: 82:[22, 38, 2, 68], Operations: [] Exploring Operation: 38-22=16, Resulting Numbers: [2, 68, 16] Generated Node #2: [2, 68, 16] from Operation: 38-22=16 Current State: 82:[2, 68, 16], Operations: ['38-22=16'] Exploring Operation: 68-2=66, Resulting Numbers: [16, 66] Generated Node #3: [16, 66] from Operation: 68-2=66 Current State: 82:[16, 66], Operations: ['38-22=16', '68-2=66'] Exploring Operation: 16+66=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[22, 38, 2, 68], Operations: [] Exploring Operation: 22+68=90, Resulting Numbers: [38, 2, 90] Generated Node #0,0: 82:[38, 2, 90] Operation: 22+68=90 Exploring Operation: 68-22=46, Resulting Numbers: [38, 2, 46] Generated Node #0,1: 82:[38, 2, 46] Operation: 68-22=46 Moving to Node #0,1 Current State: 82:[38, 2, 46], Operations: ['68-22=46'] Exploring Operation: 38+46=84, Resulting Numbers: [2, 84] Generated Node #0,1,0: 82:[2, 84] Operation: 38+46=84 Exploring Operation: 38+2=40, Resulting Numbers: [46, 40] Generated Node #0,1,1: 82:[46, 40] Operation: 38+2=40 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 82:[2, 84], Operations: ['68-22=46', '38+46=84'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[22, 38, 2, 68], Operations: [] Exploring Operation: 68-22=46, Resulting Numbers: [38, 2, 46] Generated Node #0,1: 82:[38, 2, 46] Operation: 68-22=46 Moving to Node #0,1 Current State: 82:[38, 2, 46], Operations: ['68-22=46'] Exploring Operation: 38+46=84, Resulting Numbers: [2, 84] Generated Node #0,1,0: 82:[2, 84] Operation: 38+46=84 Moving to Node #0,1,0 Current State: 82:[2, 84], Operations: ['68-22=46', '38+46=84'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 4, 14, 72, 48 ]
82
[ "72-48=24", "4*24=96", "96-14=82" ]
Current State: 82:[4, 14, 72, 48], Operations: [] Exploring Operation: 72-48=24, Resulting Numbers: [4, 14, 24] Generated Node #2: [4, 14, 24] from Operation: 72-48=24 Current State: 82:[4, 14, 24], Operations: ['72-48=24'] Exploring Operation: 4*24=96, Resulting Numbers: [14, 96] Generated Node #3: [14, 96] from Operation: 4*24=96 Current State: 82:[14, 96], Operations: ['72-48=24', '4*24=96'] Exploring Operation: 96-14=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[4, 14, 72, 48], Operations: [] Exploring Operation: 14+72=86, Resulting Numbers: [4, 48, 86] Generated Node #0,0: 82:[4, 48, 86] Operation: 14+72=86 Exploring Operation: 14-4=10, Resulting Numbers: [72, 48, 10] Generated Node #0,1: 82:[72, 48, 10] Operation: 14-4=10 Exploring Operation: 4+72=76, Resulting Numbers: [14, 48, 76] Generated Node #0,2: 82:[14, 48, 76] Operation: 4+72=76 Exploring Operation: 48-14=34, Resulting Numbers: [4, 72, 34] Generated Node #0,3: 82:[4, 72, 34] Operation: 48-14=34 Exploring Operation: 48-4=44, Resulting Numbers: [14, 72, 44] Generated Node #0,4: 82:[14, 72, 44] Operation: 48-4=44 Moving to Node #0,0 Current State: 82:[4, 48, 86], Operations: ['14+72=86'] Exploring Operation: 4+48=52, Resulting Numbers: [86, 52] Generated Node #0,0,0: 82:[86, 52] Operation: 4+48=52 Exploring Operation: 48-4=44, Resulting Numbers: [86, 44] Generated Node #0,0,1: 82:[86, 44] Operation: 48-4=44 Exploring Operation: 86-4=82, Resulting Numbers: [48, 82] Generated Node #0,0,2: 82:[48, 82] Operation: 86-4=82 Exploring Operation: 86-48=38, Resulting Numbers: [4, 38] Generated Node #0,0,3: 82:[4, 38] Operation: 86-48=38 Exploring Operation: 48/4=12, Resulting Numbers: [86, 12] Generated Node #0,0,4: 82:[86, 12] Operation: 48/4=12 Moving to Node #0,3 Current State: 82:[4, 72, 34], Operations: ['48-14=34'] Exploring Operation: 72-34=38, Resulting Numbers: [4, 38] Generated Node #0,3,0: 82:[4, 38] Operation: 72-34=38 Exploring Operation: 72-4=68, Resulting Numbers: [34, 68] Generated Node #0,3,1: 82:[34, 68] Operation: 72-4=68 Exploring Operation: 34-4=30, Resulting Numbers: [72, 30] Generated Node #0,3,2: 82:[72, 30] Operation: 34-4=30 Exploring Operation: 4+34=38, Resulting Numbers: [72, 38] Generated Node #0,3,3: 82:[72, 38] Operation: 4+34=38 Exploring Operation: 4+72=76, Resulting Numbers: [34, 76] Generated Node #0,3,4: 82:[34, 76] Operation: 4+72=76 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 82:[4, 38], Operations: ['48-14=34', '72-34=38'] Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,82 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 82:[72, 38], Operations: ['48-14=34', '4+34=38'] Exploring Operation: 72*38=2736, Resulting Numbers: [2736] 2736,82 unequal: No Solution Exploring Operation: 72+38=110, Resulting Numbers: [110] 110,82 unequal: No Solution Exploring Operation: 72-38=34, Resulting Numbers: [34] 34,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 82:[34, 76], Operations: ['48-14=34', '4+72=76'] Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 34+76=110, Resulting Numbers: [110] 110,82 unequal: No Solution Exploring Operation: 34*76=2584, Resulting Numbers: [2584] 2584,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 82:[34, 68], Operations: ['48-14=34', '72-4=68'] Exploring Operation: 68-34=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 34+68=102, Resulting Numbers: [102] 102,82 unequal: No Solution Exploring Operation: 34*68=2312, Resulting Numbers: [2312] 2312,82 unequal: No Solution Exploring Operation: 68/34=2, Resulting Numbers: [2] 2,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 82:[72, 30], Operations: ['48-14=34', '34-4=30'] Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 72*30=2160, Resulting Numbers: [2160] 2160,82 unequal: No Solution Exploring Operation: 72+30=102, Resulting Numbers: [102] 102,82 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: 82:[72, 48, 10], Operations: ['14-4=10'] Exploring Operation: 48+10=58, Resulting Numbers: [72, 58] Generated Node #0,1,0: 82:[72, 58] Operation: 48+10=58 Exploring Operation: 48-10=38, Resulting Numbers: [72, 38] Generated Node #0,1,1: 82:[72, 38] Operation: 48-10=38 Exploring Operation: 72+10=82, Resulting Numbers: [48, 82] Generated Node #0,1,2: 82:[48, 82] Operation: 72+10=82 Exploring Operation: 72-48=24, Resulting Numbers: [10, 24] Generated Node #0,1,3: 82:[10, 24] Operation: 72-48=24 Exploring Operation: 72-10=62, Resulting Numbers: [48, 62] Generated Node #0,1,4: 82:[48, 62] Operation: 72-10=62 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 82:[48, 82], Operations: ['14-4=10', '72+10=82'] Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 48*82=3936, Resulting Numbers: [3936] 3936,82 unequal: No Solution Exploring Operation: 48+82=130, Resulting Numbers: [130] 130,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 82:[72, 38], Operations: ['14-4=10', '48-10=38'] Exploring Operation: 72-38=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 72*38=2736, Resulting Numbers: [2736] 2736,82 unequal: No Solution Exploring Operation: 72+38=110, Resulting Numbers: [110] 110,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 82:[10, 24], Operations: ['14-4=10', '72-48=24'] Exploring Operation: 10*24=240, Resulting Numbers: [240] 240,82 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 82:[72, 58], Operations: ['14-4=10', '48+10=58'] Exploring Operation: 72-58=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 72+58=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 72*58=4176, Resulting Numbers: [4176] 4176,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 82:[48, 62], Operations: ['14-4=10', '72-10=62'] Exploring Operation: 48*62=2976, Resulting Numbers: [2976] 2976,82 unequal: No Solution Exploring Operation: 62-48=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 48+62=110, Resulting Numbers: [110] 110,82 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: 82:[14, 48, 76], Operations: ['4+72=76'] Exploring Operation: 14+76=90, Resulting Numbers: [48, 90] Generated Node #0,2,0: 82:[48, 90] Operation: 14+76=90 Exploring Operation: 14+48=62, Resulting Numbers: [76, 62] Generated Node #0,2,1: 82:[76, 62] Operation: 14+48=62 Exploring Operation: 76-14=62, Resulting Numbers: [48, 62] Generated Node #0,2,2: 82:[48, 62] Operation: 76-14=62 Exploring Operation: 76-48=28, Resulting Numbers: [14, 28] Generated Node #0,2,3: 82:[14, 28] Operation: 76-48=28 Exploring Operation: 48-14=34, Resulting Numbers: [76, 34] Generated Node #0,2,4: 82:[76, 34] Operation: 48-14=34 Moving to Node #0,4 Current State: 82:[14, 72, 44], Operations: ['48-4=44'] Exploring Operation: 14+72=86, Resulting Numbers: [44, 86] Generated Node #0,4,0: 82:[44, 86] Operation: 14+72=86 Exploring Operation: 72-44=28, Resulting Numbers: [14, 28] Generated Node #0,4,1: 82:[14, 28] Operation: 72-44=28 Exploring Operation: 72-14=58, Resulting Numbers: [44, 58] Generated Node #0,4,2: 82:[44, 58] Operation: 72-14=58 Exploring Operation: 44-14=30, Resulting Numbers: [72, 30] Generated Node #0,4,3: 82:[72, 30] Operation: 44-14=30 Exploring Operation: 14+44=58, Resulting Numbers: [72, 58] Generated Node #0,4,4: 82:[72, 58] Operation: 14+44=58 Moving to Node #0,0,3 Current State: 82:[4, 38], Operations: ['14+72=86', '86-48=38'] Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,82 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,82 unequal: No Solution Moving to Node #0,0,2 Current State: 82:[48, 82], Operations: ['14+72=86', '86-4=82'] Exploring Operation: 48+82=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 48*82=3936, Resulting Numbers: [3936] 3936,82 unequal: No Solution Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[86, 44], Operations: ['14+72=86', '48-4=44'] Exploring Operation: 86*44=3784, Resulting Numbers: [3784] 3784,82 unequal: No Solution Exploring Operation: 86-44=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 86+44=130, Resulting Numbers: [130] 130,82 unequal: No Solution Moving to Node #0,4,0 Current State: 82:[44, 86], Operations: ['48-4=44', '14+72=86'] Exploring Operation: 44+86=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 44*86=3784, Resulting Numbers: [3784] 3784,82 unequal: No Solution Exploring Operation: 86-44=42, Resulting Numbers: [42] 42,82 unequal: No Solution Moving to Node #0,2,4 Current State: 82:[76, 34], Operations: ['4+72=76', '48-14=34'] Exploring Operation: 76*34=2584, Resulting Numbers: [2584] 2584,82 unequal: No Solution Exploring Operation: 76+34=110, Resulting Numbers: [110] 110,82 unequal: No Solution Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,82 unequal: No Solution Moving to Node #0,0,4 Current State: 82:[86, 12], Operations: ['14+72=86', '48/4=12'] Exploring Operation: 86-12=74, Resulting Numbers: [74] 74,82 unequal: No Solution Exploring Operation: 86+12=98, Resulting Numbers: [98] 98,82 unequal: No Solution Exploring Operation: 86*12=1032, Resulting Numbers: [1032] 1032,82 unequal: No Solution Moving to Node #0,2,0 Current State: 82:[48, 90], Operations: ['4+72=76', '14+76=90'] Exploring Operation: 48+90=138, Resulting Numbers: [138] 138,82 unequal: No Solution Exploring Operation: 48*90=4320, Resulting Numbers: [4320] 4320,82 unequal: No Solution Exploring Operation: 90-48=42, Resulting Numbers: [42] 42,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[86, 52], Operations: ['14+72=86', '4+48=52'] Exploring Operation: 86+52=138, Resulting Numbers: [138] 138,82 unequal: No Solution Exploring Operation: 86*52=4472, Resulting Numbers: [4472] 4472,82 unequal: No Solution Exploring Operation: 86-52=34, Resulting Numbers: [34] 34,82 unequal: No Solution Moving to Node #0,4,2 Current State: 82:[44, 58], Operations: ['48-4=44', '72-14=58'] Exploring Operation: 44*58=2552, Resulting Numbers: [2552] 2552,82 unequal: No Solution Exploring Operation: 58-44=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 44+58=102, Resulting Numbers: [102] 102,82 unequal: No Solution Moving to Node #0,4,3 Current State: 82:[72, 30], Operations: ['48-4=44', '44-14=30'] Exploring Operation: 72*30=2160, Resulting Numbers: [2160] 2160,82 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 72+30=102, Resulting Numbers: [102] 102,82 unequal: No Solution Moving to Node #0,4,1 Current State: 82:[14, 28], Operations: ['48-4=44', '72-44=28'] Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 14*28=392, Resulting Numbers: [392] 392,82 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,82 unequal: No Solution Moving to Node #0,2,3 Current State: 82:[14, 28], Operations: ['4+72=76', '76-48=28'] Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 14*28=392, Resulting Numbers: [392] 392,82 unequal: No Solution Moving to Node #0,2,1 Current State: 82:[76, 62], Operations: ['4+72=76', '14+48=62'] Exploring Operation: 76*62=4712, Resulting Numbers: [4712] 4712,82 unequal: No Solution Exploring Operation: 76+62=138, Resulting Numbers: [138] 138,82 unequal: No Solution Exploring Operation: 76-62=14, Resulting Numbers: [14] 14,82 unequal: No Solution Moving to Node #0,2,2 Current State: 82:[48, 62], Operations: ['4+72=76', '76-14=62'] Exploring Operation: 48*62=2976, Resulting Numbers: [2976] 2976,82 unequal: No Solution Exploring Operation: 62-48=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 48+62=110, Resulting Numbers: [110] 110,82 unequal: No Solution Moving to Node #0,4,4 Current State: 82:[72, 58], Operations: ['48-4=44', '14+44=58'] Exploring Operation: 72-58=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 72+58=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 72*58=4176, Resulting Numbers: [4176] 4176,82 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 6, 16, 69, 65 ]
100
[ "6*16=96", "69-65=4", "96+4=100" ]
Current State: 100:[6, 16, 69, 65], Operations: [] Exploring Operation: 6*16=96, Resulting Numbers: [69, 65, 96] Generated Node #2: [69, 65, 96] from Operation: 6*16=96 Current State: 100:[69, 65, 96], Operations: ['6*16=96'] Exploring Operation: 69-65=4, Resulting Numbers: [96, 4] Generated Node #3: [96, 4] from Operation: 69-65=4 Current State: 100:[96, 4], Operations: ['6*16=96', '69-65=4'] Exploring Operation: 96+4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[6, 16, 69, 65], Operations: [] Exploring Operation: 69-65=4, Resulting Numbers: [6, 16, 4] Generated Node #0,0: 100:[6, 16, 4] Operation: 69-65=4 Exploring Operation: 69-16=53, Resulting Numbers: [6, 65, 53] Generated Node #0,1: 100:[6, 65, 53] Operation: 69-16=53 Moving to Node #0,0 Current State: 100:[6, 16, 4], Operations: ['69-65=4'] Exploring Operation: 16+4=20, Resulting Numbers: [6, 20] Generated Node #0,0,0: 100:[6, 20] Operation: 16+4=20 Exploring Operation: 16-6=10, Resulting Numbers: [4, 10] Generated Node #0,0,1: 100:[4, 10] Operation: 16-6=10 Moving to Node #0,1 Current State: 100:[6, 65, 53], Operations: ['69-16=53'] Exploring Operation: 65-53=12, Resulting Numbers: [6, 12] Generated Node #0,1,0: 100:[6, 12] Operation: 65-53=12 Exploring Operation: 65-6=59, Resulting Numbers: [53, 59] Generated Node #0,1,1: 100:[53, 59] Operation: 65-6=59 Moving to Node #0,0,1 Current State: 100:[4, 10], Operations: ['69-65=4', '16-6=10'] Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,100 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[6, 20], Operations: ['69-65=4', '16+4=20'] Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,100 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,100 unequal: No Solution Moving to Node #0,1,0 Current State: 100:[6, 12], Operations: ['69-16=53', '65-53=12'] Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[53, 59], Operations: ['69-16=53', '65-6=59'] Exploring Operation: 53+59=112, Resulting Numbers: [112] 112,100 unequal: No Solution Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,100 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 40, 48, 97, 95 ]
28
[ "97-95=2", "40/2=20", "48-20=28" ]
Current State: 28:[40, 48, 97, 95], Operations: [] Exploring Operation: 97-95=2, Resulting Numbers: [40, 48, 2] Generated Node #2: [40, 48, 2] from Operation: 97-95=2 Current State: 28:[40, 48, 2], Operations: ['97-95=2'] Exploring Operation: 40/2=20, Resulting Numbers: [48, 20] Generated Node #3: [48, 20] from Operation: 40/2=20 Current State: 28:[48, 20], Operations: ['97-95=2', '40/2=20'] Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[40, 48, 97, 95], Operations: [] Exploring Operation: 97-40=57, Resulting Numbers: [48, 95, 57] Generated Node #0,0: 28:[48, 95, 57] Operation: 97-40=57 Exploring Operation: 95-48=47, Resulting Numbers: [40, 97, 47] Generated Node #0,1: 28:[40, 97, 47] Operation: 95-48=47 Exploring Operation: 97-48=49, Resulting Numbers: [40, 95, 49] Generated Node #0,2: 28:[40, 95, 49] Operation: 97-48=49 Exploring Operation: 97-95=2, Resulting Numbers: [40, 48, 2] Generated Node #0,3: 28:[40, 48, 2] Operation: 97-95=2 Moving to Node #0,3 Current State: 28:[40, 48, 2], Operations: ['97-95=2'] Exploring Operation: 40/2=20, Resulting Numbers: [48, 20] Generated Node #0,3,0: 28:[48, 20] Operation: 40/2=20 Exploring Operation: 48/2=24, Resulting Numbers: [40, 24] Generated Node #0,3,1: 28:[40, 24] Operation: 48/2=24 Exploring Operation: 48-40=8, Resulting Numbers: [2, 8] Generated Node #0,3,2: 28:[2, 8] Operation: 48-40=8 Exploring Operation: 40-2=38, Resulting Numbers: [48, 38] Generated Node #0,3,3: 28:[48, 38] Operation: 40-2=38 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 28:[2, 8], Operations: ['97-95=2', '48-40=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,28 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,28 unequal: No Solution No 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: 28:[40, 24], Operations: ['97-95=2', '48/2=24'] Exploring Operation: 40*24=960, Resulting Numbers: [960] 960,28 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 40+24=64, Resulting Numbers: [64] 64,28 unequal: No Solution No 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: 28:[48, 20], Operations: ['97-95=2', '40/2=20'] Exploring Operation: 48+20=68, Resulting Numbers: [68] 68,28 unequal: No Solution Exploring Operation: 48*20=960, Resulting Numbers: [960] 960,28 unequal: No Solution Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[40, 48, 97, 95], Operations: [] Exploring Operation: 97-95=2, Resulting Numbers: [40, 48, 2] Generated Node #0,3: 28:[40, 48, 2] Operation: 97-95=2 Moving to Node #0,3 Current State: 28:[40, 48, 2], Operations: ['97-95=2'] Exploring Operation: 40/2=20, Resulting Numbers: [48, 20] Generated Node #0,3,0: 28:[48, 20] Operation: 40/2=20 Moving to Node #0,3,0 Current State: 28:[48, 20], Operations: ['97-95=2', '40/2=20'] Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
sum_heuristic
[ 10, 55, 65, 26 ]
18
[ "55-10=45", "26*45=1170", "1170/65=18" ]
Current State: 18:[10, 55, 65, 26], Operations: [] Exploring Operation: 55-10=45, Resulting Numbers: [65, 26, 45] Generated Node #2: [65, 26, 45] from Operation: 55-10=45 Current State: 18:[65, 26, 45], Operations: ['55-10=45'] Exploring Operation: 26*45=1170, Resulting Numbers: [65, 1170] Generated Node #3: [65, 1170] from Operation: 26*45=1170 Current State: 18:[65, 1170], Operations: ['55-10=45', '26*45=1170'] Exploring Operation: 1170/65=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[10, 55, 65, 26], Operations: [] Exploring Operation: 55-26=29, Resulting Numbers: [10, 65, 29] Generated Node #0,0: 18:[10, 65, 29] Operation: 55-26=29 Exploring Operation: 65-55=10, Resulting Numbers: [10, 26, 10] Generated Node #0,1: 18:[10, 26, 10] Operation: 65-55=10 Exploring Operation: 65-26=39, Resulting Numbers: [10, 55, 39] Generated Node #0,2: 18:[10, 55, 39] Operation: 65-26=39 Moving to Node #0,1 Current State: 18:[10, 26, 10], Operations: ['65-55=10'] Exploring Operation: 26-10=16, Resulting Numbers: [10, 16] Generated Node #0,1,0: 18:[10, 16] Operation: 26-10=16 Exploring Operation: 10/10=1, Resulting Numbers: [26, 1] Generated Node #0,1,1: 18:[26, 1] Operation: 10/10=1 Exploring Operation: 26-10=16, Resulting Numbers: [10, 16] Generated Node #0,1,2: 18:[10, 16] Operation: 26-10=16 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[10, 16], Operations: ['65-55=10', '26-10=16'] Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,18 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[10, 16], Operations: ['65-55=10', '26-10=16'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[26, 1], Operations: ['65-55=10', '10/10=1'] Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 26*1=26, Resulting Numbers: [26] 26,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 18:[10, 65, 29], Operations: ['55-26=29'] Exploring Operation: 29-10=19, Resulting Numbers: [65, 19] Generated Node #0,0,0: 18:[65, 19] Operation: 29-10=19 Exploring Operation: 65-10=55, Resulting Numbers: [29, 55] Generated Node #0,0,1: 18:[29, 55] Operation: 65-10=55 Exploring Operation: 65-29=36, Resulting Numbers: [10, 36] Generated Node #0,0,2: 18:[10, 36] Operation: 65-29=36 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[10, 36], Operations: ['55-26=29', '65-29=36'] Exploring Operation: 10+36=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 10*36=360, Resulting Numbers: [360] 360,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[65, 19], Operations: ['55-26=29', '29-10=19'] Exploring Operation: 65*19=1235, Resulting Numbers: [1235] 1235,18 unequal: No Solution Exploring Operation: 65+19=84, Resulting Numbers: [84] 84,18 unequal: No Solution Exploring Operation: 65-19=46, Resulting Numbers: [46] 46,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[29, 55], Operations: ['55-26=29', '65-10=55'] Exploring Operation: 29*55=1595, Resulting Numbers: [1595] 1595,18 unequal: No Solution Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 29+55=84, Resulting Numbers: [84] 84,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 18:[10, 55, 39], Operations: ['65-26=39'] Exploring Operation: 55-10=45, Resulting Numbers: [39, 45] Generated Node #0,2,0: 18:[39, 45] Operation: 55-10=45 Exploring Operation: 39-10=29, Resulting Numbers: [55, 29] Generated Node #0,2,1: 18:[55, 29] Operation: 39-10=29 Exploring Operation: 55-39=16, Resulting Numbers: [10, 16] Generated Node #0,2,2: 18:[10, 16] Operation: 55-39=16 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[10, 16], Operations: ['65-26=39', '55-39=16'] Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,18 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[39, 45], Operations: ['65-26=39', '55-10=45'] Exploring Operation: 39+45=84, Resulting Numbers: [84] 84,18 unequal: No Solution Exploring Operation: 39*45=1755, Resulting Numbers: [1755] 1755,18 unequal: No Solution Exploring Operation: 45-39=6, Resulting Numbers: [6] 6,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[55, 29], Operations: ['65-26=39', '39-10=29'] Exploring Operation: 55+29=84, Resulting Numbers: [84] 84,18 unequal: No Solution Exploring Operation: 55*29=1595, Resulting Numbers: [1595] 1595,18 unequal: No Solution Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 47, 14, 50, 2 ]
21
[ "50-47=3", "14/2=7", "3*7=21" ]
Current State: 21:[47, 14, 50, 2], Operations: [] Exploring Operation: 50-47=3, Resulting Numbers: [14, 2, 3] Generated Node #2: [14, 2, 3] from Operation: 50-47=3 Current State: 21:[14, 2, 3], Operations: ['50-47=3'] Exploring Operation: 14/2=7, Resulting Numbers: [3, 7] Generated Node #3: [3, 7] from Operation: 14/2=7 Current State: 21:[3, 7], Operations: ['50-47=3', '14/2=7'] Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[47, 14, 50, 2], Operations: [] Exploring Operation: 50-47=3, Resulting Numbers: [14, 2, 3] Generated Node #0,0: 21:[14, 2, 3] Operation: 50-47=3 Exploring Operation: 50/2=25, Resulting Numbers: [47, 14, 25] Generated Node #0,1: 21:[47, 14, 25] Operation: 50/2=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[14, 2, 3], Operations: ['50-47=3'] Exploring Operation: 14/2=7, Resulting Numbers: [3, 7] Generated Node #0,0,0: 21:[3, 7] Operation: 14/2=7 Exploring Operation: 14+2=16, Resulting Numbers: [3, 16] Generated Node #0,0,1: 21:[3, 16] Operation: 14+2=16 Moving to Node #0,0,0 Current State: 21:[3, 7], Operations: ['50-47=3', '14/2=7'] Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[47, 14, 50, 2], Operations: [] Exploring Operation: 50-47=3, Resulting Numbers: [14, 2, 3] Generated Node #0,0: 21:[14, 2, 3] Operation: 50-47=3 Moving to Node #0,0 Current State: 21:[14, 2, 3], Operations: ['50-47=3'] Exploring Operation: 14/2=7, Resulting Numbers: [3, 7] Generated Node #0,0,0: 21:[3, 7] Operation: 14/2=7 Moving to Node #0,0,0 Current State: 21:[3, 7], Operations: ['50-47=3', '14/2=7'] Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 98, 6, 26, 27 ]
38
[ "98+26=124", "6*27=162", "162-124=38" ]
Current State: 38:[98, 6, 26, 27], Operations: [] Exploring Operation: 98+26=124, Resulting Numbers: [6, 27, 124] Generated Node #2: [6, 27, 124] from Operation: 98+26=124 Current State: 38:[6, 27, 124], Operations: ['98+26=124'] Exploring Operation: 6*27=162, Resulting Numbers: [124, 162] Generated Node #3: [124, 162] from Operation: 6*27=162 Current State: 38:[124, 162], Operations: ['98+26=124', '6*27=162'] Exploring Operation: 162-124=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[98, 6, 26, 27], Operations: [] Exploring Operation: 98-27=71, Resulting Numbers: [6, 26, 71] Generated Node #0,0: 38:[6, 26, 71] Operation: 98-27=71 Exploring Operation: 98-6=92, Resulting Numbers: [26, 27, 92] Generated Node #0,1: 38:[26, 27, 92] Operation: 98-6=92 Exploring Operation: 98-26=72, Resulting Numbers: [6, 27, 72] Generated Node #0,2: 38:[6, 27, 72] Operation: 98-26=72 Exploring Operation: 27-26=1, Resulting Numbers: [98, 6, 1] Generated Node #0,3: 38:[98, 6, 1] Operation: 27-26=1 Moving to Node #0,0 Current State: 38:[6, 26, 71], Operations: ['98-27=71'] Exploring Operation: 26-6=20, Resulting Numbers: [71, 20] Generated Node #0,0,0: 38:[71, 20] Operation: 26-6=20 Exploring Operation: 6+26=32, Resulting Numbers: [71, 32] Generated Node #0,0,1: 38:[71, 32] Operation: 6+26=32 Exploring Operation: 71-26=45, Resulting Numbers: [6, 45] Generated Node #0,0,2: 38:[6, 45] Operation: 71-26=45 Exploring Operation: 71-6=65, Resulting Numbers: [26, 65] Generated Node #0,0,3: 38:[26, 65] Operation: 71-6=65 Moving to Node #0,2 Current State: 38:[6, 27, 72], Operations: ['98-26=72'] Exploring Operation: 72-6=66, Resulting Numbers: [27, 66] Generated Node #0,2,0: 38:[27, 66] Operation: 72-6=66 Exploring Operation: 72-27=45, Resulting Numbers: [6, 45] Generated Node #0,2,1: 38:[6, 45] Operation: 72-27=45 Exploring Operation: 27-6=21, Resulting Numbers: [72, 21] Generated Node #0,2,2: 38:[72, 21] Operation: 27-6=21 Exploring Operation: 72/6=12, Resulting Numbers: [27, 12] Generated Node #0,2,3: 38:[27, 12] Operation: 72/6=12 Moving to Node #0,3 Current State: 38:[98, 6, 1], Operations: ['27-26=1'] Exploring Operation: 98-6=92, Resulting Numbers: [1, 92] Generated Node #0,3,0: 38:[1, 92] Operation: 98-6=92 Exploring Operation: 6-1=5, Resulting Numbers: [98, 5] Generated Node #0,3,1: 38:[98, 5] Operation: 6-1=5 Exploring Operation: 98-1=97, Resulting Numbers: [6, 97] Generated Node #0,3,2: 38:[6, 97] Operation: 98-1=97 Exploring Operation: 98*1=98, Resulting Numbers: [6, 98] Generated Node #0,3,3: 38:[6, 98] Operation: 98*1=98 Moving to Node #0,1 Current State: 38:[26, 27, 92], Operations: ['98-6=92'] Exploring Operation: 26+27=53, Resulting Numbers: [92, 53] Generated Node #0,1,0: 38:[92, 53] Operation: 26+27=53 Exploring Operation: 27-26=1, Resulting Numbers: [92, 1] Generated Node #0,1,1: 38:[92, 1] Operation: 27-26=1 Exploring Operation: 92-26=66, Resulting Numbers: [27, 66] Generated Node #0,1,2: 38:[27, 66] Operation: 92-26=66 Exploring Operation: 92-27=65, Resulting Numbers: [26, 65] Generated Node #0,1,3: 38:[26, 65] Operation: 92-27=65 Moving to Node #0,0,2 Current State: 38:[6, 45], Operations: ['98-27=71', '71-26=45'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 6*45=270, Resulting Numbers: [270] 270,38 unequal: No Solution Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,38 unequal: No Solution Moving to Node #0,2,1 Current State: 38:[6, 45], Operations: ['98-26=72', '72-27=45'] Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,38 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 6*45=270, Resulting Numbers: [270] 270,38 unequal: No Solution Moving to Node #0,2,3 Current State: 38:[27, 12], Operations: ['98-26=72', '72/6=12'] Exploring Operation: 27+12=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 27*12=324, Resulting Numbers: [324] 324,38 unequal: No Solution Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,38 unequal: No Solution Moving to Node #0,0,3 Current State: 38:[26, 65], Operations: ['98-27=71', '71-6=65'] Exploring Operation: 26+65=91, Resulting Numbers: [91] 91,38 unequal: No Solution Exploring Operation: 26*65=1690, Resulting Numbers: [1690] 1690,38 unequal: No Solution Exploring Operation: 65-26=39, Resulting Numbers: [39] 39,38 unequal: No Solution Moving to Node #0,1,3 Current State: 38:[26, 65], Operations: ['98-6=92', '92-27=65'] Exploring Operation: 65-26=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 26+65=91, Resulting Numbers: [91] 91,38 unequal: No Solution Exploring Operation: 26*65=1690, Resulting Numbers: [1690] 1690,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[71, 20], Operations: ['98-27=71', '26-6=20'] Exploring Operation: 71-20=51, Resulting Numbers: [51] 51,38 unequal: No Solution Exploring Operation: 71*20=1420, Resulting Numbers: [1420] 1420,38 unequal: No Solution Exploring Operation: 71+20=91, Resulting Numbers: [91] 91,38 unequal: No Solution Moving to Node #0,2,0 Current State: 38:[27, 66], Operations: ['98-26=72', '72-6=66'] Exploring Operation: 27*66=1782, Resulting Numbers: [1782] 1782,38 unequal: No Solution Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,38 unequal: No Solution Moving to Node #0,1,2 Current State: 38:[27, 66], Operations: ['98-6=92', '92-26=66'] Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,38 unequal: No Solution Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 27*66=1782, Resulting Numbers: [1782] 1782,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[72, 21], Operations: ['98-26=72', '27-6=21'] Exploring Operation: 72*21=1512, Resulting Numbers: [1512] 1512,38 unequal: No Solution Exploring Operation: 72+21=93, Resulting Numbers: [93] 93,38 unequal: No Solution Exploring Operation: 72-21=51, Resulting Numbers: [51] 51,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[71, 32], Operations: ['98-27=71', '6+26=32'] Exploring Operation: 71+32=103, Resulting Numbers: [103] 103,38 unequal: No Solution Exploring Operation: 71*32=2272, Resulting Numbers: [2272] 2272,38 unequal: No Solution Exploring Operation: 71-32=39, Resulting Numbers: [39] 39,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[92, 1], Operations: ['98-6=92', '27-26=1'] Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,38 unequal: No Solution Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,38 unequal: No Solution Exploring Operation: 92*1=92, Resulting Numbers: [92] 92,38 unequal: No Solution Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,38 unequal: No Solution Moving to Node #0,3,0 Current State: 38:[1, 92], Operations: ['27-26=1', '98-6=92'] Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,38 unequal: No Solution Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,38 unequal: No Solution Exploring Operation: 1+92=93, Resulting Numbers: [93] 93,38 unequal: No Solution Exploring Operation: 1*92=92, Resulting Numbers: [92] 92,38 unequal: No Solution Moving to Node #0,3,1 Current State: 38:[98, 5], Operations: ['27-26=1', '6-1=5'] Exploring Operation: 98+5=103, Resulting Numbers: [103] 103,38 unequal: No Solution Exploring Operation: 98*5=490, Resulting Numbers: [490] 490,38 unequal: No Solution Exploring Operation: 98-5=93, Resulting Numbers: [93] 93,38 unequal: No Solution Moving to Node #0,3,2 Current State: 38:[6, 97], Operations: ['27-26=1', '98-1=97'] Exploring Operation: 6+97=103, Resulting Numbers: [103] 103,38 unequal: No Solution Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,38 unequal: No Solution Exploring Operation: 6*97=582, Resulting Numbers: [582] 582,38 unequal: No Solution Moving to Node #0,3,3 Current State: 38:[6, 98], Operations: ['27-26=1', '98*1=98'] Exploring Operation: 6*98=588, Resulting Numbers: [588] 588,38 unequal: No Solution Exploring Operation: 6+98=104, Resulting Numbers: [104] 104,38 unequal: No Solution Exploring Operation: 98-6=92, Resulting Numbers: [92] 92,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[92, 53], Operations: ['98-6=92', '26+27=53'] Exploring Operation: 92*53=4876, Resulting Numbers: [4876] 4876,38 unequal: No Solution Exploring Operation: 92+53=145, Resulting Numbers: [145] 145,38 unequal: No Solution Exploring Operation: 92-53=39, Resulting Numbers: [39] 39,38 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 50, 68, 9, 72 ]
45
[ "68-50=18", "72-9=63", "63-18=45" ]
Current State: 45:[50, 68, 9, 72], Operations: [] Exploring Operation: 68-50=18, Resulting Numbers: [9, 72, 18] Generated Node #2: [9, 72, 18] from Operation: 68-50=18 Current State: 45:[9, 72, 18], Operations: ['68-50=18'] Exploring Operation: 72-9=63, Resulting Numbers: [18, 63] Generated Node #3: [18, 63] from Operation: 72-9=63 Current State: 45:[18, 63], Operations: ['68-50=18', '72-9=63'] Exploring Operation: 63-18=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[50, 68, 9, 72], Operations: [] Exploring Operation: 72/9=8, Resulting Numbers: [50, 68, 8] Generated Node #0,0: 45:[50, 68, 8] Operation: 72/9=8 Exploring Operation: 72-68=4, Resulting Numbers: [50, 9, 4] Generated Node #0,1: 45:[50, 9, 4] Operation: 72-68=4 Exploring Operation: 68-50=18, Resulting Numbers: [9, 72, 18] Generated Node #0,2: 45:[9, 72, 18] Operation: 68-50=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[50, 9, 4], Operations: ['72-68=4'] Exploring Operation: 50-4=46, Resulting Numbers: [9, 46] Generated Node #0,1,0: 45:[9, 46] Operation: 50-4=46 Exploring Operation: 9-4=5, Resulting Numbers: [50, 5] Generated Node #0,1,1: 45:[50, 5] Operation: 9-4=5 Exploring Operation: 50-9=41, Resulting Numbers: [4, 41] Generated Node #0,1,2: 45:[4, 41] Operation: 50-9=41 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 45:[9, 46], Operations: ['72-68=4', '50-4=46'] Exploring Operation: 9*46=414, Resulting Numbers: [414] 414,45 unequal: No Solution Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,45 unequal: No Solution Exploring Operation: 9+46=55, Resulting Numbers: [55] 55,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[50, 5], Operations: ['72-68=4', '9-4=5'] Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[50, 68, 9, 72], Operations: [] Exploring Operation: 72-68=4, Resulting Numbers: [50, 9, 4] Generated Node #0,1: 45:[50, 9, 4] Operation: 72-68=4 Moving to Node #0,1 Current State: 45:[50, 9, 4], Operations: ['72-68=4'] Exploring Operation: 9-4=5, Resulting Numbers: [50, 5] Generated Node #0,1,1: 45:[50, 5] Operation: 9-4=5 Moving to Node #0,1,1 Current State: 45:[50, 5], Operations: ['72-68=4', '9-4=5'] Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic